**Solar Cell**

#### Purnomo Sidi Priambodo, Nji Raden Poespawati and Djoko Hartanto *Universitas Indonesia Indonesia*

#### **1. Introduction**

Solar cell is the most potential energy source for the future, due to its characteristics of renewable and pollution free. However, the recent technology still does not achieve high Watt/m2 and cost efficiency. Solar cell technology still needs to be developed and improved further to obtain optimal efficiency and cost. Moreover, in order to analyze and develop the solar cell technologies, it is required the understanding of solar cell fundamental concepts. The fundamentals how the solar works include 2 phenomena, i.e.: (1) Photonics electron excitation effect to generate electron-hole pairs in materials and (2) diode rectifying.

The phenomenon of photonics electron excitation is general nature evidence in any materials which absorbs photonic energy, where the photonic wavelength corresponds to energy that sufficient to excite the external orbit electrons in the bulk material. The excitation process generates electron-hole pairs which each own quantum momentum corresponds to the absorbed energy. Naturally, the separated electron and hole will be recombined with other electron-holes in the bulk material. When the recombination is occurred, it means there is no conversion energy from photonics energy to electrical energy, because there is no external electrical load can utilize this natural recombination energy.

To utilize the energy conversion from photonic to electric, the energy conversion process should not be conducted in a bulk material, however, it must be conducted in a device which has rectifying function. The device with rectifying function in electronics is called diode. Inside diode device, which is illuminated and excited by incoming light, the electronhole pairs are generated in *p* and *n*-parts of the *p-n* diode. The generated pairs are not instantly recombined in the surrounding exciting local area. However, due to rectifying function, holes will flow through *p*-part to the external electrical load, while the excited electron will flow through *n*-part to the external electrical load. Recombination process of generated electron-hole pairs ideally occurs after the generated electrons-holes experience energy degradation after passing through the external load outside of the diode device, such as shown in illustration on Figure-1.

The conventional structure of p-n diode is made by crystalline semiconductor materials of Group IV consists of silicon (Si) and germanium (Ge). As an illustration in this discussion, Si diode is used, as shown in Figure-1 above, the sun light impinges on the Si p-n diode, wavelengths shorter than the wavelength of Si bandgap energy, will be absorbed by the Si material of the diode, and exciting the external orbit electrons of the Si atoms. The electron excitation process causes the generation of electron-hole pair. The wavelengths longer than the wavelength of Si bandgap energy, will not be absorbed and not cause excitation process

Solar Cell 3

where *I* is current through the diode at forward or reverse bias condition. While, *I0* is a well known diode saturation current at reverse bias condition. *T* is an absolute temperature *oK*, *kB* is Boltzmann constant, *q* (> 0) is an electron charge and *V* is the voltage between two terminals of *p-n* ideal diode. The current capacity of the diode can be controlled by designing the diode saturation current *I0* parameter, which is governed by the following

0

*L D e ee* 

equation [1]:

donor concentration at *n*-diode side [1].

condition is shown on Figure-2.

equivalent ideal diode circuit.

/

2 2

dan *L D h hh*

*ei hi eA hD*

*Dn Dn I qA LN LN* 

where *A* is cross-section area of the diode, *ni* is concentration or number of intrinsic electronhole pair /cm3, *De* is the diffusion coefficient of negative (electron) charge, *Dh* is the diffusion coefficient of positive (hole) charge, *Le* and *Lh* are minority carrier diffusion lengths, *NA* is the extrinsic acceptor concentration at *p*-diode side and *ND* is the extrinsic

where *τ<sup>e</sup>* and *τh* are minority carrier lifetime constants, which depend on the material types used. From Equations (2) & (3) above, it is clearly shown that the diode saturation current *I0* is very depended on the structure and materials of the diode. The I-V relationship of a dark

Fig. 2. I-V relationship of ideal diode for dark or no illumination. (a) I-V graph and (b) the

<sup>0</sup> <sup>1</sup> *<sup>B</sup> qV k T IIe* (1)

(2)

(3)

to generate electron-hole pair. The excitation and electron-hole pair generation processes are engineered such that to be a useful photon to electric conversion. The fact that electron excitation occurs on ߣ > λbandgap-Si, shows the maximum limit possibility of energy conversion from sun-light to electricity, for solar cell made based on Si.

Fig. 1. Illustration of solar cell device structure in the form of p-n diode with external load. The holes flow to the left through the valanche band of diode p-part and the electrons flow through the conduction band of diode n-part.

The fundamental structure of solar cell diode does not change. The researchers have made abundance engineering experiment to improve efficiency by involving many different materials and alloys and also restructuring the solar cell fundamental structure for the following reasons:


In this Chapter, we will discuss several topics, such as: (1) Solar cell device in an ideal diode perspective; (2) Engineering methods to improve conversion energy efficiency per unit area by involving device-structure engineering and material alloys; (3) Standar solar cell fabrications and (4) Dye-sensitized solar cell (DSSC) as an alternative for inexpenssive technology.

#### **2. Solar cell device in an ideal diode perspective**

In order to be able to analyze further the solar cell performance, we need to understand the concepts of an ideal diode, as discussed in the following explanation. In general, an ideal diode with no illumination of light, will have a dark *I-V* equation as following [1]:

to generate electron-hole pair. The excitation and electron-hole pair generation processes are engineered such that to be a useful photon to electric conversion. The fact that electron excitation occurs on ߣ > λbandgap-Si, shows the maximum limit possibility of energy

Fig. 1. Illustration of solar cell device structure in the form of p-n diode with external load. The holes flow to the left through the valanche band of diode p-part and the electrons flow

The fundamental structure of solar cell diode does not change. The researchers have made abundance engineering experiment to improve efficiency by involving many different materials and alloys and also restructuring the solar cell fundamental structure for the

In this Chapter, we will discuss several topics, such as: (1) Solar cell device in an ideal diode perspective; (2) Engineering methods to improve conversion energy efficiency per unit area by involving device-structure engineering and material alloys; (3) Standar solar cell fabrications and (4) Dye-sensitized solar cell (DSSC) as an alternative for inexpenssive

In order to be able to analyze further the solar cell performance, we need to understand the concepts of an ideal diode, as discussed in the following explanation. In general, an ideal

diode with no illumination of light, will have a dark *I-V* equation as following [1]:

1. Energy conversion efficiency Watt/m2 improvement from photon to electricity.

2. Utilization of lower cost material that large availability in nature

4. The simplification of fabrication process and less waste materials

**2. Solar cell device in an ideal diode perspective** 

through the conduction band of diode n-part.

3. Utilization of recyclable materials

5. Longer solar cell life time

following reasons:

technology.

conversion from sun-light to electricity, for solar cell made based on Si.

$$I = I\_0 \left( e^{qV/k\_B T} - 1 \right) \tag{1}$$

where *I* is current through the diode at forward or reverse bias condition. While, *I0* is a well known diode saturation current at reverse bias condition. *T* is an absolute temperature *oK*, *kB* is Boltzmann constant, *q* (> 0) is an electron charge and *V* is the voltage between two terminals of *p-n* ideal diode. The current capacity of the diode can be controlled by designing the diode saturation current *I0* parameter, which is governed by the following equation [1]:

$$I\_0 = qA \left(\frac{D\_e}{L\_e} \frac{n\_i^2}{N\_A} + \frac{D\_h}{L\_h} \frac{n\_i^2}{N\_D} \right) \tag{2}$$

where *A* is cross-section area of the diode, *ni* is concentration or number of intrinsic electronhole pair /cm3, *De* is the diffusion coefficient of negative (electron) charge, *Dh* is the diffusion coefficient of positive (hole) charge, *Le* and *Lh* are minority carrier diffusion lengths, *NA* is the extrinsic acceptor concentration at *p*-diode side and *ND* is the extrinsic donor concentration at *n*-diode side [1].

$$L\_e = \sqrt{D\_e \tau\_e} \quad \text{dan} \quad L\_h = \sqrt{D\_h \tau\_h} \tag{3}$$

where *τ<sup>e</sup>* and *τh* are minority carrier lifetime constants, which depend on the material types used. From Equations (2) & (3) above, it is clearly shown that the diode saturation current *I0* is very depended on the structure and materials of the diode. The I-V relationship of a dark condition is shown on Figure-2.

Fig. 2. I-V relationship of ideal diode for dark or no illumination. (a) I-V graph and (b) the equivalent ideal diode circuit.

Solar Cell 5

Fig. 4. The Graph of the I-V characteristics of an ideal diode solar cell when non-illuminated

From Figure-4, it is shown that there are 4 output parameters, which have to be considered in solar cell. The first parameter is *ISC* that is short circuit current output of solar cell, which is measured when the output terminal is shorted or *V* is equal to 0. The value of output current *I = ISC* = *photon I* represents the current delivery capacity of solar cell at a certain illumination level and is represented by Equation (4). The second parameter is *VOC* that is the open circuit output voltage of solar cell, which is measured when the output terminal is opened or *I* is equal to 0. The value of output voltage *VOC* represents the maximum output voltage of solar cell at a certain illumination level and can be derived from Equation (4) with

> 0 ln 1 *<sup>B</sup> photon*

(6)

*P VI MP MP MP* (7)

*k T I*

*q I* 

In general, *VOC* is determined by *Iphoton*, *I0* and temperature, where *I0* absolutely depends on the structure design and the choice of materials for solar cell diode, while *Iphoton* besides depending on the structure design and the choice of materials, depends on the illumination

The maximum delivery output power is represented by the area of product *VMP* by *IMP* as

The third parameter is fill factor *FF* that represents the ratio PMP to the product *VOC* and *ISC*.

This parameter gives an insight about how "square" is the output characteristic.

(dark) and illuminated.

intensity as well.

**Solar cell output parameters** 

output current value setting at *I = 0*, as follows:

*OC*

*V*

the maximum possible area at fourth quadrant of Figure-4.

Furthermore, if an ideal diode is designed as a solar cell, when illuminated by sun-light, there will be an energy conversion from photon to electricity as illustrated by a circuit model shown on Figure-3. As already explained on Figure-1 that the electron excitation caused by photon energy from the sun, will corresponds to generation of electron-hole pair, which electron and hole are flowing through their own bands. The excited electron flow will be recombined with the hole flow after the energy reduced due to absortion by the external load.

The circuit model of Figure-3, shows a condition when an ideal diode illuminated, the ideal diode becomes a current source with an external load having a voltage drop *V*. The total output current, which is a form of energy conversion from illumination photon to electricity, is represented in the form of superposition of currents, which are resulted due to photon illumination and forward current bias caused by positive voltage across *p* and *n* terminals. The corresponding *I-V* characteristic of an ideal diode solar cell is described by the Shockley solar cell equation as follows [3]:

$$I = I\_{photon} - I\_0 \left( e^{qV/k\_B T} - 1 \right) \tag{4}$$

*photon I* is the photogenerated current, closely related to the photon flux incident to the solar cell. In general, *photon I* can be written in the following formula [2]

$$I\_{photon} = qAG\left(L\_e + \mathcal{W} + L\_{\text{lt}}\right) \tag{5}$$

where *G* is the electron-hole pair generation rate of the diode, *W* is depletion region width of the solar cell diode. The *G* value absolutely depends on material types used for the device and the illumination spectrum and intensity (see Eq 14a & b), while *W* value depends on the device structure, A is the cross-section of illuminated area. The *I-V* characteristic of an ideal diode solar cell is illustrated in Figure-4.

Fig. 3. The equivalent circuit model of an ideal diode solar cell.

Furthermore, if an ideal diode is designed as a solar cell, when illuminated by sun-light, there will be an energy conversion from photon to electricity as illustrated by a circuit model shown on Figure-3. As already explained on Figure-1 that the electron excitation caused by photon energy from the sun, will corresponds to generation of electron-hole pair, which electron and hole are flowing through their own bands. The excited electron flow will be recombined with the hole flow after the energy reduced due to absortion by the external

The circuit model of Figure-3, shows a condition when an ideal diode illuminated, the ideal diode becomes a current source with an external load having a voltage drop *V*. The total output current, which is a form of energy conversion from illumination photon to electricity, is represented in the form of superposition of currents, which are resulted due to photon illumination and forward current bias caused by positive voltage across *p* and *n* terminals. The corresponding *I-V* characteristic of an ideal diode solar cell is described by the Shockley

*photon I* is the photogenerated current, closely related to the photon flux incident to the solar

where *G* is the electron-hole pair generation rate of the diode, *W* is depletion region width of the solar cell diode. The *G* value absolutely depends on material types used for the device and the illumination spectrum and intensity (see Eq 14a & b), while *W* value depends on the device structure, A is the cross-section of illuminated area. The *I-V* characteristic of an ideal

cell. In general, *photon I* can be written in the following formula [2]

Fig. 3. The equivalent circuit model of an ideal diode solar cell.

 / <sup>0</sup> <sup>1</sup> *<sup>B</sup> qV k T*

*photon II Ie* (4)

*Iphoton qAG L W L <sup>e</sup> <sup>h</sup>* (5)

load.

solar cell equation as follows [3]:

diode solar cell is illustrated in Figure-4.

Fig. 4. The Graph of the I-V characteristics of an ideal diode solar cell when non-illuminated (dark) and illuminated.

#### **Solar cell output parameters**

From Figure-4, it is shown that there are 4 output parameters, which have to be considered in solar cell. The first parameter is *ISC* that is short circuit current output of solar cell, which is measured when the output terminal is shorted or *V* is equal to 0. The value of output current *I = ISC* = *photon I* represents the current delivery capacity of solar cell at a certain illumination level and is represented by Equation (4). The second parameter is *VOC* that is the open circuit output voltage of solar cell, which is measured when the output terminal is opened or *I* is equal to 0. The value of output voltage *VOC* represents the maximum output voltage of solar cell at a certain illumination level and can be derived from Equation (4) with output current value setting at *I = 0*, as follows:

$$V\_{OC} = \frac{k\_B T}{q} \ln\left(\frac{I\_{photon}}{I\_0} + 1\right) \tag{6}$$

In general, *VOC* is determined by *Iphoton*, *I0* and temperature, where *I0* absolutely depends on the structure design and the choice of materials for solar cell diode, while *Iphoton* besides depending on the structure design and the choice of materials, depends on the illumination intensity as well.

The maximum delivery output power is represented by the area of product *VMP* by *IMP* as the maximum possible area at fourth quadrant of Figure-4.

$$P\_{\rm MP} = V\_{\rm MP} \cdot I\_{\rm MP} \tag{7}$$

The third parameter is fill factor *FF* that represents the ratio PMP to the product *VOC* and *ISC*. This parameter gives an insight about how "square" is the output characteristic.

Solar Cell 7

Fig. 5. A generic solar cell diode structure and the incidence light direction

Fig. 6. A normalized hole-electron pair generation rate [2].

when exp / 1 *E E kT f B* , then Equation (10) can be written as

/

where E represents the energy state in crystalline. Moreover, photon absorption *α(λ)* by material is an equal representation of excitation probability of electron leaving hole towards a state in conduction band after excited by a photon. The probability is the integral accumulation of multiplication between electron occupation probability in valence band

() e *E E kT f B f E* (11)

$$FF = \frac{P\_{\rm MP}}{V\_{\rm OC} \cdot I\_{\rm SC}} = \frac{V\_{\rm MP} \cdot I\_{\rm MP}}{V\_{\rm OC} \cdot I\_{\rm SC}} \tag{8}$$

In the case of solar cell with sufficient efficiency, in general, it has FF between 0.7 and 0.85. The energy –conversion efficiency, η as the fourth parameter can be written as [2]

$$\eta = \frac{V\_{\text{MP}} \cdot I\_{\text{MP}}}{P\_{\text{in}}} = \frac{V\_{\text{OC}} \cdot I\_{\text{SC}} \cdot FF}{P\_{\text{in}}} \tag{9}$$

where *Pin* is the total power of light illumination on the cell. Energy-conversion efficiency of commercial solar cells typically lies between 12 and 14 % [2]. In designing a good solar cell, we have to consider and put any effort to make those four parameters *ISC* , *VOC* , FF and η as optimum as possible. We like to use term optimum than maximum, since the effort to obtain one parameter maximum in designing solar cell, will degrade other parameters. Hence the best is considering the optimum efficiency of solar cell.

#### **3. Improvement of solar cell performance**

In the process to improve solar cell output performance that is energy conversion efficiency from photon to electricity, which is typically lies between 12 to 14 % [2], the researchers have been conducting many efforts which can be categorized and focused on:


#### **3.1 Solar cell diode structure engineering**

In general, sun-light illuminates solar cell with the direction as shown on Figure-5.

The light illumination with *λ* > *λbandgap* will pass through without absorbed by solar cell. While the light with *λ* < *λbandgap* will be absorbed. Whatever spectrum, basically, incident light with *λ* < *λbandgap* will be absorbed as a function of exponential decay with respect to distance parameter as ( )*<sup>z</sup> e* from the top surface, where *α(λ)* is absorption coefficient and *z* is the depth distance in the solar cell diode. Absorption occurs at any absorbed wavelength are shown on Figure-6.

As shown on Figure-6, red light will be absorbed exponentially slower than the blue light. The photons with different wavelengths will be absorbed in different speed. This discrepancy can be explained and derived by using the probability of state occupancies in material, which is illustrated by Fermi function as follows [1]:

$$f(E) = \frac{1}{\exp\left[\left(E - E\_f\right)/k\_B T\right] + 1} \tag{10}$$

In the case of solar cell with sufficient efficiency, in general, it has FF between 0.7 and 0.85.

*MP MP OC SC in in V I V I FF P P*

where *Pin* is the total power of light illumination on the cell. Energy-conversion efficiency of commercial solar cells typically lies between 12 and 14 % [2]. In designing a good solar cell, we have to consider and put any effort to make those four parameters *ISC* , *VOC* , FF and η as optimum as possible. We like to use term optimum than maximum, since the effort to obtain one parameter maximum in designing solar cell, will degrade other parameters. Hence the

In the process to improve solar cell output performance that is energy conversion efficiency from photon to electricity, which is typically lies between 12 to 14 % [2], the researchers have

1. Diode device structure engineering to improve current output *Isc*, by reducing *I0* and increasing photon illumination conversion to *Iphoton* in the form of improving *G* parameter, electron-hole pair generation constant. The diode structure engineering, at the same time also improving output voltage in the form of *VOC*, and improving FF and

3. Device structure engineering to improve quantum efficiency and lowering top-surface

4. Solar cell structure engineering includes concentrating photon energy to the solar cell

The light illumination with *λ* > *λbandgap* will pass through without absorbed by solar cell. While the light with *λ* < *λbandgap* will be absorbed. Whatever spectrum, basically, incident light with *λ* < *λbandgap* will be absorbed as a function of exponential decay with respect to

is the depth distance in the solar cell diode. Absorption occurs at any absorbed wavelength

As shown on Figure-6, red light will be absorbed exponentially slower than the blue light. The photons with different wavelengths will be absorbed in different speed. This discrepancy can be explained and derived by using the probability of state occupancies in

*E E kT*

exp / 1 *f B*

<sup>1</sup> ( )

from the top surface, where *α(λ)* is absorption coefficient and *z*

(10)

finally improving the energy conversion efficiency from photon to electricity. 2. Material engineering, especially to obtain improvement on *G* parameter, electron-hole

In general, sun-light illuminates solar cell with the direction as shown on Figure-5.

*P VI FF VI VI*

The energy –conversion efficiency, η as the fourth parameter can be written as [2]

been conducting many efforts which can be categorized and focused on:

best is considering the optimum efficiency of solar cell.

lateral current flow to reduce internal resistance.

**3.1 Solar cell diode structure engineering** 

 

material, which is illustrated by Fermi function as follows [1]:

*f E*

**3. Improvement of solar cell performance** 

pair generation.

distance parameter as ( )*<sup>z</sup> e*

are shown on Figure-6.

device.

*MP MP MP OC SC OC SC*

(8)

(9)

Fig. 5. A generic solar cell diode structure and the incidence light direction

Fig. 6. A normalized hole-electron pair generation rate [2].

when exp / 1 *E E kT f B* , then Equation (10) can be written as

$$f(E) \approx \mathbf{e}^{-\left[\left(E - E\_f\right)/k\_B T\right]} \tag{11}$$

where E represents the energy state in crystalline. Moreover, photon absorption *α(λ)* by material is an equal representation of excitation probability of electron leaving hole towards a state in conduction band after excited by a photon. The probability is the integral accumulation of multiplication between electron occupation probability in valence band

Solar Cell 9

carrier diffusion lengths Lh is governed by Equation (3). If the thickness of *n+* layer *> Lh*, then most of hole-electron pairs experience local recombination, which means useless for photon to electrical energy conversion. Between *n+* and *p+* layers, there exists a depletion layer, which has a built in potential Vbi to conduct collection probability of the generated

> *A D N N <sup>W</sup> V V q NN*

where W is the depletion layer width, Vbi is the diode built in potential and VA is the applied or solar cell output voltage. The diode built in potential can be approach by the

<sup>2</sup> ln *B AD*

*kT N N <sup>V</sup> q n* 

The collection probability describes the probability that the light absorbed in a certain region of the device will generate hole-electron pairs which will be collected by depletion layer at *p-n* junction. The collected charges contribute to the output current *photon I* . However, the probability depends on the distance to the junction compared to the diffusion length. If the distance is longer than the diffusion length, then instead of contributing to the output current, those hole-electron pairs are locally recombined again, hence the collection probability is very low. The collection probability is normally high (normalized to 1) at the depletion layer. The following Figure-8 shows the occurrence of photon absorption by the device that illustrated as an exponential decay, at the same time, representing generation of hole-electron pairs. The collection probability shows that at the front (top) surface is low

*i*

*bi A*

1/2

(15)

(16)

hole-electron pairs. The width of depletion layer can be written as follows [1]:

*bi*

 

<sup>0</sup> 2 *<sup>r</sup> A D*

Fig. 7. Transition state probability illustration [4].

following Equation [1]:

and probability of possible state that can be occupied by the excited electron, furthermore those two are multiplied by a coefficient *σ(λ)* as shown in the following equation:

$$a(\lambda) \approx \sigma(\lambda) \cdot \int\_{E\_c - \frac{hc}{\lambda}}^{E\_v} f(E) \cdot (1 - f(E + \frac{hc}{\lambda})) \cdot dE \tag{12}$$

where *σ(λ)* is a cross section probability parameter represent of possible occurrence the photon to hole-electron pair generation at wavelength *λ*. Parameter *σ(λ)* is obtained by the following derivation [2]:

$$\sigma(\lambda) = D \left[ \frac{\left( \hbar c \;/\ \lambda - E\_g + E\_p \right)^2}{\exp(E\_p \;/\ k\_B T) - 1} + \frac{\left( \hbar c \;/\ \lambda - E\_g - E\_p \right)^2}{1 - \exp(E\_p \;/\ k\_B T)} \right] \tag{13}$$

where parameters *D*, *Eg* and *Ep* depend on material types used and crystalline quality, and usually are obtained by conducting experiments. *Eg* and *Ep* each are bandgap energy dan phonon absorption or emission energy respectively, *h* is the Plank constant and *c* is the light speed in vacuum. The *σ(λ)* parameter is a function of λ and naturally depends on the type of the material. Parameter absorption *α(λ)* on Equation (12) when multiplied by illumination intensity *Iint(λ)*, will represent the generation rate of hole-electron pairs at *λ* or *G(λ)*.

$$G(\lambda) = \alpha(\lambda) \cdot I\_{\text{int}}(\lambda) \approx \sigma(\lambda) \cdot I\_{\text{int}}(\lambda) \cdot \int\_{-\frac{hc}{\lambda}}^{\frac{E\_r}{r}} f(E) \cdot (1 - f(E + \frac{hc}{\lambda})) \cdot dE \tag{14-a}$$

Furthermore, the generation rate of hole-electron pair *G* can be written as the integral of *G(λ)* as following:

$$\mathbf{G} = \int\_{0}^{\lambda\_{\text{fundy}}} \mathbf{G}(\mathcal{A}) \, d\mathcal{X} \tag{14-b}$$

In a glance, the terms multiplication under the integral and the integral limits of Equations (12 and 14a) show that parameter values *G(λ)* or *α(λ)* getting larger for becoming shorter (agrees to Figure-6). *λbandgap* is the of the bandgap energy as the limit of irradiance photon to electric conversion. At λ > λbandgap, *σ(λ)* is zero and will not be absorbed or there is no electron-hole generation and does not contribute to the conversion. The following Figure-7 illustrates the distribution state of a material with respect to the Fermi function. The transition state probability represents the photon to hole-electron pair generation.

Back to Figure-5, naturally layer *n+* is a layer that more easier to generate hole-electron pairs due to photon excitation, in comparison to layer *p+*. Hence, the *n+* layer is called as an electron emitter layer. By considering Figure-5 and 6 that photon absorption and holeelectron generation occurs at the front layer of diode structure, then in order to obtain higher conversion efficiency, the *n+* layer as electron emitter layer is located on the top surface of solar cell diode structure such as shown on Figure-5 above.

However, in order to be an effective electron emitter layer, the thickness of the *n+* layer must be shorter than the minority carrier diffusion length *Lh* in *n+* layer, where the hole minority

and probability of possible state that can be occupied by the excited electron, furthermore

 ( ) ( ) (1 ( )) *v*

where *σ(λ)* is a cross section probability parameter represent of possible occurrence the photon to hole-electron pair generation at wavelength *λ*. Parameter *σ(λ)* is obtained by the

/ / ( ) exp( / ) 1 1 exp( / )

where parameters *D*, *Eg* and *Ep* depend on material types used and crystalline quality, and usually are obtained by conducting experiments. *Eg* and *Ep* each are bandgap energy dan phonon absorption or emission energy respectively, *h* is the Plank constant and *c* is the light speed in vacuum. The *σ(λ)* parameter is a function of λ and naturally depends on the type of the material. Parameter absorption *α(λ)* on Equation (12) when multiplied by illumination

intensity *Iint(λ)*, will represent the generation rate of hole-electron pairs at *λ* or *G(λ)*.

int int ( ) ( ) ( ) ( ) ( ) (1 ( ))

*hc GI I <sup>f</sup> <sup>E</sup> <sup>f</sup> E dE*

Furthermore, the generation rate of hole-electron pair *G* can be written as the integral of *G(λ)*

0

In a glance, the terms multiplication under the integral and the integral limits of Equations

to electric conversion. At λ > λbandgap, *σ(λ)* is zero and will not be absorbed or there is no electron-hole generation and does not contribute to the conversion. The following Figure-7 illustrates the distribution state of a material with respect to the Fermi function. The

Back to Figure-5, naturally layer *n+* is a layer that more easier to generate hole-electron pairs due to photon excitation, in comparison to layer *p+*. Hence, the *n+* layer is called as an electron emitter layer. By considering Figure-5 and 6 that photon absorption and holeelectron generation occurs at the front layer of diode structure, then in order to obtain higher conversion efficiency, the *n+* layer as electron emitter layer is located on the top

However, in order to be an effective electron emitter layer, the thickness of the *n+* layer must be shorter than the minority carrier diffusion length *Lh* in *n+* layer, where the hole minority

transition state probability represents the photon to hole-electron pair generation.

(12 and 14a) show that parameter values *G(λ)* or *α(λ)* getting larger for

surface of solar cell diode structure such as shown on Figure-5 above.

*bandgap G Gd* 

 

2 2

*hc E E hc E E*

*g p g p p B p B*

 

*E kT E kT*

*v*

*E*

*c*

 

*hc <sup>E</sup>*

(14-a)

(14-b)

of the bandgap energy as the limit of irradiance photon

becoming shorter

*hc <sup>f</sup> E f E dE*

(12)

(13)

those two are multiplied by a coefficient *σ(λ)* as shown in the following equation:

*E*

*c*

*D*

 

 

 

(agrees to Figure-6). *λbandgap* is the

as following:

following derivation [2]:

 

*hc <sup>E</sup>*

Fig. 7. Transition state probability illustration [4].

carrier diffusion lengths Lh is governed by Equation (3). If the thickness of *n+* layer *> Lh*, then most of hole-electron pairs experience local recombination, which means useless for photon to electrical energy conversion. Between *n+* and *p+* layers, there exists a depletion layer, which has a built in potential Vbi to conduct collection probability of the generated hole-electron pairs. The width of depletion layer can be written as follows [1]:

$$\mathcal{W} = \left[\frac{2\varepsilon\_r\varepsilon\_0}{q} \left(\frac{N\_A + N\_D}{N\_A \cdot N\_D}\right) (V\_{bi} - V\_A)\right]^{1/2} \tag{15}$$

where W is the depletion layer width, Vbi is the diode built in potential and VA is the applied or solar cell output voltage. The diode built in potential can be approach by the following Equation [1]:

$$V\_{bi} = \frac{k\_B T}{q} \ln\left(\frac{N\_A N\_D}{n\_i^2}\right) \tag{16}$$

The collection probability describes the probability that the light absorbed in a certain region of the device will generate hole-electron pairs which will be collected by depletion layer at *p-n* junction. The collected charges contribute to the output current *photon I* . However, the probability depends on the distance to the junction compared to the diffusion length. If the distance is longer than the diffusion length, then instead of contributing to the output current, those hole-electron pairs are locally recombined again, hence the collection probability is very low. The collection probability is normally high (normalized to 1) at the depletion layer. The following Figure-8 shows the occurrence of photon absorption by the device that illustrated as an exponential decay, at the same time, representing generation of hole-electron pairs. The collection probability shows that at the front (top) surface is low

Solar Cell 11

The third parameter is fill factor *FF*, which is a measure on how "square" is the output characteristic of solar cell. It is shown by the curve in the 4th quadrant of *I-V* graph in Figure-4. The shape of the curve is governed by Equation (4). It means *FF* is low for very large *I0*. The fourth parameter *η*, as shown in Equation (9), linearly depends on the other three parameters. Here, we can conclude that in term of structure design, increasing one of the parameter, for instance *ISC* will cause reduction on other parameters, for example *VOC*, and so vice versa. Finally, it is concluded that it is required to compromise between thus four

When the optimalization process of four parameters from the structure given on Figure-5 is conducted by reducing the dopant concentration of one part (in general is *p*), then the solar cell will experience and have a relatively high internal resistance, which reducing output the performance parameter *η*. Hence, the structure in Figure-5 should be modified by inserting a layer that has a lower dopant concentration as shown in the following Figure-9, and keep the higher dopant concentration layers for ohmic contacts at the top and bottom contacts. By inserting layer *p* in between layer *p+* dan *n+* will cause the contact *p* to the contact *+* will have

Fig. 9. Insertion of a lower dopant layer p in p-n junction diode to improve collection

1st generation of solar cell is indicated by the usage of material, which is based on silicon crystalline (c-Si). Typically solar cell is made from a single crystal silicon wafer (c-Si), with a simple p+-p-n+ juction diode structure (Figure-9) in large area, with bandgap energy 1.11 eV. In the development process, the usage of c-Si causes the price of solar cell very high, hence emerging the idea to use non-crystalline or poly-crystalline Si for producing solar cells. There was compromising between cost and efficiency. Using poly-crystalline material the price is cut down to the lower one since the fabrication cost is much lower, however the efficiency is going down as well, since the minority carrier lifetimes *τ<sup>e</sup>* and *τh* are shorter in poly-crystalline than in single–crystalline Si that makes lower *Iphoton* (Equations (3 - 5)). For the ground application with no limitation of area, it is considered to use lower price solar cells with lower conversion efficiency. However, for application with limited areas for

output parameters to obtain the optimal condition.

a low internal resistance, as same as between *n+* to contact *-*.

probability area and keep solar cell internal resistance lower.

**1st generation of solar cells** 

because far from the built-in voltage at depletion layer. On depletion layer, collection probability very high and give a large contribution on output current *photon I* .

Fig. 8. The collection probability of the generated hole-electron pairs at junction [5].

As explained previously, there are 4 reference parameters in designing solar cell, i.e.: *Isc, VOC, FF* and *η*. By considering the equations of those 4 parameters, it is likely that the four parameters are correlated each other. For instance, in order to increase *Isc* or *photon I* (1st parameter), we have to consider Equation (5), where the structure will depend on 2 parameters i.e. A the area of the cell surface and W the thickness of the depletion layer. While parameters G, *Le* and *Lh* depend on the materials used for the solar cell diode. Increasing A parameter (the area of diode) will not have impact to other parameters, however, increasing W parameter will have impact to other parameters. Of course, by increasing *A*, the total output current *Iphotonic* will increase proportionally, the increasing *W*, the length of collection probability of depletion layer will increase as well, where finally it is expected to improve contribution to the output current.

From Equations [15] dan [16], it is shown that structurally *W* parameter depends on *NA* and *ND*. In order to increase *W* proportionally linear, then what we can do is by reducing doping concentration of *NA* and *ND* or one of both. The consequence of reducing *NA* and/or *ND* is the linear increment of *I0*, which in the end causing reducing the total output current such as shown in Equation (4). Don't be panic, improvement *ISC* in one side and decreasing in other side due to concentration adjustment of *NA* and/or *ND* does not mean there is no meaning at all. Because at a certain *NA* and/or *ND* value *+ΔISC* that caused by *ΔW* can be much larger than *-ΔISC* that caused by *I0*. Hence, to obtain the optimal design, it is required to apply a comprehensive numerical calculation and analysis to obtain the optimal *ISC*.

For the sake of obtaining an optimal output voltage *VOC* (2nd parameter), we have to consider Equation (6). The equation shows that *VOC* is a natural logarithmic function of *ISC/I0*, it shows that by reducing *NA* and/or *ND* will cause on increasing *ISC* in root square manner and linearly proportional to *I0* that causes decreasing of *VOC*. Hence, there is a trade off that to increase *ISC* by structural engineering will cause to decrease *VOC*. At certain level, the improvement of *ISC* can be much higher compared to the decrease of *VOC*. Therefore, again, to obtain an optimal design, it is required to apply a comprehensive numerical calculation and analysis to obtain the optimal *ISC*, *VOC* and output power.

10 Solar Cells – Silicon Wafer-Based Technologies

because far from the built-in voltage at depletion layer. On depletion layer, collection

probability very high and give a large contribution on output current *photon I* .

Fig. 8. The collection probability of the generated hole-electron pairs at junction [5].

expected to improve contribution to the output current.

calculation and analysis to obtain the optimal *ISC*, *VOC* and output power.

As explained previously, there are 4 reference parameters in designing solar cell, i.e.: *Isc, VOC, FF* and *η*. By considering the equations of those 4 parameters, it is likely that the four parameters are correlated each other. For instance, in order to increase *Isc* or *photon I* (1st parameter), we have to consider Equation (5), where the structure will depend on 2 parameters i.e. A the area of the cell surface and W the thickness of the depletion layer. While parameters G, *Le* and *Lh* depend on the materials used for the solar cell diode. Increasing A parameter (the area of diode) will not have impact to other parameters, however, increasing W parameter will have impact to other parameters. Of course, by increasing *A*, the total output current *Iphotonic* will increase proportionally, the increasing *W*, the length of collection probability of depletion layer will increase as well, where finally it is

From Equations [15] dan [16], it is shown that structurally *W* parameter depends on *NA* and *ND*. In order to increase *W* proportionally linear, then what we can do is by reducing doping concentration of *NA* and *ND* or one of both. The consequence of reducing *NA* and/or *ND* is the linear increment of *I0*, which in the end causing reducing the total output current such as shown in Equation (4). Don't be panic, improvement *ISC* in one side and decreasing in other side due to concentration adjustment of *NA* and/or *ND* does not mean there is no meaning at all. Because at a certain *NA* and/or *ND* value *+ΔISC* that caused by *ΔW* can be much larger than *-ΔISC* that caused by *I0*. Hence, to obtain the optimal design, it is required to apply a comprehensive numerical calculation and analysis to obtain the optimal *ISC*. For the sake of obtaining an optimal output voltage *VOC* (2nd parameter), we have to consider Equation (6). The equation shows that *VOC* is a natural logarithmic function of *ISC/I0*, it shows that by reducing *NA* and/or *ND* will cause on increasing *ISC* in root square manner and linearly proportional to *I0* that causes decreasing of *VOC*. Hence, there is a trade off that to increase *ISC* by structural engineering will cause to decrease *VOC*. At certain level, the improvement of *ISC* can be much higher compared to the decrease of *VOC*. Therefore, again, to obtain an optimal design, it is required to apply a comprehensive numerical The third parameter is fill factor *FF*, which is a measure on how "square" is the output characteristic of solar cell. It is shown by the curve in the 4th quadrant of *I-V* graph in Figure-4. The shape of the curve is governed by Equation (4). It means *FF* is low for very large *I0*.

The fourth parameter *η*, as shown in Equation (9), linearly depends on the other three parameters. Here, we can conclude that in term of structure design, increasing one of the parameter, for instance *ISC* will cause reduction on other parameters, for example *VOC*, and so vice versa. Finally, it is concluded that it is required to compromise between thus four output parameters to obtain the optimal condition.

When the optimalization process of four parameters from the structure given on Figure-5 is conducted by reducing the dopant concentration of one part (in general is *p*), then the solar cell will experience and have a relatively high internal resistance, which reducing output the performance parameter *η*. Hence, the structure in Figure-5 should be modified by inserting a layer that has a lower dopant concentration as shown in the following Figure-9, and keep the higher dopant concentration layers for ohmic contacts at the top and bottom contacts. By inserting layer *p* in between layer *p+* dan *n+* will cause the contact *p* to the contact *+* will have a low internal resistance, as same as between *n+* to contact *-*.

Fig. 9. Insertion of a lower dopant layer p in p-n junction diode to improve collection probability area and keep solar cell internal resistance lower.

#### **1st generation of solar cells**

1st generation of solar cell is indicated by the usage of material, which is based on silicon crystalline (c-Si). Typically solar cell is made from a single crystal silicon wafer (c-Si), with a simple p+-p-n+ juction diode structure (Figure-9) in large area, with bandgap energy 1.11 eV. In the development process, the usage of c-Si causes the price of solar cell very high, hence emerging the idea to use non-crystalline or poly-crystalline Si for producing solar cells. There was compromising between cost and efficiency. Using poly-crystalline material the price is cut down to the lower one since the fabrication cost is much lower, however the efficiency is going down as well, since the minority carrier lifetimes *τ<sup>e</sup>* and *τh* are shorter in poly-crystalline than in single–crystalline Si that makes lower *Iphoton* (Equations (3 - 5)). For the ground application with no limitation of area, it is considered to use lower price solar cells with lower conversion efficiency. However, for application with limited areas for

Solar Cell 13

correct that more lower the bandgap energy; the material can be categorized as more effective in photon absorption. Hence, for photons with the same wavelength will be absorb faster in lower bandgap typed material in comparison to the larger bandgap material. Thus

The higher energy photon will be very fast absorbed and then generate hole-electron pairs with a high concentration in area close to the top surface of diode, which naturally has abundance surface defects corresponds to deep level trap close the surface. This surface defects cause a fast recombination process. Hence, it can be concluded that the usage of one diode structure with a lower bandgap energy, then a wide photon spectrum can be absorbed, however, the generated electron-hole pairs by the high energy photon will be recombined because located near the surface area with abundance defects and deep level states. Therefore, to make effective absorption and efficient conversion, the solar cell should be in the tandem structure such as illustrated in Figure-10. Further, Figure-11 shows a typical design of multi-junction or tandem solar cell incorporating III-V group of materials. While the first generation with 12 to 14% efficiency dominates the market nowadays, this second generation of solar cells based on multi-junction structure dominates the market of high efficient solar cell as well, which typically reach 35 to 47 % efficiency. The typical applications of high efficient second generation solar cell with multi-junction technology are for satellite communications and space shuttles. To design multi-junction structure, it is required to have a knowledge about crystalline lattice match. If the crystalline lattice does not match, then there will exist abundance of deep level states in the junction region that cause a short carrier life-time or it causes faster or larger local recombination process. This large local recombination, finally will reduce the output current *Iphoton*. The information regarding to the bandgap energies dan lattice match of various material are shown on

Thus two first generations, besides of dominating solar cell technologies and markets nowadays, also are dominated by the usage of mostly silicon alloy based on semiconductor material. This situation causes the ratio of the solar cell price to the Watt-output power never decrease, because it tightly compete with the usage of Si and other semiconductor

mechanism is very clear illustrated in math relation by Equations (12 and 14a).

Fig. 10. Multi-junction and cell tandem concept.

Figures-12 and 13 [4] as follows.

instances on high-rise buildings and even on satellites, space shuttles or space-lab, a higher conversion efficiency is much considered. The first generation of solar cells based on polycrystalline Si still dominates the market nowadays. The conversion energy efficiency typically reaches 12 to 14 %.

#### **3.2 Material engineering to improve conversion parameter** *G* **(electron-hole pair generation rate)**

#### **2nd generation of solar cells**

Instead of based on traditional Si wafer cystalline and polycrystalline, in the 2nd Generation solar cell, it began to use material alloys such as elemental group IV alloy for instance SiGe (silicon-germanium), binary and ternary III-V group alloy for instances InGaP, GaAs and AlGaAs. Futhermore, binary to quaternary II-VI group alloy is used as well, such as Cadmium Telluride (CdTe) and Copper Indium Galium Diselenide (CIGS) alloys. The goals of using such material alloys in solar cell diode structure is to improve the irradiance photon to electric conversion rate parameter *G* such as shown in Equation (5) and has been derived in Equations (14-a and b).

By common sense, if λbandgap is as large as possible, then we can expect that the *G* parameter goes up. This is the reason, why one applies SiGe for the solar cell, since the alloy has lower bandgap than Si, where the bandgap energy is governed by the following formula [6] where *x* represents the percent composition of Germanium:

Eg(x)= (1.155 – 0.43x + 0.0206x2 )eV for 0 < x < 0.85 (17)

and

$$\mathbf{E}\_{\rm 0}(\mathbf{x}) = (2.010 - 1.27\mathbf{x})\mathbf{e} \mathbf{V} \qquad \text{for} \quad 0.85 \le \mathbf{x} \le 1 \tag{18}$$

The usage of SiGe alloy for solar cell results in the improvement of conversion efficiency up to 18% [11].

#### **Multi-junction solar cells**

In the first generation, Solar cell diode structure used a single type material Si in the form of crystalline, poly-crystalline and amorphous. In the development of 2nd generation solar cell, the researchers use several material alloys in one single device, then it is called as multijunction solar cell. As already explained and illustrated in Figure-6 that the shorter the photonic wavelength then it will be absorbed faster inside the material. It means the shorter wavelength part of the sun light spectrum will be absorbed more than the longer part of the spectrum by the same thickness of material. The wavelengths longer than the bandgap wavelength will not be absorbed at all. The part of the spectrum not absorbed by the diode material is the inefficiency of the solar cell. In order to improve solar cell efficiency performance, then the remaining unabsorbed spectrum must be reabsorbed by the next structure that can converting become electricity. The solar cell structures in the second generation are mostly in the form of tandem structure, which consists of various alloy materials that have different bandgaps with sequence from the top surface, is the highest bandgap then continued by the lower and finaly the lowest, such as illustrated on Figure-10. There may be a question, if the lower bandgap can absorb more spectrum, why not it is used a single diode structure with very low bandgap material to absorb the overall spectrum energy? without building tandem or cascading structures. The answer is following, it is

instances on high-rise buildings and even on satellites, space shuttles or space-lab, a higher conversion efficiency is much considered. The first generation of solar cells based on polycrystalline Si still dominates the market nowadays. The conversion energy efficiency

Instead of based on traditional Si wafer cystalline and polycrystalline, in the 2nd Generation solar cell, it began to use material alloys such as elemental group IV alloy for instance SiGe (silicon-germanium), binary and ternary III-V group alloy for instances InGaP, GaAs and AlGaAs. Futhermore, binary to quaternary II-VI group alloy is used as well, such as Cadmium Telluride (CdTe) and Copper Indium Galium Diselenide (CIGS) alloys. The goals of using such material alloys in solar cell diode structure is to improve the irradiance photon to electric conversion rate parameter *G* such as shown in Equation (5) and has been derived

By common sense, if λbandgap is as large as possible, then we can expect that the *G* parameter goes up. This is the reason, why one applies SiGe for the solar cell, since the alloy has lower bandgap than Si, where the bandgap energy is governed by the following formula [6] where

Eg(x)= (1.155 – 0.43x + 0.0206x2 )eV for 0 < x < 0.85 (17)

 Eg(x)= (2.010 – 1.27x)eV for 0.85 < x < 1 (18) The usage of SiGe alloy for solar cell results in the improvement of conversion efficiency up

In the first generation, Solar cell diode structure used a single type material Si in the form of crystalline, poly-crystalline and amorphous. In the development of 2nd generation solar cell, the researchers use several material alloys in one single device, then it is called as multijunction solar cell. As already explained and illustrated in Figure-6 that the shorter the photonic wavelength then it will be absorbed faster inside the material. It means the shorter wavelength part of the sun light spectrum will be absorbed more than the longer part of the spectrum by the same thickness of material. The wavelengths longer than the bandgap wavelength will not be absorbed at all. The part of the spectrum not absorbed by the diode material is the inefficiency of the solar cell. In order to improve solar cell efficiency performance, then the remaining unabsorbed spectrum must be reabsorbed by the next structure that can converting become electricity. The solar cell structures in the second generation are mostly in the form of tandem structure, which consists of various alloy materials that have different bandgaps with sequence from the top surface, is the highest bandgap then continued by the lower and finaly the lowest, such as illustrated on Figure-10. There may be a question, if the lower bandgap can absorb more spectrum, why not it is used a single diode structure with very low bandgap material to absorb the overall spectrum energy? without building tandem or cascading structures. The answer is following, it is

**3.2 Material engineering to improve conversion parameter** *G* **(electron-hole pair** 

typically reaches 12 to 14 %.

**2nd generation of solar cells** 

in Equations (14-a and b).

**Multi-junction solar cells** 

and

to 18% [11].

*x* represents the percent composition of Germanium:

**generation rate)** 

correct that more lower the bandgap energy; the material can be categorized as more effective in photon absorption. Hence, for photons with the same wavelength will be absorb faster in lower bandgap typed material in comparison to the larger bandgap material. Thus mechanism is very clear illustrated in math relation by Equations (12 and 14a).

Fig. 10. Multi-junction and cell tandem concept.

The higher energy photon will be very fast absorbed and then generate hole-electron pairs with a high concentration in area close to the top surface of diode, which naturally has abundance surface defects corresponds to deep level trap close the surface. This surface defects cause a fast recombination process. Hence, it can be concluded that the usage of one diode structure with a lower bandgap energy, then a wide photon spectrum can be absorbed, however, the generated electron-hole pairs by the high energy photon will be recombined because located near the surface area with abundance defects and deep level states. Therefore, to make effective absorption and efficient conversion, the solar cell should be in the tandem structure such as illustrated in Figure-10. Further, Figure-11 shows a typical design of multi-junction or tandem solar cell incorporating III-V group of materials.

While the first generation with 12 to 14% efficiency dominates the market nowadays, this second generation of solar cells based on multi-junction structure dominates the market of high efficient solar cell as well, which typically reach 35 to 47 % efficiency. The typical applications of high efficient second generation solar cell with multi-junction technology are for satellite communications and space shuttles. To design multi-junction structure, it is required to have a knowledge about crystalline lattice match. If the crystalline lattice does not match, then there will exist abundance of deep level states in the junction region that cause a short carrier life-time or it causes faster or larger local recombination process. This large local recombination, finally will reduce the output current *Iphoton*. The information regarding to the bandgap energies dan lattice match of various material are shown on Figures-12 and 13 [4] as follows.

Thus two first generations, besides of dominating solar cell technologies and markets nowadays, also are dominated by the usage of mostly silicon alloy based on semiconductor material. This situation causes the ratio of the solar cell price to the Watt-output power never decrease, because it tightly compete with the usage of Si and other semiconductor

Solar Cell 15

material for the global electronics industry demand. The condition encourages the researchers to create a radical technology revolution, by using non-crystalline material that replacing Si and other semiconductor materials, and it is realized in the form of dye-

Fig. 13. Lattice constants, bandgap energies and bandgap wavelengths for important II-VI

As already well understood that the sun-light before reaching solar cell, propagates through the vacuum and air. At the moment when the light reaches the solar cell front surface, which is made by silicon material, the light experiences of reflection by the silicon surface due to the index of refraction difference between air and silicon. The reflection causes reduction of overall efficiency of the solar cell. We have to reduce the reflection in order to increase the efficiency. By borrowing the technique that has been well developed in optical science, furthermore to reduce reflection or increase absorption, it uses antireflection thin film coating structure applied on top of the front solar cell surface. Basically this technique uses Bragg reflection phenomenon, that is an interference effect caused by thin film structure. The following Figure-14 illustrates the process of Bragg reflection occurrence by the mirror stack structure. The reflectance occurs when the light incidence on an interface of two

The maximum reflection intensity occurs when the following condition is set and called as

For normal incidence *θ = 900*, with Bragg equation, distance between mirrors needed for constructive interference reflectance is *d = λ/2*. While for the requirement of destructive

2*d* 

(19)

sin

sensitized solar cell (DSSC) as the 3rd generation solar cells.

**3.3 Quantum efficiency engineering (optical design)** 

material with different index of refraction *n1 ≠ n2*.

**Antireflection (AR) thin-film coating** 

binary compounds [4].

Bragg angle [4]

Fig. 11. Typical of high efficient solar cell with dual cell tandem structure[12].

Fig. 12. Lattice constants, bandgap energies and bandgap wavelengths for III-V binary compounds, Si and Ge [4].

Fig. 11. Typical of high efficient solar cell with dual cell tandem structure[12].

Fig. 12. Lattice constants, bandgap energies and bandgap wavelengths for III-V binary

compounds, Si and Ge [4].

material for the global electronics industry demand. The condition encourages the researchers to create a radical technology revolution, by using non-crystalline material that replacing Si and other semiconductor materials, and it is realized in the form of dyesensitized solar cell (DSSC) as the 3rd generation solar cells.

Fig. 13. Lattice constants, bandgap energies and bandgap wavelengths for important II-VI binary compounds [4].

#### **3.3 Quantum efficiency engineering (optical design)**

#### **Antireflection (AR) thin-film coating**

As already well understood that the sun-light before reaching solar cell, propagates through the vacuum and air. At the moment when the light reaches the solar cell front surface, which is made by silicon material, the light experiences of reflection by the silicon surface due to the index of refraction difference between air and silicon. The reflection causes reduction of overall efficiency of the solar cell. We have to reduce the reflection in order to increase the efficiency. By borrowing the technique that has been well developed in optical science, furthermore to reduce reflection or increase absorption, it uses antireflection thin film coating structure applied on top of the front solar cell surface. Basically this technique uses Bragg reflection phenomenon, that is an interference effect caused by thin film structure. The following Figure-14 illustrates the process of Bragg reflection occurrence by the mirror stack structure. The reflectance occurs when the light incidence on an interface of two material with different index of refraction *n1 ≠ n2*.

The maximum reflection intensity occurs when the following condition is set and called as Bragg angle [4]

$$
\sin \theta = \frac{\lambda}{2d} \tag{19}
$$

For normal incidence *θ = 900*, with Bragg equation, distance between mirrors needed for constructive interference reflectance is *d = λ/2*. While for the requirement of destructive

Solar Cell 17

<sup>2</sup> <sup>2</sup>

*AR air Si AR air Si*

*n nn* 

*Material Refractive index* 

MgF2 1.3 – 1.4 Al2O3 1.8 – 1.9 Si3N4 1.8 – 2.05 SiO2 1.45 – 1.52 SiO 1.8 – 1.9 TiO2 2.3 ZnS 2.3 – 2.4 Ta2O5 2.1 – 2.3 HfO2 1.75 – 2.0

To obtain a minimum reflectance with a single thin film layer AR, we can apply Al2O3, Si3N4, SiO or HfO2 single layer. Other material can be used as AR in multi layer thin-film

The other method used to reduce reflectance and at the same time increasing photon intensity absorption is by using textured surfaces [2,4]. The simple illustration, how the light can be trapped and then absorbed by solar cell diode is shown on the following Figure-16. Generally, the textured surface can be produced by etching on silicon surface by using etch process where etching silicon in one lattice direction in crystal structure is faster than etching to the other direction. The result is in the form of pyramids as shown in the

Beside to the one explained above, there are still many methods used to fabricate textured surface, for an example by using large area grating fabrication method on top the solar cell

Furthermore, it can be obtained zero reflectance if <sup>2</sup> 0 *n nn AR air Si* . At this condition, it means that the whole incidence sun light will be absorbed in to Si solar cell diode. As an additional information that refractive index of Si *nSi ≈ 3.8* in the visible spectrum range and *nair = 1*, such that to obtain *R = 0*, then required to use a dielectric AR coating with 1.9 *n nn AR air Si* . The following Tabel-1 shows a list of materials with their corresponding refractive indices on the wavelength spectrum range in the region of visible

then the total or overall reflectance is minimum and can be written as follows [2]:

min 2

*n nn <sup>R</sup>*

and in normal incidence,

(21)

When the AR coating thickness is designed to be 0 /4 *n d AR*

Tabel 1. List of Refractive Indices of Dielectric Materials

structure with the consequence of higher fabrication cost.

and infrared [2].

**Textured Surfaces** 

following Figure-16 [2].

interference reflectance or constructive interference transmittance, the distance between mirrors is *d = λ/4*.

Fig. 14. Bragg reflection effect of mirror stacks structure with distance *d = λ/2*.

Furthermore, if there is only a single thin-film structure, as shown on Figure-15, then by using Fresnel equation and assumed that the design is for a normal incidence, then on each interface will occurs reflectance which is written as [2]

$$r\_1 = \frac{n\_{air} - n\_{AR}}{n\_{air} + n\_{AR}} \quad \text{and} \quad r\_2 = \frac{n\_{AR} - n\_{Si}}{n\_{AR} + n\_{Si}} \tag{20}$$

where *r1* is interface between air and antireflection coating (AR), and *r2* is interface between AR and silicon.

Fig. 15. Bragg reflection effect of mirror stacks structure with distance *d = λ/4*.

interference reflectance or constructive interference transmittance, the distance between

Fig. 14. Bragg reflection effect of mirror stacks structure with distance *d = λ/2*.

*air AR air AR n n*

Fig. 15. Bragg reflection effect of mirror stacks structure with distance *d = λ/4*.

*n n* 

interface will occurs reflectance which is written as [2]

1

*r*

Furthermore, if there is only a single thin-film structure, as shown on Figure-15, then by using Fresnel equation and assumed that the design is for a normal incidence, then on each

and 2

where *r1* is interface between air and antireflection coating (AR), and *r2* is interface between

*r*

*AR Si AR Si n n*

(20)

*n n* 

mirrors is *d = λ/4*.

AR and silicon.

When the AR coating thickness is designed to be 0 /4 *n d AR* and in normal incidence, then the total or overall reflectance is minimum and can be written as follows [2]:

$$R\_{\rm min} = \left(\frac{n\_{AR}^2 - n\_{air}n\_{Si}}{n\_{AR}^2 + n\_{air}n\_{Si}}\right)^2\tag{21}$$

Furthermore, it can be obtained zero reflectance if <sup>2</sup> 0 *n nn AR air Si* . At this condition, it means that the whole incidence sun light will be absorbed in to Si solar cell diode. As an additional information that refractive index of Si *nSi ≈ 3.8* in the visible spectrum range and *nair = 1*, such that to obtain *R = 0*, then required to use a dielectric AR coating with 1.9 *n nn AR air Si* . The following Tabel-1 shows a list of materials with their corresponding refractive indices on the wavelength spectrum range in the region of visible and infrared [2].


Tabel 1. List of Refractive Indices of Dielectric Materials

To obtain a minimum reflectance with a single thin film layer AR, we can apply Al2O3, Si3N4, SiO or HfO2 single layer. Other material can be used as AR in multi layer thin-film structure with the consequence of higher fabrication cost.

#### **Textured Surfaces**

The other method used to reduce reflectance and at the same time increasing photon intensity absorption is by using textured surfaces [2,4]. The simple illustration, how the light can be trapped and then absorbed by solar cell diode is shown on the following Figure-16. Generally, the textured surface can be produced by etching on silicon surface by using etch process where etching silicon in one lattice direction in crystal structure is faster than etching to the other direction. The result is in the form of pyramids as shown in the following Figure-16 [2].

Beside to the one explained above, there are still many methods used to fabricate textured surface, for an example by using large area grating fabrication method on top the solar cell

Solar Cell 19

incidence angle normal to the grating and Λ < λ, then the diffracted order photon close 900 or becoming surface wave on the surface of the solar cell structure. Because the refractive index of Si solar cell diode higher than the average textured surface, and if the thickness of textured surface *dts < λ/4nSi* , then it can be concluded that the whole incident photon energy

Priambodo et al [7] in their paper shows in detail to create and fabricate textured surface for guided mode resonance (GMR) filter by using interferometric pattern method. We can assume the substrate is solar cell diode structure, which is covered by thin film structure hafnium dioxide (HfO2) and silicon dioxide (SiO2). The first step is covering the thin film structure on solar cell by photoresist by using spin-coater, then continued by exposing to a large interferometric UV and developed such that result in large area photoresist grating

Fig. 18. SEM Picture of grating pattern on large surface with submicron period. This zero order diffracting layer is perfect to be applied for antireflection large area solar cell [7].

Furthermore, on top of the photoresist grating pattern, it is deposited a very thin layer of chromium (Cr) ~ 40-nm by using e-beam evaporator. The next step is removing the photoresist part by using acetone in ultrasonic washer, and left metal Cr grating pattern as a etching mask on top of thin film structure. Moreover, dry etching is conducted to create a large grating pattern on the thin film SiO2/HfO2 structure on top of solar cell, by using reactive ion etch (RIE). The whole structure of the solar cell device is shown on Figure-19

However, even though having advantages in improvement of gathering sun-light, but the textured surface has several disadvantages as well, i.e.: (1) more care required in handling; (2) the corrugated surface is more effective to absorb the photon energy in wide spectrum that may some part of it not useful to generate electric energy and causing heat of the solar

*<sup>q</sup>* is diffracted

*<sup>i</sup>* is set = 0 or

*i* is the incidence angle to the normal of the grating surface and

order angle, Λ is grating period and λ is photonic wavelength. When

with period < 400 nm as shown in SEM picture of Figure-18, as follows.

will be absorbed in to solar cell diode device.

where

below.

cell system [2].

structure. The large area grating fabrication is started by making photoresist grating with interferometer method, and further continued by etching to the covering layer film of top surface of solar cell structure, as has been done by Priambodo et al [7].

The pyramids shown in Figure-16 are results of intersection crystal lattice planes. Based on Miller indices, the silicon surface is aligned parallel to the (100) plane and the pyramids are formed by the (111) planes [2].

Fig. 16. Textured surface solar cell to improve absorption of solar photons.

Fig. 17. The Appearance of a textured silicon surface under an SEM [2].

In order to obtain more effective in trapping sun-light to be absorbed, the textured surface design should consider the diffraction effects of textured surface. The diffraction or grating equation is simply written as the following [4]:

$$
\sin \theta\_q = \sin \theta\_i + q \frac{\lambda}{\Lambda} \tag{22}
$$

structure. The large area grating fabrication is started by making photoresist grating with interferometer method, and further continued by etching to the covering layer film of top

The pyramids shown in Figure-16 are results of intersection crystal lattice planes. Based on Miller indices, the silicon surface is aligned parallel to the (100) plane and the pyramids are

surface of solar cell structure, as has been done by Priambodo et al [7].

Fig. 16. Textured surface solar cell to improve absorption of solar photons.

Fig. 17. The Appearance of a textured silicon surface under an SEM [2].

equation is simply written as the following [4]:

In order to obtain more effective in trapping sun-light to be absorbed, the textured surface design should consider the diffraction effects of textured surface. The diffraction or grating

sin sin *q i q*

 

(22)

formed by the (111) planes [2].

where *i* is the incidence angle to the normal of the grating surface and *<sup>q</sup>* is diffracted order angle, Λ is grating period and λ is photonic wavelength. When *<sup>i</sup>* is set = 0 or incidence angle normal to the grating and Λ < λ, then the diffracted order photon close 900 or becoming surface wave on the surface of the solar cell structure. Because the refractive index of Si solar cell diode higher than the average textured surface, and if the thickness of textured surface *dts < λ/4nSi* , then it can be concluded that the whole incident photon energy will be absorbed in to solar cell diode device.

Priambodo et al [7] in their paper shows in detail to create and fabricate textured surface for guided mode resonance (GMR) filter by using interferometric pattern method. We can assume the substrate is solar cell diode structure, which is covered by thin film structure hafnium dioxide (HfO2) and silicon dioxide (SiO2). The first step is covering the thin film structure on solar cell by photoresist by using spin-coater, then continued by exposing to a large interferometric UV and developed such that result in large area photoresist grating with period < 400 nm as shown in SEM picture of Figure-18, as follows.

Fig. 18. SEM Picture of grating pattern on large surface with submicron period. This zero order diffracting layer is perfect to be applied for antireflection large area solar cell [7].

Furthermore, on top of the photoresist grating pattern, it is deposited a very thin layer of chromium (Cr) ~ 40-nm by using e-beam evaporator. The next step is removing the photoresist part by using acetone in ultrasonic washer, and left metal Cr grating pattern as a etching mask on top of thin film structure. Moreover, dry etching is conducted to create a large grating pattern on the thin film SiO2/HfO2 structure on top of solar cell, by using reactive ion etch (RIE). The whole structure of the solar cell device is shown on Figure-19 below.

However, even though having advantages in improvement of gathering sun-light, but the textured surface has several disadvantages as well, i.e.: (1) more care required in handling; (2) the corrugated surface is more effective to absorb the photon energy in wide spectrum that may some part of it not useful to generate electric energy and causing heat of the solar cell system [2].

Solar Cell 21

discussed in the previous section, are the efforts to improve conversion efficiency in physical meaning. However, the concentrating system engineering we discussed here is an effort to improve the efficiency ratio output wattage to the cost only. In the physics sense, by the concentrating system, the solar cell device efficiency is not experiencing improvement,

The general method used for concentrating system engineering is the usage of positive (convex) lens to gather the sun irradiance and focus them to the solar cell. By concentrating the input lumen, it is expected there will be an improvement of output electricity. If the lens cost is much lower compared to the solar cell, then it can be concluded that overall it is experiencing improvement in cost efficiency. Another method for concentrating system engineering is the usage of parabolic reflector to focus sun irradiance which is collected by large area of parabolic reflector then focused to the smaller solar cell area. Both examples

Fig. 21. Two examples of concentrating system engineering concepts with (a) convex lens

The technical disadvantages of applying concentrator on solar cell is that the solar cell must be in normal direction to the sun, having larger area and heavier. This means that the system require a control system to point to the sun and finally caused getting more

Since the first time developed in 1950s, solar cells had been applied for various applications, such as for residential, national energy resources, even for spacecrafts and satellites. To make it systematic, as available in the market today, we classify the solar cell technologies in 3 mainstreams or generations. The first generation is based on Si material, while the second generations are based on material alloys of group IV, III-V and II-VI, as already explained in Section-3. While the third generation is based on organic polymer, in order to reduce the cost, improve Wattage to cost ratio and develop as many as possible solar cell, such as developed by Gratzel et al [10]. In this section, we will discuss the standard fabrication

however in cost efficiency sense, it is improved.

and (b) parabolic reflector [2].

**4. Standard solar cell fabrications** 

concentrating system engineering are shown on Figure-21 [2].

expensive. The cost efficiency should consider thus overall cost.

Fig. 19. Solar cell structure incorporating antireflective grating structure.

#### **Top-contact design**

For solar cell, which is designed to have a large current delivery capacity, the top-contact is a part of solar cell that must be considered. For large current delivery, it is required to have a large top-contact but not blocking the sunlight comes in to the solar cell structure. The design of top-contact must consider that the current transportation is evenly distributed, such that prohibited that a large lateral current flow in top surface. The losses occur in solar cell, mostly due to top-surface lateral current flow and the bad quality of metal contact with semiconductor as well, hence creates a large high internal resistance. For those reasons, the top contact is designed to have a good quality of metal semiconductor contact in the form of wire-mesh with busbars, which are collecting current from the smaller finger-mesh, as shown on Figure-20 [2]. The busbars and the fingers ensure suppressing the lateral current flow on the top surface.

Fig. 20. An Example of top-contact design for solar cells [2].

#### **Concentrating system engineering**

The solar cell system efficiency without concentrating treatment, in general, is determined by ratio converted electrical energy to the light energy input, which corresponds to total the lumen of sun irradiance per unit area m2. This is a physical efficiency evaluation. In general, the solar cells available in the market have the efficiency value in the range of 12 – 14%. This efficiency value has a direct relationship to the cost efficiency, which is represented in ratio Wattage output to the solar cell area in m2. Device structure and material engineering

For solar cell, which is designed to have a large current delivery capacity, the top-contact is a part of solar cell that must be considered. For large current delivery, it is required to have a large top-contact but not blocking the sunlight comes in to the solar cell structure. The design of top-contact must consider that the current transportation is evenly distributed, such that prohibited that a large lateral current flow in top surface. The losses occur in solar cell, mostly due to top-surface lateral current flow and the bad quality of metal contact with semiconductor as well, hence creates a large high internal resistance. For those reasons, the top contact is designed to have a good quality of metal semiconductor contact in the form of wire-mesh with busbars, which are collecting current from the smaller finger-mesh, as shown on Figure-20 [2]. The busbars and the fingers ensure suppressing the lateral current

The solar cell system efficiency without concentrating treatment, in general, is determined by ratio converted electrical energy to the light energy input, which corresponds to total the lumen of sun irradiance per unit area m2. This is a physical efficiency evaluation. In general, the solar cells available in the market have the efficiency value in the range of 12 – 14%. This efficiency value has a direct relationship to the cost efficiency, which is represented in ratio Wattage output to the solar cell area in m2. Device structure and material engineering

Fig. 19. Solar cell structure incorporating antireflective grating structure.

Fig. 20. An Example of top-contact design for solar cells [2].

**Concentrating system engineering** 

**Top-contact design** 

flow on the top surface.

discussed in the previous section, are the efforts to improve conversion efficiency in physical meaning. However, the concentrating system engineering we discussed here is an effort to improve the efficiency ratio output wattage to the cost only. In the physics sense, by the concentrating system, the solar cell device efficiency is not experiencing improvement, however in cost efficiency sense, it is improved.

The general method used for concentrating system engineering is the usage of positive (convex) lens to gather the sun irradiance and focus them to the solar cell. By concentrating the input lumen, it is expected there will be an improvement of output electricity. If the lens cost is much lower compared to the solar cell, then it can be concluded that overall it is experiencing improvement in cost efficiency. Another method for concentrating system engineering is the usage of parabolic reflector to focus sun irradiance which is collected by large area of parabolic reflector then focused to the smaller solar cell area. Both examples concentrating system engineering are shown on Figure-21 [2].

Fig. 21. Two examples of concentrating system engineering concepts with (a) convex lens and (b) parabolic reflector [2].

The technical disadvantages of applying concentrator on solar cell is that the solar cell must be in normal direction to the sun, having larger area and heavier. This means that the system require a control system to point to the sun and finally caused getting more expensive. The cost efficiency should consider thus overall cost.

#### **4. Standard solar cell fabrications**

Since the first time developed in 1950s, solar cells had been applied for various applications, such as for residential, national energy resources, even for spacecrafts and satellites. To make it systematic, as available in the market today, we classify the solar cell technologies in 3 mainstreams or generations. The first generation is based on Si material, while the second generations are based on material alloys of group IV, III-V and II-VI, as already explained in Section-3. While the third generation is based on organic polymer, in order to reduce the cost, improve Wattage to cost ratio and develop as many as possible solar cell, such as developed by Gratzel et al [10]. In this section, we will discuss the standard fabrication

Solar Cell 23

POCl3 and the temperature of furnace. The distribution Nd(z) dapat diatur sehingga the thickness of pin layer between p+ and n+ can be made as thin as possible, such that can be ignored. In the subsequent process, after pulled out the wafers from the furnace, the oxide

Metal contacts for both top and bottom contacts are applied by using a standard and conventional technology, well known as vacuum metal evaporation. The bottom metal contact of p+ part can be in the form of solid contact; however, the top contact should be in the form of wire-mesh with bus-bars and fingers as explained in previous section. To develop such wire-mesh metal contact for top surface, it is started with depositing photoresist on the top surface by spin-coating, continued by exposed by UV system, incorporating wire-mesh mask and finally developing the inverse photo-resist wire-mesh pattern. The further step is depositing metal contact layer by using a vacuum metal evaporator, which then continued by cleaning up the photo-resist and unused metal deposition by using acetone in the ultrasonic cleaner. Furthermore, to obtain a high output voltage of solar cell

The fabrication technology that introduced in the first generation seems to be very simple, however, this technology promises very effective and cost and time efficient for mass or large volume of solar cell production. On the other side, the limited applications such as for spacecrafts and satellites require higher efficiency solar cell, with much higher prices. Every single design should be made as precise and accurate as possible. A high efficient solar cell

For that purposes, it is required an apparatus that can grow crystalline structures. There are several types of technologies the their variances, which are available to grow crystalline

Because of limited space of this chapter, CVD is not explained, due to its similarity principles with chemical vapor diffusion process, explained above. Furthermore, MBE is one of several methods to grow crystalline layer structures . It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho [8]. For MBE to work, it needs an ultra vacuum chamber condition (super vacuum at 10-7 to 10-9 Pa), such that it makes possible the material growth epitaxially on crystalline wafer. The disadvantage of this MBE

structures, i.e. molecular beam epitaxy (MBE) dan chemical vapor deposition (CVD).

process is the slow growth rate, typically less than 1000-nm/hour.

layer is removed by using HF acid.

Fig. 22. Chemical (phosphorus) diffusion process [2].

panel, it is required to set a series of several cells.

must be based on single crystalline materials.

**Standard Fab for 2nd generation** 

available for solar cell fabrication for the first and second generations, by using semiconductor materials and the alloys.

#### **Standard Fab for 1st generation**

Up to now, the market is still dominated by solar cell based on Si material. The reason why market still using Si is because the technology is settled down and Si wafer are abundance available in the market. At the beginning, the solar cells used pure crystalline Si wafers, such that the price was relatively high, because the usage competed with electronics circuit industries. Moreover, there was a trend to use substrate poly crystalline Si with lower price but the consequence of energy conversion efficiency becoming lower. The energyconversion efficiency of commercial solar cells typically lies in between 12 to 14 % [2].

In this section, we will not discuss how to fabricate silicon substrate, but more emphasizing on how we fabricate solar cell structure on top of the available substrates. There are several mandatory steps that must be conducted prior to fabricate the diode structure.


There are several technologies available to be used to fabricate solar cell diode structure on Si wafer. In this discussion, 2 major methods are explained, i.e.: (1) chemical vapor diffusion dan (2) molecular beam epitaxy (MBE).

In Si semiconductor technology, it is common to make p-type Si wafer needs boron dopant to be the dopant acceptor in Si wafer, i.e. the material in group III, which is normally added to the melt in the Czochralski process. Furthermore, in order to make n-type Si wafer needs phosporus dopant to be the dopant donor in Si wafer, i.e. the material in group V. In the solar cell diode structure fabrication process in the 1st generation as shown in Figure-9, it is needed a preparation of p-type Si wafer, in this case a high concentration *p* or *p+*. Moreover, we have to deposit 2 thin layers, p and n+ respectively on top of the p+ wafer. In order make the p+pn+ diode structure, we discuss one of the method, which is very robust, i.e. by using chemical vapor diffusion method, such as shown in the following Figure-22 [2].

Instead of depositing layers p and n+ on top of p+ substrate, in this process phophorus dopants are diffused on the top surface of p+ substrate. As already known, phosphorus is a common impurity used. In this common process, a carrier gas (N2) is drifted into the POCl3 liquid creates bubles mixed of POCl3 and N2, then mixed with a small amount of oxygen, the mixed gas passed down into the heated furnace tube with p-type of Si wafers stacked inside. At the temperature about 8000 to 9000 C, the process grows oxide on top of the wafer surface containing phosphorus, then the phosphorus diffuse from the oxide into the p-type wafer. In about 15 to 30 minutes the phosphorus impurities override the boron dopant in the region about the wafer surface, to set a thin-film of heavily doped n-type region as shown in Figure-9. Naturally, phosphorus dopant is assumed to be diffused into p+ type substrate with an exponential function distribution

$$N\_d\left(z\right) = c\_0 e^{-z} \tag{22}$$

Hypothetically *c0 = |n+|+|p+|*, hence, there will be a natural structure of *p+pinn+* instead of expected *p+pn+*. The diffusion depth and c0 are mostly determined by the concentration of

available for solar cell fabrication for the first and second generations, by using

Up to now, the market is still dominated by solar cell based on Si material. The reason why market still using Si is because the technology is settled down and Si wafer are abundance available in the market. At the beginning, the solar cells used pure crystalline Si wafers, such that the price was relatively high, because the usage competed with electronics circuit industries. Moreover, there was a trend to use substrate poly crystalline Si with lower price but the consequence of energy conversion efficiency becoming lower. The energyconversion efficiency of commercial solar cells typically lies in between 12 to 14 % [2].

In this section, we will not discuss how to fabricate silicon substrate, but more emphasizing on how we fabricate solar cell structure on top of the available substrates. There are several

1. Cleaning up the substrate in the clean room, to ensure that the wafer free from the dust and all contaminant particles attached on the wafers, conformed with the standard electronic industries, i.e. rinsing detergent (if needed), DI water, alcohol, acetone, TCE

2. After cleaning step, it is ready to be continued with steps of fabricating diode structure

There are several technologies available to be used to fabricate solar cell diode structure on Si wafer. In this discussion, 2 major methods are explained, i.e.: (1) chemical vapor diffusion

In Si semiconductor technology, it is common to make p-type Si wafer needs boron dopant to be the dopant acceptor in Si wafer, i.e. the material in group III, which is normally added to the melt in the Czochralski process. Furthermore, in order to make n-type Si wafer needs phosporus dopant to be the dopant donor in Si wafer, i.e. the material in group V. In the solar cell diode structure fabrication process in the 1st generation as shown in Figure-9, it is needed a preparation of p-type Si wafer, in this case a high concentration *p* or *p+*. Moreover, we have to deposit 2 thin layers, p and n+ respectively on top of the p+ wafer. In order make the p+pn+ diode structure, we discuss one of the method, which is very robust, i.e. by using

Instead of depositing layers p and n+ on top of p+ substrate, in this process phophorus dopants are diffused on the top surface of p+ substrate. As already known, phosphorus is a common impurity used. In this common process, a carrier gas (N2) is drifted into the POCl3 liquid creates bubles mixed of POCl3 and N2, then mixed with a small amount of oxygen, the mixed gas passed down into the heated furnace tube with p-type of Si wafers stacked inside. At the temperature about 8000 to 9000 C, the process grows oxide on top of the wafer surface containing phosphorus, then the phosphorus diffuse from the oxide into the p-type wafer. In about 15 to 30 minutes the phosphorus impurities override the boron dopant in the region about the wafer surface, to set a thin-film of heavily doped n-type region as shown in Figure-9. Naturally, phosphorus dopant is assumed to be diffused into p+ type substrate

> <sup>0</sup> *<sup>z</sup> N z ce <sup>d</sup>*

Hypothetically *c0 = |n+|+|p+|*, hence, there will be a natural structure of *p+pinn+* instead of expected *p+pn+*. The diffusion depth and c0 are mostly determined by the concentration of

(22)

mandatory steps that must be conducted prior to fabricate the diode structure.

chemical vapor diffusion method, such as shown in the following Figure-22 [2].

semiconductor materials and the alloys.

dan applying ultrasonic rinsing.

dan (2) molecular beam epitaxy (MBE).

with an exponential function distribution

on wafer.

**Standard Fab for 1st generation** 

POCl3 and the temperature of furnace. The distribution Nd(z) dapat diatur sehingga the thickness of pin layer between p+ and n+ can be made as thin as possible, such that can be ignored. In the subsequent process, after pulled out the wafers from the furnace, the oxide layer is removed by using HF acid.

Fig. 22. Chemical (phosphorus) diffusion process [2].

Metal contacts for both top and bottom contacts are applied by using a standard and conventional technology, well known as vacuum metal evaporation. The bottom metal contact of p+ part can be in the form of solid contact; however, the top contact should be in the form of wire-mesh with bus-bars and fingers as explained in previous section. To develop such wire-mesh metal contact for top surface, it is started with depositing photoresist on the top surface by spin-coating, continued by exposed by UV system, incorporating wire-mesh mask and finally developing the inverse photo-resist wire-mesh pattern. The further step is depositing metal contact layer by using a vacuum metal evaporator, which then continued by cleaning up the photo-resist and unused metal deposition by using acetone in the ultrasonic cleaner. Furthermore, to obtain a high output voltage of solar cell panel, it is required to set a series of several cells.

#### **Standard Fab for 2nd generation**

The fabrication technology that introduced in the first generation seems to be very simple, however, this technology promises very effective and cost and time efficient for mass or large volume of solar cell production. On the other side, the limited applications such as for spacecrafts and satellites require higher efficiency solar cell, with much higher prices. Every single design should be made as precise and accurate as possible. A high efficient solar cell must be based on single crystalline materials.

For that purposes, it is required an apparatus that can grow crystalline structures. There are several types of technologies the their variances, which are available to grow crystalline structures, i.e. molecular beam epitaxy (MBE) dan chemical vapor deposition (CVD).

Because of limited space of this chapter, CVD is not explained, due to its similarity principles with chemical vapor diffusion process, explained above. Furthermore, MBE is one of several methods to grow crystalline layer structures . It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho [8]. For MBE to work, it needs an ultra vacuum chamber condition (super vacuum at 10-7 to 10-9 Pa), such that it makes possible the material growth epitaxially on crystalline wafer. The disadvantage of this MBE process is the slow growth rate, typically less than 1000-nm/hour.

Solar Cell 25

which makes possible of controlling alloy material and substrate temperatures accurately. Typically, material such as As needs heating up to 2500C, Ga is about 6000C and other material requires higher temperature. In order to stable the temperature, cooling system like cryogenic system is required; and (4) Shutter system, which is used to halt the deposition

For example, alloy material layer such as AlxGa1-xAs growth on GaAs. Controlling the value of x can be conducted by controlling the temperatures of both material alloy sources. The Higher the material temperature means the higher gaseous material concentration in the chamber. More over, the higher material alloy concentration in the chamber, it will cause the higher growth rate of the alloy layer. For that reasons, the data relating to the growth rate of crystalline layer vs temperature, must be tabulated to obtain the accurate and precise device

MBE system is very expensive, because the product output is very low. However, the advantage of using MBE system is accuracy and precision structure, hence resulting in relatively high efficiency and fit to be applied for production of high efficiency solar cells for

Dye-Sensitized Solar Sel (DSSC) was developed based on the needs of inexpensive solar cells. This type is considered as the third generation of solar cell. DSSC at the first time was developed by Professor Michael Gratzel in 1991. Since then, it has been one of the topical researches conducted very intensive by researchers worldwide. DSSC is considered as first break through in solar cell technology since Si solar cell. A bit difference to the conventional one, DSSC is a photoelectrochemical solar cell, which use electrolyte material as the medium of the charge transport. Beside of electrolyte, DSSC also includes several other parts such nano-crystalline porous TiO2, dye molecules that absorbed in the TiO2 porous layer, and the conductive transparence ITO glass (indium tin oxide) or TCO glass (transparent conductive oxide of SnO2) for both side of DSSC. Basically, there are 4 primary parts to build the DSSC system. The detail of the DSSC

The sun light is coming on the cathode contact side of the DSSC, where TCO is attached with TiO2 porous layer. The porous layer is filled out by the dye light absorbent material. This TiO2 porous layer with the filling dye act as *n*-part of the solar cell diode, where the electrolyte acts as *p*-part of the solar cell diode. On the other side of DSSC, there is a platinum (Pt) or gold (Au) counter-electrode to ensure a good electric contact between electrolytes and the anode. Usually the counter-electrode is covered by catalyst to speed up the redox reaction with the catalyst. The redox pairs that usually used is I-/I3-

The Dye types can be various. For example we can use Ruthenium complex. However, the price is very high, we can replace it with anthocyanin dye. This material can be obtained from the trees such as blueberry and etc. Different dyes will have different sensitivity to absorb the light, or in term of conventional solar cell, they have different *G* parameter. The peak intensity of the sun light is at yellow wavelength, which is exactly that many dye

process.

structure.

satellites and spacecrafts.

**3rd generation of solar cell** 

(iodide/triiodide).

**5. Dye Sensitized Solar Cell (DSSC)** 

components is shown in the following Figure-24 [9-10].

absorbants have the absorbing sensitivity at the yellow wavelength.

Due to the limitation space of this Chapter, CVD will not be discussed, since it has similar principal work with chemical vapor difussion process. Furthermore, MBE is one of several methods to grow crystalline layer structures . It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho.[1] In order to work, it requires a very high vacuum condition (super vacuum 10-7 to 10-9 Pa), Such that it is possible to grow material layer in the form of epitaxial crystalline. The disadvantage of MBE process is its very low growth rate, that is typically less than 1000-nm/hour. The following Figure-23 shows the detail of MBE.

Fig. 23. Molecular beam epitaxy components [8].

In order that the growing thin film layer can be done by epitaxial crystalline, the main requirements to be fulfilled are: (1) Super vacuum, such that it is possible for gaseous alloy material to align their self to form epitaxial crystalline layer. In super vacuum condition, it is possible for heated alloy materials for examples: Al, Ga, As, In, P, Sb and etc can sublimate directly from solid to the gaseous state with relatively lower temperature; (2) Heated alloy materials and the deposited substrate that makes possible the occurrence crystalline condensation form of alloy materials on the substrate; (3) Controlled system temperature,

Due to the limitation space of this Chapter, CVD will not be discussed, since it has similar principal work with chemical vapor difussion process. Furthermore, MBE is one of several methods to grow crystalline layer structures . It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho.[1] In order to work, it requires a very high vacuum condition (super vacuum 10-7 to 10-9 Pa), Such that it is possible to grow material layer in the form of epitaxial crystalline. The disadvantage of MBE process is its very low growth rate, that is typically less than 1000-nm/hour. The following Figure-23

In order that the growing thin film layer can be done by epitaxial crystalline, the main requirements to be fulfilled are: (1) Super vacuum, such that it is possible for gaseous alloy material to align their self to form epitaxial crystalline layer. In super vacuum condition, it is possible for heated alloy materials for examples: Al, Ga, As, In, P, Sb and etc can sublimate directly from solid to the gaseous state with relatively lower temperature; (2) Heated alloy materials and the deposited substrate that makes possible the occurrence crystalline condensation form of alloy materials on the substrate; (3) Controlled system temperature,

shows the detail of MBE.

Fig. 23. Molecular beam epitaxy components [8].

which makes possible of controlling alloy material and substrate temperatures accurately. Typically, material such as As needs heating up to 2500C, Ga is about 6000C and other material requires higher temperature. In order to stable the temperature, cooling system like cryogenic system is required; and (4) Shutter system, which is used to halt the deposition process.

For example, alloy material layer such as AlxGa1-xAs growth on GaAs. Controlling the value of x can be conducted by controlling the temperatures of both material alloy sources. The Higher the material temperature means the higher gaseous material concentration in the chamber. More over, the higher material alloy concentration in the chamber, it will cause the higher growth rate of the alloy layer. For that reasons, the data relating to the growth rate of crystalline layer vs temperature, must be tabulated to obtain the accurate and precise device structure.

MBE system is very expensive, because the product output is very low. However, the advantage of using MBE system is accuracy and precision structure, hence resulting in relatively high efficiency and fit to be applied for production of high efficiency solar cells for satellites and spacecrafts.

#### **5. Dye Sensitized Solar Cell (DSSC)**

#### **3rd generation of solar cell**

Dye-Sensitized Solar Sel (DSSC) was developed based on the needs of inexpensive solar cells. This type is considered as the third generation of solar cell. DSSC at the first time was developed by Professor Michael Gratzel in 1991. Since then, it has been one of the topical researches conducted very intensive by researchers worldwide. DSSC is considered as first break through in solar cell technology since Si solar cell. A bit difference to the conventional one, DSSC is a photoelectrochemical solar cell, which use electrolyte material as the medium of the charge transport. Beside of electrolyte, DSSC also includes several other parts such nano-crystalline porous TiO2, dye molecules that absorbed in the TiO2 porous layer, and the conductive transparence ITO glass (indium tin oxide) or TCO glass (transparent conductive oxide of SnO2) for both side of DSSC. Basically, there are 4 primary parts to build the DSSC system. The detail of the DSSC components is shown in the following Figure-24 [9-10].

The sun light is coming on the cathode contact side of the DSSC, where TCO is attached with TiO2 porous layer. The porous layer is filled out by the dye light absorbent material. This TiO2 porous layer with the filling dye act as *n*-part of the solar cell diode, where the electrolyte acts as *p*-part of the solar cell diode. On the other side of DSSC, there is a platinum (Pt) or gold (Au) counter-electrode to ensure a good electric contact between electrolytes and the anode. Usually the counter-electrode is covered by catalyst to speed up the redox reaction with the catalyst. The redox pairs that usually used is I-/I3- (iodide/triiodide).

The Dye types can be various. For example we can use Ruthenium complex. However, the price is very high, we can replace it with anthocyanin dye. This material can be obtained from the trees such as blueberry and etc. Different dyes will have different sensitivity to absorb the light, or in term of conventional solar cell, they have different *G* parameter. The peak intensity of the sun light is at yellow wavelength, which is exactly that many dye absorbants have the absorbing sensitivity at the yellow wavelength.

Solar Cell 27

The solar cell design has been evolving in many generations. The first generation involved Si material in the form single crystalline, poly-crystalline and amorphous. There is a tradeoff in the usage of single crystalline, polycrystalline or amorphous. Using single crystalline can be expected higher efficiency but higher cost than the polycrystalline solar cell. To obtain optimal design, the Chapter also discuss to get the optimal 4 output parameters, *ISC* , *VOC* , FF and η. Moreover, to improve the efficiency, some applying anti-relection coating thin film or corrugated thin film on top of solar cell structure. The second generation emphasize to increase the efficiency by introducing more sophisticated structure such as multi-hetero-junction structure which has a consecuence of increasing the cost. Hence there is a tradeoff in designing solar cell, to increase the conversion efficiency will have a consecuence to lower the cost efficiency or vice verca. Hence, there must be an optimal

There is a breaktrough technology that radically changes our dependency to semiconductor in fabricating solar cell, i.e by using organic material. It is called as dye sensitized solar cell (DSSC). This technology, so far still produce lower efficiency. However, this technology is

[1] R.F. Pierret, "Semiconductor Device Fundamentals," Addison-Wesley Publishing

[2] M.A. Green, "Solar Cells, Operating Principles, Technology and System Applications,"

[3] T. Markvart and L. Castaner, "Solar Cells, materials, Manufacture and Operation,"

[4] B.E.A. Saleh and M.C. Teich, "Fundamentals of Photonics," Wiley InterScience, ISBN 0-

[6] B.S. Meyerson, "Hi Speed Silicon Germanium Electronics". *Scientific American, March* 

[7] P.S. Priambodo, T.A. Maldonado and R. Magnusson, " Fabrication and characterization

[8] Cho, A. Y.; Arthur, J. R.; Jr (1975). ""Molecular beam epitaxy"". Prog. Solid State Chem.

[9] J. Poortmans and V. Arkhipov, " Thin film solar cells, fabrications, characterization and

[11] Usami, N. ; Takahashi, T. ; Fujiwara, K. ; Ujihara, T. ; Sazaki, G. ; Murakami, Y.;

applications," John Wiley & Sons, ISBN-13: 078-0-470-09126-5, 2006 [10] M. Grätzel, J. Photochem. Photobiol. C: Photochem. Rev. 4, 145–153 (2003)

Conference Record of the Twenty-Ninth IEEE, 19-24 May 2002

of high quality waveguide-mode resonant optical filters," Applied Physics Letters,

Nakajima, K. "Si/multicrystalline-SiGe heterostructure as a candidate for solar cells with high conversion efficiency", Photovoltaic Specialists Conference, 2002.

Elsevier, ISBN-13: 978-1-85617-457-1, ISBN-10: 1-85617-457-3, 2005

values for both conversion energy and cost efficiencies.

Company, ISBN 0-201-54393-1, 1996

Prentice Hall, ISBN 0-13-82270, 1982

Vol. 83 No 16, pp: 3248-3250, 20 Oct 2003

promising to produce solar cell with very low cost and easier to produce.

[5] http://pvcdrom.pveducation.org/CELLOPER/COLPROB.HTM

**6. Summary** 

**7. References** 

471-83965-5

10: 157–192

*1994, vol. 270.iii pp. 42-47*.

Fig. 24. The schematic diagram of DSSC.

#### **The principal work of DSSC**

The principle work of DSSC is shown in the following Figure-25. Basically the working principle of DSSC is based on electron excitation of dye material by the photon. The starting process begins with absorption of photon by the dyes, the electron is excited from the groundstate (D) to the excited state (D\*). The electron of the excited state then directly injected towards the conduction band (ECB) TiO2, and then goes to the external load, such that the dye molecule becomes more positive (D+). The lower electron energy flow from external circuit goes back to the counter-electrode through the catalyst and the electrolyte then supplies electron back to the dye D+ state to be back to the groundstate (D). The *G* parameter of DSSC depends mainly on the dye material and the thickness of TiO2 layer also the level of porosity of the TiO2 layer.

Fig. 25. The principles work of DSSC.

The principle work of DSSC is shown in the following Figure-25. Basically the working principle of DSSC is based on electron excitation of dye material by the photon. The starting process begins with absorption of photon by the dyes, the electron is excited from the groundstate (D) to the excited state (D\*). The electron of the excited state then directly injected towards the conduction band (ECB) TiO2, and then goes to the external load, such that the dye molecule becomes more positive (D+). The lower electron energy flow from external circuit goes back to the counter-electrode through the catalyst and the electrolyte then supplies electron back to the dye D+ state to be back to the groundstate (D). The *G* parameter of DSSC depends mainly on the dye material and the thickness of TiO2 layer also

Fig. 24. The schematic diagram of DSSC.

the level of porosity of the TiO2 layer.

Fig. 25. The principles work of DSSC.

**The principal work of DSSC** 

#### **6. Summary**

The solar cell design has been evolving in many generations. The first generation involved Si material in the form single crystalline, poly-crystalline and amorphous. There is a tradeoff in the usage of single crystalline, polycrystalline or amorphous. Using single crystalline can be expected higher efficiency but higher cost than the polycrystalline solar cell. To obtain optimal design, the Chapter also discuss to get the optimal 4 output parameters, *ISC* , *VOC* , FF and η. Moreover, to improve the efficiency, some applying anti-relection coating thin film or corrugated thin film on top of solar cell structure. The second generation emphasize to increase the efficiency by introducing more sophisticated structure such as multi-hetero-junction structure which has a consecuence of increasing the cost. Hence there is a tradeoff in designing solar cell, to increase the conversion efficiency will have a consecuence to lower the cost efficiency or vice verca. Hence, there must be an optimal values for both conversion energy and cost efficiencies.

There is a breaktrough technology that radically changes our dependency to semiconductor in fabricating solar cell, i.e by using organic material. It is called as dye sensitized solar cell (DSSC). This technology, so far still produce lower efficiency. However, this technology is promising to produce solar cell with very low cost and easier to produce.

#### **7. References**


**2** 

*Greece* 

Vasiliki Perraki

**Epitaxial Silicon Solar Cells** 

 *Department of Electrical and Computer Engineering, University of Patras,* 

Commercial solar cells are made on crystalline silicon wafers typically 300 μm thick with a cost corresponding to a large fraction of their total cost. The potential to produce good quality layers (of about 50 μm thickness), in order to decrease the cost and improve in the same time the efficiency of cells, has entered to the photovoltaic cell manufacturer priorities. The wafers thickness has been significantly decreased from 400 μm to 200 μm, between 1990 and 2006 while the cell's surface has increased from 100 cm2 to 240 cm2, and the modules efficiency from 10% to already 13 %, with the highest values above 17% (Photovoltaic Technology Platform; 2007). Advanced technology's solar cells have been fabricated on wafers of 140 μm thicknesses, resulting to efficiencies higher than 20% (Mason.N et al 2006). The cost associated to the substrate of a crystalline silicon solar cell represents about 50-55% on module level and is equally shared between the cost of base material, crystallization and sawing (Peter. K; et al 2008). The cost related to the Si base material can be reduced fabricating thinner cells, while the cost of crystallization and sawing is eliminated by depositing the Si directly on a low cost substrate, like metallurgical grade Si. The epitaxial thin- film solar cells represent an attractive alternative, among the different silicon thin film systems, with a broad thickness range of 1-100μm (Duerinckh. F; et al 2005). Conversion efficiencies of 11.5-12 % have been achieved from epitaxial solar cells grown on Upgraded Metallurgical Grade Silicon (UMG Si) substrates with an active layer of 30 μm, and an efficient BSF (Hoeymissenet. J.V; al 2008). Epitaxial cells with the same active layers deposited on highly doped multi-crystalline Si substrates by Chemical Vapor Deposition and the front and back surfaces prepared by phosphorous diffusion as well as screen printing technique, have confirmed also efficiencies 12.3% (Nieuwenhuysen. K.V; 2006). Solar cells developed by a specific process for low cost substrates of UMG silicon have led to efficiencies of 12.8% (Sanchez-Friera. P; et al 2006). Better results have been achieved from cells with an emitter epitaxially grown by CVD, onto a base epitaxialy grown (Nieuwenhuysen. K.V; et al 2008). The emitter creates a front surface field which leads to high open-circuit voltages (Voc) resulting to cell efficiencies close to 15% by optimizing the doping profile and thickness of epitaxial layers and by including a light trapping

This chapter first describes the manufacturing procedures of epitaxial silicon solar cells,

Then a one- dimensional (1D) (Perraki.V; 2010) and a three dimensional (3D) computer program (Kotsovos. K & Perraki.V; 2005), are presented, for the study of the n+pp+ type

starting from the construction of the base layer until the development of solar cells.

**1. Introduction** 

mechanism.

[12] Andreev, V.M.; Karlina, L.B.; Kazantsev, A.B.; Khvostikov, V.P.; Rumyantsev, V.D.; Sorokina, S.V.; Shvarts, M.Z.; "Concentrator tandem solar cells based on AlGaAs/GaAs-InP/InGaAs(or GaSb) structures", Photovoltaic Energy Conversion, 1994., Conference Record of the Twenty Fourth. IEEE Photovoltaic Specialists Conference - 1994, 1994 IEEE First World Conference on, 5-9 Dec 1994

## **Epitaxial Silicon Solar Cells**

Vasiliki Perraki

 *Department of Electrical and Computer Engineering, University of Patras, Greece* 

#### **1. Introduction**

28 Solar Cells – Silicon Wafer-Based Technologies

[12] Andreev, V.M.; Karlina, L.B.; Kazantsev, A.B.; Khvostikov, V.P.; Rumyantsev, V.D.;

Conference - 1994, 1994 IEEE First World Conference on, 5-9 Dec 1994

Sorokina, S.V.; Shvarts, M.Z.; "Concentrator tandem solar cells based on AlGaAs/GaAs-InP/InGaAs(or GaSb) structures", Photovoltaic Energy Conversion, 1994., Conference Record of the Twenty Fourth. IEEE Photovoltaic Specialists

> Commercial solar cells are made on crystalline silicon wafers typically 300 μm thick with a cost corresponding to a large fraction of their total cost. The potential to produce good quality layers (of about 50 μm thickness), in order to decrease the cost and improve in the same time the efficiency of cells, has entered to the photovoltaic cell manufacturer priorities. The wafers thickness has been significantly decreased from 400 μm to 200 μm, between 1990 and 2006 while the cell's surface has increased from 100 cm2 to 240 cm2, and the modules efficiency from 10% to already 13 %, with the highest values above 17% (Photovoltaic Technology Platform; 2007). Advanced technology's solar cells have been fabricated on wafers of 140 μm thicknesses, resulting to efficiencies higher than 20% (Mason.N et al 2006). The cost associated to the substrate of a crystalline silicon solar cell represents about 50-55% on module level and is equally shared between the cost of base material, crystallization and sawing (Peter. K; et al 2008). The cost related to the Si base material can be reduced fabricating thinner cells, while the cost of crystallization and sawing is eliminated by depositing the Si directly on a low cost substrate, like metallurgical grade Si. The epitaxial thin- film solar cells represent an attractive alternative, among the different silicon thin film systems, with a broad thickness range of 1-100μm (Duerinckh. F; et al 2005). Conversion efficiencies of 11.5-12 % have been achieved from epitaxial solar cells grown on Upgraded Metallurgical Grade Silicon (UMG Si) substrates with an active layer of 30 μm, and an efficient BSF (Hoeymissenet. J.V; al 2008). Epitaxial cells with the same active layers deposited on highly doped multi-crystalline Si substrates by Chemical Vapor Deposition and the front and back surfaces prepared by phosphorous diffusion as well as screen printing technique, have confirmed also efficiencies 12.3% (Nieuwenhuysen. K.V; 2006). Solar cells developed by a specific process for low cost substrates of UMG silicon have led to efficiencies of 12.8% (Sanchez-Friera. P; et al 2006). Better results have been achieved from cells with an emitter epitaxially grown by CVD, onto a base epitaxialy grown (Nieuwenhuysen. K.V; et al 2008). The emitter creates a front surface field which leads to high open-circuit voltages (Voc) resulting to cell efficiencies close to 15% by optimizing the doping profile and thickness of epitaxial layers and by including a light trapping mechanism.

> This chapter first describes the manufacturing procedures of epitaxial silicon solar cells, starting from the construction of the base layer until the development of solar cells.

> Then a one- dimensional (1D) (Perraki.V; 2010) and a three dimensional (3D) computer program (Kotsovos. K & Perraki.V; 2005), are presented, for the study of the n+pp+ type

Epitaxial Silicon Solar Cells 31

efficiencies. In order to overcome the problem this material is used as a cheap p+ -type

*Epitaxial layer* from pure Si is deposited, by chemical vapor deposition (CVD) on these impure UMG polycrystalline substrates, in an epitaxial reactor (Caymax.M, et al 1986). The wafers are first acid etched and cleaned at 1150 0C, then coated with silicon under SiH2Cl2 flow in H2 gas at 1120 0C with a growth rate 1μm. min-1 (table 2). B2H6 is used, so that to get p- type layers. When the process has been completed a control is carried out testing the quality, thickness and dopant concentration. On to this layer the n+/p junction is then built

Remove saw damage by etching

Wafer cleaning

HCl etching in epitaxial reactor

Deposition of the epitaxial layer

The technology of Liquid Phase Epitaxy (LPE) has recently applied on metallurgical grade Si

Two different approaches exist for the manufacture of the n+-p junction: the ion implantation and the diffusion from the solid phase or from the vapor phase (Overstraeten.

a. The ion implantation is characterized by excellent control of the impurity profile, low temperature processing, higher conversion efficiencies, and is rather used in the

b. The diffusion process, from both gaseous and liquid phase, is usually applied for silicon solar cell fabrication. N2, Ar and O2 are used as carrier gases, with quantities and mixing proportions as well as temperature, time and dopant concentration on the surface

*Diffusion from the vapor phase* consists of diffusion of phosphorus from the oxide formed onto the silicon surface when N2 carrier gas and POCl3 are used in a heated open-tube furnace process at 800-900 0C. Disadvantages of the method are that, diffusion appears on both sides resulting to a back parasitic junction which has to be removed and non uniformity in cases

*Diffusion from a solid phase* consists of deposition of a dopant layer at ambient temperature followed by a heat treatment, in an electrically heated tube furnace with a quartz tube, at a temperature ranging from 800 to 900 0C. This process can be performed using chemical vapor deposition (CVD), screen printing technique, spin-on or spray-on, forming thus only a

i. The CVD technique concerns the deposition, at low temperature, of a uniform phosphorus oxide on the wafer's front surface. This technique uses, highly pure,

expensive, gases ensuring a uniform profile and defined surface conditions.

manufacture of spatial solar cells, due to the high costs associated with it.

and epitaxial solar cells are realized, using a low cost screen printing technology.

substrate, on which a thin p-type epitaxial layer is formatted.

Table 2. Flow diagram of the CVD epitaxial process

with interesting results as well (Peter.K et al 2002).

**2.2 Junction formation** 

R. J. V & Mertens. R, 1986).

of very shallow junctions.

junction on the front surface.

under, a very accurate control.

epitaxial solar cells. These cells have been built on impure (low cost) polycrystalline p+ silicon substrates (Upgraded metallurgical grade UMG-Si), by a special step of thin pure Si deposition followed by conventional techniques to build a n+/p junction, contacts and antireflective coating (ARC). The software developed expresses the variations of photovoltaic parameters as a function of epilayer thickness and calculates for different values of structure parameters, the optimised cell's photovoltaic properties.

According to the one dimensional (1D) model, the photocurrent density and efficiency are calculated as a function of epilayer thickness in cases of low and high recombination velocity values, as well as in cases of different doping concentration values (Perraki.V; 2010), and their optimum values are figured.

The parameter chosen for the cell's optimisation is the epitaxial layer thickness, through variation of grain size and grain boundary recombination velocity, according to the three dimensional (3D) model (Kotsovos. K, & Perraki. V, 2005). Furthermore, a comparison among simulated 3D, 1D and corresponding experimental spectral response results under AM 1.5 illuminations, is presented.

### **2. Epitaxial silicon solar cell fabrication**

The manufacturing sequence for epitaxial silicon (Si) solar cell can be divided in the following main steps: base/active layer formation, junction formation, antireflective coating (ARC) and metallization (front and back contacts), including the oxidation technology, and auxiliary technologies. A complete flow diagram for the realisation of n+pp+ type epitaxial solar cells is presented in Table 1.

MG-Si → UMG-Si→ HEM process p+ type Si → CVD epitaxy→pp+→ Junction formation ...n+pp+ type solar cell ←Back contact formation ←Front grid structuring ←ARC← n+pp+

Table 1. Epitaxial solar cell's process

#### **2.1 Base layer**

The active layer of n+pp+ type crystalline Si solar cells is a thick layer doped with boron and is thus p-type layer with concentration of 1017 cm-3. The crystalline silicon photovoltaic technology has focused on reducing the specific consumption of the base material and increasing the efficiency of cells and modules and in the same time on using new and integrated concepts. Many research groups have tried to use very thin bases in silicon solar cells, aiming to decrease their cost. One of the possible ways for the achievement of cheap crystalline silicon solar cells on an industrial basis is the "metallurgical route". The different steps of this route are:

*Metallurgical grade* (MG), silicon powder (raw material) is upgraded by water washing, acid etching and melting, resulting to a material with insignificant properties and a measured value of diffusion length, Ln, smaller than 5 μm.

*The Upgraded Metallurgical Grade* (UMG), silicon is further purified and recrystallized into ingots by the Heat Exchange Method (HEM) so that to give crack-free ingots associated with large metal impurity segregation and cm size crystals, with better but still insignificant properties. This is due to the fact that the HEM technology allows removing metallic impurities, but the high concentration of boron, phosphorus and the presence of Si carbide precipitates are responsible for again very low measured values of Ln, and solar cell

epitaxial solar cells. These cells have been built on impure (low cost) polycrystalline p+ silicon substrates (Upgraded metallurgical grade UMG-Si), by a special step of thin pure Si deposition followed by conventional techniques to build a n+/p junction, contacts and antireflective coating (ARC). The software developed expresses the variations of photovoltaic parameters as a function of epilayer thickness and calculates for different

According to the one dimensional (1D) model, the photocurrent density and efficiency are calculated as a function of epilayer thickness in cases of low and high recombination velocity values, as well as in cases of different doping concentration values (Perraki.V; 2010),

The parameter chosen for the cell's optimisation is the epitaxial layer thickness, through variation of grain size and grain boundary recombination velocity, according to the three dimensional (3D) model (Kotsovos. K, & Perraki. V, 2005). Furthermore, a comparison among simulated 3D, 1D and corresponding experimental spectral response results under

The manufacturing sequence for epitaxial silicon (Si) solar cell can be divided in the following main steps: base/active layer formation, junction formation, antireflective coating (ARC) and metallization (front and back contacts), including the oxidation technology, and auxiliary technologies. A complete flow diagram for the realisation of n+pp+ type epitaxial

MG-Si → UMG-Si→ HEM process p+ type Si → CVD epitaxy→pp+→ Junction formation ...n+pp+ type solar cell ←Back contact formation ←Front grid structuring ←ARC← n+pp+

The active layer of n+pp+ type crystalline Si solar cells is a thick layer doped with boron and is thus p-type layer with concentration of 1017 cm-3. The crystalline silicon photovoltaic technology has focused on reducing the specific consumption of the base material and increasing the efficiency of cells and modules and in the same time on using new and integrated concepts. Many research groups have tried to use very thin bases in silicon solar cells, aiming to decrease their cost. One of the possible ways for the achievement of cheap crystalline silicon solar cells on an industrial basis is the "metallurgical route". The different

*Metallurgical grade* (MG), silicon powder (raw material) is upgraded by water washing, acid etching and melting, resulting to a material with insignificant properties and a measured

*The Upgraded Metallurgical Grade* (UMG), silicon is further purified and recrystallized into ingots by the Heat Exchange Method (HEM) so that to give crack-free ingots associated with large metal impurity segregation and cm size crystals, with better but still insignificant properties. This is due to the fact that the HEM technology allows removing metallic impurities, but the high concentration of boron, phosphorus and the presence of Si carbide precipitates are responsible for again very low measured values of Ln, and solar cell

values of structure parameters, the optimised cell's photovoltaic properties.

and their optimum values are figured.

AM 1.5 illuminations, is presented.

solar cells is presented in Table 1.

Table 1. Epitaxial solar cell's process

value of diffusion length, Ln, smaller than 5 μm.

**2.1 Base layer** 

steps of this route are:

**2. Epitaxial silicon solar cell fabrication** 

efficiencies. In order to overcome the problem this material is used as a cheap p+ -type substrate, on which a thin p-type epitaxial layer is formatted.

*Epitaxial layer* from pure Si is deposited, by chemical vapor deposition (CVD) on these impure UMG polycrystalline substrates, in an epitaxial reactor (Caymax.M, et al 1986). The wafers are first acid etched and cleaned at 1150 0C, then coated with silicon under SiH2Cl2 flow in H2 gas at 1120 0C with a growth rate 1μm. min-1 (table 2). B2H6 is used, so that to get p- type layers. When the process has been completed a control is carried out testing the quality, thickness and dopant concentration. On to this layer the n+/p junction is then built and epitaxial solar cells are realized, using a low cost screen printing technology.

Remove saw damage by etching

Wafer cleaning

HCl etching in epitaxial reactor

Deposition of the epitaxial layer

Table 2. Flow diagram of the CVD epitaxial process

The technology of Liquid Phase Epitaxy (LPE) has recently applied on metallurgical grade Si with interesting results as well (Peter.K et al 2002).

#### **2.2 Junction formation**

Two different approaches exist for the manufacture of the n+-p junction: the ion implantation and the diffusion from the solid phase or from the vapor phase (Overstraeten. R. J. V & Mertens. R, 1986).


*Diffusion from the vapor phase* consists of diffusion of phosphorus from the oxide formed onto the silicon surface when N2 carrier gas and POCl3 are used in a heated open-tube furnace process at 800-900 0C. Disadvantages of the method are that, diffusion appears on both sides resulting to a back parasitic junction which has to be removed and non uniformity in cases of very shallow junctions.

*Diffusion from a solid phase* consists of deposition of a dopant layer at ambient temperature followed by a heat treatment, in an electrically heated tube furnace with a quartz tube, at a temperature ranging from 800 to 900 0C. This process can be performed using chemical vapor deposition (CVD), screen printing technique, spin-on or spray-on, forming thus only a junction on the front surface.

i. The CVD technique concerns the deposition, at low temperature, of a uniform phosphorus oxide on the wafer's front surface. This technique uses, highly pure, expensive, gases ensuring a uniform profile and defined surface conditions.

Epitaxial Silicon Solar Cells 33

In the second case, during the diffusion process there is an exhaustible dopant source on the surface with a concentration Q (cm-2). The solution of the differential equation 1 N(

<sup>2</sup> ( , ) exp ( ) <sup>2</sup>

The surface concentration in this case is expressed as a function of the diffusion parameters

The silicon base wafers are etched, to remove damage from the wafering process (or to prepare after the CVD process) and cleaned, in order to introduce dopant impurities into the

Since the starting wafers for solar cells are p-type, phosphorus is the n- type impurity generally used. The n+-doped emitter of the cell is thus created by the diffusion of phosphorus, in high concentration which is introduced in the form of phosphine (PH) or gaseous oxychloride (POCL3) into the diffusion furnace. The later is introduced using nitrogen N2, as a carrier gas. The disadvantages of this method are the formation of a back parasitic junction as

At the high temperatures of approximately 800 0C the dopant gases react with the surface of

Si+O2 →SiO2 Silicon dioxide (SiO2) is produced on the surface and secondly, phosphine is converted to

2PH+3O2 → P2O5+H2O The P2O5 created combines with the SiO2 which is grown on the silicon surface to form

Phosphorus diffusion (at temperatures of 950 0C) as a function of diffusion time shows deviating behaviour from the theory for the case of low penetration depth. This behaviour has been explained by several authors; however it has the disadvantage for solar cells that a dead layer is created, of about 0.3 μm thickness, which reduces efficiency to approximately 10%. According to an advanced process, a dead layer can be impeded using a double diffusion process (Blacker. A. W, et al 1989). The first diffusion step consists of a predisposition coat with a low level diffusion of phosphorus at a temperature of approximately 800 0C. Then the phosphorus silicate glass layer is removed by chemical means and in a second diffusion step, this time at a temperature 1000-1100 0C, the desired

the diffusion occurs on both sides and a non uniformity for very shallow junctions.

the silicon when oxygen is added, in accordance with the chemical reaction

phosphorus pentoxide (P2O5 ) according to the following chemical reaction

liquid phosphorus silicate glass which becomes the diffusion source.

*S <sup>Q</sup> <sup>N</sup>* 

and time t is given by Eq 4:

*Dt Dt*

*<sup>j</sup>* of the n-p junction is again calculated by the ratio of the

(4)

*Dt* (5)

*<sup>t</sup>* /NS) when diffusion constant,

base in a controlled manner and form the n-p junction.

temperature and time are also determined.

**2.2.2 Emitter's diffusion procedure** 

concentration in the base silicon to surface concentration (N

*<sup>Q</sup> N t*

(Gaussian distribution) at point

The penetration depth

by Eq 5:

,t)


#### **2.2.1 Diffusion theory**

As the diffusion procedure, is usually applied for silicon solar cell fabrication, it is necessary to refer in brief the theory of diffusion, of various solid elements in the Si solid. This process obeys to Fick's second law, which is expressed in one dimension by the following partial differential equation (Carslaw. H.S; and Jaeger .J.C 1959), (Goetzberger.A, et al 1998).

$$\frac{\partial \mathcal{N}(\boldsymbol{\varrho}, t)}{\partial t} = D \frac{\partial^2 \mathcal{N}(\boldsymbol{\varrho}, t)}{\partial \boldsymbol{\varrho}^2} \tag{1}$$

Where N ( , t) stands for the concentration of the diffusing elements at point and time t and D the diffusion coefficient, characteristic of each material. This coefficient strongly depends on temperature according to the following relation (Sze. S. M. 1981).

$$D = D\_0 \exp(-\Delta \mathcal{E} / kT) \tag{2}$$

D0 and ΔΕ (activation energy) are constant for a given element over wide temperature and concentration ranges.

The temperature plays a very important role in the diffusion process due to the temperature exponential dependency of diffusion coefficient. The diffusion coefficients in relation to temperature show that metals like Ti, Ag, Au, have higher diffusion coefficients D by several orders of magnitude compared to dopants As, P, B, and consequently they diffuse faster in Si, while elements such us Cu, Fe diffuse even more quickly. Therefore solar cell technology requires excellent cleanness of laboratory and experimental devices. However diffusion time does not affect so much the depth of penetration as this is proportional to its root square.

Two solutions to the partial differential equation 1 are considered. In the first case the dopant source is inexhaustible, the surface doping concentration Ns is considered constant during the diffusion process and the bulk concentration depends on diffusion time and diffusion temperature. The mathematical solution under boundary conditions concerning the parameters Ns, t, Nx, and reads:

$$N(\mathcal{X}, t) = N\_S \text{erfc}\frac{\mathcal{X}}{2\sqrt{Dt}}\tag{3}$$

Where, erfc stands for the complementary error function distribution.

In order to calculate the depth *<sup>j</sup>* of the n-p junction, it is necessary to express the ratio of bulk concentration in the base silicon to surface concentration (N *<sup>t</sup>* /NS) as a function of / *Dt* and choose diffusion constant, temperature, and time.

ii. Screen printing is involved to thick film technologies which are characterized by low cost production, automation and reliability. In a first step, a paste rich in phosphorus is screen printed onto the silicon substrate. Then, phosphorus is diffused throughout a heat treatment in an open furnace, under typical peak temperatures between 900 and

iii. Spin-on and spray-on of doped layers yield to high throughput but non uniform

As the diffusion procedure, is usually applied for silicon solar cell fabrication, it is necessary to refer in brief the theory of diffusion, of various solid elements in the Si solid. This process obeys to Fick's second law, which is expressed in one dimension by the following partial

2

*Nt Nt* ( ,) ( ,) *<sup>D</sup>*

, t) stands for the concentration of the diffusing elements at point

and D the diffusion coefficient, characteristic of each material. This coefficient strongly

D0 and ΔΕ (activation energy) are constant for a given element over wide temperature and

The temperature plays a very important role in the diffusion process due to the temperature exponential dependency of diffusion coefficient. The diffusion coefficients in relation to temperature show that metals like Ti, Ag, Au, have higher diffusion coefficients D by several orders of magnitude compared to dopants As, P, B, and consequently they diffuse faster in Si, while elements such us Cu, Fe diffuse even more quickly. Therefore solar cell technology requires excellent cleanness of laboratory and experimental devices. However diffusion time does not affect so much the depth of penetration as this is proportional to its

Two solutions to the partial differential equation 1 are considered. In the first case the dopant source is inexhaustible, the surface doping concentration Ns is considered constant during the diffusion process and the bulk concentration depends on diffusion time and diffusion temperature. The mathematical solution under boundary conditions concerning

( ,) <sup>2</sup> *N t N erfc <sup>S</sup> Dt*

Where, erfc stands for the complementary error function distribution.

/ *Dt* and choose diffusion constant, temperature, and time.

bulk concentration in the base silicon to surface concentration (N

(3)

*<sup>t</sup>* /NS) as a function of

*<sup>j</sup>* of the n-p junction, it is necessary to express the ratio of

2

(1)

<sup>0</sup> *D D* exp( / ) *kT* (2)

and time t

differential equation (Carslaw. H.S; and Jaeger .J.C 1959), (Goetzberger.A, et al 1998).

*t* 

depends on temperature according to the following relation (Sze. S. M. 1981).

950 0C, to form the n-p junction.

surfaces.

Where N (

**2.2.1 Diffusion theory** 

concentration ranges.

root square.

the parameters Ns, t, Nx, and

In order to calculate the depth

reads: In the second case, during the diffusion process there is an exhaustible dopant source on the surface with a concentration Q (cm-2). The solution of the differential equation 1 N( ,t) (Gaussian distribution) at point and time t is given by Eq 4:

$$N(\chi, t) = \frac{Q}{\sqrt{\pi Dt}} \exp - (\frac{\mathcal{X}}{2\sqrt{Dt}})^2 \tag{4}$$

The surface concentration in this case is expressed as a function of the diffusion parameters by Eq 5:

$$N\_S = \frac{Q}{\sqrt{\pi Dt}}\tag{5}$$

The penetration depth *<sup>j</sup>* of the n-p junction is again calculated by the ratio of the concentration in the base silicon to surface concentration (N *<sup>t</sup>* /NS) when diffusion constant, temperature and time are also determined.

#### **2.2.2 Emitter's diffusion procedure**

The silicon base wafers are etched, to remove damage from the wafering process (or to prepare after the CVD process) and cleaned, in order to introduce dopant impurities into the base in a controlled manner and form the n-p junction.

Since the starting wafers for solar cells are p-type, phosphorus is the n- type impurity generally used. The n+-doped emitter of the cell is thus created by the diffusion of phosphorus, in high concentration which is introduced in the form of phosphine (PH) or gaseous oxychloride (POCL3) into the diffusion furnace. The later is introduced using nitrogen N2, as a carrier gas. The disadvantages of this method are the formation of a back parasitic junction as the diffusion occurs on both sides and a non uniformity for very shallow junctions.

At the high temperatures of approximately 800 0C the dopant gases react with the surface of the silicon when oxygen is added, in accordance with the chemical reaction

$$\text{Si} + \text{O}\_2 \rightarrow \text{SiO}\_2$$

Silicon dioxide (SiO2) is produced on the surface and secondly, phosphine is converted to phosphorus pentoxide (P2O5 ) according to the following chemical reaction

#### 2PH+3O2 → P2O5+H2O

The P2O5 created combines with the SiO2 which is grown on the silicon surface to form liquid phosphorus silicate glass which becomes the diffusion source.

Phosphorus diffusion (at temperatures of 950 0C) as a function of diffusion time shows deviating behaviour from the theory for the case of low penetration depth. This behaviour has been explained by several authors; however it has the disadvantage for solar cells that a dead layer is created, of about 0.3 μm thickness, which reduces efficiency to approximately 10%. According to an advanced process, a dead layer can be impeded using a double diffusion process (Blacker. A. W, et al 1989). The first diffusion step consists of a predisposition coat with a low level diffusion of phosphorus at a temperature of approximately 800 0C. Then the phosphorus silicate glass layer is removed by chemical means and in a second diffusion step, this time at a temperature 1000-1100 0C, the desired

Epitaxial Silicon Solar Cells 35

used, that the etching rate of silicon in an alkaline solution depends on the crystallographic orientation of silicon's front surface (Price J.B., 1983). The crystal orientation yielding to high

The anisotropic etching process takes place in weak solutions of KOH or NaOH with a concentration of 10% up to 30% at approximately 70 0C. This configuration results to inverted pyramid structures, under well determined conditions and reduces the reflection of

An additional ARC allows a further reduction to approximately 3%. In practice the best

a. The vacuum evaporation, which has the disadvantage that the smallest finger width is

b. The photoresist technique which is used if narrower contact fingers are required in

c. The screen printing technique, which uses metal pastes, and dominates in a wide range of production techniques as it is particularly cost effective, with the maximum finger

This technique is widespread in industrial solar cell manufacturing and has automating processes (Overstraeten. R.J.V; 1986). The screen printing process uses metal pastes containing in addition to 70% Ag approximately 2% sintered glass. After depositing, the layer is sintered at temperatures of about 600 0C, while the sintered glass components melt and dissolve a small layer of silicon. At the same time this melt is enriched by silver. Upon cooling a recrystallized Si layer is created as with normal alloying, which contains a high proportion of Ag and thus creates a good ohmic contact. This process gives quite low contact resistances on the n+ emitter at surface concentrations of approximately

The realizations of back surface contacts need only aluminum, in the form of paste. This element has the advantage that forms alloys at its eutectic point 577 0C, and has a good solubility with concentrations of about 1019 cm-3 in Si, while a silver palladium paste is often sintered onto this layer in different cases (Overstraeten. R. J. V, & Mertens. R, 1986). Thus a high doping p+ type is achieved in the recrystallised layer providing a Back Surface Field. Normally sintering takes place at temperatures around 800 0C with the best results. A significant increase in Voc is observed yielding thus higher values of solar cell efficiency.

The oxidation technology is applied for the manufacture of a SiO2 layer in solar cells. It is a relatively simple manufacturing process using high temperature treatment in an electrically heated tube furnace with a quartz tube under oxygen. This layer, nevertheless, plays a crucial role in silicon solar cells, with main characteristics passivation and masking effects of SiO2 regarding impurities, which contributes positively to making silicon the basic material

efficiency solar cells is <100>.

**2.4 Contacts** 

1020 cm-3.

sunlight to approximately 10 % (Goetzberger.A, et al 1998).

The technologies used for the structuring of the finger grid are three:

success has been achieved with inverted pyramids.

approximately 100 μm or at best 50 μm,

**2.4.1 The structuring of the finger grid** 

order to reduce shadowing.

width about 100 μm.

**2.4.2 Back surface contacts** 

**2.5 Oxidation technologies** 

for most semiconductor devices.

penetration depth of phosphorus is achieved. Surface concentrations of approximately 1019 cm-3 can be obtained.

#### **2.2.3 Screen printing for junction formation**

A process line based on the use of thick film technology offers advantages of low cost, automation, and reliability. The technology involves the screen printing technique for the junction formation. According to this a phosphorus*-*doped paste, containing active material, solvents and a thickener is printed through screens, onto a silicon substrate (Overstraeten. R. J 1986). After printing, the substrate is dried at 150 0C allowing thus the solvents to evaporate. The phosphorus diffuses from the printed layer into the silicon during a heat treatment in a belt furnace in nitrogen under typical peak temperatures between 900 and 950 0C. When screen printing is used for junction formation there is no parasitic junction formed at the back as in the case for open tube diffusion. However the layer that remains on the front of the cell after diffusion and the edges of the substrate which are doped due to contamination, have to be removed by etching in a proper chemical solution followed by a cleaning step.

Apart from the junction formation screen printing process can also be applied to the antireflection coating formation and the metallization (front and back contacts).

Epitaxialy growth by CVD may also be used for the n+ doped emitter formation, controlling the doping profile, on an epitaxially grown base. In this way a front surface field (FSF) is created yielding to a high open circuit voltage (Voc) and high efficiency (Nieuwenhuysen. K.V; et al 2008).

#### **2.3 Antireflection processes**

#### **2.3.1 Antireflection Coating (ARC)**

Silicon surfaces reflect more than 33% of sunlight depending upon wavelength. For the manufacture of antireflection coatings industrial inks which contain titanium dioxide (TiO2) or tantanium pentoxide (Ta2O5) as the active coating material, are used.

Two technologies are applied for this purpose:


The antireflective coating and the front side grid formation can be combined and made together by screen printing technique. In this case the TiO2 paste is firstly dried at temperatures around 200 0C, then a silver paste is added to it for the grid formation, and both are simultaneously sintered.

A further improvement can reduce total reflection to 3 – 4%. This can be achieved by using two antireflection layers, with a refractive index decreasing from the upper AR layer to the lower.

#### **2.3.2 Textured surfaces**

The textured surfaces of cells allow most of the light to be absorbed in the cell, after multiple reflections. For the construction of textured silicon surfaces the physical-chemical effect is

penetration depth of phosphorus is achieved. Surface concentrations of approximately

A process line based on the use of thick film technology offers advantages of low cost, automation, and reliability. The technology involves the screen printing technique for the junction formation. According to this a phosphorus*-*doped paste, containing active material, solvents and a thickener is printed through screens, onto a silicon substrate (Overstraeten. R. J 1986). After printing, the substrate is dried at 150 0C allowing thus the solvents to evaporate. The phosphorus diffuses from the printed layer into the silicon during a heat treatment in a belt furnace in nitrogen under typical peak temperatures between 900 and 950 0C. When screen printing is used for junction formation there is no parasitic junction formed at the back as in the case for open tube diffusion. However the layer that remains on the front of the cell after diffusion and the edges of the substrate which are doped due to contamination, have to

Apart from the junction formation screen printing process can also be applied to the

Epitaxialy growth by CVD may also be used for the n+ doped emitter formation, controlling the doping profile, on an epitaxially grown base. In this way a front surface field (FSF) is created yielding to a high open circuit voltage (Voc) and high efficiency (Nieuwenhuysen.

Silicon surfaces reflect more than 33% of sunlight depending upon wavelength. For the manufacture of antireflection coatings industrial inks which contain titanium dioxide (TiO2)

a. High vacuum evaporation technologies use almost exclusively TiO2, with a refraction index n adjusted between 1.9 and 2.3, a good transparency which favors high

b. Thick film technologies, which are used in mass production due to their lower cost. At thick film technologies, a paste containing TiO2 compounds is deposited onto the surface of silicon, either by the screen printing technique at temperatures of 600 to

The antireflective coating and the front side grid formation can be combined and made together by screen printing technique. In this case the TiO2 paste is firstly dried at temperatures around 200 0C, then a silver paste is added to it for the grid formation, and

A further improvement can reduce total reflection to 3 – 4%. This can be achieved by using two antireflection layers, with a refractive index decreasing from the upper AR layer to the

The textured surfaces of cells allow most of the light to be absorbed in the cell, after multiple reflections. For the construction of textured silicon surfaces the physical-chemical effect is

be removed by etching in a proper chemical solution followed by a cleaning step.

antireflection coating formation and the metallization (front and back contacts).

or tantanium pentoxide (Ta2O5) as the active coating material, are used.

1019 cm-3 can be obtained.

K.V; et al 2008).

**2.3 Antireflection processes 2.3.1 Antireflection Coating (ARC)** 

efficiencies and high costs.

both are simultaneously sintered.

**2.3.2 Textured surfaces** 

lower.

Two technologies are applied for this purpose:

800 0C or by the spinning on technique.

**2.2.3 Screen printing for junction formation** 

used, that the etching rate of silicon in an alkaline solution depends on the crystallographic orientation of silicon's front surface (Price J.B., 1983). The crystal orientation yielding to high efficiency solar cells is <100>.

The anisotropic etching process takes place in weak solutions of KOH or NaOH with a concentration of 10% up to 30% at approximately 70 0C. This configuration results to inverted pyramid structures, under well determined conditions and reduces the reflection of sunlight to approximately 10 % (Goetzberger.A, et al 1998).

An additional ARC allows a further reduction to approximately 3%. In practice the best success has been achieved with inverted pyramids.

#### **2.4 Contacts**

#### **2.4.1 The structuring of the finger grid**

The technologies used for the structuring of the finger grid are three:


This technique is widespread in industrial solar cell manufacturing and has automating processes (Overstraeten. R.J.V; 1986). The screen printing process uses metal pastes containing in addition to 70% Ag approximately 2% sintered glass. After depositing, the layer is sintered at temperatures of about 600 0C, while the sintered glass components melt and dissolve a small layer of silicon. At the same time this melt is enriched by silver. Upon cooling a recrystallized Si layer is created as with normal alloying, which contains a high proportion of Ag and thus creates a good ohmic contact. This process gives quite low contact resistances on the n+ emitter at surface concentrations of approximately 1020 cm-3.

#### **2.4.2 Back surface contacts**

The realizations of back surface contacts need only aluminum, in the form of paste. This element has the advantage that forms alloys at its eutectic point 577 0C, and has a good solubility with concentrations of about 1019 cm-3 in Si, while a silver palladium paste is often sintered onto this layer in different cases (Overstraeten. R. J. V, & Mertens. R, 1986). Thus a high doping p+ type is achieved in the recrystallised layer providing a Back Surface Field. Normally sintering takes place at temperatures around 800 0C with the best results. A significant increase in Voc is observed yielding thus higher values of solar cell efficiency.

#### **2.5 Oxidation technologies**

The oxidation technology is applied for the manufacture of a SiO2 layer in solar cells. It is a relatively simple manufacturing process using high temperature treatment in an electrically heated tube furnace with a quartz tube under oxygen. This layer, nevertheless, plays a crucial role in silicon solar cells, with main characteristics passivation and masking effects of SiO2 regarding impurities, which contributes positively to making silicon the basic material for most semiconductor devices.

Epitaxial Silicon Solar Cells 37

Isotropic etching of silicon occurs in a solution of nitric acid and hydrofluoric acid or in

Rinsing with deionised water must take place as the final stage, following all cleaning processes. With this processes, specific resistance values near to the theoretical value are

A one dimensional (1D) analytical model is assessed via a simulation program which takes into account the interaction and the limitations between several parameters. By modeling short circuit current density Jsc, open circuit voltage Voc and efficiency η, cells of different structure characteristics are studied. The photocurrent density and efficiency are estimated as a function of epilayer thickness d2, for various values of recombination velocity and doping concentration (Perraki V, 2010). Furthermore, the simulated and experimental plots

A three dimensional (3D) analytical model, which is based on the Green's Function method, is also implemented at the same cells. The model is applied via a simulation program to optimize the efficiency of cells. The parameter chosen for optimization is the epitaxial layer thickness via variation of grain size and grain boundary recombination velocity (Kotsovos K, & Perraki V., 2005). In addition, 3D spectral response data are compared with the 1D

The epitaxial n+pp+ type Si solar cell is divided in four main regions (front layer n+, Space Charge Region (SCR), epilayer, and substrate), with thickness d1-wn, wn+wp, d2-wp and d3,

Fig. 1. The cross section for the theoretical model of n+pp+ type epitaxial solar cell.

grains are perpendicular to the front and to the n+/p junction.

There are a number of main assumptions used for modeling which concern, the homogeneity of physical and electrical properties of the grains (doping concentration, minority carrier mobility, life time and diffusion length). The grains are columnar, in Si materials recrystallized by the Heat Exchange Method, becoming increasingly large when considering successively, bottom, middle and top wafers in the ingot. These columnar

The front surface recombination velocity SF has a value of 104 cm/s and the back surface SB 1015 cm/s. A perfect abrupt interface between the heavily doped substrate with thickness higher

combination with acetic acid and phosphoric acid (H3PO4).

of quantum efficiency are compared, under 1000W/m2 irradiation.

achieved.

results.

**3. Mathematical model** 

**3.1 One dimensional model** 

respectively, figure 1.

*Dry oxidation* is achieved when silicon is heated without the addition of water vapour, and takes place according to the chemical reaction

$$\text{Si} + \text{O}\_2 \to \text{SiO}\_2$$

As it is known, oxygen diffuses through the SiO2 layer which is formed, there is no saturation thickness and the layer thickness grows in proportion to time or in proportion to the square root of time at greater layer thickness than 1 μm.

*Wet oxidation*, is achieved when silicon is exposed to water vapor, during the oxidation process and obeys to the following chemical reaction

$$\text{2Si} + \text{O}\_2 + \text{2H}\_2\text{O} \rightarrow \text{2SiO}\_2 + \text{2H}\_2\text{O}$$

Due to the hydrogen presence in case of wet oxidation the rate of growth is significantly higher than that of dry oxidation (Wolf H. F., 1976). Other influences that also alter the growth rate of SiO2 are the doping concentration of silicon, the orientation of Si surfaces and the addition of chlorine ions during the oxidation process.

The use of SiO2 as a passivating layer in solar cells has shown that dry oxidation under high oxidation temperatures yields very low surface recombination rates, which can be reduced even further by an annealing process at about 4500 C, and depends upon the crystallographic orientation of silicon surfaces.

The masking effect of a SiO2 layer in the diffusion process relies upon the fact that the diffusion rate of many diffusants in silicon dioxide is lower by orders of magnitude than in silicon itself. The required SiO2 layer thickness, for different diffusion temperatures and times, shows that boron is masked by significantly thinner SiO2 layers than is phosphorus. Furthermore, SiO2 is used for masking in alkaline etching processes as well as for surface texturing (Goetzberger.A, et al 1998).

#### **2.6 Back Surface Field (BSF)**

The required p+ doping in the starting wafer, in order to create a Back Surface Field, (BSF), is achieved by diffusion of boron. BBr3 serves as the boron source for this purpose, which can be handled in a very similar manner to POCl3. As it is known, a BSF is necessary for high efficiency solar cells.

In industrial practice, aluminium with a eutectic point 577 0C, is introduced onto the surface for the creation of a BSF. This is processed by vacuum evaporation or by screen printing technique at approximately 800 0C.

#### **2.7 Auxiliary technologies**

Auxiliary processes such as etching and cleaning are necessary for the manufacture of solar cells.

Etching and cleaning techniques are used in order to make the surfaces of silicon wafers free of contaminants like molecular (residues of the lapping, polishing etc), ionic (from the etching solutions), or atomic (heavy metals). The most widely used procedure for surface cleaning is currently the RCA cleaning (named after the company RCA). This process is based upon the use of hydrogen peroxide (H2O2) firstly as an addition to a weak solution of ammonium hydroxide (NH4OH) and secondly hydrochloric acid (HCl).

Etching of silicon dioxide layers occurs mainly in a weak solution of hydrofluoric acid, or in combination with ammonium fluoride (NH4F).

*Dry oxidation* is achieved when silicon is heated without the addition of water vapour, and

Si+ O2→ SiO2 As it is known, oxygen diffuses through the SiO2 layer which is formed, there is no saturation thickness and the layer thickness grows in proportion to time or in proportion to

*Wet oxidation*, is achieved when silicon is exposed to water vapor, during the oxidation

2Si+ O2+2H20 → 2SiO2+2H2 Due to the hydrogen presence in case of wet oxidation the rate of growth is significantly higher than that of dry oxidation (Wolf H. F., 1976). Other influences that also alter the growth rate of SiO2 are the doping concentration of silicon, the orientation of Si surfaces and

The use of SiO2 as a passivating layer in solar cells has shown that dry oxidation under high oxidation temperatures yields very low surface recombination rates, which can be reduced even further by an annealing process at about 4500 C, and depends upon the

The masking effect of a SiO2 layer in the diffusion process relies upon the fact that the diffusion rate of many diffusants in silicon dioxide is lower by orders of magnitude than in silicon itself. The required SiO2 layer thickness, for different diffusion temperatures and times, shows that boron is masked by significantly thinner SiO2 layers than is phosphorus. Furthermore, SiO2 is used for masking in alkaline etching processes as well as for surface

The required p+ doping in the starting wafer, in order to create a Back Surface Field, (BSF), is achieved by diffusion of boron. BBr3 serves as the boron source for this purpose, which can be handled in a very similar manner to POCl3. As it is known, a BSF is necessary for high

In industrial practice, aluminium with a eutectic point 577 0C, is introduced onto the surface for the creation of a BSF. This is processed by vacuum evaporation or by screen printing

Auxiliary processes such as etching and cleaning are necessary for the manufacture of solar

Etching and cleaning techniques are used in order to make the surfaces of silicon wafers free of contaminants like molecular (residues of the lapping, polishing etc), ionic (from the etching solutions), or atomic (heavy metals). The most widely used procedure for surface cleaning is currently the RCA cleaning (named after the company RCA). This process is based upon the use of hydrogen peroxide (H2O2) firstly as an addition to a weak solution of

Etching of silicon dioxide layers occurs mainly in a weak solution of hydrofluoric acid, or in

ammonium hydroxide (NH4OH) and secondly hydrochloric acid (HCl).

takes place according to the chemical reaction

the square root of time at greater layer thickness than 1 μm.

the addition of chlorine ions during the oxidation process.

crystallographic orientation of silicon surfaces.

texturing (Goetzberger.A, et al 1998).

**2.6 Back Surface Field (BSF)** 

technique at approximately 800 0C.

combination with ammonium fluoride (NH4F).

**2.7 Auxiliary technologies** 

efficiency solar cells.

cells.

process and obeys to the following chemical reaction

Isotropic etching of silicon occurs in a solution of nitric acid and hydrofluoric acid or in combination with acetic acid and phosphoric acid (H3PO4).

Rinsing with deionised water must take place as the final stage, following all cleaning processes. With this processes, specific resistance values near to the theoretical value are achieved.

#### **3. Mathematical model**

A one dimensional (1D) analytical model is assessed via a simulation program which takes into account the interaction and the limitations between several parameters. By modeling short circuit current density Jsc, open circuit voltage Voc and efficiency η, cells of different structure characteristics are studied. The photocurrent density and efficiency are estimated as a function of epilayer thickness d2, for various values of recombination velocity and doping concentration (Perraki V, 2010). Furthermore, the simulated and experimental plots of quantum efficiency are compared, under 1000W/m2 irradiation.

A three dimensional (3D) analytical model, which is based on the Green's Function method, is also implemented at the same cells. The model is applied via a simulation program to optimize the efficiency of cells. The parameter chosen for optimization is the epitaxial layer thickness via variation of grain size and grain boundary recombination velocity (Kotsovos K, & Perraki V., 2005). In addition, 3D spectral response data are compared with the 1D results.

#### **3.1 One dimensional model**

The epitaxial n+pp+ type Si solar cell is divided in four main regions (front layer n+, Space Charge Region (SCR), epilayer, and substrate), with thickness d1-wn, wn+wp, d2-wp and d3, respectively, figure 1.

Fig. 1. The cross section for the theoretical model of n+pp+ type epitaxial solar cell.

There are a number of main assumptions used for modeling which concern, the homogeneity of physical and electrical properties of the grains (doping concentration, minority carrier mobility, life time and diffusion length). The grains are columnar, in Si materials recrystallized by the Heat Exchange Method, becoming increasingly large when considering successively, bottom, middle and top wafers in the ingot. These columnar grains are perpendicular to the front and to the n+/p junction.

The front surface recombination velocity SF has a value of 104 cm/s and the back surface SB 1015 cm/s. A perfect abrupt interface between the heavily doped substrate with thickness higher

Epitaxial Silicon Solar Cells 39

The contribution of the space charge region QSCR is expressed by the following relation (Sze

The total photocurrent density Jsc arising from the minority carriers generated very near the junction in the n- layer, in the epilayer and in the space charge region can be calculated from

The flux of photons as a function of wavelength, Ν (λ), was defined by a discretized AM1.5

The open circuit voltage depends on the Boltzmann constant, k, the solar cell operating temperate, T, the elementary electron charge, q, and the logarithm of the ratio between the

Moreover, efficiency η (%) which is the most important parameter in the evaluation process of photovoltaic cells, is proportional to the open-circuit voltage Voc, the photocurrent density

Several assessments have been admitted in order to simplify the 3D model and obtain the excess minority carrier density from the solution of the three-dimensional diffusion equation

The p/p+ junction is considered as a low/high junction, incorporating a strong BSF. It is assumed that the p+ region's contribution to the total photocurrent is negligible (Dugas.J, &

The heat exchange method provides polycrystalline silicon with columnar grains, as shown in figure 2. The grain boundaries are surfaces of very small width compared to the grain size, characterized by a distribution of interface states. They are perpendicular to the n+/p junction, becoming increasingly large when considering successively, bottom, middle and top wafers in the ingot. Their physical and electrical properties, concerning the doping concentration, the mobility and diffusion length of minority carriers, along the three dimensions are homogeneous, for each region. There are ignored effects of other

The front and back surface recombination velocity SF and SB are the same as in (Luque. A, & Hegeduw. S., 2003), and their values are assumed as 104 cm/sec and 1015 cm/sec respectively. The effective grain boundary recombination velocity is assumed constant all over the surface of the grain and has been estimated to vary from 102 to 106 cm/sec. It

0 ln( 1) *SC*

 

1.1

0.4 () () *SC tot J qQ N d* 

*OC kT <sup>J</sup> <sup>V</sup>*

Jsc, fill factor FF, and inversely proportional to the incident power of sunlight.

The contribution of the three regions of the solar cell is:

the Eq. 12 as a function of the cell's quantum efficiency.

photocurrent and dark current density, Jsc /J0.

**3.2 Three dimensional model (3D)** 

imperfections of the crystal structure.

*QSCR=[1-R][exp-(αnWn+αpWp)-1]exp-αn(d1-Wn)* (10)

*Qtot=Qp+Qn+QSCR* (11)

(12)

*q J* (13)

.S.M 1981)

solar spectrum.

in each region.

Qualid. J, 1985).

compared to its diffusion length and the lowly doped epilayer, consists a low/high junction p/p+. This junction produces a strong BSF while the p+ layer does not contribute to the total photocurrent (Luque. A, & Hegeduw. S., 2003).

The expression, for the effective recombination velocity, Seff, at the epilayer/substrate interface describing the quality of the back surface of the base, is given by the following equation (Godlewski. M; et al 1973):

$$S\_{\rm eff} = \frac{N\_A D\_{n^+}}{N\_{A^{+}} L\_{n^+}} \frac{(\frac{S\_B L\_{n^+}}{D\_{n^+}} \cosh \frac{d\_3}{L\_{n^+}} + \sinh \frac{d\_3}{L\_{n^+}})}{\left(\cosh \frac{d\_3}{L\_{n^+}} + \frac{S\_B L\_{n^+}}{D\_{n^+}} \sinh \frac{d\_3}{L\_{n^+}}\right)}\tag{6}$$

Where, the terms ΝΑ, ΝΑ+,Ln, Ln+, Dn, Dn+ stand for the material's doping concentration, electron diffusion length and diffusion constant in the epilayer and the substrate respectively and SB for the recombination velocity at the back surface. Due to the low/ high junction the following simplified relation (Arora. J, et al 1981) gives the expression for Seff.

$$S\_{\rm eff} = \frac{N\_A D\_{n^+}}{N\_{A^+} L\_{n^+}} \tag{7}$$

The terms *NA*, *NA+*, *Dn+* and *Ln+* are assumed constant all over of these regions' bulk. The analytical form of the quantum efficiency of the front layer Qp, is described by the following relation (Hovel H J 1975), (Sze. S. M, 1981):

$$Q\_{P} = \left[1 - R\right] \frac{a\_{n}L\_{P}}{\left(a\_{n}L\_{P}\right)^{2} - 1} \times \frac{-\left(\frac{S\_{\rm P}L\_{P}}{D\_{P}} + a\_{n}L\_{P}\right) + \left[\frac{S\_{\rm P}L\_{P}}{D\_{P}} + \sinh\frac{d\_{1} - w\_{n}}{L\_{P}}\right] \exp\left(-a\_{n}d\_{1} - a\_{n}w\_{n}\right)}{\frac{S\_{\rm P}L\_{P}}{D\_{P}} \sinh\frac{d\_{1} - w\_{n}}{L\_{P}} + \cosh\frac{d\_{1} - w\_{n}}{L\_{P}}} \tag{8}$$

$$+ a\_{n}L\_{P}\exp\left(-a\_{n}d\_{1} - a\_{n}w\_{n}\right)]\tag{8}$$

Where Lp, Dp and αn stand for hole diffusion length, diffusion coefficient and absorption coefficient in the front layer and R and SF stand for reflection coefficient and front surface recombination velocity, respectively.

The base region quantum yield Qn, can be calculated from the following relation

$$Q\_n = \left[1 - R\right] \frac{\alpha\_P L\_n}{\left(\alpha\_p L\_n\right)^2 - 1} \exp\left(-\left(\alpha\_n d\_1 + \alpha\_p \mathcal{W}\_p\right)\right)$$

$$\frac{1}{\alpha\_P L\_n} \frac{d\_2 - w\_p}{L\_n} + \frac{S\_{\text{eff}} L\_n}{D\_n} \cosh\frac{d\_2 - w\_p}{L\_n} + \left(\alpha\_p L\_n - \frac{S\_{\text{eff}} L\_n}{D\_n}\right) \exp-\alpha\_p (d\_2 - w\_p)}{\frac{S\_{\text{eff}} L\_n}{D\_n} \sinh\frac{d\_2 - w\_p}{L\_n} + \cosh\frac{d\_2 - w\_p}{L\_n}}\tag{9}$$

αp stands for the absorption coefficient in the base layer p.

compared to its diffusion length and the lowly doped epilayer, consists a low/high junction p/p+. This junction produces a strong BSF while the p+ layer does not contribute to the total

The expression, for the effective recombination velocity, Seff, at the epilayer/substrate interface describing the quality of the back surface of the base, is given by the following

*B n*

*<sup>A</sup> nn n n eff A n <sup>B</sup> <sup>n</sup>*

Where, the terms ΝΑ, ΝΑ+,Ln, Ln+, Dn, Dn+ stand for the material's doping concentration, electron diffusion length and diffusion constant in the epilayer and the substrate respectively and SB for the recombination velocity at the back surface. Due to the low/ high junction the following simplified relation (Arora. J, et al 1981) gives the expression for Seff.

> *<sup>A</sup> <sup>n</sup> eff A n*

The analytical form of the quantum efficiency of the front layer Qp, is described by the

*S*

[1 ] [ ( )1 sinh cosh

The base region quantum yield Qn, can be calculated from the following relation

*P n*

*L* 

*nn n n P n*

*LD L D <sup>L</sup> SL d w d w*

2 2

αp stands for the absorption coefficient in the base layer p.

1 exp( )]

*<sup>L</sup> D DL L QR x <sup>L</sup> S L dw dw*

The terms *NA*, *NA+*, *Dn+* and *Ln+* are assumed constant all over of these regions' bulk.

*n P P PP P*

*F P n n n P*

 

Where Lp, Dp and αn stand for hole diffusion length, diffusion coefficient and absorption coefficient in the front layer and R and SF stand for reflection coefficient and front surface

> <sup>2</sup> <sup>1</sup> [1 ] exp( ( )) ( )1 *P n n n p p*

sinh cosh ( )exp ( )

*eff n p p nn n*

*DL L*

[ ] sinh cosh

*p eff n p eff n*

*d w SL d w SL*

2 2

 

*<sup>L</sup> Q R d W*

*N D*

 

*N L*

*ND D L L*

*N L d d S L*

3 3

(7)

1 1

( )[ cosh sinh ]exp( )

*SL SL dw dw <sup>L</sup> d aw*

*PP P*

*DL L*

*F P F P n n n P n nn*

1 1

*nL dw <sup>p</sup> n nn* (8)

(6)

1

 

2

(9)

*P n p p*

*L d w*

 

3 3

*nn n*

*LD L*

( cosh sinh )

*S L d d*

(cosh sinh )

photocurrent (Luque. A, & Hegeduw. S., 2003).

*S*

following relation (Hovel H J 1975), (Sze. S. M, 1981):

2

recombination velocity, respectively.

equation (Godlewski. M; et al 1973):

*P*

The contribution of the space charge region QSCR is expressed by the following relation (Sze .S.M 1981)

$$Q\_{\mathcal{SCR}} \equiv \{1\text{-}R\} [\exp\text{-}(a\_n \mathcal{VV}\_n + a\_p \mathcal{VV}\_p)\text{-}1] \exp\text{-}a\_n(d\_1 \text{-} \mathcal{VV}\_n) \tag{10}$$

The contribution of the three regions of the solar cell is:

$$Q\_{tot} = Q\_p + Q\_n + Q\_{SCR} \tag{11}$$

The total photocurrent density Jsc arising from the minority carriers generated very near the junction in the n- layer, in the epilayer and in the space charge region can be calculated from the Eq. 12 as a function of the cell's quantum efficiency.

$$J\_{SC} = q \int\_{0.4}^{1.1} Q\_{tot}(\lambda) N(\lambda) d\lambda \tag{12}$$

The flux of photons as a function of wavelength, Ν (λ), was defined by a discretized AM1.5 solar spectrum.

The open circuit voltage depends on the Boltzmann constant, k, the solar cell operating temperate, T, the elementary electron charge, q, and the logarithm of the ratio between the photocurrent and dark current density, Jsc /J0.

$$V\_{\rm OC} = \frac{kT}{q} \ln(\frac{I\_{\rm SC}}{I\_0} + 1) \tag{13}$$

Moreover, efficiency η (%) which is the most important parameter in the evaluation process of photovoltaic cells, is proportional to the open-circuit voltage Voc, the photocurrent density Jsc, fill factor FF, and inversely proportional to the incident power of sunlight.

#### **3.2 Three dimensional model (3D)**

Several assessments have been admitted in order to simplify the 3D model and obtain the excess minority carrier density from the solution of the three-dimensional diffusion equation in each region.

The p/p+ junction is considered as a low/high junction, incorporating a strong BSF. It is assumed that the p+ region's contribution to the total photocurrent is negligible (Dugas.J, & Qualid. J, 1985).

The heat exchange method provides polycrystalline silicon with columnar grains, as shown in figure 2. The grain boundaries are surfaces of very small width compared to the grain size, characterized by a distribution of interface states. They are perpendicular to the n+/p junction, becoming increasingly large when considering successively, bottom, middle and top wafers in the ingot. Their physical and electrical properties, concerning the doping concentration, the mobility and diffusion length of minority carriers, along the three dimensions are homogeneous, for each region. There are ignored effects of other imperfections of the crystal structure.

The front and back surface recombination velocity SF and SB are the same as in (Luque. A, & Hegeduw. S., 2003), and their values are assumed as 104 cm/sec and 1015 cm/sec respectively. The effective grain boundary recombination velocity is assumed constant all over the surface of the grain and has been estimated to vary from 102 to 106 cm/sec. It

Epitaxial Silicon Solar Cells 41

specific boundary conditions when the device is operated under short circuit, concerning the grain boundary recombination velocity in the active layer Sng and the effective back surface recombination velocity Seff at the low / high junction. The simplified relation gives the expression for effective electron recombination velocity Seff, as a function of the material's doping concentration of the active layer and the substrate (ΝΑ, ΝΑ+), assumed constant all over of these regions' bulk (Eq.7). Moreover the grain boundary recombination velocity in the front and the active layer is considered the same and symbolized as Sgb. The solution of the continuity equations (14) and (16) is obtained in analytical form using the Green's function method. This procedure is briefly described in (kotsovos. K & Perraki. V; 2005). The analytical expression of the front layer photocurrent density Jp is derived, by differentiating the hole density distribution in the junction edge region z=d1-wn presented in

sin( )sin( ) cos( )cos( ) ( 1)

1

(17)

(18)

 

 

(19)

*mx ny mn L*

*peff peff peff <sup>n</sup> n n <sup>p</sup>*

sin( )sin( ) cos( )cos( ) ( 1)

2 2

sinh( ) cosh( )

*L L*

 

{cosh( ) ) sinh( )} )

2 2 2 2 ( ) ( )

*neff neff*

*p p p p d w d w*

*p p*

*kx ly kl L*

[ ]

The photogenerated current in the Space Charge Region (equal to the number of photons

*SCR J qFe <sup>e</sup>* 

*n neff neff neff*

*d w d w Ne L e L L*

1 1

*L L L dw dw dw <sup>N</sup>*

[ exp( ( ))]

where the variables *x* and *y* represent arbitrary points inside the grain and *Mx, Ny, Lpeff, Np*

In a similar way the analytical expression of the base region photocurrent density Jn is given, in the form of infinite series, by differentiating the electron density distribution in the

the form of infinite series (Halder. N.C, & Williams. T. R., 1983):

(,,) 4

*J xy q F*

*p*

1

junction edge region *z=d2 –wp* by the relation

*neff*

 

2 2

1 1

*L L*

2 2

 

*n*

Where *Kx, Ly, Lneff, Nn* are expressed as functions of S*eff*, S*ng* ,D*n*, X*g*, Y*g*, L*<sup>n</sup>*.

1 ( ) ( ){1 } *d wn w w n p*

*<sup>L</sup> dw dw N*

2 2 ,

*k l neff*

4

*J q Fe*

*n*

absorbed), is derived by the 1D model (Sze. S. M, 1981):

*peff peff*

are expressed by proper equations as functions of Spg ,Dp, Xg, Yg, Lp, and SF.

<sup>1</sup> ( )

*neff x y g g*

*L K L kX lY*

*<sup>p</sup> d w*

sinh( ) cosh( )

 

exp( ( )){ cosh( ) sinh( )}

*peff x y g g*

*L M N mX nY*

2 2 ,

*n n p peff n p*

*dw dw N L dw N*

*m n peff*

Fig. 2. Ideal crystal orientation and cross section for the theoretical model of n+pp+ type epitaxial solar cell (with columnar grains).

depends basically on the interface state density at the grain boundary and the doping concentration of the semiconductor material (Card. H.C, & Yang. E.,1977).

The solution of the three-dimensional diffusion equation provides the excess minority carrier density.

The steady state continuity equation for the top side of the junction under illumination is expressed by the following relation (Sze. S. M, 1981):

$$\nabla^2(p\_n - p\_{n0}) - \frac{p\_n - p\_{n0}}{L\_p^2} = -\frac{\alpha(\lambda)\mathcal{F}(\lambda)\exp(-\alpha(\lambda)z)}{D\_p} \tag{14}$$

Where, pn-pn0 , Lp and Dp stand for the excess minority carrier density in the front layer, the minority carrier diffusion length and the diffusion coefficient respectively. The material absorption coefficient α(λ) is given by Runyan (Runyan. W. R, (1976)) and the light generation rate F (number of photons of wavelength λ inserting the front side per unit area and unit time) is given by the following relation

$$F(\lambda) = \mathbf{N}(0, \lambda)(1 \text{-} R(\lambda))\tag{15}$$

With N(0,λ) representing the number of photons of wavelength λ incident on the surface per unit area and unit time (depth x=0) and R(λ) the reflection coefficient of light at the front side. This coefficient is calculated, for an antireflective coating of single layer (TiO2) with optimal thickness 77 nm, (Heavens. O. S, 1991). There is a metal coverage coefficient of 13.1%, corresponding to the front metal grid and cell series resistance (Rs) of about 1.7 Ω.

The boundary conditions which accompany Eq. 14 when the solar cell is short circuited involve the front surface recombination velocity SF and the grain boundary recombination velocity in the front region Spg.

The diffusion equation for the base region is expressed by a similar form like in the front layer:

$$\nabla^2(n\_p - n\_{p0}) - \frac{n\_p - n\_{p0}}{\mathcal{L}\_n^2} = -\frac{\alpha(\lambda)\mathcal{F}(\lambda)\exp(-\alpha(\lambda)z)}{D\_n} \tag{16}$$

Where, np-np0 expresses the excess of electron concentration, Ln the corresponding diffusion length and Dn electron diffusion coefficient. The previous equation is subjected also to

 Fig. 2. Ideal crystal orientation and cross section for the theoretical model of n+pp+ type

concentration of the semiconductor material (Card. H.C, & Yang. E.,1977).

2 0 0 2

depends basically on the interface state density at the grain boundary and the doping

The solution of the three-dimensional diffusion equation provides the excess minority

The steady state continuity equation for the top side of the junction under illumination is

( ) ( )exp( ( ) ) ( ) *n n n n p p*

Where, pn-pn0 , Lp and Dp stand for the excess minority carrier density in the front layer, the minority carrier diffusion length and the diffusion coefficient respectively. The material absorption coefficient α(λ) is given by Runyan (Runyan. W. R, (1976)) and the light generation rate F (number of photons of wavelength λ inserting the front side per unit area

 F(λ)=N(0,λ)(1-R(λ)) (15) With N(0,λ) representing the number of photons of wavelength λ incident on the surface per unit area and unit time (depth x=0) and R(λ) the reflection coefficient of light at the front side. This coefficient is calculated, for an antireflective coating of single layer (TiO2) with optimal thickness 77 nm, (Heavens. O. S, 1991). There is a metal coverage coefficient of 13.1%, corresponding to the front metal grid and cell series resistance (Rs) of about 1.7 Ω. The boundary conditions which accompany Eq. 14 when the solar cell is short circuited involve the front surface recombination velocity SF and the grain boundary recombination

The diffusion equation for the base region is expressed by a similar form like in the front layer:

( ) ( )exp( ( ) ) ( ) *p p*

Where, np-np0 expresses the excess of electron concentration, Ln the corresponding diffusion length and Dn electron diffusion coefficient. The previous equation is subjected also to

*n n*

*L D*

*n n F z*

 

(16)

 

0 2

*p p*

*n n*

*p p <sup>L</sup> <sup>D</sup>* 

*p p F z*

 

(14)

 

epitaxial solar cell (with columnar grains).

expressed by the following relation (Sze. S. M, 1981):

and unit time) is given by the following relation

<sup>2</sup> <sup>0</sup>

velocity in the front region Spg.

carrier density.

specific boundary conditions when the device is operated under short circuit, concerning the grain boundary recombination velocity in the active layer Sng and the effective back surface recombination velocity Seff at the low / high junction. The simplified relation gives the expression for effective electron recombination velocity Seff, as a function of the material's doping concentration of the active layer and the substrate (ΝΑ, ΝΑ+), assumed constant all over of these regions' bulk (Eq.7). Moreover the grain boundary recombination velocity in the front and the active layer is considered the same and symbolized as Sgb.

The solution of the continuity equations (14) and (16) is obtained in analytical form using the Green's function method. This procedure is briefly described in (kotsovos. K & Perraki. V; 2005). The analytical expression of the front layer photocurrent density Jp is derived, by differentiating the hole density distribution in the junction edge region z=d1-wn presented in the form of infinite series (Halder. N.C, & Williams. T. R., 1983):

$$\begin{aligned} \mathcal{J}\_p(\mathbf{x}, \mathbf{y}, \mathcal{X}) &= 4q\alpha F \times \\ \sum\_{m,n}^{\infty} \frac{L\_{peff} M\_x^2 N\_y^2 \sin(mX\_{\mathcal{S}}) \sin(nY\_{\mathcal{S}})}{mn(\alpha^2 L\_{peff}^2 - 1)} \cos(m\mathbf{x}) \cos(n\mathbf{y}) \end{aligned}$$

$$\times \frac{N\_p + aL\_{\rm{pref}} - \exp(-a(d\_1 - w\_n)) \{N\_p \cosh(\frac{d\_1 - w\_n}{L\_{\rm{pref}}}) + \sinh(\frac{d\_1 - w\_n}{L\_{\rm{pref}}})\}}{N\_p \sinh(\frac{d\_1 - w\_n}{L\_{\rm{pref}}}) + \cosh(\frac{d\_1 - w\_n}{L\_{\rm{pref}}})} - aL\_{\rm{pref}} \exp(-a(d\_1 - w\_n)) \{ (17) \}$$

where the variables *x* and *y* represent arbitrary points inside the grain and *Mx, Ny, Lpeff, Np* are expressed by proper equations as functions of Spg ,Dp, Xg, Yg, Lp, and SF.

In a similar way the analytical expression of the base region photocurrent density Jn is given, in the form of infinite series, by differentiating the electron density distribution in the junction edge region *z=d2 –wp* by the relation

$$\begin{split} \mathcal{J}\_{n} &= 4\eta\alpha \mathcal{F} e^{-\alpha(d\_{1}+w\_{\mathcal{V}})} \times \\ &\sum\_{k,l}^{\infty} \frac{L\_{n\text{eff}} K\_{x}^{2} L\_{y}^{2} \sin(kX\_{\mathcal{g}}) \sin(lY\_{\mathcal{g}})}{k!(\alpha^{2} L\_{n\text{eff}}^{2} - 1)} \cos(kx) \cos(ly) \\ &\times [\alpha L\_{n\text{eff}} - \frac{N\_{n} \{\cosh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}}) - e^{-\alpha(d\_{2}-w\_{\mathcal{V}})} \} + \sinh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}})] + \alpha L\_{n\text{eff}} e^{-\alpha(d\_{2}-w\_{\mathcal{V}})} \\ &\times \frac{N\_{n} \{\cosh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}}) + \cosh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}})}{N\_{n\text{eff}} \{\cosh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}}) + \cosh(\frac{d\_{2}-w\_{\mathcal{V}}}{L\_{n\text{eff}}})}] \end{split} \tag{18}$$

Where *Kx, Ly, Lneff, Nn* are expressed as functions of S*eff*, S*ng* ,D*n*, X*g*, Y*g*, L*<sup>n</sup>*. The photogenerated current in the Space Charge Region (equal to the number of photons absorbed), is derived by the 1D model (Sze. S. M, 1981):

$$J\_{SCR} = qFe^{-\alpha(d\_1 - w\_n)} \{ 1 - e^{-\alpha(w\_n + w\_p)} \} \tag{19}$$

Epitaxial Silicon Solar Cells 43

and doping concentration ND), and substrate (thickness d3, diffusion length Ln+ and doping

The experimental values of epilayer properties (thickness d2, base doping concentration NA, diffusion length Ln) and the best results of measured photocurrent density Jsc, open circuit

The one dimensional model was utilized to perform simulations that indicate the dependency of cell's photovoltaic properties on recombination velocity and doping level, for the cells (B2, from the bottom of the ingot) as well as for cells (T2, from the top of the ingot). Optimal photocurrent density and efficiency are calculated as a function of epilayer thickness for two different values of recombination velocity, and two different values of

Figure 3 shows that the photocurrent density is little influenced (Hoeymissen,J. V; et al 2008) in cases of low recombination velocity (102 cm/sec). On the contrary photocurrent density is heavily affected by the epilayer thickness in case of high recombination velocity (106 cm/sec) and a value ~30 mA /cm2 is achieved for epilayer thickness values much higher than 65 μm. The evaluation of these results shows that the epilayer thickness of 50 μm represents a second best value, in case of low recombination velocity. The gain, for thicker epilayers than this, is minor with an increment in Jsc of approximately ~ 0.05 mA /cm2,

The plots of the efficiency with respect to epilayer thickness for two different values of

It is observed that the efficiency of the studied cells, calculated for recombination velocity values of 100 cm/sec saturates (η~13.8%) for epilayer thickness values higher than ~65μm where the gain is minimal. However for recombination velocity values of 2.5x106 cm/sec the efficiency is lower enough for thin epilayers and saturates for thickness values higher than 85μm. Higher efficiencies are referred to cells with small grains, in comparison to those of large grains, because of the presence of fewer recombination centres. Annotating these results it is found that when the epilayer thickness of these cells decreases to values ≤ 50 μm the maximum theoretical efficiency decreases by a percentage of 0.03 % to 0.07 % for Seff =100 cm/ sec. It is particularly recommended that a second best value of epilayer thickness equals to 50

μm, given that the gain for higher epilayer thickness values is of minor importance.

voltage Voc and efficiency η for the cells under investigation are shown in table 4.

Cell d2 (μm) NA(cm-3) Ln (μm) Jph(mA/cm2 ) Voc (V) η (%) B2 64 1.5x1016 64 25.05 542 9.3 T2 64 1.5x1016 71 26.17 558 10.12

Cell d1 (μm) Lp(μm) ND (cm-3) d3(μm) Ln+ (μm) NA+(cm-3) B2 0.4 1 1.5x1020 300 13 2.9x1019 T2 0.4 1 1.5x1020 300 18 1.9 x1019

concentration NA+), assigned to the model parameters are shown in Table 3.

Table 3. Experimental values of emitter and substrate characteristics.

Table 4. Experimental values of epilayer properties.

**5.1.1 Influence of recombination velocity** 

when the epilayer thickness increases by steps of 5 μm.

recombination velocity are illustrated in figure 4.

**5.1 One dimensional model** 

doping concentration.

The total photocurrent is given from the sum of all current densities in each region considering as it has been early referred (Dugas. J.& Qualid. J, 1985) that the substrate contribution is negligible:

$$I\_{sc} = I\_p + I\_n + I\_{SCR} \tag{20}$$

A similar analysis might also carried out, for the determination of the dark saturation current (*J0*) by solving the continuity equations, for both regions, (Halder. N. C, & Williams. T. R., 1983). The derived expression of *J0* is then used for the calculation of open circuit voltage from Eq 13.

#### **4. Optimization**

A computer program has been developed according to the mathematical analysis which implements the 1D model previously described (3.1) for the optimization of cells parameters. The values of ref1ection coefficient R(λ) which depends on the wavelength λ and is related to the anti reflecting coating, as well as the photon flux Ν (λ) defined by a discretized AM1.5 solar spectrum, are inserted in the program via the modelling procedure. The grid structure of the cell covering about 13.1% of the front surface and the Back Surface Field are inserted in a similar way. Material properties are considered as previously described, however the required data must be inserted by the user manually e.g., data concerning front layer and substrate (thickness, doping concentration), concentration of the front layer ND, front surface recombination velocity SF and effective recombination velocity Seff, e.t.c. This data is then used as the starting point for the optimisation process. The program calculates the external quantum efficiency of the studied cells in a wavelength range from 0.4μm to 1.1μm, under 1000 W/m2 illumination (AM1.5 spectrum). The optimisation is carried out by introducing the lower and upper bounds of the epilayer thickness which are 40 and 100 μm respectively (Perraki. V & Giannakopoulos. A.; 2005). The simulation is then performed in batch mode with respect to the input data, controlling the input and output of the simulator at the same time.

After completion of this operation, results are interpreted and assessed by the output interface. The simulated short circuit current density is initially evaluated through numerical integration for the corresponding spectrum, while efficiency of the cells is investigated in the next step.

A 3D model is applied (3.2) to the same type of cells in order to optimize their epitaxial layer thickness, taking into account the structure parameters. The program computes the external quantum efficiency of the studied cells. It also provides, through numerical integration, results for the optimum photocurrent density and efficiency for various values of grain size and grain boundary recombination velocity.

A comparison between the 3D simulated and experimental results of photocurrent, and efficiency under AM1.5 irradiance is performed, as well as between the quantum efficiency curves calculated through 3D model and the corresponding 1D results of the studied cells.

#### **5. Influence of structure parameters on cell's properties**

The simulations for n+pp+ type epitaxial silicon solar cells, have been performed under AM 1.5 spectral conditions. The experimental values, of emitter (thickness d1, diffusion length LP

The total photocurrent is given from the sum of all current densities in each region considering as it has been early referred (Dugas. J.& Qualid. J, 1985) that the substrate

A similar analysis might also carried out, for the determination of the dark saturation current (*J0*) by solving the continuity equations, for both regions, (Halder. N. C, & Williams. T. R., 1983). The derived expression of *J0* is then used for the calculation of open circuit

A computer program has been developed according to the mathematical analysis which implements the 1D model previously described (3.1) for the optimization of cells parameters. The values of ref1ection coefficient R(λ) which depends on the wavelength λ and is related to the anti reflecting coating, as well as the photon flux Ν (λ) defined by a discretized AM1.5 solar spectrum, are inserted in the program via the modelling procedure. The grid structure of the cell covering about 13.1% of the front surface and the Back Surface Field are inserted in a similar way. Material properties are considered as previously described, however the required data must be inserted by the user manually e.g., data concerning front layer and substrate (thickness, doping concentration), concentration of the front layer ND, front surface recombination velocity SF and effective recombination velocity Seff, e.t.c. This data is then used as the starting point for the optimisation process. The program calculates the external quantum efficiency of the studied cells in a wavelength range from 0.4μm to 1.1μm, under 1000 W/m2 illumination (AM1.5 spectrum). The optimisation is carried out by introducing the lower and upper bounds of the epilayer thickness which are 40 and 100 μm respectively (Perraki. V & Giannakopoulos. A.; 2005). The simulation is then performed in batch mode with respect to the input data, controlling

After completion of this operation, results are interpreted and assessed by the output interface. The simulated short circuit current density is initially evaluated through numerical integration for the corresponding spectrum, while efficiency of the cells is

A 3D model is applied (3.2) to the same type of cells in order to optimize their epitaxial layer thickness, taking into account the structure parameters. The program computes the external quantum efficiency of the studied cells. It also provides, through numerical integration, results for the optimum photocurrent density and efficiency for various values of grain size

A comparison between the 3D simulated and experimental results of photocurrent, and efficiency under AM1.5 irradiance is performed, as well as between the quantum efficiency curves calculated through 3D model and the corresponding 1D results of the studied cells.

The simulations for n+pp+ type epitaxial silicon solar cells, have been performed under AM 1.5 spectral conditions. The experimental values, of emitter (thickness d1, diffusion length LP

the input and output of the simulator at the same time.

and grain boundary recombination velocity.

**5. Influence of structure parameters on cell's properties** 

investigated in the next step.

*sc <sup>p</sup> n SCR J JJJ* (20)

contribution is negligible:

voltage from Eq 13.

**4. Optimization** 

and doping concentration ND), and substrate (thickness d3, diffusion length Ln+ and doping concentration NA+), assigned to the model parameters are shown in Table 3. 


Table 3. Experimental values of emitter and substrate characteristics.

The experimental values of epilayer properties (thickness d2, base doping concentration NA, diffusion length Ln) and the best results of measured photocurrent density Jsc, open circuit voltage Voc and efficiency η for the cells under investigation are shown in table 4.


Table 4. Experimental values of epilayer properties.

#### **5.1 One dimensional model**

The one dimensional model was utilized to perform simulations that indicate the dependency of cell's photovoltaic properties on recombination velocity and doping level, for the cells (B2, from the bottom of the ingot) as well as for cells (T2, from the top of the ingot). Optimal photocurrent density and efficiency are calculated as a function of epilayer thickness for two different values of recombination velocity, and two different values of doping concentration.

#### **5.1.1 Influence of recombination velocity**

Figure 3 shows that the photocurrent density is little influenced (Hoeymissen,J. V; et al 2008) in cases of low recombination velocity (102 cm/sec). On the contrary photocurrent density is heavily affected by the epilayer thickness in case of high recombination velocity (106 cm/sec) and a value ~30 mA /cm2 is achieved for epilayer thickness values much higher than 65 μm. The evaluation of these results shows that the epilayer thickness of 50 μm represents a second best value, in case of low recombination velocity. The gain, for thicker epilayers than this, is minor with an increment in Jsc of approximately ~ 0.05 mA /cm2, when the epilayer thickness increases by steps of 5 μm.

The plots of the efficiency with respect to epilayer thickness for two different values of recombination velocity are illustrated in figure 4.

It is observed that the efficiency of the studied cells, calculated for recombination velocity values of 100 cm/sec saturates (η~13.8%) for epilayer thickness values higher than ~65μm where the gain is minimal. However for recombination velocity values of 2.5x106 cm/sec the efficiency is lower enough for thin epilayers and saturates for thickness values higher than 85μm. Higher efficiencies are referred to cells with small grains, in comparison to those of large grains, because of the presence of fewer recombination centres. Annotating these results it is found that when the epilayer thickness of these cells decreases to values ≤ 50 μm the maximum theoretical efficiency decreases by a percentage of 0.03 % to 0.07 % for Seff =100 cm/ sec. It is particularly recommended that a second best value of epilayer thickness equals to 50 μm, given that the gain for higher epilayer thickness values is of minor importance.

Epitaxial Silicon Solar Cells 45

B2,10^15 B2,10^17

T2,10^15 T2,10^17

29

40

little is gained when the epitaxial layer becomes thicker.

11,7

doping concentrations of 1015 cm-3, and 1017 cm-3.

40

50

60

Epilayer thickness d2(μm)

Fig. 6. Variation of the cell's efficiency as a function of epilayer thickness d2 calculated for

70

80

90

B2,10^15 B2,10^17 T2,10^15 T2,10^17

100

12,2 12,7

13,2 13,7

η %(%)

14,2 14,7

15,2

50

60

Fig. 5. Variation of the short circuit current density Jsc of the cells, as a function of base thickness d2 calculated for doping concentration values of 1015cm-3, and 1017 cm-3.

70

Epilayer thickness d2 (μm)

30.47 mA /cm2, which are higher than experimental values. According to the calculated results when the epilayer thickness of B2 cells decreases to values ≤50 μm, photocurrent density decreases for the different values of doping concentrations by approximately 0.05- 0.08 mA/cm2. It can be considered again that 50 μm, represent a second best value, since

Simulated data of cell efficiency, η, present a rise of its maximum value, as shown in figure 6, which is well above from maximum values experimentally obtained, and a shift of the optimum epilayer thickness to lower values. Higher efficiency has been calculated for cells with doping concentration of 1017 cm-3 compared to the one calculated for cells with doping

80

90

100

29,5

Jsc(mA/cm2)

30

30,5

Fig. 3. Variation of short circuit current density, Jsc, of the studied cells (B2 with small grains, T2 with large grains) versus epilayer thickness d2, calculated for Seff=100 cm/sec and 2.5x106 cm/sec.

Fig. 4. Efficiency graph versus base thickness d2 of the cells under investigation, calculated for Seff =100 cm/ sec and 2.5x10^6 cm/sec.

#### **5.1.2 Influence of doping concentration**

The same model was used to perform simulations indicating the relation between photovoltaic properties and doping concentration. When doping concentration increased from 1015 to 1017 cm-3 simulated data of the short circuit current density, Jsc, showed a small decrease, due to Auger recombination and minority charge carriers' mobility.

Figure 5, illustrates the variation of Jsc with respect to epilayer thickness for two different values of doping. Maximum photocurrent densities are delivered from cells with epilayer thickness equal to 65 and 70 μm (B2 and T2 cells respectively). They vary between 29.6 and

B2,100 T2,100 B2,2.5\*10^6 T2,2.5\*10^6

11,5

12

12,5

η(%)

for Seff =100 cm/ sec and 2.5x10^6 cm/sec.

**5.1.2 Influence of doping concentration** 

13 13,5

14

Jsc(mA/cm2

cm/sec.

)

40

50

60

70

Epilayer thickness d2 (μm)

40 50 60 70 80 90 100 Epilayer thickness d2 (μm)

Fig. 4. Efficiency graph versus base thickness d2 of the cells under investigation, calculated

The same model was used to perform simulations indicating the relation between photovoltaic properties and doping concentration. When doping concentration increased from 1015 to 1017 cm-3 simulated data of the short circuit current density, Jsc, showed a small

Figure 5, illustrates the variation of Jsc with respect to epilayer thickness for two different values of doping. Maximum photocurrent densities are delivered from cells with epilayer thickness equal to 65 and 70 μm (B2 and T2 cells respectively). They vary between 29.6 and

decrease, due to Auger recombination and minority charge carriers' mobility.

Fig. 3. Variation of short circuit current density, Jsc, of the studied cells (B2 with small grains, T2 with large grains) versus epilayer thickness d2, calculated for Seff=100 cm/sec and 2.5x106

80

B2,100 B2,2.5x10^6 T2,100 T2,2.5x10^6

90

100

Fig. 5. Variation of the short circuit current density Jsc of the cells, as a function of base thickness d2 calculated for doping concentration values of 1015cm-3, and 1017 cm-3.

30.47 mA /cm2, which are higher than experimental values. According to the calculated results when the epilayer thickness of B2 cells decreases to values ≤50 μm, photocurrent density decreases for the different values of doping concentrations by approximately 0.05- 0.08 mA/cm2. It can be considered again that 50 μm, represent a second best value, since little is gained when the epitaxial layer becomes thicker.

Simulated data of cell efficiency, η, present a rise of its maximum value, as shown in figure 6, which is well above from maximum values experimentally obtained, and a shift of the optimum epilayer thickness to lower values. Higher efficiency has been calculated for cells with doping concentration of 1017 cm-3 compared to the one calculated for cells with doping

Fig. 6. Variation of the cell's efficiency as a function of epilayer thickness d2 calculated for doping concentrations of 1015 cm-3, and 1017 cm-3.

Epitaxial Silicon Solar Cells 47

A 3D model was utilized to perform simulations that show the influence of grain boundary recombination velocity Sgb and grain size on cell's properties. The calculated results indicate the influence of grain boundary recombination velocity on the photocurrent and on the efficiency for various values of grain size for the cells B2 (from the bottom of the ingot) as well as for the cells T2 (from the top of the ingot). The plots are obtained for values of epilayer thickness maximizing the photocurrent which are not necessarily equal to the experimental. These optimal values of epilayer thickness used in the graph vary and depend

The graph of optimal photocurrent as a function of recombination velocity shows, figure 8, that it is seriously affected by recombinations in the grain boundaries of small grains, given that a significant amount of the photogenerated carriers recombine in the grain boundaries

10^2 10^3 10^4 10^5 10^6

grain 10μm grain100μm grain500μm

Sgb (cm/sec)

Fig. 8. Optimal short circuit current dependence on grain boundary recombination velocity

It is shown that the photocurrent density falls rapidly for grains with size 10 μm and high values of grain boundary recombination velocities. However, the effect of grain boundary

Figure 9 demonstrates the efficiency of the cells B2 in relation with the grain boundary recombination velocity for different grain sizes, which is calculated for optimal base thickness. It can be pointed that for small grain size, the efficiency is largely affected by grain boundary recombination, with a rapid decrease for recombination velocities greater

For larger grain sizes (500 μm), there is not so strong decrease with the recombination velocity, while insignificant decrease is observed in the efficiency for values lower than 103

The graphs of optimal photocurrent as a function of grain boundary recombination velocity (figure 10) show that it is less affected from recombination in the grain boundaries for large

grain sizes (cells T2), compared to cells with small grain sizes, (cells B2 in figure 8).

recombination velocity is not so important for larger grain sizes (100 and 500 μm).

when grain's size is lower or comparable to the base diffusion length.

**5.2 Three dimensional model** 

Sgb of the cell B2, with grain size as parameter.

Jsc (mA/cm2

than 103 cm/sec.

cm/sec.

)

on grain size and Sgb

of 1015 cm-3. It is noticed that solar cell efficiency is insignificantly influenced by epilayer thickness variations. It is pointed that if the epilayer thickness of the small grain cell is reduced to values ≤50 μm, the efficiency decrease is less than 0.03%. Similarly a decrease in epilayer thickness, of T2 cells, to 50 μm results in a decrease of their maximum efficiency by 0.04 %.

The optimized cell parameters Jsc and η for an optimum value of doping concentration show that even they are higher compared to the experimental ones, (Perraki. V.; 2010) they do not present significant differences for the two different types of cells. This is due to the fact that cell parameters introduced to the model were not very different and diffusion length values were high in all cases. It must be noted however that the optimum values of photocurrent density, efficiency and epilayer thickness calculated by this model are different than the ones corresponding to maximum Jph and η and equal the values of saturation. When the epilayer thickness increases beyond the optimum value in steps of 5 μm, Jsc and η increase by a rate lower than 0.05mA/cm2 and 0.05% respectively. Taking all these into account, we can consider that the optimum value of efficiency is obtained for epilayer thickness values equal to or lower than 50 μm, which is much lower than base thickness and base diffusion length values of any solar cell.

The comparison between the experimental and the optimized quantum efficiency plots of B2 and T2 cells, (calculated by the 1D model) is presented in figure 7. The chosen model parameters, as shown in tables 3 and 4, provide a good fit to the measured QE data for wavelength values above 0.8 μm, whereas optimized curves indicate higher response for the lower part of the spectrum. The response of the experimental devices related to the contribution of the n+ heavily doped front region (for low wavelengths of the solar radiation) is significantly lower than that of the simulated results, due to the non passivated surface.

Moreover, the spectral response of B2 is significantly higher compared to the one of T2 cell near the blue part of the solar spectrum, although cell T2 has higher experimental values of Jsc, Voc, and η. This may be explained by differences of the reflection coefficient between experimental and simulated devices and /or by the presence of fewer recombination centers in smaller inter-grain surfaces.

Fig. 7. Optimized external quantum efficiency for cells B2, and T2, evaluated for experimental values included in tables 3 and 4, and comparison with the experimental ones.

of 1015 cm-3. It is noticed that solar cell efficiency is insignificantly influenced by epilayer thickness variations. It is pointed that if the epilayer thickness of the small grain cell is reduced to values ≤50 μm, the efficiency decrease is less than 0.03%. Similarly a decrease in epilayer thickness, of T2 cells, to 50 μm results in a decrease of their maximum efficiency by

The optimized cell parameters Jsc and η for an optimum value of doping concentration show that even they are higher compared to the experimental ones, (Perraki. V.; 2010) they do not present significant differences for the two different types of cells. This is due to the fact that cell parameters introduced to the model were not very different and diffusion length values were high in all cases. It must be noted however that the optimum values of photocurrent density, efficiency and epilayer thickness calculated by this model are different than the ones corresponding to maximum Jph and η and equal the values of saturation. When the epilayer thickness increases beyond the optimum value in steps of 5 μm, Jsc and η increase by a rate lower than 0.05mA/cm2 and 0.05% respectively. Taking all these into account, we can consider that the optimum value of efficiency is obtained for epilayer thickness values equal to or lower than 50 μm, which is much lower than base thickness and base diffusion

The comparison between the experimental and the optimized quantum efficiency plots of B2 and T2 cells, (calculated by the 1D model) is presented in figure 7. The chosen model parameters, as shown in tables 3 and 4, provide a good fit to the measured QE data for wavelength values above 0.8 μm, whereas optimized curves indicate higher response for the lower part of the spectrum. The response of the experimental devices related to the contribution of the n+ heavily doped front region (for low wavelengths of the solar radiation) is significantly lower than that of the simulated results, due to the non passivated

Moreover, the spectral response of B2 is significantly higher compared to the one of T2 cell near the blue part of the solar spectrum, although cell T2 has higher experimental values of Jsc, Voc, and η. This may be explained by differences of the reflection coefficient between experimental and simulated devices and /or by the presence of fewer recombination centers

> 0,4 0,56 0,72 0,88 1,04 Wavelenght λ(μm)

experimental values included in tables 3 and 4, and comparison with the experimental ones.

Fig. 7. Optimized external quantum efficiency for cells B2, and T2, evaluated for

B2opt T2opt B2exp T2exp

0.04 %.

surface.

length values of any solar cell.

in smaller inter-grain surfaces.

0

20

40

QE(%)

60

80

100

#### **5.2 Three dimensional model**

A 3D model was utilized to perform simulations that show the influence of grain boundary recombination velocity Sgb and grain size on cell's properties. The calculated results indicate the influence of grain boundary recombination velocity on the photocurrent and on the efficiency for various values of grain size for the cells B2 (from the bottom of the ingot) as well as for the cells T2 (from the top of the ingot). The plots are obtained for values of epilayer thickness maximizing the photocurrent which are not necessarily equal to the experimental. These optimal values of epilayer thickness used in the graph vary and depend on grain size and Sgb

The graph of optimal photocurrent as a function of recombination velocity shows, figure 8, that it is seriously affected by recombinations in the grain boundaries of small grains, given that a significant amount of the photogenerated carriers recombine in the grain boundaries when grain's size is lower or comparable to the base diffusion length.

Fig. 8. Optimal short circuit current dependence on grain boundary recombination velocity Sgb of the cell B2, with grain size as parameter.

It is shown that the photocurrent density falls rapidly for grains with size 10 μm and high values of grain boundary recombination velocities. However, the effect of grain boundary recombination velocity is not so important for larger grain sizes (100 and 500 μm).

Figure 9 demonstrates the efficiency of the cells B2 in relation with the grain boundary recombination velocity for different grain sizes, which is calculated for optimal base thickness. It can be pointed that for small grain size, the efficiency is largely affected by grain boundary recombination, with a rapid decrease for recombination velocities greater than 103 cm/sec.

For larger grain sizes (500 μm), there is not so strong decrease with the recombination velocity, while insignificant decrease is observed in the efficiency for values lower than 103 cm/sec.

The graphs of optimal photocurrent as a function of grain boundary recombination velocity (figure 10) show that it is less affected from recombination in the grain boundaries for large grain sizes (cells T2), compared to cells with small grain sizes, (cells B2 in figure 8).

Epitaxial Silicon Solar Cells 49

10^2 10^3 10^4 10^5

grain5000μm grain 10000μm

Sgb (cm/sec)

Fig. 11. Variation of the efficiency η as a function of grain boundary recombination velocity

(a) (b) Fig. 12. Optimized external quantum efficiency and comparison with 3D model, for the cells

Figure 11 illustrates the efficiency of the cells T2 as a function of grain boundary recombination velocity for different grain sizes, which is calculated for optimal base thickness. It can be observed that for large grain size, (5000 μm) the efficiency is less affected for grain boundary recombination for Sgb values higher than 103 cm/sec, compared to the case of small grain size, Fig. 9. A smoother decrease is observed in case of cells with even

B2 (a) and T2 (b), evaluated for experimental values included in tables 3 and 4.

Sgb, calculated for optimal base thickness and variable grain sizes (cell T2).

12.200

12.250

12.300

Efficiency

η(%)

12.350

12.400

12.450

Fig. 9. Variation of efficiency η of the cell B2, as a function of grain boundary recombination velocity Sgb, calculated for optimal base thickness and variable grain sizes.

Therefore, for grains with size 5000 μm, and high values of grain boundary recombination velocities the photocurrent does not fall rapidly. It is evident that, for cells with even larger grain sizes (10000 μm) the influence of grain boundary recombination velocity is even more insignificant.

Fig. 10. Optimal short circuit current dependence on grain boundary recombination velocity Sgb of the cell T2, with grain size as parameter.

48 Solar Cells – Silicon Wafer-Based Technologies

10^2 10^3 10^4 10^5 10^6

grain 10μm grain100μm grain500μm

Sgb (cm/sec)

Fig. 9. Variation of efficiency η of the cell B2, as a function of grain boundary recombination

Therefore, for grains with size 5000 μm, and high values of grain boundary recombination velocities the photocurrent does not fall rapidly. It is evident that, for cells with even larger grain sizes (10000 μm) the influence of grain boundary recombination velocity is even more

10^2 10^3 10^4 10^5

grain5000μm grain10000μm

Sgb (cm/sec)

Fig. 10. Optimal short circuit current dependence on grain boundary recombination velocity

velocity Sgb, calculated for optimal base thickness and variable grain sizes.

4

25,8 25,85 25,9 25,95 26 26,05 26,1 26,15 26,2 26,25 26,3

Sgb of the cell T2, with grain size as parameter.

Jsc (mA/cm2

)

2.004

4.004

6.004

Efficiency

insignificant.

η(%)

8.004

10.004

12.004

14.004

Fig. 11. Variation of the efficiency η as a function of grain boundary recombination velocity Sgb, calculated for optimal base thickness and variable grain sizes (cell T2).

Fig. 12. Optimized external quantum efficiency and comparison with 3D model, for the cells B2 (a) and T2 (b), evaluated for experimental values included in tables 3 and 4.

Figure 11 illustrates the efficiency of the cells T2 as a function of grain boundary recombination velocity for different grain sizes, which is calculated for optimal base thickness. It can be observed that for large grain size, (5000 μm) the efficiency is less affected for grain boundary recombination for Sgb values higher than 103 cm/sec, compared to the case of small grain size, Fig. 9. A smoother decrease is observed in case of cells with even

Epitaxial Silicon Solar Cells 51

Duerinckh. F; Nieuwenhuysen. K.V; Kim. H; Kuzma-Filipek. I; Dekkers. H; Beaucarne. G;

Industrial Screen-printing Processes" *Progress in Photovoltaics* 2005,pp673 Dugas.J, and Qualid. J, (1985), "3d modelling of grain size and doping concentration influence on polycrystalline silicon solar cells", *6th ECPVSEC*, (1985) p. 79. Godlewski. M; Baraona.C.R and Brandhorst.H.W 1973, *Proc 10th IEEE PV Specialist Conf.*

Goetzberger.A, Knobloch. J, Voss. B; *Crystalline Silicon Solar Cells*, John willey & Sons 1998. Halder. N.C, and Williams. T. R., (1983);"Grain Boundary Effects in Polycrystalline Silicon

Hoeymissen. J.Van; Kuzma-Filipek. I; Nieuwenhuysen. K. Van; Duerinckh. F; Beaucarne. G;

Hovel. H. J. (1975) Solar cells *Semiconductors and Semimetals* vol. II (New York: Academic

Luque. A, Hegeduw. S.,(ed) "*Handbook photovoltaic Science and Engineering* '' Wiley, 2003. Mason. N; Schultz. O; Russel. R; Glunz. S.W; Warta. W; (2006) "20.1% Efficient Large

Kotsovos. K and Perraki.V; (2005) "Structure optimisation according to a 3D model applied

Nieuwenhuysen. K. Van; Duerinckh. F; Kuzma. I; Gestel. D.V; Beaucarne. G; Poortmans. J;

Overstraeten. R.J.V, Mertens. R, (1986), *Physics Technology and Use of Photovoltaics*, Adam

Perraki. V and Giannakopoulos.A; (2005); Numerical simulation and optimization of epitaxial solar cells; *Proceedings 20th EPVSEC* Barcelona 2005, pp1279. Perraki.V; (2010) "Modeling of recombination velocity and doping influence in epitaxial silicon solar cells" *Solar Energy Materials & Solar Cells 94* (2010) 1597-1603. Peter.K; Kopecer.R; Fath. P; Bucher. E; Zahedi. C; *Sol. Energy Mat. Sol. Cells* 74 (2002) pp 219. Peter. K; R.Kopecek. R; Soiland. A; Enebakk. E; (2008) ″Future potential for SOG-Si Feedstock from the metallurgical process route″ *Proc.23rd EUPVSEC* (2008) pp 947 Photovoltaic Technology Platform; (2007) "A Strategic Research Agenda for PV Energy

J. Poortmans. J; (2008) " Tnin-film epitaxial solar cells on low cost Si substrates: closing the efficiency gap with bulk Si cells using advanced photonic structures and

on epitaxial silicon solar cells :A comparative study*" Solar Energy Materials and Solar* 

Area Cell on 140 micron thin silicon wafer", *Proc. 21st EUPVSEC*, Dresden 2006, pp

(2006) " Progress in epitaxial deposition on low-cost substrates for thin- film crystalline silicon solar cells at IMEC" *Journal of Crystal Growth* (2006) pp 438.. Nieuwenhuysen. K.Van; Duerinckx. K; Kuzma. F; Payo. I; Beaucarne. M.R; Poortmans. G;

(2008); Epitaxially grown emitters for thin film crystalline silicon solar cells *Thin* 

Heavens. O. S, (1991); *The Optical Properties of Thin solid Films*, Dover, 1991.

Kotsovos. K; 1996, *Final year student Thesis*, University of Patras,Greece,1996

emitters", *Proceedings 23rd EUPVSEC* 2008 pp 2037.

(1973) P.40

Solar Cells", *Solar Cells* 8 (1983) 201.

*Cells* 89 (2005) 113-127.

*Solid Film*, 517, (2008) pp 383-384.

Technology"; *European Communities,* 2007 Price J.B., *Semiconductor Silicon*, Princeton, NJ, 1983, p. 339

Runyan. W. R, (1976) *Southeastern Methodist University Report* 83 -13 (1976).

Hilger Ltd 1986.

521

and Poortmans. J; (2005) "Large –area Epitaxial Silicon Solar Cells Based on

larger grain sizes (10000 μm). It is obvious that solar cell efficiency saturates if Sgb is lower than 103 cm/sec and the gain is minimal for smaller values of grain boundary recombination velocity. In this case, efficiency is limited from bulk recombination, which is directly related to the base effective diffusion length Ln. However when grain boundary recombination velocity is reduced, the optimal layer thickness increases, until it reaches a value close to the device diffusion length Ln .This parameter seems to affect the value of optimal epilayer thickness. For higher Sgb values the maximum efficiency shifts to thickness values lower than the base diffusion length. However, for very elevated values of grain boundary recombination velocities and small grain size, the optimal thickness saturates to a value, which is the same for cells with thin or thick epilayer. The plots of Lneff and optimal epilayer thickness as a function of Sgb, show similar dependence on Sgb and grain size, with almost equal values (Kotsovos. K & Perraki.V, 2005).

The optimized 1D external quantum efficiency and the 3D graphs are demonstrated for the cells B2 and T2 in figure 12a and b respectively (kotsovos. K, 1996). Since the influence of grain boundaries has not been taken into account in the 1D model it has shown superior response compared to the 3D equivalent for wavelength values higher than 0.6 μm (cell T2). Lower values of spectral response are observed in case of large grains (cell T2) and λ> 0.6 μm, possible due to the presence of more recombination centers in larger intergrain surfaces. However, very good accordance is observed between 1D and 3D plots for cells B2.

#### **6. Conclusions**

The optimal photocurrent and conversion efficiency for epitaxial solar cells are influenced by the recombination velocity. The best values of epilayer thickness and the effective base diffusion length are higher for lower values of grain boundary recombination velocities, resulting to higher efficiency values.

The comparison between the simulated 1D and experimental QE curves indicates concurrence for wavelengths greater than 0.8 μm. However, the measured spectral response close to the blue part of the spectrum was considerable lower compared to simulation data. On the other hand the comparison of the simulated 1D and 3D QE curves shows good agreement only for wavelengths lower than 0.6 μm for cells T2 and very good agreement for cells B2.

#### **7. References**

Arora. J, Singh. S, and Mathur. P., (1981), *Solid State Electronics*, 24 (1981), p.739-747.

Blacker. A. W, et al (1989) *Proc. 9th EUPVSEC*, Freiburg, Germany, p.328.

Card. H.C, and Yang. E., (1977), *IEEE Trans. Electron Devices*, 29 (1977) 397.


larger grain sizes (10000 μm). It is obvious that solar cell efficiency saturates if Sgb is lower than 103 cm/sec and the gain is minimal for smaller values of grain boundary recombination velocity. In this case, efficiency is limited from bulk recombination, which is directly related to the base effective diffusion length Ln. However when grain boundary recombination velocity is reduced, the optimal layer thickness increases, until it reaches a value close to the device diffusion length Ln .This parameter seems to affect the value of optimal epilayer thickness. For higher Sgb values the maximum efficiency shifts to thickness values lower than the base diffusion length. However, for very elevated values of grain boundary recombination velocities and small grain size, the optimal thickness saturates to a value, which is the same for cells with thin or thick epilayer. The plots of Lneff and optimal epilayer thickness as a function of Sgb, show similar dependence on Sgb and grain size, with almost

The optimized 1D external quantum efficiency and the 3D graphs are demonstrated for the cells B2 and T2 in figure 12a and b respectively (kotsovos. K, 1996). Since the influence of grain boundaries has not been taken into account in the 1D model it has shown superior response compared to the 3D equivalent for wavelength values higher than 0.6 μm (cell T2). Lower values of spectral response are observed in case of large grains (cell T2) and λ> 0.6 μm, possible due to the presence of more recombination centers in larger intergrain surfaces.

The optimal photocurrent and conversion efficiency for epitaxial solar cells are influenced by the recombination velocity. The best values of epilayer thickness and the effective base diffusion length are higher for lower values of grain boundary recombination velocities,

The comparison between the simulated 1D and experimental QE curves indicates concurrence for wavelengths greater than 0.8 μm. However, the measured spectral response close to the blue part of the spectrum was considerable lower compared to simulation data. On the other hand the comparison of the simulated 1D and 3D QE curves shows good agreement only for wavelengths lower than 0.6 μm for cells T2 and very good agreement for

Arora. J, Singh. S, and Mathur. P., (1981), *Solid State Electronics*, 24 (1981), p.739-747.

Carslaw. H.S; and Jaeger .J.C; 1959; *Conduction Heat in Solids*, 2nd ed, Oxford University

Caymax. M; Perraki. V; Pastol.J. L; Bourée. J.E; Eycmans. M; Mertens. R; Revel. G; Rodot. M;

(1986)"resent results on epitaxial solar cells made from metallurgical grade Si"

Blacker. A. W, et al (1989) *Proc. 9th EUPVSEC*, Freiburg, Germany, p.328. Card. H.C, and Yang. E., (1977), *IEEE Trans. Electron Devices*, 29 (1977) 397.

*Proc.2nd Int.PVSE Conf* (Beijing1986)171.

However, very good accordance is observed between 1D and 3D plots for cells B2.

equal values (Kotsovos. K & Perraki.V, 2005).

**6. Conclusions** 

cells B2.

**7. References** 

resulting to higher efficiency values.

Press, London 1959.


**3** 

**A New Model for Extracting the Physical** 

As worldwide energy demand increases, conventional sources of energy, fossils fuels such as coal, petroleum and natural gas will be exhausted in the near future. Therefore, renewable resources will have to play a significant role in the world's future supply. Solar energy occupies one of the most important places among these various possible alternative energy sources. The direct photovoltaic conversion of sunlight into electricity seems to be extremely promising. Solar cells furnish the most important long-duration power supply for satellites and space vehicles. They have also been successfully employed in terrestrial application. A solar cell (also called photovoltaic cell or photoelectric cell) is a solid state device that converts the energy of sunlight directly into electricity by the photovoltaic effect. Assemblies of cells are used to make solar modules, also known as solar panels. The energy generated from these solar modules, referred to as solar power, is an example of solar energy. photovoltaic system uses various materials and technologies such as crystalline Silicon (c-Si), Cadmium telluride (CdTe), Gallium arsenide (GaAs), chalcopyrite films of Copper-Indium-Selenide (CuInSe2) and Organic materials are attractive because of their light eight, processability, and the ease of designing the materials on the molecular level. Solar cells are usually assessed by measuring the current voltage characteristics of the device under standard condition of illumination and then extracting a set of parameters from the data. The major parameters are usually the diode saturation current, the series resistance, the ideality factor, the photocurrent and the shunt conduction. The extraction and interpretation has a variety of important application. These parameters can, for instance, be used for quality control during production or to provide insights into the operation of the

A solar cell is simply diode of large-area forward bias with a photovoltage. The photovoltage is created from the dissociation of electron-hole pairs created by incident photons within the built-in field of the junction or diode. The operating current of a solar

**1. Introduction** 

devices, thereby leading to improvements in devices.

**2. Equivalent circuit of solar cells** 

cell is given by:

**Parameters from I-V Curves of Organic** 

**and Inorganic Solar Cells** 

N. Nehaoua, Y. Chergui and D. E. Mekki

*Physics Department, LESIMS laboratory,* 

*Badji Mokhtar University* 

*Algeria* 

Sanchez-Friera. P;et al;(2006)"Epitaxial Solar Cells Over Upgraded Metallurgical Silicon Substrates: The Epimetsi Project" *IEEE 4th World Conference on Photovoltaic Energy Conversion*, pp1548-1551.

Sze. S. M; *Physics of Semiconductor Devices*, 2nd Ed, 1981, p 802

Wolf H. F., *Silicon Semiconductor Data*, Pergamon Press, 1976.

## **A New Model for Extracting the Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells**

N. Nehaoua, Y. Chergui and D. E. Mekki *Physics Department, LESIMS laboratory, Badji Mokhtar University Algeria* 

#### **1. Introduction**

52 Solar Cells – Silicon Wafer-Based Technologies

Sanchez-Friera. P;et al;(2006)"Epitaxial Solar Cells Over Upgraded Metallurgical Silicon

*Conversion*, pp1548-1551.

Sze. S. M; *Physics of Semiconductor Devices*, 2nd Ed, 1981, p 802 Wolf H. F., *Silicon Semiconductor Data*, Pergamon Press, 1976.

Substrates: The Epimetsi Project" *IEEE 4th World Conference on Photovoltaic Energy* 

As worldwide energy demand increases, conventional sources of energy, fossils fuels such as coal, petroleum and natural gas will be exhausted in the near future. Therefore, renewable resources will have to play a significant role in the world's future supply. Solar energy occupies one of the most important places among these various possible alternative energy sources. The direct photovoltaic conversion of sunlight into electricity seems to be extremely promising. Solar cells furnish the most important long-duration power supply for satellites and space vehicles. They have also been successfully employed in terrestrial application. A solar cell (also called photovoltaic cell or photoelectric cell) is a solid state device that converts the energy of sunlight directly into electricity by the photovoltaic effect. Assemblies of cells are used to make solar modules, also known as solar panels. The energy generated from these solar modules, referred to as solar power, is an example of solar energy. photovoltaic system uses various materials and technologies such as crystalline Silicon (c-Si), Cadmium telluride (CdTe), Gallium arsenide (GaAs), chalcopyrite films of Copper-Indium-Selenide (CuInSe2) and Organic materials are attractive because of their light eight, processability, and the ease of designing the materials on the molecular level.

Solar cells are usually assessed by measuring the current voltage characteristics of the device under standard condition of illumination and then extracting a set of parameters from the data. The major parameters are usually the diode saturation current, the series resistance, the ideality factor, the photocurrent and the shunt conduction. The extraction and interpretation has a variety of important application. These parameters can, for instance, be used for quality control during production or to provide insights into the operation of the devices, thereby leading to improvements in devices.

#### **2. Equivalent circuit of solar cells**

A solar cell is simply diode of large-area forward bias with a photovoltage. The photovoltage is created from the dissociation of electron-hole pairs created by incident photons within the built-in field of the junction or diode. The operating current of a solar cell is given by:

A New Model for Extracting the

Fig. 2. Solar cell I-V Characteristics.

**4.1 Previous works** 

**4. Solar cell parameters extraction** 

the photocurrent and the shunt conductance.

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 55


An accurate knowledge of solar cell parameters from experimental data is of vital importance for the design of solar cells and for the estimates of their performance. The major parameters are usually the diode saturation current, the series resistance, the ideality factor,

The evaluation of these parameters has been the subject of investigation of several authors. Some of the methods use selected parts of the current-voltage (I-V) characteristic (Charles et al, 1981; 1985) and those that exploit the whole characteristic (Easwarakhanthan et al, 1986; phang et al, 1986). (Santakrus et al, 2009) presents the use of properties of special trans function theory (STFT) for determining the ideality factor of real solar cell. (Priyank et al, 2007) method gives the value of series Rs and shunt resistance Rsh using illuminated I-V characteristics in third and fourth quadrants and the Voc-Isc characteristics of the cell. In the work of (Bashahu et al, 2007), up to 22 methods for the determination of solar cell ideality factor (n), have been presented, most of them use the single I-V data set. (Ortiz-Conde et al,

the fill factor. The fill factor is useful parameters for quality control test.

The fill factor determines the shape of the solar cell I-V characteristics. Its value is higher than 0.7 for good cells. The series and shunt resistance account for a decrease in

> 0 0 *FF I V P sc oc m P P*

(3)

$$\begin{aligned} I &= I\_{ph} - I\_d - I\_p\\ I &= I\_{ph} - I\_s \left[ \exp\left(\frac{\beta}{n} (V + IR\_s) \right) - 1 \right] - \frac{V + IR\_s}{R\_{sh}} \end{aligned} \tag{1}$$

Where, Iph, Is, n, Rs and Gsh (=1/Rsh) being the photocurrent, the diode saturation current, the diode quality factor, the series resistance and the shunt conductance, respectively. Ip is the shunt current and β=q/kT is the usual inverse thermal voltage. The shunt resistance is considered Rsh= (1/Gsh)>>Rs.

The circuit model of solar cell corresponding to equation (1) is presented in figure (1).

Fig. 1. Equivalent circuit model of the illuminated solar cell.

The single diode model considered here is rather simple, efficient and sufficiently accurate for process optimization and system design tasks. The single diode model can also be used to fit solar modules and arrays where the cells are series and/or parallel connected, provided that the cell to cell variations are not important.

#### **3. Solar cell output parameters**

The graph of current as a function of voltage I=f (V) for a solar cell passes through three significant points as illustrated in figure 2 below.


$$FF = \frac{I\_m V\_m}{I\_{scV\_{oc}}} \tag{2}$$

The fill factor determines the shape of the solar cell I-V characteristics. Its value is higher than 0.7 for good cells. The series and shunt resistance account for a decrease in the fill factor. The fill factor is useful parameters for quality control test.


$$\eta = \frac{FF I\_{\text{sc}} V\_{\text{oc}}}{P\_0} = \frac{P\_m}{P\_0} \tag{3}$$

Fig. 2. Solar cell I-V Characteristics.

#### **4. Solar cell parameters extraction**

#### **4.1 Previous works**

54 Solar Cells – Silicon Wafer-Based Technologies

exp 1

The circuit model of solar cell corresponding to equation (1) is presented in figure (1).

*<sup>s</sup> ph s <sup>s</sup>*

*n R*

*V IR I I V IR*

Where, Iph, Is, n, Rs and Gsh (=1/Rsh) being the photocurrent, the diode saturation current, the diode quality factor, the series resistance and the shunt conductance, respectively. Ip is the shunt current and β=q/kT is the usual inverse thermal voltage. The shunt resistance is

The single diode model considered here is rather simple, efficient and sufficiently accurate for process optimization and system design tasks. The single diode model can also be used to fit solar modules and arrays where the cells are series and/or parallel connected,

The graph of current as a function of voltage I=f (V) for a solar cell passes through three



> *oc m m scV I V FF*

*<sup>I</sup>* (2)

depend on its size, and remains fairly constant with changing light intensity.


*sh*

(1)

*ph d p*

*II I I*

Fig. 1. Equivalent circuit model of the illuminated solar cell.

provided that the cell to cell variations are not important.

directly proportional to light intensity and size.

significant points as illustrated in figure 2 below.

**3. Solar cell output parameters** 

considered Rsh= (1/Gsh)>>Rs.

An accurate knowledge of solar cell parameters from experimental data is of vital importance for the design of solar cells and for the estimates of their performance. The major parameters are usually the diode saturation current, the series resistance, the ideality factor, the photocurrent and the shunt conductance.

The evaluation of these parameters has been the subject of investigation of several authors. Some of the methods use selected parts of the current-voltage (I-V) characteristic (Charles et al, 1981; 1985) and those that exploit the whole characteristic (Easwarakhanthan et al, 1986; phang et al, 1986). (Santakrus et al, 2009) presents the use of properties of special trans function theory (STFT) for determining the ideality factor of real solar cell. (Priyank et al, 2007) method gives the value of series Rs and shunt resistance Rsh using illuminated I-V characteristics in third and fourth quadrants and the Voc-Isc characteristics of the cell. In the work of (Bashahu et al, 2007), up to 22 methods for the determination of solar cell ideality factor (n), have been presented, most of them use the single I-V data set. (Ortiz-Conde et al,

A New Model for Extracting the

et al, 2001, 2004; Nehaoua et al 2010):

Where Isc is the short circuit current.

F(θ) is described by the equation:

method is given by:

written as:

The term between brackets is equal to *I V IR s s* exp *<sup>n</sup>*

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 57

6, the conductance G will be independent of the photo-current Iph. This equation can be

Consequently, by minimizing the sum of the squares of the conductance residuals instead of minimizing the sum of the squares of current residuals as in (Easwarakhanthan et al, 1986). Using this method, the number of parameters to be extracted is reduced from five Ө = (Is, n, Rs, Gsh, Iph) to only four parameters Ө= (Is, n, Rs, Gsh). The fifth parameter, the photocurrent, can be easily deduced using Eq. (1) at V=0, which yield to the following equation (Chegaar

> 1 exp 1 *sc s ph sc s sh p I R I I RG I*

Newton's method can be used to obtain an approximation to the exact solution. Newton's

 

*<sup>F</sup> <sup>J</sup>* 

For minimizing the sum of the squares, it is necessary to solve the equations F(Ө)=0, where

 *<sup>S</sup> <sup>F</sup>* 

Although Newton's method converges only locally and may diverge under an improper choice of reasonably good starting values for the parameters, it remains attractive with the number of variables being limited (four in this case) and their partial derivatives easily. To illustrate the approach, we have first applied the method to a computer calculated curve reproducing the same solar cell characteristic used by Eswarakhantan et al. To test the effects of different initial values on the method, the known exact solutions were multiplied by the factors [0.5-1.7] respectively and after carrying out the calculations; the extracted solar cell parameters were almost identical to the theoretical ones. Also noticed is the obvious and expected fact that the CPU calculation time decreases quickly when the initial values used are closer to the exact solution. In order to test the quality of the fit to the

*i i* 1 

Where J(Ө) is the Jacobian matrix which elements are defined by:

experimental data, the percentage error is calculated as follows:

<sup>1</sup>

 

*n n*

*s s* exp *sh I V IR G*

 

and when replaced in equation

(7)

*n* 

(8)

*J F* (9)

(10)

(11)

*e II I i i i cal* , 100 / *<sup>i</sup>* (12)

2006) have proposed an elegant method to extract the five parameters based on the calculation of the co-content function (CC) from the exact explicit analytical solution of the illuminated current–voltage characteristics, but this method has only been tested on a plastic solar cell. An accurate method using the Lambert W-function has been presented by (Jain and Kapoor, 2004, 2005) to study different parameters of organic solar cells, but it has been validated only on simulated I–V characteristics. A combination of lateral and vertical optimization was used ( Haouari-Merbah et al, 2005; Ferhat-Hamida et al, 2002) to extract the parameters of an illuminated solar cell. (Zagrouba et al, 2010; Sellami et al, 2007) propose to perform a numerical technique based on genetic algorithms (GAs) to identify the five electrical parameters (Iph, Is, Rs, Rsh and n) of multicrystalline silicon photovoltaic (PV) solar cells and modules, but this technique is influenced by the choice of the initial values of population. A novel parameter extraction method for the one-diode solar cell model is proposed by (Wook et al, 2010) the method deduces the characteristic curve of an ideal solar cell without resistance using the I-V characteristic curve measured.

#### **4.2 Proposed method of parameters extraction**

The I-V characteristics of the solar cell can be presented by either a two diode model (Kaminsky et al, 1997) or by a single diode model (Sze et al, 1981). Under illumination and normal operating conditions, the single diode model is however the most popular model for solar cells (Datta et al, 1967). In this case, the current voltage (I-V) relation of an illuminated solar cell is given by Equation 1.

Equation 1 is implicit and cannot be solved analytically. The proper approach is to apply least squares techniques by taking into account the measured data over the entire experimental I-V curve and a suitable nonlinear algorithm in order to minimize the sum of the squared errors. In this section we propose a new technique that uses the measured current-voltage curve and its derivative (Chegaar et al, 2004; Nehaoua et al 2010). A non linear least squares optimization algorithm based on the Newton model is hence used to evaluate the solar cell parameters. The problem, we have, is to minimize the objective function S with respect to the set of parameters θ:

$$S(\theta) = \sum\_{i=1}^{N} \left[ \frac{G - G\_i(V\_{i'}, I\_{i'}\theta)}{G\_i(V\_{i'}, I\_{i'}\theta)} \right]^2 \tag{4}$$

Where *Ө* is the set of unknown parameters *Ө*= (Is, n, Rs, Gsh) and Ii, Vi are the measured current, voltage and the computed conductance *G dI dV ii i* / respectively at the ith point among N measured data points. Note that the differential conductance is determined numerically for the whole I-V curve using a method based on the least squares principle and a convolution. The conductance G can be written as:

$$G = -\frac{\mathcal{V}}{1 + R\_s \mathcal{V}} \tag{5}$$

Where ψ is given by:

$$\Psi = \frac{\beta}{n} \left\{ I\_{ph} + I\_p - I - \mathbf{G}\_{sli} \left( V + R\_s I \right) \right\} + \mathbf{G}\_{sli} \tag{6}$$

The term between brackets is equal to *I V IR s s* exp *<sup>n</sup>* and when replaced in equation 6, the conductance G will be independent of the photo-current Iph. This equation can be written as:

$$\Psi = \frac{\beta}{n} I\_s \exp\left(\frac{\beta}{n} (V + IR\_s)\right) + G\_{sh} \tag{7}$$

Consequently, by minimizing the sum of the squares of the conductance residuals instead of minimizing the sum of the squares of current residuals as in (Easwarakhanthan et al, 1986). Using this method, the number of parameters to be extracted is reduced from five Ө = (Is, n, Rs, Gsh, Iph) to only four parameters Ө= (Is, n, Rs, Gsh). The fifth parameter, the photocurrent, can be easily deduced using Eq. (1) at V=0, which yield to the following equation (Chegaar et al, 2001, 2004; Nehaoua et al 2010):

$$I\_{pli} = I\_{sc} \left( 1 + R\_s G\_{sli} \right) + I\_p \left( \exp \frac{\beta I\_{sc} R\_s}{n} - 1 \right) \tag{8}$$

Where Isc is the short circuit current.

56 Solar Cells – Silicon Wafer-Based Technologies

2006) have proposed an elegant method to extract the five parameters based on the calculation of the co-content function (CC) from the exact explicit analytical solution of the illuminated current–voltage characteristics, but this method has only been tested on a plastic solar cell. An accurate method using the Lambert W-function has been presented by (Jain and Kapoor, 2004, 2005) to study different parameters of organic solar cells, but it has been validated only on simulated I–V characteristics. A combination of lateral and vertical optimization was used ( Haouari-Merbah et al, 2005; Ferhat-Hamida et al, 2002) to extract the parameters of an illuminated solar cell. (Zagrouba et al, 2010; Sellami et al, 2007) propose to perform a numerical technique based on genetic algorithms (GAs) to identify the five electrical parameters (Iph, Is, Rs, Rsh and n) of multicrystalline silicon photovoltaic (PV) solar cells and modules, but this technique is influenced by the choice of the initial values of population. A novel parameter extraction method for the one-diode solar cell model is proposed by (Wook et al, 2010) the method deduces the characteristic curve of an ideal solar

The I-V characteristics of the solar cell can be presented by either a two diode model (Kaminsky et al, 1997) or by a single diode model (Sze et al, 1981). Under illumination and normal operating conditions, the single diode model is however the most popular model for solar cells (Datta et al, 1967). In this case, the current voltage (I-V) relation of an illuminated

Equation 1 is implicit and cannot be solved analytically. The proper approach is to apply least squares techniques by taking into account the measured data over the entire experimental I-V curve and a suitable nonlinear algorithm in order to minimize the sum of the squared errors. In this section we propose a new technique that uses the measured current-voltage curve and its derivative (Chegaar et al, 2004; Nehaoua et al 2010). A non linear least squares optimization algorithm based on the Newton model is hence used to evaluate the solar cell parameters. The problem, we have, is to minimize the objective

1

*G*

*N*

( , ,) ( ) ( , ,)

*i i ii G GVI <sup>S</sup>*

Where *Ө* is the set of unknown parameters *Ө*= (Is, n, Rs, Gsh) and Ii, Vi are the measured current, voltage and the computed conductance *G dI dV ii i* / respectively at the ith point among N measured data points. Note that the differential conductance is determined numerically for the whole I-V curve using a method based on the least squares principle and

*GVI*

1 *<sup>s</sup>*

*I I I G V RI G ph <sup>p</sup> sh s sh <sup>n</sup>*

*R* 

*i ii*

2

(6)

(4)

(5)

cell without resistance using the I-V characteristic curve measured.

**4.2 Proposed method of parameters extraction** 

function S with respect to the set of parameters θ:

a convolution. The conductance G can be written as:

Where ψ is given by:

solar cell is given by Equation 1.

Newton's method can be used to obtain an approximation to the exact solution. Newton's method is given by:

$$\theta\_i = \theta\_{i-1} - \left[f(\theta)\right]^{-1} F(\theta) \tag{9}$$

Where J(Ө) is the Jacobian matrix which elements are defined by:

$$J = \frac{\partial F}{\partial \theta} \tag{10}$$

For minimizing the sum of the squares, it is necessary to solve the equations F(Ө)=0, where F(θ) is described by the equation:

$$F(\theta) = \frac{\partial S}{\partial \theta} \tag{11}$$

Although Newton's method converges only locally and may diverge under an improper choice of reasonably good starting values for the parameters, it remains attractive with the number of variables being limited (four in this case) and their partial derivatives easily. To illustrate the approach, we have first applied the method to a computer calculated curve reproducing the same solar cell characteristic used by Eswarakhantan et al. To test the effects of different initial values on the method, the known exact solutions were multiplied by the factors [0.5-1.7] respectively and after carrying out the calculations; the extracted solar cell parameters were almost identical to the theoretical ones. Also noticed is the obvious and expected fact that the CPU calculation time decreases quickly when the initial values used are closer to the exact solution. In order to test the quality of the fit to the experimental data, the percentage error is calculated as follows:

$$e\_i = \left(I\_i - I\_{i,cal}\right) \left(100 \,\mathrm{/\,I\_i}\right) \tag{12}$$

A New Model for Extracting the

straightforward and easy to use.

Cell (33°C) Gsh (Ω-1) Rs (Ω) n Is(µA) Iph(A)

Module (45°C) Gsh (Ω-1) Rs (Ω) n Is(µA) Iph(A)

Gsh (mΩ-1) Rs (Ω) n

Is(nAcm-2) Iph(mAcm-2)

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 59

characteristics of different types of solar cells from inorganic to organic solar cells with completely different physical characteristics and under different temperatures. In contrast to other methods that have already been developed for this purpose, the proposed method has no limitation condition on the voltage. Furthermore, the presented method, tested for the selected cases, is more reliable to obtain physically meaningful parameters and is

Method ( Chegaar M et

Method of this work

0.0114 0.0392 1.4425 0.2296 0.7606

0.001445 1.2373 47.35 2.4920 1.0333

Method of this work

4.88 3.16 2.29 12.08 7.66

al ,2006)

0.0094 0.0376 1.4841 0.3374 0.7603

0.00145 1.1619 50.99 6.3986 1.030

Method (Chegaar et

RMSE (%) MBE (%) MAE (%)

al,2006)

5.07 8.58 2.31 13.6 7.94

Method (Easwarakhantan et

Table 1. Extracted parameters for commercial silicon solar cell and module.

Solar cell (33°C) 0.442 -0.016 0.310 Module (45°C) 0.252 -0.008 0.204 Organic solar cell (27°C) 1.806 0.638 1.201

Table 3. Statistical indicators of accuracy for the method of this work.

al, 1986)

 0.0186 0.0364 1.4837 0.3223 0.7608

 0.00182 1.2057 48.450 3.2876 1.0318

Co-content

Table 2. Extracted parameters for an organic solar cell.

5.07 8.59 2.31 13.6 7.94

function (Ortiz, 2006)

Where *Ii,cal* is the current calculated for each *Vi,* by solving the implicit Eq.(1) with the determined set of parameters ( *Iph, n, Rs, Gsh, Is*). (*Ii, Vi*) are respectively the measured current and voltage at the *i*th point among *N* considered measured data points avoiding the measurements close to the open-circuit condition where the current is not well-defined (Chegaar M et al, 2006). Statistical analysis of the results has also been performed. The root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE) are the fundamental measures of accuracy. Thus, RMSE, MBE and MAE are given by:

$$\begin{aligned} RMSE &= \left(\sum \left|e\right|\_i^2 \ne N\right)^{1/2} \\ MSE &= \sum e\_i \ne N \\ MAE &= \sum \left|e\right|\_i \ne N \end{aligned} \tag{13}$$

*N* is the number of measurements data taken into account.

As test examples, the method has been successfully applied on solar cells under illumination and used to extract the parameters of interest using experimental I–V characteristics of different solar cells and under different temperatures. It has been successfully applied to the measured I–V data of inorganic solar cells. These devices are a 57 mm diameter commercial silicon solar cell at a temperature of 33°C and a solar module in which 36 polycrystalline silicon solar cells are connected in series at 45°C. It has also been successful when applied to an illuminated organic solar cell, where the currents are generally 1000 times smaller and have high series resistances compared to inorganic (silicon) solar cells. The results obtained are compared with previously published data related to the same devices and good agreement is reported. Comparisons are also made with experimental data for the different devices.

#### **4.3 Results and discussion**

The experimental current–voltage (I–V) data were taken from (Easwarakhantan et al, 1986) for the commercial silicon solar cell and module and from (Ortiz-Conde et al, 2006) for the organic solar cell. The extracted parameters obtained using the method proposed here for the silicon solar cell and modules are given in Table 1. Satisfactory agreement is obtained for most of the extracted parameters. Those of the organic solar cell are shown in Table 2. A comparison with different methods is also given, and good agreement is reported. Statistical indicators of accuracy for the method of this work are shown in Table 3.

The best fits are obtained for the silicon solar cell and module with a root mean square error less than 1% and 2% for the organic solar cell. In figures 3, 4 and 5, the solid squares are the experimental data for the different solar cell and the solid line is the fitted curve derived from Equation (1) with the parameters shown in Table 1 for the silicon solar cell and module and Table 2 for the organic solar cell.

Good agreement is observed, especially for the inorganic solar cells. It is therefore necessary to emphasize that the proposed method is not based on the I-V characteristics alone but also on the derivative of this curve, i.e. the conductance G. Indeed, it has been demonstrated that it is not sufficient to obtain a numerical agreement between measured and fitted I-V data to verify the validity of a theory, but also the conductance data have to be predicted to show the physical applicability of the used theory. The interesting points with the procedure described herein is the fact that it has been successfully applied to experimental I–V

Where *Ii,cal* is the current calculated for each *Vi,* by solving the implicit Eq.(1) with the determined set of parameters ( *Iph, n, Rs, Gsh, Is*). (*Ii, Vi*) are respectively the measured current and voltage at the *i*th point among *N* considered measured data points avoiding the measurements close to the open-circuit condition where the current is not well-defined (Chegaar M et al, 2006). Statistical analysis of the results has also been performed. The root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE) are the fundamental measures of accuracy. Thus, RMSE, MBE and MAE are given by:

> 1/2 <sup>2</sup> /

*i*

(13)

/ /

*i i*

As test examples, the method has been successfully applied on solar cells under illumination and used to extract the parameters of interest using experimental I–V characteristics of different solar cells and under different temperatures. It has been successfully applied to the measured I–V data of inorganic solar cells. These devices are a 57 mm diameter commercial silicon solar cell at a temperature of 33°C and a solar module in which 36 polycrystalline silicon solar cells are connected in series at 45°C. It has also been successful when applied to an illuminated organic solar cell, where the currents are generally 1000 times smaller and have high series resistances compared to inorganic (silicon) solar cells. The results obtained are compared with previously published data related to the same devices and good agreement is reported. Comparisons are also made with experimental data for the different

The experimental current–voltage (I–V) data were taken from (Easwarakhantan et al, 1986) for the commercial silicon solar cell and module and from (Ortiz-Conde et al, 2006) for the organic solar cell. The extracted parameters obtained using the method proposed here for the silicon solar cell and modules are given in Table 1. Satisfactory agreement is obtained for most of the extracted parameters. Those of the organic solar cell are shown in Table 2. A comparison with different methods is also given, and good agreement is reported. Statistical

The best fits are obtained for the silicon solar cell and module with a root mean square error less than 1% and 2% for the organic solar cell. In figures 3, 4 and 5, the solid squares are the experimental data for the different solar cell and the solid line is the fitted curve derived from Equation (1) with the parameters shown in Table 1 for the silicon solar cell and module

Good agreement is observed, especially for the inorganic solar cells. It is therefore necessary to emphasize that the proposed method is not based on the I-V characteristics alone but also on the derivative of this curve, i.e. the conductance G. Indeed, it has been demonstrated that it is not sufficient to obtain a numerical agreement between measured and fitted I-V data to verify the validity of a theory, but also the conductance data have to be predicted to show the physical applicability of the used theory. The interesting points with the procedure described herein is the fact that it has been successfully applied to experimental I–V

indicators of accuracy for the method of this work are shown in Table 3.

*RMSE e N*

*MBE e N MAE e N*

 

 

*N* is the number of measurements data taken into account.

devices.

**4.3 Results and discussion** 

and Table 2 for the organic solar cell.

characteristics of different types of solar cells from inorganic to organic solar cells with completely different physical characteristics and under different temperatures. In contrast to other methods that have already been developed for this purpose, the proposed method has no limitation condition on the voltage. Furthermore, the presented method, tested for the selected cases, is more reliable to obtain physically meaningful parameters and is straightforward and easy to use.


Table 1. Extracted parameters for commercial silicon solar cell and module.




Table 3. Statistical indicators of accuracy for the method of this work.

A New Model for Extracting the

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 61

I-V characteristics and fitted curves

Fig. 5. Experimental data (■) and the fitted curve (-) for the organic solar cell.

experimental data fitted curve

Figures 6-13 show the effect of the series resistance and shunt resistance on the currentvoltage (I-V), power-voltage (P-V) characteristics and their effect on the fill factor (FF) and conversion efficiency (η). Change in the shape of the I-V curve due to changes in parameters values. First, as seen in fig.6, the shape of the I-V curve in the voltage source region is depressed horizontally with a gradual increase in the value of series resistance from zero, too, the power conversion decrease with a gradual increase in the value of series resistance. When shunt resistance decreases from infinity, the shape of the I-V curve in the current source region is depressed leftward as shown in fig.10, and the power conversion decrease too. Second, figure 8, 9, 12 and 13 show the effect of the series resistance and shunt resistance on the fill factor (FF) and conversion efficiency (η). Where the fill factor (FF) and conversion efficiency (η) values decrease when the values of series and shunt conductance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Voltage (V)

**4.4 Effects of parameters on the shape of the I-V curve** 

(Gsh=1/Rsh) increase.

0

1

2

3

4

Current (A)

5

6

7

8 x 10-3

Fig. 3. Experimental data (■) and the fitted curve (-) for the commercial silicon solar cell.

Fig. 4. Experimental data (■) and the fitted curve (-) for the commercial silicon solar module.

I-V characteristics and fitted curves

experiental data fitted curve

Fig. 3. Experimental data (■) and the fitted curve (-) for the commercial silicon solar cell.



0

0.2

0.4

Current (A)

0.6

0.8

1

1.2

Current (A)


Voltage (V)

I-V characteristics and fitted curves

experimental data fitted curve

Fig. 4. Experimental data (■) and the fitted curve (-) for the commercial silicon solar module.


Voltage (V)

Fig. 5. Experimental data (■) and the fitted curve (-) for the organic solar cell.

#### **4.4 Effects of parameters on the shape of the I-V curve**

Figures 6-13 show the effect of the series resistance and shunt resistance on the currentvoltage (I-V), power-voltage (P-V) characteristics and their effect on the fill factor (FF) and conversion efficiency (η). Change in the shape of the I-V curve due to changes in parameters values. First, as seen in fig.6, the shape of the I-V curve in the voltage source region is depressed horizontally with a gradual increase in the value of series resistance from zero, too, the power conversion decrease with a gradual increase in the value of series resistance. When shunt resistance decreases from infinity, the shape of the I-V curve in the current source region is depressed leftward as shown in fig.10, and the power conversion decrease too. Second, figure 8, 9, 12 and 13 show the effect of the series resistance and shunt resistance on the fill factor (FF) and conversion efficiency (η). Where the fill factor (FF) and conversion efficiency (η) values decrease when the values of series and shunt conductance (Gsh=1/Rsh) increase.

A New Model for Extracting the

Fig. 8. Effect of series resistance on the η and FF.

Fig. 9. Effect of series resistance on the η and FF.

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 63

Fig. 6. Effect of series resistance on the I-V characteristics of an illumination solar cell.

Fig. 7. Effect of series resistance on the P-V characteristics of an illumination solar cell.

Fig. 6. Effect of series resistance on the I-V characteristics of an illumination solar cell.

Fig. 7. Effect of series resistance on the P-V characteristics of an illumination solar cell.

Fig. 8. Effect of series resistance on the η and FF.

Fig. 9. Effect of series resistance on the η and FF.

A New Model for Extracting the

Fig. 12. Effect of shunt resistance on the η and FF.

Fig. 13. Effect of shunt resistance on the η and FF.

This contribution present and analyse a simple and powerful method of extracting solar cell parameters which affect directly the conversion efficiency, the power conversion, the fill

**5. Conclusion** 

Physical Parameters from I-V Curves of Organic and Inorganic Solar Cells 65

Fig. 10. Effect of shun resistance on the I-V characteristics of an illumination solar.

Fig. 11. Effect of shun resistance on the P-V characteristics of an illumination solar.

Fig. 10. Effect of shun resistance on the I-V characteristics of an illumination solar.

Fig. 11. Effect of shun resistance on the P-V characteristics of an illumination solar.

Fig. 12. Effect of shunt resistance on the η and FF.

Fig. 13. Effect of shunt resistance on the η and FF.

#### **5. Conclusion**

This contribution present and analyse a simple and powerful method of extracting solar cell parameters which affect directly the conversion efficiency, the power conversion, the fill

**4** 

**Trichromatic High Resolution-LBIC:** 

Javier Navas, Rodrigo Alcántara, Concha Fernández-Lorenzo

Laser Beam Induced Current (LBIC) imaging is a nondestructive characterization technique which can be used for research into semiconductor and photovoltaic devices (Dimassi et al., 2008). Since its first application to p-n junction photodiode structures used in HgCdTe infrared focal plane arrays in the late 1980s, many experimental studies have demonstrated the LBIC technique's capacity to electrically map active regions in semiconductors, as it enables defects and details to be observed which are unobservable with an optical microscope (van Dyk et al., 2007). Thus, the LBIC technique has been used for research in different fields related to photovoltaic energy: the superficial study of silicon structures (Sontag et al. 2002); the study of grain boundaries on silicon based solar cells (Nishioka et al., 2007); the study of polycrystalline solar cells (Nichiporuk et al., 2006); the study of thin film photovoltaic modules (Vorasayan et al., 2009); the study of non-silicon based photovoltaic or semiconductor devices (van Dyk et al., 2007) and the study of dye-sensitized

In this technique, a highly stabilized laser beam is focused on the photoactive surface of a cell and performs a two-dimensional scan of the photoactive surface, measuring the photoresponse generated point to point. A correlation between the number of incident photons and the quantity of photoelectrons generated derived from the photocurrent measurement makes it possible to obtain the photoconverter efficiency, which is the quantum efficiency of the device at each point of the active surface. Thus, the LBIC technique allows images of photovoltaic devices to be obtained dependent upon superficial variation in quantum efficiency. Usually photocurrent values are measured at short circuit as it is a linear function of the radiation power in a wide range and the interaction coefficient is proportional to the quantum photoefficiency (Bisconti et al., 1997). Three main factors can be associated to the level of photocurrent generated by a photovoltaic surface: (a) the limit values of photon energy that are necessary for electron transfer between valence and conduction bands, (b) the intrinsic characteristics of electron-hole recombination, and (c)

So, the numerical value of the photoefficiency signal generated at each point is computer stored according to its positional coordinates. Using the stored signal, an image is generated

**1. Introduction** 

solar cells (Navas et al., 2009).

photon penetration into the active material.

**A System for the Micrometric** 

and Joaquín Martín-Calleja

*University of Cádiz* 

*Spain* 

**Characterization of Solar Cells** 

factor and current-voltage shape of the solar cell. These parameters are: the ideality factor, the series resistance, diode saturation current and shunt conductance. This technique is not only based on the current-voltage characteristics but also on the derivative of this curve, the conductance G. by using this method, the number of parameters to be extracted is reduced from five Is, n, Rs, Gsh, Iph to only four parameters Is, n, Rs, Gsh. The method has been successfully applied to a silicon solar cell, a module and an organic solar cell under different temperatures. The results obtained are in good agreement with those published previously. The method is very simple to use. It allows real time characterisation of different types of solar cells and modules in indoor or outdoor conditions.

#### **6. References**

Bashahu, M. & Nkundabakura,P.(2007) Solar energy. 81 856-863.


## **Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells**

Javier Navas, Rodrigo Alcántara, Concha Fernández-Lorenzo and Joaquín Martín-Calleja *University of Cádiz Spain* 

#### **1. Introduction**

66 Solar Cells – Silicon Wafer-Based Technologies

factor and current-voltage shape of the solar cell. These parameters are: the ideality factor, the series resistance, diode saturation current and shunt conductance. This technique is not only based on the current-voltage characteristics but also on the derivative of this curve, the conductance G. by using this method, the number of parameters to be extracted is reduced from five Is, n, Rs, Gsh, Iph to only four parameters Is, n, Rs, Gsh. The method has been successfully applied to a silicon solar cell, a module and an organic solar cell under different temperatures. The results obtained are in good agreement with those published previously. The method is very simple to use. It allows real time characterisation of different types of

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Chegaar, M.; Ouennoughi, Z. & Guechi,F.(2004). Vacuum. 75, 367–72.

Jain,A & Kapoor, A.(2005), *Solar energy mater, solar cells*. 86, 197-205. Jain., A & Kapoor, A.(2004),*Solar energy mater, solar cells*. 81, 269-277.

Nehaoua ,N., Chergui ,Y. , Mekki, D. E.(2010) *Vacuum* , 84 : 326–329.

solar cell I-V characteristics. *Solar cells* 18, 1-12.

solar cell model, solar energy 84, 1008-1019.

maximum power extraction. *Solar energy* 84, 860-866.

Chegaar, M.; G. Azzouzi, Mialhe,P.(2006).*Solid-state Electronics*. 50, 1234-1237.

**6. References** 

192, 35.

46, 615–619.

90, 352–61.

1472-1476.

*Cells*. 93 (2009) 1423–1426.

*Cells.* 87, 225–33.

Laser Beam Induced Current (LBIC) imaging is a nondestructive characterization technique which can be used for research into semiconductor and photovoltaic devices (Dimassi et al., 2008). Since its first application to p-n junction photodiode structures used in HgCdTe infrared focal plane arrays in the late 1980s, many experimental studies have demonstrated the LBIC technique's capacity to electrically map active regions in semiconductors, as it enables defects and details to be observed which are unobservable with an optical microscope (van Dyk et al., 2007). Thus, the LBIC technique has been used for research in different fields related to photovoltaic energy: the superficial study of silicon structures (Sontag et al. 2002); the study of grain boundaries on silicon based solar cells (Nishioka et al., 2007); the study of polycrystalline solar cells (Nichiporuk et al., 2006); the study of thin film photovoltaic modules (Vorasayan et al., 2009); the study of non-silicon based photovoltaic or semiconductor devices (van Dyk et al., 2007) and the study of dye-sensitized solar cells (Navas et al., 2009).

In this technique, a highly stabilized laser beam is focused on the photoactive surface of a cell and performs a two-dimensional scan of the photoactive surface, measuring the photoresponse generated point to point. A correlation between the number of incident photons and the quantity of photoelectrons generated derived from the photocurrent measurement makes it possible to obtain the photoconverter efficiency, which is the quantum efficiency of the device at each point of the active surface. Thus, the LBIC technique allows images of photovoltaic devices to be obtained dependent upon superficial variation in quantum efficiency. Usually photocurrent values are measured at short circuit as it is a linear function of the radiation power in a wide range and the interaction coefficient is proportional to the quantum photoefficiency (Bisconti et al., 1997). Three main factors can be associated to the level of photocurrent generated by a photovoltaic surface: (a) the limit values of photon energy that are necessary for electron transfer between valence and conduction bands, (b) the intrinsic characteristics of electron-hole recombination, and (c) photon penetration into the active material.

So, the numerical value of the photoefficiency signal generated at each point is computer stored according to its positional coordinates. Using the stored signal, an image is generated

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 69

radiation from the selected laser through the whole system's main optical pathway. A Micos SMC Pollux stepper motor controller with an integrated two-phase stepper motor, capable of moving 1.8°/0.9° per step has been used for motor control. Command programming and configuration is executed via a RS232 interface, which allows velocity movement definition,

A highly transparent nonpolarizing beamsplitter, made from BK7 glass with antireflecting coating, has been placed on the optical path. This beamsplitter plays a double role, depending on whether it is working in reflection or in transmission. In reflection, the reflected beam is used for irradiating the sample, whereas the transmitted beam allows one to monitor the stability of the laser power emission by using a silicon photodiode (see Figure 1). By means of the ratio between the induced current and this signal it is possible to obtain

The optical system between the beamsplitter and the sample works similarly to a confocal system, so that the beam specularly reflected by the sample surface follows an optical path which coincides with the irradiation path, but in the opposite sense. The intensity of this beam that is reflected by beam splitter is measured by a second silicon photodiode which allows one to obtain information on the reflecting properties of the photoactive surface. This information is particularly interesting for the evaluation of the photoconversion internal quantum efficiency. Moreover, when the photovoltaic device under study has a photon transparent support as in dye-sensitized solar cells, the transmittance signal can also be

This system is most important since an optimum focusing of the laser on the photoactive surface is one of the main limiting factors of the spatial resolution. Any focusing errors will lead to unacceptable results. The focusing system designed consists basically of three subsystems: a focusing lens mounted on a motorized stage with micrometric movement, a beam expander built with two opposing microscope objectives and a calculation algorithm which allows a computer to optimize the focusing process, and which we will analyze in detail later. The spot size at the focus is directly related to the focal distance and inversely

point to point moves, and multiple unit control with only one communication port.

Fig. 1. General outline of the LBIC system.

measured (see Figure 1).

a normalized value for the external quantum efficiency.

of the photoconversion efficiency of the surface scanned. It is interesting to note that the whole photoactive surface acts as an integrating system. That is, independent of the irradiated area or its position, the entire photogenerated signal is always obtained via the system's two connectors.

The spatial resolution of the images obtained depends on the size of the laser spot. That is, images generated using the LBIC technique have the best possible resolution when the focusing of the beam on the cell is optimum. Thus, it is essential to use a laser as the irradiation system because it provides optimal focusing of the photon beam on the photoactive surface and therefore a higher degree of spatial resolution in the images obtained. This provides enhanced structural detail of the material at a micrometric level which can be related with the quantum yield of the photovoltaic device. However, the monochromatic nature of lasers means that it is impossible to obtain information about the response of the device under solar irradiation conditions. No real irradiation source can simultaneously provide a spectral distribution similar to the emission of the sun with the characteristics of a laser emission in terms of non divergence and Gaussian power distribution.

Nowadays, there are several LBIC systems with different configurations which have been developed by research groups and allowing interesting results to be obtained (Bisconti et al., 1997). In general, these systems are based on a laser source which, by using different optomechanical systems to prepare the radiation beam, is directed at a system which focalizes it on the active surface of the device. There are two options for performing a superficial scan in low spatial resolution systems: using a beam deflection technique or placing the photovoltaic device on a biaxial displacement system which positions the photoactive surface in the right position for each measurement. The system must incorporate the right electrical contacts, as well as the necessary electronic systems, to gather the photocurrent signal and prepare it to be measured so that an image can be created which is related with the quantum efficiency of the device under study. However, high resolution (HR) spatial systems (HR-LBIC) must use a very short focal distance focusing lens, which prevents deflection systems being used to perform the scan and makes it necessary to opt for systems with biaxial displacement along the photoactive surface.

#### **2. LBIC system description**

The different components which make up the subsystems of the equipment, such as the elements used for focusing the beam on the active surface, controlling the radiant power, controlling the reflected radiant power, etc., are placed along the optical axis (see Figure 1). In our system we have used the following as excitation radiation emissions: a 632.8 nm He– Ne laser made by Uniphase ©, model 1125, with a nominal power of 10 mW; a 532 nm DPSS laser made by Shangai Dream Lasers Technology ©, model SDL-532–150T, with a nominal power of 150 mW; and a 473 nm DPSS laser by Shangai Dream Lasers Technology©, model SDL-473–040T, with a nominal power of 40 mW. Each of the lasers is mounted on a system allowing optimal adjustment of the optical pathway, with a predetermined angle between them. In turn, a shutter is placed in the optical pathway of each laser which makes it possible to establish the radiation used in each scan. In order to reduce the laser power to the required values, a continuous neutral density filter is placed next the laser exit windows. The layout of the three lasers enables their beams to come together on a mirror supported on a stepper motor, which being set at a predefined angle makes it possible to direct the radiation from the selected laser through the whole system's main optical pathway. A Micos SMC Pollux stepper motor controller with an integrated two-phase stepper motor, capable of moving 1.8°/0.9° per step has been used for motor control. Command programming and configuration is executed via a RS232 interface, which allows velocity movement definition, point to point moves, and multiple unit control with only one communication port.

Fig. 1. General outline of the LBIC system.

68 Solar Cells – Silicon Wafer-Based Technologies

of the photoconversion efficiency of the surface scanned. It is interesting to note that the whole photoactive surface acts as an integrating system. That is, independent of the irradiated area or its position, the entire photogenerated signal is always obtained via the

The spatial resolution of the images obtained depends on the size of the laser spot. That is, images generated using the LBIC technique have the best possible resolution when the focusing of the beam on the cell is optimum. Thus, it is essential to use a laser as the irradiation system because it provides optimal focusing of the photon beam on the photoactive surface and therefore a higher degree of spatial resolution in the images obtained. This provides enhanced structural detail of the material at a micrometric level which can be related with the quantum yield of the photovoltaic device. However, the monochromatic nature of lasers means that it is impossible to obtain information about the response of the device under solar irradiation conditions. No real irradiation source can simultaneously provide a spectral distribution similar to the emission of the sun with the characteristics of a laser emission in terms of non divergence and Gaussian power

Nowadays, there are several LBIC systems with different configurations which have been developed by research groups and allowing interesting results to be obtained (Bisconti et al., 1997). In general, these systems are based on a laser source which, by using different optomechanical systems to prepare the radiation beam, is directed at a system which focalizes it on the active surface of the device. There are two options for performing a superficial scan in low spatial resolution systems: using a beam deflection technique or placing the photovoltaic device on a biaxial displacement system which positions the photoactive surface in the right position for each measurement. The system must incorporate the right electrical contacts, as well as the necessary electronic systems, to gather the photocurrent signal and prepare it to be measured so that an image can be created which is related with the quantum efficiency of the device under study. However, high resolution (HR) spatial systems (HR-LBIC) must use a very short focal distance focusing lens, which prevents deflection systems being used to perform the scan and makes it necessary to opt

The different components which make up the subsystems of the equipment, such as the elements used for focusing the beam on the active surface, controlling the radiant power, controlling the reflected radiant power, etc., are placed along the optical axis (see Figure 1). In our system we have used the following as excitation radiation emissions: a 632.8 nm He– Ne laser made by Uniphase ©, model 1125, with a nominal power of 10 mW; a 532 nm DPSS laser made by Shangai Dream Lasers Technology ©, model SDL-532–150T, with a nominal power of 150 mW; and a 473 nm DPSS laser by Shangai Dream Lasers Technology©, model SDL-473–040T, with a nominal power of 40 mW. Each of the lasers is mounted on a system allowing optimal adjustment of the optical pathway, with a predetermined angle between them. In turn, a shutter is placed in the optical pathway of each laser which makes it possible to establish the radiation used in each scan. In order to reduce the laser power to the required values, a continuous neutral density filter is placed next the laser exit windows. The layout of the three lasers enables their beams to come together on a mirror supported on a stepper motor, which being set at a predefined angle makes it possible to direct the

for systems with biaxial displacement along the photoactive surface.

**2. LBIC system description** 

system's two connectors.

distribution.

A highly transparent nonpolarizing beamsplitter, made from BK7 glass with antireflecting coating, has been placed on the optical path. This beamsplitter plays a double role, depending on whether it is working in reflection or in transmission. In reflection, the reflected beam is used for irradiating the sample, whereas the transmitted beam allows one to monitor the stability of the laser power emission by using a silicon photodiode (see Figure 1). By means of the ratio between the induced current and this signal it is possible to obtain a normalized value for the external quantum efficiency.

The optical system between the beamsplitter and the sample works similarly to a confocal system, so that the beam specularly reflected by the sample surface follows an optical path which coincides with the irradiation path, but in the opposite sense. The intensity of this beam that is reflected by beam splitter is measured by a second silicon photodiode which allows one to obtain information on the reflecting properties of the photoactive surface. This information is particularly interesting for the evaluation of the photoconversion internal quantum efficiency. Moreover, when the photovoltaic device under study has a photon transparent support as in dye-sensitized solar cells, the transmittance signal can also be measured (see Figure 1).

This system is most important since an optimum focusing of the laser on the photoactive surface is one of the main limiting factors of the spatial resolution. Any focusing errors will lead to unacceptable results. The focusing system designed consists basically of three subsystems: a focusing lens mounted on a motorized stage with micrometric movement, a beam expander built with two opposing microscope objectives and a calculation algorithm which allows a computer to optimize the focusing process, and which we will analyze in detail later. The spot size at the focus is directly related to the focal distance and inversely

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 71

there are no biphotonic processes in normal conditions and (c) the power is low enough as to ignore thermal effects, then we can say that the intensity of the current supplied by the cell must be proportional to the density of incident photons and to the photoconversion efficiency of the cell. This implies that for an ideally homogeneous photoconversion surface, the current intensity generated will be independent of the focusing level, since, except when the size of the beam is larger than the active surface, the total number of photons will be a constant independent of its focusing level. In such a case the measure of current intensity

The situation is quite different if the photoconversion surface has heterogeneities. In that case, the size of the heterogeneity would match the size of the photon beam. The definition of heterogeneity would depend on the type of cell we are working with. In monocrystalline solar cells we may consider the cell's edges or the electron-collecting conducting elements (fingers); in polycrystalline solar cells, in addition to the previously mentioned ones, we may also consider the grain boundaries, the dislocations or any other photoconversion defects and, in dye sensitized solar cells, porous semiconductors density irregularities, dye adsorption concentration, etc. The current ISC generated will depend on the illuminated surface quantum yield average value, which, at the same time is dependant of the spot size and the distribution power. This dependence can be used to optimally focus the laser beam on the active surface. The basic experimental set-up has been defined before (see Figure 1). According to this diagram, the solar cell or photoelectrical active surface is placed on the YZ plane. Orthogonal to this surface and placed along the X-axis, a laser beam falls on. This laser is focused by a microscope objective lens, which can travel along that axis by means of a computer-controlled motorized stage. In turn, the solar cell is fixed to two motorized stages

For every position along the l coordinate, a value for the short circuit current is obtained (ISC) that is proportional to its quantum efficiency. The graphic representation of ISC(l) versus

In order to analyze the ISC-curve, it is assumed that the photoactive surface is equivalent to an independent set of photoconversion spatial pixels, each one having individual quantum efficiencies in the 0–100% range. These quantum efficiencies can be individually measured only if the size of the laser beam used as probe is equal or lesser than the aforementioned spatial pixels. If the laser beam spot is greater than these basic units, the electric response obtained will be equivalent to the product of the quantum efficiency distribution values of

Figure 2A shows an example of an ISC-curve. This one was obtained after performing a scan through a metallic current collector on a Silicon monocrystalline (mc-Si) solar cell. In this case, the laser beam has been focused by means of a 10x microscope objective lens, generating a minimum spot (w0) on the order of 1.2 m in diameter. Initially, the whole laser spot falls on a high photoconversion efficiency surface, generating a high ISC value, showing small variations caused by little heterogeneities (zone 1), later, when the laser starts to intercept the finger, a gradual ISC decreasing is generated (zone 2). If the collector width is greater than the laser spot diameter, the laser beam must travel through an area in which only a minimum current, associated to the diffuse light, is generated (zone 3). Subsequently the spot will gradually fall again on the photoactive sector (zone 4) until the spot again fully

Δl=ඥΔy2+Δz2 . (4)

would not be used to judge whether the laser beam is optimally focused.

which allow it to move on the YZ plane, along a coordinate named l so that

the affected units multiplied by the laser beam geometry photonic intensity.

l gives rise to the so-called ISC-curve.

related to the size of the prefocused beam. In this case, the focusing lenses we have used were, either a 16x microscope objective (F:11 mm) or a 10x one (F:15.7 mm), both supplied by Owis GMBH. The beam emitted by the lasers we previously mentioned has a size of 0.81 mm in the TEM00 mode, and it has been enlarged up to 7.6 mm by means a beam expander made up of two microscope objectives, coaxially and confocally arranged, with a 63x:4x rate. In order to eliminate as many parasitic emissions as possible, a spatial filter is placed at the confocal point of expander system and the resulting emission of the system is diaphragmed to the indicated nominal diameter (7.6 mm). Focusing with objectives of different magnification values will produce different beam parameters at the focus, affecting the resolution capacity to which photoactive surfaces can be studied.

We have decided to use a system configuration consisting of a fixed beam and mobile sample moving along orthogonal directions (YZ plane) with respect to the irradiation optical axis. The biaxial movement of the photoactive surface is achieved by using a system of motorized stages with numerical control and displacement resolution of 0.5 m. Special care has been taken to ensure the minimization of the asymmetrically suspended masses so as to avoid the generation of gravitational torsional forces. All optomechanical elements utilized in this system have been provided by Owis GMBH. Moreover, two low ohmic electric contacts are used to extract the electrons generated.

#### **3. Focusing algorithm**

A TEM00 mode laser beam presents a Gaussian irradiance distribution. This distribution is not modified by the focusing or reflecting of the beam by means of spherical optical elements and the irradiance is calculated by means of the expression

$$\mathbf{I}\{\mathbf{r}\} = \mathbf{I}\_0 \cdot \exp\left(\mathbf{-}\frac{2\mathbf{r}^2}{\mathbf{w}^2}\right),\tag{1}$$

where r is the distance from the center of the optical axis and w the so-called Gaussian radius, defined as the distance from the optical axis to the position at which the intensity decreases to 1/e2 of the value on the optical axis.

When a monochromatic Gaussian beam is focused, the Gaussian radius in the area near the focus fits the equation

$$\mathbf{w}^2(\mathbf{x}) = \mathbf{w}\_0^2 \left[ 1 + \left( \frac{\lambda \mathbf{x}}{\mathrm{m} \mathbf{w}\_0^2} \right)^2 \right] \tag{2}$$

where x is the coordinate along the propagation axis with the origin of coordinates being defined at the focal point, the wavelength value, n the refraction index of the medium and w0 is the Gaussian radius value at the focus. The latter can be obtained from the expression

$$\mathbf{w}\_0 = \left(\frac{2\lambda}{\mathbf{n}}\right) \left(\frac{\mathbf{F}}{\mathbf{D}}\right) \tag{3}$$

where F is the focal distance of the lens and D is the Gaussian diameter of the prefocused beam. For a monochromatic beam, the energy irradiance is proportional to the photon irradiance. As we explained above, in an ideal focusing process, the beam power remains constant, which implies that the number of photons is also kept constant. Assuming that (a) only the photons absorbed can generate electron–hole pairs according to a given quantum yield, (b)

related to the size of the prefocused beam. In this case, the focusing lenses we have used were, either a 16x microscope objective (F:11 mm) or a 10x one (F:15.7 mm), both supplied by Owis GMBH. The beam emitted by the lasers we previously mentioned has a size of 0.81 mm in the TEM00 mode, and it has been enlarged up to 7.6 mm by means a beam expander made up of two microscope objectives, coaxially and confocally arranged, with a 63x:4x rate. In order to eliminate as many parasitic emissions as possible, a spatial filter is placed at the confocal point of expander system and the resulting emission of the system is diaphragmed to the indicated nominal diameter (7.6 mm). Focusing with objectives of different magnification values will produce different beam parameters at the focus, affecting the

We have decided to use a system configuration consisting of a fixed beam and mobile sample moving along orthogonal directions (YZ plane) with respect to the irradiation optical axis. The biaxial movement of the photoactive surface is achieved by using a system of motorized stages with numerical control and displacement resolution of 0.5 m. Special care has been taken to ensure the minimization of the asymmetrically suspended masses so as to avoid the generation of gravitational torsional forces. All optomechanical elements utilized in this system have been provided by Owis GMBH. Moreover, two low ohmic

A TEM00 mode laser beam presents a Gaussian irradiance distribution. This distribution is not modified by the focusing or reflecting of the beam by means of spherical optical

where r is the distance from the center of the optical axis and w the so-called Gaussian radius, defined as the distance from the optical axis to the position at which the intensity

When a monochromatic Gaussian beam is focused, the Gaussian radius in the area near the

<sup>2</sup> <sup>ቈ</sup>1+ <sup>൬</sup> <sup>λ</sup><sup>x</sup> πnw0 2൰ 2

where x is the coordinate along the propagation axis with the origin of coordinates being defined at the focal point, the wavelength value, n the refraction index of the medium and w0 is the Gaussian radius value at the focus. The latter can be obtained from the expression

where F is the focal distance of the lens and D is the Gaussian diameter of the prefocused beam. For a monochromatic beam, the energy irradiance is proportional to the photon irradiance. As we explained above, in an ideal focusing process, the beam power remains constant, which implies that the number of photons is also kept constant. Assuming that (a) only the photons absorbed can generate electron–hole pairs according to a given quantum yield, (b)

2r<sup>2</sup>

w2ቁ, (1)

, (2)

<sup>D</sup>ቁ, (3)

Iሺrሻ=I0· exp ቀ-

w2ሺxሻ=w0

w0= ቀ 2λ <sup>π</sup> ቁ ቀ<sup>F</sup>

resolution capacity to which photoactive surfaces can be studied.

electric contacts are used to extract the electrons generated.

decreases to 1/e2 of the value on the optical axis.

elements and the irradiance is calculated by means of the expression

**3. Focusing algorithm** 

focus fits the equation

there are no biphotonic processes in normal conditions and (c) the power is low enough as to ignore thermal effects, then we can say that the intensity of the current supplied by the cell must be proportional to the density of incident photons and to the photoconversion efficiency of the cell. This implies that for an ideally homogeneous photoconversion surface, the current intensity generated will be independent of the focusing level, since, except when the size of the beam is larger than the active surface, the total number of photons will be a constant independent of its focusing level. In such a case the measure of current intensity would not be used to judge whether the laser beam is optimally focused.

The situation is quite different if the photoconversion surface has heterogeneities. In that case, the size of the heterogeneity would match the size of the photon beam. The definition of heterogeneity would depend on the type of cell we are working with. In monocrystalline solar cells we may consider the cell's edges or the electron-collecting conducting elements (fingers); in polycrystalline solar cells, in addition to the previously mentioned ones, we may also consider the grain boundaries, the dislocations or any other photoconversion defects and, in dye sensitized solar cells, porous semiconductors density irregularities, dye adsorption concentration, etc. The current ISC generated will depend on the illuminated surface quantum yield average value, which, at the same time is dependant of the spot size and the distribution power. This dependence can be used to optimally focus the laser beam on the active surface.

The basic experimental set-up has been defined before (see Figure 1). According to this diagram, the solar cell or photoelectrical active surface is placed on the YZ plane. Orthogonal to this surface and placed along the X-axis, a laser beam falls on. This laser is focused by a microscope objective lens, which can travel along that axis by means of a computer-controlled motorized stage. In turn, the solar cell is fixed to two motorized stages which allow it to move on the YZ plane, along a coordinate named l so that

$$
\Delta \mathbf{l} = \sqrt{\Delta \mathbf{y}^2 + \Delta \mathbf{z}^2} \,. \tag{4}
$$

For every position along the l coordinate, a value for the short circuit current is obtained (ISC) that is proportional to its quantum efficiency. The graphic representation of ISC(l) versus l gives rise to the so-called ISC-curve.

In order to analyze the ISC-curve, it is assumed that the photoactive surface is equivalent to an independent set of photoconversion spatial pixels, each one having individual quantum efficiencies in the 0–100% range. These quantum efficiencies can be individually measured only if the size of the laser beam used as probe is equal or lesser than the aforementioned spatial pixels. If the laser beam spot is greater than these basic units, the electric response obtained will be equivalent to the product of the quantum efficiency distribution values of the affected units multiplied by the laser beam geometry photonic intensity.

Figure 2A shows an example of an ISC-curve. This one was obtained after performing a scan through a metallic current collector on a Silicon monocrystalline (mc-Si) solar cell. In this case, the laser beam has been focused by means of a 10x microscope objective lens, generating a minimum spot (w0) on the order of 1.2 m in diameter. Initially, the whole laser spot falls on a high photoconversion efficiency surface, generating a high ISC value, showing small variations caused by little heterogeneities (zone 1), later, when the laser starts to intercept the finger, a gradual ISC decreasing is generated (zone 2). If the collector width is greater than the laser spot diameter, the laser beam must travel through an area in which only a minimum current, associated to the diffuse light, is generated (zone 3). Subsequently the spot will gradually fall again on the photoactive sector (zone 4) until the spot again fully

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 73

The transition slope between points with different quantum efficiency is defined as the values taken by the dISC/dl derivative, which is related to the laser beam size. As it has been aforementioned, the smaller the spot size, the more abrupt the ISC transition between points with a different superficial photoactivity and the larger the absolute value of dISC/dl. If the

Fig. 3. (A) Numerical derivative of the ISC-curve shown in Figure 2A. (B) Representation of

Figure 3A shows the derivative of the ISC-curve previously shown in Figure 2A in a way that makes possible to recognize the above-mentioned one to five zones. Attention should be drawn to the fact that the absolute maximum values of the derivative are associated to transitions between photoconversion units with greater differential quantum efficiency. From this representation a new magnitude called can be defined as the absolute difference

dISCሺlሻ

At this point it is very easy to conclude that, the smaller the spot size (focused laser beam), the higher value. Then, the representation of according to the focal lens position, x, must result in a Focal-curve showing a peak distribution (Figure 3B). In it, the optimum focusing

The determination of the xf position from the Focal-curve can be accomplished by numerical or algebraic methods. In both cases, several artifacts that habitually appear in the Focalcurve obtained as noise, asymmetric contour or multipeaks must be minimized. To diminish the associated noise to each scan point of the Focal-curve, the applying of an accumulation method is the more appropriated way, either to individual points or to full scans. However, the other two artifacts do not show a clear dependence on known procedures. Normally, discerned or undiscerned multilevel photoactive structures can lead to obtain multipeaks and asymmetric contours, but other several circumstances can be cause of them. No particular dependence of these artifacts with the experimental methodology (EM1 or EM2) or with the derivative analysis system has been observed. To apply the numerical method, it

dl <sup>ቁ</sup> -min <sup>ቀ</sup>

dISCሺlሻ

dl <sup>ቁ</sup>. (5)

dl is constant, then the derivative can be easily obtained as the dISC.

**3.2 Focal-curve: Derivative analysis** 

the value versus positions of the focal lens.

between the maximum and minimum:

**3.3 Treatment of the Focal-curve** 

Δ=Δ+-Δ-

=max ቀ

position, xf, corresponds to that one in which the value of is the maximum.

Fig. 2. (A) ISC-curve obtained after performing a linear scan along a l superficial coordinate on a Si(MC) solar cell and through a current collector. (B) ISC-curve generated at different positions of the focal lens along X-axis.

falls on the high efficiency photoactive surface (zone 5). When the laser is not perfectly focused, the spot size diameter on the surface is larger than w0 and the same scan through the metallic collector generates an ISC-curve where signal measured at each position is a mean value of a wide zone. This generates a softer transition between regions with abrupt changes of their quantum efficiencies. In other words, the smaller the spot size, the more abrupt the ISC transition between zones with different superficial photoactivity due to the different photoconversion units are better detected. Figure 2B shows the aforementioned variations of the ISC-curve according to the focal lens position. The ISC-curve in the center of the figure (numbered as 3) corresponds to that one appearing in Figure 2A, that is, the curve generated when the focal lens is in the optimum focusing position, i.e. the smallest spot size.

#### **3.1 Scan methodologies**

In order to obtain a data set with information about the optimum focusing position two experimental methodologies can be used. The first one, so called EM1, involves performing successive linear scans along a l coordinate on the photoactive surface, from different xf focal lens positions. This methodology will lead us to an EM1(Il, xf) matrix, whose graphic representation by scan vectors is similar than the one shown in Figure 3B. The second methodology, called EM2, is a particular case of the first one and involves synchronizing the displacement along the l coordinate with the focal lens displacement along the x coordinate. Then, only a vector data set is obtained and it is equivalent to the main diagonal of the aforementioned data EM1(Il, xf) matrix, so a substantial reduction in the number of experimental points is achieved. In this case, the evaluation of the EM2(xf) data vector is carried out by defining several data subsets of n points of length, ranging from the first point to the total number of points minus n. So, to analyze the previously defined data set, the numerical analysis using derivative function has been used. The purpose is to generate a new data set with a singular point associated to the optimum focusing position. This new data set is named Focal-curve. With this aim, the ISC-curve data set properties must be numerically evaluated.

#### **3.2 Focal-curve: Derivative analysis**

72 Solar Cells – Silicon Wafer-Based Technologies

Fig. 2. (A) ISC-curve obtained after performing a linear scan along a l superficial coordinate on a Si(MC) solar cell and through a current collector. (B) ISC-curve generated at different

falls on the high efficiency photoactive surface (zone 5). When the laser is not perfectly focused, the spot size diameter on the surface is larger than w0 and the same scan through the metallic collector generates an ISC-curve where signal measured at each position is a mean value of a wide zone. This generates a softer transition between regions with abrupt changes of their quantum efficiencies. In other words, the smaller the spot size, the more abrupt the ISC transition between zones with different superficial photoactivity due to the different photoconversion units are better detected. Figure 2B shows the aforementioned variations of the ISC-curve according to the focal lens position. The ISC-curve in the center of the figure (numbered as 3) corresponds to that one appearing in Figure 2A, that is, the curve generated when the focal lens is in the optimum focusing position, i.e. the smallest

In order to obtain a data set with information about the optimum focusing position two experimental methodologies can be used. The first one, so called EM1, involves performing successive linear scans along a l coordinate on the photoactive surface, from different xf focal lens positions. This methodology will lead us to an EM1(Il, xf) matrix, whose graphic representation by scan vectors is similar than the one shown in Figure 3B. The second methodology, called EM2, is a particular case of the first one and involves synchronizing the displacement along the l coordinate with the focal lens displacement along the x coordinate. Then, only a vector data set is obtained and it is equivalent to the main diagonal of the aforementioned data EM1(Il, xf) matrix, so a substantial reduction in the number of experimental points is achieved. In this case, the evaluation of the EM2(xf) data vector is carried out by defining several data subsets of n points of length, ranging from the first point to the total number of points minus n. So, to analyze the previously defined data set, the numerical analysis using derivative function has been used. The purpose is to generate a new data set with a singular point associated to the optimum focusing position. This new data set is named Focal-curve. With this aim, the ISC-curve data set properties must be

positions of the focal lens along X-axis.

spot size.

**3.1 Scan methodologies** 

numerically evaluated.

The transition slope between points with different quantum efficiency is defined as the values taken by the dISC/dl derivative, which is related to the laser beam size. As it has been aforementioned, the smaller the spot size, the more abrupt the ISC transition between points with a different superficial photoactivity and the larger the absolute value of dISC/dl. If the dl is constant, then the derivative can be easily obtained as the dISC.

Fig. 3. (A) Numerical derivative of the ISC-curve shown in Figure 2A. (B) Representation of the value versus positions of the focal lens.

Figure 3A shows the derivative of the ISC-curve previously shown in Figure 2A in a way that makes possible to recognize the above-mentioned one to five zones. Attention should be drawn to the fact that the absolute maximum values of the derivative are associated to transitions between photoconversion units with greater differential quantum efficiency. From this representation a new magnitude called can be defined as the absolute difference between the maximum and minimum:

$$
\Delta \equiv \Delta\_{+} \text{-} \Delta\_{\text{\textdegree}} \equiv \max \left( \frac{\text{dl}\_{\text{SC}}(\text{l})}{\text{dl}} \right) \cdot \text{min} \left( \frac{\text{dl}\_{\text{SC}}(\text{l})}{\text{dl}} \right) . \tag{5}
$$

At this point it is very easy to conclude that, the smaller the spot size (focused laser beam), the higher value. Then, the representation of according to the focal lens position, x, must result in a Focal-curve showing a peak distribution (Figure 3B). In it, the optimum focusing position, xf, corresponds to that one in which the value of is the maximum.

#### **3.3 Treatment of the Focal-curve**

The determination of the xf position from the Focal-curve can be accomplished by numerical or algebraic methods. In both cases, several artifacts that habitually appear in the Focalcurve obtained as noise, asymmetric contour or multipeaks must be minimized. To diminish the associated noise to each scan point of the Focal-curve, the applying of an accumulation method is the more appropriated way, either to individual points or to full scans. However, the other two artifacts do not show a clear dependence on known procedures. Normally, discerned or undiscerned multilevel photoactive structures can lead to obtain multipeaks and asymmetric contours, but other several circumstances can be cause of them. No particular dependence of these artifacts with the experimental methodology (EM1 or EM2) or with the derivative analysis system has been observed. To apply the numerical method, it

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 75

where h is the Planck constant, c the speed of light, k the Boltzmann constant, T the absolute

With the lasers used in our system, which are described above, in section 2, using Planck's law and setting the initial irradiation power value, the power of the red laser (632.8 nm), as P0, the irradiation power for the other two lasers is calculated to be 1.12P0 for both casually. By means of this ratio, the relative powers of the three wavelengths are close to the profile of solar radiation. These three wavelengths are placed in the range of the maximum irradiance in the solar spectrum or black body emission curve, i.e., around the maximum of the energy

The main features for obtaining representative quantum efficiency maps of a photoactive surface are related with the geometry of the system and the different positioning parameters of the optical elements of the system. Furthermore, with the trichromatic system shown in this chapter, it is necessary to take into account the relative irradiation power of the lasers and the unification of the three optical pathways. Thus, the most relevant aspects in the

1. The angle of incidence of the laser must be normal to the photoactive surface in order to minimize the size of the spot. The incidence of the laser beam used perpendicular to the surface can be assured by observing the reflected radiation, the trajectory of which will only coincide with the incident radiation if it is perpendicular to the photoactive surface. Furthermore, this is a necessary condition when trying to obtain reflectance maps correlatable with photoefficiency maps, in accordance with the optical geometry used. 2. The distance between the focal lens and the point of incidence on the surface must remain constant, independent of the laser incidence coordinates over the surface which is derived from the y-z movement of the motorized platform. Thanks to the system being completely automated and controlled by specially designed software, the

3. With the beam selector mirror, the optical trajectory of each of the lasers used must coincide completely with the others, and furthermore, all of them must come into contact on the photoactive surface with the right power to generate radiation

The bidimensional scans of the surface under study are performed in sequence; first, opening the shutter of the active laser and positioning the mirror; then, setting the focusing lens at the right distance according to the laser to be used; and finally, establishing the irradiation power for each of the lasers. Under these conditions, using the photocurrent values generated in each scan, it is possible to obtain the quantum efficiency values for the device. Thus, using the spectral response, it is possible to obtain a matrix of the external

ሾEQEሺλሻሿij=ሾSRሺλሻሿij

where EQE() is the external quantum efficiency, SR() the spectral response, e the elementary charge, h the Planck constant, c the rate of the light, and the wavelength.

hc eλ

, (8)

1

expሺhcΤ ሻ <sup>λ</sup>kT -1, (7)

Meሺλሻ<sup>=</sup> <sup>8</sup>πhc λ5

temperature, and the wavelength.

system are considered in the following way:

focusing positions are stored and saved for later use.

resembling that of the black hole, as mentioned earlier.

quantum efficiency of the scans performed, following the expression

emission.

**4.1 Working procedure** 

is enough to determine the focal lens position in which the peak distribution shows a maximum, and to associate that value with xf. This is a very quickly methodology but shows significant errors and limitations due to the aforementioned artifacts. The maximum obtainable resolution with this method depends on the incremental value used in the focal lens positioning. A resolution improvement in one order of magnitude implies to measure a number of data two greater orders of magnitude. In the other side, the algebraic method involves adjusting a mathematical peak function to the Focal-curve and then determining xf as the x value that maximizing the adjusted mathematical peak function. This methodology makes it possible mathematically to determine the maximum of the adjusted curve with as much precision as it is necessary.

In previous tests carried out by means of computerized simulation techniques it was demonstrated that a Pseudo-Voigt type 2 function is one of the peak functions that allows a better adjustment (Poce-Fatou et al., 2002; Fernández-Lorenzo et al., 2006). This function is a linear combination of the Gauss and the Lorentz distribution functions, i.e.

$$\mathbf{V}\text{(\(\infty\)=V\_0+V\_m)}\text{sf}\left[\text{sf}\frac{2}{\text{n}\left(\text{x\,\,}\right)^2+\text{w}\_{\text{L}}^2}+\text{(1-sf)}\frac{\sqrt{4\text{ln}2}}{\sqrt{\text{m}\,\text{w}\_{\text{G}}}}\text{er}^{\{4\text{ln}2/\text{w}\_{\text{G}}^2\}\text{(\(\infty\)}}\right],\tag{6}$$

where V(x) represents the values of , L or according to the position of the focal lens, wL and wG are the respectively FWHM (Full Width at Half Maximum) values of the Lorentzian and Gaussian functions, Vm is the peak amplitude or height, sf is a proportionality factor, V0 is the displacement constant of the dependent variable and xf is the curve maximum position. With this focusing system and algorithm, a spot size of 7.1 x 10-12 m2 is easily obtained.

#### **4. LBIC under trichromatic laser radiation: approximation to the solar radiation**

Using lasers as the irradiation source is the best solution in LBIC technique as they have a highly monochromatic emission with a quasi parallel beam with minimal divergence and Gaussian power distribution in TEM00 mode. These characteristics allow them to be focalized with maximum efficiency. However, using monochromatic radiation beams means that the maps obtained are only representative of the photoefficiency at the wavelength of this type of radiation, and it is not possible to obtain measurements of how the behavior of the system is different at other wavelengths. So, studying the same area with a red-greenblue trichromatic model makes it possible to create characteristic maps associated with each wavelength. Combining them in a suitable way, with irradiation power ratios regulated following a standard emission such as Planck's law or solar emission, makes it possible to approximate to the behavior of the photovoltaic device when it is irradiated with polychromatic radiation, for example, solar emissions. In the literature, it is possible to find a work where LBIC images under solar radiation are obtained (Vorster and van Dyk, 2007). This system uses, as irradiation source, a divergent lamp by which the spot diameter obtained in the focus is about 140 m and a low spatial resolution can be obtained. So, the methodology that we describe here is a first approach for obtaining high resolution LBIC images that approximate the behavior of a photoactive surface under solar radiation.

The first approach is to assume that the solar emission was blackbodylike with a temperature of 5780 K, as we can assume from literature data (Lipinski et al, 2006). The energy distribution emitted by a black body can be expressed using the Planck's equation

$$\text{Me(\lambda)} = \frac{8 \text{nhc}}{\lambda^5} \frac{1}{\exp(\text{hc/\lambda kT}) \cdot 1},\tag{7}$$

where h is the Planck constant, c the speed of light, k the Boltzmann constant, T the absolute temperature, and the wavelength.

With the lasers used in our system, which are described above, in section 2, using Planck's law and setting the initial irradiation power value, the power of the red laser (632.8 nm), as P0, the irradiation power for the other two lasers is calculated to be 1.12P0 for both casually. By means of this ratio, the relative powers of the three wavelengths are close to the profile of solar radiation. These three wavelengths are placed in the range of the maximum irradiance in the solar spectrum or black body emission curve, i.e., around the maximum of the energy emission.

#### **4.1 Working procedure**

74 Solar Cells – Silicon Wafer-Based Technologies

is enough to determine the focal lens position in which the peak distribution shows a maximum, and to associate that value with xf. This is a very quickly methodology but shows significant errors and limitations due to the aforementioned artifacts. The maximum obtainable resolution with this method depends on the incremental value used in the focal lens positioning. A resolution improvement in one order of magnitude implies to measure a number of data two greater orders of magnitude. In the other side, the algebraic method involves adjusting a mathematical peak function to the Focal-curve and then determining xf as the x value that maximizing the adjusted mathematical peak function. This methodology makes it possible mathematically to determine the maximum of the adjusted curve with as

In previous tests carried out by means of computerized simulation techniques it was demonstrated that a Pseudo-Voigt type 2 function is one of the peak functions that allows a better adjustment (Poce-Fatou et al., 2002; Fernández-Lorenzo et al., 2006). This function is a

> <sup>2</sup> <sup>+</sup>�1-sf� <sup>√</sup>4ln2 √πwG

where V(x) represents the values of , L or according to the position of the focal lens, wL and wG are the respectively FWHM (Full Width at Half Maximum) values of the Lorentzian and Gaussian functions, Vm is the peak amplitude or height, sf is a proportionality factor, V0 is the displacement constant of the dependent variable and xf is the curve maximum position. With this focusing system and algorithm, a spot size of 7.1 x 10-12 m2 is easily obtained.

Using lasers as the irradiation source is the best solution in LBIC technique as they have a highly monochromatic emission with a quasi parallel beam with minimal divergence and Gaussian power distribution in TEM00 mode. These characteristics allow them to be focalized with maximum efficiency. However, using monochromatic radiation beams means that the maps obtained are only representative of the photoefficiency at the wavelength of this type of radiation, and it is not possible to obtain measurements of how the behavior of the system is different at other wavelengths. So, studying the same area with a red-greenblue trichromatic model makes it possible to create characteristic maps associated with each wavelength. Combining them in a suitable way, with irradiation power ratios regulated following a standard emission such as Planck's law or solar emission, makes it possible to approximate to the behavior of the photovoltaic device when it is irradiated with polychromatic radiation, for example, solar emissions. In the literature, it is possible to find a work where LBIC images under solar radiation are obtained (Vorster and van Dyk, 2007). This system uses, as irradiation source, a divergent lamp by which the spot diameter obtained in the focus is about 140 m and a low spatial resolution can be obtained. So, the methodology that we describe here is a first approach for obtaining high resolution LBIC

e-�4ln2 wG

<sup>2</sup> <sup>⁄</sup> ��x-xf� 2

�, (6)

linear combination of the Gauss and the Lorentz distribution functions, i.e.

wL 4�x-xf� 2 +wL

**4. LBIC under trichromatic laser radiation: approximation to the solar** 

images that approximate the behavior of a photoactive surface under solar radiation.

The first approach is to assume that the solar emission was blackbodylike with a temperature of 5780 K, as we can assume from literature data (Lipinski et al, 2006). The energy distribution emitted by a black body can be expressed using the Planck's equation

π

much precision as it is necessary.

**radiation** 

<sup>V</sup>�x�=V0+Vm �sf <sup>2</sup>

The main features for obtaining representative quantum efficiency maps of a photoactive surface are related with the geometry of the system and the different positioning parameters of the optical elements of the system. Furthermore, with the trichromatic system shown in this chapter, it is necessary to take into account the relative irradiation power of the lasers and the unification of the three optical pathways. Thus, the most relevant aspects in the system are considered in the following way:


The bidimensional scans of the surface under study are performed in sequence; first, opening the shutter of the active laser and positioning the mirror; then, setting the focusing lens at the right distance according to the laser to be used; and finally, establishing the irradiation power for each of the lasers. Under these conditions, using the photocurrent values generated in each scan, it is possible to obtain the quantum efficiency values for the device. Thus, using the spectral response, it is possible to obtain a matrix of the external quantum efficiency of the scans performed, following the expression

$$[\text{EQE}(\lambda)]\_{\text{ij}} = [\text{SR}(\lambda)]\_{\text{ij}} \frac{\text{hc}}{\text{eV}} \tag{8}$$

where EQE() is the external quantum efficiency, SR() the spectral response, e the elementary charge, h the Planck constant, c the rate of the light, and the wavelength.

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 77

Due to the existence of two distinct phases, an electron conducting region and a liquid electrolyte, the electrical response of the device under illumination is not immediate. In contrast, it takes some time (in the order of seconds) before it reaches and keeps its maximum value. This is the socalled characteristic response time. Furthermore, once the irradiation is interrupted, the electrical signal does not disappear instantaneously, but it decays smoothly. This decay time is related to the electron lifetime in the semiconductor (Fredin et al., 2007) and depends on both the trap-limited diffusion transport in the semiconductor (Peter, 2007) and the specific kinetics of the electron transfer reaction in the liquid phase (Gregg, 2004). The decay features in this case can be viewed as a charge*/*discharge process typical of a capacitor. Rise and decay times should be taken into

account when employing techniques to measure quantum yields in DSSCs.

Fig. 4. A scheme of the structure and components of the dye-sensitized solar cells.

difficult task if the standard procedure is used.

The LBIC technique has not been used commonly to characterize DSSCs due to the blurring effect of the slow response of the device to optical excitation and subsequent decay. Hence, to get good spatial resolution the laser beam has to be focused on a very narrow spot. This produces local heating and degradation of the dye*/*oxide system. This problem can be surmounted by using filters that reduce the light intensity. However, this strategy also reduces the photoconversion signal, which must be amplified to get significant results. Furthermore, as mentioned above, excitation of a single spot requires stopping the scan so that the signal is stabilized properly. This increases the chances of degradation and the time length of the experiment. Hence, a time of 5 s for the rise and decay processes (typical in many DSSCs) implies that to obtain the LBIC signal, we need to (a) irradiate the spot, (b) wait 5 s until the maximum value of the signal (either photocurrent or photovoltage) is achieved, (c) stop the illumination and wait another 5 s until the signal reaches its minimum value and (d) move forward to the next spot and repeat the process. For example, using this procedure we would need 29 days to scan a 500 × 500 μm2 cell with 1 μm resolution. In summary, in contrast to silicon solar cells, to obtain clear LBIC images for DSSCs is a

Many papers can be found in the literature regarding the response time in DSSCs as a function of the composition and structure of the semiconductor (Cao et al., 1996) and the kinetics of the recombination reaction from open circuit voltage decays (Walker et al., 2006). In this chapter we show an experimental view of the rise and decay signal in DSSCs and the empirical equations that describe their time dependence. Starting from the kinetic constants derived from the experiments, we have devised a mathematical algorithm that makes it possible to correct the photocurrent data so that reliable quantum yields can be extracted.

Taking the definition of the spectral response to be the relationship between the photocurrent generated and the irradiation power, the external quantum efficiency is

$$[\text{EQE}(\lambda)]\_{\text{ij}} = \frac{\text{Ils} \cdot \text{O} \lambda \text{ l}\_{\text{ij}}}{\text{P}\_{\text{in}}(\lambda)} \frac{\text{hc}}{\text{e} \lambda'} \tag{9}$$

where ISC() is the short-circuit current generated and Pin() the irradiation power. Likewise, it is also possible to obtain internal quantum efficiency matrixes following

$$[\text{IQE}(\lambda)]\_{\vec{\eta}} = \frac{[\text{EQE}(\lambda)]\_{\vec{\eta}}}{1 \cdot [\text{R}(\lambda)]\_{\vec{\eta}}} = \frac{[\text{I}\_{\text{SC}}(\lambda)]\_{\vec{\eta}}}{\text{P}\_{\text{in}}(\lambda)} \frac{\text{hc}}{\text{e}\lambda} \frac{1}{1 \cdot [\text{R}(\lambda)]\_{\vec{\eta}}} \tag{10}$$

where IQE() is the internal quantum efficiency and R() is the reflectance.

After calculating the three matrixes of quantum efficiency (internal or external), a colour image can be created reflecting the behaviour of the device under irradiation with the three wavelengths used. To do this, an image analysis program is used which adapts each value of the matrixes obtained to a common scale between 0 and 255 for the three colours red, green and blue; then the three matrixes are combined to obtain a colour image. This image provides information about the behaviour of the material under irradiation with the three wavelengths used.

Furthermore, using the data matrixes obtained, micrometric quantum efficiency values can be obtained which are approximate to those which would be obtained under solar irradiation, as the irradiation power values were set applying Planck's law. Mathematically, according to this approximation, the external quantum efficiency can be expressed as

$$\left[\left(\text{EQE}\right)\_{\text{i}}\right]\_{\text{solar}} = \frac{\text{hc}}{\text{e}} \left[\frac{\left(\text{I}\_{\text{SC}}\right)\_{\text{i}}\right]\_{\text{632.8am}} + \left[\left(\text{I}\_{\text{SC}}\right)\_{\text{i}}\right]\_{\text{532am}} + \left[\left(\text{I}\_{\text{SC}}\right)\_{\text{i}}\right]\_{\text{473am}}}{\left[\text{P}\_{\text{in}}\lambda\right]\_{\text{632.8am}} + \left[\text{P}\_{\text{in}}\lambda\right]\_{\text{532am}} + \left[\text{P}\_{\text{in}}\lambda\right]\_{\text{473am}}}\right] \tag{11}$$

where all the variables have been defined above, and they are expressed for the wavelengths of the laser beam used in each of the scans.

So, the method described in this work investigates the photoresponse of the devices to study at three specific wavelengths. The relative flux distribution of the three wavelengths attempt to match the corresponding wavelengths in the solar spectrum. Obviously, this methodology is an approximation because we attempt to simulate a multispectral radiation as the solar emission with only three specific wavelengths. So, the results obtained will be an approximation to the optoelectrical behavior of the devices under solar illumination.

#### **5. Algorithm for improving photoresponse of dye-sensitized solar cells**

Dye-sensitized solar cell (DSSC) is an interesting alternative to photovoltaic solar cells based on solid-state semiconductor junctions due to the remarkable low cost of its basic materials and simplicity of fabrication. DSSC technology enables the flexible combination of different substrates (PET, glass), semiconducting oxides, redox shuttles, solvents and dyes (O'Regan and Grätzel, 1991). When a DSSC is illuminated in the range in which the dye absorbs light, the dye molecules are excited to upper electronic states, from which they inject electrons into the conduction band of the semiconductor. The dye molecules become oxidized, whereas the photogenerated electrons diffuse through the semiconductor nanostructure until they are collected by the front electrode. The electrolyte with the redox pair plays the role of a hole conductor, regenerating the oxidized dye molecules and transporting electron acceptors towards the counter electrode. A scheme of a typical DSSC is shown in Figure 4.

Taking the definition of the spectral response to be the relationship between the photocurrent generated and the irradiation power, the external quantum efficiency is <sup>ሾ</sup>EQEሺλሻሿij= <sup>ሾ</sup>ISCሺλሻሿij

where ISC() is the short-circuit current generated and Pin() the irradiation power. Likewise,

After calculating the three matrixes of quantum efficiency (internal or external), a colour image can be created reflecting the behaviour of the device under irradiation with the three wavelengths used. To do this, an image analysis program is used which adapts each value of the matrixes obtained to a common scale between 0 and 255 for the three colours red, green and blue; then the three matrixes are combined to obtain a colour image. This image provides information about the behaviour of the material under irradiation with the three

Furthermore, using the data matrixes obtained, micrometric quantum efficiency values can be obtained which are approximate to those which would be obtained under solar irradiation, as the irradiation power values were set applying Planck's law. Mathematically,

632.8nm+ൣሺISCሻij<sup>൧</sup>

where all the variables have been defined above, and they are expressed for the wavelengths

So, the method described in this work investigates the photoresponse of the devices to study at three specific wavelengths. The relative flux distribution of the three wavelengths attempt to match the corresponding wavelengths in the solar spectrum. Obviously, this methodology is an approximation because we attempt to simulate a multispectral radiation as the solar emission with only three specific wavelengths. So, the results obtained will be an

ሾPinλሿ632.8nm+ሾPinλሿ532nm+ሾPinλሿ473nm

according to this approximation, the external quantum efficiency can be expressed as

approximation to the optoelectrical behavior of the devices under solar illumination.

**5. Algorithm for improving photoresponse of dye-sensitized solar cells** 

Dye-sensitized solar cell (DSSC) is an interesting alternative to photovoltaic solar cells based on solid-state semiconductor junctions due to the remarkable low cost of its basic materials and simplicity of fabrication. DSSC technology enables the flexible combination of different substrates (PET, glass), semiconducting oxides, redox shuttles, solvents and dyes (O'Regan and Grätzel, 1991). When a DSSC is illuminated in the range in which the dye absorbs light, the dye molecules are excited to upper electronic states, from which they inject electrons into the conduction band of the semiconductor. The dye molecules become oxidized, whereas the photogenerated electrons diffuse through the semiconductor nanostructure until they are collected by the front electrode. The electrolyte with the redox pair plays the role of a hole conductor, regenerating the oxidized dye molecules and transporting electron acceptors towards the counter electrode. A scheme of a typical DSSC is shown in Figure 4.

it is also possible to obtain internal quantum efficiency matrixes following

where IQE() is the internal quantum efficiency and R() is the reflectance.

1-ሾRሺλሻሿij

<sup>ሾ</sup>IQEሺλሻሿij= <sup>ሾ</sup>EQEሺλሻሿij

wavelengths used.

ൣሺEQEሻij൧

of the laser beam used in each of the scans.

solar<sup>=</sup> hc e ൣሺISCሻij൧ Pinሺλሻ

<sup>=</sup> <sup>ሾ</sup>ISCሺλሻሿij Pinሺλሻ

hc eλ

> hc eλ

1 1-ሾRሺλሻሿij

532nm+ൣሺISCሻij<sup>൧</sup>

473nm

, (9)

, (10)

൨, (11)

Due to the existence of two distinct phases, an electron conducting region and a liquid electrolyte, the electrical response of the device under illumination is not immediate. In contrast, it takes some time (in the order of seconds) before it reaches and keeps its maximum value. This is the socalled characteristic response time. Furthermore, once the irradiation is interrupted, the electrical signal does not disappear instantaneously, but it decays smoothly. This decay time is related to the electron lifetime in the semiconductor (Fredin et al., 2007) and depends on both the trap-limited diffusion transport in the semiconductor (Peter, 2007) and the specific kinetics of the electron transfer reaction in the liquid phase (Gregg, 2004). The decay features in this case can be viewed as a charge*/*discharge process typical of a capacitor. Rise and decay times should be taken into account when employing techniques to measure quantum yields in DSSCs.

Fig. 4. A scheme of the structure and components of the dye-sensitized solar cells.

The LBIC technique has not been used commonly to characterize DSSCs due to the blurring effect of the slow response of the device to optical excitation and subsequent decay. Hence, to get good spatial resolution the laser beam has to be focused on a very narrow spot. This produces local heating and degradation of the dye*/*oxide system. This problem can be surmounted by using filters that reduce the light intensity. However, this strategy also reduces the photoconversion signal, which must be amplified to get significant results. Furthermore, as mentioned above, excitation of a single spot requires stopping the scan so that the signal is stabilized properly. This increases the chances of degradation and the time length of the experiment. Hence, a time of 5 s for the rise and decay processes (typical in many DSSCs) implies that to obtain the LBIC signal, we need to (a) irradiate the spot, (b) wait 5 s until the maximum value of the signal (either photocurrent or photovoltage) is achieved, (c) stop the illumination and wait another 5 s until the signal reaches its minimum value and (d) move forward to the next spot and repeat the process. For example, using this procedure we would need 29 days to scan a 500 × 500 μm2 cell with 1 μm resolution. In summary, in contrast to silicon solar cells, to obtain clear LBIC images for DSSCs is a difficult task if the standard procedure is used.

Many papers can be found in the literature regarding the response time in DSSCs as a function of the composition and structure of the semiconductor (Cao et al., 1996) and the kinetics of the recombination reaction from open circuit voltage decays (Walker et al., 2006). In this chapter we show an experimental view of the rise and decay signal in DSSCs and the empirical equations that describe their time dependence. Starting from the kinetic constants derived from the experiments, we have devised a mathematical algorithm that makes it possible to correct the photocurrent data so that reliable quantum yields can be extracted.

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 79

Setting the conditions for performing the scan depends on the cell under study, particularly those conditions related to the dwell time of the laser on each point and the amount of energy received. Among these factors are these following considerations: (a) dimensions of the surface to scan, (b) spatial resolution or the distance between points, (c) irradiation power, and (d) dwell time for each point. For the dwell time, the total exposure time must be considered, even when measurements for each point are taken more than once to average the results. From these data the total number of photons affecting each irradiation point can

With the irradiation conditions set, the time-evolution curves for the charge/discharge processes of the cell under study are then developed. To do this, one point of the cell is irradiated with the same amount of photonic energy to be used during the scan. Using a continuous emission laser, irradiation conditions can be established by using a set of neutral density filters and a shutter, such as, for example, the body of a reflex photographic camera. During the selected pulse time, until the system stabilizes, the evolution of the photosignal is recorded. The data obtained for the discharge process are adjusted to a decreasing

ISC=Ir+I0 · e-ASCt

Ilim=I0

ASCC ASCD

Furthermore, in most cases, but not always, it is observed experimentally that charge process is faster than the discharge process so the charge process has less influence. In Figure 6A, the charge process lasts about 7 s, while the discharge process takes approximately 16 s. Correcting the charge process effect in the algorithm involves a simple change of scale depending on the response time, calculated with the data of the timeevolution curves and the dwell time. Thus, the correction derived from the charge process, involving multiplying the signal by the correction factor, does not result in a substantial improvement in the quality of the LBIC images. However, it is fundamental for calculating the cell's quantum efficiency. Consequently, the algorithm is based on correcting the contributions of the previously irradiated points, which depend on the discharge process, and correcting the signal level due to the charge process. The time-evolution curves are obtained with the laser beam focalized on one point of the photoactive surface, accepting

where ISC is the short circuit photocurrent, Ir is the residual current remaining in the system, I0 is the short circuit steady-state photocurrent, ASC is the rate constant of the discharge process, and t is the time. Using this equation and with specifically designed software, simulations of the photogenerated signal have been developed, which prove the initial hypotheses for the application of this methodology. It is seen that the smaller the rate constant the greater the influence of the discharge process in the LBIC image. Also, it is also concluded that the limit intensity (Ilim) that the signal of a cell can reach depends on the relationship between the velocity constants of the charge (ASCC)/discharge (ASCD) process

, (12)

. (13)

be established with their overall total composing the LBIC image.

**5.1.2 Determining the time-evolution curves** 

exponential function following the equation

and the short circuit steady-state photocurrent, expressed as

**5.1.1 Setting irradiation conditions** 

So, in this chapter, we show a methodology for evaluating and correcting the effects of the charge/discharge processes of DSSCs, enabling clear, high-resolution LBIC images to be obtained without having to increase the scanning time. The methodology is based on a simple, prior evaluation of the time evolution of the photosignal for the charge/discharge processes, before establishing a mathematical algorithm applied point by point over the signal of the cell registered during the LBIC scan, correcting the contribution of previously illuminated points to subsequent ones.

Fig. 5. (A) Time-evolution curve of the discharge process for a cell irradiated with a 532 nm laser, a power of 350 W, and different exposure times to the radiation. (B) Comparison of two time evolution curve of the discharge process in which the photonic energy is identical but has been generated with different irradiation power and exposure time.

#### **5.1 Methodology description**

The methodology developed is based on the evaluation of time-evolution curves of the response times for charge/ discharge processes. Based on this, an algorithm corrects the contributions of previous points to the signal of the active one. To perform an LBIC scan within a reasonable time requires dwell times in the order of milliseconds at each point of the scan. This means the system acts as if it were subjected to a set of light pulses, one for each point of the scan. The response of the system depends on the amount of energy received in each pulse. Figure 5A shows time-evolution curves of the photosignal generated by a DSSC at different pulse times using a 532 nm laser and irradiation power of 350 W. The decay curve is not the same in all cases but rather it depends on the exposure time of the irradiated point. Figure 5B shows two time-evolution curves for the photosignal, one with a 1/8 s pulse and an irradiation power of 500 W and the other a 1/2 s pulse with an irradiation power of 125 W so the amount of energy in both cases is constant. This graph shows that the cell behaves the same in both cases, implying that the response during the discharge process of each irradiated point depends on the light energy received. That is, the product of the irradiation power and exposure time. Thus, it is necessary to set the irradiation conditions to be used for performing the scan with the LBIC system in order to obtain the charge/discharge curves of the cell under study under the same conditions.

#### **5.1.1 Setting irradiation conditions**

78 Solar Cells – Silicon Wafer-Based Technologies

So, in this chapter, we show a methodology for evaluating and correcting the effects of the charge/discharge processes of DSSCs, enabling clear, high-resolution LBIC images to be obtained without having to increase the scanning time. The methodology is based on a simple, prior evaluation of the time evolution of the photosignal for the charge/discharge processes, before establishing a mathematical algorithm applied point by point over the signal of the cell registered during the LBIC scan, correcting the contribution of previously

Fig. 5. (A) Time-evolution curve of the discharge process for a cell irradiated with a 532 nm laser, a power of 350 W, and different exposure times to the radiation. (B) Comparison of two time evolution curve of the discharge process in which the photonic energy is identical

The methodology developed is based on the evaluation of time-evolution curves of the response times for charge/ discharge processes. Based on this, an algorithm corrects the contributions of previous points to the signal of the active one. To perform an LBIC scan within a reasonable time requires dwell times in the order of milliseconds at each point of the scan. This means the system acts as if it were subjected to a set of light pulses, one for each point of the scan. The response of the system depends on the amount of energy received in each pulse. Figure 5A shows time-evolution curves of the photosignal generated by a DSSC at different pulse times using a 532 nm laser and irradiation power of 350 W. The decay curve is not the same in all cases but rather it depends on the exposure time of the irradiated point. Figure 5B shows two time-evolution curves for the photosignal, one with a 1/8 s pulse and an irradiation power of 500 W and the other a 1/2 s pulse with an irradiation power of 125 W so the amount of energy in both cases is constant. This graph shows that the cell behaves the same in both cases, implying that the response during the discharge process of each irradiated point depends on the light energy received. That is, the product of the irradiation power and exposure time. Thus, it is necessary to set the irradiation conditions to be used for performing the scan with the LBIC system in order to obtain the charge/discharge curves of the cell under study under the same conditions.

but has been generated with different irradiation power and exposure time.

illuminated points to subsequent ones.

**5.1 Methodology description** 

Setting the conditions for performing the scan depends on the cell under study, particularly those conditions related to the dwell time of the laser on each point and the amount of energy received. Among these factors are these following considerations: (a) dimensions of the surface to scan, (b) spatial resolution or the distance between points, (c) irradiation power, and (d) dwell time for each point. For the dwell time, the total exposure time must be considered, even when measurements for each point are taken more than once to average the results. From these data the total number of photons affecting each irradiation point can be established with their overall total composing the LBIC image.

#### **5.1.2 Determining the time-evolution curves**

With the irradiation conditions set, the time-evolution curves for the charge/discharge processes of the cell under study are then developed. To do this, one point of the cell is irradiated with the same amount of photonic energy to be used during the scan. Using a continuous emission laser, irradiation conditions can be established by using a set of neutral density filters and a shutter, such as, for example, the body of a reflex photographic camera. During the selected pulse time, until the system stabilizes, the evolution of the photosignal is recorded. The data obtained for the discharge process are adjusted to a decreasing exponential function following the equation

$$\mathbf{I}\_{\rm SC} = \mathbf{I}\_{\rm r} + \mathbf{I}\_0 \cdot \mathbf{e}^{\rm Asct} \,, \tag{12}$$

where ISC is the short circuit photocurrent, Ir is the residual current remaining in the system, I0 is the short circuit steady-state photocurrent, ASC is the rate constant of the discharge process, and t is the time. Using this equation and with specifically designed software, simulations of the photogenerated signal have been developed, which prove the initial hypotheses for the application of this methodology. It is seen that the smaller the rate constant the greater the influence of the discharge process in the LBIC image. Also, it is also concluded that the limit intensity (Ilim) that the signal of a cell can reach depends on the relationship between the velocity constants of the charge (ASCC)/discharge (ASCD) process and the short circuit steady-state photocurrent, expressed as

$$\mathbf{I}\_{\rm lim} = \mathbf{I}\_0 \frac{\mathbf{A}\_{\rm SCC}}{\mathbf{A}\_{\rm SCD}}.\tag{13}$$

Furthermore, in most cases, but not always, it is observed experimentally that charge process is faster than the discharge process so the charge process has less influence. In Figure 6A, the charge process lasts about 7 s, while the discharge process takes approximately 16 s. Correcting the charge process effect in the algorithm involves a simple change of scale depending on the response time, calculated with the data of the timeevolution curves and the dwell time. Thus, the correction derived from the charge process, involving multiplying the signal by the correction factor, does not result in a substantial improvement in the quality of the LBIC images. However, it is fundamental for calculating the cell's quantum efficiency. Consequently, the algorithm is based on correcting the contributions of the previously irradiated points, which depend on the discharge process, and correcting the signal level due to the charge process. The time-evolution curves are obtained with the laser beam focalized on one point of the photoactive surface, accepting

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 81

In order to test the system described here, LBIC scans were performed on various samples. We show results obtained using three different kind of solar cells such as a polycrystalline silicon solar cell, an amorphous thin film silicon solar cell, and a dye-sensitized solar cell.

We include the results obtained with a polycrystalline silicon solar cell manufactured by ISOFOTON, S.A. Different studies were carried out on this device with differing degrees of

Fig. 7. LBIC images of the three scans performed and the image created by combining these. The data used to construct these images are of EQE on a relative scale for each image.

First, LBIC scans were carried out with the three lasers mentioned above on a 1x1 cm2 area of the surface of the cell with a resolution of 20 m. The irradiation power for the red laser was 5 W, and 5.6 W for the green and blue ones. These values comply with the emission of a blackbody at 5780 K, in accordance with Planck's law (equation (7)). Figure 7 shows the

resolution. Groups of the scans performed with the three lasers are shown below.

**6. Applications** 

**6.1 Polycrystalline silicon solar cell** 

that no dependency exists with regards to the position of this point since the discharge process can be associated with the diffusion processes occurring inside the cell.

Fig. 6. (A)Representation of experimental data of the charge and discharge process of a cell irradiated with a power of 292 W, and a comparison with a theoretical instantaneous response. (B) Simulation of the evolution of the irradiated sports showing how the photovoltaic response is influenced by the previously excited points.

#### **5.1.3 Correcting the LBIC image**

Now, the correction of the discharge process will be describe. From the equation obtained for the cell, the experimental values obtained while taking the LBIC image are corrected, thus eliminating the contribution of the previously irradiated points to the photosignal. The number of points of the scan to be considered as contributing to the signal of one given point is a characteristic of the cell under study and depends on the characteristic parameters of the discharge curve, as is shown in Figure 6B. To evaluate the number of points, the experimental values of the time evolution of the discharge process are adjusted to equation (12), and the time necessary for total discharge is taken as being from when the signal is below 1% of the maximum registered value of the photosignal for that cell in those measuring conditions. With this time, and the dwell time, it is possible to obtain the number of points that have to be considered as contributing to the signal measured and whose contribution has to be corrected to apply the correction to the original image. The extent of this contribution is established using equation (12) and the adjustment parameters obtained, depending on the time passed since a point has been irradiated.

Thus, the real photocurrent signal generated by the irradiated point of the cell is defined as the difference between the photocurrent measured (Im) and the contribution of the previously irradiated points. This is expressed mathematically using the equation

$$\mathbf{I}\_{\rm SC} = \mathbf{I}\_{\rm m} \cdot \sum\_{i=1}^{i=1} \left( \mathbf{I}\_{\rm r} + \mathbf{I}\_{0} \cdot \mathbf{e}^{\cdot \cdot \text{As} \cdot \text{it}\_{\rm t}} \right) = \mathbf{I}\_{\rm m} \cdot \mathbf{n} \mathbf{I}\_{\rm r} \cdot \mathbf{I}\_{0} \sum\_{i=1}^{i=1} \mathbf{e}^{\cdot \cdot \text{As} \cdot \text{it}\_{\rm t}},\tag{14}$$

where ISC is the real short circuit photocurrent generated at the active point, Im is the signal measured at that active point during the LBIC scan, n is the number of previously irradiated points to consider, tr is the dwell time; the other variables have been defined above.

### **6. Applications**

80 Solar Cells – Silicon Wafer-Based Technologies

that no dependency exists with regards to the position of this point since the discharge

Fig. 6. (A)Representation of experimental data of the charge and discharge process of a cell irradiated with a power of 292 W, and a comparison with a theoretical instantaneous response. (B) Simulation of the evolution of the irradiated sports showing how the

Now, the correction of the discharge process will be describe. From the equation obtained for the cell, the experimental values obtained while taking the LBIC image are corrected, thus eliminating the contribution of the previously irradiated points to the photosignal. The number of points of the scan to be considered as contributing to the signal of one given point is a characteristic of the cell under study and depends on the characteristic parameters of the discharge curve, as is shown in Figure 6B. To evaluate the number of points, the experimental values of the time evolution of the discharge process are adjusted to equation (12), and the time necessary for total discharge is taken as being from when the signal is below 1% of the maximum registered value of the photosignal for that cell in those measuring conditions. With this time, and the dwell time, it is possible to obtain the number of points that have to be considered as contributing to the signal measured and whose contribution has to be corrected to apply the correction to the original image. The extent of this contribution is established using equation (12) and the adjustment parameters obtained,

Thus, the real photocurrent signal generated by the irradiated point of the cell is defined as the difference between the photocurrent measured (Im) and the contribution of the

where ISC is the real short circuit photocurrent generated at the active point, Im is the signal measured at that active point during the LBIC scan, n is the number of previously irradiated

i=1

i=1 , (14)

previously irradiated points. This is expressed mathematically using the equation

ISC=Im- ∑ �Ir+I0·e-ASCitr� =Im-nIr-I0 ∑ e-ASCitr i=n

points to consider, tr is the dwell time; the other variables have been defined above.

photovoltaic response is influenced by the previously excited points.

depending on the time passed since a point has been irradiated.

i=n

**5.1.3 Correcting the LBIC image** 

process can be associated with the diffusion processes occurring inside the cell.

In order to test the system described here, LBIC scans were performed on various samples. We show results obtained using three different kind of solar cells such as a polycrystalline silicon solar cell, an amorphous thin film silicon solar cell, and a dye-sensitized solar cell.

#### **6.1 Polycrystalline silicon solar cell**

We include the results obtained with a polycrystalline silicon solar cell manufactured by ISOFOTON, S.A. Different studies were carried out on this device with differing degrees of resolution. Groups of the scans performed with the three lasers are shown below.

Fig. 7. LBIC images of the three scans performed and the image created by combining these. The data used to construct these images are of EQE on a relative scale for each image.

First, LBIC scans were carried out with the three lasers mentioned above on a 1x1 cm2 area of the surface of the cell with a resolution of 20 m. The irradiation power for the red laser was 5 W, and 5.6 W for the green and blue ones. These values comply with the emission of a blackbody at 5780 K, in accordance with Planck's law (equation (7)). Figure 7 shows the

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 83

performed. In turn, using the EQE values, an image was constructed using the procedure

Fig. 9. LBIC images of the three intermediate resolution scans performed using EQE values

Secondly, scans are shown which were performed on a small surface area, but with greater resolution. The surface area scanned was 2x1.5 mm2 with a resolution of 5 m. The irradiation conditions were the same as those described above. Figure 9 shows the three scans performed, as well as the combined image. In this figure it is possible to observe small differences in the photoelectric properties of the device depending on the laser used. In the area marked with a circle two clearly distinct regions of differing quantum efficiency can be observed with the green and blue lasers, something which does not happen with the red laser. This difference in efficiency between the two zones becomes more pronounced as the wavelength is reduced. In other words, the depth of penetration decreases, and so we can conclude that this difference in efficiency is due to an artefact on the surface of the cell. It is also possible to observe that the definition of the grain boundaries depends on the wavelength used to do the scan, with the longer wavelength (red laser) leading to better definition, while with the blue laser (shorter wavelength) the grain boundaries can hardly be seen. We will study in greater detail below the differences which can be observed in the

on a relative scale for each image and the combined image using all three.

grain boundaries depending on the wavelength of the laser.

described which approximates the behaviour of the cell under solar radiation.

images obtained for the three scans, each one using EQE data on a relative scale. That is, a scale of greys is used which are between the maximum and minimum EQE for each of the images (A-B-C). From Figure 7 it is possible to observe that the conversion of the device depends on the irradiation wavelength used. Macroscopically, a greater quantum efficiency, or photoconversion, is observed when the cell is irradiated with the red laser. This can be seen clearly in Figure 7D, a combined image using those obtained in the scans with each of the lasers, and in which the colour red is seen to dominate most of the image. There are regions where red is not the predominant colour (e.g. the area shown with a square), due to the conversion being greater for one of the other lasers. However, the conversion with blue radiation is similar to that obtained with red. Microscopically, differences can be seen in the scans performed depending on the wavelength used, such as in the area marked with a circle in the images in Figure 7. Furthermore, the maximum and minimum EQE values in each scan are shown in table 2. From these values, an increase in conversion of between 5 and 6 % can be seen in the scan performed with the red laser (632.8 nm) compared with those carried out with the green (532 nm) and blue (473 nm) lasers, just as we had concluded qualitatively before from a simple visual observation.


Fig. 8. EQE image approximated to solar radiation using equation (12).

Also, from equation (11) it is possible to obtain EQE values which should be an approximation of the result which would be reached if the device were subjected to solar radiation (see figure 8). The maximum and minimum values obtained are shown in table 1. It is observed that the maximum EQE value for the image constructed with the approximation to solar irradiation is among the maximum values for the three scans

images obtained for the three scans, each one using EQE data on a relative scale. That is, a scale of greys is used which are between the maximum and minimum EQE for each of the images (A-B-C). From Figure 7 it is possible to observe that the conversion of the device depends on the irradiation wavelength used. Macroscopically, a greater quantum efficiency, or photoconversion, is observed when the cell is irradiated with the red laser. This can be seen clearly in Figure 7D, a combined image using those obtained in the scans with each of the lasers, and in which the colour red is seen to dominate most of the image. There are regions where red is not the predominant colour (e.g. the area shown with a square), due to the conversion being greater for one of the other lasers. However, the conversion with blue radiation is similar to that obtained with red. Microscopically, differences can be seen in the scans performed depending on the wavelength used, such as in the area marked with a circle in the images in Figure 7. Furthermore, the maximum and minimum EQE values in each scan are shown in table 2. From these values, an increase in conversion of between 5 and 6 % can be seen in the scan performed with the red laser (632.8 nm) compared with those carried out with the green (532 nm) and blue (473 nm) lasers, just as we had concluded

/ nm EQE / nm EQE

632. 8 0.950 0 473 0.895 0 532 0.902 0 Approximation to sunlight 0.917 0

Table 1. Maximum and minimum EQE values for the scans performed and the image

Fig. 8. EQE image approximated to solar radiation using equation (12).

Also, from equation (11) it is possible to obtain EQE values which should be an approximation of the result which would be reached if the device were subjected to solar radiation (see figure 8). The maximum and minimum values obtained are shown in table 1. It is observed that the maximum EQE value for the image constructed with the approximation to solar irradiation is among the maximum values for the three scans

Maximum Minimum Maximum Minimum

qualitatively before from a simple visual observation.

obtained as an approximation to solar irradiation.

performed. In turn, using the EQE values, an image was constructed using the procedure described which approximates the behaviour of the cell under solar radiation.

Fig. 9. LBIC images of the three intermediate resolution scans performed using EQE values on a relative scale for each image and the combined image using all three.

Secondly, scans are shown which were performed on a small surface area, but with greater resolution. The surface area scanned was 2x1.5 mm2 with a resolution of 5 m. The irradiation conditions were the same as those described above. Figure 9 shows the three scans performed, as well as the combined image. In this figure it is possible to observe small differences in the photoelectric properties of the device depending on the laser used. In the area marked with a circle two clearly distinct regions of differing quantum efficiency can be observed with the green and blue lasers, something which does not happen with the red laser. This difference in efficiency between the two zones becomes more pronounced as the wavelength is reduced. In other words, the depth of penetration decreases, and so we can conclude that this difference in efficiency is due to an artefact on the surface of the cell. It is also possible to observe that the definition of the grain boundaries depends on the wavelength used to do the scan, with the longer wavelength (red laser) leading to better definition, while with the blue laser (shorter wavelength) the grain boundaries can hardly be seen. We will study in greater detail below the differences which can be observed in the grain boundaries depending on the wavelength of the laser.

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 85

difference in the absorption coefficient, which depends on the irradiation wavelength and thus in the difference in the depth of penetration. The green laser provides results halfway between the others. If we wanted to obtain information about carrier diffusion lengths from the grain boundary, the results would differ depending on the irradiation wavelength used. Figure 11 shows the profiles that would be obtained for each scan. These profiles have been obtained as an average of all the horizontal profiles of the scans performed and setting the minimum photocurrent value on the grain boundary common to all the profiles of each scan. Thus, it can be observed that the LBIC signal is influenced in a larger region from the grain boundary as the wavelength increases. These profiles could make it possible to obtain diffusion length values, for example by following the model presented by Yagi et al. using the analysis of the electrical properties of grain boundaries in polycrystalline silicon solar cells (Yagi et al. 2004). But as Figure 11 shows, it would be necessary to bear in mind the

Fig. 11. Average LBIC signal profiles obtained for each of the three high resolution scans

We include the results obtained with an amorphous thin film silicon solar cell manufactured by GADIR SOLAR, S.A. LBIC scans were carried out with the three lasers on a 350x350 m2 area of the surface of the cell and were performed with a spatial resolution of 1 m. The irradiation power for the red laser was 335 W and 375 W for the green and blues ones. These values comply with the emission of a blackbody at 5780 K, in accordance with Planck's law. Figure 12 shows the images obtained for the three scans, each one using EQE data on relative scale (maximum and minimum EQE for each of the images A-B-C). The scanned surface is the zone where the solar cell has been marked by laser ablation in order to separate the different cells that make up the solar cell. In the Figure 12 we can see that the laser marking is composed of three lines made point by point with different diameter which leads to the width and depth of each line is different. In the images obtained using the red laser, the three lines are perfectly defined, but it is difficult to see in the scans performed with other two lasers. In turn, macroscopically, greater quantum efficiency is observed

irradiation source used.

performed of a grain boundary.

**6.2 Amorphous thin film silicon solar cell** 

The maximum and minimum EQE values in each scan are shown in table 2. From these values, greater conversion can be observed in the scan performed with the red laser compared with those performed with the green and blue ones.



Fig. 10. LBIC images obtained of the three high resolution scans (1 µm) performed using EQE values on a relative scale for each image and the combined images using all three.

Thirdly, high resolution scans were performed. The scans covered a surface area of 286x225 m2, and were performed with a spatial resolution of 1 m. The irradiation conditions were those described above for the two previous examples. Figure 10 shows the images obtained from the three scans performed. In the images obtained with the red laser, a perfectly defined grain boundary can be observed. On the other hand, this grain boundary is practically impossible to see in the scan performed with the blue laser due to the difference in the absorption coefficient, which depends on the irradiation wavelength and thus in the difference in the depth of penetration. The green laser provides results halfway between the others. If we wanted to obtain information about carrier diffusion lengths from the grain boundary, the results would differ depending on the irradiation wavelength used. Figure 11 shows the profiles that would be obtained for each scan. These profiles have been obtained as an average of all the horizontal profiles of the scans performed and setting the minimum photocurrent value on the grain boundary common to all the profiles of each scan. Thus, it can be observed that the LBIC signal is influenced in a larger region from the grain boundary as the wavelength increases. These profiles could make it possible to obtain diffusion length values, for example by following the model presented by Yagi et al. using the analysis of the electrical properties of grain boundaries in polycrystalline silicon solar cells (Yagi et al. 2004). But as Figure 11 shows, it would be necessary to bear in mind the irradiation source used.

Fig. 11. Average LBIC signal profiles obtained for each of the three high resolution scans performed of a grain boundary.

#### **6.2 Amorphous thin film silicon solar cell**

84 Solar Cells – Silicon Wafer-Based Technologies

The maximum and minimum EQE values in each scan are shown in table 2. From these values, greater conversion can be observed in the scan performed with the red laser

632. 8 0.881 0.286 473 0.860 0.308 532 0.872 0.234 Approximation to sunlight 0.873 0.284

Table 2. Maximum and minimum EQE values for the 2x1.5 mm2 scans and those which

Fig. 10. LBIC images obtained of the three high resolution scans (1 µm) performed using EQE values on a relative scale for each image and the combined images using all three.

Thirdly, high resolution scans were performed. The scans covered a surface area of 286x225 m2, and were performed with a spatial resolution of 1 m. The irradiation conditions were those described above for the two previous examples. Figure 10 shows the images obtained from the three scans performed. In the images obtained with the red laser, a perfectly defined grain boundary can be observed. On the other hand, this grain boundary is practically impossible to see in the scan performed with the blue laser due to the

Maximum Minimum Maximum Minimum

/ nm EQE / nm EQE

compared with those performed with the green and blue ones.

would be obtained as an approximation to solar irradiation.

We include the results obtained with an amorphous thin film silicon solar cell manufactured by GADIR SOLAR, S.A. LBIC scans were carried out with the three lasers on a 350x350 m2 area of the surface of the cell and were performed with a spatial resolution of 1 m. The irradiation power for the red laser was 335 W and 375 W for the green and blues ones. These values comply with the emission of a blackbody at 5780 K, in accordance with Planck's law. Figure 12 shows the images obtained for the three scans, each one using EQE data on relative scale (maximum and minimum EQE for each of the images A-B-C). The scanned surface is the zone where the solar cell has been marked by laser ablation in order to separate the different cells that make up the solar cell. In the Figure 12 we can see that the laser marking is composed of three lines made point by point with different diameter which leads to the width and depth of each line is different. In the images obtained using the red laser, the three lines are perfectly defined, but it is difficult to see in the scans performed with other two lasers. In turn, macroscopically, greater quantum efficiency is observed

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 87

Fig. 13. EQE image approximated to solar radiation using equation (14) for an amorphous

The maximum and minimum EQE values in each scan are shown in table 3. From these values, a decrease in conversion of 4 and 8 % can be seen in the scans performed with green laser and blue one, respectively. From equation (11) it is possible to obtain EQE values which should be an approximation of the result which would be reached if the device were subject to solar radiation. The maximum and minimum EQE values in this case are shown in table 4. In turn, an image using EQE values approximated to solar radiation has been constructed using the procedure describes previously. This image is shown in Figure 13.

The dye-sensitized solar cell used in this chapter was made by authors following the next procedure: Two fluorine-doped tin dioxide coated transparent glass plates (2x2 cm2 sheet resistance 15 square−1) supplied by Solaronix were used as the electrode and counterelectrode. Using nanoparticulated TiO2 with a nominal particle size of 25 nm, supplied by Degussa Co., a paste was developed using nitric acid and ethanol at a proportion of 1:3.25. A thin layer of paste was deposited on the electrode plate using the doctor blade method and sintered at 450 °C for 1 h. The thickness of the TiO2 films was 90.5 m. A mixture of 0.5*M* 4-tert-butylpyridine, 0.1*M* lithium iodide, and 0.05*M* iodine in 3-methoxypropionitrile as a solvent, was used as an electrolyte. A catalytic layer of Pt was deposited on the counterelectrode by decomposing a superficially sprayed solution of 0.01*M* H2PtCl6 in 2-propanol at 380 °C. Finally, the electrode plate with the sintered layer of TiO2 was immersed in dye solution. The dye used was an ethanolic solution of Ru535 (formerly known as N3,

LBIC scans were carried out with the three lasers mentioned above on a 300x300 m2 area of the surface of the cell and were performed with a spatial resolution of 1 m. In accordance with Planck's law, the irradiation power for the red laser was 6.62 W, and 7.41 W for the green and blues ones. First, the photocurrent values obtained from the three scans were corrected using the algorithm described in section 5. The LBIC images built from photocurrent values measured are shown in Figures 14A, 15A and 16B for lasers red, green and blue, respectively. The images built using the corrected values are shown in Figures

thin film silicon solar cell.

**6.3 Dye-sensitized solar cell** 

C26H20O10N6S2Ru).

Fig. 12. LBIC images of the three high resolution scans performed using EQE values on a relative scale for each image and the combined image using all three.

when the cell is irradiated with the red laser. This can be seen clearly in Figure 12D, a combined image using those obtained in the scans with each of the lasers, and in which the color red is seen to dominate most of the image. In the zone inside of two of the lines, the red color is not predominant, due to the conversion being greater for one of the other lasers.


Table 3. Maximum and minimum EQE values for scans of an amorphous thin film silicon solar cell and those which would be obtained as an approximation to solar irradiation.

Fig. 13. EQE image approximated to solar radiation using equation (14) for an amorphous thin film silicon solar cell.

The maximum and minimum EQE values in each scan are shown in table 3. From these values, a decrease in conversion of 4 and 8 % can be seen in the scans performed with green laser and blue one, respectively. From equation (11) it is possible to obtain EQE values which should be an approximation of the result which would be reached if the device were subject to solar radiation. The maximum and minimum EQE values in this case are shown in table 4. In turn, an image using EQE values approximated to solar radiation has been constructed using the procedure describes previously. This image is shown in Figure 13.

#### **6.3 Dye-sensitized solar cell**

86 Solar Cells – Silicon Wafer-Based Technologies

Fig. 12. LBIC images of the three high resolution scans performed using EQE values on a

/ nm EQE / nm EQE

632. 8 0.330 0.064 473 0.303 0.011 532 0.318 0.029 Approximation to sunlight 0.237 0.048 Table 3. Maximum and minimum EQE values for scans of an amorphous thin film silicon solar cell and those which would be obtained as an approximation to solar irradiation.

when the cell is irradiated with the red laser. This can be seen clearly in Figure 12D, a combined image using those obtained in the scans with each of the lasers, and in which the color red is seen to dominate most of the image. In the zone inside of two of the lines, the red color is not predominant, due to the conversion being greater for one of the other

Maximum Minimum Maximum Minimum

relative scale for each image and the combined image using all three.

lasers.

The dye-sensitized solar cell used in this chapter was made by authors following the next procedure: Two fluorine-doped tin dioxide coated transparent glass plates (2x2 cm2 sheet resistance 15 square−1) supplied by Solaronix were used as the electrode and counterelectrode. Using nanoparticulated TiO2 with a nominal particle size of 25 nm, supplied by Degussa Co., a paste was developed using nitric acid and ethanol at a proportion of 1:3.25. A thin layer of paste was deposited on the electrode plate using the doctor blade method and sintered at 450 °C for 1 h. The thickness of the TiO2 films was 90.5 m. A mixture of 0.5*M* 4-tert-butylpyridine, 0.1*M* lithium iodide, and 0.05*M* iodine in 3-methoxypropionitrile as a solvent, was used as an electrolyte. A catalytic layer of Pt was deposited on the counterelectrode by decomposing a superficially sprayed solution of 0.01*M* H2PtCl6 in 2-propanol at 380 °C. Finally, the electrode plate with the sintered layer of TiO2 was immersed in dye solution. The dye used was an ethanolic solution of Ru535 (formerly known as N3, C26H20O10N6S2Ru).

LBIC scans were carried out with the three lasers mentioned above on a 300x300 m2 area of the surface of the cell and were performed with a spatial resolution of 1 m. In accordance with Planck's law, the irradiation power for the red laser was 6.62 W, and 7.41 W for the green and blues ones. First, the photocurrent values obtained from the three scans were corrected using the algorithm described in section 5. The LBIC images built from photocurrent values measured are shown in Figures 14A, 15A and 16B for lasers red, green and blue, respectively. The images built using the corrected values are shown in Figures

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 89

Fig. 15. (A) LBIC image for the DSSC using green laser. (B) The same image modified using

Fig. 16. (A) LBIC image for the DSSC using blue laser. (B) The same image modified using

our algorithm.

our algorithm.

14B, 15B and 16B. In turn, in Figures 14-16 the histograms of the photocurrent values, in both cases, are shown. In these histograms, for the three lasers, it is observed that the measured photocurrent values are higher than the photocurrent values obtained after applying the algorithm. This is obvious because each measured point of the cells has contributions from the previously irradiated (an effect that can be easily observed in Figure 6). The corrected images (Figures 14B, 15B, and 16B) display improvement in clarity. These improvements can be easily observed in the scans made with the red laser, where the artefacts in the surface of the cell can be seen with better definition.

From the values corrected and using the equation (11) the values of EQE can be obtained for each scan. Figure 17 shows the image obtained applying the algorithm described to obtain images which would be obtained as an approximation to solar irradiation. From this image, the maximum and minimum values of EQE are obtained. These values are shown in table 4.


Table 4. Maximum and minimum EQE values for scans of a dye-sensitized solar cell and those which would be obtained as an approximation to solar irradiation.

Fig. 14. (A) LBIC image for the DSSC using red laser. (B) The same image modified using our algorithm.

14B, 15B and 16B. In turn, in Figures 14-16 the histograms of the photocurrent values, in both cases, are shown. In these histograms, for the three lasers, it is observed that the measured photocurrent values are higher than the photocurrent values obtained after applying the algorithm. This is obvious because each measured point of the cells has contributions from the previously irradiated (an effect that can be easily observed in Figure 6). The corrected images (Figures 14B, 15B, and 16B) display improvement in clarity. These improvements can be easily observed in the scans made with the red laser, where the

From the values corrected and using the equation (11) the values of EQE can be obtained for each scan. Figure 17 shows the image obtained applying the algorithm described to obtain images which would be obtained as an approximation to solar irradiation. From this image, the maximum and minimum values of EQE are obtained. These values are shown in table 4.

Maximum Minimum Maximum Minimum

/ nm EQE / nm EQE

those which would be obtained as an approximation to solar irradiation.

632. 8 0.309 0.096 473 0.265 0.110 532 0.253 0.100 Approximation to sunlight 0.276 0.102 Table 4. Maximum and minimum EQE values for scans of a dye-sensitized solar cell and

Fig. 14. (A) LBIC image for the DSSC using red laser. (B) The same image modified using

our algorithm.

artefacts in the surface of the cell can be seen with better definition.

Fig. 15. (A) LBIC image for the DSSC using green laser. (B) The same image modified using our algorithm.

Fig. 16. (A) LBIC image for the DSSC using blue laser. (B) The same image modified using our algorithm.

Trichromatic High Resolution-LBIC: A System for the Micrometric Characterization of Solar Cells 91

Fredin, K.; Nissfolk, J.; Boschjloo, G.; Hagfeldt, A. (2007). The influence of cations on charge

Gregg, B.A. (2004). Interfacial processes in dye-sensitized solar cell. *Coordination Chemistry Reviews*, Vol.248, No.13-14, (July 2004), pp. 1215-1224, ISSN 0010-8545. Lipinski, W.; Thommen, D.; Steinfeld, A. (2006). Unsteady radiative heat transfer within a

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Nichiporuk, O.; Kaminski, A.; Lemiti, M.; Fave, A.; Litvinenko, S. & Skryshevsky, V. (2006).

Nishioka, k.; Yagi, T.; Uraoka, Y. & Fuyuki, T. (2007). Effect of hydrogen plasma treatment

O'Regan, B.; Grätzel, M. (1991). A low-cost, high-efficiency solar cell based on dye-sensitized

Peter, L.M. (2007). Characterization and modeling of dye-sensitized solar cells. *Journal of Physical Chemistry C*, Vol. 111, No.18, (April 2007), pp. 6601-6612, ISSN 1932-7447 Poce-Fatou, J.A.; Martín, J.; Alcántara, R.; Fernández-Lorenzo, C. (2002). A precision method

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Vorasayan, P.; Betts, T.R.; Tiwari, A.N. & Gottschalg, R. (2009). Multi-laser LBIC system for

Vorster, F.J.; van Dyk, E.E. (2007). High saturation solar light induced current scanning of

Walker, A.B.; Peter, L.M.; Lobato, K.; Cameron, P.J. (2006). Analysis of photovoltage decay

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*Films*, Vol.511–512, (July 2006), pp. 248-251, ISSN 0040-6090

ISSN 0169-4332.

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improving laser beam induced current images of dye sensitized solar cells. *Review of Scientific Instruments*, Vol.80, No.1(June 2009), pp. 063102-1-063102-7, ISSN 0034-

Passivation of the surface of rear contact solar cells by porous silicon. *Thin Solid* 

on grain boundaries in polycrystalline silicon solar cell evalulated by laser beam induced current. *Solar Energy Materials & Solar Cells*, Vol.91, No.1, (January 2007),

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Fig. 17. EQE image approximated to solar radiation for a dye-sensitized solar cell.

#### **7. Conclusions**

We have described the fundamentals of computer-controlled equipment for scanning the surface of photovoltaic devices, which is capable of obtaining simultaneously LBIC, and specular reflection/transmittance based images. Several algorithm included in the system have been described. These ones are: (a) the algorithm for focusing the laser beam over the photoactive surface in order to obtain high resolution LBIC images; (b) the algorithm for obtaining images which are approximated to the behavior of photovoltaic devices under solar irradiation conditions, and (c) we have showed the algorithm for improving photoresponse of dye-sensitized solar cells. In turn, we have showed results obtained using three different kinds of solar cells such as a polycrystalline silicon solar cell, an amorphous thin film silicon solar cell, and a dye-sensitized solar cell. In this way, we have tested the goodness of our LBIC system for studying different photovoltaic devices.

#### **8. References**


Fig. 17. EQE image approximated to solar radiation for a dye-sensitized solar cell.

goodness of our LBIC system for studying different photovoltaic devices.

100, No.42, (October 1996), pp. 17021-17027, ISSN 1520-6106.

We have described the fundamentals of computer-controlled equipment for scanning the surface of photovoltaic devices, which is capable of obtaining simultaneously LBIC, and specular reflection/transmittance based images. Several algorithm included in the system have been described. These ones are: (a) the algorithm for focusing the laser beam over the photoactive surface in order to obtain high resolution LBIC images; (b) the algorithm for obtaining images which are approximated to the behavior of photovoltaic devices under solar irradiation conditions, and (c) we have showed the algorithm for improving photoresponse of dye-sensitized solar cells. In turn, we have showed results obtained using three different kinds of solar cells such as a polycrystalline silicon solar cell, an amorphous thin film silicon solar cell, and a dye-sensitized solar cell. In this way, we have tested the

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resolution laser beam induced current focusing for photoactive surface

**7. Conclusions** 

**8. References** 

0927-0248.

characterization. *Applied Surface Science*, Vol.253, No.4 (May 2006), pp. 2179-2188, ISSN 0169-4332.


**5** 

*Taiwan, R.O.C.* 

**Silicon Solar Cells: Structural Properties of** 

The screen-printed silver (Ag) thick-film is the most widely used front side contact in industrial crystalline silicon solar cells. The front contacts have the roles of efficiently contacting with the silicon (Si) and transporting the photogenerated current without adversely affecting the cell properties and without damaging the p-n junction. Although it is rapid, has low cost and is simplicity, high quality screen-printed silver contact is not easy to make due to the complicated composition in the silver paste. Commercially available silver pastes generally consist of silver powders, lead-glass frit powders and an organic vehicle system. The organic constituents of the silver paste are burned out at temperatures below 500°C. Ag particles, which are ~70-85wt% and can be different in shape and size distribution, show good conductivity and minor corrosive characteristics. The concentration of glass frit is usually less than 5wt %; however, the glass frit in the silver paste plays a critical role for achieving good quality contacts to high-doping emitters. The optimization of

The melting characteristics of the glass frit and also of the dissolved silver have significant influence on contact resistance and fill factors (FFs). Glass frit advances sintering of the silver particles, wets and merges the antireflection coating. Moreover, glass frit forms a glass layer between Si and Ag-bulk, and can further react with Si-bulk and forms pin-holes on the

This chapter first describes the Ag-bulk/Si contact structures of the crystalline silicon solar cells. Then, the influences of the Ag-contacts/Si-substrate on performance of the resulted solar cells are investigated. The objective of this chapter was to improve the understanding of front side contact formation by analyzing the Ag-bulk/Si contact structures resulting from different degrees of firing. The observed microscopic contact structure and the resulting solar-cell performance are combined to clarify the mechanism behind the hightemperature contact formation. Samples were fired either at a optimal temperature of ~780°C or at a temperature of over-fired for silver paste to study the effect of firing temperature. The melting characteristics of the glass frit determine the firing condition suitable for low contact resistance and high fill factors. In addition, it was found the post forming gas annealing can help overfired solar cells recover their FF. The results show that after 400°C post forming gas annealing for 25min, the over-fired cells improve their FF. On the other hand, both of the optimally-fired and the under-fired cells did not show similar

the glass frit constitution can help achieve adequate photovoltaic properties.

Si surface upon high temperature firing.

**1. Introduction** 

**Ag-Contacts/Si-Substrate** 

*Industrial Technology Research Institute ,* 

Ching-Hsi Lin, Shih-Peng Hsu and Wei-Chih Hsu

Yagi, T.; Nishioka, K.; Uraoka, Y.; Fuyuki, T. (2004). Analysis of electrical properties of grain boundaries in silicon solar cell using laser beam induced current. *Japanese Journal of Applied Physics*, Vol.43, No.7A, (July 2004), pp. 4068-4072, ISSN 0021-4922.

### **Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate**

Ching-Hsi Lin, Shih-Peng Hsu and Wei-Chih Hsu *Industrial Technology Research Institute , Taiwan, R.O.C.* 

#### **1. Introduction**

92 Solar Cells – Silicon Wafer-Based Technologies

Yagi, T.; Nishioka, K.; Uraoka, Y.; Fuyuki, T. (2004). Analysis of electrical properties of grain

*Applied Physics*, Vol.43, No.7A, (July 2004), pp. 4068-4072, ISSN 0021-4922.

boundaries in silicon solar cell using laser beam induced current. *Japanese Journal of* 

The screen-printed silver (Ag) thick-film is the most widely used front side contact in industrial crystalline silicon solar cells. The front contacts have the roles of efficiently contacting with the silicon (Si) and transporting the photogenerated current without adversely affecting the cell properties and without damaging the p-n junction. Although it is rapid, has low cost and is simplicity, high quality screen-printed silver contact is not easy to make due to the complicated composition in the silver paste. Commercially available silver pastes generally consist of silver powders, lead-glass frit powders and an organic vehicle system. The organic constituents of the silver paste are burned out at temperatures below 500°C. Ag particles, which are ~70-85wt% and can be different in shape and size distribution, show good conductivity and minor corrosive characteristics. The concentration of glass frit is usually less than 5wt %; however, the glass frit in the silver paste plays a critical role for achieving good quality contacts to high-doping emitters. The optimization of the glass frit constitution can help achieve adequate photovoltaic properties.

The melting characteristics of the glass frit and also of the dissolved silver have significant influence on contact resistance and fill factors (FFs). Glass frit advances sintering of the silver particles, wets and merges the antireflection coating. Moreover, glass frit forms a glass layer between Si and Ag-bulk, and can further react with Si-bulk and forms pin-holes on the Si surface upon high temperature firing.

This chapter first describes the Ag-bulk/Si contact structures of the crystalline silicon solar cells. Then, the influences of the Ag-contacts/Si-substrate on performance of the resulted solar cells are investigated. The objective of this chapter was to improve the understanding of front side contact formation by analyzing the Ag-bulk/Si contact structures resulting from different degrees of firing. The observed microscopic contact structure and the resulting solar-cell performance are combined to clarify the mechanism behind the hightemperature contact formation. Samples were fired either at a optimal temperature of ~780°C or at a temperature of over-fired for silver paste to study the effect of firing temperature. The melting characteristics of the glass frit determine the firing condition suitable for low contact resistance and high fill factors. In addition, it was found the post forming gas annealing can help overfired solar cells recover their FF. The results show that after 400°C post forming gas annealing for 25min, the over-fired cells improve their FF. On the other hand, both of the optimally-fired and the under-fired cells did not show similar

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 95

Screen printing and the subsequent firing process are the dominant metallization techniques for the industrial production of crystalline silicon solar cells. The front contact of the cell is designed to offer minimum series resistance, while minimizing optical shadowing. The high current density of the cell can be achieved by the low shadowing loss due to the high aspect ratio of the front grid. However, a compromise between the shadowing loss and the resistive loss due to the front grid is needed. The finger-pattern with the bus bar typically covers between 6-10% of the cell surface. To achieve good performance contact, the printing parameters should be selected based on criteria directly related to the silver paste. All parameters such as the screen off-contact distance, squeegee speed and shore hardness of

the squeegee rubber must be optimized and matched according to the requirements.

The industrial requirements for technical screen printing regarding excellent print performance, long screen life and higher process yields have increased significantly over recent years. The high mesh count stainless steel mesh is well suited for fine line, high volume printing. The screen should have good tension consistency and suitable flexibility required for the constant deformation associated with off-contact printing. Besides, the combinations of mesh count and thread diameter should be capable of printing the grid

The fast firing techniques are usually applied for electrode formation. During the firing step, the contact is formed within a few seconds at peak temperature around 800°C. A typical firing profile of a commercial crystalline silicon solar cell is shown in Figure 2. The optimal firing profile should feature low series resistance and high fill factor (FF). A high series resistance of a solar cell usually degrades the output power by decreasing the fill factor. The total series resistance is the sum of the rear metal contact resistance, the emitter sheet resistance, the substrate resistance, the front contact resistance, and the grid resistance.

Fig. 2. A typical firing profile of a commercial crystalline silicon solar cell.

A good front-contact of the crystalline silicon solar cell requires Ag-electrode to interact with a very shallow emitter-layer of Si. An overview of the theory of the solar cell contact resistance has been reported (Schroder & Meier, 1984). Despite the success of the screen printing and the subsequent firing process, many aspects of the physics of the front-contact

**2.2 Screen printing and firing** 

thickness electrode requires.

**2.3 Contact mechanisms** 

effects. The FF remains the same or even worse after post annealing. Upon overfiring, more silver dissolve in the molten glassy phase than that of optimally fired; however, some of the supersaturated silver in the glass was unable to recrystallize because of the rapid cooling process. The post annealing helps the supersaturated silver precipitate in the glass phase or on silicon surface. This helps in recovering high FF and low contact resistance. An increase in the size and number of silver crystallites at the interface and in the glass phase can improve the current transportation.

### **2. Overview of Ag contacts on crystalline Si solar cells**

#### **2.1 Silver paste**

Currently, screen printing a silver paste followed by sintering is used for the deposition of the front contacts on almost all industrial crystalline silicon solar cells. Metallization with a silver paste is reliable and particularly fast. The silver paste have to meet several requirements: opening the dielectric antireflection layer and forming a contact with good mechanical adhesion and low contact resistance. For most crystalline silicon solar cells, SiNx is used as an antireflection coating. The surface must be easily wetted by the paste. Figure 1 shows a typical front-electrode configuration of a commercial crystalline silicon solar cell. The electrode-pattern consists of several grid fingers that collect current from the neighboring regions and then collected into a bus bar. The bus bar has to be able to be soldered.

The contact performance is influenced by the paste content, the rheology and the wetting behavior.

Commercially available silver pastes generally consist of silver powders, lead-glass frit powders and an organic vehicle system. The glass frit is used to open the antireflection coating and provide the mechanical adhesion. The glass frit also promotes contact formation. The organic vehicle system primarily includes polymer binder and solvent with small molecular weight. Other additives like rheological material are also included in the paste for better printing. The paste system must have a fine line capability. This requires a well-balanced thixotropy and low flow properties during printing, drying and firing. In addition, the paste should have wide range for firing process window.

#### **2.2 Screen printing and firing**

94 Solar Cells – Silicon Wafer-Based Technologies

effects. The FF remains the same or even worse after post annealing. Upon overfiring, more silver dissolve in the molten glassy phase than that of optimally fired; however, some of the supersaturated silver in the glass was unable to recrystallize because of the rapid cooling process. The post annealing helps the supersaturated silver precipitate in the glass phase or on silicon surface. This helps in recovering high FF and low contact resistance. An increase in the size and number of silver crystallites at the interface and in the glass phase can

Currently, screen printing a silver paste followed by sintering is used for the deposition of the front contacts on almost all industrial crystalline silicon solar cells. Metallization with a silver paste is reliable and particularly fast. The silver paste have to meet several requirements: opening the dielectric antireflection layer and forming a contact with good mechanical adhesion and low contact resistance. For most crystalline silicon solar cells, SiNx is used as an antireflection coating. The surface must be easily wetted by the paste. Figure 1 shows a typical front-electrode configuration of a commercial crystalline silicon solar cell. The electrode-pattern consists of several grid fingers that collect current from the neighboring regions and then collected into a bus bar. The bus bar has to be able to be

Fig. 1. A typical front-electrode configuration of a commercial crystalline silicon solar cell. The contact performance is influenced by the paste content, the rheology and the wetting

Commercially available silver pastes generally consist of silver powders, lead-glass frit powders and an organic vehicle system. The glass frit is used to open the antireflection coating and provide the mechanical adhesion. The glass frit also promotes contact formation. The organic vehicle system primarily includes polymer binder and solvent with small molecular weight. Other additives like rheological material are also included in the paste for better printing. The paste system must have a fine line capability. This requires a well-balanced thixotropy and low flow properties during printing, drying and firing. In

addition, the paste should have wide range for firing process window.

improve the current transportation.

**2.1 Silver paste** 

soldered.

behavior.

**2. Overview of Ag contacts on crystalline Si solar cells** 

Screen printing and the subsequent firing process are the dominant metallization techniques for the industrial production of crystalline silicon solar cells. The front contact of the cell is designed to offer minimum series resistance, while minimizing optical shadowing. The high current density of the cell can be achieved by the low shadowing loss due to the high aspect ratio of the front grid. However, a compromise between the shadowing loss and the resistive loss due to the front grid is needed. The finger-pattern with the bus bar typically covers between 6-10% of the cell surface. To achieve good performance contact, the printing parameters should be selected based on criteria directly related to the silver paste. All parameters such as the screen off-contact distance, squeegee speed and shore hardness of the squeegee rubber must be optimized and matched according to the requirements.

The industrial requirements for technical screen printing regarding excellent print performance, long screen life and higher process yields have increased significantly over recent years. The high mesh count stainless steel mesh is well suited for fine line, high volume printing. The screen should have good tension consistency and suitable flexibility required for the constant deformation associated with off-contact printing. Besides, the combinations of mesh count and thread diameter should be capable of printing the grid thickness electrode requires.

The fast firing techniques are usually applied for electrode formation. During the firing step, the contact is formed within a few seconds at peak temperature around 800°C. A typical firing profile of a commercial crystalline silicon solar cell is shown in Figure 2. The optimal firing profile should feature low series resistance and high fill factor (FF). A high series resistance of a solar cell usually degrades the output power by decreasing the fill factor. The total series resistance is the sum of the rear metal contact resistance, the emitter sheet resistance, the substrate resistance, the front contact resistance, and the grid resistance.

Fig. 2. A typical firing profile of a commercial crystalline silicon solar cell.

#### **2.3 Contact mechanisms**

A good front-contact of the crystalline silicon solar cell requires Ag-electrode to interact with a very shallow emitter-layer of Si. An overview of the theory of the solar cell contact resistance has been reported (Schroder & Meier, 1984). Despite the success of the screen printing and the subsequent firing process, many aspects of the physics of the front-contact

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 97

The microstructural properties of the screen-printed Ag-bulk/Si contacts were examined by TEM (Lin et al., 2008). TEM results confirmed that the glassy-phase plays an important role in contact properties. The typical Ag-bulk/Si microstructure, which includes localized large glassy-phase region, is shown in Figure 4(a). The area where Ag-bulk directly contact with Si through SEM observation is actually with a very thin glass layer (<5nm) in between as shown in Figure 4(b). This possibly can be attributed to shape-effect of Ag particles and to the existence of the glassy-phase. Ag particles do not sinter into a very compact structure and a porous Ag-bulk is formed, resulting in a complex contact structure. In this study, it was found that in optimal fired contacts, there are at least three different microstructures, illustrated in Figure 5(a)-(c) (Lin et al., 2008). The combination effects of glassy-phase and the dissolved metal atoms have a crucial influence on Ag-bulk/Si-emitter structures, and

Fig. 4. (a) TEM bright field cross-sectional image of the the Ag-bulk/Si contact structure with localized large glassy-phase region. (b) HRTEM of the Ag-bulk/Si interface. There is a

Fig. 3. SEM image of a pyramid-textured silicon surface structure

consequently, the current transport across the interface is affected.

very thin glass layer between Si and Ag-bulk.

**3.2 Interface microstructure** 

formation are not fully clear. The major reason is probably because the metal-silicon interface for screen printed fingers is non-uniform in structure and composition. The Ag particles can interact with the Si surface in a few seconds at temperatures that are considerably lower than the eutectic point.

Many mechanisms have been proposed to explain how contact formation is though to occur. The general understanding of the mechanisms agree that the glass frit play a critical role on front-contact formation. Silver and silicon are dissolved in the glass frit upon firing. When cooled, Ag particles recrystallized (Weber 2002, Schubert et al. 2004). It has been suggested that Ag crystallites serve as current pickup points and that conduction from the Ag crystallites to the bulk of the Ag grid takes place via tunneling (Ballif et al., 2003). The effect of glass frit and Ag particles on the electrical characteristics of the cell was also reported (Hoornstra et al. 2005, Hillali et al. 2005, Hillali et al. 2006). It was further suggested that lead oxide gets reduced by the silicon. The generated lead then alloys with the silver and silver contact crystallites are formed from the liquid Ag-Pb phase (Schubert et al. 2004, Schubert et al. 2006). Due to the complicate and non-uniform features of the contact interface, more evidence and further microstructure investigation is still needed. The objective of this chapter was to improve the understanding of front side contact formation by analyzing the Ag-bulk/Si contact structures resulting from different degrees of firing. The influences of the Ag-contacts/Si-substrate on performance of the resulted solar cells are also investigated.

#### **3. Structural properties of Ag-contacts/Si-substrate**

#### **3.1 Sample preparation**

This study is based on industrial single-crystalline silicon solar cells with a SiNx antireflection coating, screen-printed silver thick-film front contacts and a screen-printed aluminum back-surface-field (BSF). The contact pattern was screen printed using commercial silver paste on top of the SiNx antireflective-coating (ARC) and fired rapidly in a belt furnace. The exact silver paste compositions are not disclosed by the paste manufacturers. The glass frit contents are estimated from the results found in this work. The boron-doped p-type 0.5-2Ωcm, 200-230μm thick (100) CZ single-crystalline Si wafers were used for all the experiments. Si wafers were first chemically cleaned and surface texturized and then followed by POCl3 diffusion to form the n+ emitters. The resulted pyramid-shaped silicon surface is sharp and smooth, as shown in Figure 3. After phosphorus glass removal, a single layer plasma-enhanced chemical vapor deposition (PECVD) SiNx antireflection coating was deposited on the emitters. Then, both the screen-printed Ag and the Al contacts were cofired in a lamp-heated belt IR furnace.

In this work, cells were fired either at a optimal temperature of ~780°C or at a temperature of over-fired for silver paste to study the effect of firing temperature. Some cells were further post annealed in forming gas (N2:H2=85:15) at 400°C for 25min. The forming gas anneal improve the fill factor (FF) for some over-fired cells.

Transmission electron microscopy (TEM) and Scanning electron microscopy (SEM) was used to study the microstructures and features at contact interface. Microstructural characterization of the contact interface was performed using a JEM-2100F transmission electron microscope (TEM) operated at 200kV. Cross-sectional TEM sample foils were prepared by mechanically thinning followed by focused-ion-beam (FIB) microsampling to electron transparency. Current-voltage (I-V) measurements were taken under a WACOM solar simulator using AM1.5 spectrum. The cells were kept at 25°C while testing.

Fig. 3. SEM image of a pyramid-textured silicon surface structure

#### **3.2 Interface microstructure**

96 Solar Cells – Silicon Wafer-Based Technologies

formation are not fully clear. The major reason is probably because the metal-silicon interface for screen printed fingers is non-uniform in structure and composition. The Ag particles can interact with the Si surface in a few seconds at temperatures that are

Many mechanisms have been proposed to explain how contact formation is though to occur. The general understanding of the mechanisms agree that the glass frit play a critical role on front-contact formation. Silver and silicon are dissolved in the glass frit upon firing. When cooled, Ag particles recrystallized (Weber 2002, Schubert et al. 2004). It has been suggested that Ag crystallites serve as current pickup points and that conduction from the Ag crystallites to the bulk of the Ag grid takes place via tunneling (Ballif et al., 2003). The effect of glass frit and Ag particles on the electrical characteristics of the cell was also reported (Hoornstra et al. 2005, Hillali et al. 2005, Hillali et al. 2006). It was further suggested that lead oxide gets reduced by the silicon. The generated lead then alloys with the silver and silver contact crystallites are formed from the liquid Ag-Pb phase (Schubert et al. 2004, Schubert et al. 2006). Due to the complicate and non-uniform features of the contact interface, more evidence and further microstructure investigation is still needed. The objective of this chapter was to improve the understanding of front side contact formation by analyzing the Ag-bulk/Si contact structures resulting from different degrees of firing. The influences of the Ag-contacts/Si-substrate on performance of the resulted solar cells are also investigated.

This study is based on industrial single-crystalline silicon solar cells with a SiNx antireflection coating, screen-printed silver thick-film front contacts and a screen-printed aluminum back-surface-field (BSF). The contact pattern was screen printed using commercial silver paste on top of the SiNx antireflective-coating (ARC) and fired rapidly in a belt furnace. The exact silver paste compositions are not disclosed by the paste manufacturers. The glass frit contents are estimated from the results found in this work. The boron-doped p-type 0.5-2Ωcm, 200-230μm thick (100) CZ single-crystalline Si wafers were used for all the experiments. Si wafers were first chemically cleaned and surface texturized and then followed by POCl3 diffusion to form the n+ emitters. The resulted pyramid-shaped silicon surface is sharp and smooth, as shown in Figure 3. After phosphorus glass removal, a single layer plasma-enhanced chemical vapor deposition (PECVD) SiNx antireflection coating was deposited on the emitters. Then, both the screen-printed Ag and the Al contacts

In this work, cells were fired either at a optimal temperature of ~780°C or at a temperature of over-fired for silver paste to study the effect of firing temperature. Some cells were further post annealed in forming gas (N2:H2=85:15) at 400°C for 25min. The forming gas

Transmission electron microscopy (TEM) and Scanning electron microscopy (SEM) was used to study the microstructures and features at contact interface. Microstructural characterization of the contact interface was performed using a JEM-2100F transmission electron microscope (TEM) operated at 200kV. Cross-sectional TEM sample foils were prepared by mechanically thinning followed by focused-ion-beam (FIB) microsampling to electron transparency. Current-voltage (I-V) measurements were taken under a WACOM

solar simulator using AM1.5 spectrum. The cells were kept at 25°C while testing.

considerably lower than the eutectic point.

**3. Structural properties of Ag-contacts/Si-substrate** 

were cofired in a lamp-heated belt IR furnace.

anneal improve the fill factor (FF) for some over-fired cells.

**3.1 Sample preparation** 

The microstructural properties of the screen-printed Ag-bulk/Si contacts were examined by TEM (Lin et al., 2008). TEM results confirmed that the glassy-phase plays an important role in contact properties. The typical Ag-bulk/Si microstructure, which includes localized large glassy-phase region, is shown in Figure 4(a). The area where Ag-bulk directly contact with Si through SEM observation is actually with a very thin glass layer (<5nm) in between as shown in Figure 4(b). This possibly can be attributed to shape-effect of Ag particles and to the existence of the glassy-phase. Ag particles do not sinter into a very compact structure and a porous Ag-bulk is formed, resulting in a complex contact structure. In this study, it was found that in optimal fired contacts, there are at least three different microstructures, illustrated in Figure 5(a)-(c) (Lin et al., 2008). The combination effects of glassy-phase and the dissolved metal atoms have a crucial influence on Ag-bulk/Si-emitter structures, and consequently, the current transport across the interface is affected.

Fig. 4. (a) TEM bright field cross-sectional image of the the Ag-bulk/Si contact structure with localized large glassy-phase region. (b) HRTEM of the Ag-bulk/Si interface. There is a very thin glass layer between Si and Ag-bulk.

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 99

The schematic Ag-bulk/thick-glass-layer/Si contact structure shown in Figure 5(b) may arise if there are large glass-frit clusters and/or large voids at the interface plane prior to high temperature treatment. Upon firing, the glass frits soften and flow all around. The flow behavior of the molten glassy-phase, to a degree, is associated with capillary attraction force caused by the tiny spacing between Ag particles, and it also depends on their wetting ability to the antireflection layer. Large and thick glassy-phase region is very likely due to the agglomeration of the molten glass frit at high temperature, and is responsible for a

Another interesting feature shown in Fig. 4(a) is the curve-shaped glassy-phase/Si boundary, which suggests the occurrence of mild etching of Si-bulk by the Agsupersaturated glassy-phase. Penetration of native SiOx and SiNx ARC is essential for making good electrical contact with the Si emitter, thus achieving a low contact resistance. However, this must be achieved without etching all the way through the p-n junction and results in shorting the cell. It is found that a smooth curve-shaped Si surface is a distinguishable phenomenon for samples fired optimally (Lin et al., 2008). Underfired samples usually have sharp and straight interface under <110> beam direction, while rough

Even for optimally fired samples, the residual antireflection coating can be observed at some locations, especially in the valley area of the pyramid-shaped textured structure as shown in Figure 7. Amorphous antireflection layer is thus in between the glassy-phase and Si-bulk. This lead to an Ag-bulk/glass-layer/ARC/Si contact structure as illustrated in Figure 5(c). Here, ARC (~100nm thick prior to firing) includes native SiOx layer and SiNx ARC. To some extent, the residual SiNx under the contacts help to reduce surface recombination. Microstructures studies revealed that there is more residual ARC in underfired samples

Fig. 7. TEM bright field cross-sectional image. Even for optimally fired samples, the residual antireflection coating can be observed at some locations, especially in the valley area of the pyramid-shaped textured structure. This leads to an Ag-bulk/glass-layer/ARC/Si contact

significant variation in glass-layer thickness.

Si surface is usually observed for overfired samples.

structure.

Figure 6 shows a high-resolution TEM (HRTEM) contrast of the Ag embryos on Si-bulk. This results in Ag-bulk/thin-glass-layer/Si contact structure which is schematic drawing in Figure 5(a). It is suggested that Ag-bulk/thin-glass-layer/Si contact structure shown in Figure 5(a) is the most decisive path for current transportation (Lin et al., 2008).

Fig. 5. Schematic drawing of the three major microstructures present in optimal fired Agbulk/Si contacts: (a) Ag-bulk/thin-glass-layer/Si; (b) Ag-bulk/thick-glass-layer/Si; and (c) Ag-bulk/glass-layer/ARC/Si contact structure.

Fig. 6. HRTEM contrast of the Ag embryos on Si-bulk. This results in Ag-bulk/thin-glasslayer/Si contact structure.

Figure 6 shows a high-resolution TEM (HRTEM) contrast of the Ag embryos on Si-bulk. This results in Ag-bulk/thin-glass-layer/Si contact structure which is schematic drawing in Figure 5(a). It is suggested that Ag-bulk/thin-glass-layer/Si contact structure shown in

Figure 5(a) is the most decisive path for current transportation (Lin et al., 2008).

(a) (b) (c)

Ag-bulk/glass-layer/ARC/Si contact structure.

layer/Si contact structure.

Fig. 5. Schematic drawing of the three major microstructures present in optimal fired Agbulk/Si contacts: (a) Ag-bulk/thin-glass-layer/Si; (b) Ag-bulk/thick-glass-layer/Si; and (c)

Fig. 6. HRTEM contrast of the Ag embryos on Si-bulk. This results in Ag-bulk/thin-glass-

The schematic Ag-bulk/thick-glass-layer/Si contact structure shown in Figure 5(b) may arise if there are large glass-frit clusters and/or large voids at the interface plane prior to high temperature treatment. Upon firing, the glass frits soften and flow all around. The flow behavior of the molten glassy-phase, to a degree, is associated with capillary attraction force caused by the tiny spacing between Ag particles, and it also depends on their wetting ability to the antireflection layer. Large and thick glassy-phase region is very likely due to the agglomeration of the molten glass frit at high temperature, and is responsible for a significant variation in glass-layer thickness.

Another interesting feature shown in Fig. 4(a) is the curve-shaped glassy-phase/Si boundary, which suggests the occurrence of mild etching of Si-bulk by the Agsupersaturated glassy-phase. Penetration of native SiOx and SiNx ARC is essential for making good electrical contact with the Si emitter, thus achieving a low contact resistance. However, this must be achieved without etching all the way through the p-n junction and results in shorting the cell. It is found that a smooth curve-shaped Si surface is a distinguishable phenomenon for samples fired optimally (Lin et al., 2008). Underfired samples usually have sharp and straight interface under <110> beam direction, while rough Si surface is usually observed for overfired samples.

Even for optimally fired samples, the residual antireflection coating can be observed at some locations, especially in the valley area of the pyramid-shaped textured structure as shown in Figure 7. Amorphous antireflection layer is thus in between the glassy-phase and Si-bulk. This lead to an Ag-bulk/glass-layer/ARC/Si contact structure as illustrated in Figure 5(c). Here, ARC (~100nm thick prior to firing) includes native SiOx layer and SiNx ARC. To some extent, the residual SiNx under the contacts help to reduce surface recombination. Microstructures studies revealed that there is more residual ARC in underfired samples

Fig. 7. TEM bright field cross-sectional image. Even for optimally fired samples, the residual antireflection coating can be observed at some locations, especially in the valley area of the pyramid-shaped textured structure. This leads to an Ag-bulk/glass-layer/ARC/Si contact structure.

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 101

TEM micrographs in Figure 9(a) and (c) show the precipitates in the large solidified glassyphase region which is enclosed with Si and Ag-bulk (Lin et al., 2008). The selected area diffraction (SAD) pattern (Figure 9(d)) reveals that only Ag precipitates exist. As shown in Figure 9(a) and its schematic drawing in Figure 9(b), the dissolved Ag atoms near Si-bulk tend to nucleate on the Si surface and lead to an Ag-crystallite-free zone in close vicinity of the Si surface. Also, an Ag-crystallite-free zone near the bulk-Ag can be found. Few or virtually no Ag microcrystallites were found in the Ag-crystallite-free zone. This indicates that the observed Ag microcrystallites are not un-melted Ag particles which were trapped or suspended in the glassy region; instead, they are precipitates from Ag supersaturation

Fig. 9. (a) TEM bright field image. The large glassy-phase enclosed with Si and Ag-bulk. (b) Ag precipitates in the large solidified glassy-phase region. (c) Schematic drawing of image in (b). (d) Selected-area-diffraction pattern of the glassy-phase region shown in (b).

The occurrence of the observed Ag-crystallite-free zone can be accounted for by the diffusion-dependent nucleation mechanism (Porter and Easterling, 1981) as illustrated in Figure 10 (Lin et al., 2008). Upon heating, the dispersed lead silicate glass frits soften into molten phase, in the mean time. They further merged and surrounded the Ag particles due

molten glassy-phase.

Only Ag crystallites exist.

than in optimally fired samples. In addition, no Ag embryo was found on Si-bulk because the residual ARC helps inhibit Ag diffusion onto Si substrate.

It is still not clear how does glassy-phase, which is a molten phase of the glass frit, etch or interact with the SiNx ARC? It was reported that the SiNx ARC can be opened during the firing step by a reaction between the PbO (glass) and SiNx (Horteis et al., 2010). In the reaction, lead oxide (PbO) was reduced to lead. By tracing Pb content, this work shows that Pb precipitates usually appear in the area where SiNx ARC can be found. That is, lead embedded in the glassy-phase with an Ag-bulk/glass-layer/ARC/Si contact structure as illustrated in Figure 5(c). The Pb concentration in glassy-phase, which originates from lead silicate glass frit, is much higher than that in ARC. Therefore, Pb can serve as a good tracer to distinguish glassy-phase-area from ARC using energy dispersive spectroscopy (EDS). Figure 8 shows Pb precipitates in the glassy phase. The inset in Figure 8 is an energy dispersive spectroscopy (EDS) mapping. This work suggests that during the firing process, the amorphous SiNx ARC was incorporated into the already-existing glass phase. It is like two loose glassy-phase merge to each other upon firing. It is shown in this work that the SiNx ARC in more dense structure, ex. deposited at 850°C through low-pressure CVD (LPCVD), is difficult to merge in the lead silicate glass phase.

Fig. 8. TEM bright field image shows Pb precipitates in the glassy phase. The inset is the energy dispersive spectroscopy (EDS) mapping.

#### **3.3 Crystallite-free zone in glassy phase**

Commercially available Ag pastes consist of Ag powders, lead-glass frit powders and an organic vehicle system. It was found that the glass frit plays a very important role during contact formation. Upon firing, the glass frits soften and flow all around. Furthermore, the melted lead silicate glass dissolves the Ag particles. The melted glass also merges the amorphous silicon nitride layer. Upon further heating, the melted glass etches into the silicon bulk underneath and results in non-smooth silicon surface.

than in optimally fired samples. In addition, no Ag embryo was found on Si-bulk because

It is still not clear how does glassy-phase, which is a molten phase of the glass frit, etch or interact with the SiNx ARC? It was reported that the SiNx ARC can be opened during the firing step by a reaction between the PbO (glass) and SiNx (Horteis et al., 2010). In the reaction, lead oxide (PbO) was reduced to lead. By tracing Pb content, this work shows that Pb precipitates usually appear in the area where SiNx ARC can be found. That is, lead embedded in the glassy-phase with an Ag-bulk/glass-layer/ARC/Si contact structure as illustrated in Figure 5(c). The Pb concentration in glassy-phase, which originates from lead silicate glass frit, is much higher than that in ARC. Therefore, Pb can serve as a good tracer to distinguish glassy-phase-area from ARC using energy dispersive spectroscopy (EDS). Figure 8 shows Pb precipitates in the glassy phase. The inset in Figure 8 is an energy dispersive spectroscopy (EDS) mapping. This work suggests that during the firing process, the amorphous SiNx ARC was incorporated into the already-existing glass phase. It is like two loose glassy-phase merge to each other upon firing. It is shown in this work that the SiNx ARC in more dense structure, ex. deposited at 850°C through low-pressure CVD

Fig. 8. TEM bright field image shows Pb precipitates in the glassy phase. The inset is the

Commercially available Ag pastes consist of Ag powders, lead-glass frit powders and an organic vehicle system. It was found that the glass frit plays a very important role during contact formation. Upon firing, the glass frits soften and flow all around. Furthermore, the melted lead silicate glass dissolves the Ag particles. The melted glass also merges the amorphous silicon nitride layer. Upon further heating, the melted glass etches into the

the residual ARC helps inhibit Ag diffusion onto Si substrate.

(LPCVD), is difficult to merge in the lead silicate glass phase.

energy dispersive spectroscopy (EDS) mapping.

silicon bulk underneath and results in non-smooth silicon surface.

**3.3 Crystallite-free zone in glassy phase** 

TEM micrographs in Figure 9(a) and (c) show the precipitates in the large solidified glassyphase region which is enclosed with Si and Ag-bulk (Lin et al., 2008). The selected area diffraction (SAD) pattern (Figure 9(d)) reveals that only Ag precipitates exist. As shown in Figure 9(a) and its schematic drawing in Figure 9(b), the dissolved Ag atoms near Si-bulk tend to nucleate on the Si surface and lead to an Ag-crystallite-free zone in close vicinity of the Si surface. Also, an Ag-crystallite-free zone near the bulk-Ag can be found. Few or virtually no Ag microcrystallites were found in the Ag-crystallite-free zone. This indicates that the observed Ag microcrystallites are not un-melted Ag particles which were trapped or suspended in the glassy region; instead, they are precipitates from Ag supersaturation molten glassy-phase.

Fig. 9. (a) TEM bright field image. The large glassy-phase enclosed with Si and Ag-bulk. (b) Ag precipitates in the large solidified glassy-phase region. (c) Schematic drawing of image in (b). (d) Selected-area-diffraction pattern of the glassy-phase region shown in (b). Only Ag crystallites exist.

The occurrence of the observed Ag-crystallite-free zone can be accounted for by the diffusion-dependent nucleation mechanism (Porter and Easterling, 1981) as illustrated in Figure 10 (Lin et al., 2008). Upon heating, the dispersed lead silicate glass frits soften into molten phase, in the mean time. They further merged and surrounded the Ag particles due

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 103

between. In addition, high-density Ag-embryo was found on Si-bulk for samples fired optimally. In Figure 11, Ag embryos with sizes less than 5 nm in diameter nucleate epitaxially on the Si surface. The Ag-embryo density is more than 2×1016cm-2, which was counted via TEM. This results in Ag-bulk/thin-glass-layer/Si contact structure. The lack of Ag-bulk/Si direct contact for optimally fired samples leads to a reasonable assumption that Ag-bulk/thinglass-layer/Si contact structure is the most decisive path for current transporting across the interface. The glass layer between Ag-embryos and Ag-bulk for samples fired optimally is too thin (<5nm) to be an effective barrier to electron transfers, which can occur by tunneling.

Fig. 11. Cross-sectional HRTEM of the Ag embryos on Si-bulk. This results in Ag-bulk/thin-

The schematics of a possible conductance mechanisms across the Ag-bulk/thin-glasslayer/Si contact structure is shown in Figure 12. Current transport between Si substrate and front contact is enabled by separated silver crystallites. Since the curved regions of the tinypricipitate/glass-phase interface have higher field intensity due to the small radius of curvature; therefore, the breakdown voltage is less (Sze S.M., 1981). Besides the curvedinterface effect mentioned above, the metal-supersaturated glassy-phase has better conductivity. The embedded metal precipitates in glassy-phase, as shown in Figure 9, can retain the charge and form the interfacial charge storage centers. In addition, the embedded Ag precipitates can be charged and discharged by quantum-mechanical tunneling of electrons. Moreover, the dissolved Ag can substantially increase the trap density at the interface, thereby allowing shorter times for the transportation. Thus, current can transport through the thick glassy-phase not only by multi-tunneling steps between Ag precipitates, but also by thermally excited electrons hopping from one isolated precipitate to the next. In the case of a current transport by multi-tunneling steps between microscopic Ag precipitates, high Ag-precipitate density in the glassy-phase could help to decrease the

specific contact resistance of samples (Gzowski et al. 1982, Ballif et al. 2003).

Many of the ideas that were discussed with regard to Ag-particles/thick-glass-layer/Si microstructure can be carried over to Ag-particles/thin-glass-layer/Si (Figure 5(a)). Only the thick glassy-phase is replaced by an ultrathin glass layer, and this has important consequences for the current conduction across the interface. It was reported (Rollert et al.,

glass-layer/Si contact structure.

to capillary attraction force. Some Ag atoms then dissolved in the molten glassy-phase. The observed Ag precipitates confirm the dissolution of Ag because a critical Ag supersaturation must be exceeded for nucleation to occur. Higher temperature increases the Ag dissolution in the glassy-phase. In the mean time, the majority un-dissolved Ag particles, which are in contact with one another, sinter or coalesce to achieve Ag-bulk via interdiffusion of Ag atoms. The molten glassy-phase can further merge (or etch) the amorphous antireflection coating and, therefore, is in direct contact with the Si-bulk. The formation of Ag-crystallitefree zone is attributed to the nucleation and growth of Ag crystallites on Si-bulk. Upon cooling, the dissolved Ag was drained from the surrounding area to Si surface and an Agcrystallite-free zone results. The width of the Ag-crystallite-free zone is affected by the cooling rate. High cooling rate will produce narrow Ag-crystallite-free zone. This helps in tunneling-assisted carrier transportation. A narrow (width < 20nm) Ag-crystallite-free zone was observed in a large glassy-phase region for optimally fired samples.

It can be found that Ag precipitates in glassy-phase tend to coarsen into larger crystallites with smaller total interfacial area. Also, wide Ag-crystallite-free zones, which surround the large Ag precipitate, were observed. However, the combination effects of low Ag-precipitate density and wide Ag-crystallite-free zone are not favor for current transportation. It, therefore, suggests that long stay in high temperature as well as low cooling rate is of particular concern in the design of firing profile.

Fig. 10. (a) Schematic cross-section drawing of the Ag-embryo on Si-bulk. (b) Schematic drawing of the dissolved Ag-concentration profile near an Ag embryo.

#### **4. Impacts of contact structure on performance of solar cell**

#### **4.1 A possible mechanism for carrier transportation**

The current transport across screen-printed front-side contact of crystalline Si solar cells should be strongly affected by the contact microstructures. This study shows that the area where Agbulk directly contact Si, through SEM observation, is actually with a very thin glass layer in

to capillary attraction force. Some Ag atoms then dissolved in the molten glassy-phase. The observed Ag precipitates confirm the dissolution of Ag because a critical Ag supersaturation must be exceeded for nucleation to occur. Higher temperature increases the Ag dissolution in the glassy-phase. In the mean time, the majority un-dissolved Ag particles, which are in contact with one another, sinter or coalesce to achieve Ag-bulk via interdiffusion of Ag atoms. The molten glassy-phase can further merge (or etch) the amorphous antireflection coating and, therefore, is in direct contact with the Si-bulk. The formation of Ag-crystallitefree zone is attributed to the nucleation and growth of Ag crystallites on Si-bulk. Upon cooling, the dissolved Ag was drained from the surrounding area to Si surface and an Agcrystallite-free zone results. The width of the Ag-crystallite-free zone is affected by the cooling rate. High cooling rate will produce narrow Ag-crystallite-free zone. This helps in tunneling-assisted carrier transportation. A narrow (width < 20nm) Ag-crystallite-free zone

It can be found that Ag precipitates in glassy-phase tend to coarsen into larger crystallites with smaller total interfacial area. Also, wide Ag-crystallite-free zones, which surround the large Ag precipitate, were observed. However, the combination effects of low Ag-precipitate density and wide Ag-crystallite-free zone are not favor for current transportation. It, therefore, suggests that long stay in high temperature as well as low cooling rate is of

Fig. 10. (a) Schematic cross-section drawing of the Ag-embryo on Si-bulk. (b) Schematic

The current transport across screen-printed front-side contact of crystalline Si solar cells should be strongly affected by the contact microstructures. This study shows that the area where Agbulk directly contact Si, through SEM observation, is actually with a very thin glass layer in

drawing of the dissolved Ag-concentration profile near an Ag embryo.

**4. Impacts of contact structure on performance of solar cell** 

**4.1 A possible mechanism for carrier transportation** 

was observed in a large glassy-phase region for optimally fired samples.

particular concern in the design of firing profile.

between. In addition, high-density Ag-embryo was found on Si-bulk for samples fired optimally. In Figure 11, Ag embryos with sizes less than 5 nm in diameter nucleate epitaxially on the Si surface. The Ag-embryo density is more than 2×1016cm-2, which was counted via TEM. This results in Ag-bulk/thin-glass-layer/Si contact structure. The lack of Ag-bulk/Si direct contact for optimally fired samples leads to a reasonable assumption that Ag-bulk/thinglass-layer/Si contact structure is the most decisive path for current transporting across the interface. The glass layer between Ag-embryos and Ag-bulk for samples fired optimally is too thin (<5nm) to be an effective barrier to electron transfers, which can occur by tunneling.

Fig. 11. Cross-sectional HRTEM of the Ag embryos on Si-bulk. This results in Ag-bulk/thinglass-layer/Si contact structure.

The schematics of a possible conductance mechanisms across the Ag-bulk/thin-glasslayer/Si contact structure is shown in Figure 12. Current transport between Si substrate and front contact is enabled by separated silver crystallites. Since the curved regions of the tinypricipitate/glass-phase interface have higher field intensity due to the small radius of curvature; therefore, the breakdown voltage is less (Sze S.M., 1981). Besides the curvedinterface effect mentioned above, the metal-supersaturated glassy-phase has better conductivity. The embedded metal precipitates in glassy-phase, as shown in Figure 9, can retain the charge and form the interfacial charge storage centers. In addition, the embedded Ag precipitates can be charged and discharged by quantum-mechanical tunneling of electrons. Moreover, the dissolved Ag can substantially increase the trap density at the interface, thereby allowing shorter times for the transportation. Thus, current can transport through the thick glassy-phase not only by multi-tunneling steps between Ag precipitates, but also by thermally excited electrons hopping from one isolated precipitate to the next. In the case of a current transport by multi-tunneling steps between microscopic Ag precipitates, high Ag-precipitate density in the glassy-phase could help to decrease the specific contact resistance of samples (Gzowski et al. 1982, Ballif et al. 2003).

Many of the ideas that were discussed with regard to Ag-particles/thick-glass-layer/Si microstructure can be carried over to Ag-particles/thin-glass-layer/Si (Figure 5(a)). Only the thick glassy-phase is replaced by an ultrathin glass layer, and this has important consequences for the current conduction across the interface. It was reported (Rollert et al.,

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 105

be less than 5nm. In addition, the dissolved Ag could improve the electrical conductivity of the glass layer. It, therefore, suggest that carriers through the ultrathin glass layer are the most decisive path for current transportation. A possible mechanism for carriers passing through

The interface microstructure analysis of the screen-printed front-side contact shown in this work is based on industrial-type rapid firing-profile, which results in good contact quality. Although Ag-paste composition and characteristics can be different between manufacturers, the results and trends shown in this work have high degree similarity to other screen-printed crystalline Si solar cells using different types of Ag-paste. Further understanding of the effects of the paste constituents and firing conditions on the contact interface can lead to the development of better, more reproducible, and higher performance contacts in the future.

The fill factor, FF, is a measure of the squareness of the I-V characteristic. The fill factor is given: FF=(VmaxImax)/(VocIsc), where Voc is the open-circuit voltage and Isc is the short-circuit current. Vmax and Imax are voltage and current at maximum power point (Pmax) respectively. The graphical interpretation of Pmax is the area of the largest rectangle below the I-V curve. In practice, FF is less than one because series and parallel resistances will always result in a

It was found that the glass frit plays an important role during contact formation. During firing procedures, the glass frits firstly get fluid, wet and merge the SiNx dielectric layer. It was then etching into silicon substrate. It was known that defects and impurities tend to move to surface upon high temperature treatments to release their high thermodynamic energies. Therefore, the etching degree of silicon by the glass fluid, to some extent, affects the quality of the contacts. On cooling down, silver precipitates, which serve as a transport medium, recrystallize on silicon surface as well as in the glassy phase. This chapter shows that silver precipitates during cooling and the etching degree of silicon during firing are

On cooling down from high temperature firing, the over-saturated silver tends to precipitate. Figure 13(a) shows a SEM microstructure image of optimally fired sample. Besides precipitating in the glassy phase, high density Ag recrystallizes appear on the silicon substrate. The area where silver directly contacts to Si through SEM observation is actually with a very thin glass layer in between. The dissolved Ag atoms near Si-bulk tend to nucleate on the Si surface. Ag-embryo on Si can serve as current pickup points and that conduction from the Agembryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. Thus, the abilities to generate high density Ag embryos on Si-bulk and to keep the glass layer thin are crucial in achieving good electrical contact. The observed Ag precipitates confirms the dissolution of Ag because a critical Ag supersaturation must be exceeded for nucleation to occur. In the case of underfiring, the less dissolved Ag reducing the supersaturation, and

therefore, fewer Ag precipitates grow on Si during cooling as shown in Figure 13(b).

Penetration of native SiOx and SiNx antireflective coating is essential for making good electrical contact to the Si emitter, thus achieving a low contact resistance. However, this must be achieved without etching all the way through the p-n junction and results in shorting the cell. It is found that a smooth curve-shaped Si surface is a distinguishable phenomenon for samples fired optimally. Underfired samples usually have sharp and straight interface, while rough Si surface is usually observed for overfired samples. As shown in Figure 14(a) and (b), overfiring results in rough Si surface. Rough Si surface

FF decrease. A good value for industrial silicon solar cells is ~76-78%.

important for achieving good quality contacts.

the thin glass layer is illustrated by considering electron tunnel, as shown in Figure 12.

**4.2 Effects on fill factor** 

1987) that if the Ag-bulk is in direct contact with the Si and if there was no glass layer in between, the Ag would diffuse at least 5μm deep during the firing cycle and it would shunt the p-n junction. The high-density Ag-embryo on Si found in this study originates from the dissolved Ag in glassy phase, which is in direct contact with Si-bulk. This should play an important role in current transport across the interface. This could be supported by the observation of less Ag-embryo on Si was found for underfired samples, which result in poorer FF of the cell compared to those of optimally fired samples. In the case of underfired samples, the dissolution of Ag is much less; it therefore reduces the supersaturation of Ag. Thus, few Ag precipitates were detected on Si.

Fig. 12. (a) Schematic cross-section drawing of the Ag-embryo on Si-bulk. (b) Schematic energy-band drawing of a possible conductance mechanisms across Ag-bulk/thin-glasslayer/Si contact structure.

As shown in Figure 12, Ag-embryo on Si could serve as current pickup points and that conduction from the Ag-embryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. An increase in the width and the number of Ag precipitates on Si may improve the probability of the encounter of thin glass regions where tunneling can take place. Also, due to tunneling-assisted carrier transport, the fraction of thin glass regions at Ag-bulk/Si interface is critical in reducing the macroscopic contact resistance. Thus, the abilities to generate high-density Ag-embryos on Si-bulk and to keep the glass layer thin are crucial in achieving good electrical contact.

It was reported (Card & Rhoderick 1971, Kumar & Dahlke 1977) that if the insulator layer is sufficiently thick, the tunneling probability through the insulator layer is negligible. Alternatively, if the insulator layer is very thin (< 5nm), little impediment is provided to carrier transport. This study confirms that the spacing between Ag-embryos and Ag-bulk can be less than 5nm. In addition, the dissolved Ag could improve the electrical conductivity of the glass layer. It, therefore, suggest that carriers through the ultrathin glass layer are the most decisive path for current transportation. A possible mechanism for carriers passing through the thin glass layer is illustrated by considering electron tunnel, as shown in Figure 12.

The interface microstructure analysis of the screen-printed front-side contact shown in this work is based on industrial-type rapid firing-profile, which results in good contact quality. Although Ag-paste composition and characteristics can be different between manufacturers, the results and trends shown in this work have high degree similarity to other screen-printed crystalline Si solar cells using different types of Ag-paste. Further understanding of the effects of the paste constituents and firing conditions on the contact interface can lead to the development of better, more reproducible, and higher performance contacts in the future.

#### **4.2 Effects on fill factor**

104 Solar Cells – Silicon Wafer-Based Technologies

1987) that if the Ag-bulk is in direct contact with the Si and if there was no glass layer in between, the Ag would diffuse at least 5μm deep during the firing cycle and it would shunt the p-n junction. The high-density Ag-embryo on Si found in this study originates from the dissolved Ag in glassy phase, which is in direct contact with Si-bulk. This should play an important role in current transport across the interface. This could be supported by the observation of less Ag-embryo on Si was found for underfired samples, which result in poorer FF of the cell compared to those of optimally fired samples. In the case of underfired samples, the dissolution of Ag is much less; it therefore reduces the supersaturation of Ag.

Fig. 12. (a) Schematic cross-section drawing of the Ag-embryo on Si-bulk. (b) Schematic energy-band drawing of a possible conductance mechanisms across Ag-bulk/thin-glass-

As shown in Figure 12, Ag-embryo on Si could serve as current pickup points and that conduction from the Ag-embryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. An increase in the width and the number of Ag precipitates on Si may improve the probability of the encounter of thin glass regions where tunneling can take place. Also, due to tunneling-assisted carrier transport, the fraction of thin glass regions at Ag-bulk/Si interface is critical in reducing the macroscopic contact resistance. Thus, the abilities to generate high-density Ag-embryos on Si-bulk and to keep the glass layer thin are

It was reported (Card & Rhoderick 1971, Kumar & Dahlke 1977) that if the insulator layer is sufficiently thick, the tunneling probability through the insulator layer is negligible. Alternatively, if the insulator layer is very thin (< 5nm), little impediment is provided to carrier transport. This study confirms that the spacing between Ag-embryos and Ag-bulk can

Thus, few Ag precipitates were detected on Si.

layer/Si contact structure.

crucial in achieving good electrical contact.

The fill factor, FF, is a measure of the squareness of the I-V characteristic. The fill factor is given: FF=(VmaxImax)/(VocIsc), where Voc is the open-circuit voltage and Isc is the short-circuit current. Vmax and Imax are voltage and current at maximum power point (Pmax) respectively. The graphical interpretation of Pmax is the area of the largest rectangle below the I-V curve. In practice, FF is less than one because series and parallel resistances will always result in a FF decrease. A good value for industrial silicon solar cells is ~76-78%.

It was found that the glass frit plays an important role during contact formation. During firing procedures, the glass frits firstly get fluid, wet and merge the SiNx dielectric layer. It was then etching into silicon substrate. It was known that defects and impurities tend to move to surface upon high temperature treatments to release their high thermodynamic energies. Therefore, the etching degree of silicon by the glass fluid, to some extent, affects the quality of the contacts. On cooling down, silver precipitates, which serve as a transport medium, recrystallize on silicon surface as well as in the glassy phase. This chapter shows that silver precipitates during cooling and the etching degree of silicon during firing are important for achieving good quality contacts.

On cooling down from high temperature firing, the over-saturated silver tends to precipitate. Figure 13(a) shows a SEM microstructure image of optimally fired sample. Besides precipitating in the glassy phase, high density Ag recrystallizes appear on the silicon substrate. The area where silver directly contacts to Si through SEM observation is actually with a very thin glass layer in between. The dissolved Ag atoms near Si-bulk tend to nucleate on the Si surface. Ag-embryo on Si can serve as current pickup points and that conduction from the Agembryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. Thus, the abilities to generate high density Ag embryos on Si-bulk and to keep the glass layer thin are crucial in achieving good electrical contact. The observed Ag precipitates confirms the dissolution of Ag because a critical Ag supersaturation must be exceeded for nucleation to occur. In the case of underfiring, the less dissolved Ag reducing the supersaturation, and therefore, fewer Ag precipitates grow on Si during cooling as shown in Figure 13(b).

Penetration of native SiOx and SiNx antireflective coating is essential for making good electrical contact to the Si emitter, thus achieving a low contact resistance. However, this must be achieved without etching all the way through the p-n junction and results in shorting the cell. It is found that a smooth curve-shaped Si surface is a distinguishable phenomenon for samples fired optimally. Underfired samples usually have sharp and straight interface, while rough Si surface is usually observed for overfired samples. As shown in Figure 14(a) and (b), overfiring results in rough Si surface. Rough Si surface

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 107

For optimum solar cell efficiency, the current-voltage curve must be as rectangular as possible. The new paste design should increase the fill factor of the solar cell without hurting the short-circuit current density. The current-voltage (I-V) characteristic of an ideal silicon solar cell is plotted in Figure 15 denoted as curve-1. In Figure 15, Curve-2 shows the effect of shunt resistance on the current-voltage characteristic of a solar cell (series resistance Rs=0). The shunt resistance, Rsh, has little effect on the short-circuit current, but reduces the open-circuit voltage. Curce-3 shows the effect of series resistance on the current-voltage characteristic of a solar cell (Rsh∞). Conversely, the series resistance, Rs, has no effect on the open-circuit current, but reduces the short-circuit current. Sources of series resistance include the metal contacts. The extreme current-voltage characteristic, ex. Curve-2 or Curve-3 shown in Figure 15, is not difficult to explain. However, the original sources for I-V curve denoted as Curve-4 in Figure 15 remain unclear. It is not unusually to have I-V feature similar to that of Curve-4. The difference between the curve-1 and curve-4 (the rounded corner of the I-V curve) is probably due to the non-uniform contact resistance of the front contact. Although it is known that the curve can be rounded by series resistance, in practice

curve shapes are often found that cannot be explained by the single series resistance.

Fig. 15. Current-voltage (I-V) characteristic of a silicon solar cell. The I-V curve for an ideal

The front-contact interface for screen printed fingers is non-uniform in structure and composition. The complicate interface-structure influences the series resistance and the fill factor of the cell. From the view of contact-formation mechanism described in this chapter, the melting characteristics of the glass frit determine whether the paste together with the

It was found the post forming gas annealing can help overfired solar cells recover their F.F. The results show that after 400°C post forming gas annealing for 25min, the overfired cells improve their FF. On the other hand, both of the optimally-fired and the under-fired cells did not show

The mechanism of FF recovers for overfired cells after post forming-gas annealing was further investigated. It was found that the supersaturated silver in the glassy-phase plays a very important role for FF recover. More Ag can dissolve in the molten glassy phase for overfired samples than that of optimally fired counterparts. Either higher temperature or

similar effects. The FF remains the same or even worse after conducting post-annealing.

firing condition is suitable for low contact resistance and high fill factors.

cell is denoted as curve-1.

Fig. 13. (a) SEM cross-sectional image of the optimally fired sample. Besides precipitating in the glassy phase, high density Ag recrystallizes on the <111> planes of the pyramid Si. (b) SEM cross-sectional image of the underfired sample. Fewer Ag precipitates grow on Si.

Fig. 14. (a) SEM cross-sectional image of the overfired sample. More bulk Si, especially in the area near the tip of the pyramid, was etched during firing. (b) TEM bright field crosssectional image of the overfired sample.

increase the possibility of undesired surface recombination. Furthermore, as shown in Figure 14(a), more bulk Si, especially in the area near the tip of the pyramid, was etched during firing. The overetching of Si may result in locally shunt of the cell.

In general, the relation between the current density through the contact and the potential across it is non-linear for metal-semiconductor contacts (Schroder and Meier, 1984). The metalsilicon interface for screen printed fingers is known to be non-uniform in structure and composition. It is found the melting characteristics of the glass frit and its ability to dissolved Ag have significant influence on contact resistance and fill factors (FF). Glass frit advances sintering of the Ag particles, wets and merges the antireflection coating. Moreover, glass frit forms a glass layer between Si and Ag-bulk, and can further react with Si-bulk and forms pinholes on the Si surface upon high temperature firing. Typical firing temperatures of a commercial solar cell were between 750C and 800C, where the optimum balance between the Ag-crystallite density and the distribution of the glass layer should be found.

Fig. 13. (a) SEM cross-sectional image of the optimally fired sample. Besides precipitating in the glassy phase, high density Ag recrystallizes on the <111> planes of the pyramid Si. (b) SEM cross-sectional image of the underfired sample. Fewer Ag precipitates grow on Si.

Fig. 14. (a) SEM cross-sectional image of the overfired sample. More bulk Si, especially in the

increase the possibility of undesired surface recombination. Furthermore, as shown in Figure 14(a), more bulk Si, especially in the area near the tip of the pyramid, was etched

In general, the relation between the current density through the contact and the potential across it is non-linear for metal-semiconductor contacts (Schroder and Meier, 1984). The metalsilicon interface for screen printed fingers is known to be non-uniform in structure and composition. It is found the melting characteristics of the glass frit and its ability to dissolved Ag have significant influence on contact resistance and fill factors (FF). Glass frit advances sintering of the Ag particles, wets and merges the antireflection coating. Moreover, glass frit forms a glass layer between Si and Ag-bulk, and can further react with Si-bulk and forms pinholes on the Si surface upon high temperature firing. Typical firing temperatures of a commercial solar cell were between 750C and 800C, where the optimum balance between the

area near the tip of the pyramid, was etched during firing. (b) TEM bright field cross-

during firing. The overetching of Si may result in locally shunt of the cell.

Ag-crystallite density and the distribution of the glass layer should be found.

sectional image of the overfired sample.

For optimum solar cell efficiency, the current-voltage curve must be as rectangular as possible. The new paste design should increase the fill factor of the solar cell without hurting the short-circuit current density. The current-voltage (I-V) characteristic of an ideal silicon solar cell is plotted in Figure 15 denoted as curve-1. In Figure 15, Curve-2 shows the effect of shunt resistance on the current-voltage characteristic of a solar cell (series resistance Rs=0). The shunt resistance, Rsh, has little effect on the short-circuit current, but reduces the open-circuit voltage. Curce-3 shows the effect of series resistance on the current-voltage characteristic of a solar cell (Rsh∞). Conversely, the series resistance, Rs, has no effect on the open-circuit current, but reduces the short-circuit current. Sources of series resistance include the metal contacts. The extreme current-voltage characteristic, ex. Curve-2 or Curve-3 shown in Figure 15, is not difficult to explain. However, the original sources for I-V curve denoted as Curve-4 in Figure 15 remain unclear. It is not unusually to have I-V feature similar to that of Curve-4. The difference between the curve-1 and curve-4 (the rounded corner of the I-V curve) is probably due to the non-uniform contact resistance of the front contact. Although it is known that the curve can be rounded by series resistance, in practice curve shapes are often found that cannot be explained by the single series resistance.

Fig. 15. Current-voltage (I-V) characteristic of a silicon solar cell. The I-V curve for an ideal cell is denoted as curve-1.

The front-contact interface for screen printed fingers is non-uniform in structure and composition. The complicate interface-structure influences the series resistance and the fill factor of the cell. From the view of contact-formation mechanism described in this chapter, the melting characteristics of the glass frit determine whether the paste together with the firing condition is suitable for low contact resistance and high fill factors.

It was found the post forming gas annealing can help overfired solar cells recover their F.F. The results show that after 400°C post forming gas annealing for 25min, the overfired cells improve their FF. On the other hand, both of the optimally-fired and the under-fired cells did not show similar effects. The FF remains the same or even worse after conducting post-annealing.

The mechanism of FF recovers for overfired cells after post forming-gas annealing was further investigated. It was found that the supersaturated silver in the glassy-phase plays a very important role for FF recover. More Ag can dissolve in the molten glassy phase for overfired samples than that of optimally fired counterparts. Either higher temperature or

Silicon Solar Cells: Structural Properties of Ag-Contacts/Si-Substrate 109

interface structure. It can be found that the Ag crystals in the glassy phase grow to larger size either by electron beam annealing or by heat treatments, indicating a better current transportation. The Ag area coverage at the Si-Ag interface is increased. More and larger Ag crystallites in the glassy phase increase the contact area fraction, which improves the probability of tunneling from Ag crystallites to the Ag bulk. The better conductance contributes to lower contact resistance and a higher FF. Also shown in Figure 16(b), more Ag embryos were generated and result in a locally decreased contact resistance. The rounded-corner feature of the I-V curve, as shown as Curve-4 in Figure 15, can be improved. The rounded-corner feature of the I-V curve is caused by combination effects of resistance and recombination. Control the process better and decrease the carriers' jumping-path can

Despite the success of the screen printing and the subsequent firing process, many aspects of the physics of the front-contact formation are not fully clear. The major reason is probably because the contact-interface for screen printed fingers is non-uniform in structure and composition. The contact microstructures have a high impact on current-transport across the

This chapter first presents the Ag-bulk/Si contact structures of the crystalline silicon solar cells. Then, the influences of the Ag-contacts/Si-substrate on performance of the resulted cells are investigated. The objective of this work was to improve the understanding of front-side contact formation by analyzing the individual contact types and their role in the Ag-bulk/Si contact. Microstructure analyzing confirmed that the glassy-phase plays an important role in contact properties. The location where Ag-bulk directly contact Si-substrate, through SEM observation, is actually a very thin glass layer in between. High density Ag-embryos on Sibulk were found for samples fired optimally. It is suggested that Ag-bulk/thin-glass-layer/Si contact is the most decisive path for current transportation. Possible conductance mechanisms

Ag-embryo on Si could serve as current pickup points and that conduction from the Agembryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. Thus, the abilities to generate high density Ag embryos on Si-bulk and to keep the glass

This chapter also reports that after 400°C post forming-gas annealing for 25min, the overfired cells improve their FF. The mechanism for FF enhancement of the overfired cells after post-annealing is related to the supersaturated silver in glassy-phase. The postannealing helps the supersaturated silver further precipitate in the glassy-phase or move to already exist Ag crystallites. More and larger Ag crystallites in the glassy phase increase the contact-area fraction, which improves the probability of tunneling from silver crystallites to

The interface microstructure analysis of the screen-printed front-side contact shown in this work is based on industrial-type rapid firing-profile. Although Ag-paste composition and characteristics can be different per manufacturer, the results and trends shown in this work have high degree similarity to other screen-printed cell using different type Ag-paste. Further understanding the effects of the paste constituents and firing conditions on the contact-interface can lead to develop a better, more reproducible, and higher performance

improve the fill factor of the cell.

of electrons across the contact interface are also discussed.

layer thin are crucial in achieving good electrical contact.

**5. Conclusion** 

contact-interface.

the silver bulk.

screen-printed electrode.

longer heating time increases the Ag dissolution in the glassy-phase. Some of the supersaturated silver in the glass for overfired cells was unable to recrystallize because of the rapid cooling process. The post-annealing helps the supersaturated silver further precipitate in the glassy-phase or move to already exist Ag crystallites. The number of small precipitates is increased and the conductivity of the insulating glass is improved. Postannealing the overfired cells thus results in recovering high FF and low contact resistance. An increase in the size and number of silver crystallites at the interface and in the glass phase can improve the current transportation.

Post-annealing of overfired cells helps the supersaturated Ag precipitate. It also coalesce the pre-formed Ag crystallites. More Ag embryos were generated and grew to larger size, which decreased the contact resistance, and enhanced the F.F. As shown in Table 1, the forminggas anneal reduces the contact resistance, and thus, it improves the FF for the overfired cells. In Table 1, the post-annealing increases the FF by 1.5~9%. However, it should be mentioned that the cells cannot be overfired too much. It must be avoided to etch all the way through the p-n junction, which results in shorting the cell. The overetching of Si underneath may result in locally shunt of the cell. Besides, overfiring results in rough Si surface. Rough Si surface increase the possibility of undesired surface recombination.


Table 1. The forming gas anneal improves the FF for the overfired cells.

The mechanism for FF enhancement of the overfired cells after post-annealing is related to the supersaturated Ag. Figure 16(a) shows a HRTEM image of the silicon/electrode

Fig. 16. (a) HR TEM contrast of more and large Ag crystallites in the glassy phase. (b) HR TEM contrast of contact interface. Ag precipitates are closer to Ag-bulk.

interface structure. It can be found that the Ag crystals in the glassy phase grow to larger size either by electron beam annealing or by heat treatments, indicating a better current transportation. The Ag area coverage at the Si-Ag interface is increased. More and larger Ag crystallites in the glassy phase increase the contact area fraction, which improves the probability of tunneling from Ag crystallites to the Ag bulk. The better conductance contributes to lower contact resistance and a higher FF. Also shown in Figure 16(b), more Ag embryos were generated and result in a locally decreased contact resistance. The rounded-corner feature of the I-V curve, as shown as Curve-4 in Figure 15, can be improved. The rounded-corner feature of the I-V curve is caused by combination effects of resistance and recombination. Control the process better and decrease the carriers' jumping-path can improve the fill factor of the cell.

#### **5. Conclusion**

108 Solar Cells – Silicon Wafer-Based Technologies

longer heating time increases the Ag dissolution in the glassy-phase. Some of the supersaturated silver in the glass for overfired cells was unable to recrystallize because of the rapid cooling process. The post-annealing helps the supersaturated silver further precipitate in the glassy-phase or move to already exist Ag crystallites. The number of small precipitates is increased and the conductivity of the insulating glass is improved. Postannealing the overfired cells thus results in recovering high FF and low contact resistance. An increase in the size and number of silver crystallites at the interface and in the glass

Post-annealing of overfired cells helps the supersaturated Ag precipitate. It also coalesce the pre-formed Ag crystallites. More Ag embryos were generated and grew to larger size, which decreased the contact resistance, and enhanced the F.F. As shown in Table 1, the forminggas anneal reduces the contact resistance, and thus, it improves the FF for the overfired cells. In Table 1, the post-annealing increases the FF by 1.5~9%. However, it should be mentioned that the cells cannot be overfired too much. It must be avoided to etch all the way through the p-n junction, which results in shorting the cell. The overetching of Si underneath may result in locally shunt of the cell. Besides, overfiring results in rough Si surface. Rough Si

> Voc/Voc (%)

1 -0.68 -0.25 2.66 1.71 2 -0.30 -0.27 1.75 1.16 3 -0.36 -0.05 4.68 4.25 4 -1.92 -0.61 3.19 0.58 5 -0.01 -0.68 9.13 8.38

The mechanism for FF enhancement of the overfired cells after post-annealing is related to the supersaturated Ag. Figure 16(a) shows a HRTEM image of the silicon/electrode

Fig. 16. (a) HR TEM contrast of more and large Ag crystallites in the glassy phase. (b) HR

TEM contrast of contact interface. Ag precipitates are closer to Ag-bulk.

FF/FF (%)

Eff/Eff (%)

phase can improve the current transportation.

Sample # Jsc/Jsc

surface increase the possibility of undesired surface recombination.

Table 1. The forming gas anneal improves the FF for the overfired cells.

(%)

Despite the success of the screen printing and the subsequent firing process, many aspects of the physics of the front-contact formation are not fully clear. The major reason is probably because the contact-interface for screen printed fingers is non-uniform in structure and composition. The contact microstructures have a high impact on current-transport across the contact-interface.

This chapter first presents the Ag-bulk/Si contact structures of the crystalline silicon solar cells. Then, the influences of the Ag-contacts/Si-substrate on performance of the resulted cells are investigated. The objective of this work was to improve the understanding of front-side contact formation by analyzing the individual contact types and their role in the Ag-bulk/Si contact. Microstructure analyzing confirmed that the glassy-phase plays an important role in contact properties. The location where Ag-bulk directly contact Si-substrate, through SEM observation, is actually a very thin glass layer in between. High density Ag-embryos on Sibulk were found for samples fired optimally. It is suggested that Ag-bulk/thin-glass-layer/Si contact is the most decisive path for current transportation. Possible conductance mechanisms of electrons across the contact interface are also discussed.

Ag-embryo on Si could serve as current pickup points and that conduction from the Agembryo to Ag-bulk takes place via tunneling through the ultrathin glass layer in between. Thus, the abilities to generate high density Ag embryos on Si-bulk and to keep the glass layer thin are crucial in achieving good electrical contact.

This chapter also reports that after 400°C post forming-gas annealing for 25min, the overfired cells improve their FF. The mechanism for FF enhancement of the overfired cells after post-annealing is related to the supersaturated silver in glassy-phase. The postannealing helps the supersaturated silver further precipitate in the glassy-phase or move to already exist Ag crystallites. More and larger Ag crystallites in the glassy phase increase the contact-area fraction, which improves the probability of tunneling from silver crystallites to the silver bulk.

The interface microstructure analysis of the screen-printed front-side contact shown in this work is based on industrial-type rapid firing-profile. Although Ag-paste composition and characteristics can be different per manufacturer, the results and trends shown in this work have high degree similarity to other screen-printed cell using different type Ag-paste. Further understanding the effects of the paste constituents and firing conditions on the contact-interface can lead to develop a better, more reproducible, and higher performance screen-printed electrode.

**6** 

**Possibilities of Usage LBIC Method for** 

Light Beam Induced method works on principle of exposure very small area of a solar cell, usually by laser beam focused directly on the solar cell surface. This point light source moves over measured solar cell in direction of both X and Y axis. Thanks to local current voltage response the XY current - voltage distribution in investigated solar cell can be measured. Acquainted data are then arranged in form of a current map and the behaviour of whole solar cell single parts is thus visible. Most common quantity measured by Light Beam

Induced method is Current (LBIC) which is set near local ISC current.

Fig. 1. Diagrammatical demonstration of measuring system (Vanek J, Fort T, 2007)

destructive characterization of structure of solar cells.

If the inner resistance of the measured amplifier is set to high value then the response of light is matching to VOC and the method is designed as LBIV. There was some attempt to track the local maximum power point and to record local power value (LBIP) but the most widespread method is LIBC for this predicative feature. In such current map is possible to determine majority of local defects, therefor the LBIC is the useful method to provide a non-

**1. Introduction** 

**Characterisation of Solar Cells** 

Jiri Vanek and Kristyna Jandova

*Brno University of Technology* 

*Czech Republic* 

#### **6. Acknowledgements**

It is gratefully acknowledged that this work has been supported by Bureau of Energy, Ministry of Economics Affairs, Taiwan. The authors would also like to thank Shu-Chi Hsu and Chih-Jen Lin for their TEM operation.

#### **7. References**


## **Possibilities of Usage LBIC Method for Characterisation of Solar Cells**

Jiri Vanek and Kristyna Jandova *Brno University of Technology Czech Republic* 

#### **1. Introduction**

110 Solar Cells – Silicon Wafer-Based Technologies

It is gratefully acknowledged that this work has been supported by Bureau of Energy, Ministry of Economics Affairs, Taiwan. The authors would also like to thank Shu-Chi Hsu

Ballif C., D. M. Huljić, G. Willeke, and A. Hessler-Wysser (2003). Silver thick-film contacts

Hilali M.M., K. Nakayahiki, C. Khadilkar, R. C. Reedy, A. Rohatgi, A. Shaikh, S. Kim, and S.

Hilali M.M., M. M. Al-Jassim, B. To, H. Moutinho, A. Rohatgi, and S. Asher (2005). *Journal of The Electrochemical Society,* Vol. 152, pp. G742-G749. ISSN 0013-4651. Hoornstra J., G. Schubert, K. Broek, F. Granek, C. LePrince (2005). Lead free metallization

Horteis M, T. Gutberlet, A. Reller, and S.W. Glunz (2010). High-temperature contact

Lin C.-H., S.-Y. Tsai, S.-P. Hsu, and M.-H. Hsieh (2008). Investigation of Ag-bulk/glassy-

Porter D.A. and K.E. Easterling (1981), *Phase Transformations in Metals and Alloys*, Chapman

Rollert F., N. A. Stolwijk, and H. Mehrer (1987), Solubility, diffusion and thermodynamic

Schroder D.K. & Meier D.L. (1984). Solar cell contact resistance – a review, *IEEE Transactions* 

Schubert G., F. Huster, P. Fath (2004), Current Transport Mechanism in printed Ag Thick

*19th European Photovoltaic Solar Energy Conference*, Paris, France, pp. 813-817. Schubert G., F. Huster, and P. Fath (2006). Physical understanding of printed thick-film front

developments, *Solar Energy Materials & Solar Cells*, Vol. 90, pp. 3399-3406. Sze S.M.(1981). *Physics of Semiconductor Devices*, 2nd Edition, John Wiley & Sons, New York,

Weber L. (2002), Equilibrium solid solubility of silicon in silver, *Metallurgical and Materials* 

interface, *Applied Physics Letters*, Vol. 82, pp. 1878-1880. ISSN 0003-6951. Card H.C. and E. H. Rhoderick (1971). Studies of tunnel MOS diodes I. Interface effects in silicon Schottky diodes, *Journal of Physics D: Applied Physics*, Vol. 4, pp. 1589. Gzowski O., L. Murawski, and K. Trzebiatowski (1982). The surface conductivity of lead

glasses, *Journal of Physics D: Applied Physics, Vol*. 15, pp. 1097-1101.

*The Electrochemical Society*, Vol. 153, pp. A5-A11. ISSN 0013-4651.

contacts, *Advanced Functional Mateials*, Vol. 20, pp. 476-484. Kumar V. and W. E. Dahlke (1977), Solid State Electron., Vol. 20, pp. 143.

*Energy Materials & Solar Cells*, Vol. 92, pp. 1011-1015.

*on Electron Devices*, Vol. 31, pp. 637-647. ISSN 0018-9383.

on highly doped n-type silicon emitters: structural and electronic properties of the

Sridharan (2006). Effect of Ag particle size in thick-film Ag paste on the electrical and physical properties of screen printed contacts and silicon solar cells, *Journal of* 

paste for crystalline silicon solar cells: from model to results, *31st IEEE PVSC* 

formation on n-type silicon: basic reactions and contact model for seed-layer

phase/Si heterostructures of printed Ag contacts on crystalline Si solar cells, *Solar* 

properties of silver in silicon, *Journal of Physics D: Applied Physics*, Vol. 20, pp. 1148-

Film Contacts to an n-type Emitter of a Crystalline Silicon Solar Cell, *Proceedings of* 

contacts of crystalline Si solar cells—Review of existing models and recent

**6. Acknowledgements** 

**7. References** 

and Chih-Jen Lin for their TEM operation.

*conference*, Orlando, Florida.

& Hall, New York.

ISBN 10-0471-0566-18.

*Transactions A*, Vol. 33, pp. 1145-1150.

1155.

Light Beam Induced method works on principle of exposure very small area of a solar cell, usually by laser beam focused directly on the solar cell surface. This point light source moves over measured solar cell in direction of both X and Y axis. Thanks to local current voltage response the XY current - voltage distribution in investigated solar cell can be measured. Acquainted data are then arranged in form of a current map and the behaviour of whole solar cell single parts is thus visible. Most common quantity measured by Light Beam Induced method is Current (LBIC) which is set near local ISC current.

Fig. 1. Diagrammatical demonstration of measuring system (Vanek J, Fort T, 2007)

If the inner resistance of the measured amplifier is set to high value then the response of light is matching to VOC and the method is designed as LBIV. There was some attempt to track the local maximum power point and to record local power value (LBIP) but the most widespread method is LIBC for this predicative feature. In such current map is possible to determine majority of local defects, therefor the LBIC is the useful method to provide a nondestructive characterization of structure of solar cells.

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 113

(Nanometers) <sup>400</sup> <sup>450</sup> <sup>500</sup> <sup>550</sup> <sup>600</sup> <sup>650</sup> <sup>700</sup> <sup>750</sup>

(Nanometers) <sup>750</sup> <sup>800</sup> <sup>850</sup> <sup>900</sup> <sup>950</sup> <sup>1000</sup> <sup>1050</sup> <sup>1100</sup>

On the other hand when the wavelength is closer to energy of band gab the spectral efficiency is higher. When photon with high energy impacts silicon atom there is high probability to excitation of valence electron to non-stable energy band and in short time the electron is moving to lower stable energy band. The energy difference is lost and change to heat. Therefor spectral response of higher wavelength photons should be higher than of

Light sources with wavelengths of various colors were used for scanning of samples – Table 2. Various wavelengths of light were used to show the different defects in different depth under the surface of silicon solar cells. See Table 1. Apart from laser, highly illuminating LED diodes installed in a tube similar to that of LASER were used. The tube was a capsule enabling smooth installation of the LED diode instead of laser. It also enabled

The LBIC method is realized by the movement of the light source (focused LED diode or laser) fixed on the grid of the pen XY plotter MUTOH IP-210 near the solar cell surface. Thanks to the local response of the solar cell to incident light we get the scan of local current differences (we were using the measurement PC card Tedia PCA-1208). From the obtained data we can get the whole picture of the solar cell current response to light. From this

For light exposure LASERs and high luminous LED diodes were used. They were inserted into a special container with the same dimensions like the LASERs. The container was used for smooth assembling in the same grid like the LASER and for holding the focusing lens

We have studied set of four samples of solar cells with known defects like swirl defect,

All global parameters of these test cells were known from previous measurements. These

source laser LED LED LED color infrared red green blue wavelength 830 nm 660 nm 560 nm 430 nm

0.1 0.4 0.9 1.5 2.4 3.4 5.2 7.0

8.4 11 19 33 54 156 613 2857

Wavelength

Penetration Depth (Micrometers)

Wavelength

Penetration Depth (Micrometers

regulation of illumination.

and screening slide.

Table 1. Photon Absorption Depth in Silicon (c-Si PC1D 300K)

photons of lower wavelength (even they have higher energy).

**2. Light beam induced current measurement** 

picture we can read the most local type of defect.

scratches, diffusion fail and missing contacts act.

parameters are showed in Table 3.

Table 2. Used light sources

Fig. 2. Operating point of measuring amplifier and resultant method

#### **1.1 Different wavelengths of light source used in LBIC**

The effect on the absorption coefficient and penetration depth, defined as distance that light travels before the intensity falls to 36% (1/e), is clearly shown in figure 3. Note that the data in figure 3 represent unstrained bulk material with no voltage applied. By introducing strain or electrical bias, it is possible to shift the curves slightly to a higher wavelength due to a reduction in the effective band gap.

Fig. 3. Absorption coefficient and penetration depth of various bulk materials as a function of wavelength. (Intel,Photodetectors, 2004)

In cases where the photon energy is greater than the band gap energy, an electron has a high probability of being excited into the conduction band, thus becoming mobile. This interaction is also known as the photoelectric effect, and is dependent upon a critical wavelength above which photons have insufficient energy to excite or promote an electron positioned in the valence band and produce an electron-hole pair. When photons exceed the critical wavelength (usually beyond 1100 nanometres for silicon) band gap energy is greater than the intrinsic photon energy, and photons pass completely through the substrate. Table 1 lists the depths (in microns) at which 90 percent of incident photons are absorbed by a typical solar cell.

The effect on the absorption coefficient and penetration depth, defined as distance that light travels before the intensity falls to 36% (1/e), is clearly shown in figure 3. Note that the data in figure 3 represent unstrained bulk material with no voltage applied. By introducing strain or electrical bias, it is possible to shift the curves slightly to a higher wavelength due to a

Fig. 3. Absorption coefficient and penetration depth of various bulk materials as a function

In cases where the photon energy is greater than the band gap energy, an electron has a high probability of being excited into the conduction band, thus becoming mobile. This interaction is also known as the photoelectric effect, and is dependent upon a critical wavelength above which photons have insufficient energy to excite or promote an electron positioned in the valence band and produce an electron-hole pair. When photons exceed the critical wavelength (usually beyond 1100 nanometres for silicon) band gap energy is greater than the intrinsic photon energy, and photons pass completely through the substrate. Table 1 lists the depths (in

microns) at which 90 percent of incident photons are absorbed by a typical solar cell.

Fig. 2. Operating point of measuring amplifier and resultant method

**1.1 Different wavelengths of light source used in LBIC** 

reduction in the effective band gap.

of wavelength. (Intel,Photodetectors, 2004)


Table 1. Photon Absorption Depth in Silicon (c-Si PC1D 300K)

On the other hand when the wavelength is closer to energy of band gab the spectral efficiency is higher. When photon with high energy impacts silicon atom there is high probability to excitation of valence electron to non-stable energy band and in short time the electron is moving to lower stable energy band. The energy difference is lost and change to heat. Therefor spectral response of higher wavelength photons should be higher than of photons of lower wavelength (even they have higher energy).

#### **2. Light beam induced current measurement**

Light sources with wavelengths of various colors were used for scanning of samples – Table 2. Various wavelengths of light were used to show the different defects in different depth under the surface of silicon solar cells. See Table 1. Apart from laser, highly illuminating LED diodes installed in a tube similar to that of LASER were used. The tube was a capsule enabling smooth installation of the LED diode instead of laser. It also enabled regulation of illumination.

The LBIC method is realized by the movement of the light source (focused LED diode or laser) fixed on the grid of the pen XY plotter MUTOH IP-210 near the solar cell surface. Thanks to the local response of the solar cell to incident light we get the scan of local current differences (we were using the measurement PC card Tedia PCA-1208). From the obtained data we can get the whole picture of the solar cell current response to light. From this picture we can read the most local type of defect.

For light exposure LASERs and high luminous LED diodes were used. They were inserted into a special container with the same dimensions like the LASERs. The container was used for smooth assembling in the same grid like the LASER and for holding the focusing lens and screening slide.

We have studied set of four samples of solar cells with known defects like swirl defect, scratches, diffusion fail and missing contacts act.

All global parameters of these test cells were known from previous measurements. These parameters are showed in Table 3.


Table 2. Used light sources

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 115

response is assigned black color. For authenticity of measurement the pictures are kept in

Fig. 6. Analyses of output local current of the sample no. 1 by usage of focused LED diode

Fig. 7. Analyses of output local current of the sample no. 3 by usage of focused LED diode

with middle wavelength 650 nm (red LED, T=297 K)

with middle wavelength 650 nm (red LED, T=297 K)

their original setting.

Fig. 5. Front and back side of monocrystaline silicon solar cell.


Table 3. Data for global parameters of tested solar cells (Solartec s.r.o, 2005)

There are presented two results for each wavelength (colour of light) of inducing radiation to the chosen samples for a better comparison. There were the sample no. 1 and no 3 chosen. The maximal value of local current is assigned the white color and the minimal current

Fig. 4. Laser used in LBIC

Fig. 5. Front and back side of monocrystaline silicon solar cell.

Isc [A]

Table 3. Data for global parameters of tested solar cells (Solartec s.r.o, 2005)

Uoc [V]

Im [A]

1 2,729 2,842 0,576 2,628 0,476 1,252 76,5 12,04 2 2,344 2,511 0,559 2,293 0,461 1,057 75,4 10,17 3 2,426 2,602 0,560 2,344 0,466 1,092 74,9 10,50 4 2,500 2,670 0,567 2,473 0,459 1,136 75,1 10,92

There are presented two results for each wavelength (colour of light) of inducing radiation to the chosen samples for a better comparison. There were the sample no. 1 and no 3 chosen. The maximal value of local current is assigned the white color and the minimal current

Um [V]

Pm [W]

FF [%] EEF [%]

[A]

**Sample** I450

response is assigned black color. For authenticity of measurement the pictures are kept in their original setting.

Fig. 6. Analyses of output local current of the sample no. 1 by usage of focused LED diode with middle wavelength 650 nm (red LED, T=297 K)


Fig. 7. Analyses of output local current of the sample no. 3 by usage of focused LED diode with middle wavelength 650 nm (red LED, T=297 K)

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 117

For the green LED diode (middle wavelength 560 nm, figures 8 and 9) the defect is still well

From the principle of photovoltaic effect it is clear that the light with sufficiently long wavelength passes through the solar cell without generation of photocurrent. With a shorter wavelength the light is absorbed faster from impact light to solar cell and that is why the

The wavelength of red light is the longest for the used light sources; therefore the penetration depth is the longest. This is proven by well-market visibility of swirl defect

Along the way the wavelength of blue light is the shortest and it causes the full loss of visibility of this defect. This is caused by the absorption of the light near the solar cell

The wavelength of green color light is between the wavelengths of red and blue color light. Therefore the green color light penetrates to a deeper depth than the blue color light but not

The swirl defect for the blue color (wavelength 430 nm, figures. 10 and 11) is almost

We may think that the blue color light is not important for LBIC diagnostic because it does not allow the bulk defect detection. If you look at the figure closely, you can observe a decreased affectivity of solar cell in the top right-hand corner of solar cell no 3. (the area of dark gray). These inhomogeneities are due to irregular diffusion during solar cell manufacturing. By the usage of light of red color spectrum this defect is not possible to detect. These defects are surface defects. Even the green colour light can make these

Fig. 10. Analyses of output local current of the sample no. 1 by usage of focused LED diode

visible, but not as well-marked as for the red colour (middle wavelength 650 nm).

penetration depth is shorter.

so deep as the red color light.

invisible.

which is the defect made in bulk of material.

surface where the swirl defect is not taking effect yet.

inhomogeneities visible, but they can be easily overlooked.

with middle wavelength 430 nm (blue LED, T=297 K)

As mentioned above all samples contain a swirl defect. If you look at the pictures produced by red LED (wavelength 650 nm, figs 6 and 7) this defect is clearly visible.


Fig. 8. Analyses of output local current of the sample no. 1 by usage of focused LED diode with middle wavelength 560 nm (green LED, T=297 K)


Fig. 9. Analyses of output local current of the sample no. 1 by usage of focused LED diode with middle wavelength 560 nm (green LED, T=297 K)

As mentioned above all samples contain a swirl defect. If you look at the pictures produced

Fig. 8. Analyses of output local current of the sample no. 1 by usage of focused LED diode

Fig. 9. Analyses of output local current of the sample no. 1 by usage of focused LED diode

with middle wavelength 560 nm (green LED, T=297 K)

with middle wavelength 560 nm (green LED, T=297 K)

by red LED (wavelength 650 nm, figs 6 and 7) this defect is clearly visible.

For the green LED diode (middle wavelength 560 nm, figures 8 and 9) the defect is still well visible, but not as well-marked as for the red colour (middle wavelength 650 nm).

From the principle of photovoltaic effect it is clear that the light with sufficiently long wavelength passes through the solar cell without generation of photocurrent. With a shorter wavelength the light is absorbed faster from impact light to solar cell and that is why the penetration depth is shorter.

The wavelength of red light is the longest for the used light sources; therefore the penetration depth is the longest. This is proven by well-market visibility of swirl defect which is the defect made in bulk of material.

Along the way the wavelength of blue light is the shortest and it causes the full loss of visibility of this defect. This is caused by the absorption of the light near the solar cell surface where the swirl defect is not taking effect yet.

The wavelength of green color light is between the wavelengths of red and blue color light. Therefore the green color light penetrates to a deeper depth than the blue color light but not so deep as the red color light.

The swirl defect for the blue color (wavelength 430 nm, figures. 10 and 11) is almost invisible.

We may think that the blue color light is not important for LBIC diagnostic because it does not allow the bulk defect detection. If you look at the figure closely, you can observe a decreased affectivity of solar cell in the top right-hand corner of solar cell no 3. (the area of dark gray). These inhomogeneities are due to irregular diffusion during solar cell manufacturing. By the usage of light of red color spectrum this defect is not possible to detect. These defects are surface defects. Even the green colour light can make these inhomogeneities visible, but they can be easily overlooked.

Fig. 10. Analyses of output local current of the sample no. 1 by usage of focused LED diode with middle wavelength 430 nm (blue LED, T=297 K)

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 119

Among other defects we count scratches and scrapes which are well-marked by all colors even if they are surface defects. This is due to the damage of solar cell structure by higher

We can compare results for sample no. 3 with the figure produced by the infrared laser M4LA5-30-830 (wavelength 830nm, Fig. 12.). This is the longest wavelength and the

The swirl defect displayed by the infrared laser is the most intensive which is the proof of the deepest penetration depth. The obtained picture is slightly defocused in comparison with previous pictures. This is due complicated focusing system of impacting beam because IR light is not visible. The focusing is performed by a special specimen used for focusing the IR laser. The big intensity of defect and a little defocused picture produce a partial loss of

The result of solar cell scanning is array of values corresponding to local current response to impacting light beam. This array of value is depending on AD convertor but mostly the result is the 12-bit value matrix which is converted to 8 bit (grey tone picture) graphic output. A value 0 corresponds to the darkest black and value 255 corresponds to the lightest white. By the changing of the corresponding colour interval we can visualize the defects

Fig. 13. Front and back side of tested monocrystaline silicon solar cell 710B1.

which are hidden for graphic analyse and improve the output picture.

recombination or higher reflection of damaged surface.

penetration depth is the deepest.

information about the surface defect.

**2.1 Graphic analyses of LBIC data** 

Fig. 11. Analyses of output local current of the sample no. 3 by usage of focused LED diode with middle wavelength 430 nm (blue LED, T=297 K)

Fig. 12. Analyses of output local current of the sample no. 3 by usage of focused infrared laser (830nm, T=297K)

Among other defects we count scratches and scrapes which are well-marked by all colors even if they are surface defects. This is due to the damage of solar cell structure by higher recombination or higher reflection of damaged surface.

We can compare results for sample no. 3 with the figure produced by the infrared laser M4LA5-30-830 (wavelength 830nm, Fig. 12.). This is the longest wavelength and the penetration depth is the deepest.

The swirl defect displayed by the infrared laser is the most intensive which is the proof of the deepest penetration depth. The obtained picture is slightly defocused in comparison with previous pictures. This is due complicated focusing system of impacting beam because IR light is not visible. The focusing is performed by a special specimen used for focusing the IR laser. The big intensity of defect and a little defocused picture produce a partial loss of information about the surface defect.

#### **2.1 Graphic analyses of LBIC data**

118 Solar Cells – Silicon Wafer-Based Technologies

Fig. 11. Analyses of output local current of the sample no. 3 by usage of focused LED diode

Fig. 12. Analyses of output local current of the sample no. 3 by usage of focused infrared

with middle wavelength 430 nm (blue LED, T=297 K)

laser (830nm, T=297K)

The result of solar cell scanning is array of values corresponding to local current response to impacting light beam. This array of value is depending on AD convertor but mostly the result is the 12-bit value matrix which is converted to 8 bit (grey tone picture) graphic output. A value 0 corresponds to the darkest black and value 255 corresponds to the lightest white. By the changing of the corresponding colour interval we can visualize the defects which are hidden for graphic analyse and improve the output picture.

Fig. 13. Front and back side of tested monocrystaline silicon solar cell 710B1.

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 121

Fig. 16. Output LBIC scan of sample 710B1 in coloured nonlinear selected interval measured

Thanks to different wavelength of used light illumination we can detect different defect and structures depending on penetration depth of light photon. However, the experiments have showed that we can detect structures behind of expected depth like contact bar on the back side of solar cells. This contact we did not detect using long wavelength (IR-980 nm or red-630 nm LED) but they were clearly visible using short wave length (green-525 nm, blue-430 nm or UV-400 nm LED). Nevertheless using long wavelength enable to clearly detect deep material defects like swirl which are not clearly detectable by UV or blue wavelength

Projection of back side contact bar to short wavelength LBIC picture can be explain by theory of secondary emission of long wavelength light (~1100 nm) which has penetration depth (~2800m) much more higher then solar cells depth. Incident high energy light is absorbed in front surface of solar cell and generates electron-hole pair. Part of this carrier charges are separated and generated photocurrent. Because of small penetration depth of impacting photon, most of carrier charges generate near surface area. Thank to high recombination rate on surface a big amount of this carrier charges recombine and emit IR light. The spectral efficiency of impacting photon wavelength is low so the output primary photocurrent is low, too, and do not cover the current induced by secondary emitted photons with energy near silicon band gap and with high spectral efficiency. IR light incidents on back metal contact are absorbed without generation electron-hole pair. Light incident to back surface without metallic contact is reflected back and is absorbed inside substrate volume. This theory was verify by scanning of solar cell illuminated by UV light

values of 0 to 3.95 grey tone colour (T = 298 K,S = 650 nm)

but this wavelength enables to detect surface defect.

(Fig. 18) in IR region (Fig. 19).

**3. Projection of solar cell back side contact to the LBIC image** 

Fig. 14. Output LBIC scan of sample 710B1 in maximal converted interval measured values to grey tone colour (T = 298 K, λS = 650 nm)

Fig. 15. Output LBIC scan of sample 710B1 in linear selected interval measured values of 3.71 to 3.91 grey tone colour (T = 298 K,S = 650 nm)

Fig. 14. Output LBIC scan of sample 710B1 in maximal converted interval measured values

Fig. 15. Output LBIC scan of sample 710B1 in linear selected interval measured values of

to grey tone colour (T = 298 K, λS = 650 nm)

3.71 to 3.91 grey tone colour (T = 298 K,S = 650 nm)

Fig. 16. Output LBIC scan of sample 710B1 in coloured nonlinear selected interval measured values of 0 to 3.95 grey tone colour (T = 298 K,S = 650 nm)

#### **3. Projection of solar cell back side contact to the LBIC image**

Thanks to different wavelength of used light illumination we can detect different defect and structures depending on penetration depth of light photon. However, the experiments have showed that we can detect structures behind of expected depth like contact bar on the back side of solar cells. This contact we did not detect using long wavelength (IR-980 nm or red-630 nm LED) but they were clearly visible using short wave length (green-525 nm, blue-430 nm or UV-400 nm LED). Nevertheless using long wavelength enable to clearly detect deep material defects like swirl which are not clearly detectable by UV or blue wavelength but this wavelength enables to detect surface defect.

Projection of back side contact bar to short wavelength LBIC picture can be explain by theory of secondary emission of long wavelength light (~1100 nm) which has penetration depth (~2800m) much more higher then solar cells depth. Incident high energy light is absorbed in front surface of solar cell and generates electron-hole pair. Part of this carrier charges are separated and generated photocurrent. Because of small penetration depth of impacting photon, most of carrier charges generate near surface area. Thank to high recombination rate on surface a big amount of this carrier charges recombine and emit IR light. The spectral efficiency of impacting photon wavelength is low so the output primary photocurrent is low, too, and do not cover the current induced by secondary emitted photons with energy near silicon band gap and with high spectral efficiency. IR light incidents on back metal contact are absorbed without generation electron-hole pair. Light incident to back surface without metallic contact is reflected back and is absorbed inside substrate volume. This theory was verify by scanning of solar cell illuminated by UV light (Fig. 18) in IR region (Fig. 19).

Possibilities of Usage LBIC Method for Characterisation of Solar Cells 123

Fig. 19. Photoluminescence of solar cell 24B3 illuminated by UV-400 nm light, scan through

Fig. 20. Photoluminescence of solar cell 24B3 illuminated by UV-400 nm light, scanned

strong dependence of LBIC characteristics on the used light source wavelength.

The measurement of solar cells using the LBIC method makes possible to most type of defect detection. Various wavelengths of light were used to spot different defects at different depths under the surface of silicon solar cells. This chapter presents the LBIC analysis of set silicon solar cells prepared up-to-date technique. The measurements have demonstrated a

through IR filter (742 nm and more) - measurable luminescence.

**4. Conclusion** 

blue filter (380- 460nm) – no strong luminescence.

Fig. 17. Projection of back contact bar in LBIC of the sample 57A3 by usage of focused LED diode with middle wavelength 430 nm (blue LED, T=297 K)

Fig. 18. Theory of projection back side contact during secondary emission of long wavelength light.

a) front side surface, b) back side surface, c) metallic contact on back side, d) short wavelength light e) emitted long wavelength light.

Fig. 17. Projection of back contact bar in LBIC of the sample 57A3 by usage of focused LED

Fig. 18. Theory of projection back side contact during secondary emission of long

a) front side surface, b) back side surface, c) metallic contact on back side, d) short

wavelength light e) emitted long wavelength light.

diode with middle wavelength 430 nm (blue LED, T=297 K)

wavelength light.

Fig. 19. Photoluminescence of solar cell 24B3 illuminated by UV-400 nm light, scan through blue filter (380- 460nm) – no strong luminescence.

Fig. 20. Photoluminescence of solar cell 24B3 illuminated by UV-400 nm light, scanned through IR filter (742 nm and more) - measurable luminescence.

#### **4. Conclusion**

The measurement of solar cells using the LBIC method makes possible to most type of defect detection. Various wavelengths of light were used to spot different defects at different depths under the surface of silicon solar cells. This chapter presents the LBIC analysis of set silicon solar cells prepared up-to-date technique. The measurements have demonstrated a strong dependence of LBIC characteristics on the used light source wavelength.

**1. Introduction**

silicon solar cells.

and process control.

to 220,000 metric tons for the time being.

B. Erik Ydstie and Juan Du *Carnegie Mellon University*

**Producing Poly-Silicon from Silane** 

**in a Fluidized Bed Reactor** 

The accumulated world solar cell capacity was 2.54 GW in 2006, 89.9% based on mono- or multi-crystalline silicon wafer technology, 7.4% thin film silicon, and 2.6% direct wafering (Neuhaus & Münzer, 2007). The rapidly expanding market and high cost of silicon led to the development of thin-film technologies such as the Cadmium Telluride (CdTe), Copper-Indium-Gallium Selenide (CIGS), Dye Sensitized Solar Cells, amorphous Si on steel and many other. The market share for thin-film technology jumped to nearly 20% of the total

There are more than 25 types of solar cells and modules in current use (Green & Emery, 1993). Technology based on mono-crystalline and multi-crystalline silicon wafers presently dominate and will probably continue to dominate since raw material availability is not a problem given that silicon is abundant and cheap. Solar cells based on rare-earth metals pose a challenge since the cost of the raw materials tend to fluctuate and availability is limited. However the cost of silicon solar cells and the raw material, solar grade poly-silicon is too high and this technology will be displaced unless cost effective alternatives are found to make

Figure 1 shows the approximate distributions for the different costs in producing a silicon based solar module (Muller et al., 2006). The figure shows where there is significant incentive to reduce costs. The areas of solar grade silicon (SOG) production and wafer manufacture stand out. These processes are presently not well optimized and many opportunities exist to improve the manufacturing technology through process innovation, retro-fit, optimization

Poly-silicon, the feedstock for the semiconductor and photovoltaic industries, was in short supply during the beginning of the last decade due to the expansion of the photovoltaic (PV) industry and limited recovery of reject silicon from the semiconductor industry. The relative market share of silicon for the electronic and solar industries is depicted in Figure 2. This figure shows the growing importance of the the solar cell industry in the poly-silicon market. Take last year as an example, a total amount of 170,000 metric tons of poly-silicon was produced and 85% was consumed by solar industry while only 15% was consumed by the semiconductor industry. This represents a complete reversal of the situation less than two decades ago. During the last decade, the total PV industry demand for feedstock grew by more than 20% annually. The forecasted growth rate for the next decade is a conservative 15% per year. The available silicon capacities for both semiconductor and PV industry are limited

7.7 GW of solar cells production in 2009 (Cavallaro, 2010).

*USA*

**7**

Even better results could be achieved by using LASERs instead of focused LED diodes. The problem of using LED diodes is the weak intensity of light beam connected with low photocurrent and superposition with surrounding noise.

#### **5. Acknowledgement**

This research and work has been supported by the project of CZ.1.05/2.1.00/01.0014 and by the project FEKT-S-11-7.

#### **6. References**

Vasicek, T. Diploma theses, 2004, Brno University of Technology, Brno


## **Producing Poly-Silicon from Silane in a Fluidized Bed Reactor**

B. Erik Ydstie and Juan Du *Carnegie Mellon University USA*

#### **1. Introduction**

124 Solar Cells – Silicon Wafer-Based Technologies

Even better results could be achieved by using LASERs instead of focused LED diodes. The problem of using LED diodes is the weak intensity of light beam connected with low

This research and work has been supported by the project of CZ.1.05/2.1.00/01.0014 and by

volume08issue02/ art06\_siliconphoto/p05\_photodetectors.htm, Citeted 2004 Vanek, J., Brzokoupil, V., Vasicek, T., Kazelle, J., Chobola, Z., Barinka, R. The Comparison

Vaněk, J., Kazelle, J., Brzokoupil, V., Vašíček, T., Chobola, Z., Bařinka, R. The Comparison of

Vaněk, J.; Chobola, Z.; Vašíček, T.; Kazelle, J. The LBIC method appended to noise

Vaněk, J., Kazelle, J., Bařinka, R. Lbic method with different wavelength of light source. In

Vaněk, J., Kubíčková, K., Bařinka, R. Properties of solar cells by low an very low

Vaněk, J., Boušek, J., Kazelle, J., Bařinka, R. Different Wavelenghts of light source used in

Vaněk, J.; Fořt, T.; Jandová, K. Solar cell back side contact projection to the front side lbic

Vaněk, J.; Fořt, T.; Jandová, K.; Bařinka, R. Projection fo solar cell back side contact to the

Vaněk, J.; Dolenský, J.; Jandová, K.; Kazelle, J. Dynamic light beam induced voltage testing

Vysoké učení technické v Brně. 2008. p. 153 - 156. ISBN 978-80-214-3717-3. Vaněk, J.; Jandová, K.; Kazelle, J.; Bařinka, R.; Poruba, A. Secondary photocurrent, current

WIP-Renewable Energies. 2005. p. 1287 - 1290. ISBN 3-936338-19-1.

Renewable Energies. 2006. p. 324 - 327. ISBN 3-936338-20-5.

between Noise Spectroscopy and LBIC In *The 11th Electronic Devices and Systems Conference. The 11th Electronic Devices and Systems Conference*. Brno: MSD, 2004, s.

LBIC Method with Noise Spectroscopy. Photovoltaic Devices. Kranjska Gora,

spectroscopy II. In *Twentieth Eur. Photovoltaic SolarEnergy Conf*. Barcelona, Spain,

*IMAPS CS International Conference* 2005. Brno, MSD s.r.o. 2005. p. 232 - 236. ISBN 80-

illumanation intensity. In *IMAPS CS International Conference* 2005. Brno, MSD s.r.o.

LBIC. In *21st European Photovoltaic Solar Energy Conference*. Dresden, Germeny, WIP-

image. In *8th ABA Advanced Batteries and Accumulators*. Brno, TIMEART agency.

LBIC image. In *EDS'07*. Brno, TIMEART agency. 2007. p. 253 - 255. ISBN 978-80-

method of solar cell. In *EDS ´08 IMAPS Cs International Conference Proceedings*. Brno,

generated from secondary emitted photons. In *23rd European Photovoltaic Solar Energy Conference*, 1-5 September 2008, Valencia, Spain. 2008. p. 323 - 325. ISBN 3-

photocurrent and superposition with surrounding noise.

454 - 457, ISBN 80-214-2701-9

Slovenia, *PV-NET*. 2004. p. 60 - 60.

2005. p. 237 - 241. ISBN 80-214-2990-9.

2007. p. 253 - 255. ISBN 978-80-214-3424-0.

Vasicek, T. Diploma theses, 2004, Brno University of Technology, Brno Pek, I. Diploma theses , 2005, Brno University of Technology, Brno

Intel, Photodetectors, On-line : http://www.intel.com/technology/itj/2004/

**5. Acknowledgement** 

the project FEKT-S-11-7.

214-2990-9.

214-3470-7.

936338-24-8.

**6. References** 

The accumulated world solar cell capacity was 2.54 GW in 2006, 89.9% based on mono- or multi-crystalline silicon wafer technology, 7.4% thin film silicon, and 2.6% direct wafering (Neuhaus & Münzer, 2007). The rapidly expanding market and high cost of silicon led to the development of thin-film technologies such as the Cadmium Telluride (CdTe), Copper-Indium-Gallium Selenide (CIGS), Dye Sensitized Solar Cells, amorphous Si on steel and many other. The market share for thin-film technology jumped to nearly 20% of the total 7.7 GW of solar cells production in 2009 (Cavallaro, 2010).

There are more than 25 types of solar cells and modules in current use (Green & Emery, 1993). Technology based on mono-crystalline and multi-crystalline silicon wafers presently dominate and will probably continue to dominate since raw material availability is not a problem given that silicon is abundant and cheap. Solar cells based on rare-earth metals pose a challenge since the cost of the raw materials tend to fluctuate and availability is limited. However the cost of silicon solar cells and the raw material, solar grade poly-silicon is too high and this technology will be displaced unless cost effective alternatives are found to make silicon solar cells.

Figure 1 shows the approximate distributions for the different costs in producing a silicon based solar module (Muller et al., 2006). The figure shows where there is significant incentive to reduce costs. The areas of solar grade silicon (SOG) production and wafer manufacture stand out. These processes are presently not well optimized and many opportunities exist to improve the manufacturing technology through process innovation, retro-fit, optimization and process control.

Poly-silicon, the feedstock for the semiconductor and photovoltaic industries, was in short supply during the beginning of the last decade due to the expansion of the photovoltaic (PV) industry and limited recovery of reject silicon from the semiconductor industry. The relative market share of silicon for the electronic and solar industries is depicted in Figure 2. This figure shows the growing importance of the the solar cell industry in the poly-silicon market. Take last year as an example, a total amount of 170,000 metric tons of poly-silicon was produced and 85% was consumed by solar industry while only 15% was consumed by the semiconductor industry. This represents a complete reversal of the situation less than two decades ago. During the last decade, the total PV industry demand for feedstock grew by more than 20% annually. The forecasted growth rate for the next decade is a conservative 15% per year. The available silicon capacities for both semiconductor and PV industry are limited to 220,000 metric tons for the time being.

in a Fluidized Bed Reactor 3

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 127

Metallurgical grade silicon (MG-Si) at about 98.5-99.5% purity is sold to many different markets. The majority of MG-Si is used for silicones and aluminum alloys (Surek, 2005). A much smaller portion is for fumed silica, medical and cosmetic products and micro-electronics. A small but rapidly growing proportion is used for solar applications. Metallurgical silicon is converted to high-purity poly-silicon through two distinct routes. In the metallurgical route the silicon is purified through a combination of steps targeted at different impurities (Muller et al., 2010). Leaching with calcium based slags may remove some impurities whereas directional solidification takes advantage of the high liquid-solid segregation coefficient of metallic impurities and leaching eliminates metallic silicides in the grain boundaries. One bottleneck of this process is low purity and yield relative to the chemical route. Only a small percentage of the current market is based on this approach

High purity poly-silicon suitable for solar cells and micro-electronics can also be produced by a chemical route which typically proceeds in two steps. In the first step MG-Si reacts with HCl to form a range of chlorosilanes, including tri-chlorosilane (TCS). TCS has a normal boiling point of 31.8*oC* so that it can be purified by distillation. One process alternative for producing TCS is shown in Figure 5. Poly-silicon is then produced in the same manufacturing facility by pyrolysis of TCS in reactors that are commonly referred to as Bell or Siemens reactors (del Coso et al., 2007). In the Bell reactor TCS passes over high purity silicon starter rods which are

Fig. 4. Silicon based Solar Cell Production Process.

Fig. 5. The production of highly pure TCS from MG-Si.

(Fishman, 2008).

Fig. 1. The cost distribution of a silicon solar module.

Fig. 2. Poly-Silicon Production and consumption for Electronic and PV Industries (Fishman, 2008).

Fig. 3. The supply chain for solar cell modules.

Six companies supplied most of the poly-silicon consumed worldwide in the year of 2000, namely, REC Silicon, Hemlock Semi-Conductor, Wacker, MEMC, Tokuyama and Mitsubishi (Goetzberger et al., 2002). Those companies still cover most of the world wide production capacity and produced over 75% of the poly-silicon in 2010.

#### **2. Solar grade poly-silicon production**

Figure 3 illustrates the typical silicon solar cell production. The supply chain starts with the carbothermic reduction of silicates in an electric arc furnace. In this process large amounts of electrical energy breaks the silicon-oxygen bond in the SiO2 via the endothermic reaction with carbon. Molten Si-metal with entrained impurities is withdrawn from the bottom of the furnace while CO2 and fine SiO2 particles escape with the flu-gas (Muller et al., 2006).

2 Will-be-set-by-IN-TECH

Fig. 2. Poly-Silicon Production and consumption for Electronic and PV Industries (Fishman,

Six companies supplied most of the poly-silicon consumed worldwide in the year of 2000, namely, REC Silicon, Hemlock Semi-Conductor, Wacker, MEMC, Tokuyama and Mitsubishi (Goetzberger et al., 2002). Those companies still cover most of the world wide production

Figure 3 illustrates the typical silicon solar cell production. The supply chain starts with the carbothermic reduction of silicates in an electric arc furnace. In this process large amounts of electrical energy breaks the silicon-oxygen bond in the SiO2 via the endothermic reaction with carbon. Molten Si-metal with entrained impurities is withdrawn from the bottom of the furnace while CO2 and fine SiO2 particles escape with the flu-gas (Muller et al., 2006).

Fig. 1. The cost distribution of a silicon solar module.

Fig. 3. The supply chain for solar cell modules.

**2. Solar grade poly-silicon production**

capacity and produced over 75% of the poly-silicon in 2010.

2008).

Fig. 4. Silicon based Solar Cell Production Process.

Fig. 5. The production of highly pure TCS from MG-Si.

Metallurgical grade silicon (MG-Si) at about 98.5-99.5% purity is sold to many different markets. The majority of MG-Si is used for silicones and aluminum alloys (Surek, 2005). A much smaller portion is for fumed silica, medical and cosmetic products and micro-electronics. A small but rapidly growing proportion is used for solar applications.

Metallurgical silicon is converted to high-purity poly-silicon through two distinct routes. In the metallurgical route the silicon is purified through a combination of steps targeted at different impurities (Muller et al., 2010). Leaching with calcium based slags may remove some impurities whereas directional solidification takes advantage of the high liquid-solid segregation coefficient of metallic impurities and leaching eliminates metallic silicides in the grain boundaries. One bottleneck of this process is low purity and yield relative to the chemical route. Only a small percentage of the current market is based on this approach (Fishman, 2008).

High purity poly-silicon suitable for solar cells and micro-electronics can also be produced by a chemical route which typically proceeds in two steps. In the first step MG-Si reacts with HCl to form a range of chlorosilanes, including tri-chlorosilane (TCS). TCS has a normal boiling point of 31.8*oC* so that it can be purified by distillation. One process alternative for producing TCS is shown in Figure 5. Poly-silicon is then produced in the same manufacturing facility by pyrolysis of TCS in reactors that are commonly referred to as Bell or Siemens reactors (del Coso et al., 2007). In the Bell reactor TCS passes over high purity silicon starter rods which are

in a Fluidized Bed Reactor 5

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 129

the bulk silicon to a specific particle size distribution suitable for use as seed particles. However, this technique is expensive and causes severe contamination problems. Moreover, the crushing results in a non-spherical seed particle which presents an undesired surface for silicon deposition. The other technique for producing silicon seed particles involves the recycling small particles generated in and removed from the fluidized bed (Odden et al., 2005). In the fluidized bed, the majority of silicon produced during thermal decomposition undergoes heterogeneous deposition on the surface of the seed while a certain amount of silicon is formed homogeneously as gas dust recycled back into the reactor as seed particles (Caussat et al., 1995a). However, those amount of silicon is not sufficient to meet the entire demand for new seed particles. The combination of the recycled homogeneous particles and seed particles produced by crushing (Kojima & Morisawa, 1991) can provide an effective means of re seeding. More importantly, these homogeneously formed particles are amorphous

A novel seed generator for continuously supplying silicon seed particles solves the above problems (Hsu et al., 1982). This seed generator produces precursor silicon seed via thermal decomposition of silicon containing gas. This device generates uniformly shaped seed particles with desirable fluidization characteristics and silicon deposition. The scheme of silicon production process is illustrated in Figure 6. It comprises a primary fluidized bed reactor and a silicon seed generator. The seed particles are introduced into the primary

Hogness *et al.* (Hogness et al., 1936) was one of the earliest to undertake a series of experiments to study the thermal decomposition of silane. They concluded that the reaction was homogeneous and first order. The hydrogen acted as an inhibitor for the decomposition and no reactions between hydrogen and silicon to form silane was observed. Zambov (Zambov, 1992) investigated the kinetics of homogeneous decomposition of silane and their experimental results showed that homogeneous and heterogeneous pyrolysis coexisted. Furthermore they developed a mathematical model to demonstrate that the ratio of

Fig. 6. Fluidized bed reactor with seed generator.

such that they do not provide desirable surface for deposition neither.

fluidized bed reactor through seed particle inlet (Steinbach et al., 2002).

**4. Silane pyrolysis in fluidized beds**

heated to about 1150*oC* by electrical resistance heating. The gas decomposes as

$$2HSiCl\_3 \rightarrow Si + 2HCl + SiCl\_4$$

Silicon deposits on the silicon rods as in a chemical vapor deposition process. 9N(99.999999999%) silicon is used for micro-electronics applications. Silicon which is 6N or better is called solar grade silicon (SOG-Si) and it can be used to produce high quality solar cells (Talalaev, 2009).

The free space reactor provides an alternative to the Siemens reactor. It has lower capital and operating cost. However, its disadvantage is that it is difficult to regulate the melting process to generate ingots and wafers. This process has not been used industrially on a large scale yet (Fishman, 2008).

The annual price for solar grade silicon went through a very sharp maximum in 2008 due to high demand and limited poly-silicon production capacity. The increase in price was expected (Woditsch & Koch, 2002) and led to a similar increase in the cost of wafers. The price of solar grade silicon is expected to stabilize in the coming decade as new technologies are introduced and capacity is added to the supply chain: The classical TCS process was designed for micro-electronics manufacture where silicon cost is not as critical as in the solar cell industry. Some companies have retro-fitted their processes to produce solar rather than micro-electronics grade silicon. The pyrolysis process has been made suitable for high volume production of poly-silicon; reactive separation and complex instead of simple distillation has been proposed to reduce energy requirements; and fluid bed reactor technology is set to replace the Bell reactors during the next decade. Finally, progress has been made in making solar grade silicon directly using metallurgical routes. All attempts have not been as successful as was hoped for yet. Nevertheless, it is very likely that solar grade silicon prices can be reduced to \$25-30 per kg in the next decade if the tempo of industry expansion is maintained (Neuhaus & Münzer, 2007).

#### **3. Fluidized bed reactor**

Fluidized bed reactors have excellent heat and mass transfer characteristics and can be utilized for Silane decomposition to overcome the energy waste problem in Siemens process. The energy consumption is reduced because the decomposition operates at a lower temperature and cooling devices are not required. In addition fluidized beds have high throughput rate and operate continuously reducing further capital and operating costs. The final product consist of small granules of high purity silicon that are easy to handle compared to powder produced by free space reactor (Odden et al., 2005).

In the fluidized bed reactor (Kunii & Levenspiel, 1991), the reactive gas is introduced into the reactor together with preheated fluidizing gases, such as hydrogen or helium. Heat for the thermal decomposition is supplied by external heating equipment. Pyrolysis of silicon containing gas produces silicon deposition on seed particles, the subsequent particle growth is due to heterogeneous chemical vapor deposition as well as scavenging of homogeneous silicon nuclei. This results in a high deposition rate by a combination of heterogeneous and homogeneous decomposition reactions. As the silicon seed particles grow, the larger particles move to the lower part of the bed and are removed as a final product. The continuous removal of silicon seed particles after they have grown to the desired size leads to depletion of particles and it is necessary to introduce additional silicon seed particles into the fluidized bed to replace those removed final product (Würfel, 2005).

Two techniques are used to provide a continuous supply of pure silicon seed particles to the fluidized bed reactor. One technique uses a hammer mill or roller crushers to reduce 4 Will-be-set-by-IN-TECH

2*HSiCl*<sup>3</sup> → *Si* + 2*HCl* + *SiCl*<sup>4</sup> Silicon deposits on the silicon rods as in a chemical vapor deposition process. 9N(99.999999999%) silicon is used for micro-electronics applications. Silicon which is 6N or better is called solar grade silicon (SOG-Si) and it can be used to produce high quality solar

The free space reactor provides an alternative to the Siemens reactor. It has lower capital and operating cost. However, its disadvantage is that it is difficult to regulate the melting process to generate ingots and wafers. This process has not been used industrially on a large scale yet

The annual price for solar grade silicon went through a very sharp maximum in 2008 due to high demand and limited poly-silicon production capacity. The increase in price was expected (Woditsch & Koch, 2002) and led to a similar increase in the cost of wafers. The price of solar grade silicon is expected to stabilize in the coming decade as new technologies are introduced and capacity is added to the supply chain: The classical TCS process was designed for micro-electronics manufacture where silicon cost is not as critical as in the solar cell industry. Some companies have retro-fitted their processes to produce solar rather than micro-electronics grade silicon. The pyrolysis process has been made suitable for high volume production of poly-silicon; reactive separation and complex instead of simple distillation has been proposed to reduce energy requirements; and fluid bed reactor technology is set to replace the Bell reactors during the next decade. Finally, progress has been made in making solar grade silicon directly using metallurgical routes. All attempts have not been as successful as was hoped for yet. Nevertheless, it is very likely that solar grade silicon prices can be reduced to \$25-30 per kg in the next decade if the tempo of industry expansion is maintained

Fluidized bed reactors have excellent heat and mass transfer characteristics and can be utilized for Silane decomposition to overcome the energy waste problem in Siemens process. The energy consumption is reduced because the decomposition operates at a lower temperature and cooling devices are not required. In addition fluidized beds have high throughput rate and operate continuously reducing further capital and operating costs. The final product consist of small granules of high purity silicon that are easy to handle compared to powder

In the fluidized bed reactor (Kunii & Levenspiel, 1991), the reactive gas is introduced into the reactor together with preheated fluidizing gases, such as hydrogen or helium. Heat for the thermal decomposition is supplied by external heating equipment. Pyrolysis of silicon containing gas produces silicon deposition on seed particles, the subsequent particle growth is due to heterogeneous chemical vapor deposition as well as scavenging of homogeneous silicon nuclei. This results in a high deposition rate by a combination of heterogeneous and homogeneous decomposition reactions. As the silicon seed particles grow, the larger particles move to the lower part of the bed and are removed as a final product. The continuous removal of silicon seed particles after they have grown to the desired size leads to depletion of particles and it is necessary to introduce additional silicon seed particles into the fluidized bed to

Two techniques are used to provide a continuous supply of pure silicon seed particles to the fluidized bed reactor. One technique uses a hammer mill or roller crushers to reduce

heated to about 1150*oC* by electrical resistance heating. The gas decomposes as

cells (Talalaev, 2009).

(Neuhaus & Münzer, 2007).

**3. Fluidized bed reactor**

produced by free space reactor (Odden et al., 2005).

replace those removed final product (Würfel, 2005).

(Fishman, 2008).

Fig. 6. Fluidized bed reactor with seed generator.

the bulk silicon to a specific particle size distribution suitable for use as seed particles. However, this technique is expensive and causes severe contamination problems. Moreover, the crushing results in a non-spherical seed particle which presents an undesired surface for silicon deposition. The other technique for producing silicon seed particles involves the recycling small particles generated in and removed from the fluidized bed (Odden et al., 2005). In the fluidized bed, the majority of silicon produced during thermal decomposition undergoes heterogeneous deposition on the surface of the seed while a certain amount of silicon is formed homogeneously as gas dust recycled back into the reactor as seed particles (Caussat et al., 1995a). However, those amount of silicon is not sufficient to meet the entire demand for new seed particles. The combination of the recycled homogeneous particles and seed particles produced by crushing (Kojima & Morisawa, 1991) can provide an effective means of re seeding. More importantly, these homogeneously formed particles are amorphous such that they do not provide desirable surface for deposition neither.

A novel seed generator for continuously supplying silicon seed particles solves the above problems (Hsu et al., 1982). This seed generator produces precursor silicon seed via thermal decomposition of silicon containing gas. This device generates uniformly shaped seed particles with desirable fluidization characteristics and silicon deposition. The scheme of silicon production process is illustrated in Figure 6. It comprises a primary fluidized bed reactor and a silicon seed generator. The seed particles are introduced into the primary fluidized bed reactor through seed particle inlet (Steinbach et al., 2002).

#### **4. Silane pyrolysis in fluidized beds**

Hogness *et al.* (Hogness et al., 1936) was one of the earliest to undertake a series of experiments to study the thermal decomposition of silane. They concluded that the reaction was homogeneous and first order. The hydrogen acted as an inhibitor for the decomposition and no reactions between hydrogen and silicon to form silane was observed. Zambov (Zambov, 1992) investigated the kinetics of homogeneous decomposition of silane and their experimental results showed that homogeneous and heterogeneous pyrolysis coexisted. Furthermore they developed a mathematical model to demonstrate that the ratio of

in a Fluidized Bed Reactor 7

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 131

Fig. 7. Reaction pathways for conversion of silane to silicon. (Lai et al., 1986)

Computational fluid dynamics offers a powerful approach to understanding the complex phenomena that occur between the gas phase and the particles in the fluidized bed. The Lagrangian and Eulerian models have been developed to describe the hydrodynamics of gas solid flows for the multiphase systems (Piña et al., 2006). The Lagrangian model solves the Newtonian equations of motion for each individual particle in the gas solid system. However the large number of equations cause computational difficulties to simulate industrial fluidize beds reactors. The Eulerian model treats all different phases as continuous and fully interpenetrating. Generalized Navier-Stokes equations are employed for the interacting

Constitutive equations are necessary to close the governing relations and describe the dynamics of the solid phase. To model solid particles as a separated phase, granular theory is employed to determine its physical parameters. The highly reduced number of equations in the Eulerian model needs much less effort to solve in comparison to the Lagrangian model. Modeling the hydrodynamics of gas-solid multiphase systems with Eulerian models has

Commercial software has been used to solve the models mentioned above. FEMLAB solves the partial differential equations by simulating fluidized bed reactors (Balaji et al., 2010). The simulations account for dynamic transport and hydrodynamic phenomena. Mahecha-Botero *et al*. (Mahecha-Botero et al., 2005) presented a generalized dynamic model to simulate complex fluidized bed catalytic systems. The model describes a broad range of multi-phase catalytic systems subject to mass and energy transfer among different phases, changes in the molar/volumetric flow due to the reactions and different hydrodynamic flow regimes. The generalized model (Mahecha-Botero et al., 2006) dealt with anisotropic mass diffusion and heat conduction and was used for different flow regimes which included bubble phase, emulsion phase and freeboard. The model was applied to simulate an oxychlorination fluidized bed reactor for the production of ethylene dichloride from ethylene. An exchange term was introduced to simulate the fluidized bed reactor as interpenetrating continua, composed of two interacting phases. The numerical results were very similar to those of Abba *et al.* (Abba et al., 2002) and gave good agreement with industrial reactor measured results.

**5. Computational fluid dynamics modeling**

shown a promising approach for fluidized bed reactors.

phases.

homogeneous decomposition to heterogeneous deposition grew with increasing temperature and pressure and thus resulted in a substantial degradation of the layer thickness uniformity. A suitable model for silane pyrolysis was developed by Lai *et al.* (Lai et al., 1986) to describe different reaction mechanisms in fluidized bed reactors. They assumed that silane decomposed by heterogeneous and homogeneous decomposition, and occurred via seven pathways as following:


Heterogeneous decomposition of silane on the existing silicon seed particles (pathway 1) or on the formed nuclei (pathway 2) lead to a chemical vapor deposition of silicon. The reaction rate was described by first order form published by Iya *et al.* (Iya et al., 1982).

Homogeneous decomposition forms a gaseous precursor (pathway 3) that nucleate a new solid phase of silicon, which is called silicon vapor. The concentration of vapor given by Hogness (Hogness et al., 1936) and Caussat (Caussat et al., 1995b) was always negligible as they can be suppressed by diffusion aided growth and coalescence of fines.

By pathway 4 nucleation of critical size nuclei, occurs whenever supersaturation is exceeded. The concentration of silicon vapor can be suppressed by diffusion and condensation on large particles (pathway 5). We assume here that nucleation occurs by the homogeneous nucleation theory. The molecular bombardment rate of small particles (pathway 4) is calculated by the classical expression of kinetic theory while the diffusion rate to large particles (pathway 6) is readily obtained from film theory of mass transfer. The coagulation rate of the fines in pathway 6 was determined by the coagulation coefficient which only depend on the average size of the fines. Scavenging rate was also proportional to a scavenging coefficient depending on the size of particles. Those seven pathways are widely used in practice to describe the reaction mechanism to produce silicon from silane.

Two significant problems exist for industrial practice: fines formation and particle agglomeration (Cadoret et al., 2007). For the problem of fines formation, their experimental study showed that for the inlet concentration of the reactive gas less than 20%, silane conversion was quite complete and fines formation limited. The fines ratio never exceeded 3% regardless of inlet concentration of silane. This encouraging result demonstrated that silicon chemical vapor deposition on powders in a fluidized bed was possible and efficient. The other new observation that chemical reactions of gaseous species on cold surfaces was the cause of fines formation was in complete contradiction with previous works (Hsu et al., 1982) (Lai et al., 1986), for which fines were formed homogeneously in fluidized bed. As to the problem of particle agglomeration, they observed that the presence of silane in the reactor could modify particle cohesiveness. The more plausible explanation for this modification was the reactive species adsorbed on particle surfaces could act as a glue for solids (Caussat et al., 1995a).

6 Will-be-set-by-IN-TECH

homogeneous decomposition to heterogeneous deposition grew with increasing temperature and pressure and thus resulted in a substantial degradation of the layer thickness uniformity. A suitable model for silane pyrolysis was developed by Lai *et al.* (Lai et al., 1986) to describe different reaction mechanisms in fluidized bed reactors. They assumed that silane decomposed by heterogeneous and homogeneous decomposition, and occurred via seven

Heterogeneous decomposition of silane on the existing silicon seed particles (pathway 1) or on the formed nuclei (pathway 2) lead to a chemical vapor deposition of silicon. The reaction

Homogeneous decomposition forms a gaseous precursor (pathway 3) that nucleate a new solid phase of silicon, which is called silicon vapor. The concentration of vapor given by Hogness (Hogness et al., 1936) and Caussat (Caussat et al., 1995b) was always negligible as

By pathway 4 nucleation of critical size nuclei, occurs whenever supersaturation is exceeded. The concentration of silicon vapor can be suppressed by diffusion and condensation on large particles (pathway 5). We assume here that nucleation occurs by the homogeneous nucleation theory. The molecular bombardment rate of small particles (pathway 4) is calculated by the classical expression of kinetic theory while the diffusion rate to large particles (pathway 6) is readily obtained from film theory of mass transfer. The coagulation rate of the fines in pathway 6 was determined by the coagulation coefficient which only depend on the average size of the fines. Scavenging rate was also proportional to a scavenging coefficient depending on the size of particles. Those seven pathways are widely used in practice to describe the

Two significant problems exist for industrial practice: fines formation and particle agglomeration (Cadoret et al., 2007). For the problem of fines formation, their experimental study showed that for the inlet concentration of the reactive gas less than 20%, silane conversion was quite complete and fines formation limited. The fines ratio never exceeded 3% regardless of inlet concentration of silane. This encouraging result demonstrated that silicon chemical vapor deposition on powders in a fluidized bed was possible and efficient. The other new observation that chemical reactions of gaseous species on cold surfaces was the cause of fines formation was in complete contradiction with previous works (Hsu et al., 1982) (Lai et al., 1986), for which fines were formed homogeneously in fluidized bed. As to the problem of particle agglomeration, they observed that the presence of silane in the reactor could modify particle cohesiveness. The more plausible explanation for this modification was the reactive species adsorbed on particle surfaces could act as a glue for solids (Caussat et al.,

1. Chemical vapor deposition on silicon particles (heterogeneous deposition);

rate was described by first order form published by Iya *et al.* (Iya et al., 1982).

they can be suppressed by diffusion aided growth and coalescence of fines.

2. Chemical vapor deposition on fines (heterogeneous deposition);

3. Homogeneous decomposition to form Silicon vapor;

reaction mechanism to produce silicon from silane.

1995a).

pathways as following:

4. Coalescence of formation of fines; 5. Diffusion-aided growth of fines; 6. Growth of fines by coagulation; 7. Scavenging of fines by particles;

Fig. 7. Reaction pathways for conversion of silane to silicon. (Lai et al., 1986)

#### **5. Computational fluid dynamics modeling**

Computational fluid dynamics offers a powerful approach to understanding the complex phenomena that occur between the gas phase and the particles in the fluidized bed. The Lagrangian and Eulerian models have been developed to describe the hydrodynamics of gas solid flows for the multiphase systems (Piña et al., 2006). The Lagrangian model solves the Newtonian equations of motion for each individual particle in the gas solid system. However the large number of equations cause computational difficulties to simulate industrial fluidize beds reactors. The Eulerian model treats all different phases as continuous and fully interpenetrating. Generalized Navier-Stokes equations are employed for the interacting phases.

Constitutive equations are necessary to close the governing relations and describe the dynamics of the solid phase. To model solid particles as a separated phase, granular theory is employed to determine its physical parameters. The highly reduced number of equations in the Eulerian model needs much less effort to solve in comparison to the Lagrangian model. Modeling the hydrodynamics of gas-solid multiphase systems with Eulerian models has shown a promising approach for fluidized bed reactors.

Commercial software has been used to solve the models mentioned above. FEMLAB solves the partial differential equations by simulating fluidized bed reactors (Balaji et al., 2010). The simulations account for dynamic transport and hydrodynamic phenomena. Mahecha-Botero *et al*. (Mahecha-Botero et al., 2005) presented a generalized dynamic model to simulate complex fluidized bed catalytic systems. The model describes a broad range of multi-phase catalytic systems subject to mass and energy transfer among different phases, changes in the molar/volumetric flow due to the reactions and different hydrodynamic flow regimes. The generalized model (Mahecha-Botero et al., 2006) dealt with anisotropic mass diffusion and heat conduction and was used for different flow regimes which included bubble phase, emulsion phase and freeboard. The model was applied to simulate an oxychlorination fluidized bed reactor for the production of ethylene dichloride from ethylene. An exchange term was introduced to simulate the fluidized bed reactor as interpenetrating continua, composed of two interacting phases. The numerical results were very similar to those of Abba *et al.* (Abba et al., 2002) and gave good agreement with industrial reactor measured results.

in a Fluidized Bed Reactor 9

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 133

*Mi* = *mini*. (1)

*<sup>i</sup>* (2)

*<sup>i</sup>* while particle

Fig. 8. The network representation of population balance

*dMi*

The rate of addition of particles to interval *i* from the environment is *qin*

*f a <sup>i</sup>* = *f a*,*in <sup>i</sup>* − *f*

*dt* <sup>=</sup> *qi* <sup>+</sup> *ri* <sup>+</sup> *fi*−<sup>1</sup> <sup>−</sup> *fi* <sup>+</sup> *<sup>f</sup> <sup>a</sup>*

*<sup>i</sup>* <sup>−</sup> *<sup>q</sup>out <sup>i</sup>* .

> *a*,*out <sup>i</sup>* ,

*<sup>i</sup>* represents particle transition to interval *i* due to agglomeration or nucleation, and

The rate of material transfer from the fluid phase to the particle is represented by *ri*. The term,

*<sup>i</sup>* represents the rate of change due to agglomeration, breakage or nucleation. The value can

*<sup>i</sup>* represents particle transition out of an interval due to breakage or agglomeration. These terms are often referred to as birth and death in the population balance literature. Finally, the rate of transition of particles from one size interval to the next, caused by particle growth, is represented by *fi*−<sup>1</sup> for flow into interval *<sup>i</sup>* and *fi* for flow out of interval *<sup>i</sup>*. By connecting several of these balances together we get the network description of the particulate system illustrated in Figure 8. The model was validated by experimental data from pilot plant tests (**?**) and it was used for pilot plant design and scale-up. It also was used for further development of control strategies and study of dynamical stability of particles' behavior in fluidization

*<sup>i</sup>* , so the total external flow of particles is represented by

*qi* = *qin*

interval (*ni*) is thereby given by the expression

The mass balance for size interval *i* is written

withdrawal is *qout*

be expressed so that

*a*,*in*

*f a*

*f a*,*out*

where *f*

processes.

Guenther *et al.* (Guenther et al., 2001) presented an althernative method for simulating fluidized bed reactors using the computational codes MFIX (Multiphase Flow with Interphase eXchanges) developed at the US Department of Energy National Energy Technology Laboratory. Three-dimensional simulations of silane pyrolysis were carried out by using MFIX. The reaction chemistry was described by the homogeneous and heterogeneous reactions described above. The results showed excellent agreement with experimental measurements and demonstrated that these methods can predict qualitatively the dynamical behavior of fluidized bed reactors for silane pyrolysis. Caussat *et al.* (Cadoret et al., 2007) used MFIX for transient simulations for silicon fluidized bed chemical vapor deposition from silane on coarse powders. The three-dimensional simulations provided better results than two-dimension simulations. The model predicts the temporal and spatial evolutions of local void fractions, gas and particle velocities and silicon deposition rate.

White *et al.* (White, 2007) used FLUENT to capture the dynamics of gas flow through a bed of particles with one constant average size. The inputs to FLUENT were reactor geometry, gas flow rates and temperature, heater duty, particle hold-up and average size. The CFD calculations predicted the bed properties such as the overall bed density and the temperature as functions of height. This study formed the basis for a multi-scale model for silane pyrolysis in FBR (Du et al., 2009)

#### **6. The dynamics of particulate phase**

Fluidized bed reactor dynamics are characterized by the production, growth and decay of particles contained in a continuous phase. Such dynamics can be found everywhere in the chemical engineering field, such as crystallization, granulation and fluidized bed vapor decomposition. Particularly for the solar grade silicon production process in a fluidized bed, the particles grow with heterogeneous chemical vapor deposition and homogeneous decomposition. White *et al.* (White et al., 2006) developed a dynamical model to represent the size distribution for silicon particles growth. The idea for the model development is based on classical population balance proposed by Hulburt and Katz (Hulburt & Katz, 1964). Hulburt *et al.* used the theory of statistical mechanics to develop an infinite dimensional phase space description of the particle behavior. The resulting balance equations express the conservation of probability in the phase space. A set of integro-partial differential equations are generated if the population balance is incorporated with mass balance for the continuous phase. However it requires significant computational efforts to solve those equations. Moment transformation and discretization are two commonly used methods to solve those equations. Randolph and Larson (Randolph & Larson, 1971) proposed the use of moment transformation while Clough (Cooper & Clough, 1985) used orthogonal collocation. Hounslow (Hounslow, 1990) and Henson *et al.* (Henson, 2003) employed various discretization techniques to solve them.

Du *et al.* (Du et al., 2009) reduced the continuous population balance to finite dimensional space by discretizing the size of particles into a finite number of size intervals. In each size interval, both mass balance and number balance are established and the discrete population balance is obtained by comparing those two balance equations. This approach ensures that conservation laws are maintained at all discretization levels and facilitates computation without additional discretization.

Figure 8 illustrates the modeling approach developed by White *et al*. and how it describes how particles change as a function of time. In this method particles are distributed among *N* discrete size intervals, characterized by an average mass *mi* for *i* = 1, ..., *N*. The relationship between the total mass of particles (*Mi*) in an interval and the number of particles in each 8 Will-be-set-by-IN-TECH

Guenther *et al.* (Guenther et al., 2001) presented an althernative method for simulating fluidized bed reactors using the computational codes MFIX (Multiphase Flow with Interphase eXchanges) developed at the US Department of Energy National Energy Technology Laboratory. Three-dimensional simulations of silane pyrolysis were carried out by using MFIX. The reaction chemistry was described by the homogeneous and heterogeneous reactions described above. The results showed excellent agreement with experimental measurements and demonstrated that these methods can predict qualitatively the dynamical behavior of fluidized bed reactors for silane pyrolysis. Caussat *et al.* (Cadoret et al., 2007) used MFIX for transient simulations for silicon fluidized bed chemical vapor deposition from silane on coarse powders. The three-dimensional simulations provided better results than two-dimension simulations. The model predicts the temporal and spatial evolutions of local

White *et al.* (White, 2007) used FLUENT to capture the dynamics of gas flow through a bed of particles with one constant average size. The inputs to FLUENT were reactor geometry, gas flow rates and temperature, heater duty, particle hold-up and average size. The CFD calculations predicted the bed properties such as the overall bed density and the temperature as functions of height. This study formed the basis for a multi-scale model for silane pyrolysis

Fluidized bed reactor dynamics are characterized by the production, growth and decay of particles contained in a continuous phase. Such dynamics can be found everywhere in the chemical engineering field, such as crystallization, granulation and fluidized bed vapor decomposition. Particularly for the solar grade silicon production process in a fluidized bed, the particles grow with heterogeneous chemical vapor deposition and homogeneous decomposition. White *et al.* (White et al., 2006) developed a dynamical model to represent the size distribution for silicon particles growth. The idea for the model development is based on classical population balance proposed by Hulburt and Katz (Hulburt & Katz, 1964). Hulburt *et al.* used the theory of statistical mechanics to develop an infinite dimensional phase space description of the particle behavior. The resulting balance equations express the conservation of probability in the phase space. A set of integro-partial differential equations are generated if the population balance is incorporated with mass balance for the continuous phase. However it requires significant computational efforts to solve those equations. Moment transformation and discretization are two commonly used methods to solve those equations. Randolph and Larson (Randolph & Larson, 1971) proposed the use of moment transformation while Clough (Cooper & Clough, 1985) used orthogonal collocation. Hounslow (Hounslow, 1990) and Henson *et al.* (Henson, 2003) employed various discretization techniques to solve them. Du *et al.* (Du et al., 2009) reduced the continuous population balance to finite dimensional space by discretizing the size of particles into a finite number of size intervals. In each size interval, both mass balance and number balance are established and the discrete population balance is obtained by comparing those two balance equations. This approach ensures that conservation laws are maintained at all discretization levels and facilitates computation

Figure 8 illustrates the modeling approach developed by White *et al*. and how it describes how particles change as a function of time. In this method particles are distributed among *N* discrete size intervals, characterized by an average mass *mi* for *i* = 1, ..., *N*. The relationship between the total mass of particles (*Mi*) in an interval and the number of particles in each

void fractions, gas and particle velocities and silicon deposition rate.

in FBR (Du et al., 2009)

**6. The dynamics of particulate phase**

without additional discretization.

Fig. 8. The network representation of population balance

interval (*ni*) is thereby given by the expression

$$M\_i = m\_i n\_i. \tag{1}$$

The mass balance for size interval *i* is written

$$\frac{dM\_i}{dt} = q\_i + r\_i + f\_{i-1} - f\_i + f\_i^a \tag{2}$$

The rate of addition of particles to interval *i* from the environment is *qin <sup>i</sup>* while particle withdrawal is *qout <sup>i</sup>* , so the total external flow of particles is represented by

$$q\_i = q\_i^{in} - q\_i^{out}.$$

The rate of material transfer from the fluid phase to the particle is represented by *ri*. The term, *f a <sup>i</sup>* represents the rate of change due to agglomeration, breakage or nucleation. The value can be expressed so that

$$f\_i^a = f\_i^{a,in} - f\_i^{a,out} \text{ \AA$$

where *f a*,*in <sup>i</sup>* represents particle transition to interval *i* due to agglomeration or nucleation, and *f a*,*out <sup>i</sup>* represents particle transition out of an interval due to breakage or agglomeration. These terms are often referred to as birth and death in the population balance literature. Finally, the rate of transition of particles from one size interval to the next, caused by particle growth, is represented by *fi*−<sup>1</sup> for flow into interval *<sup>i</sup>* and *fi* for flow out of interval *<sup>i</sup>*. By connecting several of these balances together we get the network description of the particulate system illustrated in Figure 8. The model was validated by experimental data from pilot plant tests (**?**) and it was used for pilot plant design and scale-up. It also was used for further development of control strategies and study of dynamical stability of particles' behavior in fluidization processes.

in a Fluidized Bed Reactor 11

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 135

are generated with increasing silane concentration from 57% to 100%. Kojima *et al.* (Kojima & Morisawa, 1991) recommended the following operating conditions: bed temperature is 600*oC*, gas velocity ratio is 4 and inlet silane concentration is 43%. For both groups, the recommended

While considerable research effort has been devoted to understanding of the reaction mechanisms and model development for fluidized bed reactors, not much attention has been paid to the study of control technology for the silicon production process. Since this system is complex and typically have limited availability of measurements, complicated control strategies are not suitable to be implemented in the practice. Inventory control (Farschman et al., 1998) is a simple method for control of complex systems and thus has potential for industrial application. It distinguishes itself from other control methods in that it addresses the question of measurement and manipulated variables' selections. We apply inventory control strategy to control particle size distribution by manipulating the total mass of the

The objective of our inventory control system is to control the average particle size in the fluidized bed reactor. We manipulate the seed and product flow rates to achieve the control objective. An inventory control strategy for the total mass hold-up of particles is written as:

where *K* is the proportional control gain. *M* is the total mass hold up and *M*∗ is the desired

where *S* is the seed addition flow rate, *Y* is the silicon production rate and *P* is the product removal rate. The product flow rate can be manipulated to keep the total mass hold-up to a

*dt* <sup>=</sup> <sup>−</sup>*K*(*<sup>M</sup>* <sup>−</sup> *<sup>M</sup>*∗) (4)

*dt* <sup>=</sup> *<sup>S</sup>* <sup>+</sup> *<sup>Y</sup>* <sup>−</sup> *<sup>P</sup>* (5)

*P* = *S* + *Y* + *K*(*M* − *M*∗) (6)

*dM*

*dM*

hold up. The mass balance of the solid phase is expressed as:

desired value *M*∗ by using the following control action:

Fig. 9. Model Validation.

particles.

seed particle size is between 0.15 and 0.3 *melimeter*.

#### **7. Multi-scale modeling**

Du *et al.* (Du et al., 2009) proposed a multi-scale approach for accurate modeling of the entire process. The hydrodynamics were modeled using CFD, which provides a basis for a simplified reactor flow model. The kinetic terms and the reactor temperature and concentrations are expressed as functions of reactor dimensions, void volume and time in the CFD module. Reactor temperature and concentration from the CFD module provides inputs to the CVD module. The CVD module calculates the overall process yield which provided an input to the population balance module. The average particle diameter is then calculated by population balance module and imported into the CFD module to complete model integration. In continuation of the above mentioned works by White *et al.* (White et al., 2007), Balaji *et al.* (Balaji et al., 2010) presented the complete multi-scale modeling approach including the effect of computational fluid dynamics along with population balance and chemical vapor deposition models. For the first time in the field of silicon production using fluidized beds, they coupled all the effects pertaining to the system (using partial differential equations (CFD), ordinary differential equations (PBM) and algebraic equations (CVD)) and they solved the resulting nonlinear partial differential algebraic equations with a computationally efficient and inexpensive solution methodology.

In order to verify the multi-scale model, we compare the numerical results with experimental data. The relationship between particle flow rates and average particle size at steady state is derived as (White, 2007),

$$1 + \frac{P}{S} = \frac{n\_p}{n\_s} (\frac{D\_{ap}}{D\_{as}})^3 \tag{3}$$

where *P* is the product withdraw flow rate and *S* is the seed addition rate. *Dap* is the average particle diameter of product and *Das* is the average particle diameter of seed. *np* is the number of particles being removed and *ns* is the number of particles being added.

If ln (1 + *P*/*S*) = ln *np*/*ns* + 3 ln *Dap*/*Das* holds true, then it implies that *np*/*ns* = 1, which means no nucleation, agglomeration, or breakage is present. On the other hand *np*/*ns <* 1 indicates that particle agglomeration takes place in the reactor and *np*/*ns >* 1 means that particle breakage occurs in the pilot plant. The dashed lines in Figure 9 represent the analytical expression. The numerical results in Figure 9 agree with both analytical solution and experimental results which supports that the multi-scale model can be used for further control studies.

#### **8. Operation and control**

Bed temperature is one key factor for the deposition rate and the quality of the deposition. Inlet silane concentration also affect the deposition rate as well as fines formation and agglomeration. The fluidization mode is determined by a gas velocity ratio between superficial gas velocity *u* and minimum fluidization velocity *um f* . All these variables must be coordinated in a multi-variables process control strategy.

A careful selection of the fluidization velocity and silane concentration in the feed limit fines formation and agglomeration. In order to avoid slugging and poor gas-solid contact we adjust fluidization velocity or the ratio bed height to bed diameter during reactor design. Usually hydrogen is used as fluidization gas as it is able to decrease the formation of fines compared to other inert gas such as nitrogen.

Hsu *et al.* (Hsu et al., 1987) proposed that the optimal bed temperature for fluidized bed reactor is 600 <sup>−</sup> <sup>700</sup>*oC* and gas velocity ratio is between 3 and 5. Within this range, fines elutriation percentage is generally under 10% of the mass of Si in the silane feed. The maximum fine formation is 9.5% at the inlet silane concentration of 57%, no excessive fines

Fig. 9. Model Validation.

10 Will-be-set-by-IN-TECH

Du *et al.* (Du et al., 2009) proposed a multi-scale approach for accurate modeling of the entire process. The hydrodynamics were modeled using CFD, which provides a basis for a simplified reactor flow model. The kinetic terms and the reactor temperature and concentrations are expressed as functions of reactor dimensions, void volume and time in the CFD module. Reactor temperature and concentration from the CFD module provides inputs to the CVD module. The CVD module calculates the overall process yield which provided an input to the population balance module. The average particle diameter is then calculated by population balance module and imported into the CFD module to complete model integration. In continuation of the above mentioned works by White *et al.* (White et al., 2007), Balaji *et al.* (Balaji et al., 2010) presented the complete multi-scale modeling approach including the effect of computational fluid dynamics along with population balance and chemical vapor deposition models. For the first time in the field of silicon production using fluidized beds, they coupled all the effects pertaining to the system (using partial differential equations (CFD), ordinary differential equations (PBM) and algebraic equations (CVD)) and they solved the resulting nonlinear partial differential algebraic equations with a

In order to verify the multi-scale model, we compare the numerical results with experimental data. The relationship between particle flow rates and average particle size at steady state is

where *P* is the product withdraw flow rate and *S* is the seed addition rate. *Dap* is the average particle diameter of product and *Das* is the average particle diameter of seed. *np* is the number

which means no nucleation, agglomeration, or breakage is present. On the other hand *np*/*ns <* 1 indicates that particle agglomeration takes place in the reactor and *np*/*ns >* 1 means that particle breakage occurs in the pilot plant. The dashed lines in Figure 9 represent the analytical expression. The numerical results in Figure 9 agree with both analytical solution and experimental results which supports that the multi-scale model can be used for further

Bed temperature is one key factor for the deposition rate and the quality of the deposition. Inlet silane concentration also affect the deposition rate as well as fines formation and agglomeration. The fluidization mode is determined by a gas velocity ratio between superficial gas velocity *u* and minimum fluidization velocity *um f* . All these variables must

A careful selection of the fluidization velocity and silane concentration in the feed limit fines formation and agglomeration. In order to avoid slugging and poor gas-solid contact we adjust fluidization velocity or the ratio bed height to bed diameter during reactor design. Usually hydrogen is used as fluidization gas as it is able to decrease the formation of fines compared

Hsu *et al.* (Hsu et al., 1987) proposed that the optimal bed temperature for fluidized bed reactor is 600 <sup>−</sup> <sup>700</sup>*oC* and gas velocity ratio is between 3 and 5. Within this range, fines elutriation percentage is generally under 10% of the mass of Si in the silane feed. The maximum fine formation is 9.5% at the inlet silane concentration of 57%, no excessive fines

)<sup>3</sup> (3)

holds true, then it implies that *np*/*ns* = 1,

computationally efficient and inexpensive solution methodology.

1 + *P <sup>S</sup>* <sup>=</sup> *np ns* ( *Dap Das*

of particles being removed and *ns* is the number of particles being added.

*Dap*/*Das*

+ 3 ln

be coordinated in a multi-variables process control strategy.

*np*/*ns* 

**7. Multi-scale modeling**

derived as (White, 2007),

If ln (1 + *P*/*S*) = ln

**8. Operation and control**

to other inert gas such as nitrogen.

control studies.

are generated with increasing silane concentration from 57% to 100%. Kojima *et al.* (Kojima & Morisawa, 1991) recommended the following operating conditions: bed temperature is 600*oC*, gas velocity ratio is 4 and inlet silane concentration is 43%. For both groups, the recommended seed particle size is between 0.15 and 0.3 *melimeter*.

While considerable research effort has been devoted to understanding of the reaction mechanisms and model development for fluidized bed reactors, not much attention has been paid to the study of control technology for the silicon production process. Since this system is complex and typically have limited availability of measurements, complicated control strategies are not suitable to be implemented in the practice. Inventory control (Farschman et al., 1998) is a simple method for control of complex systems and thus has potential for industrial application. It distinguishes itself from other control methods in that it addresses the question of measurement and manipulated variables' selections. We apply inventory control strategy to control particle size distribution by manipulating the total mass of the particles.

The objective of our inventory control system is to control the average particle size in the fluidized bed reactor. We manipulate the seed and product flow rates to achieve the control objective. An inventory control strategy for the total mass hold-up of particles is written as:

$$\frac{dM}{dt} = -K(M - M^\*)\tag{4}$$

where *K* is the proportional control gain. *M* is the total mass hold up and *M*∗ is the desired hold up. The mass balance of the solid phase is expressed as:

$$\frac{dM}{dt} = \mathbf{S} + \mathbf{Y} - \mathbf{P} \tag{5}$$

where *S* is the seed addition flow rate, *Y* is the silicon production rate and *P* is the product removal rate. The product flow rate can be manipulated to keep the total mass hold-up to a desired value *M*∗ by using the following control action:

$$P = S + Y + K(M - M^\*) \tag{6}$$

in a Fluidized Bed Reactor 13

Producing Poly-Silicon from Silane in a Fluidized Bed Reactor 137

pilot plant tests. An inventory based control is applied to control the total mass hold up of the solid phase and the simulation results demonstrate that such simple control strategy can be

Abba, A., I., R. Grace, J. & T. Bi, H. (2002). Variable-gas-density fluidized bed reactor model for catalytic processes, *Chemical engineering science* 57(22-23): 4797–4807. Balaji, S., Du, J., White, C. & Ydstie, B. (2010). Multi-scale modeling and control of fluidized beds for the production of solar grade silicon, *Powder Technology* 199(1): 23–31. Cadoret, L., Reuge, N., Pannala, S., Syamlal, M., Coufort, C. & Caussat, B. (2007). Silicon cvd

Caussat, B., Hemati, M. & Couderc, J. (1995a). Silicon deposition from silane or disilane in a

Caussat, B., Hemati, M. & Couderc, J. (1995b). Silicon deposition from silane or disilane in a

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Cooper, D. & Clough, D. (1985). Experimental tracking of particle-size distribution in a

del Coso, G., del Canizo, C., Tobias, I. & Luque, A. (2007). Increase on siemens reactor

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Farschman, C., Viswanath, K. & Erik Ydstie, B. (1998). Process systems and inventory control,

Goetzberger, A., Luther, J. & Willeke, G. (2002). Solar cells: past, present, future, *Solar energy*

Green, M. & Emery, K. (1993). Solar cell efficiency tables, *Progress in Photovoltaics: Research and*

Guenther, C., OŠBrien, T. & Syamlal, M. (2001). A numerical model of silane pyrolysis in a

Henson, M. (2003). Dynamic modeling of microbial cell populations, *Current opinion in*

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Hounslow, M. (1990). A discretized population balance for continuous systems at steady state,

Hsu, G., Levin, H., Hogle, R., Praturi, A. & Lutwack, R. (1982). Fluidized bed silicon

Hsu, G., Rohatgi, N. & Houseman, J. (1987). Silicon particle growth in a fluidized-bed reactor,

gas-solids fluidized bed, *Proceedings of the International Conference on Multiphase Flow*.

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using the electre iii method, *Energy Policy* 38(1): 463–474.

fluidized bed, *Powder technology* 44(2): 169–177.

Fishman, O. (2008). Solar silicon, *Advanced materials & processes* p. 33.

*Spanish Conference on*, IEEE, pp. 25–28.

*AIChE Journal* 44(8): 1841–1857.

*Applications* 1(1): 25–29.

*biotechnology* 14(5): 460–467.

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fluidized bed–part ii: Theoretical analysis and modeling, *Chemical engineering science*

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throughput by tailoring temperature profile of polysilicon rods, *Electron Devices, 2007*

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used to control the average particle size.

50(22): 3625–3635.

50(22): 3625–3635.

*Systems*.

**10. References**

(a) Control total and seed hold up in FBR (b) Particle size using inventory control

Furthermore we apply inventory control to maintain the seed hold up to a desired value and the control action is in the form of

$$S = -\sum\_{i=1}^{N\_s} Y\_i - K\_s \left(\sum\_{i=1}^{N\_s} M\_i - M\_{\text{seed}}^\*\right) \tag{7}$$

where *Ns* is the total number of size intervals for the particle seeds and *Yi* is the silicon production rate in the seed size intervals, *Ks* is the proportional gain.

Simulation of controlling the total and seed particle hold-up is shown in Figures 10(a) and 10(b). The hold-up of particles in the system is shown in Figure 10(a). The product and seed flow rates required to achieve the control are also shown. The first steady state (SS1) represents operation when *M*∗ total = 75 and *M*<sup>∗</sup> seed = 15. The subsequent steady states are achieved when *M*∗ seed is increased to 20 and 25. The average particle size and size distribution achieved during each steady state are shown in Figure 10(b). This simulation shows we can control the average product size as well as the product distribution. As the hold up of seed particles increases relative to the total hold up, the average size decreases. The interval representation of the size distribution supports this result. In this simulation, we assumed that the largest seed size interval, *Ns*, was interval 10 out of 20 and that the distribution of seed particles flowing into the system was constant.

#### **9. Conclusions**

This chapter reviewed the past and current work for modeling and operation of fluidized bed reactor processes for producing solar grade poly-silicon. Currently the shortage of low-cost solar grade silicon is one major factor preventing environmentally friendly solar energy from becoming important in the energy market. Energy consumption is the main cost driver for poly-silicon production process which is highly energy intensive. Fluidized bed reactors serve as an alternative to the Siemens process which dominates the solar grade silicon market. Several companies have attempted to commercialize the fluidized bed reactor process and the process has been scaled up to commercial scale. It has been shown that FBR technology produces poly-silicon at acceptable purity levels and an acceptable price. Extensive research has been carried out to study the chemical kinetics of silane pyrolysis and to model the fluid dynamics in the fluidized beds. The particle growth process due to silicon deposition is captured by discretized population balances which uses ordinary differential and algebraic equations to simulate the distribution function for the particles change as a function of time and operating conditions. A multi-scale modeling approach was applied to couple the population balance with computational fluid dynamics model and reaction model to represented the whole process. The model has been validated with experimental data from pilot plant tests. An inventory based control is applied to control the total mass hold up of the solid phase and the simulation results demonstrate that such simple control strategy can be used to control the average particle size.

#### **10. References**

12 Will-be-set-by-IN-TECH

(a) Control total and seed hold up in FBR (b) Particle size using inventory control

Furthermore we apply inventory control to maintain the seed hold up to a desired value and

where *Ns* is the total number of size intervals for the particle seeds and *Yi* is the silicon

Simulation of controlling the total and seed particle hold-up is shown in Figures 10(a) and 10(b). The hold-up of particles in the system is shown in Figure 10(a). The product and seed flow rates required to achieve the control are also shown. The first steady state (SS1) represents

during each steady state are shown in Figure 10(b). This simulation shows we can control the average product size as well as the product distribution. As the hold up of seed particles increases relative to the total hold up, the average size decreases. The interval representation of the size distribution supports this result. In this simulation, we assumed that the largest seed size interval, *Ns*, was interval 10 out of 20 and that the distribution of seed particles

This chapter reviewed the past and current work for modeling and operation of fluidized bed reactor processes for producing solar grade poly-silicon. Currently the shortage of low-cost solar grade silicon is one major factor preventing environmentally friendly solar energy from becoming important in the energy market. Energy consumption is the main cost driver for poly-silicon production process which is highly energy intensive. Fluidized bed reactors serve as an alternative to the Siemens process which dominates the solar grade silicon market. Several companies have attempted to commercialize the fluidized bed reactor process and the process has been scaled up to commercial scale. It has been shown that FBR technology produces poly-silicon at acceptable purity levels and an acceptable price. Extensive research has been carried out to study the chemical kinetics of silane pyrolysis and to model the fluid dynamics in the fluidized beds. The particle growth process due to silicon deposition is captured by discretized population balances which uses ordinary differential and algebraic equations to simulate the distribution function for the particles change as a function of time and operating conditions. A multi-scale modeling approach was applied to couple the population balance with computational fluid dynamics model and reaction model to represented the whole process. The model has been validated with experimental data from

seed is increased to 20 and 25. The average particle size and size distribution achieved

 *Ns* ∑ *i*=1

*Mi* − *M*<sup>∗</sup>

seed 

seed = 15. The subsequent steady states are achieved

(7)

the control action is in the form of

flowing into the system was constant.

operation when *M*∗

**9. Conclusions**

when *M*∗

*S* = −

total = 75 and *M*<sup>∗</sup>

production rate in the seed size intervals, *Ks* is the proportional gain.

*Ns* ∑ *i*=1

*Yi* − *Ks*


**8** 

*France* 

**Silicon-Based Third Generation Photovoltaics** 

In order to ensure the widespread use of photovoltaic (PV) technology for terrestrial applications, the cost per watt must be significantly lower than 1\$ / Watt level. Actually, the wafer based Silicon (Si) solar cells referred also as the 1st generation solar cells are the most mature technology on PV market. However such PV devices are material and energy intensive with conversion efficiencies which do not exceed in average 16 %. In 2008 the average cost of industrial 1 Wp Si solar cell with conversion efficiency of 14.5 % (multicrystalline Si cell of 150 x 150 mm2, 220 m of thick, SiN antireflecting coating with back surface field and screen printing contacts) achieved approximately 2.1 € assuming the production volume of 30 – 50 M Wp / per year (Sinke et al., 2008). At that cost level, the PV electricity still remains more expensive comparing with traditional nuclear or thermal power engineering. One of the most promising strategies for lowering PV costs is the use of thin film technology, referred also as 2nd generation solar cells. It involves low cost and low energy intensity deposition techniques of PV material onto inexpensive large area low-cost substrates. Such processes can bring costs down but because of the defects inherent in the lower quality processing methods, have

Material limitations of the 1st generation solar cells and efficiency limitations of the 2nd generation solar cells are initiated boring of the Si-based 3rd generation photovoltaic. Its main goal is to significantly increase the conversion efficiency of low-cost photovoltaic product. Indeed, the Carnot limit on the conversion of sunlight to electricity is 95% as opposed to the theoretical upper limit of 30% for a standard solar cell (Shockley & Queisser 1961). This suggests the performance of solar cells could be improved 2 – 3 times if different

The two most important power loss mechanisms in single-band gap photovoltaic cells are *(1)* the inability to absorb photons with energy less than the band gap and *(2)* thermalisation of photon energy exceeding the gap (Fig. 1). Longer wavelength is not absorbed by the solar cell material. Shorter wavelength generates an electron-hole pair greater than the bandgap of the p-n junction material. The excess of energy is lost as heat because the electron (hole) relaxes to the conduction (valence) band edges. The amounts of the losses are around 23 % and 33 % of the incoming solar energy, respectively (Nelson, 2003). Other losses are junction loss, contact loss and the recombination loss. Theory predicts (Shockley & Queisser 1961) that the highest single – junction solar cell efficiency is roughly 30%, assuming such factors as the intensity of one sun (no sunlight concentration), a one-junction solar cell (a single material with a single

reduced efficiencies compared to the 1st generation solar cells.

concepts permitting to reduce the power losses were used.

bandgap), and one electron-hole pair produced from each incoming photon.

**1. Introduction** 

Tetyana Nychyporuk and Mustapha Lemiti

*UMR CNRS 5270, INSA de Lyon,* 

*University of Lyon, Nanotechnology Institute of Lyon (INL),* 


### **Silicon-Based Third Generation Photovoltaics**

Tetyana Nychyporuk and Mustapha Lemiti

*University of Lyon, Nanotechnology Institute of Lyon (INL), UMR CNRS 5270, INSA de Lyon, France* 

#### **1. Introduction**

14 Will-be-set-by-IN-TECH

138 Solar Cells – Silicon Wafer-Based Technologies

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Boston.

In order to ensure the widespread use of photovoltaic (PV) technology for terrestrial applications, the cost per watt must be significantly lower than 1\$ / Watt level. Actually, the wafer based Silicon (Si) solar cells referred also as the 1st generation solar cells are the most mature technology on PV market. However such PV devices are material and energy intensive with conversion efficiencies which do not exceed in average 16 %. In 2008 the average cost of industrial 1 Wp Si solar cell with conversion efficiency of 14.5 % (multicrystalline Si cell of 150 x 150 mm2, 220 m of thick, SiN antireflecting coating with back surface field and screen printing contacts) achieved approximately 2.1 € assuming the production volume of 30 – 50 M Wp / per year (Sinke et al., 2008). At that cost level, the PV electricity still remains more expensive comparing with traditional nuclear or thermal power engineering. One of the most promising strategies for lowering PV costs is the use of thin film technology, referred also as 2nd generation solar cells. It involves low cost and low energy intensity deposition techniques of PV material onto inexpensive large area low-cost substrates. Such processes can bring costs down but because of the defects inherent in the lower quality processing methods, have reduced efficiencies compared to the 1st generation solar cells.

Material limitations of the 1st generation solar cells and efficiency limitations of the 2nd generation solar cells are initiated boring of the Si-based 3rd generation photovoltaic. Its main goal is to significantly increase the conversion efficiency of low-cost photovoltaic product. Indeed, the Carnot limit on the conversion of sunlight to electricity is 95% as opposed to the theoretical upper limit of 30% for a standard solar cell (Shockley & Queisser 1961). This suggests the performance of solar cells could be improved 2 – 3 times if different concepts permitting to reduce the power losses were used.

The two most important power loss mechanisms in single-band gap photovoltaic cells are *(1)* the inability to absorb photons with energy less than the band gap and *(2)* thermalisation of photon energy exceeding the gap (Fig. 1). Longer wavelength is not absorbed by the solar cell material. Shorter wavelength generates an electron-hole pair greater than the bandgap of the p-n junction material. The excess of energy is lost as heat because the electron (hole) relaxes to the conduction (valence) band edges. The amounts of the losses are around 23 % and 33 % of the incoming solar energy, respectively (Nelson, 2003). Other losses are junction loss, contact loss and the recombination loss. Theory predicts (Shockley & Queisser 1961) that the highest single – junction solar cell efficiency is roughly 30%, assuming such factors as the intensity of one sun (no sunlight concentration), a one-junction solar cell (a single material with a single bandgap), and one electron-hole pair produced from each incoming photon.

Silicon-Based Third Generation Photovoltaics 141

spectrum or air mass zero (AM0) spectrum is richer in ultraviolet light than the typical terrestrial solar spectrum (air mass 1.5 or AM1.5). Taking into account that the ultraviolet light is converted into electricity less efficiently than the other parts of the spectrum, the resulting efficiencies for AM0 are thus lower (Green et al., 2010). Since cells are typically measured under the spectrum for their intended use and efficiencies are not easily converted, this chapter will indicate efficiencies measured under non-concentrated AM1.5 at

Up today the tandem cells have been developing on monolithic integration of non-abundant III –V materials by means of rather expensive technologies of fabrication like molecular beam epitaxy (MBE) or metal-organic chemical vapor deposition (MOCVD). Currently commercially available multijunction cells consist of three subcells (GaInP/GaAs/Ge), which all have the same lattice parameter and are grown in a monolithic stack (Fig. 3). The subcells in this monolithic stack are series connected through the tunnel junctions. The record efficiency of 32% was achieved in 2010 for this type of cells (Green et al., 2010). These high-efficiency solar cells are being increasingly used in solar concentrator systems, where development of both the solar cells and the associated optical and thermal control elements are actively being pursued. The performance of tandem solar cells has been demonstrated, but work is continuing to increase the numbers of junctions and optimize the bandgap junctions. The choice of materials with optimal or near-optimal bandgap is severely limited by the lattice matching constraint of these cells. Another approach to increasing of multijunction solar cell efficiency is the incorporation of materials with a mismatch in the lattice constant. Graded composition buffers between the lattice mismatched subcells are used to reduce the density of the threaded dislocations resulting from the lattice mismatch strain. Lattice mismatch technology opens the parameter space for junction materials, allowing the choice of materials with more optimal bandgaps and a potential for higher cell

Fig. 4. Using of multijunction solar cells

for Mars rover missions 1.

25° unless otherwise specified.

Fig. 3. Schematic view of GaInP/GaAs/Ge

1 http://marsrovers.nasa.gov/gallery/press/spirit/20060104a.html

solar cell.

efficiency.

To efficiently convert the whole solar spectrum into the electricity three main families of approaches have been proposed (Green et al., 2005) (Green, 2002): *(i)* increasing the number of bandgaps (*tandem cell* concept); *(ii)* capturing carriers before thermalisation, and *(iii)* multiple carrier pair generation per high energy photon or single carrier pair generation with multiple low energy photons. Up to now, tandem or in other words multijunction cells provide the best-known example of such high-efficiency approaches. Indeed, the loss process *(2)* of Fig. 1 can be largely eliminated if the energy of the absorbed photon is just a little higher that the cell bandgap. The concept of tandem solar cells is based on the use of several solar cells (or subcells) of different bandgaps stacked on top of each other (Fig. 2), with the highest bandgap cell uppermost and lowest on the bottom. The incident light is automatically filtered as it passes through the stack. Each cell absorbs the light that it can most efficiently convert, with the rest passing through to underlying lower bandgap cells (Green et al., 2007). The using of multiple subcells in the tandem cell structure permits to divide the broad solar spectrum on smaller sections, each of which can be converted to electricity more efficiently. Performance increases as the number of subcells increases, with the direct sunlight conversion efficiency of 86.8 % calculated for an infinite stack of independently operated subcells (Marti & Araujo, 1996). The efficiency limit reaches 42.5 % and 47.5 % for 2- and 3-subcell tandem solar cells (Nelson, 2003) as compared to 30% of one junction solar cell.

Fig. 2. Tandem cell approach (Green, 2003).

Fig. 1. Loss processes in a standard solar cell: *(1)* non-absorption of below band gap photons; *(2)* lattice thermalisation loss; *(3)*  and *(4)* junction and contact voltage losses; *(5)* recombination loss (Green, 2003).

Having to independently operate each subcell is a complication best avoided. Usually, subcells are designed with their current output matched so that they can be connected in series. This constrain reduces performance. Moreover, it makes the design very sensitive to the spectral content of the sunlight. Once the output current of one subcell in a series connection drops more than about 5 % below that of the next worst, the best for overall performance is to short-circuit the low-output subcell, otherwise it will consume, rather than generate power.

It should be also noted the common point of confusion about solar cells efficiency. The measured efficiency of solar cell depends on the spectrum of its light source. The space solar

To efficiently convert the whole solar spectrum into the electricity three main families of approaches have been proposed (Green et al., 2005) (Green, 2002): *(i)* increasing the number of bandgaps (*tandem cell* concept); *(ii)* capturing carriers before thermalisation, and *(iii)* multiple carrier pair generation per high energy photon or single carrier pair generation with multiple low energy photons. Up to now, tandem or in other words multijunction cells provide the best-known example of such high-efficiency approaches. Indeed, the loss process *(2)* of Fig. 1 can be largely eliminated if the energy of the absorbed photon is just a little higher that the cell bandgap. The concept of tandem solar cells is based on the use of several solar cells (or subcells) of different bandgaps stacked on top of each other (Fig. 2), with the highest bandgap cell uppermost and lowest on the bottom. The incident light is automatically filtered as it passes through the stack. Each cell absorbs the light that it can most efficiently convert, with the rest passing through to underlying lower bandgap cells (Green et al., 2007). The using of multiple subcells in the tandem cell structure permits to divide the broad solar spectrum on smaller sections, each of which can be converted to electricity more efficiently. Performance increases as the number of subcells increases, with the direct sunlight conversion efficiency of 86.8 % calculated for an infinite stack of independently operated subcells (Marti & Araujo, 1996). The efficiency limit reaches 42.5 % and 47.5 % for 2- and 3-subcell tandem solar cells (Nelson, 2003) as compared to 30% of one

Having to independently operate each subcell is a complication best avoided. Usually, subcells are designed with their current output matched so that they can be connected in series. This constrain reduces performance. Moreover, it makes the design very sensitive to the spectral content of the sunlight. Once the output current of one subcell in a series connection drops more than about 5 % below that of the next worst, the best for overall performance is to short-circuit the low-output subcell, otherwise it will consume, rather than

It should be also noted the common point of confusion about solar cells efficiency. The measured efficiency of solar cell depends on the spectrum of its light source. The space solar

Fig. 2. Tandem cell approach (Green, 2003).

junction solar cell.

generate power.

Fig. 1. Loss processes in a standard solar cell: *(1)* non-absorption of below band gap photons; *(2)* lattice thermalisation loss; *(3)*  and *(4)* junction and contact voltage losses; *(5)* recombination loss (Green, 2003).

spectrum or air mass zero (AM0) spectrum is richer in ultraviolet light than the typical terrestrial solar spectrum (air mass 1.5 or AM1.5). Taking into account that the ultraviolet light is converted into electricity less efficiently than the other parts of the spectrum, the resulting efficiencies for AM0 are thus lower (Green et al., 2010). Since cells are typically measured under the spectrum for their intended use and efficiencies are not easily converted, this chapter will indicate efficiencies measured under non-concentrated AM1.5 at 25° unless otherwise specified.

Fig. 3. Schematic view of GaInP/GaAs/Ge solar cell.

Fig. 4. Using of multijunction solar cells for Mars rover missions 1.

Up today the tandem cells have been developing on monolithic integration of non-abundant III –V materials by means of rather expensive technologies of fabrication like molecular beam epitaxy (MBE) or metal-organic chemical vapor deposition (MOCVD). Currently commercially available multijunction cells consist of three subcells (GaInP/GaAs/Ge), which all have the same lattice parameter and are grown in a monolithic stack (Fig. 3). The subcells in this monolithic stack are series connected through the tunnel junctions. The record efficiency of 32% was achieved in 2010 for this type of cells (Green et al., 2010). These high-efficiency solar cells are being increasingly used in solar concentrator systems, where development of both the solar cells and the associated optical and thermal control elements are actively being pursued. The performance of tandem solar cells has been demonstrated, but work is continuing to increase the numbers of junctions and optimize the bandgap junctions. The choice of materials with optimal or near-optimal bandgap is severely limited by the lattice matching constraint of these cells. Another approach to increasing of multijunction solar cell efficiency is the incorporation of materials with a mismatch in the lattice constant. Graded composition buffers between the lattice mismatched subcells are used to reduce the density of the threaded dislocations resulting from the lattice mismatch strain. Lattice mismatch technology opens the parameter space for junction materials, allowing the choice of materials with more optimal bandgaps and a potential for higher cell efficiency.

<sup>1</sup> http://marsrovers.nasa.gov/gallery/press/spirit/20060104a.html

Silicon-Based Third Generation Photovoltaics 143

on. Many reviews addressing this problematic since appeared (one of the good recent reviews is Ref (Bulutay & Ossicini, 2010)). In this paragraph we will only underline some

*Ab initio* calculations using density functional theory (DFT) indicate that the increasing of the optical bandgap of Si nanocrystals (or in other words quantum dots (QDs)) is expected to vary from 1.4 to 2.4 eV for a nanocrystal size of 8-2.5 nm (Ögüt et al., 1997). However, further DFT calculations have found that in addition to quantum confinement effect in small QDs, the matrix has a strong influence of the resulting energy levels (König et al., 2009). With increasing polarity of the bonds between the nanocrystal and the matrix, there is an increasing dominance of the interface strain over quantum confinement. For a 2 nm diameter nanocrystal, this strain is such that the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap is significantly reduced in a polar SiO2 matrix but not much affected in a less polar SiNx or nonpolar SiC matrix (König et al., 2009). It is also shown the reduction in gap energy on going from a QD in vacuum to the one embedded in a dielectric. An additional freedom of material design can be also introduced by impurity doping and interconnections between Si QDs, the both ones modify its optical and electrical transport properties (Nychyporuk et al., 2009) (Mimura et al., 1999).

Si QDs offer the potential to tune the effective bandgap, through quantum confinement, and allow fabrication of optimized tandem devices in one growth run in a thin film process.

Different technological approaches allowing formation of Si quantum dots in a dielectric matrix have already been developed, permitting to obtain Si nanocrystals as small as 1 nm in diameter. Between the most used deposition techniques one can cite reactive evaporation, ion implantation, sputtering and plasma enhanced chemical vapor deposition (PECVD). Considerable work has been done on the growth of Si nanocrystals embedded in silicon oxide dielectric matrices (SiO2) (Zacharias et al., 2002) (Stegemann et al., 2010), silicon nitride (Si3N4) (Kim et al., 2006) (Cho et al., 2005) (Mercaldo et al., 2010) (So et al., 2010) and silicon carbide (SiC) (Song et al., 2008) (Kurokawa et al., 2006) (Gradmann et al., 2010) (Löper et al., 2010) (Cho et al., 2007). An accurate control of the size and density of Si nanocrystals is mandatory in bandgap engineering for solar cell applications. It should be noted that Si nanocrystals prepared by different methods present slightly different properties which depend on the preparation procedure, because of different defect density, different degree of interconnections between the nanocrystals, different surface termination, and so on. Conventionally, Si QDs in dielectric matrix like SiO2, Si3N4 and SiC can be synthetized by self-organized growth from Si rich dielectric layers, which are thermodynamically unstable and therefore undergo phase separation upon appropriate post-annealing step to form nanocrystals. For example for Si rich oxide layer, the precipitation occurs according to the

> <sup>2</sup> 1 2 2 *<sup>x</sup> x x SiO SiO Si*

It should be noted that due to the fact that both the polarity and length of the bonds decrease towards those of Si-Si for SiO2 to Si3N4 and SiC, this implies that the segregation

important points resulting from quantum confinement effect.

**3. Silicon quantum dot solar cells** 

**3.1 Fabrication of Si QD nanostructures** 

following:

In 2010 the cost of multijunction solar cells still remains too high to allow their use outside of specified applications (for example space applications, Mars rover missions (Crisp et al., 2004) (Fig. 4)…). The high cost is mainly due to the complex structure and the high price of materials. In this context the fabrication of multijunction solar cells on the base of abundant low-cost materials that do not cause toxicity in the environment and by using approaches amenable to large scale mass production, like thin film deposition techniques, remains challenging.

#### **2. Silicon based tandem cells**

Silicon is a benign readily available material, which is widely used for solar cell fabrication. It has a bandgap of 1.12 eV at 300 K, which is close to optimal not only for standard, single p – n junction cell, but also for the bottom cell in a 2-cell or even a 3-cell tandem stack (Conibeer et al., 2008). Therefore a solar cell entirely based of Si and its dielectric compounds (referred also as *all-Si tandem solar cell*) with other abundant elements (i. e. silicon dioxide, nitrides or carbides) fabricated with thin film techniques, is advantageous in terms of potential for large scale manufacturing and in long term availability of its constituents. As was already mentioned previously, thin film low-temperature deposition techniques results in high defect density films. Hence solar cells must be thin enough to limit recombination due to their short diffusion lengths, which in turn means they must have high absorption coefficients.

For AM1.5 solar spectrum the optimal bandgap of the top cell required to maximize conversion efficiency is ~1.7 to 1.8 eV for a 2-cell tandem with a Si bottom cell and 1.5 eV and 2.0 eV for the middle and upper cells for a 3-cell tandem (Meillaud et al., 2006). It should be also noted that for terrestrial applications (AM1.5 solar spectrum), the highest bandgap necessary for the Si-based tandem solar cells is limited to 3.1 eV, the energy at which the absorption from the encapsulation material, such as ethylene-vinyl acetate (EVA), starts to play an important role.

#### **2.1 Quantum confinement in Si nanostructures**

To increase Si bangap, nanoscale size dependent quantum confinement effect can be used. Indeed, the quantum confinement effect manifests itself by significant modification of electronic band structure of Si nanocrystals when their size is reduced to below the exciton Bohr radius (~4.9 nm) of bulk Si crystals. In particular, quantum confinement effect provokes the increasing of the effective bandgap of Si nanocrystals. Moreover, for indirect bandgap semiconductors, like Si, geometrical confinement of carriers increases the overlap of electron and hole wavefunctions in momentum space and thus enhances the oscillator strength and as a consequence increases its absorption coefficient. From this effect, one can expect Si nanocrystals to behave as direct bandgap semiconductors. However, there is some evidence suggesting that the momentum conservation rule is only partially broken and Si nanocrystal strongly preserves the indirect bandgap nature of bulk Si crystals (Kovalev et al., 1999). Si nanostructures are thus the perfect candidates for higher bandgap materials in all-Si tandem cell approach.

Since the observation in 1990 of strong room-temperature photoluminescence from nanostructured porous Si (Canham, 1990), significant scientific interest has been focused of the simulation of optical and electrical properties of Si nanostructures regarding their size, shape, surface termination, number and degree of interconnections, impurity doping and so

In 2010 the cost of multijunction solar cells still remains too high to allow their use outside of specified applications (for example space applications, Mars rover missions (Crisp et al., 2004) (Fig. 4)…). The high cost is mainly due to the complex structure and the high price of materials. In this context the fabrication of multijunction solar cells on the base of abundant low-cost materials that do not cause toxicity in the environment and by using approaches amenable to large scale mass production, like thin film deposition techniques, remains

Silicon is a benign readily available material, which is widely used for solar cell fabrication. It has a bandgap of 1.12 eV at 300 K, which is close to optimal not only for standard, single p – n junction cell, but also for the bottom cell in a 2-cell or even a 3-cell tandem stack (Conibeer et al., 2008). Therefore a solar cell entirely based of Si and its dielectric compounds (referred also as *all-Si tandem solar cell*) with other abundant elements (i. e. silicon dioxide, nitrides or carbides) fabricated with thin film techniques, is advantageous in terms of potential for large scale manufacturing and in long term availability of its constituents. As was already mentioned previously, thin film low-temperature deposition techniques results in high defect density films. Hence solar cells must be thin enough to limit recombination due to their short diffusion lengths, which in turn means they must have high absorption

For AM1.5 solar spectrum the optimal bandgap of the top cell required to maximize conversion efficiency is ~1.7 to 1.8 eV for a 2-cell tandem with a Si bottom cell and 1.5 eV and 2.0 eV for the middle and upper cells for a 3-cell tandem (Meillaud et al., 2006). It should be also noted that for terrestrial applications (AM1.5 solar spectrum), the highest bandgap necessary for the Si-based tandem solar cells is limited to 3.1 eV, the energy at which the absorption from the encapsulation material, such as ethylene-vinyl acetate (EVA),

To increase Si bangap, nanoscale size dependent quantum confinement effect can be used. Indeed, the quantum confinement effect manifests itself by significant modification of electronic band structure of Si nanocrystals when their size is reduced to below the exciton Bohr radius (~4.9 nm) of bulk Si crystals. In particular, quantum confinement effect provokes the increasing of the effective bandgap of Si nanocrystals. Moreover, for indirect bandgap semiconductors, like Si, geometrical confinement of carriers increases the overlap of electron and hole wavefunctions in momentum space and thus enhances the oscillator strength and as a consequence increases its absorption coefficient. From this effect, one can expect Si nanocrystals to behave as direct bandgap semiconductors. However, there is some evidence suggesting that the momentum conservation rule is only partially broken and Si nanocrystal strongly preserves the indirect bandgap nature of bulk Si crystals (Kovalev et al., 1999). Si nanostructures are thus the perfect candidates for higher bandgap materials in

Since the observation in 1990 of strong room-temperature photoluminescence from nanostructured porous Si (Canham, 1990), significant scientific interest has been focused of the simulation of optical and electrical properties of Si nanostructures regarding their size, shape, surface termination, number and degree of interconnections, impurity doping and so

challenging.

coefficients.

**2. Silicon based tandem cells** 

starts to play an important role.

all-Si tandem cell approach.

**2.1 Quantum confinement in Si nanostructures** 

on. Many reviews addressing this problematic since appeared (one of the good recent reviews is Ref (Bulutay & Ossicini, 2010)). In this paragraph we will only underline some important points resulting from quantum confinement effect.

*Ab initio* calculations using density functional theory (DFT) indicate that the increasing of the optical bandgap of Si nanocrystals (or in other words quantum dots (QDs)) is expected to vary from 1.4 to 2.4 eV for a nanocrystal size of 8-2.5 nm (Ögüt et al., 1997). However, further DFT calculations have found that in addition to quantum confinement effect in small QDs, the matrix has a strong influence of the resulting energy levels (König et al., 2009). With increasing polarity of the bonds between the nanocrystal and the matrix, there is an increasing dominance of the interface strain over quantum confinement. For a 2 nm diameter nanocrystal, this strain is such that the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap is significantly reduced in a polar SiO2 matrix but not much affected in a less polar SiNx or nonpolar SiC matrix (König et al., 2009). It is also shown the reduction in gap energy on going from a QD in vacuum to the one embedded in a dielectric. An additional freedom of material design can be also introduced by impurity doping and interconnections between Si QDs, the both ones modify its optical and electrical transport properties (Nychyporuk et al., 2009) (Mimura et al., 1999).

#### **3. Silicon quantum dot solar cells**

Si QDs offer the potential to tune the effective bandgap, through quantum confinement, and allow fabrication of optimized tandem devices in one growth run in a thin film process.

#### **3.1 Fabrication of Si QD nanostructures**

Different technological approaches allowing formation of Si quantum dots in a dielectric matrix have already been developed, permitting to obtain Si nanocrystals as small as 1 nm in diameter. Between the most used deposition techniques one can cite reactive evaporation, ion implantation, sputtering and plasma enhanced chemical vapor deposition (PECVD). Considerable work has been done on the growth of Si nanocrystals embedded in silicon oxide dielectric matrices (SiO2) (Zacharias et al., 2002) (Stegemann et al., 2010), silicon nitride (Si3N4) (Kim et al., 2006) (Cho et al., 2005) (Mercaldo et al., 2010) (So et al., 2010) and silicon carbide (SiC) (Song et al., 2008) (Kurokawa et al., 2006) (Gradmann et al., 2010) (Löper et al., 2010) (Cho et al., 2007). An accurate control of the size and density of Si nanocrystals is mandatory in bandgap engineering for solar cell applications. It should be noted that Si nanocrystals prepared by different methods present slightly different properties which depend on the preparation procedure, because of different defect density, different degree of interconnections between the nanocrystals, different surface termination, and so on.

Conventionally, Si QDs in dielectric matrix like SiO2, Si3N4 and SiC can be synthetized by self-organized growth from Si rich dielectric layers, which are thermodynamically unstable and therefore undergo phase separation upon appropriate post-annealing step to form nanocrystals. For example for Si rich oxide layer, the precipitation occurs according to the following:

$$SiO\_x \rightarrow \frac{x}{2}SiO\_2 + \left(1 - \frac{x}{2}\right)Si$$

It should be noted that due to the fact that both the polarity and length of the bonds decrease towards those of Si-Si for SiO2 to Si3N4 and SiC, this implies that the segregation

Silicon-Based Third Generation Photovoltaics 145

approach it is still possible to fabricate well – ordered and uniform Si nanocrystals in a film

A simple technique to prepare the multilayer structure known also as superlattices of Si QDs in silicon oxide matrix was firstly reported by Zacharias (Zacharias et al., 2002) . It consists in deposition of alternating layers of stoichometric Si oxide (SiO2) and Si rich oxide (SRO) of thicknesses down to 2 nm. This precision is normally achieved by using RF magnetron sputtering or plasma enhanced chemical vapor deposition (PECVD) technique. The deposition consisting typically of 20-50 bi-layers is followed by the annealing step is N2 ambient from 1050 to 1150°C for 1 h. During the annealing step, the surface energy minimization favors the precipitation of Si in the SRO layer into approximately spherical QDs (Conibeer et al., 2008). This process is illustrated on Fig. 5 (a). The diameter of Si QDs is constrained by the SRO layer thickness and quite uniform size dispersion is achieved within about 10% (Zacharias et al., 2002) . The density of the QDs can be varied by the composition of the SRO layer. Fig. 5 (b) shows typical transmission electron microscope (TEM) of the multi-structure SiQDs in SiO2 matrix grown by this method. TEM evidence indicates that these nanocrystals tend to be spherical – as surface energy minimization would dictate - and at this scale would have energy levels confined in all three dimensions and hence can be

Nowadays, the phase separation, solid state crystallization and optical properties of SiO2/SRO/SiO2 superlattices are already well understood. However, it is a major challenge to achieve charge carrier transport through a network of Si QDs embedded in a SiO2 matrix. Therefore, other Si based host matrices such as Si3N4 or SiC that feature lower energy band offsets with respect to the Si band edges and thus higher carrier mobility are attractive.

For the reasons stated above, it was explored the fabrication of Si QDs in silicon nitride matrix. Thick layers of silicon-rich nitride, when annealed at above 1000°C, precipitate to Si QD (Kim et al., 2005). Multilayered structures also result in Si QD formation with controlled size of the Si QDs (Cho et al., 2005). The annealing temperature can also be used to modify the nitride matrix, with it being amorphous below 1150°C but with crystalline nitride phases, in addition to the Si QDs, appearing at temperatures ranging from 1150 to 1200° (Scardera et al., 2008). Multilayered structures can be deposited by sputtering or by PECVD with growth parameters and annealing conditions very similar to those for oxide giving good control of QD sizes. The main difference is the extra H incorporation with PECVD that requires an initial low-temperature anneal to drive off excess hydrogen and prevent bubble

Si QDs can also be grown *in situ* during PECVD deposition, where they form in the gas phase (Lelièvre et al., 2006). There is much less control over size and shape but no hightemperature anneal is required to form the Si QDs (Fig. 6 (a)). Multilayer growth using this *in-situ* technique has also been attempted with irregular shaped but reasonably uniform

The formation of Si quantum dots in SiO2/Si3N4 hybrid matrix was also reported (Di et al., 2010). In this approach alternating silicon rich oxide and Si3N4 layers were produced followed by post-deposition anneals. In addition, it should be noted that Si3N4 acts as a better diffusion barrier compared to SiO2. It restricts the displacement of Si atoms as well as

with a high dot density (Surana et al., 2010).

**3.1.1 Si QDs in silicon oxide matrix** 

considered as quantum dots.

sized Si QDs (Fig. 6 (b)).

**3.1.2 Si QDs in silicon nitride matrix** 

formation during the high-temperature anneal (Cho et al., 2005).

dopant atoms under high processing temperatures.

and precipitation effect for Si in the three matrices would decrease such that in SiC formation of QDs is likely to be most difficult.

(b)

Fig. 5. (a) Multi-layer structure illustrating precipitation of Si QDs in a Si-rich layer; (b) TEM image of a superlattice of Si QDs in SiO2 matrix (Conibeer et al., 2008).

The QD size and density control are normally realized by changing the chemical stoichiometry of the bulk films. By reducing the Si-richness in a bulk Si-based matrix, smaller nanocrystals can be achieved. Nevertheless, this will simultaneously reduce the density of nanocrystals in the film due to the reduced Si-richness. The low density of QDs with desired size leads to a negative effect on the electrical conductivity of the films. Moreover, the assumption that all the excess Si precipitates to nanocrystals turns out to be oversimplification. In fact, it has been observed that only half the excess Si clusters in these precipitates upon annealing at 1000°C for 30 min, in material deposited by PECVD, with a considerable amount of suboxide material forming in the matrix. Therefore, the method allowing a fabrication of high density, but narrow size distributed Si QDs films via superlattice approach, firstly reported by Zacharias (Zacharias et al., 2002) , was adopted by the majority of researchers. It should be mentioned that even without using the multilayer

and precipitation effect for Si in the three matrices would decrease such that in SiC

(a)

(b) Fig. 5. (a) Multi-layer structure illustrating precipitation of Si QDs in a Si-rich layer; (b) TEM

The QD size and density control are normally realized by changing the chemical stoichiometry of the bulk films. By reducing the Si-richness in a bulk Si-based matrix, smaller nanocrystals can be achieved. Nevertheless, this will simultaneously reduce the density of nanocrystals in the film due to the reduced Si-richness. The low density of QDs with desired size leads to a negative effect on the electrical conductivity of the films. Moreover, the assumption that all the excess Si precipitates to nanocrystals turns out to be oversimplification. In fact, it has been observed that only half the excess Si clusters in these precipitates upon annealing at 1000°C for 30 min, in material deposited by PECVD, with a considerable amount of suboxide material forming in the matrix. Therefore, the method allowing a fabrication of high density, but narrow size distributed Si QDs films via superlattice approach, firstly reported by Zacharias (Zacharias et al., 2002) , was adopted by the majority of researchers. It should be mentioned that even without using the multilayer

image of a superlattice of Si QDs in SiO2 matrix (Conibeer et al., 2008).

formation of QDs is likely to be most difficult.

approach it is still possible to fabricate well – ordered and uniform Si nanocrystals in a film with a high dot density (Surana et al., 2010).

#### **3.1.1 Si QDs in silicon oxide matrix**

A simple technique to prepare the multilayer structure known also as superlattices of Si QDs in silicon oxide matrix was firstly reported by Zacharias (Zacharias et al., 2002) . It consists in deposition of alternating layers of stoichometric Si oxide (SiO2) and Si rich oxide (SRO) of thicknesses down to 2 nm. This precision is normally achieved by using RF magnetron sputtering or plasma enhanced chemical vapor deposition (PECVD) technique. The deposition consisting typically of 20-50 bi-layers is followed by the annealing step is N2 ambient from 1050 to 1150°C for 1 h. During the annealing step, the surface energy minimization favors the precipitation of Si in the SRO layer into approximately spherical QDs (Conibeer et al., 2008). This process is illustrated on Fig. 5 (a). The diameter of Si QDs is constrained by the SRO layer thickness and quite uniform size dispersion is achieved within about 10% (Zacharias et al., 2002) . The density of the QDs can be varied by the composition of the SRO layer. Fig. 5 (b) shows typical transmission electron microscope (TEM) of the multi-structure SiQDs in SiO2 matrix grown by this method. TEM evidence indicates that these nanocrystals tend to be spherical – as surface energy minimization would dictate - and at this scale would have energy levels confined in all three dimensions and hence can be considered as quantum dots.

Nowadays, the phase separation, solid state crystallization and optical properties of SiO2/SRO/SiO2 superlattices are already well understood. However, it is a major challenge to achieve charge carrier transport through a network of Si QDs embedded in a SiO2 matrix. Therefore, other Si based host matrices such as Si3N4 or SiC that feature lower energy band offsets with respect to the Si band edges and thus higher carrier mobility are attractive.

#### **3.1.2 Si QDs in silicon nitride matrix**

For the reasons stated above, it was explored the fabrication of Si QDs in silicon nitride matrix. Thick layers of silicon-rich nitride, when annealed at above 1000°C, precipitate to Si QD (Kim et al., 2005). Multilayered structures also result in Si QD formation with controlled size of the Si QDs (Cho et al., 2005). The annealing temperature can also be used to modify the nitride matrix, with it being amorphous below 1150°C but with crystalline nitride phases, in addition to the Si QDs, appearing at temperatures ranging from 1150 to 1200° (Scardera et al., 2008). Multilayered structures can be deposited by sputtering or by PECVD with growth parameters and annealing conditions very similar to those for oxide giving good control of QD sizes. The main difference is the extra H incorporation with PECVD that requires an initial low-temperature anneal to drive off excess hydrogen and prevent bubble formation during the high-temperature anneal (Cho et al., 2005).

Si QDs can also be grown *in situ* during PECVD deposition, where they form in the gas phase (Lelièvre et al., 2006). There is much less control over size and shape but no hightemperature anneal is required to form the Si QDs (Fig. 6 (a)). Multilayer growth using this *in-situ* technique has also been attempted with irregular shaped but reasonably uniform sized Si QDs (Fig. 6 (b)).

The formation of Si quantum dots in SiO2/Si3N4 hybrid matrix was also reported (Di et al., 2010). In this approach alternating silicon rich oxide and Si3N4 layers were produced followed by post-deposition anneals. In addition, it should be noted that Si3N4 acts as a better diffusion barrier compared to SiO2. It restricts the displacement of Si atoms as well as dopant atoms under high processing temperatures.

Silicon-Based Third Generation Photovoltaics 147

To be successfully applied as a material for all-Si tandem solar cells, the small size of Si QDs is not the single prerequisite. It is also necessary to assure their high density in order to achieve a direct tunneling of the photogenerated charge carriers between the QDs. This still constitutes the bottleneck of the approaches cited above. Recently, the fabrication of thin films composed by highly packed Si QDs with a controlled bandgap values was reported (Nychyporuk et al., 2009). This approach is based on the *in-situ* nucleation of Si QDs in the gas phase during PECVD deposition by using SiH4 as a gas precursor. Indeed, the dust particle formation in Ar-SiH4 plasma is known to be a time-dependent four step process occurring in the gas phase: *(i)* polymerization phase, *(ii)* accumulation phase, *(ii)* coalescence and *(iv)* surface deposition growth. During the polymerization phase, the nucleation of extremely small particles (~1 nm) takes place. They progressively grow in size with time and at the end of the polymerization phase, starting from about 1 nm, a short accumulation phase begins. During this phase the nanoparticles size remains constant and only their density increases in the plasma environment. The coalescence phase starts once the nanoparticles critical density is reached. The small nanoparticles (~1 nm) begin to agglomerate at least two by two to form larger nanoclusters. In consequence, a number of interconnections between the nanoparticles increases. The final phase corresponds to the plasma species deposition on the surface of strongly agglomerated nanoparticles. During this phase a hydrogenated amorphous Si shell layer is formed around the crystalline Si core. The thickness of this amorphous shell increases with time. The square wave modulation of the power amplitude applied to the plasma has been found as a suitable technique permitting to obtain the deposition of Si QDs with required size. It consists of alternating periods of plasma switching time followed by the plasma extinction time. As a result, Si QDs grown in the gas phase during the plasma switching time were deposited on a substrate (Fig. 8). The careful tuning of the plasma switching time permits to precisely control the phase of Si QD growth and as a consequence their size and degree of interconnections between them. Si QD based thin films deposited under dusty plasma conditions appear to be promising candidates for all-Si tandem solar cell applications.

A requirement for a tandem cell element is the presence of some form of junction for carrier separation. Phosphorous (P) and boron (B) are excellent dopants in bulk Si as they have a high solid solubility and alter the conductivity of the bulk Si by several orders of magnitude.

Doping of Si nanostructures is a subject of intense research (Tsu et al., 1994) (Holtz & Zhao, 2004) (Erwin et al., 2005) (Norris et al., 2008) (Ossicini et al., 2006). Unfortunately, the main difficult in existing doping techniques arises from the fluctuation of impurity number per nanocrystal in a nanocrystal assembly. For Si nanocrystals as small as few nanometers in diameter, the expression of the doping level in the form of "impurity concentration" is not suitable and it should be expressed as "impurity numbers" because it changes digitally. For example, doping of one impurity atom into a nanocrystal of 3 nm in diameter (~ about 700 atoms) corresponds to an impurity concentration of 7.0 × 1019 atoms/cm3. At this doping level, bulk Si is a degenerate semiconductor and exhibits metallic behavior. However, by means of electron spin resonance (ESR) spectroscopy it was shown that Si nanocrystals do not become metallic even under heavily doped conditions. Therefore, in nanocrystals, addition or subtraction of a single impurity atom drastically changes the electronic structure

Hence they are good initial choices to study the doping in the Si nanocrystals.

**3.1.4 Interconnected Si QDs forming thin films** 

**3.2 Shallow-impurity doped Si nanostructures** 

Fig. 6. *In-situ* grown Si QDs in the gas phase and dispersed in Si3N4 matrix: (a) One layer structure (Lelièvre et al., 2006); (b) multi-layer structure (Conibeer et al., 2008).

#### **3.1.3 Si QDs in silicon carbide matrix**

Si QDs in a SiC matrix offer an even lower barrier height and hence potentially better electronic transport properties. However, the low barrier height also limits the minimum size of QDs to about 3 nm or else the quantum-confined levels are likely to rise above the level of the barrier, which should be around 2.3 eV for amorphous SiC. Si QDs in SiC matrix have been formed in a single thick layer by Si-rich carbide deposition followed by hightemperature annealing at between 800° and 1100°C in a very similar process to that for oxide (Fig. 7). Si1-xCx/SiC multilayers have also been deposited by sputtering to give better control over the Si QD as with oxide and nitride matrices. However, contrary to these previous matrices, the both Si and SiC QDs have been produced by high temperature annealing of Si –rich SiC layer or in a SiC1-xCx/SiC multistructure. The formation of SiC nanocrystals can hinder the formation of Si QDs.

Fig. 7. Cross-sectional HRTEM image of Sirich SiC layer after the thermal annealing (Conibeer, 2010).

Fig. 8. TEM image interconnected Si QDs forming thin films.

(a) (b)

Si QDs in a SiC matrix offer an even lower barrier height and hence potentially better electronic transport properties. However, the low barrier height also limits the minimum size of QDs to about 3 nm or else the quantum-confined levels are likely to rise above the level of the barrier, which should be around 2.3 eV for amorphous SiC. Si QDs in SiC matrix have been formed in a single thick layer by Si-rich carbide deposition followed by hightemperature annealing at between 800° and 1100°C in a very similar process to that for oxide (Fig. 7). Si1-xCx/SiC multilayers have also been deposited by sputtering to give better control over the Si QD as with oxide and nitride matrices. However, contrary to these previous matrices, the both Si and SiC QDs have been produced by high temperature annealing of Si –rich SiC layer or in a SiC1-xCx/SiC multistructure. The formation of SiC nanocrystals can

Fig. 8. TEM image interconnected Si QDs

**20 nm** 

forming thin films.

Fig. 6. *In-situ* grown Si QDs in the gas phase and dispersed in Si3N4 matrix: (a) One layer

structure (Lelièvre et al., 2006); (b) multi-layer structure (Conibeer et al., 2008).

**3.1.3 Si QDs in silicon carbide matrix** 

hinder the formation of Si QDs.

Fig. 7. Cross-sectional HRTEM image of Sirich SiC layer after the thermal annealing

(Conibeer, 2010).

#### **3.1.4 Interconnected Si QDs forming thin films**

To be successfully applied as a material for all-Si tandem solar cells, the small size of Si QDs is not the single prerequisite. It is also necessary to assure their high density in order to achieve a direct tunneling of the photogenerated charge carriers between the QDs. This still constitutes the bottleneck of the approaches cited above. Recently, the fabrication of thin films composed by highly packed Si QDs with a controlled bandgap values was reported (Nychyporuk et al., 2009). This approach is based on the *in-situ* nucleation of Si QDs in the gas phase during PECVD deposition by using SiH4 as a gas precursor. Indeed, the dust particle formation in Ar-SiH4 plasma is known to be a time-dependent four step process occurring in the gas phase: *(i)* polymerization phase, *(ii)* accumulation phase, *(ii)* coalescence and *(iv)* surface deposition growth. During the polymerization phase, the nucleation of extremely small particles (~1 nm) takes place. They progressively grow in size with time and at the end of the polymerization phase, starting from about 1 nm, a short accumulation phase begins. During this phase the nanoparticles size remains constant and only their density increases in the plasma environment. The coalescence phase starts once the nanoparticles critical density is reached. The small nanoparticles (~1 nm) begin to agglomerate at least two by two to form larger nanoclusters. In consequence, a number of interconnections between the nanoparticles increases. The final phase corresponds to the plasma species deposition on the surface of strongly agglomerated nanoparticles. During this phase a hydrogenated amorphous Si shell layer is formed around the crystalline Si core. The thickness of this amorphous shell increases with time. The square wave modulation of the power amplitude applied to the plasma has been found as a suitable technique permitting to obtain the deposition of Si QDs with required size. It consists of alternating periods of plasma switching time followed by the plasma extinction time. As a result, Si QDs grown in the gas phase during the plasma switching time were deposited on a substrate (Fig. 8). The careful tuning of the plasma switching time permits to precisely control the phase of Si QD growth and as a consequence their size and degree of interconnections between them. Si QD based thin films deposited under dusty plasma conditions appear to be promising candidates for all-Si tandem solar cell applications.

#### **3.2 Shallow-impurity doped Si nanostructures**

A requirement for a tandem cell element is the presence of some form of junction for carrier separation. Phosphorous (P) and boron (B) are excellent dopants in bulk Si as they have a high solid solubility and alter the conductivity of the bulk Si by several orders of magnitude. Hence they are good initial choices to study the doping in the Si nanocrystals.

Doping of Si nanostructures is a subject of intense research (Tsu et al., 1994) (Holtz & Zhao, 2004) (Erwin et al., 2005) (Norris et al., 2008) (Ossicini et al., 2006). Unfortunately, the main difficult in existing doping techniques arises from the fluctuation of impurity number per nanocrystal in a nanocrystal assembly. For Si nanocrystals as small as few nanometers in diameter, the expression of the doping level in the form of "impurity concentration" is not suitable and it should be expressed as "impurity numbers" because it changes digitally. For example, doping of one impurity atom into a nanocrystal of 3 nm in diameter (~ about 700 atoms) corresponds to an impurity concentration of 7.0 × 1019 atoms/cm3. At this doping level, bulk Si is a degenerate semiconductor and exhibits metallic behavior. However, by means of electron spin resonance (ESR) spectroscopy it was shown that Si nanocrystals do not become metallic even under heavily doped conditions. Therefore, in nanocrystals, addition or subtraction of a single impurity atom drastically changes the electronic structure

Silicon-Based Third Generation Photovoltaics 149

an electron-hole pair is not released in the form of photon. This energy is given to a third carrier, which after the interaction losses its excess energy as thermal vibrations. Since this process is a three-particle interaction, it is normally only significant in strongly nonequilibrium conditions or when the carrier density is very high. For doped nanocrystals the value of Auger rate is four to five orders of magnitude larger than the radiative rate of excitons, and thus one shallow impurity can almost completely kill PL from the nanocrystal. Hence with increasing of average impurity numbers in a nanocrystal assembly, the PL intensity is expected to decrease. This effect was really observed in p-type Si nanocrystals. As one can see on Fig. 9 (a) with increasing of B concentration, the PL intensity

monotonously decreases (Fujii et al., 1998) (Müller et al., 1999) (Stegner et al., 2008).

and impurity concentration (Fujii et al., 2010).

**3.2.1 Dark resistivity measurements** 

In P-doped Si nanocrystals, the situation is different. When the phosphorous concentration is relatively low, the PL intensity increases slightly compared to that of the undoped Si nanocrystals (Fig. 9 b) (Fujii et al., 2000) (Mimura et al., 2000) (Tchebotareva et al., 2005). The increase of the PL intensity indicates that non-radiative recombination processes are quenched by P doping. One of the possible explanation is that electrons supplied by P are captured by the dangling bonds, which inactivate the nonradiative recombination centers and compensate donors (Stegner et al., 2008) (Lenahan et al., 1998). It should be also noted that the PL intensity also strongly depends on the size of the shallow-doped Si nanocrystals. There are many theoretical studies on preferential localization of impurities in Si nanocrystals. It should to be noted that it is almost impossible to control experimentally the location of impurities in nanocrystals. However, the information on localization was experimentally obtained (Kovalev et al., 1998). It was shown that P dopants are localized at or close to the surface of Si nanocrystal. On the contrary, the B atoms are primary incorporated into the Si nanocrystal core. However, the preferential localization of impurities may depend on nanocrystal growth process and the surface termination. Therefore, properties of dopant may be quite different between Si nanocrystals grown by the decomposition of SiH4, phase separation of SRO and so on. In any cases the doping efficiency by B atoms is much smaller than that of P atoms due to larger formation energy of B-doped Si nanocrystals than P-doped ones (Kovalev et al., 1998) (Ossicini et al., 2005). To what concerns the optical and electrical properties, contrary to the intrinsic Si nanocrystals, the shallow doped Si nanocrystals present new degree of freedom to control them. For example, the size is one of the main parameters to control optical bandgap of the intrinsic Si nanocrystals. On the other hand, due to the difference in the electronic band structure in the case of doped and codoped Si nanocrystals (obtained by the simultaneous doping by B and P atoms), the optical bandgap is determined by the combination of the size

It is worth noting that the impurity atoms alter the formation kinetics of Si nanocrystals. Indeed, the average size of P-doped Si nanocrystals is increased compared to the undoped ones under the same experimental conditions (Conibeer et al., 2010), and in some experiments this increasing was almost double. Contrary to the doping with P, the doping with B results in the forming of smaller Si nanocrystals compared to the undoped case (Hao et al., 2009). The crystalline volume fraction was found to decrease with increasing of B concentration (Hao et al., 2009), which suggests that boron suppresses Si crystallization. One

The resistivity of the Si QD material is an important parameter for photovoltaic applications. The influence of the doping concentration on resistivity of Si QD superlattices was studied

of the possible reasons is the local deformations induced by the impurity atoms.

and the resultant optical and electrical transport properties. So, for solar cell application, the development of a technique permitting to control the "impurity number" with extremely high accuracy is indispensable.

Up to now, an accurate control of "impurity number" in a Si nanocrystal has not been achieved. One of the largest problems of the growth of doped Si nanocrystals is that impurity atoms are pushed out of nanocrystals to surrounding matrices by the so-called selfpurification effect. This effect can be understood by considering very high formation energy of doped nanocrystals (Ossicini et al., 2005). Impurity concentration in nanocrystals is thus always different from average concentration in a whole system. In the worst case, the number of impurity in a nanocrystal becomes zero even when average concentration is rather high. The development of viable technique to characterize impurities, especially "active" impurities doped into nanocrystals, is crucial. The resistivity measurements are thus complemented with ESR spectroscopy as well as PL spectroscopy.

As it was discussed previously, numerous methods have been reported for the growth of intrinsic Si QDs. On the other hand, a limited number of studies are published concerning the growth of shallow impurity-doped Si QDs with the diameter below 10 nm. One of the mostly used methods for shallow-impurity doping of Si nanocrystals is plasma decomposition of SiH4 by adding dopant precursors (diborane (B2H6) and phosphine (PH3)) (Pi et al., 2008) (Stegner et al., 2008). This method permits to obtain a variety of morphologies from densely packed nanocrystalline films to nanoparticle powder by controlling process parameters (Nychyporuk et al., 2009). Another method is incorporation of doping atoms into SRO layers by simultaneous co-sputtering of Si, SiO2 and P2O5 (or B2O3) in SiO2/SRO superlattice approach described previously (Mimura et al., 2000). During the annealing, Si nanocrystals are grown in phosphosilicate (PSG) (n-type Si QDs) or borosilicate (BSG) (p-type Si QDs) thin films. It should be also noted that the impurity concentration in nanocrystals is different from that of the matrices because the segregation coefficient strongly depends on the kind of impurities and surrounding medium.

Fig. 9. PL spectra of (a) B-doped (Mimura et al., 1999) and (b) P-doped Si nanocrystals (Fujii et al., 2002) at room temperature for different doping concentrations.

The presence of impurity atoms inside Si nanocrystals can be confirmed by the PL spectroscopy. Indeed, the introduction of extra carriers by impurity doping makes the threebody Auger process possible (Kovalev et al., 2008). In Auger recombination, the energy of

and the resultant optical and electrical transport properties. So, for solar cell application, the development of a technique permitting to control the "impurity number" with extremely

Up to now, an accurate control of "impurity number" in a Si nanocrystal has not been achieved. One of the largest problems of the growth of doped Si nanocrystals is that impurity atoms are pushed out of nanocrystals to surrounding matrices by the so-called selfpurification effect. This effect can be understood by considering very high formation energy of doped nanocrystals (Ossicini et al., 2005). Impurity concentration in nanocrystals is thus always different from average concentration in a whole system. In the worst case, the number of impurity in a nanocrystal becomes zero even when average concentration is rather high. The development of viable technique to characterize impurities, especially "active" impurities doped into nanocrystals, is crucial. The resistivity measurements are

As it was discussed previously, numerous methods have been reported for the growth of intrinsic Si QDs. On the other hand, a limited number of studies are published concerning the growth of shallow impurity-doped Si QDs with the diameter below 10 nm. One of the mostly used methods for shallow-impurity doping of Si nanocrystals is plasma decomposition of SiH4 by adding dopant precursors (diborane (B2H6) and phosphine (PH3)) (Pi et al., 2008) (Stegner et al., 2008). This method permits to obtain a variety of morphologies from densely packed nanocrystalline films to nanoparticle powder by controlling process parameters (Nychyporuk et al., 2009). Another method is incorporation of doping atoms into SRO layers by simultaneous co-sputtering of Si, SiO2 and P2O5 (or B2O3) in SiO2/SRO superlattice approach described previously (Mimura et al., 2000). During the annealing, Si nanocrystals are grown in phosphosilicate (PSG) (n-type Si QDs) or borosilicate (BSG) (p-type Si QDs) thin films. It should be also noted that the impurity concentration in nanocrystals is different from that of the matrices because the segregation

thus complemented with ESR spectroscopy as well as PL spectroscopy.

coefficient strongly depends on the kind of impurities and surrounding medium.

Fig. 9. PL spectra of (a) B-doped (Mimura et al., 1999) and (b) P-doped Si nanocrystals (Fujii

The presence of impurity atoms inside Si nanocrystals can be confirmed by the PL spectroscopy. Indeed, the introduction of extra carriers by impurity doping makes the threebody Auger process possible (Kovalev et al., 2008). In Auger recombination, the energy of

et al., 2002) at room temperature for different doping concentrations.

high accuracy is indispensable.

an electron-hole pair is not released in the form of photon. This energy is given to a third carrier, which after the interaction losses its excess energy as thermal vibrations. Since this process is a three-particle interaction, it is normally only significant in strongly nonequilibrium conditions or when the carrier density is very high. For doped nanocrystals the value of Auger rate is four to five orders of magnitude larger than the radiative rate of excitons, and thus one shallow impurity can almost completely kill PL from the nanocrystal. Hence with increasing of average impurity numbers in a nanocrystal assembly, the PL intensity is expected to decrease. This effect was really observed in p-type Si nanocrystals. As one can see on Fig. 9 (a) with increasing of B concentration, the PL intensity monotonously decreases (Fujii et al., 1998) (Müller et al., 1999) (Stegner et al., 2008).

In P-doped Si nanocrystals, the situation is different. When the phosphorous concentration is relatively low, the PL intensity increases slightly compared to that of the undoped Si nanocrystals (Fig. 9 b) (Fujii et al., 2000) (Mimura et al., 2000) (Tchebotareva et al., 2005). The increase of the PL intensity indicates that non-radiative recombination processes are quenched by P doping. One of the possible explanation is that electrons supplied by P are captured by the dangling bonds, which inactivate the nonradiative recombination centers and compensate donors (Stegner et al., 2008) (Lenahan et al., 1998). It should be also noted that the PL intensity also strongly depends on the size of the shallow-doped Si nanocrystals.

There are many theoretical studies on preferential localization of impurities in Si nanocrystals. It should to be noted that it is almost impossible to control experimentally the location of impurities in nanocrystals. However, the information on localization was experimentally obtained (Kovalev et al., 1998). It was shown that P dopants are localized at or close to the surface of Si nanocrystal. On the contrary, the B atoms are primary incorporated into the Si nanocrystal core. However, the preferential localization of impurities may depend on nanocrystal growth process and the surface termination. Therefore, properties of dopant may be quite different between Si nanocrystals grown by the decomposition of SiH4, phase separation of SRO and so on. In any cases the doping efficiency by B atoms is much smaller than that of P atoms due to larger formation energy of B-doped Si nanocrystals than P-doped ones (Kovalev et al., 1998) (Ossicini et al., 2005).

To what concerns the optical and electrical properties, contrary to the intrinsic Si nanocrystals, the shallow doped Si nanocrystals present new degree of freedom to control them. For example, the size is one of the main parameters to control optical bandgap of the intrinsic Si nanocrystals. On the other hand, due to the difference in the electronic band structure in the case of doped and codoped Si nanocrystals (obtained by the simultaneous doping by B and P atoms), the optical bandgap is determined by the combination of the size and impurity concentration (Fujii et al., 2010).

It is worth noting that the impurity atoms alter the formation kinetics of Si nanocrystals. Indeed, the average size of P-doped Si nanocrystals is increased compared to the undoped ones under the same experimental conditions (Conibeer et al., 2010), and in some experiments this increasing was almost double. Contrary to the doping with P, the doping with B results in the forming of smaller Si nanocrystals compared to the undoped case (Hao et al., 2009). The crystalline volume fraction was found to decrease with increasing of B concentration (Hao et al., 2009), which suggests that boron suppresses Si crystallization. One of the possible reasons is the local deformations induced by the impurity atoms.

#### **3.2.1 Dark resistivity measurements**

The resistivity of the Si QD material is an important parameter for photovoltaic applications. The influence of the doping concentration on resistivity of Si QD superlattices was studied

Silicon-Based Third Generation Photovoltaics 151

(a) (b)

(c) (d)

Fig. 11. Dark resistivity of Si QD/SiO2 multilayer films for various (a) phosphorous (Hao et al., 2009) and (c) boron (Conibeer et al., 2010) doping levels.; Temperature dependence of the resistance of the Si QD films with various (b) phosphorous (Hao et al., 2009) and (d)

Regarding to photovoltaic applications, the optical bandgap and the absorption coefficient of Si QDs are the very first physical parameters to be studied and optimized prior to solar cell fabrication. Optical methods provide an easy and sensitive tool for measuring the electronic structure of quantum objects, since they require minimal sample preparation and the measurements are sensitive to the quantum effects. The energy gaps of Si QDs could be determined, for example, from photoluminescence (PL) measurements, whereas the

Experimental energy gaps of isolated Si QDs in SiO2 and SiNx matrices reported by several research groups are shown on Fig. 12 (Cho et al., 2004) (Park et al., 2000) (Takeoka

absorption coefficient from the transmission-reflection measurements.

boron (Hao et al., 2009) concentrations .

**3.3 Optical properties of Si QDs** 

**3.3.1 Bandgap of Si QDs** 

(Hao et al., 2009, 2009a), (Conibeer et al., 2010) (Ficcadenti et al., 2009). The contact resistances in the above measurements were determined by using the TLM (Transmission Line Model) method proposed by Reeves and Harrison (Reeves & Harrison, 1982). This method involves measurement of the resistance between several pairs of contacts, which have identical areas, but are separated by different spaces (Fig. 10). The dark resistivity is then defined as:*dark =V×d×w/I×l* , where *d* is the thickness of Si QD superlattice, *w* is the length of Al pad and *l* is the spacing of Al pads.

To perform the dark resistivity measurements, the Si QD superlattices were grown on the quartz substrate. The ohmic contacts were obtained by thermal evaporation of Al, followed by sintering at a temperature (500-530°C) lower than the Al-Si eutectic temperature to allow the Al to spike down into the film (Voz et al., 2000). The schematic view of the final structure for the lateral resistivity measurements is presented on the Fig. 10.

Fig. 11 (a) and (c) represents the room temperature dark resistivity of Si QD/SiO2 multilayer films for various phosphorous and boron doping levels, respectively. As one can see, the introduction of a slight amount of P and B drastically changes the dark resistivity of the films, from 108 cm for the undoped samples to 102 – 10 cm for doped ones, which is 6 -7 orders of magnitude lower than that of the undoped samples. This decrease in resistivity may be the consequence of an increase in mobile carrier concentration due to a rise in the number of active dopants in the film.

The TLM method was also used to measure the temperature dependence of the resistance of the Si QD films with various (b) phosphorous (Hao et al., 2009) and (d) boron (Hao et al., 2009) concentrations (Fig. 11 (b) and (d), respectively). These measurements permit to estimate the values of the activation energy (*Ea*), that is in a n- (p-) doped semiconductor the energy difference between the conduction (valance) band and Fermi level. The activation energy was calculated by using relation *R* ≈ *exp(Ea/kT)*. As one can see, with the increasing of the doping level, for both types of impurities the activation energy decreases from ~0.5 eV to 0.1 eV. This result is consistent with the view that the observed resistivity decreases are a consequence of an increase in carrier concentration due to more active dopants in the film. The decrease in *Ea* accompanying the drop in resistivity indicates that the Fermi level energy is moving toward the conduction (valance) band for n- (p-) type doped Si QDs.

Fig. 10. Schematic layout of the Al contacts on a film for dark resistivity measurements (Hao et al., 2009).

150 Solar Cells – Silicon Wafer-Based Technologies

(Hao et al., 2009, 2009a), (Conibeer et al., 2010) (Ficcadenti et al., 2009). The contact resistances in the above measurements were determined by using the TLM (Transmission Line Model) method proposed by Reeves and Harrison (Reeves & Harrison, 1982). This method involves measurement of the resistance between several pairs of contacts, which have identical areas, but are separated by different spaces (Fig. 10). The dark resistivity is

To perform the dark resistivity measurements, the Si QD superlattices were grown on the quartz substrate. The ohmic contacts were obtained by thermal evaporation of Al, followed by sintering at a temperature (500-530°C) lower than the Al-Si eutectic temperature to allow the Al to spike down into the film (Voz et al., 2000). The schematic view of the final structure

Fig. 11 (a) and (c) represents the room temperature dark resistivity of Si QD/SiO2 multilayer films for various phosphorous and boron doping levels, respectively. As one can see, the introduction of a slight amount of P and B drastically changes the dark resistivity of the films, from 108 cm for the undoped samples to 102 – 10 cm for doped ones, which is 6 -7 orders of magnitude lower than that of the undoped samples. This decrease in resistivity may be the consequence of an increase in mobile carrier concentration due to a rise in the

The TLM method was also used to measure the temperature dependence of the resistance of the Si QD films with various (b) phosphorous (Hao et al., 2009) and (d) boron (Hao et al., 2009) concentrations (Fig. 11 (b) and (d), respectively). These measurements permit to estimate the values of the activation energy (*Ea*), that is in a n- (p-) doped semiconductor the energy difference between the conduction (valance) band and Fermi level. The activation energy was calculated by using relation *R* ≈ *exp(Ea/kT)*. As one can see, with the increasing of the doping level, for both types of impurities the activation energy decreases from ~0.5 eV to 0.1 eV. This result is consistent with the view that the observed resistivity decreases are a consequence of an increase in carrier concentration due to more active dopants in the film. The decrease in *Ea* accompanying the drop in resistivity indicates that the Fermi level energy

Fig. 10. Schematic layout of the Al contacts on a film for dark resistivity measurements (Hao

is moving toward the conduction (valance) band for n- (p-) type doped Si QDs.

*dark =V×d×w/I×l* , where *d* is the thickness of Si QD superlattice, *w* is the

then defined as:

et al., 2009).

number of active dopants in the film.

length of Al pad and *l* is the spacing of Al pads.

for the lateral resistivity measurements is presented on the Fig. 10.

Fig. 11. Dark resistivity of Si QD/SiO2 multilayer films for various (a) phosphorous (Hao et al., 2009) and (c) boron (Conibeer et al., 2010) doping levels.; Temperature dependence of the resistance of the Si QD films with various (b) phosphorous (Hao et al., 2009) and (d) boron (Hao et al., 2009) concentrations .

#### **3.3 Optical properties of Si QDs**

Regarding to photovoltaic applications, the optical bandgap and the absorption coefficient of Si QDs are the very first physical parameters to be studied and optimized prior to solar cell fabrication. Optical methods provide an easy and sensitive tool for measuring the electronic structure of quantum objects, since they require minimal sample preparation and the measurements are sensitive to the quantum effects. The energy gaps of Si QDs could be determined, for example, from photoluminescence (PL) measurements, whereas the absorption coefficient from the transmission-reflection measurements.

#### **3.3.1 Bandgap of Si QDs**

Experimental energy gaps of isolated Si QDs in SiO2 and SiNx matrices reported by several research groups are shown on Fig. 12 (Cho et al., 2004) (Park et al., 2000) (Takeoka

Silicon-Based Third Generation Photovoltaics 153

The absorption coefficient was experimentally determined for Si QDs in deferent matrices. Fig. 14 shows the global absorption coefficient of SiNx layers of different stoichiometries with Si QDs embedded inside (Nychyporuk et al., 2008). The absorption coefficient of polycrystalline silicon (poly-Si) is also added for comparison. As it can be seen, the global absorption coefficient of the composite SiNx decreases with stoichiometric ratio R (i.e. with decreasing of Si QD size and density) and its band-edge shifts to higher energies. Its magnitude is being much lower than that one of the absorption coefficient of poly-Si. No evidence of oscillator strength enhancement was observed and the global absorption coefficient is limited principally by the volume fraction of Si QDs inside the dielectric matrices. These why, the maximum absorption coefficient, approaching this one of the bulk Si, was found in the case of interconnected Si QDs forming thin films (Nychyporuk et al.,

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Photon energy, eV

While the optical properties of the various ensembles of individual Si nanocrystals have been investigated by many researchers, relatively little attention was paid to the transport properties of 3D ensembles of such QDs. In this paragraph we will only briefly review the main results on the transport mechanisms obtained previously in the literature. A complete review of the electrical transport mechanisms in 3D ensembles of disordered Si nanocrystallites embedded in insulating continuous matrices can be found in Ref. (Balberg et al., 2010). To what concerns the transport processes in nanocrystalline Si superlattices,

The transport properties of the ensembles of disordered Si QDs in insulating matrix could be explained in terms of the percolation theory, which has already been successfully implemented to explain the transport processes in granular metals (Abeles et al., 1975).

Fig. 14. Global absorption coefficient of SiNx layers of different stoichiometries with embedded Si QDs. The absorption coefficient of poly-Si is also presented for comparison

**3.3.2 Optical absorption of Si QDs** 

2.0x105

**3.4 Electrical transport mechanisms in Si QD ensembles** 

they were well reviewed in Ref. (Lockwood & Tsybeskov, 2004).

**3.4.1 Disordered Si QDs in insulating matrix** 

4.0x105

Global absorption coefficient (cm-1)

(Nychyporuk et al., 2008).

6.0x105

8.0x105

R=[NH3

]/[SiH4 ] R= 1.5 R= 3 R= 4 R= 5 Poly-Si

2009).

et al., 2000). As one can see the bandgap values of Si nanostructured material could be adjusted in the large range (up to 3.1 eV), covering an important part of the solar spectrum. The results obtained by different teams are in good agreement where the matrix is the same but are quite different for QDs in oxide compared to nitride, particularly for small QDs. They are also qualitatively consistent with the results from *ab-initio* modeling (König et al., 2009) (Ögüt et al., 1997), which had been carried out for the confined energy levels in Si QD consisting of a few hundred atoms. One can observe the expected increasing of confinement energy with decreasing QD size, but also that the aminoterminated QDs (silicon nitride) have energies about 0.5 eV more than the hydroxylterminated ones (silicon oxide). The last one observation is consistent with the explanation for the enhanced energies of QDs in nitride given by Yang et al (Yang et al., 2004), that the reason for it is due to better passivation of Si QDs by nitrogen atoms eliminating the strain at the Si/Si3N4 interface.

Influence of interconnections between the QDs on tuning of their bandgap was also studied (Nychyporuk et al., 2009) (Degoli et al., 2000). Indeed, electronic coupling between the neighboring low-dimensional Si nano-objects constituting a complex quantum system must be considered. This coupling leading to intense energy transfer processes between the electronically communicating quantum objects determines physical properties of the whole quantum system and, therefore, has to be taken into account, of course. It was shown that when the nanocrystals (Allan & Delerue, 2007) (Bulutay, 2007) start to touch each other, the bandgap value of the assembly begins to decrease rapidly (Fig. 13). Thus, the bandgap of the interconnected nanostructures depends not only on the nanocrystal dimension but also on the degree and number of interconnections between them.

Fig. 12. Experimental energy gaps of threedimensionally confined Si QDs in SiO2 and SiNx matrices (300°C) for several research groups (Takeoka et al., 2000) (Kim et al., 2004), (Kim et al., 2005) (Yang et al., 2004) (Fangsuwannarak, 2007).

Fig. 13. Evolution of the bandgap of the quantum system constituted of 27 interconnected Si QDs as a function of the distance between the QDs.

#### **3.3.2 Optical absorption of Si QDs**

152 Solar Cells – Silicon Wafer-Based Technologies

et al., 2000). As one can see the bandgap values of Si nanostructured material could be adjusted in the large range (up to 3.1 eV), covering an important part of the solar spectrum. The results obtained by different teams are in good agreement where the matrix is the same but are quite different for QDs in oxide compared to nitride, particularly for small QDs. They are also qualitatively consistent with the results from *ab-initio* modeling (König et al., 2009) (Ögüt et al., 1997), which had been carried out for the confined energy levels in Si QD consisting of a few hundred atoms. One can observe the expected increasing of confinement energy with decreasing QD size, but also that the aminoterminated QDs (silicon nitride) have energies about 0.5 eV more than the hydroxylterminated ones (silicon oxide). The last one observation is consistent with the explanation for the enhanced energies of QDs in nitride given by Yang et al (Yang et al., 2004), that the reason for it is due to better passivation of Si QDs by nitrogen atoms

Influence of interconnections between the QDs on tuning of their bandgap was also studied (Nychyporuk et al., 2009) (Degoli et al., 2000). Indeed, electronic coupling between the neighboring low-dimensional Si nano-objects constituting a complex quantum system must be considered. This coupling leading to intense energy transfer processes between the electronically communicating quantum objects determines physical properties of the whole quantum system and, therefore, has to be taken into account, of course. It was shown that when the nanocrystals (Allan & Delerue, 2007) (Bulutay, 2007) start to touch each other, the bandgap value of the assembly begins to decrease rapidly (Fig. 13). Thus, the bandgap of the interconnected nanostructures depends not only on the nanocrystal dimension but also on

> Fig. 13. Evolution of the bandgap of the quantum system constituted of 27

distance between the QDs.

interconnected Si QDs as a function of the

eliminating the strain at the Si/Si3N4 interface.

the degree and number of interconnections between them.

Fig. 12. Experimental energy gaps of threedimensionally confined Si QDs in SiO2 and SiNx matrices (300°C) for several research groups (Takeoka et al., 2000) (Kim et al., 2004), (Kim et al., 2005) (Yang et al., 2004)

(Fangsuwannarak, 2007).

The absorption coefficient was experimentally determined for Si QDs in deferent matrices. Fig. 14 shows the global absorption coefficient of SiNx layers of different stoichiometries with Si QDs embedded inside (Nychyporuk et al., 2008). The absorption coefficient of polycrystalline silicon (poly-Si) is also added for comparison. As it can be seen, the global absorption coefficient of the composite SiNx decreases with stoichiometric ratio R (i.e. with decreasing of Si QD size and density) and its band-edge shifts to higher energies. Its magnitude is being much lower than that one of the absorption coefficient of poly-Si. No evidence of oscillator strength enhancement was observed and the global absorption coefficient is limited principally by the volume fraction of Si QDs inside the dielectric matrices. These why, the maximum absorption coefficient, approaching this one of the bulk Si, was found in the case of interconnected Si QDs forming thin films (Nychyporuk et al., 2009).

Fig. 14. Global absorption coefficient of SiNx layers of different stoichiometries with embedded Si QDs. The absorption coefficient of poly-Si is also presented for comparison (Nychyporuk et al., 2008).

#### **3.4 Electrical transport mechanisms in Si QD ensembles**

While the optical properties of the various ensembles of individual Si nanocrystals have been investigated by many researchers, relatively little attention was paid to the transport properties of 3D ensembles of such QDs. In this paragraph we will only briefly review the main results on the transport mechanisms obtained previously in the literature. A complete review of the electrical transport mechanisms in 3D ensembles of disordered Si nanocrystallites embedded in insulating continuous matrices can be found in Ref. (Balberg et al., 2010). To what concerns the transport processes in nanocrystalline Si superlattices, they were well reviewed in Ref. (Lockwood & Tsybeskov, 2004).

#### **3.4.1 Disordered Si QDs in insulating matrix**

The transport properties of the ensembles of disordered Si QDs in insulating matrix could be explained in terms of the percolation theory, which has already been successfully implemented to explain the transport processes in granular metals (Abeles et al., 1975).

Silicon-Based Third Generation Photovoltaics 155

is determined by the tunneling of charge carriers under Coulomb blockage2 between adjacent nanocrystallites similar to the case encountered in granular metals in the dielectric regime (Abeles et al., 1975) (Balberg et al., 2004). Indeed, as long as Si QDs or clusters of Si QDs are small enough, they "keep" the carrier that resides in them and become charged when an excess charge carrier reaches them. Hence, the transport through the system can

Fig. 16. Dependence of the dark conductivity and the photoconductivity on the Si content

With increasing of Si content (Fig. 15 (b)), the interparticle distance decreases and the tunneling-connected quantum dot clusters grow in size. The "delocalization" of the carrier from its confinement in the individual quantum dot to larger regions of the ensemble will take place, i.e., the charge carrier will belong to a cluster of QDs rather than to an individual QD. Correspondingly, this will also yield a decrease in the local charging energy in comparison with that of the isolated QD and the distance to which the charge carrier could wander will increase and as a consequence the conductivity of the ensemble will increase as well. The charge carrier transport in the case of regime *(c)* is thus determined by the

As one can see from the Fig. 16, the maximal possible conductivity is assured in the case of highly percolating system of Si QDs (regime *(e)*). However, the conduction in this regime is quite different from that one of the granular metals since there are still boundaries between touching Si QDs. In fact, the corresponding migration process is similar to that in polycrystalline semiconductors, but now the boundaries are on the quantum scale. It was suggested that in this regime the migration dominates the transport properties and the global conductivity is limited by the interface between the touching QDs (Balberg, 2010).

2 The transfer of an electron from a given neutral particle to an adjacent neutral particle, charges this particle by one (positive) elementary charge *(q)* and that of the adjacent particle by one (negative) elementary charge. If the capacitance of the individual particle in its corresponding environment is *C0*, the energy needed to be supplied for the above "electron-hole" transfer by tunneling is then: *E=q2/C0*. This energy, which opposes to the transfer of charge carriers, is known as the Coulomb blockage energy, which is of the order of a tenth of an eV. In general, one can say, that a tunneling process is

(related to the number of Si QDs in ensemble)

intracluster migration and by the intercluster tunneling.

thermally activated when it requires a supply of energy.

take place only if a corresponding charging (or Coulomb) energy is provided.

Indeed, this theory describes the effect of the system's connectivity on its geometrical and physical properties. In the case of granular metals, in a system of *N* metallic spheres embedded randomly in an insulating matrix, there will be a critical density of spheres *Nc* above which a "continuous" metallic network will be formed and a metallic bulk-like conduction will dominate. Correspondingly, *Nc* is the classical percolation threshold (Fonseca & Balberg, 1993) (Balberg et al., 2004). For *N < Nc*, the electron transfer between the individual grains is possible only by tunneling (Abeles et al., 1975) (Balberg et al., 2004).

To what concerns the ensemble of Si QDs, there can be distinguished five different structural-electrical regimes, such that in each of them we may expect a different transport mechanism to dominate. These regimes are *(a)* uniformly dispersed in insulating matrix isolated spherical QDs; *(b)* the transition regime, where some of the QDs starts to "touch" their neighbors; *(c)* the intermediate regime, where clusters of "touching" QDs are formed; *(d)* the percolation transition regime where the above clusters form a global continuous network; and *(e)* the regime where the percolation cluster of "touching" QDs is well formed and geometrically non-"touching" QDs are rarely found. Fig. 15 (a), (b) and (c) present typical examples of ensembles of Si QDs corresponding to regimes *(a)*, *(c)* and *(e)*, respectively. It is worth noting that the connectivity between "touching" QDs in ensembles of semiconductor QDs is different than in granular metals. Usually there are narrow (no more than 0.5 nm wide) boundaries formed between the nanoparticles, which involves at least a different crystallographic orientation of the touching crystallites. This quantum size "grain boundary" limit has not been studied so far. In a literature the charge transfer process between such "touching" QDs was termed as "migration" (Antonova et al., 2008) (Balberg et al., 2007).

Fig. 15. HRTEM images of the ensembles of Si QDs corresponding to different structuralelectrical regimes: (a) uniformly dispersed isolated spherical QDs (regime *a*), (b) clusters of "touching" QDs (regime *c*) and (c) percolation clusters of "touching" QDs (regime e) (Antonova et al., 2008).

The effect of the connectivity on the transport properties (dark and photoconductivity) of the ensembles of Si QDS is illustrated on Fig. 16. As one can see, the global picture of transport in Si QDs ensembles is reminiscent of that of granular metals, but the details are quite different. For the samples with low Si content (related to the number of Si QDs in the ensemble), which are characterized by the isolated Si QDs (regime *a*), the local conductivity

154 Solar Cells – Silicon Wafer-Based Technologies

Indeed, this theory describes the effect of the system's connectivity on its geometrical and physical properties. In the case of granular metals, in a system of *N* metallic spheres embedded randomly in an insulating matrix, there will be a critical density of spheres *Nc* above which a "continuous" metallic network will be formed and a metallic bulk-like conduction will dominate. Correspondingly, *Nc* is the classical percolation threshold (Fonseca & Balberg, 1993) (Balberg et al., 2004). For *N < Nc*, the electron transfer between the individual grains is possible only by tunneling (Abeles et al., 1975) (Balberg et al.,

To what concerns the ensemble of Si QDs, there can be distinguished five different structural-electrical regimes, such that in each of them we may expect a different transport mechanism to dominate. These regimes are *(a)* uniformly dispersed in insulating matrix isolated spherical QDs; *(b)* the transition regime, where some of the QDs starts to "touch" their neighbors; *(c)* the intermediate regime, where clusters of "touching" QDs are formed; *(d)* the percolation transition regime where the above clusters form a global continuous network; and *(e)* the regime where the percolation cluster of "touching" QDs is well formed and geometrically non-"touching" QDs are rarely found. Fig. 15 (a), (b) and (c) present typical examples of ensembles of Si QDs corresponding to regimes *(a)*, *(c)* and *(e)*, respectively. It is worth noting that the connectivity between "touching" QDs in ensembles of semiconductor QDs is different than in granular metals. Usually there are narrow (no more than 0.5 nm wide) boundaries formed between the nanoparticles, which involves at least a different crystallographic orientation of the touching crystallites. This quantum size "grain boundary" limit has not been studied so far. In a literature the charge transfer process between such "touching" QDs was termed as "migration" (Antonova et al., 2008) (Balberg et

(a) (b) (c)

The effect of the connectivity on the transport properties (dark and photoconductivity) of the ensembles of Si QDS is illustrated on Fig. 16. As one can see, the global picture of transport in Si QDs ensembles is reminiscent of that of granular metals, but the details are quite different. For the samples with low Si content (related to the number of Si QDs in the ensemble), which are characterized by the isolated Si QDs (regime *a*), the local conductivity

Fig. 15. HRTEM images of the ensembles of Si QDs corresponding to different structuralelectrical regimes: (a) uniformly dispersed isolated spherical QDs (regime *a*), (b) clusters of "touching" QDs (regime *c*) and (c) percolation clusters of "touching" QDs (regime e)

2004).

al., 2007).

(Antonova et al., 2008).

is determined by the tunneling of charge carriers under Coulomb blockage2 between adjacent nanocrystallites similar to the case encountered in granular metals in the dielectric regime (Abeles et al., 1975) (Balberg et al., 2004). Indeed, as long as Si QDs or clusters of Si QDs are small enough, they "keep" the carrier that resides in them and become charged when an excess charge carrier reaches them. Hence, the transport through the system can take place only if a corresponding charging (or Coulomb) energy is provided.

Fig. 16. Dependence of the dark conductivity and the photoconductivity on the Si content (related to the number of Si QDs in ensemble)

With increasing of Si content (Fig. 15 (b)), the interparticle distance decreases and the tunneling-connected quantum dot clusters grow in size. The "delocalization" of the carrier from its confinement in the individual quantum dot to larger regions of the ensemble will take place, i.e., the charge carrier will belong to a cluster of QDs rather than to an individual QD. Correspondingly, this will also yield a decrease in the local charging energy in comparison with that of the isolated QD and the distance to which the charge carrier could wander will increase and as a consequence the conductivity of the ensemble will increase as well. The charge carrier transport in the case of regime *(c)* is thus determined by the intracluster migration and by the intercluster tunneling.

As one can see from the Fig. 16, the maximal possible conductivity is assured in the case of highly percolating system of Si QDs (regime *(e)*). However, the conduction in this regime is quite different from that one of the granular metals since there are still boundaries between touching Si QDs. In fact, the corresponding migration process is similar to that in polycrystalline semiconductors, but now the boundaries are on the quantum scale. It was suggested that in this regime the migration dominates the transport properties and the global conductivity is limited by the interface between the touching QDs (Balberg, 2010).

<sup>2</sup> The transfer of an electron from a given neutral particle to an adjacent neutral particle, charges this particle by one (positive) elementary charge *(q)* and that of the adjacent particle by one (negative) elementary charge. If the capacitance of the individual particle in its corresponding environment is *C0*, the energy needed to be supplied for the above "electron-hole" transfer by tunneling is then: *E=q2/C0*. This energy, which opposes to the transfer of charge carriers, is known as the Coulomb blockage energy, which is of the order of a tenth of an eV. In general, one can say, that a tunneling process is thermally activated when it requires a supply of energy.

Silicon-Based Third Generation Photovoltaics 157

is shown on the Fig. 20. At this photon energy both the lowest and the second minibands are populated. The photocurrent originating in this excitation is shown on Fig. 21. Current flows also in first and second minibands, which means that relaxation due to scattering is not fast enough to confine transport to the band edge. However, transport of photocarriers is strongly affected by the inelastic interactions, and is the closest to the sequential tunneling regime. We can thus conclude that in the case of high internal fields, excess charge is

The sequential resonance tunneling enhances the photocarrier collection and reduces radiative recombination losses (Raisky et al., 1999). However it should be noted that SRT increases both photocurrent (Iph) and dark current (Idc). The total current of a photovoltaic device is the difference of these two currents, and thus, to take advantage of SRT, a solar cell possessing a superlattice structure should be designed to have the resonance in the region

The main challenge of the tandem structure is to achieve sufficient carrier mobility and hence a reasonable conductivity. This generally requires formation of a true superlattice with overlap of the wave function for adjacent QDs, which in turns requires either close spacing between Si nanocrystals or low barrier height. Transport properties strongly depend on the matrix in which the Si quantum dots are embedded. Indeed, the electron or the hole wavefunctions exponentially decay with distance. Fig. 22 shows the penetration length of the wave function of electron of a single quantum well into different high-bandgap materials having different barrier heights. As one can see, the tunneling probability heavily depends on the barrier height. The penetration length is bigger for the materials with lower barrier height. Thus Si3N4 and SiC giving lower barriers than SiO2, allow larger dot spacing for a given tunneling current. For example, the QDs in SiO2 matrix would have to be separated by no more than 1-2 nm of matrix, while they could be separated by more than

The influence of the fluctuations in spacing and size of the QDs on the carrier mobility was also investigated (Jiang & Green, 2006). The calculations have shown that the interdot distance has larger impact on the calculated carrier mobility while the dot size can be used

Recently it have been reported on the realization of interdigitated silicon QD solar cells on quartz substrate(Conibeer et al., 2010). Schematic view of the fabricated solar cells is shown on the Fig. 23 (a). The p-n diodes were fabricated by sputtering alternating layers of SiO2 and SRO onto quartz substrate with in situ B and P doping. The top B doped bi-layers were selectively etched to create isolated p-type mesas and to access the buried P doped bi-layers. Aluminium contacts were deposited by evaporation, patterned and sintered to create ohmic contacts on both p- and n-type layers. The area of the fabricated interdigitated solar cells was 0.12 cm-2. One of the derivatives of the presented approach was the fabrication of the pi-n diodes. Indeed, it is expected that the intrinsic layer will have a longer lifetime that the

I-V measurements in the dark and under 1-sun illumination (Fig. 23 (b)) indicate a good rectifying junction and generation of an open-circuit voltage, VOC, up to 492 mV (Conibeer, 2010). The high sheet resistance of the deposited layers, in conjunction with the insulating

quartz substrates, causes an unavoidable high series resistance in the device.

transported via sequential tunneling in the miniband where it is generated.

where *Iph» Idc.* 

4 nm of SiC.

to control the band energy level.

**3.5 Fabrication of Si QD PV devices** 

doped material leading to an improved photocurrent.

Form the photovoltaic point of view, the thin films constituted of interconnected Si QDs are the most promising candidates for higher bandgap materials in all-Si tandem cell approach. Indeed, the highly percolating system of Si QDs will ensure the most favorable conditions for the electronic transport between the nanocrystals and, as it was discussed previously, the bandgap value in such structures could be adjusted in the large range covering the major part of the solar spectrum (Nychyporuk et al., 2009).

#### **3.4.2 Nanocrystalline Si superlattices**

Nanocrystalline Si superlattices have been proposed as candidates for the high bandgap absorber component in all-Si tandem solar cells. They consists of thin dielectric and Si QD based layers alternating in one direction, i.e., heterostructure type –I superlattices. The period of such a superlattice usually is much larger than the lattice constant but is smaller than the electron mean free path. Such a structure possesses, in addition to a periodic potential of the crystalline lattice, a potential due to the alternating semiconductor layers. The existence of such a potential significantly changes the energy bandstructure of the semiconductors from which the superlattice is formed. The coupling among QDs occurs, leading to a splitting of the quantized carrier energy levels of single dots and formation of three-dimensional minibands (Lazarenkova & Balandin, 2001) (Jiang & Green, 2006) as sketched on Fig. 17 (shaded areas).

The charge carrier mobility, which has a crucial impact on a charge-collection efficiency in solar cells, depends on the dominant transport regime at given operating conditions, which may be described by mini-band transport, sequential tunneling or Wannier-Stark hopping (Wacker, 2002). The sequential resonant tunneling (SRT) was suggested to be the most prominent for efficient carrier collection in Si QD solar cells (Raisky et al., 1999).

The schematic view of the sequential resonant tunneling transfer in a multiple-quantumwell structure is depicted on Fig. 18. Electrons tunnel from the ground state of the *j*th well into an excited state of the *(j+1)*th well. The tunneling process is then followed by intrasubband energy relaxation from the excited state to the ground state. This two-step scheme can be repeated as many times as needed to build the required thickness for optimal solar absorption. Resonance occurs when the *E2-E1* =│*q***F***d*│ condition is satisfied where *E1* and *E2* are the ground and first excited subband energies of the quantum well, *q* the electron charge, *F* the internal electric field, and *d* the spatial structural period. From Fig. 18 it is clear that the bottleneck of electron transfer is the last (*Nth*) well, where carriers have to transfer through a significantly thicker right barrier than inside the multiple-quantum-well region. This can lead to charge build up and, consequently, screening of the built-in field.

The photogeneration and transport in superlattice absorbers, on the example of a Si-SiOx multilayer structure embedded in the intrinsic region of a p-i-n diode was recently numerically investigated (Aeberhard, 2011). The model system under investigation is shown on the Fig. 19. It consists of a set of four coupled quantum wells of 6 monolayer3 (ML) width with layers separated by oxide barriers of 3-ML thickness, embedded in the intrinsic region of a Si p-i-n diode. The doping density was 1018 cm-3 for both electrons and holes. Insertion of the oxide barriers leads to an increase of the effective bandgap in the central region of the diode from 1.1 to 1.3 eV. The spectral rate of carrier generation in the confined states under illumination with monochromatic light at photon energy 1.65 eV and intensity of 10 kW/m2

<sup>3</sup> The monolayer thickness is half the Si lattice constant, i.e., 2.716 Å.

Form the photovoltaic point of view, the thin films constituted of interconnected Si QDs are the most promising candidates for higher bandgap materials in all-Si tandem cell approach. Indeed, the highly percolating system of Si QDs will ensure the most favorable conditions for the electronic transport between the nanocrystals and, as it was discussed previously, the bandgap value in such structures could be adjusted in the large range covering the major

Nanocrystalline Si superlattices have been proposed as candidates for the high bandgap absorber component in all-Si tandem solar cells. They consists of thin dielectric and Si QD based layers alternating in one direction, i.e., heterostructure type –I superlattices. The period of such a superlattice usually is much larger than the lattice constant but is smaller than the electron mean free path. Such a structure possesses, in addition to a periodic potential of the crystalline lattice, a potential due to the alternating semiconductor layers. The existence of such a potential significantly changes the energy bandstructure of the semiconductors from which the superlattice is formed. The coupling among QDs occurs, leading to a splitting of the quantized carrier energy levels of single dots and formation of three-dimensional minibands (Lazarenkova & Balandin, 2001) (Jiang & Green, 2006) as

The charge carrier mobility, which has a crucial impact on a charge-collection efficiency in solar cells, depends on the dominant transport regime at given operating conditions, which may be described by mini-band transport, sequential tunneling or Wannier-Stark hopping (Wacker, 2002). The sequential resonant tunneling (SRT) was suggested to be the most

The schematic view of the sequential resonant tunneling transfer in a multiple-quantumwell structure is depicted on Fig. 18. Electrons tunnel from the ground state of the *j*th well into an excited state of the *(j+1)*th well. The tunneling process is then followed by intrasubband energy relaxation from the excited state to the ground state. This two-step scheme can be repeated as many times as needed to build the required thickness for optimal solar absorption. Resonance occurs when the *E2-E1* =│*q***F***d*│ condition is satisfied where *E1* and *E2* are the ground and first excited subband energies of the quantum well, *q* the electron charge, *F* the internal electric field, and *d* the spatial structural period. From Fig. 18 it is clear that the bottleneck of electron transfer is the last (*Nth*) well, where carriers have to transfer through a significantly thicker right barrier than inside the multiple-quantum-well region. This can lead to charge build up and, consequently, screening of the built-in field. The photogeneration and transport in superlattice absorbers, on the example of a Si-SiOx multilayer structure embedded in the intrinsic region of a p-i-n diode was recently numerically investigated (Aeberhard, 2011). The model system under investigation is shown on the Fig. 19. It consists of a set of four coupled quantum wells of 6 monolayer3 (ML) width with layers separated by oxide barriers of 3-ML thickness, embedded in the intrinsic region of a Si p-i-n diode. The doping density was 1018 cm-3 for both electrons and holes. Insertion of the oxide barriers leads to an increase of the effective bandgap in the central region of the diode from 1.1 to 1.3 eV. The spectral rate of carrier generation in the confined states under illumination with monochromatic light at photon energy 1.65 eV and intensity of 10 kW/m2

prominent for efficient carrier collection in Si QD solar cells (Raisky et al., 1999).

3 The monolayer thickness is half the Si lattice constant, i.e., 2.716 Å.

part of the solar spectrum (Nychyporuk et al., 2009).

**3.4.2 Nanocrystalline Si superlattices** 

sketched on Fig. 17 (shaded areas).

is shown on the Fig. 20. At this photon energy both the lowest and the second minibands are populated. The photocurrent originating in this excitation is shown on Fig. 21. Current flows also in first and second minibands, which means that relaxation due to scattering is not fast enough to confine transport to the band edge. However, transport of photocarriers is strongly affected by the inelastic interactions, and is the closest to the sequential tunneling regime. We can thus conclude that in the case of high internal fields, excess charge is transported via sequential tunneling in the miniband where it is generated.

The sequential resonance tunneling enhances the photocarrier collection and reduces radiative recombination losses (Raisky et al., 1999). However it should be noted that SRT increases both photocurrent (Iph) and dark current (Idc). The total current of a photovoltaic device is the difference of these two currents, and thus, to take advantage of SRT, a solar cell possessing a superlattice structure should be designed to have the resonance in the region where *Iph» Idc.* 

The main challenge of the tandem structure is to achieve sufficient carrier mobility and hence a reasonable conductivity. This generally requires formation of a true superlattice with overlap of the wave function for adjacent QDs, which in turns requires either close spacing between Si nanocrystals or low barrier height. Transport properties strongly depend on the matrix in which the Si quantum dots are embedded. Indeed, the electron or the hole wavefunctions exponentially decay with distance. Fig. 22 shows the penetration length of the wave function of electron of a single quantum well into different high-bandgap materials having different barrier heights. As one can see, the tunneling probability heavily depends on the barrier height. The penetration length is bigger for the materials with lower barrier height. Thus Si3N4 and SiC giving lower barriers than SiO2, allow larger dot spacing for a given tunneling current. For example, the QDs in SiO2 matrix would have to be separated by no more than 1-2 nm of matrix, while they could be separated by more than 4 nm of SiC.

The influence of the fluctuations in spacing and size of the QDs on the carrier mobility was also investigated (Jiang & Green, 2006). The calculations have shown that the interdot distance has larger impact on the calculated carrier mobility while the dot size can be used to control the band energy level.

#### **3.5 Fabrication of Si QD PV devices**

Recently it have been reported on the realization of interdigitated silicon QD solar cells on quartz substrate(Conibeer et al., 2010). Schematic view of the fabricated solar cells is shown on the Fig. 23 (a). The p-n diodes were fabricated by sputtering alternating layers of SiO2 and SRO onto quartz substrate with in situ B and P doping. The top B doped bi-layers were selectively etched to create isolated p-type mesas and to access the buried P doped bi-layers. Aluminium contacts were deposited by evaporation, patterned and sintered to create ohmic contacts on both p- and n-type layers. The area of the fabricated interdigitated solar cells was 0.12 cm-2. One of the derivatives of the presented approach was the fabrication of the pi-n diodes. Indeed, it is expected that the intrinsic layer will have a longer lifetime that the doped material leading to an improved photocurrent.

I-V measurements in the dark and under 1-sun illumination (Fig. 23 (b)) indicate a good rectifying junction and generation of an open-circuit voltage, VOC, up to 492 mV (Conibeer, 2010). The high sheet resistance of the deposited layers, in conjunction with the insulating quartz substrates, causes an unavoidable high series resistance in the device.

Silicon-Based Third Generation Photovoltaics 159

(a)

(b) Fig. 23. (a) Schematic representation of the fabricated interdigitated devices (Conibeer et al., 2010); (b) Dark and illuminated I-V measurements of p-i-n diodes with 4 nm SRO/2 nm

Fig. 22. Penetration length of the wave function of confined electron into barrier layers. Vb represents a barrier height for each barrier material (Aeberhard, 2011).

Fig. 21. Spatially and energy-resolved charge carrier short-circuit photocurrent density in the quantum well region under monochromatic illumination with energy of 1.65 eV and intensity of 10kW/m2 (Aeberhard, 2011).

SiO2 bilayers.

Fig. 17. The energy bandstructure of a semiconductor type-I heterostructure superlattice : Eg1 and Eg2 are the bandgaps, Ec1 and Ec2 are the bottoms of the conduction bands of narrow bandgap and wide bandgap semiconductors, respectively; d is the period of the heterostructure superlattice (Mitin, 2010).

Fig. 18. Sequential resonant tunneling transfer in multiple-quantum-well structure. *E1* and *E2* are the energies of the ground and first excited states in the quantum well, respectively, and *d* the superlattice period (Raisky et al., 1999).

Fig. 19. Spatial structure and doping profile of the p-i-n model system (Aeberhard, 2011).

Fig. 20. Spatially and energy resolved charge carrier photogeneration rate in the quantum well region at short-circuit conditions and under monochromatic illumination with energy of 1.65 eV and intensity of 10kW/m2 (Aeberhard, 2011).

Fig. 18. Sequential resonant tunneling transfer in multiple-quantum-well structure. *E1* and *E2* are the energies of the ground and first excited states in the quantum well, respectively, and *d* the superlattice

Fig. 20. Spatially and energy resolved charge carrier photogeneration rate in the quantum well region at short-circuit conditions and under monochromatic illumination with energy of 1.65 eV and intensity of

10kW/m2 (Aeberhard, 2011).

period (Raisky et al., 1999).

Fig. 17. The energy bandstructure of a semiconductor type-I heterostructure superlattice : Eg1 and Eg2 are the bandgaps, Ec1 and Ec2 are the bottoms of the conduction bands of narrow bandgap and wide bandgap

semiconductors, respectively; d is the

Fig. 19. Spatial structure and doping profile of the p-i-n model system

(Aeberhard, 2011).

period of the heterostructure superlattice (Mitin, 2010).

Fig. 21. Spatially and energy-resolved charge carrier short-circuit photocurrent density in the quantum well region under monochromatic illumination with energy of 1.65 eV and intensity of 10kW/m2 (Aeberhard, 2011).

Fig. 22. Penetration length of the wave function of confined electron into barrier layers. Vb represents a barrier height for each barrier material (Aeberhard, 2011).

Fig. 23. (a) Schematic representation of the fabricated interdigitated devices (Conibeer et al., 2010); (b) Dark and illuminated I-V measurements of p-i-n diodes with 4 nm SRO/2 nm SiO2 bilayers.

Silicon-Based Third Generation Photovoltaics 161

The first prototypes of Si QD PV devices were successfully developed. Up today they present VOC, ISC and fill factor (FF) values which still lower than those ones of the 1st generation PV cells based on bulk Si – but all these problems are being addressed. The next step implies the further optimization of the fabrication parameters, developing of the

Nanowire solar cells demonstrated to date have been primarily based on hybrid organicinorganic materials or have utilized compound semiconductors such as CdSe. Huynh *et al*. utilized CdSe nanorods as the electron-conducting layer of a hole conducting polymermatrix solar cell (Huynh et al., 2002) and produced an efficiency of 1.7 % for AM 1.5 irradiation. Similar structures have been demonstrated for dye-sensitized solar cells using titania or ZnO nanowires, with efficiencies ranging from 0.5 % to 1.5 % (Law et al., 2005). These results show the benefits of using nanowires for enhanced charge transport in nanostructured solar cells compared to other nanostructured architectures. The Si nanowires (Si NW) solar cells have a potential to provide the equal or better performance to crystalline Si solar cells with processing methods similar to thin film solar cells (Tsakalakos et al., 2007)

The techniques to produce nanowires are normally divided into *(i)* bottom up and *(ii)* top

The bottom up approach starts with individual atoms and molecules and builds up the desired nanostructures. One of the mostly used methods in this family of approaches is the Vapor Liquid Solid (VLS) method which uses metal nanotemplates on Si wafer or on Si thin film (Kelzenberg et al., 2008) (Tian et al., 2007) (Tsakalakos et al., 2007, 2007a). In this method a liquid metal cluster acts as the energetically favored site for vapor-phase reactant absorption and when supersaturated, the nucleation site for crystallization. An important feature of this approach for nanowire growth is that phase diagrams can be used to choose a catalyst material that forms a liquid alloy with the nanowire material of interest, i.e. Si in our case. Also, a range of potential growth temperatures can be defined from the phase diagram such that there is coexistence of liquid alloy with solid nanowire phase. The main advantages of the VLS method which should be cited are the rather high growth rate of

several 100 nm/min and the fact that perfectly single crystalline nanowires form.

A schematic diagram illustrating the growth of Si nanowires by the VLS mechanism is shown on (Fig. 25 (a)). When the nanocatalysts become supersaturated with Si, a nucleation event occurs producing a solid/liquid Si/Au-Si alloy interface. In order to minimize the interfacial free energy, subsequent solid growth/crystallization occurs at this initial interface, which thus imposes the highly anisotropic growth constrain required for producing nanowires. Its growth continues in the presence of reactant as long as catalyst nanocatalyst remains in the liquid state. Typically the growth is performed by using SiH4 as the Si reactant, and diborane and phosphine as p- and n-type dopants, respectively. The growth can be carried out using Ar, He or H2 as carrier gas, which enables an added degree of freedom for the nanowire growth. For exemple, the use of H2 as a carrier gas can

efficient doping technique and defect passivation.

**4. Silicon nanowire solar cells** 

(Uchiyama et al., 2010) (Andra et al., 2008).

**4.1 Fabrication of Si nanowires** 

**4.1.1 Bottom up approach** 

down approaches.

The high resistance severely limits both the short-circuit current and the fill factor of the cells, particularly under illumination. Significant improvement is expected once the parasitic series resistance is eliminated.

Further evidence that this photovoltaic effect occurs in a material with an increased bandgap is given by temperature dependent I-V mesurements, from which an electronic bandgap for the Si QD nanostructure materials can be extracted. A bandgap of 1.8 eV was extracted for a structure containing Si QDs with a nominal diameter of 4 nm. However, this value will be due to a combination of other components in series with the material bandgap, hence the true material bandgap will be less than 1.8 eV.

Homojunction Si QD devices have also been fabricated in a SiC matrix using the superlattice approach (Song et al., 2009). Fig. 24 (a) shows a schematic diagram of a n-type Si QD: SiC/ p-type Si QD:SiC homojunction solar cell fabricated on a quartz substrate. The n-type Si QD emitter was approximately 200 nm thick and the p-type base layer is approximately 300 nm thick. This devices have given VOC of 82 mV that is promising initial value for a Si QDs in SiC solar cells on quartz substrate. Improvement of the device structure and optimization of dopant incorporation is expected to improve this value.

Fig. 24. (a) Schematic diagram of a n-type Si QD: SiC/ p-type Si QD:SiC/ quartz homojunction solar cell (Song et al., 2009); (b) The concept of the transport improvement: alternating layers of Si3N4 and SRO.

Current in both these SiO2 and SiC matrix devices was very small, due principally to the very high lateral resistance and also because of the small amount of absorption in the approximately 200 nm of material used. Indeed, as it was discussed in the previous paragraph, transport in these devices relies on tunneling and hopping between adjacent QDs. To maximize the tunneling probability, the barrier heights between QDs must be low, but this then compromises the degree of quantum confinement and the height of the confined energy levels and hence the effective bandgap obtained. The solution is to introduce anisotropy between the growth, *z*, direction and the *x-y* plane. This can achieved by maintaining strong confinement through the use of a large barrier height oxide in the plane, but to intersperse these layers with layers of lower barrier height such as Si3N4 or SiC, thus giving higher tunneling probability in the z direction (Fig. 24 (b)) (Di et al., 2010). The very first results on this approach were rather promising and showed the decreasing in the vertical resistivity of such Si QD nanostructures with SiNx interlayers (Di et al., 2010). To what concerns the increasing of the VOC the most potential route is the passivation of the defects through the hydrogenation.

The high resistance severely limits both the short-circuit current and the fill factor of the cells, particularly under illumination. Significant improvement is expected once the parasitic

Further evidence that this photovoltaic effect occurs in a material with an increased bandgap is given by temperature dependent I-V mesurements, from which an electronic bandgap for the Si QD nanostructure materials can be extracted. A bandgap of 1.8 eV was extracted for a structure containing Si QDs with a nominal diameter of 4 nm. However, this value will be due to a combination of other components in series with the material bandgap, hence the

Homojunction Si QD devices have also been fabricated in a SiC matrix using the superlattice approach (Song et al., 2009). Fig. 24 (a) shows a schematic diagram of a n-type Si QD: SiC/ p-type Si QD:SiC homojunction solar cell fabricated on a quartz substrate. The n-type Si QD emitter was approximately 200 nm thick and the p-type base layer is approximately 300 nm thick. This devices have given VOC of 82 mV that is promising initial value for a Si QDs in SiC solar cells on quartz substrate. Improvement of the device structure and optimization of

(a) (b)

homojunction solar cell (Song et al., 2009); (b) The concept of the transport improvement:

Current in both these SiO2 and SiC matrix devices was very small, due principally to the very high lateral resistance and also because of the small amount of absorption in the approximately 200 nm of material used. Indeed, as it was discussed in the previous paragraph, transport in these devices relies on tunneling and hopping between adjacent QDs. To maximize the tunneling probability, the barrier heights between QDs must be low, but this then compromises the degree of quantum confinement and the height of the confined energy levels and hence the effective bandgap obtained. The solution is to introduce anisotropy between the growth, *z*, direction and the *x-y* plane. This can achieved by maintaining strong confinement through the use of a large barrier height oxide in the plane, but to intersperse these layers with layers of lower barrier height such as Si3N4 or SiC, thus giving higher tunneling probability in the z direction (Fig. 24 (b)) (Di et al., 2010). The very first results on this approach were rather promising and showed the decreasing in the vertical resistivity of such Si QD nanostructures with SiNx interlayers (Di et al., 2010). To what concerns the increasing of the VOC the most potential route is the passivation of the

Fig. 24. (a) Schematic diagram of a n-type Si QD: SiC/ p-type Si QD:SiC/ quartz

series resistance is eliminated.

true material bandgap will be less than 1.8 eV.

alternating layers of Si3N4 and SRO.

defects through the hydrogenation.

dopant incorporation is expected to improve this value.

The first prototypes of Si QD PV devices were successfully developed. Up today they present VOC, ISC and fill factor (FF) values which still lower than those ones of the 1st generation PV cells based on bulk Si – but all these problems are being addressed. The next step implies the further optimization of the fabrication parameters, developing of the efficient doping technique and defect passivation.

#### **4. Silicon nanowire solar cells**

Nanowire solar cells demonstrated to date have been primarily based on hybrid organicinorganic materials or have utilized compound semiconductors such as CdSe. Huynh *et al*. utilized CdSe nanorods as the electron-conducting layer of a hole conducting polymermatrix solar cell (Huynh et al., 2002) and produced an efficiency of 1.7 % for AM 1.5 irradiation. Similar structures have been demonstrated for dye-sensitized solar cells using titania or ZnO nanowires, with efficiencies ranging from 0.5 % to 1.5 % (Law et al., 2005). These results show the benefits of using nanowires for enhanced charge transport in nanostructured solar cells compared to other nanostructured architectures. The Si nanowires (Si NW) solar cells have a potential to provide the equal or better performance to crystalline Si solar cells with processing methods similar to thin film solar cells (Tsakalakos et al., 2007) (Uchiyama et al., 2010) (Andra et al., 2008).

#### **4.1 Fabrication of Si nanowires**

The techniques to produce nanowires are normally divided into *(i)* bottom up and *(ii)* top down approaches.

#### **4.1.1 Bottom up approach**

The bottom up approach starts with individual atoms and molecules and builds up the desired nanostructures. One of the mostly used methods in this family of approaches is the Vapor Liquid Solid (VLS) method which uses metal nanotemplates on Si wafer or on Si thin film (Kelzenberg et al., 2008) (Tian et al., 2007) (Tsakalakos et al., 2007, 2007a). In this method a liquid metal cluster acts as the energetically favored site for vapor-phase reactant absorption and when supersaturated, the nucleation site for crystallization. An important feature of this approach for nanowire growth is that phase diagrams can be used to choose a catalyst material that forms a liquid alloy with the nanowire material of interest, i.e. Si in our case. Also, a range of potential growth temperatures can be defined from the phase diagram such that there is coexistence of liquid alloy with solid nanowire phase. The main advantages of the VLS method which should be cited are the rather high growth rate of several 100 nm/min and the fact that perfectly single crystalline nanowires form.

A schematic diagram illustrating the growth of Si nanowires by the VLS mechanism is shown on (Fig. 25 (a)). When the nanocatalysts become supersaturated with Si, a nucleation event occurs producing a solid/liquid Si/Au-Si alloy interface. In order to minimize the interfacial free energy, subsequent solid growth/crystallization occurs at this initial interface, which thus imposes the highly anisotropic growth constrain required for producing nanowires. Its growth continues in the presence of reactant as long as catalyst nanocatalyst remains in the liquid state. Typically the growth is performed by using SiH4 as the Si reactant, and diborane and phosphine as p- and n-type dopants, respectively. The growth can be carried out using Ar, He or H2 as carrier gas, which enables an added degree of freedom for the nanowire growth. For exemple, the use of H2 as a carrier gas can

Silicon-Based Third Generation Photovoltaics 163

(a) (b)

(a) (b) Fig. 26. (a) SEM image of a Si NW carpet grown from Au nanoparticles (150 nm diameter)

catalyst/nanowire interface of a Si NW with a <110> growth axis. Scale bar is 5 nm (Wu et

In top down approach relies on dimentional reduction through selective etching and various nanoimprinting techniques. For example, well aligned Si NW arrays can be obtained by electroless metal-assisted chemical etching in HF/AgNO3 solution. Basically, a noble metal is deposited on the surface in the form of nanoparticles which act as catalyst for Si etching in HF solution containing an oxidizing agent. As a consequence, the etching only occurs in the vicinity of the metal nanoparticles and results in the formation of well defined mesopores

One of the main advantages of the top – down methods as compared to the bottom –up is that it is possible to start the processing by using conventional wafers with already performed diffusion regions (ex. p+nn+ ) and then etch it into SiNWs. Each nanowire will

on a multicrystalline Si wafer (Andra 2008); (b) HRTEM image of the gold

(20-100 nm in diameter (Fang et al., 2008) (Peng et al., 2005) (Fig. 27 (a)).

al., 2004).

**4.1.2 Top down approach** 

Fig. 25. (a) Schematic diagram illustrating the growth of Si nanowires by the VLS

mechanism. (b) Binary phase diagram of Au-Si (Zhong et al., 2007).

passivate the growing solid surface and reduce the roughness (Wu et al., 2004) while Ar and He can enhance radial deposition of a specific composition shell.

Most frequently gold is taken as a template for nanowire growth. The Au-Si binary phase diagram (Fig. 25 (b)) predicts that Au nanocatalysts will form liquid alloy droplets with Si at temperatures higher than the eutectic point which is 363°C. The Au nanocatalysts can be prepared either from commercially available gold colloids or by depositing a thin Au film followed by a heating step above the eutectic temperature during which a Au-Si liquid film forms to disintegrate into nano-droplets. Another simple and effective method for producing metal nanoparticles (Au, Ag…) at room temperature is based on their electroless deposition on the surface of Si or hydrogenated Si nitride films (Nychyporuk et al., 2010). It should be mentioned that it is still a controversial issue how gold is incorporated into the wire and thus how it influences the electronic properties of the nanowire. Gold is a deeplevel defect in bulk Si and if it is also true for nanowires grown from Au droplets. Hence the alternative metals like In, Sn, Al (Ball et al., 2010) are actually under investigation for using as nanocatalysts during the nanowire growth.

Si NWs grow with a diameter similar to that of the template droplet. The nanowire diameters are on average 1-2 nm larger than the starting nanocatalyst size. As a result a carpet of perfect single crystalline NWs of 10 to 200 nm in diameter and several micrometers in length can be grown on the crystalline substrate (Fig. 26 (a)) (Andra 2008). Highresolution transmission electron microscopy (HRTEM) was used to define in detail the structures of these nanowires (Wu et al., 2004). As synthesized Si NWs are single crystalline nanostructures with uniform diameters. Studies of the ends of the nanowires show that they often terminate with Au nanoparticles (Fig. 26 (b)). In addition, the crystallographic growth directions of Si NWs have also been investigated using HRTEM and systematic measurements reveal that the growth axes are related to their diameters (Wu et al., 2004) (Cui et al., 2001a). For diameters between 3 and 10 nm, 95% of the Si NWs were found to grow along the <110> direction, for diameters between 10 and 20 nm, 61% of the Si NWs grow along the <112> direction, and for diameters between 20 and 30 nm, 64% of the Si NWs grow along the <111> direction. These results demonstrate a clear preference for growth along the <110> direction in the smallest Si NWs and along <111> direction in larger ones (Zhong et al., 2007). Cross-sectional HRTEM analysis has revealed that the nanowires could have triangular, rectangular and hexagonal cross section with well – developed facets (Vo et al., 2006) (Jie et al., 2006) (Zhang et al., 2005).

The VLS method permits to fabricate the nanowires of well-defined length with diameters as small as 3 nm (Wu et al., 2004). The electronic properties can be precisely controlled by introducing dopant reactants during the growth. Addition of different ratios of diborane or phosphine to silane reactant during growth produces p- or n- type Si nanowires with effective doping concentrations directly related to the silane: dopant gas ratios (Cui et al., 2000) (Cui et al., 2001) (Zheng et al., 2004) (Fukata, 2009). It was demonstrated that B and P can be used to change the conductivity of Si NWS over many orders of magnitude (Cui et al., 2000). The carrier mobility in SiNWs can reach that one in bulk Si at a doping concentration of 1020 cm-3 and decreases for smaller diameter wires. Temperature dependent measurements made on heavily doped SiNWs show no evidence for single electron charging at temperatures down to 4.2 K, and thus suggest that SiNWs possess a high degree of structural and doping uniformity. Moreover, TEM studies of boron- and phosphorous doped SiNWs have shown that contrary to Si QDs the introduction of impurity atoms during the nanowire growth does not change their crystallinity. The ability to prepare welldefined doped nanowire during synthesis distinguishes nanowires from QDs.

passivate the growing solid surface and reduce the roughness (Wu et al., 2004) while Ar and

Most frequently gold is taken as a template for nanowire growth. The Au-Si binary phase diagram (Fig. 25 (b)) predicts that Au nanocatalysts will form liquid alloy droplets with Si at temperatures higher than the eutectic point which is 363°C. The Au nanocatalysts can be prepared either from commercially available gold colloids or by depositing a thin Au film followed by a heating step above the eutectic temperature during which a Au-Si liquid film forms to disintegrate into nano-droplets. Another simple and effective method for producing metal nanoparticles (Au, Ag…) at room temperature is based on their electroless deposition on the surface of Si or hydrogenated Si nitride films (Nychyporuk et al., 2010). It should be mentioned that it is still a controversial issue how gold is incorporated into the wire and thus how it influences the electronic properties of the nanowire. Gold is a deeplevel defect in bulk Si and if it is also true for nanowires grown from Au droplets. Hence the alternative metals like In, Sn, Al (Ball et al., 2010) are actually under investigation for using

Si NWs grow with a diameter similar to that of the template droplet. The nanowire diameters are on average 1-2 nm larger than the starting nanocatalyst size. As a result a carpet of perfect single crystalline NWs of 10 to 200 nm in diameter and several micrometers in length can be grown on the crystalline substrate (Fig. 26 (a)) (Andra 2008). Highresolution transmission electron microscopy (HRTEM) was used to define in detail the structures of these nanowires (Wu et al., 2004). As synthesized Si NWs are single crystalline nanostructures with uniform diameters. Studies of the ends of the nanowires show that they often terminate with Au nanoparticles (Fig. 26 (b)). In addition, the crystallographic growth directions of Si NWs have also been investigated using HRTEM and systematic measurements reveal that the growth axes are related to their diameters (Wu et al., 2004) (Cui et al., 2001a). For diameters between 3 and 10 nm, 95% of the Si NWs were found to grow along the <110> direction, for diameters between 10 and 20 nm, 61% of the Si NWs grow along the <112> direction, and for diameters between 20 and 30 nm, 64% of the Si NWs grow along the <111> direction. These results demonstrate a clear preference for growth along the <110> direction in the smallest Si NWs and along <111> direction in larger ones (Zhong et al., 2007). Cross-sectional HRTEM analysis has revealed that the nanowires could have triangular, rectangular and hexagonal cross section with well – developed facets

The VLS method permits to fabricate the nanowires of well-defined length with diameters as small as 3 nm (Wu et al., 2004). The electronic properties can be precisely controlled by introducing dopant reactants during the growth. Addition of different ratios of diborane or phosphine to silane reactant during growth produces p- or n- type Si nanowires with effective doping concentrations directly related to the silane: dopant gas ratios (Cui et al., 2000) (Cui et al., 2001) (Zheng et al., 2004) (Fukata, 2009). It was demonstrated that B and P can be used to change the conductivity of Si NWS over many orders of magnitude (Cui et al., 2000). The carrier mobility in SiNWs can reach that one in bulk Si at a doping concentration of 1020 cm-3 and decreases for smaller diameter wires. Temperature dependent measurements made on heavily doped SiNWs show no evidence for single electron charging at temperatures down to 4.2 K, and thus suggest that SiNWs possess a high degree of structural and doping uniformity. Moreover, TEM studies of boron- and phosphorous doped SiNWs have shown that contrary to Si QDs the introduction of impurity atoms during the nanowire growth does not change their crystallinity. The ability to prepare well-

defined doped nanowire during synthesis distinguishes nanowires from QDs.

He can enhance radial deposition of a specific composition shell.

as nanocatalysts during the nanowire growth.

(Vo et al., 2006) (Jie et al., 2006) (Zhang et al., 2005).

Fig. 25. (a) Schematic diagram illustrating the growth of Si nanowires by the VLS mechanism. (b) Binary phase diagram of Au-Si (Zhong et al., 2007).

Fig. 26. (a) SEM image of a Si NW carpet grown from Au nanoparticles (150 nm diameter) on a multicrystalline Si wafer (Andra 2008); (b) HRTEM image of the gold catalyst/nanowire interface of a Si NW with a <110> growth axis. Scale bar is 5 nm (Wu et al., 2004).

#### **4.1.2 Top down approach**

In top down approach relies on dimentional reduction through selective etching and various nanoimprinting techniques. For example, well aligned Si NW arrays can be obtained by electroless metal-assisted chemical etching in HF/AgNO3 solution. Basically, a noble metal is deposited on the surface in the form of nanoparticles which act as catalyst for Si etching in HF solution containing an oxidizing agent. As a consequence, the etching only occurs in the vicinity of the metal nanoparticles and results in the formation of well defined mesopores (20-100 nm in diameter (Fang et al., 2008) (Peng et al., 2005) (Fig. 27 (a)).

One of the main advantages of the top – down methods as compared to the bottom –up is that it is possible to start the processing by using conventional wafers with already performed diffusion regions (ex. p+nn+ ) and then etch it into SiNWs. Each nanowire will

Silicon-Based Third Generation Photovoltaics 165

experimentally proved that Si nanowire materials have exhibited properties such as ultrahigh surface area ratio, low reflection, absorption of wideband light, and tunable bandgap.

In 2003, scanning tunneling spectroscopy measurements on individual oxide-removed Si NWs showed that the optical gap of Si NWs increased with decreasing of Si NW diameter from 1.1 eV for 7 nm to 3.5 eV to 1.3 nm (Ma et al., 2003). Since, a large number of theoretical and experimental works have been done to explore the effect of the chemical passivation, surface reconstruction, cross section geometry and growth orientation on electronic structure of SiNWs (Fernández-Serra et al., 2006) (Yan et al., 2007) (Vo et al., 2006). For example, it was shown than the bandgap of [110] SiNWs is the smallest among those of the [100], [112], and [111] wires of the same diameter (Cui et al., 2000). It should be also noted that the magnitude of the energy increase/decrease in SiNWs induced by quantum confinement is different for each point of the bandstructure. It was predicted that the conduction-band-minimum (CBM) energy increases more near the X point than near the . Therefore for nanowires with sufficiently small dimensions, this difference in the energy shifts at different points in the Brillouin zone is large enough to move the CBM at the X point above the CBM at the point (Vo et al., 2006). Then a transition from an indirect to direct gap material occurs. The indirect to direct transition does not depend on the special cross-sectional shapes and the bandgaps of [110] SiNWs remain direct event for SiNWs with dimensions up to 7 nm. The dependence of the bandgap on SiNW dimension *D* is shown on the Fig. 28 (a). It is obvious that the smaller the dimension of the nanowire the larger the bandgap due to quantum confinement. As *D* decreases from 7 to 1 nm, the bandgap increases from 1.5 to 2.7 eV. In addition to the size dependence, the energy gap also shows significantly different change with respect to the crosssectional shape. The bandgaps of rectangular and hexagonal SiNWs are rather close while

Fig. 28. (a) Bandgap of SiNWs versus the transverse dimension *D*. (b) Bandgap of SiNWs

The significant cross-sectional shape effects on band gap and size dependence can be understood from the concept of surface –to-volume ratio (SVR). Because of the quantum confinement effect, the band gap increases as the material dimension is reduced, thus

**4.2.1 Bandgap of quantum SiNWs** 

distinctly smaller than that of the triangular SiNWs.

versus SVR (Yao et al., 2008).

thus present the p-n junction already formed. However this method presents some drawbacks. One of them is rather poor size control.

To overcome this problem colloidal crystal patterning combined with metal-assisted etching was applied (Wang et al., 2010) (Wang et al., 2010). The main idea is the next one. The sphere lithography is based on the self-organization of micrometer/nanometer spheres into a monolayer with a hexagonal close-packed structure. Typical material used for the spheres are silica and polystyrene, which are commercially available with narrow size distribution. The deposition of a monolayer of the spheres on a substrate is used as a patterning mask for thin metallic film evaporated on the Si wafer. After the sphere dissolution, the Si surface that comes in contact with the metal is selectively etched, leaving behind an array of Si NWs whose diameter is predefined by the size of holes in the metal film, while the length is determined by the etching time. This method enables the formation of large scale arrays with long – range periodicity of vertically standing nanorods/nanowires with well controlled diameter, length and density (Fig. 27 (b)). It should be however noted that this methods does not permit to achieve SiNWs with the diameters lower than 50 nm and thus potentially cannot be applied for all-Si tandem solar cell.

Fig. 27. SEM images of Si NWs obtained by (a) simple metal-assisted etching technique (Andra 2008) and (b) by colloidal crystal patterning combined with metal-assisted etching approach (Wang et al., 2010).

#### **4.2 Optical properties of Si nanowires**

A variety of the optical techniques have shown that the properties of nanowires are different to those of their bulk counterparts, however the interpretation of these measurements is not always straightforward. The wavelength of light used to probe the sample is usually smaller than the wire length, but larger than the wire diameter. Hence, the probe light used in the optical measurement cannot be focused solely onto the nanowire and the wire and the substrate on which the wire rests (or host material if the wire is embedded in a template) are probed simultaneously. For example, for measurements such as photoluminescence, if the substrate does not luminesce or absorb in the frequency range of the measurements, PL measures the luminescence of the nanowire directly and the substrate can be ignored. In reflection and transmission measurements, even a non-absorbing substrate can modify the measured spectra of nanowires. However, despite these technical difficulties it was

thus present the p-n junction already formed. However this method presents some

To overcome this problem colloidal crystal patterning combined with metal-assisted etching was applied (Wang et al., 2010) (Wang et al., 2010). The main idea is the next one. The sphere lithography is based on the self-organization of micrometer/nanometer spheres into a monolayer with a hexagonal close-packed structure. Typical material used for the spheres are silica and polystyrene, which are commercially available with narrow size distribution. The deposition of a monolayer of the spheres on a substrate is used as a patterning mask for thin metallic film evaporated on the Si wafer. After the sphere dissolution, the Si surface that comes in contact with the metal is selectively etched, leaving behind an array of Si NWs whose diameter is predefined by the size of holes in the metal film, while the length is determined by the etching time. This method enables the formation of large scale arrays with long – range periodicity of vertically standing nanorods/nanowires with well controlled diameter, length and density (Fig. 27 (b)). It should be however noted that this methods does not permit to achieve SiNWs with the diameters lower than 50 nm and thus

(a) (b)

A variety of the optical techniques have shown that the properties of nanowires are different to those of their bulk counterparts, however the interpretation of these measurements is not always straightforward. The wavelength of light used to probe the sample is usually smaller than the wire length, but larger than the wire diameter. Hence, the probe light used in the optical measurement cannot be focused solely onto the nanowire and the wire and the substrate on which the wire rests (or host material if the wire is embedded in a template) are probed simultaneously. For example, for measurements such as photoluminescence, if the substrate does not luminesce or absorb in the frequency range of the measurements, PL measures the luminescence of the nanowire directly and the substrate can be ignored. In reflection and transmission measurements, even a non-absorbing substrate can modify the measured spectra of nanowires. However, despite these technical difficulties it was

Fig. 27. SEM images of Si NWs obtained by (a) simple metal-assisted etching technique (Andra 2008) and (b) by colloidal crystal patterning combined with metal-assisted etching

drawbacks. One of them is rather poor size control.

potentially cannot be applied for all-Si tandem solar cell.

approach (Wang et al., 2010).

**4.2 Optical properties of Si nanowires** 

experimentally proved that Si nanowire materials have exhibited properties such as ultrahigh surface area ratio, low reflection, absorption of wideband light, and tunable bandgap.

#### **4.2.1 Bandgap of quantum SiNWs**

In 2003, scanning tunneling spectroscopy measurements on individual oxide-removed Si NWs showed that the optical gap of Si NWs increased with decreasing of Si NW diameter from 1.1 eV for 7 nm to 3.5 eV to 1.3 nm (Ma et al., 2003). Since, a large number of theoretical and experimental works have been done to explore the effect of the chemical passivation, surface reconstruction, cross section geometry and growth orientation on electronic structure of SiNWs (Fernández-Serra et al., 2006) (Yan et al., 2007) (Vo et al., 2006). For example, it was shown than the bandgap of [110] SiNWs is the smallest among those of the [100], [112], and [111] wires of the same diameter (Cui et al., 2000). It should be also noted that the magnitude of the energy increase/decrease in SiNWs induced by quantum confinement is different for each point of the bandstructure. It was predicted that the conduction-band-minimum (CBM) energy increases more near the X point than near the . Therefore for nanowires with sufficiently small dimensions, this difference in the energy shifts at different points in the Brillouin zone is large enough to move the CBM at the X point above the CBM at the point (Vo et al., 2006). Then a transition from an indirect to direct gap material occurs. The indirect to direct transition does not depend on the special cross-sectional shapes and the bandgaps of [110] SiNWs remain direct event for SiNWs with dimensions up to 7 nm. The dependence of the bandgap on SiNW dimension *D* is shown on the Fig. 28 (a). It is obvious that the smaller the dimension of the nanowire the larger the bandgap due to quantum confinement. As *D* decreases from 7 to 1 nm, the bandgap increases from 1.5 to 2.7 eV. In addition to the size dependence, the energy gap also shows significantly different change with respect to the crosssectional shape. The bandgaps of rectangular and hexagonal SiNWs are rather close while distinctly smaller than that of the triangular SiNWs.

Fig. 28. (a) Bandgap of SiNWs versus the transverse dimension *D*. (b) Bandgap of SiNWs versus SVR (Yao et al., 2008).

The significant cross-sectional shape effects on band gap and size dependence can be understood from the concept of surface –to-volume ratio (SVR). Because of the quantum confinement effect, the band gap increases as the material dimension is reduced, thus

Silicon-Based Third Generation Photovoltaics 167

Important factors that determine the transport properties of Si nanowires include the wire diameter (important for both classical and quantum size effect), surface conditions, crystal quality, and the crystallographic orientation along the wire axis (Ramayya et al., 2006)

Electronic transport phenomena in Si nanowires can be roughly divided into two categories: ballistic transport and diffusive transport. Ballistic transport phenomena occur when the electrons can travel across the nanowire without any scattering. In this case the conduction is mainly determined by the contact between the nanowire and the external circuit. Ballistic transport phenomena are usually observed in very short quantum wires. On the other hand, for nanowires with length much larger than the carrier mean free path, the electrons (or holes) undergo numerous scattering events when they travel along the wire. In this case, the transport is in the diffusive regime, and the conduction is dominated by carrier scattering within the wires, due to lattice vibrations, boundary scattering, lattice and other structural

The electronic transport behavior of Si nanowires may be categorized based on the relative magnitudes of three length scales: carriers mean free path, the de Broglie wavelength of electrons, and the wire diameter. For wire diameters much larger than the carrier mean free path, the nanowiers exhibit transport properties similar to bulk materials, which are independent of the wire diameter, since the scattering due to the wire boundary is negligible, compared to other scattering mechanisms. For wire diameters comparable or smaller than the carrier mean free path, but still larger than the de Broglie wavelength of the electrons, the transport in the nanowire is in the classical finite regime, where the band structure of the nanowire is still similar to that of the bulk, while the scattering events at the wire boundary alter their transport behavior. For wire diameters comparable to electronic wavelength (de Broglie wavelength of electrons), the electronic density of states is altered dramatically and quantum sub-bands are formed due to quantum confinement effect at the wire boundary. In this regime, the transport properties are further influenced by the change in the band structure. Therefore, transport properties for nanowires in the classical finite size and quantum size regimes are highly diameter-dependent. Experimentally it was shown that the carrier mobility in SiNWs can reach that one in bulk Si at a doping

concentration of 1020 cm-3 and decreases for smaller diameter wires (Cui et al., 2000).

**4.4 Comparison of axial and radial p-n junction nanowire solar cells** 

Because of the enhanced surface-to-volume ratio of the nanowires, their transport behavior may be modified by changing their surface conditions. For example, it was shown on the n-InP nanowires, that coating of the surface of these nanowires with a layer of redox molecules, the conductance may be changed by orders of magnitude (Duan et al., 2002).

Independently of the nanowire preparation method two designs of NW solar cells are now under consideration with p-n junction either radial or axial (Fig. 30). In the radial case the pn junction covers the whole outer cylindrical surface of the NWs. This was achieved either by gas doping or by CVD deposition of a shell oppositely doped to the wire (Fang, 2008) (Peng, 2005) (Tian 2007). In the axial variant, the p-n junction cuts the NW in two cylindrical parts and require minimal processing steps (Andra 2008). However, solar cells that absorb photons and collect charges along orthogonal directions meet the optimal relation between the absorption values and minority charge carrier diffusion lengths (Fig. 30 (a)) (Hochbaum 2010). A solar cell consisting of arrays of radial p-n junction nanowires (Fig. 30 (b)) may

**4.3 Electrical transport in SiNWs** 

(Duan et al., 2002).

defects and impurity atoms.

leading to an increase of SVR. In other words, SVR has the impact of enlarging band gap. At the same transverse dimension, triangular SiNW has larger SVR than those of the rectangular SiNW and hexagonal SiNW. As a result, its larger SVR induces the largest band gap among those of the rectangular and hexagonal SiNWs and the strongest size dependence. The bandgap values versus SVR of the SiNWs are shown in Fig. 28 (b). The SVR effect on the bandgap of [110] SiNWs with any cross-sectional shape and area can be described by a universal expression (Yao et al., 2008)

$$\text{E}\_{\text{G}}\text{ (eV)} \text{=} 1.28 + 0.37 \times \text{S (nm} \text{-} ^\text{I)}\text{.}$$

where *S* is the value of the SVR in unit of nm-1. The bandgap of SiNWs are usually difficult to measure, but their transverse cross-sectional shape and dimension are easy to know, so it is of significance to predict the bandgap values of SiNWs by using the above expression.

#### **4.2.2 Optical reflection and absorption in SiNWs**

Si NW PV devices show improved optical characteristics compared to planar devices. Fig. 29 (a) shows typical optical reflectance spectra of SiNW film as compared to solid Si film of the same thickness (~10m) (Tsakalakos et al., 2007a). As one can see, the reflectance of the nanowire film is less than 5% over the majority of the spectrum from the UV to the near IR and begins to increase at ~700°nm to a values of ~41% at the Si band edge (1100 nm), similar to the bulk Si. It is clear that the nanowires impart a significant reduction of the reflectance compared to the solid film. More striking is the fact that the transmission of the nanowire samples is also significantly reduced for wavelength greater than ~700°nm (Fig. 29 (b)). This residual absorption is attributed to strong IR light trapping4 coupled with the presence of the surface states on the nanowires that absorb below bandgap light. However, the level of optical absorption does not change with passivation, which further indicates that light trapping plays a dominant role in the enhanced absorption of the structures at all wavelength. It should be also noted that the absorption edge of a nanowire film shifts to longer wavelength and approaches the bulk value as the nanowire density is increased. Essentially, the Si nanowire arrays act as sub-wavelength cylindrical scattering elements, with the mactroscopic optical properties being dependent on nanowire pitch, length, and diameter.

Fig. 29. Total (a) reflectance and (b) transmission data from integrated sphere measurements for 11 m thick solid Si film and nanowire film on glass substrate (Tsakalakos et al., 2007).

<sup>4</sup> Light trapping is typically defined as the ratio of the effective path length for light rays confined within a structure with respect to its thickness.

#### **4.3 Electrical transport in SiNWs**

166 Solar Cells – Silicon Wafer-Based Technologies

leading to an increase of SVR. In other words, SVR has the impact of enlarging band gap. At the same transverse dimension, triangular SiNW has larger SVR than those of the rectangular SiNW and hexagonal SiNW. As a result, its larger SVR induces the largest band gap among those of the rectangular and hexagonal SiNWs and the strongest size dependence. The bandgap values versus SVR of the SiNWs are shown in Fig. 28 (b). The SVR effect on the bandgap of [110] SiNWs with any cross-sectional shape and area can be

EG (eV)=1.28+0.37 x S (nm-1), where *S* is the value of the SVR in unit of nm-1. The bandgap of SiNWs are usually difficult to measure, but their transverse cross-sectional shape and dimension are easy to know, so it is of significance to predict the bandgap values of SiNWs by using the above expression.

Si NW PV devices show improved optical characteristics compared to planar devices. Fig. 29 (a) shows typical optical reflectance spectra of SiNW film as compared to solid Si film of the same thickness (~10m) (Tsakalakos et al., 2007a). As one can see, the reflectance of the nanowire film is less than 5% over the majority of the spectrum from the UV to the near IR and begins to increase at ~700°nm to a values of ~41% at the Si band edge (1100 nm), similar to the bulk Si. It is clear that the nanowires impart a significant reduction of the reflectance compared to the solid film. More striking is the fact that the transmission of the nanowire samples is also significantly reduced for wavelength greater than ~700°nm (Fig. 29 (b)). This residual absorption is attributed to strong IR light trapping4 coupled with the presence of the surface states on the nanowires that absorb below bandgap light. However, the level of optical absorption does not change with passivation, which further indicates that light trapping plays a dominant role in the enhanced absorption of the structures at all wavelength. It should be also noted that the absorption edge of a nanowire film shifts to longer wavelength and approaches the bulk value as the nanowire density is increased. Essentially, the Si nanowire arrays act as sub-wavelength cylindrical scattering elements, with the mactroscopic optical

Fig. 29. Total (a) reflectance and (b) transmission data from integrated sphere measurements for 11 m thick solid Si film and nanowire film on glass substrate (Tsakalakos et al., 2007).

4 Light trapping is typically defined as the ratio of the effective path length for light rays confined

described by a universal expression (Yao et al., 2008)

**4.2.2 Optical reflection and absorption in SiNWs** 

properties being dependent on nanowire pitch, length, and diameter.

within a structure with respect to its thickness.

Important factors that determine the transport properties of Si nanowires include the wire diameter (important for both classical and quantum size effect), surface conditions, crystal quality, and the crystallographic orientation along the wire axis (Ramayya et al., 2006) (Duan et al., 2002).

Electronic transport phenomena in Si nanowires can be roughly divided into two categories: ballistic transport and diffusive transport. Ballistic transport phenomena occur when the electrons can travel across the nanowire without any scattering. In this case the conduction is mainly determined by the contact between the nanowire and the external circuit. Ballistic transport phenomena are usually observed in very short quantum wires. On the other hand, for nanowires with length much larger than the carrier mean free path, the electrons (or holes) undergo numerous scattering events when they travel along the wire. In this case, the transport is in the diffusive regime, and the conduction is dominated by carrier scattering within the wires, due to lattice vibrations, boundary scattering, lattice and other structural defects and impurity atoms.

The electronic transport behavior of Si nanowires may be categorized based on the relative magnitudes of three length scales: carriers mean free path, the de Broglie wavelength of electrons, and the wire diameter. For wire diameters much larger than the carrier mean free path, the nanowiers exhibit transport properties similar to bulk materials, which are independent of the wire diameter, since the scattering due to the wire boundary is negligible, compared to other scattering mechanisms. For wire diameters comparable or smaller than the carrier mean free path, but still larger than the de Broglie wavelength of the electrons, the transport in the nanowire is in the classical finite regime, where the band structure of the nanowire is still similar to that of the bulk, while the scattering events at the wire boundary alter their transport behavior. For wire diameters comparable to electronic wavelength (de Broglie wavelength of electrons), the electronic density of states is altered dramatically and quantum sub-bands are formed due to quantum confinement effect at the wire boundary. In this regime, the transport properties are further influenced by the change in the band structure. Therefore, transport properties for nanowires in the classical finite size and quantum size regimes are highly diameter-dependent. Experimentally it was shown that the carrier mobility in SiNWs can reach that one in bulk Si at a doping concentration of 1020 cm-3 and decreases for smaller diameter wires (Cui et al., 2000).

Because of the enhanced surface-to-volume ratio of the nanowires, their transport behavior may be modified by changing their surface conditions. For example, it was shown on the n-InP nanowires, that coating of the surface of these nanowires with a layer of redox molecules, the conductance may be changed by orders of magnitude (Duan et al., 2002).

#### **4.4 Comparison of axial and radial p-n junction nanowire solar cells**

Independently of the nanowire preparation method two designs of NW solar cells are now under consideration with p-n junction either radial or axial (Fig. 30). In the radial case the pn junction covers the whole outer cylindrical surface of the NWs. This was achieved either by gas doping or by CVD deposition of a shell oppositely doped to the wire (Fang, 2008) (Peng, 2005) (Tian 2007). In the axial variant, the p-n junction cuts the NW in two cylindrical parts and require minimal processing steps (Andra 2008). However, solar cells that absorb photons and collect charges along orthogonal directions meet the optimal relation between the absorption values and minority charge carrier diffusion lengths (Fig. 30 (a)) (Hochbaum 2010). A solar cell consisting of arrays of radial p-n junction nanowires (Fig. 30 (b)) may

Silicon-Based Third Generation Photovoltaics 169

to the minority –electron diffusion length allows carriers to traverse the cell even if the diffusion length is low, provided that the trap density is relatively low in the depletion

An optimally designed radial p-n junction nanowire cell should be doped as high as possible in both n- and p- type regions, have a narrow emitter width, have a radius approximately equal to the diffusion length of the electrons in the p-type core, and have a length approximately equal to the thickness of the material. It is crucial that the trap density near the p-n junction is relatively low. Therefore one would prefer to use doping mechanisms that will getter impurities away from the junction. By exploiting the radial p-n junction nanowire geometry, extremely large efficiency gains up to 11% are possible to be

By using VLS method (Tian et al., 2007) (Kelzenberg et al., 2008) (Rout et al., 2008) (Fang et al., 2008) (Perraud et al., 2009) as well as by the etching method (Garnett et al., 2008) (Peng et al., 2005). SiNW based photovoltaic devices were experimentally demonstrated. Nearly all the works were concerned with Si wafers as a substrate. However, it should be noted that for competitive solar cells, low cost substrates, such as glass or metal foils are to be preferred. Schematic view of the VLS fabricated structure of the SiNW array solar cells is illustrated on Fig. 31 (a). The n-type SiNWs were prepared by the VLS method on (100) ptype Si substrate (14-22 cm). Device fabrication started from the evaporation of 2-nm thick gold film followed by annealing at 550°C for 10 min under H2 flow to form Au nanocatalyzers. SiNWs were subsequently grown at 500° with SiH4 diluted in H2 as the gas precursor. N-type doping was achieved by adding PH3 to SiH4, with PH3/SiH4 ratio of 2x10- 3 corresponding to a nominal phosphorous density of 1020cm-3. After the VLS growth the gold catalysts were etched off in KI/I2 solution, and the doping impurities were activated by rapid thermal annealing at 750° for 5 min. The SiNW array was then embedded into spinon-glass (SOG) matrix. Indeed, SOG matrix ensures a good mechanical stability of the SiNW array and enables further processing steps, such as front surface planarization and electrical contact deposition. The planarization step is normally performed by the chemicalmechanical polishing. To form the front contacts indium-tin-oxide (ITO) was firstly deposited on planarized SOG surface followed by the deposition of Ni/Al contact grid. As back electrical contact, the sputtered and annealed Al was used. The area of the fabricated

The sheet resistance of n-type SiNWs embedded into SOG matrix was estimated to be 10-4 /sq. I-V measurements in the dark and under 1-sun illumination (Fig. 31 (b)) indicate a good rectifying junction. The measured ISC, VOC and FF were 17 mA/cm2, 250mV and 44%, respectively, leading to an energy-conversion efficiency of 1.9%. The VOC of Si NW solar cell was shown to be increased up to 580 mV (Peng et al., 2005). The parasitic series resistance found for SiNW solar cells (~5 cm-2) was slightly larger than in the standard 1st generation solar cells (~2 cm-2), however the p-n junction reverse current was of the order of 1 A/cm2 with is about 100 times bigger than in typical Si solar cells (~1 pA/cm2). Such a high pn junction reverse current indicates a high density of localized electronic states within the bandgap, which act as generation-recombination centers. These states may come from contamination of Si by gold which is used as catalyst for VLS growth. Other types of metallic catalysers, like Sn, were also used (Uchiyama et al., 2010).

region.

obtained.

**4.5 Fabrication of Si QD PV devices** 

SiNW solar cell was 2.3 cm-2.

provide a solution to this device design and optimization issue. A nanowire with a p-n junction in the radial direction would enable a decoupling of the requirements for light absorption and carrier extraction into orthogonal spatial directions. Each individual p-n junction nanowire in the cell could be long in the direction of incident light, allowing for optimal light absorption, but thin in another dimension, thereby allowing for effective carrier collection.

Fig. 30. Schematic views of the (a) axial and (b) radial nanowire solar cell. Light penetration into the cell is characterized by the optical thickness of the material ( is the absorption coefficient), while the mean free path of generated minority carriers is given by their diffusion length. In the case of axial nanowire solar cell, light penetrates deep into the cell, but the electron-diffusion length is too short to allow the collection of all light-generated carriers (Kayes et al., 2005).

The comparison between the axial and radial p-n junction technologies for solar cell applications was performed in details in Ref (Kayes et al., 2005). In the case of radial p-n junction, the short-circuit current (*Isc*) increases with the nanowire length and plateaus when the length of the nanowire become much greater than the optical thickness of the material. Also, *Isc* was essentially independent on the nanowire radius, provided that the radius (*R*) was less than the minority carrier diffusion length (*Ln*). However, it decreases steeply when *R > Ln*. *Isc* is essentially independent of trap density in the depletion region. Being rather sensitive to a number of traps in the depletion region, the open circuit voltage *Voc* decreases with increasing nanowire length, and increases with nanowire radius. On the other hand the trap density in the quasineutral regions had relatively less effect on *Voc*. The optimal nanowire dimensions are obtained when the nanowire has a radius approximately equal to *Ln* and a length that is determined by the specific tradeoff between the increase in *Isc* and the decrease in *Voc* with length. In the case of low trap density in the depletion region, the maximum efficiency is obtained for nanowires having a length approximately equal to the optical thickness. For higher trap densities smaller nanowire lengths are optimal.

Radial p-n junction nanowire cells trend to favor high doping levels to produce high cell efficiencies. High doping will lead to decreased charge-carrier mobility and a decreased depletion region width, but in turn high doping advantageously increases the build-in voltage. Because carriers can travel approximately one diffusion length through a quasineutral region before recombining, making the nanowire radius approximately equal

provide a solution to this device design and optimization issue. A nanowire with a p-n junction in the radial direction would enable a decoupling of the requirements for light absorption and carrier extraction into orthogonal spatial directions. Each individual p-n junction nanowire in the cell could be long in the direction of incident light, allowing for optimal light absorption, but thin in another dimension, thereby allowing for effective

(a) (b)

Fig. 30. Schematic views of the (a) axial and (b) radial nanowire solar cell. Light penetration into the cell is characterized by the optical thickness of the material ( is the absorption coefficient), while the mean free path of generated minority carriers is given by their diffusion length. In the case of axial nanowire solar cell, light penetrates deep into the cell, but the electron-diffusion length is too short to allow the collection of all light-generated

The comparison between the axial and radial p-n junction technologies for solar cell applications was performed in details in Ref (Kayes et al., 2005). In the case of radial p-n junction, the short-circuit current (*Isc*) increases with the nanowire length and plateaus when the length of the nanowire become much greater than the optical thickness of the material. Also, *Isc* was essentially independent on the nanowire radius, provided that the radius (*R*) was less than the minority carrier diffusion length (*Ln*). However, it decreases steeply when *R > Ln*. *Isc* is essentially independent of trap density in the depletion region. Being rather sensitive to a number of traps in the depletion region, the open circuit voltage *Voc* decreases with increasing nanowire length, and increases with nanowire radius. On the other hand the trap density in the quasineutral regions had relatively less effect on *Voc*. The optimal nanowire dimensions are obtained when the nanowire has a radius approximately equal to *Ln* and a length that is determined by the specific tradeoff between the increase in *Isc* and the decrease in *Voc* with length. In the case of low trap density in the depletion region, the maximum efficiency is obtained for nanowires having a length approximately equal to the

optical thickness. For higher trap densities smaller nanowire lengths are optimal.

Radial p-n junction nanowire cells trend to favor high doping levels to produce high cell efficiencies. High doping will lead to decreased charge-carrier mobility and a decreased depletion region width, but in turn high doping advantageously increases the build-in voltage. Because carriers can travel approximately one diffusion length through a quasineutral region before recombining, making the nanowire radius approximately equal

carrier collection.

carriers (Kayes et al., 2005).

to the minority –electron diffusion length allows carriers to traverse the cell even if the diffusion length is low, provided that the trap density is relatively low in the depletion region.

An optimally designed radial p-n junction nanowire cell should be doped as high as possible in both n- and p- type regions, have a narrow emitter width, have a radius approximately equal to the diffusion length of the electrons in the p-type core, and have a length approximately equal to the thickness of the material. It is crucial that the trap density near the p-n junction is relatively low. Therefore one would prefer to use doping mechanisms that will getter impurities away from the junction. By exploiting the radial p-n junction nanowire geometry, extremely large efficiency gains up to 11% are possible to be obtained.

#### **4.5 Fabrication of Si QD PV devices**

By using VLS method (Tian et al., 2007) (Kelzenberg et al., 2008) (Rout et al., 2008) (Fang et al., 2008) (Perraud et al., 2009) as well as by the etching method (Garnett et al., 2008) (Peng et al., 2005). SiNW based photovoltaic devices were experimentally demonstrated. Nearly all the works were concerned with Si wafers as a substrate. However, it should be noted that for competitive solar cells, low cost substrates, such as glass or metal foils are to be preferred. Schematic view of the VLS fabricated structure of the SiNW array solar cells is illustrated on Fig. 31 (a). The n-type SiNWs were prepared by the VLS method on (100) ptype Si substrate (14-22 cm). Device fabrication started from the evaporation of 2-nm thick gold film followed by annealing at 550°C for 10 min under H2 flow to form Au nanocatalyzers. SiNWs were subsequently grown at 500° with SiH4 diluted in H2 as the gas precursor. N-type doping was achieved by adding PH3 to SiH4, with PH3/SiH4 ratio of 2x10- 3 corresponding to a nominal phosphorous density of 1020cm-3. After the VLS growth the gold catalysts were etched off in KI/I2 solution, and the doping impurities were activated by rapid thermal annealing at 750° for 5 min. The SiNW array was then embedded into spinon-glass (SOG) matrix. Indeed, SOG matrix ensures a good mechanical stability of the SiNW array and enables further processing steps, such as front surface planarization and electrical contact deposition. The planarization step is normally performed by the chemicalmechanical polishing. To form the front contacts indium-tin-oxide (ITO) was firstly deposited on planarized SOG surface followed by the deposition of Ni/Al contact grid. As back electrical contact, the sputtered and annealed Al was used. The area of the fabricated SiNW solar cell was 2.3 cm-2.

The sheet resistance of n-type SiNWs embedded into SOG matrix was estimated to be 10-4 /sq. I-V measurements in the dark and under 1-sun illumination (Fig. 31 (b)) indicate a good rectifying junction. The measured ISC, VOC and FF were 17 mA/cm2, 250mV and 44%, respectively, leading to an energy-conversion efficiency of 1.9%. The VOC of Si NW solar cell was shown to be increased up to 580 mV (Peng et al., 2005). The parasitic series resistance found for SiNW solar cells (~5 cm-2) was slightly larger than in the standard 1st generation solar cells (~2 cm-2), however the p-n junction reverse current was of the order of 1 A/cm2 with is about 100 times bigger than in typical Si solar cells (~1 pA/cm2). Such a high pn junction reverse current indicates a high density of localized electronic states within the bandgap, which act as generation-recombination centers. These states may come from contamination of Si by gold which is used as catalyst for VLS growth. Other types of metallic catalysers, like Sn, were also used (Uchiyama et al., 2010).

Silicon-Based Third Generation Photovoltaics 171

Allan, G. & Delerue, C. (2007), Energy transfer between semiconductor nanocrystals:

Andra, G.; Pietsch, M.; Sivakov, V.; Stelzner, Th.; Gawlik, A.; Christiansen, S.& Falk, F.

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235329.

However, for a moment by using this catalyzer it is difficult to achieve the diameter of SiNWs less that 200 nm. The electronic states in the bandgap may also come from a lack of passivation of surface defects. The passivation step is rather crucial for SiNW solar cells, since SiNW have very high SVR ratio and their opto-electronic properties strongly depends on the surface passivation.

Fig. 31. (a) Structure of the SiNW array solar cell. A p-n junction is formed between the ntype SiNWs and the p-type Si substrate; (b) Dark and illuminated I-V measurements of ntype SiNWs on p-type Si substrate (Perraud et al., 2009).

The theoretical value of the efficiency for Si nanowire solar cells is predicted to be as high as 16%, which makes them perfect candidates for higher bandgap bricks in all-Si tandem cell approach. The first prototypes of SiNW solar cells have excellent antireflection capabilities and shown the presence of the photovoltaic effect. However, up today there was no evidence that this photovoltaic effect occurred in a material with an increased bandgap.

#### **5. Conclusions**

Silicon based third generation photovoltaics is a quickly developing field, which integrates the knowledge from material science and photovoltaics. Today the first prototypes of both Si QD solar cells and Si NWs solar cells have already been developed. For a moment they present VOC, ISC and FF values which still lower than those ones of the 1st generation PV cells based on bulk Si – but all these problems are being addressed. It is too prematurely to draw the conclusions while the further optimization steps of the fabrication parameters were not performed. We should not forget that, for example, although the airplane was not invented until the early 20th century, Leonardo da Vinci sketched a flying machine four centuries earlier.

#### **6. References**

Abeles, B.; Pinch, H. L. & Gittleman, J. I. (1975), Percolation conductivity in W-Al2O3 granular metal films, *Phys. Rev. Lett.*, Vol. 35, pp. 247-250.

Aeberhard, U. (2011), Theory and simulation of photogeneration and transport in Si-SiOx superlattice absorbers, *Nanoscale Research Letters*, Vol. 6, p. 242.

However, for a moment by using this catalyzer it is difficult to achieve the diameter of SiNWs less that 200 nm. The electronic states in the bandgap may also come from a lack of passivation of surface defects. The passivation step is rather crucial for SiNW solar cells, since SiNW have very high SVR ratio and their opto-electronic properties strongly

(a) (b)

The theoretical value of the efficiency for Si nanowire solar cells is predicted to be as high as 16%, which makes them perfect candidates for higher bandgap bricks in all-Si tandem cell approach. The first prototypes of SiNW solar cells have excellent antireflection capabilities and shown the presence of the photovoltaic effect. However, up today there was no evidence that this photovoltaic effect occurred in a material with an increased

Silicon based third generation photovoltaics is a quickly developing field, which integrates the knowledge from material science and photovoltaics. Today the first prototypes of both Si QD solar cells and Si NWs solar cells have already been developed. For a moment they present VOC, ISC and FF values which still lower than those ones of the 1st generation PV cells based on bulk Si – but all these problems are being addressed. It is too prematurely to draw the conclusions while the further optimization steps of the fabrication parameters were not performed. We should not forget that, for example, although the airplane was not invented until the early 20th century, Leonardo da Vinci sketched a flying machine four centuries

Abeles, B.; Pinch, H. L. & Gittleman, J. I. (1975), Percolation conductivity in W-Al2O3

Aeberhard, U. (2011), Theory and simulation of photogeneration and transport in Si-SiOx

granular metal films, *Phys. Rev. Lett.*, Vol. 35, pp. 247-250.

superlattice absorbers, *Nanoscale Research Letters*, Vol. 6, p. 242.

Fig. 31. (a) Structure of the SiNW array solar cell. A p-n junction is formed between the ntype SiNWs and the p-type Si substrate; (b) Dark and illuminated I-V measurements of n-

type SiNWs on p-type Si substrate (Perraud et al., 2009).

depends on the surface passivation.

bandgap.

earlier.

**6. References** 

**5. Conclusions** 


Silicon-Based Third Generation Photovoltaics 173

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**9** 

*1,2Malaysia 3Iraq* 

**Optical Insights into Enhancement of Solar Cell Performance Based on Porous Silicon Surfaces** 

The amount of light reflection from the surface is the main obstacle in efficient solar cell performance because reflection is related to the refractive index of the material. For instance, the silicon (Si) refractive index is 3.5, (which can rise by up to 35%), which prevents an electron-hole pair from being generated and could reduce the efficiency of photovoltaic converters. Antireflection coatings ARC are able to reduce surface reflection, increase conversion efficiency, extend the life of converters, and improve the electrophysical and

Porous Si (PS) is attractive in solar cell applications because of its efficient ARC and other properties such as band gap broadening, wide absorption spectrum, and optical transmission range (700–1000 nm). Furthermore, PS can also be used for surface passivation and texturization [2–6]. The potential advantages of PS as an ARC for solar cells include surface passivation and removal of the dead-layer diffused region. Moreover, PS is able to convert higher energy solar

The vibrations, electronic, and optical properties of PS have been studied using various experimental techniques. Of these, the electrochemical etching process is a promising technique for fabricating PS [8–11]. According to the quantum confinement model, a heterojunction can be formed between the Si substrate and porous layers because the latter

Recently, Ben Rabha and Bessais [13] used chemical vapor etching to perform the front PS layer and buried metallic contacts of multicrystalline silicon solar cells to reduce reflectivity to 8% in the 450–950 nm wavelength range, yielding a simple and low-cost technology with 12% conversion efficiency. Yae et al. [14] deposited fine platinum (Pt) particles on multicrystalline n-Si wafers by electroless displacement reaction in a hexachloroplatinic acid solution containing HF. The reflectance of the wafers was reduced from 30% to 6% by the formation of porous layer. Brendel [15] performed electrochemical etching of PS layer into the substrate based on

The present work aims to investigate the effect of PS on performance of Si solar cells. Optical properties such as refractive index and optical dielectric constant are investigated.

homoepitaxial growth of monocrystalline Si films, yielding a module efficiency of 10%.

radiation into spectrum light, which is absorbed more efficiently into bulk Si [7].

has a wider band gap (1.8–2.2 eV) compared with crystalline Si (c-Si) [12].

**1. Introduction** 

characterization of photovoltaic converters [1].

Asmiet Ramizy1,3, Y. Al-Douri2, Khalid Omar1 and Z. Hassan1

 *2Institute of Nano Electronic Engineering, University Malaysia Perlis* 

*1Nano-Optoelectronics Research and Technology Laboratory, School of Physics, Universiti Sains Malaysia, Penang,* 

*3University of Anbar-collage of sciences-physics department,* 


### **Optical Insights into Enhancement of Solar Cell Performance Based on Porous Silicon Surfaces**

Asmiet Ramizy1,3, Y. Al-Douri2, Khalid Omar1 and Z. Hassan1

*1Nano-Optoelectronics Research and Technology Laboratory, School of Physics, Universiti Sains Malaysia, Penang, 2Institute of Nano Electronic Engineering, University Malaysia Perlis 3University of Anbar-collage of sciences-physics department, 1,2Malaysia* 

*3Iraq* 

#### **1. Introduction**

178 Solar Cells – Silicon Wafer-Based Technologies

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The amount of light reflection from the surface is the main obstacle in efficient solar cell performance because reflection is related to the refractive index of the material. For instance, the silicon (Si) refractive index is 3.5, (which can rise by up to 35%), which prevents an electron-hole pair from being generated and could reduce the efficiency of photovoltaic converters. Antireflection coatings ARC are able to reduce surface reflection, increase conversion efficiency, extend the life of converters, and improve the electrophysical and characterization of photovoltaic converters [1].

Porous Si (PS) is attractive in solar cell applications because of its efficient ARC and other properties such as band gap broadening, wide absorption spectrum, and optical transmission range (700–1000 nm). Furthermore, PS can also be used for surface passivation and texturization [2–6]. The potential advantages of PS as an ARC for solar cells include surface passivation and removal of the dead-layer diffused region. Moreover, PS is able to convert higher energy solar radiation into spectrum light, which is absorbed more efficiently into bulk Si [7].

The vibrations, electronic, and optical properties of PS have been studied using various experimental techniques. Of these, the electrochemical etching process is a promising technique for fabricating PS [8–11]. According to the quantum confinement model, a heterojunction can be formed between the Si substrate and porous layers because the latter has a wider band gap (1.8–2.2 eV) compared with crystalline Si (c-Si) [12].

Recently, Ben Rabha and Bessais [13] used chemical vapor etching to perform the front PS layer and buried metallic contacts of multicrystalline silicon solar cells to reduce reflectivity to 8% in the 450–950 nm wavelength range, yielding a simple and low-cost technology with 12% conversion efficiency. Yae et al. [14] deposited fine platinum (Pt) particles on multicrystalline n-Si wafers by electroless displacement reaction in a hexachloroplatinic acid solution containing HF. The reflectance of the wafers was reduced from 30% to 6% by the formation of porous layer. Brendel [15] performed electrochemical etching of PS layer into the substrate based on homoepitaxial growth of monocrystalline Si films, yielding a module efficiency of 10%.

The present work aims to investigate the effect of PS on performance of Si solar cells. Optical properties such as refractive index and optical dielectric constant are investigated.

Optical Insights into Enhancement

of Solar Cell Performance Based on Porous Silicon Surfaces 181

**b** 

**c** 

**a** 

Fig. 2. Solar cells setup (a) p-n junction layers, (b) metal mask, and (c) contact I-V

Ag contact /PS Al contact/PS

**Voltage(V)** -4 -3 -2 -1 0 1 2 3 4

characterization

**Current(A)**




0.0

0.1

0.2

0.3

Enhancing solar cell efficiency can be realized by manipulating back reflected mirrors, and the results are promising for solar cell manufacturing because of the simplicity, lower-cost technology, and suitability for mass production of the method.

#### **2. Experimental procedure**

#### **2.1 PS Structure formation**

An n-type Si wafer with a dimension of 1 cm x 1 cm x 283 µm, (111) orientation, resistivity of 0.75 Ω.cm, and doping concentration of 1.8 x 1017 x cm-3 was etched through an electrochemical process to produce the porous structure. The wafer was placed in an electrolyte solution [hydrofluoric acid (HF): Ethanol, 1:4] with a current density of 60 mA/cm2 at an etching time of 30 min. To produce solar cells on both sides of the PS, the PS wafer was fabricated by electrochemical etching at the current density of 60 mA/cm2 for 15 min on each side.

Before the etching process, the Si substrate was cleaned using the Radio Corporation of America (RCA) method to remove the oxide layer, and then immersed in HF acid to remove the native oxide. The electrochemical cell is made of Teflon and has a circular aperture with a radius of 0.4 cm, with the silicon wafer sealed below. The cell consists of a two-electrode system with the Si wafer as the anode and platinum as the cathode, as shown in Fig. 1. The process was carried out at room temperature. After etching, all samples were rinsed with ethanol and air-dried. Surface morphology and structural properties of the samples under treatment were characterized using scanning electron microscopy (SEM). The PS optical reflectance was obtained using an optical reflectometer (Filmetrics F20) with an integrating sphere. Fourier transform infrared spectroscopy (FTIR) of the PS samples was performed, and photoluminescence (PL) spectroscopy was performed at room temperature using He-Cd laser (λ=325 nm).

Fig. 1. Schematic of the electrochemical etching setup

Enhancing solar cell efficiency can be realized by manipulating back reflected mirrors, and the results are promising for solar cell manufacturing because of the simplicity, lower-cost

An n-type Si wafer with a dimension of 1 cm x 1 cm x 283 µm, (111) orientation, resistivity of 0.75 Ω.cm, and doping concentration of 1.8 x 1017 x cm-3 was etched through an electrochemical process to produce the porous structure. The wafer was placed in an electrolyte solution [hydrofluoric acid (HF): Ethanol, 1:4] with a current density of 60 mA/cm2 at an etching time of 30 min. To produce solar cells on both sides of the PS, the PS wafer was fabricated by electrochemical etching at the current density of 60 mA/cm2 for 15

Before the etching process, the Si substrate was cleaned using the Radio Corporation of America (RCA) method to remove the oxide layer, and then immersed in HF acid to remove the native oxide. The electrochemical cell is made of Teflon and has a circular aperture with a radius of 0.4 cm, with the silicon wafer sealed below. The cell consists of a two-electrode system with the Si wafer as the anode and platinum as the cathode, as shown in Fig. 1. The process was carried out at room temperature. After etching, all samples were rinsed with ethanol and air-dried. Surface morphology and structural properties of the samples under treatment were characterized using scanning electron microscopy (SEM). The PS optical reflectance was obtained using an optical reflectometer (Filmetrics F20) with an integrating sphere. Fourier transform infrared spectroscopy (FTIR) of the PS samples was performed, and photoluminescence (PL) spectroscopy was performed at room temperature using He-

technology, and suitability for mass production of the method.

**2. Experimental procedure 2.1 PS Structure formation** 

min on each side.

Cd laser (λ=325 nm).

Fig. 1. Schematic of the electrochemical etching setup

Fig. 2. Solar cells setup (a) p-n junction layers, (b) metal mask, and (c) contact I-V characterization

Optical Insights into Enhancement

the formation of PS.

**Reflectance**

**0.02**

**0.04**

**0.06**

**0.08**

**0.10**

**0.12**

**0.14**

**0.16**

**0.18**

for preferred pore walls during the etching processing.

Fig. 5. Reflectance spectra for PS N (100) and P (100)

of Solar Cell Performance Based on Porous Silicon Surfaces 183

The SEM images in Figs. 3 (a) and (b) reveal the grains of the surface texturing with similar grain geometry, which is caused by the isotropic character of the HF/ethanol etching and the optimal conditions for current density and etching time. Moreover, similar morphology is apparent in the SEM images of all etched surfaces. The depth of porosity increased with the N-type silicon wafers compared with P-type, as shown in Figs. 4 (a) and (b), which may be due the abundance of electron-hole pair charge carriers that lead to extra chemical interaction between the electrolyte solution and the surface of the silicon wafer, resulting in

The surface reflections of PS N (100) show a reduction of incoming light reflection and an increase in capturing the light of the wide wavelength range compared with PS P (100) reflection, as illustrated in Fig. 5. This caused the N (100) surface formed to be preferentially dissolved because of the preferred pore tips. However, the P (100) surface is most effective

Figure 6 reveals the Raman spectra of bulk silicon, which show a sharp line in the spectra with FWHM of 3.5 cm-1 shifted by 522 cm-1 relative to the laser line incident. However, the PS spectra became broader relative to the 517 cm-1 sharp with FWHM of 8.2 cm-1 in PS P (100) and shifted to 510 cm-1 with (FWHM) of 17.3 cm-1 in PS N (100), which is attributed to the quantum confinement effect on electronic wave function of silicon nanocrystals [16] Figure 7 shows the PL spectrum of PS P (100) at 698.9 nm (1.77 eV) with FWHM of about 140 nm. In PS N (100), PL at 670.35 nm (1.82 eV) with FWHM of 123 nm is evident. The PL output intensity in the N-type becomes stronger because of an increase in the number of emitted photons on the porous surface. The peak shift increase with N-type PS compared with P-type wafers, which can be attributed to the abundance of charge carriers, enhances the spontaneous etching rate of silicon. The particles are confined into a lower dimension, leading to higher

efficiency. Without these charge carriers, the etching process substantially slows down.

**Wavelength (nm) 300 400 500 600 700 800 900 1000 1100**

**PS P(100) PS N(100)**

**3. Effect of doping-type of porous on silicon solar cell performance** 

#### **2.2 Solar cell fabrication**

After the (RCA) cleaning and oxidation, the silicon wafer underwent spin-coating. A liquid containing photoresistant material was placed at the center of the wafer. The spinning process was conducted at room temperature at the speed of 300 rpm for 20 s. After spin-coating, the wafer was placed back into the furnace for 20 min at 200 °C to remove moisture. The mask was designed by the photoplotter technique placed directly above the sample and exposed to UVlight for 25 s to form a patterned coating on the surface. Doping diffusion was carried out using a tube furnace at the temperature of 1100 °C for 60 min using N2 flow gas. The top surface area of the wafer was doped with boron to be P-type. Prior to the contact evaporating process, the oxidation layer was removed using an etching solution of NH4F:H2O, and then mixed with HF with a mole ratio of 1:7. Aluminum evaporation was used for the back metal contact, whereas silver was used for front metallization. Figure 1 shows the setup of the solar cells. Contact annealing was performed at 400 °C for 20 min to pledge ohmic contact (see Fig. 1), as well as to improve the contact properties. A back reflected mirror with reflectivity >89% was used to enhance solar cell efficiency. The structure of the PS solar cells consists of a metal mask contact of grid pattern with a finger width of 300 µm and finger spacing of 600 µm.

The fabricated device was analyzed using current-voltage (I-V) measurement, with the lens placed under solar simulator illumination. A solar cell using unetched c-Si was fabricated under the same conditions for comparison.

Fig. 3. SEM images of PS formed on (a) N (100), (b) P (100)

Fig. 4. Cross-sectional SEM images of PS on (a) both sides of the c-Si wafer and (b) on the 47 polished front

After the (RCA) cleaning and oxidation, the silicon wafer underwent spin-coating. A liquid containing photoresistant material was placed at the center of the wafer. The spinning process was conducted at room temperature at the speed of 300 rpm for 20 s. After spin-coating, the wafer was placed back into the furnace for 20 min at 200 °C to remove moisture. The mask was designed by the photoplotter technique placed directly above the sample and exposed to UVlight for 25 s to form a patterned coating on the surface. Doping diffusion was carried out using a tube furnace at the temperature of 1100 °C for 60 min using N2 flow gas. The top surface area of the wafer was doped with boron to be P-type. Prior to the contact evaporating process, the oxidation layer was removed using an etching solution of NH4F:H2O, and then mixed with HF with a mole ratio of 1:7. Aluminum evaporation was used for the back metal contact, whereas silver was used for front metallization. Figure 1 shows the setup of the solar cells. Contact annealing was performed at 400 °C for 20 min to pledge ohmic contact (see Fig. 1), as well as to improve the contact properties. A back reflected mirror with reflectivity >89% was used to enhance solar cell efficiency. The structure of the PS solar cells consists of a metal mask contact of grid pattern with a finger width of 300 µm and finger spacing of 600 µm. The fabricated device was analyzed using current-voltage (I-V) measurement, with the lens placed under solar simulator illumination. A solar cell using unetched c-Si was fabricated

a

b

b

a

**2.2 Solar cell fabrication** 

under the same conditions for comparison.

Fig. 3. SEM images of PS formed on (a) N (100), (b) P (100)

polished front

Fig. 4. Cross-sectional SEM images of PS on (a) both sides of the c-Si wafer and (b) on the 47

#### **3. Effect of doping-type of porous on silicon solar cell performance**

The SEM images in Figs. 3 (a) and (b) reveal the grains of the surface texturing with similar grain geometry, which is caused by the isotropic character of the HF/ethanol etching and the optimal conditions for current density and etching time. Moreover, similar morphology is apparent in the SEM images of all etched surfaces. The depth of porosity increased with the N-type silicon wafers compared with P-type, as shown in Figs. 4 (a) and (b), which may be due the abundance of electron-hole pair charge carriers that lead to extra chemical interaction between the electrolyte solution and the surface of the silicon wafer, resulting in the formation of PS.

The surface reflections of PS N (100) show a reduction of incoming light reflection and an increase in capturing the light of the wide wavelength range compared with PS P (100) reflection, as illustrated in Fig. 5. This caused the N (100) surface formed to be preferentially dissolved because of the preferred pore tips. However, the P (100) surface is most effective for preferred pore walls during the etching processing.

Figure 6 reveals the Raman spectra of bulk silicon, which show a sharp line in the spectra with FWHM of 3.5 cm-1 shifted by 522 cm-1 relative to the laser line incident. However, the PS spectra became broader relative to the 517 cm-1 sharp with FWHM of 8.2 cm-1 in PS P (100) and shifted to 510 cm-1 with (FWHM) of 17.3 cm-1 in PS N (100), which is attributed to the quantum confinement effect on electronic wave function of silicon nanocrystals [16]

Figure 7 shows the PL spectrum of PS P (100) at 698.9 nm (1.77 eV) with FWHM of about 140 nm. In PS N (100), PL at 670.35 nm (1.82 eV) with FWHM of 123 nm is evident. The PL output intensity in the N-type becomes stronger because of an increase in the number of emitted photons on the porous surface. The peak shift increase with N-type PS compared with P-type wafers, which can be attributed to the abundance of charge carriers, enhances the spontaneous etching rate of silicon. The particles are confined into a lower dimension, leading to higher efficiency. Without these charge carriers, the etching process substantially slows down.

Fig. 5. Reflectance spectra for PS N (100) and P (100)

Optical Insights into Enhancement

of Solar Cell Performance Based on Porous Silicon Surfaces 185

Fig. 8. Current-voltage characteristics of PS N (100) and P (100) solar cells

Table 1. Fill factor (FF) and efficiency ( )

**silicon surfaces** 

parameter.

Samples Vm(V) Im(mA) Voc(V) Isc (mA) FF Efficiency(

of PS N (100) and P (100)

Si as- grown 0.26 5.09 0.34 5.1 0.77 3.34 % P-type PS 0.33 10.03 0.41 10.2 0.81 8.4 % N-type PS 0.36 12.1 0.42 12.2 0.85 10.85 %

**4. New optical features to enhance solar cell performance based on porous** 

The efficiency of photovoltaic energy conversion must be enhanced to reduce the cost of solar cell modules for energy generation. In this process, photons from solar radiation fall on a solar cell that generate electron and hole pairs, which are then collected at the contact points. However, a drawback of solar photovoltaic energy conversion is that most of the semiconducting materials used are sensitive only to a part of the solar radiation spectrum. Figure 9a shows cross-sectional SEM images of chemically treated samples. These images show that the thickness is uniform throughout the obtained porous layer, indicating that the etching process forms a uniform porous density layer on the surface. The SEM images in Figs. 9 (b) and (c) illustrate the treated surface with similar grain geometry because of the isotropic character of HF/ethanol etching and the optimal conditions of the current density and etching time. The images show that the entire surface of the sample is etched, and that most of the pores are spherical. In addition to the short-branched pores, the porous surface formed on the front polished side has discrete pores. In contrast, the PS surface formed on the unpolished backside is shaped in small pores, which could be attributed to an increase in surface roughness for the unpolished backside that is proportional to the etching

)

Fig. 6. Raman spectra of PS prepared by electrochemical etching

Fig. 7. PL spectra of PS prepared by electrochemical etching

The experimental data in Fig. 8 and Table 1 show that the solar cell with PS N (100) increases the short-circuit current to 12.2, open current voltage to 0.36, and conversation efficiency to 10.85 in comparison to the solar cell fabricated with PS P (100).

Fig. 6. Raman spectra of PS prepared by electrochemical etching

Fig. 7. PL spectra of PS prepared by electrochemical etching

**Intensity(a.u)**

0

50

100

150

200

250

10.85 in comparison to the solar cell fabricated with PS P (100).

The experimental data in Fig. 8 and Table 1 show that the solar cell with PS N (100) increases the short-circuit current to 12.2, open current voltage to 0.36, and conversation efficiency to

**Wavelength(nm)** 400 500 600 700 800

**N(100) P(100)**

Fig. 8. Current-voltage characteristics of PS N (100) and P (100) solar cells


Table 1. Fill factor (FF) and efficiency ( ) of PS N (100) and P (100)

#### **4. New optical features to enhance solar cell performance based on porous silicon surfaces**

The efficiency of photovoltaic energy conversion must be enhanced to reduce the cost of solar cell modules for energy generation. In this process, photons from solar radiation fall on a solar cell that generate electron and hole pairs, which are then collected at the contact points. However, a drawback of solar photovoltaic energy conversion is that most of the semiconducting materials used are sensitive only to a part of the solar radiation spectrum.

Figure 9a shows cross-sectional SEM images of chemically treated samples. These images show that the thickness is uniform throughout the obtained porous layer, indicating that the etching process forms a uniform porous density layer on the surface. The SEM images in Figs. 9 (b) and (c) illustrate the treated surface with similar grain geometry because of the isotropic character of HF/ethanol etching and the optimal conditions of the current density and etching time. The images show that the entire surface of the sample is etched, and that most of the pores are spherical. In addition to the short-branched pores, the porous surface formed on the front polished side has discrete pores. In contrast, the PS surface formed on the unpolished backside is shaped in small pores, which could be attributed to an increase in surface roughness for the unpolished backside that is proportional to the etching parameter.

Optical Insights into Enhancement

reflectometry.

of Solar Cell Performance Based on Porous Silicon Surfaces 187

Figure 10 shows the three-dimensional topographic images of the PS etched surfaces with the pyramidal shape distributed over the entire surface. The pyramidal shape indicates that the increase in surface roughness is because of the effect of the etching parameters on surface characterization. The high degree of roughness of the PS surface implies the possibility of using the porous layer as an ARC because the surface texture reduces light reflection. The scattering in PS is possibly because of the roughness in relation to the thickness of the porous layer [17], whereas the attenuation of the reflectivity is because of scattering and transmission at the porous and bulk interfaces [17, 18]. This parameter is important in enhancing the photoconversion process for solar cells, which confirms that PS can be utilized as an ARC. Meanwhile, the reflection measurement was taken using optical

(a)

(b) (c)

Fig. 10. AFM images of PS (a) as-grown, (b) polished front side, and (c) unpolished back side The results in Fig. 11 demonstrate that the PS that formed on both sides has lower reflectivity value compared with results of other studies [13–15]. These results were

confirmed by the absorption spectrum, as shown in Fig. 12.

Fig. 9. Cross-sectional SEM images of PS on (a) both sides of the c-Si wafer, (b) on the polished front side c-Si wafer, and (c) on the unpolished backside c-Si wafer

 

(a)

 

 **(b)** 

Fig. 9. Cross-sectional SEM images of PS on (a) both sides of the c-Si wafer, (b) on the

polished front side c-Si wafer, and (c) on the unpolished backside c-Si wafer

Polished side

Bulk silicon

Unpolished side

(b)

(c)

Figure 10 shows the three-dimensional topographic images of the PS etched surfaces with the pyramidal shape distributed over the entire surface. The pyramidal shape indicates that the increase in surface roughness is because of the effect of the etching parameters on surface characterization. The high degree of roughness of the PS surface implies the possibility of using the porous layer as an ARC because the surface texture reduces light reflection. The scattering in PS is possibly because of the roughness in relation to the thickness of the porous layer [17], whereas the attenuation of the reflectivity is because of scattering and transmission at the porous and bulk interfaces [17, 18]. This parameter is important in enhancing the photoconversion process for solar cells, which confirms that PS can be utilized as an ARC. Meanwhile, the reflection measurement was taken using optical reflectometry.

Fig. 10. AFM images of PS (a) as-grown, (b) polished front side, and (c) unpolished back side The results in Fig. 11 demonstrate that the PS that formed on both sides has lower reflectivity value compared with results of other studies [13–15]. These results were confirmed by the absorption spectrum, as shown in Fig. 12.

Optical Insights into Enhancement

0.50 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.08

A

%R

of Solar Cell Performance Based on Porous Silicon Surfaces 189

Figures 13 and 14 show the FTIR spectra of the silicon as grown and PS as a function of reflectivity and absorptivity, respectively. The results show an agreement with the results demonstrated in Figs. 4 and 5, indicating that our PS sample has high absorption and low reflection spectra compared with the as-grown sample. This may be attributed to the increase of porosity that leads to an increase in PS density over the surface of the sample.

7800.0 7000 6000 5000 4000 3000 2000 1500 1000 500 370.0

**PS backside**

cm-1

7800.0 7000 6000 5000 4000 3000 2000 1500 1000 500 370.0

cm-1

Fig. 13. FTIR reflection spectra of Si (as grown) and PS of both sides

**PS frontside**

**PS frontside**

**PS backside**

**Si as-grown**

**Si as-grown**

Fig. 14. FTIR absorption spectra of Si (as grown) and PS of both sides

Fig. 11. The reflectance spectra of Si (as grown) and PS of both sides

Fig. 12. The reflectance spectra of Si (as grown) and PS of both sides.

Fig. 11. The reflectance spectra of Si (as grown) and PS of both sides

**Absorption**

**0.5**

**0.6**

**0.7**

**0.8**

**0.9**

**1.0**

**0.0**

**0.1**

**0.2**

**0.3**

**0.4**

**0.5**

**Reflection**

Fig. 12. The reflectance spectra of Si (as grown) and PS of both sides.

**Wavelegth(nm) 300 400 500 600 700 800 900 1000 1100**

**Wavelength (nm) 300 400 500 600 700 800 900 1000 1100**

> **Si as-grown PS front side PS back side**

**Si as-grown PS front side** Figures 13 and 14 show the FTIR spectra of the silicon as grown and PS as a function of reflectivity and absorptivity, respectively. The results show an agreement with the results demonstrated in Figs. 4 and 5, indicating that our PS sample has high absorption and low reflection spectra compared with the as-grown sample. This may be attributed to the increase of porosity that leads to an increase in PS density over the surface of the sample.

Fig. 13. FTIR reflection spectra of Si (as grown) and PS of both sides

Fig. 14. FTIR absorption spectra of Si (as grown) and PS of both sides

Optical Insights into Enhancement

Samples *R*<sup>s</sup>

PS formed on the

PS formed on both

PS on both sides

(η) of Si and PS

[21].

(Ω)

*R*sh (kΩ)

of Solar Cell Performance Based on Porous Silicon Surfaces 191

Fig. 16. Current-voltage (IV) characteristics of Si (as grown) and Si of different sides

*V*<sup>m</sup> (V)

Si as-grown 70.4 2.98 0.26 6.71 0.31 6.72 83 4.34

unpolished side 7.14 149.8 0.41 7.24 0.43 8.83 78 7.38

sides 7.9 4.86 0.44 11.65 0.45 12.37 84 12.75

with lens 2.81 18.77 0.41 15.12 0.49 15.5 88 15.4

where R is reflectivity. The refractive index *n* is an important physical parameter related to microscopic atomic interactions. Theoretically, the two different approaches in viewing this subject are the refractive index related to density and the local polarizability of these entities

In contrast, the crystalline structure represented by a delocalized picture, *n* , is closely related to the energy band structure of the material, complicated quantum mechanical analysis requirements, and the obtained results. Many attempts have been made to relate

Table 2. Investigated series resistance Rs, shunt resistance Rsh, maximum voltage Vm, maximum current Im, open-circuit voltage Voc, short-circuit current Isc, FF, and efficiency

*I*m (mA) *V*oc (V) *I*sc

(mA) *FF* (%) Efficiency

() (%)

Figure 15 illustrates the PL spectrum of the PS formed on the unpolished side, revealing a peak at 681.3 nm (1.82 eV) with FWHM of 330 mV. For the PS formed on the front polished side, the peak located at 666.9 nm (1.86 eV) with a FWHM of approximately 180 mV is obtained. The PS formed on the front polished side has a blue shift luminescence, indicating that the particles are confined into the lower dimension. The energy gaps of the PS increased to 1.82 and 1.86, respectively, and the broadening of the energy gap occurs with a decrease in the crystallite size.

Fig. 15. PL spectra of PS on both sides of the c-Si wafer

The efficiency of the solar cells fabricated with PS formed on both sides of the wafer increased compared with one side of the PS and bulk Si solar cells, respectively, as shown in Fig. 16. This can be attributed to an increase in the open circuit voltage without losing the short circuit current of the solar cells, as shown in Table 2. The porous surface texturing properties are able to enhance and increase the conversion efficiency of Si solar cells, and the resulting efficiency from this procedure is more promising compared with the other solar cells fabricated under similar conditions [19].

#### **5. Optical properties**

The results in Figs. 4 and 6 are used to calculate the refractive index and optical dielectric constant of Si and PS using the following equation [20]:

$$m = \frac{1 + R^{1/2}}{1 - R^{1/2}} \tag{1}$$

Figure 15 illustrates the PL spectrum of the PS formed on the unpolished side, revealing a peak at 681.3 nm (1.82 eV) with FWHM of 330 mV. For the PS formed on the front polished side, the peak located at 666.9 nm (1.86 eV) with a FWHM of approximately 180 mV is obtained. The PS formed on the front polished side has a blue shift luminescence, indicating that the particles are confined into the lower dimension. The energy gaps of the PS increased to 1.82 and 1.86, respectively, and the broadening of the energy gap occurs with a decrease

The efficiency of the solar cells fabricated with PS formed on both sides of the wafer increased compared with one side of the PS and bulk Si solar cells, respectively, as shown in Fig. 16. This can be attributed to an increase in the open circuit voltage without losing the short circuit current of the solar cells, as shown in Table 2. The porous surface texturing properties are able to enhance and increase the conversion efficiency of Si solar cells, and the resulting efficiency from this procedure is more promising compared with the other solar

The results in Figs. 4 and 6 are used to calculate the refractive index and optical dielectric

1 1

*n*

1/2 1/2

(1)

*R*

*R*

in the crystallite size.

Fig. 15. PL spectra of PS on both sides of the c-Si wafer

constant of Si and PS using the following equation [20]:

cells fabricated under similar conditions [19].

**5. Optical properties** 

Fig. 16. Current-voltage (IV) characteristics of Si (as grown) and Si of different sides


Table 2. Investigated series resistance Rs, shunt resistance Rsh, maximum voltage Vm, maximum current Im, open-circuit voltage Voc, short-circuit current Isc, FF, and efficiency (η) of Si and PS

where R is reflectivity. The refractive index *n* is an important physical parameter related to microscopic atomic interactions. Theoretically, the two different approaches in viewing this subject are the refractive index related to density and the local polarizability of these entities [21].

In contrast, the crystalline structure represented by a delocalized picture, *n* , is closely related to the energy band structure of the material, complicated quantum mechanical analysis requirements, and the obtained results. Many attempts have been made to relate

Optical Insights into Enhancement

**6. Ionicity character** 

[41]:

of Solar Cell Performance Based on Porous Silicon Surfaces 193

The systematic theoretical studies of the electronic structures, optical properties, and charge distributions have already been reported in the literature [34,35]. However, detailed calculations on covalent and ionic bonds have not reached the same degree of a priori completeness as what can be attained in the case of metallic properties. The difficulty in defining the ionicity lies in transforming a qualitative or verbal concept into a quantitative, mathematical formula. Several empirical approaches have been developed [36] in yielding analytic results that can be used for exploring the trends in materials properties. In many applications, these empirical approaches do not give highly accurate results for each specific material; however, they still can be very useful. The stimulating assumption of Phillips [36] concerning the relationship of the macroscopic (dielectric constant, structure) and the microscopic (band gap, covalent, and atomic charge densities) characteristics of a covalent crystal is based essentially on the isotropic model of a covalent semiconductor, whereas Christensen et al. [37] performed self-consistent calculations and used model potentials derived from a realistic GaAs potential where additional external potentials were added to the anion and cation sites. However, in general, the ionicities found by Christensen et al. tend to be somewhat larger than those found by Phillips. In addition, Garcia and Cohen [38] achieved the mapping of the ionicity scale by an unambiguous procedure based on the measure of the asymmetry of the first principle valence charge distribution [39]. As for the Christensen scale, their results were somewhat larger than those of the Phillips scale. Zaoui et al. [40] established an empirical formula for the calculation of ionicity based on the measure of the asymmetry of the total valence charge density, and their results are in agreement with those of the Phillips scale. In the present work, the ionicity, fi, was calculated using different formulas [41], and the theory yielded formulas with three attractive features. Only the energy gap EgΓX was required as the input, the computation of fi itself was trivial, and the accuracy of the results reached that of ab initio calculations. This option is attractive because it considers the hypothetical structure and simulation of experimental conditions that are difficult to achieve in the laboratory (e.g., very high pressure). The goal of the current study is to understand how qualitative concepts, such as ionicity, can be related to energy gap EgΓX with respect to the nearest-neighbor distance, d, cohesive energy, Ecoh, and refractive index, n0. Our calculations are based on the energy gap EgΓX reported previously [34,42–45], and the energy gap that follows chemical trends is described by a homopolar energy gap. Numerous attempts have been made to face the differences between energy levels. Empirical pseudopotential methods based on optical spectra encountered the same problems using an elaborate (but not necessarily more accurate) study based on one-electron atomic or crystal potential. As mentioned earlier, d, Ecoh, and n0 have been reported elsewhere for Si and PS. One reason for presenting these data in the present work is that the validity of our calculations, in principle, is not restricted in space. Thus, they will no doubt prove valuable for future work in this field. An important observation for studying ionicity, *<sup>i</sup> f* , is the distinguished difference between the values of the energy gaps of the semiconductors, EgΓX, as seen in Table 2; hence, the energy gaps EgΓX are predominantly dependent on fi . The differences between the energy gaps Egrx have led us to consider these models, and the bases of our models are the energy gaps, EgΓX, as seen in Table 4. The fitting of these data gives the following empirical formulas

the refractive index and the energy gap Eg through simple relationships [22–27]. However, these relationships of *n* are independent of temperature and incident photon energy. Here, the various relationships between *n* and *Eg* are reviewed. Ravindra et al. [27] suggested different relationships between the band gap and the high frequency refractive index and presented a linear form of *n* as a function of *Eg* :

$$
\varepsilon\_{\text{ill}} = \alpha + \beta \varepsilon\_{\text{g}} \,\prime \tag{2}
$$

where α = 4.048 and β = −0.62 eV−1.

To be inspired by the simple physics of light refraction and dispersion, Herve and Vandamme [28] proposed the empirical relation as

$$m = \sqrt{1 + \left(\frac{A}{E\_{\mathcal{S}} + B}\right)^2} \quad \text{or} \tag{3}$$

where A = 13.6 eV and B = 3.4 eV. Ghosh et al. [29] took a different approach to the problem by considering the band structure and quantum-dielectric formulations of Penn [30] and Van Vechten [31]. Introducing A as the contribution from the valence electrons and B as a constant additive to the lowest band gap Eg, the expression for the high-frequency refractive index is written as

$$\left(\mu^2 - 1 = \frac{A}{\left(E\_{\mathcal{S}} + B\right)^2}\right) \tag{4}$$

where A = 25Eg + 212, B = 0.21Eg + 4.25, and (Eg+B) refers to an appropriate average energy gap of the material. Thus, these three models of variation *n* with energy gap have been calculated. The calculated refractive indices of the end-point compounds are shown in Table 3, with the optical dielectric constant calculated using <sup>2</sup> *n* [32], which is dependent on the refractive index. In Table 1, the calculated values of using the three models are also investigated. Increasing the porosity percentage from 60% (front side) to 80% (back side) uses weight measurements [33] that lead to a decreasing refractive index. As with Ghosh et al. [29], this is more appropriate for studying porous silicon solar cell optical properties, which showed lower reflectivity and more absorption as compared to other models.


aRef. [27], bRef. [28], cRef. [29], dRef. [20] exp. eusing Equation (1)

Table 3. Calculated refractive indices for Si and PS using Ravindra et al. [27], Herve and Vandamme [28], and Ghosh et al. [29] models compared with others that corresponds to the optical dielectric constant

#### **6. Ionicity character**

192 Solar Cells – Silicon Wafer-Based Technologies

the refractive index and the energy gap Eg through simple relationships [22–27]. However, these relationships of *n* are independent of temperature and incident photon energy. Here, the various relationships between *n* and *Eg* are reviewed. Ravindra et al. [27] suggested different relationships between the band gap and the high frequency refractive index and

To be inspired by the simple physics of light refraction and dispersion, Herve and

*g A*

where A = 13.6 eV and B = 3.4 eV. Ghosh et al. [29] took a different approach to the problem by considering the band structure and quantum-dielectric formulations of Penn [30] and Van Vechten [31]. Introducing A as the contribution from the valence electrons and B as a constant additive to the lowest band gap Eg, the expression for the high-frequency refractive

*E B* 

*E B*

calculated using <sup>2</sup>

3.35a 2.91b 2.89c 3.46d 3.46e

3.17a 2.79b 2.77c 1.8e

2.94a 2.68b 2.66c 2.38e

Table 3. Calculated refractive indices for Si and PS using Ravindra et al. [27], Herve and Vandamme [28], and Ghosh et al. [29] models compared with others that corresponds to the

*A*

<sup>2</sup> 1 *g*

where A = 25Eg + 212, B = 0.21Eg + 4.25, and (Eg+B) refers to an appropriate average energy gap of the material. Thus, these three models of variation *n* with energy gap have been calculated. The calculated refractive indices of the end-point compounds are shown in Table 3,

investigated. Increasing the porosity percentage from 60% (front side) to 80% (back side) uses weight measurements [33] that lead to a decreasing refractive index. As with Ghosh et al. [29], this is more appropriate for studying porous silicon solar cell optical properties, which showed

2

*Eg* , (2)

, (3)

, (4)

*n* [32], which is dependent on

using the three models are also

11.22a 8.46b 8.35c 11.97e

10.04a 7.78b 7.67c 3.24e

8.64a 7.18b 7.07c 5.66e

*n* 

1

*n*

2

*n*

lower reflectivity and more absorption as compared to other models.

the refractive index. In Table 1, the calculated values of

Samples *n*

aRef. [27], bRef. [28], cRef. [29], dRef. [20] exp. eusing Equation (1)

presented a linear form of *n* as a function of *Eg* :

Vandamme [28] proposed the empirical relation as

where α = 4.048 and β = −0.62 eV−1.

with the optical dielectric constant

PS formed on the unpolished side

PS formed on the front polished

optical dielectric constant

index is written as

Si

side

The systematic theoretical studies of the electronic structures, optical properties, and charge distributions have already been reported in the literature [34,35]. However, detailed calculations on covalent and ionic bonds have not reached the same degree of a priori completeness as what can be attained in the case of metallic properties. The difficulty in defining the ionicity lies in transforming a qualitative or verbal concept into a quantitative, mathematical formula. Several empirical approaches have been developed [36] in yielding analytic results that can be used for exploring the trends in materials properties. In many applications, these empirical approaches do not give highly accurate results for each specific material; however, they still can be very useful. The stimulating assumption of Phillips [36] concerning the relationship of the macroscopic (dielectric constant, structure) and the microscopic (band gap, covalent, and atomic charge densities) characteristics of a covalent crystal is based essentially on the isotropic model of a covalent semiconductor, whereas Christensen et al. [37] performed self-consistent calculations and used model potentials derived from a realistic GaAs potential where additional external potentials were added to the anion and cation sites. However, in general, the ionicities found by Christensen et al. tend to be somewhat larger than those found by Phillips. In addition, Garcia and Cohen [38] achieved the mapping of the ionicity scale by an unambiguous procedure based on the measure of the asymmetry of the first principle valence charge distribution [39]. As for the Christensen scale, their results were somewhat larger than those of the Phillips scale. Zaoui et al. [40] established an empirical formula for the calculation of ionicity based on the measure of the asymmetry of the total valence charge density, and their results are in agreement with those of the Phillips scale. In the present work, the ionicity, fi, was calculated using different formulas [41], and the theory yielded formulas with three attractive features. Only the energy gap EgΓX was required as the input, the computation of fi itself was trivial, and the accuracy of the results reached that of ab initio calculations. This option is attractive because it considers the hypothetical structure and simulation of experimental conditions that are difficult to achieve in the laboratory (e.g., very high pressure). The goal of the current study is to understand how qualitative concepts, such as ionicity, can be related to energy gap EgΓX with respect to the nearest-neighbor distance, d, cohesive energy, Ecoh, and refractive index, n0. Our calculations are based on the energy gap EgΓX reported previously [34,42–45], and the energy gap that follows chemical trends is described by a homopolar energy gap. Numerous attempts have been made to face the differences between energy levels. Empirical pseudopotential methods based on optical spectra encountered the same problems using an elaborate (but not necessarily more accurate) study based on one-electron atomic or crystal potential. As mentioned earlier, d, Ecoh, and n0 have been reported elsewhere for Si and PS. One reason for presenting these data in the present work is that the validity of our calculations, in principle, is not restricted in space. Thus, they will no doubt prove valuable for future work in this field. An important observation for studying ionicity, *<sup>i</sup> f* , is the distinguished difference between the values of the energy gaps of the semiconductors, EgΓX, as seen in Table 2; hence, the energy gaps EgΓX are predominantly dependent on fi . The differences between the energy gaps Egrx have led us to consider these models, and the bases of our models are the energy gaps, EgΓX, as seen in Table 4. The fitting of these data gives the following empirical formulas [41]:

Optical Insights into Enhancement

physical properties of such compounds.

**7. Material stiffness** 

of Solar Cell Performance Based on Porous Silicon Surfaces 195

The difficulty involved with such calculations resides with the lack of a theoretical framework that can describe the physical properties of crystals. Generally speaking, any definition of ionicity is likely to be imperfect. Although we may argue that, for many of these compounds, the empirically calculated differences are of the same order as the differences between the reported measured values, these trends are still expected to be real [47]. The unchanged ionicity characters of bulk Si and PS are noticed. In conclusion, the empirical models obtained for the ionicity give results in good agreement with the results of other scales, which in turn demonstrate the validity of our models to predict some other

The bulk modulus is known as a reflectance of the crucial material stiffness in different industries. Many authors [50–55] have made various efforts to explore the thermodynamic properties of solids, particularly in examining the thermodynamic properties such as the inter-atomic separation and the bulk modulus of solids with different approximations and best-fit relations [52–55]. Computing the important number of structural and electronic properties of solids with great accuracy has now become possible, even though the ab initio calculations are complex and require significant effort. Therefore, additional empirical approaches have been developed [36, 47] to compute properties of materials. In many cases, the empirical methods offer the advantage of applicability to a broad class of materials and to illustrate trends. In many applications, these empirical approaches do not provide highly accurate results for each specific material; however, they are still very useful. Cohen [46] established an empirical formula for calculating bulk modulus B0 based on the nearestneighbor distance, and the result is in agreement with the experimental values. Lam et al. [56] derived an analytical expression for the bulk modulus from the total energy that gives similar numerical results even though this expression is different in structure from the empirical formula. Furthermore, they obtained an analytical expression for the pressure derivative B0 of the bulk modulus. Meanwhile, our group [57] used a concept based on the energy gap along Γ-X and transition pressure to establish an empirical formula for the calculation of the bulk modulus, the results of which are in good agreement with the experimental data and other calculations. In the present work, we have established an empirical formula for the calculation of bulk modulus B0 of a specific class of materials, and the theory yielded a formula with three attractive features. Apparently, only the energy gap along Γ -X and transition pressure are required as an input, and the computation of B0 in itself is trivial. The consideration of the hypothetical structure and simulation of the

experimental conditions are required to make practical use of this formula.

The aim of the present study is to determine how a qualitative concept, such as the bulk modulus, can be related to the energy gap. We [57] obtained a simple formula for the bulk moduli of diamond and zinc-blende solids using scaling arguments for the relevant bonding and volume. The dominant effect in these materials has been argued to be the degree of covalence, as characterized by the homopolar gap, Eh of Phillips, [36] and the gap along Γ-X [57]. Our calculation is based upon the energy gap along Γ-X which has been reported previously [42–45], and the energy gaps that follow chemical trends are described by homopolar and heteropolar energy gaps. Empirical pseudopotential methods based on

$$\mathcal{L}f\_i = \mathcal{L}\left(\frac{\left(d \ne \mathcal{E}\_{\mathcal{S}^{\Gamma X}}\right)}{\mathbf{4}}\right) \tag{5}$$

$$f\_i = \mathcal{X}\left(\frac{\left(E\_{\text{coh}} \ne E\_{\text{g\Gamma}X}\right)}{\mathbf{2}}\right) \tag{6}$$

$$f\_i = \lambda \left(\frac{\left(n\_0 \,/\, E\_{g\Gamma \mathcal{X}}\right)}{4}\right) \tag{7}$$

where EgΓX is the energy gap in (eV), d the nearest-neighbor distance in (Å), Ecoh the cohesive energy in (eV), n0 the refractive index, and λ is a parameter separating the strongly ionic materials from the weakly ionic ones. Thus, λ = 0, 1, and 6 are for the Groups IV, III–V, and II–VI semiconductors, respectively. The calculated ionicity values compared with those of Phillips [36], Christensen et al. [37], Garcia and Cohen [38], and Zaoui et al. [40] are given in Table 2. We may conclude that the present ionicities, which were calculated differently than in the definition of Phillips, are in good agreement with the empirical ionicity values, and exhibit the same chemical trends as those found in the values derived from the Phillips theory or those of Christensen et al. [37], Garcia and Cohen [38], and Zaoui et al. [40] (Table 2).


aRef. [46], bRef. [47], cRef. [48], dRef. [29], eRef. [41]: Formulas (5–7), f Ref. [49], gRef. [36], hRef. [37], i Ref. [38], j Ref. [40]

Table 4. Calculated ionicity character for Si and PS along with those of Phillips [36], Christensen et al. [37], Garcia and Cohen [38], Zaoui et al. [40], and Al-Douri et al. [41] The difficulty involved with such calculations resides with the lack of a theoretical framework that can describe the physical properties of crystals. Generally speaking, any definition of ionicity is likely to be imperfect. Although we may argue that, for many of these compounds, the empirically calculated differences are of the same order as the differences between the reported measured values, these trends are still expected to be real [47]. The unchanged ionicity characters of bulk Si and PS are noticed. In conclusion, the empirical models obtained for the ionicity give results in good agreement with the results of other scales, which in turn demonstrate the validity of our models to predict some other physical properties of such compounds.

### **7. Material stiffness**

194 Solar Cells – Silicon Wafer-Based Technologies

*<sup>d</sup> <sup>E</sup> <sup>f</sup>* 

*E E <sup>f</sup>* 

*<sup>n</sup> <sup>E</sup> <sup>f</sup>* 

*i*

*i*

*i*

Cohen [38], and Zaoui et al. [40] (Table 2).

Si 2.35 2.32 3.673c 0e 0f

aRef. [46], bRef. [47], cRef. [48], dRef. [29], eRef. [41]: Formulas (5–7), f

Ref. [49], gRef. [36], hRef. [37], i

Table 4. Calculated ionicity character for Si and PS along with those of Phillips [36], Christensen et al. [37], Garcia and Cohen [38], Zaoui et al. [40], and Al-Douri et al. [41]

(eV) *n*<sup>0</sup>

Samples *d*<sup>a</sup> (Å) *E*coh b

PS formed on the unpolished side

PS formed on the front polished side

Ref. [38], j

Ref. [40]

 / 4 *g X*

 / 2 *coh g X*

 <sup>0</sup> / 4 *g X*

 

where EgΓX is the energy gap in (eV), d the nearest-neighbor distance in (Å), Ecoh the cohesive energy in (eV), n0 the refractive index, and λ is a parameter separating the strongly ionic materials from the weakly ionic ones. Thus, λ = 0, 1, and 6 are for the Groups IV, III–V, and II–VI semiconductors, respectively. The calculated ionicity values compared with those of Phillips [36], Christensen et al. [37], Garcia and Cohen [38], and Zaoui et al. [40] are given in Table 2. We may conclude that the present ionicities, which were calculated differently than in the definition of Phillips, are in good agreement with the empirical ionicity values, and exhibit the same chemical trends as those found in the values derived from the Phillips theory or those of Christensen et al. [37], Garcia and

> ƒi cal. ƒi

g ƒi

2.77d 0 0 0 0 0 1.82

2.66d 0 0 0 0 0 1.86

h ƒi i ƒi

0 0 0 0 1.1

<sup>j</sup> *E*gΓX (eV)

 

(5)

(6)

(7)

 

> The bulk modulus is known as a reflectance of the crucial material stiffness in different industries. Many authors [50–55] have made various efforts to explore the thermodynamic properties of solids, particularly in examining the thermodynamic properties such as the inter-atomic separation and the bulk modulus of solids with different approximations and best-fit relations [52–55]. Computing the important number of structural and electronic properties of solids with great accuracy has now become possible, even though the ab initio calculations are complex and require significant effort. Therefore, additional empirical approaches have been developed [36, 47] to compute properties of materials. In many cases, the empirical methods offer the advantage of applicability to a broad class of materials and to illustrate trends. In many applications, these empirical approaches do not provide highly accurate results for each specific material; however, they are still very useful. Cohen [46] established an empirical formula for calculating bulk modulus B0 based on the nearestneighbor distance, and the result is in agreement with the experimental values. Lam et al. [56] derived an analytical expression for the bulk modulus from the total energy that gives similar numerical results even though this expression is different in structure from the empirical formula. Furthermore, they obtained an analytical expression for the pressure derivative B0 of the bulk modulus. Meanwhile, our group [57] used a concept based on the energy gap along Γ-X and transition pressure to establish an empirical formula for the calculation of the bulk modulus, the results of which are in good agreement with the experimental data and other calculations. In the present work, we have established an empirical formula for the calculation of bulk modulus B0 of a specific class of materials, and the theory yielded a formula with three attractive features. Apparently, only the energy gap along Γ -X and transition pressure are required as an input, and the computation of B0 in itself is trivial. The consideration of the hypothetical structure and simulation of the experimental conditions are required to make practical use of this formula.

> The aim of the present study is to determine how a qualitative concept, such as the bulk modulus, can be related to the energy gap. We [57] obtained a simple formula for the bulk moduli of diamond and zinc-blende solids using scaling arguments for the relevant bonding and volume. The dominant effect in these materials has been argued to be the degree of covalence, as characterized by the homopolar gap, Eh of Phillips, [36] and the gap along Γ-X [57]. Our calculation is based upon the energy gap along Γ-X which has been reported previously [42–45], and the energy gaps that follow chemical trends are described by homopolar and heteropolar energy gaps. Empirical pseudopotential methods based on

Optical Insights into Enhancement

previous results.

Si

PS formed on the unpolished side

PS formed on the front polished side

**8. Conclusions** 

results.

Samples *B*0 cal.

(GPa)

101a' 91.5a'' 100a'''

61.4a' 150.7a'' 165a'''

60.1a' 148.5a'' 169a'''

*B*0 exp.b (GPa)

a'Ref. [57], a''Ref. [60], a'''Ref. [61], bRef. [46], cRef. [62], dRef. [63], eRef. [64]

Table 5. Calculated bulk modulus for Si and PS together with experimental values, and the

PS formed on the unpolished backside of the c-Si wafer showed an increase in surface roughness compared with one formed on the polished front side. The high degree of roughness along with the presence of the nanocrystal layer implies that the surface used as an ARC, which can reduce the reflection of light and increase light trapping on a wide wavelength range. This parameter is important in enhancing the photo conversion process for solar cell devices. PS formed on both sides has low reflectivity value. Fabricated solar cells show that the conversion efficiency is 15.4% compared with the unetched sample and other results [13, 15]. The results of the refractive index and optical dielectric constant of Si and PS are investigated. The results of Ghosh et al. proved the appropriate for studying porous silicon solar cell optical properties. The mentioned models of ionicity in our study indicated a good accordance with other scales .other side, the empirical model obtained for the bulk modulus gives results that are in good overall agreement with previous

results of Cohen [46], Lam et al. [56], Al-Douri et al. [57] values, and others [43,44]

of Solar Cell Performance Based on Porous Silicon Surfaces 197

[e.g., the B0 for Si is 100.7 GPa and the pressure for the transition to β-Sn is 12.5 GPa (125 kbar), whereas for GaSb, B0 is 55.5 GPa and the transition pressure to β-Sn is 7.65 GPa (76.5 kbar)]. This correlation fails for a compound such as ZnS that has a smaller value of B0 than Si but has a larger transition pressure. In conclusion, the empirical model obtained for the bulk modulus gives results that are in good overall agreement with

> *B*0 [46] (GPa)

*B*0 [56] (GPa)

98 98 100 92 92c

*B*0 [57]

(GPa) *B*0 (GPa) *<sup>P</sup>*<sup>t</sup>

 e (GPa)

93.6d 12.5

optical spectra encounter the same problems using an elaborate (but not necessarily more accurate) study based on one electron atomic or crystal potential. One of the earliest approaches [58] involved in correlating the transition pressure with the optical band gap [e.g., the band gap for α-Sn is zero and the pressure for a transition to β-Sn is vanishingly small, whereas for Si with a band gap of 1 eV, the pressure for the same transition is approximately 12.5 GPa (125 kbar)]. A more recent effort is from Van Vechten [59], who used the dielectric theory of Phillips [36] to scale the zinc-blende to β-Sn transition with the ionic and covalent components of the chemical bond. The theory is a considerable improvement with respect to earlier efforts, but is limited to the zinc-blende to β-Sn transition. As mentioned, EgΓX and Pt have been reported elsewhere for several semiconducting compounds. One reason for presenting these data in the current work is that the validity of our calculations is not restricted in computed space. Thus, the data is bound prove valuable for future work in this field.

An important reason for studying B0 is the observation of clear differences between the energy gap along Γ-X in going from the group IV, III–V, and II–VI semiconductors in Table 4, where one can see the effect of the increasing covalence. As covalence increases, the pseudopotential becomes more attractive and pulls the charge more toward the core region, thereby reducing the number of electrons available for bonding. The modulus generally increases with the increasing covalence, but not as quickly as predicted by the uniform density term. Hence, the energy gaps are predominantly dependent on B0. A likely origin for the above result is the increase of ionicity and the loss of covalence. The effect of ionicity reduces the amount of bonding charge and the bulk modulus. This picture is essentially consistent with the present results; hence, the ionic contribution to B0 is of the order 40%–50% smaller. The differences between the energy gaps have led us to consider this model.

The basis of our model is the energy gap as seen in Table 4. The fitting of these data gives the following empirical formula [57]:

$$B\_0 = \left(\Im 0 + \mathcal{X}10\right) \left[ \left(P\_t^{1/2} \mid E\_{\text{g}^\Gamma X}\right) / \Im\right] \tag{8}$$

where EgΓX is the energy gap along Γ-X (in eV), Pt is the transition pressure (in GPa ''kbar''), and λ is an empirical parameter that accounts for the effect of ionicity; λ = 0; 1, 5 for group IV, III–V, and II–VI semiconductors, respectively. In Table 5, the calculated bulk modulus values are compared with the experimental values and the results of Cohen [46], Lam et al. [56], and Al-Douri et al. [57].

We may conclude that the present bulk moduli calculated in a different way than in the definition of Cohen are in good agreement with the experimental values. Furthermore, the moduli exhibit the same chemical trends as those found for the values derived from the experimental values, as seen in Table 5. The results of our calculations are in reasonable agreement with the results of Cohen [46] and the experiments of Lam et al. [56], and are more accurate than in our previous work [57]. As mentioned previously, an approach [57] that elucidates the correlation of the transition pressure with the optical band gap exists. This procedure gives a rough correlation and fails badly for some materials such as AlSb that have a larger band gap than Si but have a lower transition pressure [64]. From the above empirical formula, a correlation is evident between the transition pressure and B0

optical spectra encounter the same problems using an elaborate (but not necessarily more accurate) study based on one electron atomic or crystal potential. One of the earliest approaches [58] involved in correlating the transition pressure with the optical band gap [e.g., the band gap for α-Sn is zero and the pressure for a transition to β-Sn is vanishingly small, whereas for Si with a band gap of 1 eV, the pressure for the same transition is approximately 12.5 GPa (125 kbar)]. A more recent effort is from Van Vechten [59], who used the dielectric theory of Phillips [36] to scale the zinc-blende to β-Sn transition with the ionic and covalent components of the chemical bond. The theory is a considerable improvement with respect to earlier efforts, but is limited to the zinc-blende to β-Sn transition. As mentioned, EgΓX and Pt have been reported elsewhere for several semiconducting compounds. One reason for presenting these data in the current work is that the validity of our calculations is not restricted in computed space. Thus, the data is

An important reason for studying B0 is the observation of clear differences between the energy gap along Γ-X in going from the group IV, III–V, and II–VI semiconductors in Table 4, where one can see the effect of the increasing covalence. As covalence increases, the pseudopotential becomes more attractive and pulls the charge more toward the core region, thereby reducing the number of electrons available for bonding. The modulus generally increases with the increasing covalence, but not as quickly as predicted by the uniform density term. Hence, the energy gaps are predominantly dependent on B0. A likely origin for the above result is the increase of ionicity and the loss of covalence. The effect of ionicity reduces the amount of bonding charge and the bulk modulus. This picture is essentially consistent with the present results; hence, the ionic contribution to B0 is of the order 40%–50% smaller. The differences between the energy gaps have led us

The basis of our model is the energy gap as seen in Table 4. The fitting of these data gives

1/2 *B PE* <sup>0</sup> 30 10 / / 3

where EgΓX is the energy gap along Γ-X (in eV), Pt is the transition pressure (in GPa ''kbar''), and λ is an empirical parameter that accounts for the effect of ionicity; λ = 0; 1, 5 for group IV, III–V, and II–VI semiconductors, respectively. In Table 5, the calculated bulk modulus values are compared with the experimental values and the results of Cohen [46],

We may conclude that the present bulk moduli calculated in a different way than in the definition of Cohen are in good agreement with the experimental values. Furthermore, the moduli exhibit the same chemical trends as those found for the values derived from the experimental values, as seen in Table 5. The results of our calculations are in reasonable agreement with the results of Cohen [46] and the experiments of Lam et al. [56], and are more accurate than in our previous work [57]. As mentioned previously, an approach [57] that elucidates the correlation of the transition pressure with the optical band gap exists. This procedure gives a rough correlation and fails badly for some materials such as AlSb that have a larger band gap than Si but have a lower transition pressure [64]. From the above empirical formula, a correlation is evident between the transition pressure and B0

*<sup>t</sup> g X* (8)

bound prove valuable for future work in this field.

to consider this model.

the following empirical formula [57]:

Lam et al. [56], and Al-Douri et al. [57].

[e.g., the B0 for Si is 100.7 GPa and the pressure for the transition to β-Sn is 12.5 GPa (125 kbar), whereas for GaSb, B0 is 55.5 GPa and the transition pressure to β-Sn is 7.65 GPa (76.5 kbar)]. This correlation fails for a compound such as ZnS that has a smaller value of B0 than Si but has a larger transition pressure. In conclusion, the empirical model obtained for the bulk modulus gives results that are in good overall agreement with previous results.


a'Ref. [57], a''Ref. [60], a'''Ref. [61], bRef. [46], cRef. [62], dRef. [63], eRef. [64]

Table 5. Calculated bulk modulus for Si and PS together with experimental values, and the results of Cohen [46], Lam et al. [56], Al-Douri et al. [57] values, and others [43,44]

#### **8. Conclusions**

PS formed on the unpolished backside of the c-Si wafer showed an increase in surface roughness compared with one formed on the polished front side. The high degree of roughness along with the presence of the nanocrystal layer implies that the surface used as an ARC, which can reduce the reflection of light and increase light trapping on a wide wavelength range. This parameter is important in enhancing the photo conversion process for solar cell devices. PS formed on both sides has low reflectivity value. Fabricated solar cells show that the conversion efficiency is 15.4% compared with the unetched sample and other results [13, 15]. The results of the refractive index and optical dielectric constant of Si and PS are investigated. The results of Ghosh et al. proved the appropriate for studying porous silicon solar cell optical properties. The mentioned models of ionicity in our study indicated a good accordance with other scales .other side, the empirical model obtained for the bulk modulus gives results that are in good overall agreement with previous results.

Optical Insights into Enhancement

of Solar Cell Performance Based on Porous Silicon Surfaces 199

[33] Halimaoui A. 1997, 'Porous silicon formation by anodization', in: L. Canham (Ed.),

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[47] W.A. Harison, Electronic Structure and the Properties of Solids, General Publishing

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[28] P. J. L. Herve, L. K. J. Vandamme, J. Appl. Phys. 77 (1995) 5476 [29] D. K. Ghosh, L. K. Samanta, G. C. Bhar, Infrared Phys. 24 (1984) 34

Properties of porous silicon, INSPEC, UK (1997) 18

[37] N.E. Christensen, S. Stapathy, Z. Pawlowska, Phys. Rev. B36 (1987) 1032

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[50] A.M. Sherry, M. Kumar, J. Phys. Chem. Solids 52 (1991) 1145

[52] M. Kumar, S.P. Upadhyaya, Phys. Stat. Sol. B 181 (1994) 55

[56] P.K. Lam, M.L. Cohen, G. Martinez, Phys. Rev. B 35 (1987) 9190. [57] Y. Al-Douri, H. Abid, H. Aourag, Physica B 322 (2002) 179.

[60] Y. Al-Douri, H. Abid, H. Aourag, Mater. Chem. Phys. 87 (2004) 14.

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[42] I.M. Tsidilkovski, Band Structure of Semiconductors, Pergamon, Oxford, 1982 [43] K. Strossner, S. Ves, Chul Koo Kim, M. Cardona, Phys. Rev. B33 (1986) 4044 [44] C. Albert, A. Joullié, A.M. Joullié, C. Ance, Phys. Rev. B27 (1984) 4946 [45] R.G. Humphreys, V. Rossler, M. Cardona, Phys. Rev. B18 (1978) 5590

[34] J.R. Chelikowsky, M.L. Cohen, Phys. Rev. B14 (1976) 556 [35] C.S. Wang, B.M. Klein, Phys. Rev. B24 (1981) 3393

[38] A. Garcia, M.L. Cohen, Phys. Rev. B47 (1993) 4215 [39] A. Garcia, M.L. Cohen, Phys. Rev. B47 (1993) 4221

[46] M.L. Cohen, Phys. Rev. B32 (1985) 7988

Company, Toronto, 1989

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[53] M. Kumar, Physica B 205 (1995) 175

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[25] Y. Al-Douri, Y. P. Feng, A. C. H. Huan, Solid State Commun. 148 (2008) 521

[27] N. M. Ravindra, S. Auluck, V. K. Srivastava, Phys. Stat. Sol. (b) 93 (1979) K155

[24] Y. Al-Douri, Mater. Chem. Phys. 82 (2003) 49

[30] D. R. Penn, Phys. Rev. 128 (1962) 2093 [31] J. A. Van Vechten, Phys. Rev. 182 (1969) 891 [32] G. A. Samara, Phys. Rev. B 27 (1983) 3494

163

#### **9. Acknowledgement**

Support from FRGS grant and Universiti Sains Malaysia aregratefully acknowledged.

#### **10. References**


[1] V.M. Aroutiounia, K.S.h. Martirosyana, S. Hovhannisyana, G. Soukiassianb, J. Contemp.

[2] Wisam J Aziz, Asmat Ramizy, K. Ibrahim, Khalid Omar, Z. Hassan, Journal of

[3] Asmiet Ramizy, Wisam J Aziz, Z. Hassan, Khalid Omar and K. Ibrahim, Microelectronics

[4] Wisam J. Aziz, Asmiet Ramizy, K. Ibrahim, Z. Hassan, Khalid Omar, In Press,

[5] Asmiet Ramizy, Wisam J. Aziz, Z. Hassan, Khalid. Omar and K. Ibrahim, In Press,

[6] Asmiet Ramizy, Z. Hassan, Khalid Omar, Y. Al-Douri, M. A. Mahdi. Applied Surface Science, Applied Surface Science, Vol. 257, Iss. 14, (2011) pp. 6112–6117. [7] Asmiet Ramizy, Wisam J. Aziz, Z. Hassan, Khalid Omar, and K. Ibrahim, Accepted,

[10] J. Guobin, S. Winfried, A. Tzanimir, K. Martin, J. Mater. Sci. Mater. Electron. 19 (2008)

[12] M. Yamaguchi, Super-high efficiency III–V tandem and multijunction cells, in: M.D.

[14] S. Yae, T. Kobayashi, T. Kawagishi, N. Fukumuro, H. Matsuda, Solar Energy 80 (2006)

[17] G. Lerondel, R. Romestain, in: L. Canham (Ed.), Reflection and Light Scat tering in Porous Silicon, Properties of porous silicon, INSPEC, UK, 1997, p. 241. [18] Asmiet Ramizy, Z. Hassan, K. Omar, J. Mater. Sci. Elec, (First available online).

[19] J. A. Wisam, Ramizy.Asmiet, I. K, O. Khalid, and H. Z, Journal of Optoelectronic and

[20] M. A. Mahdi, S. J. Kasem, J. J. Hassen, A. A. Swadi, S. K. J.Al-Ani, Int. J.Nanoelectronics

Archer, R. Hill (Eds.), Clean Electricity from Photovoltaics, Super-High Effi- ciency III–V Tandem and Multijunction Cells, Imperial College Press, London, 2001, p.

International, Vol. 27, No. 2, pp. 117-120, 2010.

[11] F. Yan, X. Bao, T. Gao, Solid State Commun. 91 (1994) 341.

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Advance Materials 11 (2009) pp.1632

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[8] D.-H. Oha, T.W. Kim, W.J. Chob, K.K. D, J. Ceram. Process. Res. 9 (2008) 57. [9] G. Barillaro, A. Nannini, F. Pieri, J. Electrochem. Soc. C 180 (2002) 149.

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Corrected Proof, Available online 17 January 2011,OPTIK, Int. J. Light Electron

Support from FRGS grant and Universiti Sains Malaysia aregratefully acknowledged.

**9. Acknowledgement** 

Phys. 43 (2008) 72.

Materials Science-Poland.

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and Materials 2 (2009) 163

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Nov. (2009)

Opt.

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347.

701.

**10. References** 


**Evaluation the Accuracy of One-Diode and Two-Diode Models for a Solar Panel Based** 

Mohsen Taherbaneh, Gholamreza Farahani and Karim Rahmani

Increasingly, using lower energy cost system to overcome the need of human beings is of interest in today's energy conservation environment. To address the solution, several approaches have been undertaken in past. Where, renewable energy sources such as photovoltaic systems are one of the suitable options that will study in this paper. Furthermore, significant work has been carried out in the area of photovoltaic system as one of the main types of renewable energy sources whose utilization becomes more common due to its nature. On the other hand, modeling and simulation of a photovoltaic system could be used to predict system electrical behaviour in various environmental and load conditions. In this modeling, solar panels are one of the essential parts of a photovoltaic system which convert solar energy to electrical energy and have nonlinear I-V characteristic curves. Accurate prediction of the system electrical behaviour needs to have comprehensive and precise models for all parts of the system especially their solar panels. Consequently, it provides a valuable tool in order to investigate the electrical behaviour of the solar cell/panel. In the literature, models that used to express electrical behaviour of a solar cell/panel are mostly one-diode or two-diode models with a specific and close accuracy with respect to each other. One-diode model has five variable parameters and two-diode model has seven variable parameters in different environmental conditions respectively. During the last decades, different approaches have been developed in order to identify electrical characteristics of both models. (Castaner & Silvestre, 2002) have introduced and evaluated two separate models (one-diode and two-diode models) for a solar cell but dependency of the models parameters on environmental conditions has not been fully considered. Hence, the proposed models are not completely accurate. (Sera et al., 2007) have introduced a photovoltaic panel model based on datasheet values; however with some restrict assumptions. Series and shunt resistances of the proposed model have been stated constant and their dependencies on environmental conditions have been ignored. Furthermore, dark-saturation current has been considered as a variable which depend on the temperature but its variations with irradiance has been also neglected. Model equations

have been merely stated for a solar panel which composed by several series cells.

**1. Introduction** 

 *Iranian Research Organization for Science and Technology, Tehran,* 

**Open-Air Climate Measurements** 

*Electrical and Information Technology Department,* 

*Iran* 

[63] Y. Al-Douri, H. Abid, H. Aourag, Mater. Lett. 59 (2005) 2032 [64] J.R. Chelikowsky, Phys. Rev. B 35 (1987) 1174. **10** 

## **Evaluation the Accuracy of One-Diode and Two-Diode Models for a Solar Panel Based Open-Air Climate Measurements**

Mohsen Taherbaneh, Gholamreza Farahani and Karim Rahmani *Electrical and Information Technology Department, Iranian Research Organization for Science and Technology, Tehran, Iran* 

#### **1. Introduction**

200 Solar Cells – Silicon Wafer-Based Technologies

[63] Y. Al-Douri, H. Abid, H. Aourag, Mater. Lett. 59 (2005) 2032

Increasingly, using lower energy cost system to overcome the need of human beings is of interest in today's energy conservation environment. To address the solution, several approaches have been undertaken in past. Where, renewable energy sources such as photovoltaic systems are one of the suitable options that will study in this paper. Furthermore, significant work has been carried out in the area of photovoltaic system as one of the main types of renewable energy sources whose utilization becomes more common due to its nature. On the other hand, modeling and simulation of a photovoltaic system could be used to predict system electrical behaviour in various environmental and load conditions. In this modeling, solar panels are one of the essential parts of a photovoltaic system which convert solar energy to electrical energy and have nonlinear I-V characteristic curves. Accurate prediction of the system electrical behaviour needs to have comprehensive and precise models for all parts of the system especially their solar panels. Consequently, it provides a valuable tool in order to investigate the electrical behaviour of the solar cell/panel. In the literature, models that used to express electrical behaviour of a solar cell/panel are mostly one-diode or two-diode models with a specific and close accuracy with respect to each other. One-diode model has five variable parameters and two-diode model has seven variable parameters in different environmental conditions respectively.

During the last decades, different approaches have been developed in order to identify electrical characteristics of both models. (Castaner & Silvestre, 2002) have introduced and evaluated two separate models (one-diode and two-diode models) for a solar cell but dependency of the models parameters on environmental conditions has not been fully considered. Hence, the proposed models are not completely accurate. (Sera et al., 2007) have introduced a photovoltaic panel model based on datasheet values; however with some restrict assumptions. Series and shunt resistances of the proposed model have been stated constant and their dependencies on environmental conditions have been ignored. Furthermore, dark-saturation current has been considered as a variable which depend on the temperature but its variations with irradiance has been also neglected. Model equations have been merely stated for a solar panel which composed by several series cells.

Evaluation the Accuracy of One-Diode and Two-Diode

Rs

Diode Rp

branch.

Iph

be taken into account.

for one-diode model.

Models for a Solar Panel Based Open-Air Climate Measurements 203

diode model (Fig. 1a) or to an equivalent circuit of two-diode model (Fig. 1b) containing photocurrent source, a diode or two diodes, a shunt resistor and a series resistor in the load

Iph

(a) (b)


+

**I**

Fig. 1. The equivalent circuits of one-diode and two-diode models of a solar cell.

s T v iR

s s T 1 T 2 v iR v iR

v iRs <sup>a</sup> <sup>s</sup> j j ph 0

One-diode model and two-diode model can be represented by Eqs. (1) and (2) accordingly:

<sup>V</sup> <sup>s</sup> ph 0 <sup>T</sup>

V V <sup>j</sup> <sup>s</sup> ph 01 <sup>02</sup> Tj

i I I (e 1) I (e 1) , V <sup>j</sup> 1,2 R q

Where, one-diode model has five unknown parameters; ph 0 s I ,I ,n,R and R and the two- <sup>p</sup> diode model has seven unknown parameters; ph 01 1 02 2 s I ,I ,n ,I ,n ,R and R . On the other p hand, a solar panel is composed of parallel combination of several cell strings and a string contains several cells in series. Therefore, the both models can be also stated for a solar panel. In this research, the idea is to compare the accuracy of the two mentioned models for a solar panel. As it is known, the unknown parameters of the models are functions of the incident solar irradiation and panel temperature; hence dependency between them should

In this section, evaluation of the unknown one-diode model parameters based on five equations are presented. The specific five points (are shown in Fig. 2) on the I-V curve are used to define the equations, where sc I is the short circuit current, xI is the current at V 0.5V x oc , xx I is current at V 0.5(V V ) xx oc mp , Voc is the open circuit voltage and V mp is the voltage at the maximum power point. In this study, the mentioned points are generated for 113 operating conditions between 15-65°C and 100-1000W/m2 to solve the five coupled implicit nonlinear equations for a solar panel that consists of 36 series connected poly-crystalline silicon solar cells at different operating conditions. By solving the nonlinear equations in a specific environmental condition, we will find five unknown parameters of the model in one operating condition. Equation (3) shows the system nonlinear equations

> p v iR nkT F i I I (e ) , a <sup>j</sup> 1,2,...,5 R q

(3)

p v iR nkT i I I (e 1) , V R q

p

(2)

(1)

v iR n kT

Rp D1

D2

Rs

+

**I**


(De Soto et al., 2006) have also described a detailed model for a solar panel based on data provided by manufacturers. Several equations for the model have been expressed and one of them is derivative of open-circuit voltage respect to the temperature but with some assumptions. Shunt and series resistances have been considered constant through the paper, also their dependency over environmental conditions has been ignored. Meanwhile, only dependency of dark-saturation current to temperature has been considered. (Celik & Acikgoz, 2007) have also presented an analytical one-diode model for a solar panel. In this model, an approximation has been considered to describe the series and shunt resistances; they have been stated by the slopes at the open-circuit voltage and short-circuit current, respectively. Dependencies of the model parameters over environmental conditions have been briefly expressed. Therefore, the model is not suitable for high accuracy applications.

(Chenni et al., 2007) have used a model based on four parameters to evaluate three popular types of photovoltaic panels; thin film, multi and mono crystalline silicon. In the proposed model, value of shunt resistance has been considered infinite. The dark-saturation current has been dependent only on the temperature. (Gow & Manning, 1999) have demonstrated a circuit-based simulation model for a photovoltaic cell. The interaction between a proposed power converter and a photovoltaic array has been also studied. In order to extract the initial values of the model parameters at standard conditions, it has been assumed that the slope of current-voltage curve in open-circuit voltage available from the manufacturers. Clearly, this parameter is not supported by a solar panel datasheet and it is obtained only through experiment.

There are also several researches regarding evaluation of solar panel's models parameters from different conditions point of view by (Merbah et al., 2005; Xiao et al., 2004; Walker, 2001). In all of them, solar panel's models have been proposed with some restrictions.

The main goal of this study is investigation the accuracy of two mentioned models in the open-air climate measurements. At first step of the research, a new approach to model a solar panel is fully introduced that it has high accuracy. The approach could be used to define the both models (on-diode and two diode models) with a little bit modifications. Meanwhile, the corresponding models parameters will also evaluate and compare. To assess the accuracy of the models, several extracted I-V characteristic curves are utilized using comprehensive designed measurement system. In order to coverage of a wide range of environmental conditions, almost one hundred solar panel I-V curves have been extracted from the measurement system during several days of the year in different seasons. Hence, the rest of chapter is organized as follows.

In section 2 of the report, derivation of an approach to evaluate the models accuracy will be described. Nonlinear mathematical expressions for both models are fully derived. The Newton's method is selected to solve the nonlinear models equations. A measurement system in order to extract I-V curves of solar panel is described in section 3. In section 4, the extracted unknown parameters of the models for according to former approach are presented. Results and their interpretation are presented in section 5. Detailed discussion on the results of the research and conclusions will provide in the final section.

#### **2. Study method**

The characteristics of a solar cell "current versus voltage" under environmental conditions (irradiance and temperature) is usually translated either to an equivalent circuits of one-

(De Soto et al., 2006) have also described a detailed model for a solar panel based on data provided by manufacturers. Several equations for the model have been expressed and one of them is derivative of open-circuit voltage respect to the temperature but with some assumptions. Shunt and series resistances have been considered constant through the paper, also their dependency over environmental conditions has been ignored. Meanwhile, only dependency of dark-saturation current to temperature has been considered. (Celik & Acikgoz, 2007) have also presented an analytical one-diode model for a solar panel. In this model, an approximation has been considered to describe the series and shunt resistances; they have been stated by the slopes at the open-circuit voltage and short-circuit current, respectively. Dependencies of the model parameters over environmental conditions have been briefly expressed. Therefore, the model is not suitable for high accuracy applications. (Chenni et al., 2007) have used a model based on four parameters to evaluate three popular types of photovoltaic panels; thin film, multi and mono crystalline silicon. In the proposed model, value of shunt resistance has been considered infinite. The dark-saturation current has been dependent only on the temperature. (Gow & Manning, 1999) have demonstrated a circuit-based simulation model for a photovoltaic cell. The interaction between a proposed power converter and a photovoltaic array has been also studied. In order to extract the initial values of the model parameters at standard conditions, it has been assumed that the slope of current-voltage curve in open-circuit voltage available from the manufacturers. Clearly, this parameter is not supported by a solar panel datasheet and it is obtained only

There are also several researches regarding evaluation of solar panel's models parameters from different conditions point of view by (Merbah et al., 2005; Xiao et al., 2004; Walker, 2001). In all of them, solar panel's models have been proposed with some restrictions. The main goal of this study is investigation the accuracy of two mentioned models in the open-air climate measurements. At first step of the research, a new approach to model a solar panel is fully introduced that it has high accuracy. The approach could be used to define the both models (on-diode and two diode models) with a little bit modifications. Meanwhile, the corresponding models parameters will also evaluate and compare. To assess the accuracy of the models, several extracted I-V characteristic curves are utilized using comprehensive designed measurement system. In order to coverage of a wide range of environmental conditions, almost one hundred solar panel I-V curves have been extracted from the measurement system during several days of the year in different seasons. Hence,

In section 2 of the report, derivation of an approach to evaluate the models accuracy will be described. Nonlinear mathematical expressions for both models are fully derived. The Newton's method is selected to solve the nonlinear models equations. A measurement system in order to extract I-V curves of solar panel is described in section 3. In section 4, the extracted unknown parameters of the models for according to former approach are presented. Results and their interpretation are presented in section 5. Detailed discussion on

The characteristics of a solar cell "current versus voltage" under environmental conditions (irradiance and temperature) is usually translated either to an equivalent circuits of one-

the results of the research and conclusions will provide in the final section.

through experiment.

**2. Study method** 

the rest of chapter is organized as follows.

diode model (Fig. 1a) or to an equivalent circuit of two-diode model (Fig. 1b) containing photocurrent source, a diode or two diodes, a shunt resistor and a series resistor in the load branch.

Fig. 1. The equivalent circuits of one-diode and two-diode models of a solar cell.

One-diode model and two-diode model can be represented by Eqs. (1) and (2) accordingly:

$$\mathbf{i} = \mathbf{I}\_{\mathrm{ph}} - \mathbf{I}\_0 (\mathbf{e}^{\frac{\mathbf{v} + \mathrm{i}\mathbf{R}\_s}{V\_\Gamma}} - \mathbf{1}) - \frac{\mathbf{v} + \mathrm{i}\mathbf{R}\_s}{\mathbf{R}\_\mathbb{P}} \qquad , \qquad \mathbf{V}\_\Gamma = \frac{\mathrm{nkT}}{\mathbf{q}} \tag{1}$$

$$\mathbf{i} = \mathbf{I}\_{\mathrm{ph}} - \mathbf{I}\_{01} (\mathbf{e}^{\frac{\mathbf{v} + i\mathbf{R}\_s}{V\_{\mathrm{T}1}}} - \mathbf{1}) - \mathbf{I}\_{02} (\mathbf{e}^{\frac{\mathbf{v} + i\mathbf{R}\_s}{V\_{\mathrm{T}2}}} - \mathbf{1}) - \frac{\mathbf{v} + i\mathbf{R}\_s}{R\_p} \qquad , \qquad \mathbf{V}\_{\mathrm{T}j} = \frac{\mathbf{n}\_j \mathbf{k} \mathbf{T}}{\mathbf{q}} \quad \mathbf{j} = \mathbf{1}, 2 \tag{2}$$

Where, one-diode model has five unknown parameters; ph 0 s I ,I ,n,R and R and the two- <sup>p</sup> diode model has seven unknown parameters; ph 01 1 02 2 s I ,I ,n ,I ,n ,R and R . On the other p hand, a solar panel is composed of parallel combination of several cell strings and a string contains several cells in series. Therefore, the both models can be also stated for a solar panel. In this research, the idea is to compare the accuracy of the two mentioned models for a solar panel. As it is known, the unknown parameters of the models are functions of the incident solar irradiation and panel temperature; hence dependency between them should be taken into account.

In this section, evaluation of the unknown one-diode model parameters based on five equations are presented. The specific five points (are shown in Fig. 2) on the I-V curve are used to define the equations, where sc I is the short circuit current, xI is the current at V 0.5V x oc , xx I is current at V 0.5(V V ) xx oc mp , Voc is the open circuit voltage and V mp is the voltage at the maximum power point. In this study, the mentioned points are generated for 113 operating conditions between 15-65°C and 100-1000W/m2 to solve the five coupled implicit nonlinear equations for a solar panel that consists of 36 series connected poly-crystalline silicon solar cells at different operating conditions. By solving the nonlinear equations in a specific environmental condition, we will find five unknown parameters of the model in one operating condition. Equation (3) shows the system nonlinear equations for one-diode model.

$$\mathbf{F}\_{\mathbf{j}} = -\mathbf{i}\_{\mathbf{j}} + \mathbf{I}\_{\mathbf{ph}} - \mathbf{I}\_{0} (\mathbf{e}^{\frac{\mathbf{v} + i\mathbf{R}\_{s}}{\mathbf{a}}}) - \frac{\mathbf{v} + i\mathbf{R}\_{s}}{\mathbf{R}\_{\mathbf{p}}} \qquad , \qquad \mathbf{a} = \frac{\mathbf{nkT}}{\mathbf{q}} \quad \mathbf{j} = 1, 2, ..., 5 \tag{3}$$

Evaluation the Accuracy of One-Diode and Two-Diode

the both models.

**3. Measurement system** 

standard conditions based on datasheets.

Models for a Solar Panel Based Open-Air Climate Measurements 205

The points are also generated for the 113 operating conditions to solve the seven coupled implicit nonlinear equations for the solar panel. Solving the nonlinear equations in a specific environmental condition leads to define seven unknown model parameters in one operating condition. Equation (4) shows the system nonlinear equations for the two-diode model.

v iR G i I I (e 1) I (e 1) , <sup>R</sup>

Figs. 4 and 5 show the implemented algorithms in order to solve the nonlinear equations for

A block diagram of a measurement system is shown in Fig. 6. The main function of this system is extracting the solar panel's I-V curves. In this system, an AVR microcontroller (ATMEGA64) is used as the central processing unit. This unit measures, processes and controls input data. Then the processed data transmit to a PC through a serial link. In the proposed system, the PC has two main tasks; monitoring (acquiring the results) and programming the microcontroller. Extracting the solar panel's I-V curves shall be carried out in different environmental conditions. Different levels of received solar irradiance are achieved by changing in solar panel's orientation which is performed by controlling two DC motors in horizontal and vertical directions. Although the ambient temperature changing is not controllable, the measurements are carried out in different days and different conditions in order to cover this problem. A portable pyranometer and thermometer are used for measuring the environmental conditions; irradiance and temperature. Hence, 113 acceptable I-V curves *(out of two hundred)* were extracted. Motor driver block diagram is also shown in Fig. 7. Driving the motors is achieved through two full bridge PWM choppers with current protection. Table 1 reports electrical specifications of the under investigation solar panel at

k

*Standard conditions* **Irradiance (W/m2)** <sup>1000</sup>

Table 1. Datasheet information of the under investigation solar panel

q

k

s s 1 2 v iR v iR a a <sup>s</sup> j j ph 01 <sup>02</sup>

n kT a , k 1,2 , j 1,2 ,...,7

**Solar Panel Poly-Crystalline Silicon Solar Panel** 

**Temperature (°C)** 25 Isc (A) 2.98 Voc (V) 20.5 Impp (A) 2.73 Vmpp (V) 16.5 Pmpp (W) 45 ns 36 np 1 ki (%/°C ) 0.07 kv (mv/°C) -0.038

p

(4)

Fig. 2. Five points on the I-V curve of a solar panel are used to solve the nonlinear equations.

Former approach is used to solve seven coupled implicit nonlinear equations of the twodiode model for a solar panel. The specific seven points (are shown in Fig. 3) on the I-V curve are used to define the equations, where bI is the current at mp b V V <sup>3</sup> , cI is the current at mp c 2V V <sup>3</sup> , eI is the current at mp oc e 2V V V 3 and fI is the current at mp oc f V 2V V 3 .

Fig. 3. Seven points on the I-V curve of a solar panel to solve the nonlinear equations.

The points are also generated for the 113 operating conditions to solve the seven coupled implicit nonlinear equations for the solar panel. Solving the nonlinear equations in a specific environmental condition leads to define seven unknown model parameters in one operating condition. Equation (4) shows the system nonlinear equations for the two-diode model.

$$\mathbf{G}\_{\mathbf{j}} = -\mathbf{i}\_{\mathbf{j}} + \mathbf{I}\_{\mathrm{ph}} - \mathbf{I}\_{01} \left( \mathbf{e}^{\frac{\mathbf{a}\_{1}}{\mathbf{a}\_{1}}} - \mathbf{1} \right) - \mathbf{I}\_{02} \left( \mathbf{e}^{\frac{\mathbf{v} + i\mathbf{R}\_{s}}{\mathbf{a}\_{2}}} - \mathbf{1} \right) - \frac{\mathbf{v} + i\mathbf{R}\_{s}}{\mathbf{R}\_{\mathbf{P}}},\tag{4}$$
 
$$\mathbf{a}\_{\mathbf{k}} = \frac{\mathbf{n}\_{\mathbf{k}} \, \mathrm{kT}}{\mathbf{q}}, \qquad \qquad \mathbf{k} = \mathbf{1}, 2 \quad \mathbf{j} = \mathbf{1}, 2, \dots, 7$$

Figs. 4 and 5 show the implemented algorithms in order to solve the nonlinear equations for the both models.

#### **3. Measurement system**

204 Solar Cells – Silicon Wafer-Based Technologies

Fig. 2. Five points on the I-V curve of a solar panel are used to solve the nonlinear equations.

Former approach is used to solve seven coupled implicit nonlinear equations of the twodiode model for a solar panel. The specific seven points (are shown in Fig. 3) on the I-V

e

V

2V V

3

b

V

and fI is the current at

V

<sup>3</sup> , cI is the

curve are used to define the equations, where bI is the current at mp

<sup>3</sup> , eI is the current at mp oc

Fig. 3. Seven points on the I-V curve of a solar panel to solve the nonlinear equations.

current at mp c

mp oc

3 .

V 2V

f

V

V

2V

A block diagram of a measurement system is shown in Fig. 6. The main function of this system is extracting the solar panel's I-V curves. In this system, an AVR microcontroller (ATMEGA64) is used as the central processing unit. This unit measures, processes and controls input data. Then the processed data transmit to a PC through a serial link. In the proposed system, the PC has two main tasks; monitoring (acquiring the results) and programming the microcontroller. Extracting the solar panel's I-V curves shall be carried out in different environmental conditions. Different levels of received solar irradiance are achieved by changing in solar panel's orientation which is performed by controlling two DC motors in horizontal and vertical directions. Although the ambient temperature changing is not controllable, the measurements are carried out in different days and different conditions in order to cover this problem. A portable pyranometer and thermometer are used for measuring the environmental conditions; irradiance and temperature. Hence, 113 acceptable I-V curves *(out of two hundred)* were extracted. Motor driver block diagram is also shown in Fig. 7. Driving the motors is achieved through two full bridge PWM choppers with current protection. Table 1 reports electrical specifications of the under investigation solar panel at standard conditions based on datasheets.


Table 1. Datasheet information of the under investigation solar panel

Evaluation the Accuracy of One-Diode and Two-Diode

Fig. 5. Flowchart of extraction the two-diode model parameters

Models for a Solar Panel Based Open-Air Climate Measurements 207

Fig. 4. Flowchart of extraction the one-diode model parameters

Fig. 4. Flowchart of extraction the one-diode model parameters

Fig. 5. Flowchart of extraction the two-diode model parameters

Evaluation the Accuracy of One-Diode and Two-Diode

implementation a variable load, which will be discussed below.

across the panel output ports.

**3.1.1 Discrete method** 

electronic load is suitable.

**3.1.2 Continuous method** 

described in Eq. (6).

values by switching of n resistors.

Fig. 8. The proposed switching load circuit

Models for a Solar Panel Based Open-Air Climate Measurements 209

environmental conditions. In order to extract a solar panels' I-V curve, it is sufficient to change the panel current between zero (open-circuit) to its maximum value (short-circuit) continuously or step by step when environmental condition was stable (the incident solar irradiance and panel temperature). Then the characteristic curve could be obtained by measuring the corresponding voltages and currents. Therefore, a variable load is required

Since the solar panel's I-V curve is nonlinear, the load variation profile has a significant impact on the precision of the extracted curve. If the load resistance (or conductance) varies linearly, the density of the measured points will be high near Isc or Voc and it is not desired. Hence, the nonlinear electronic load is more suitable. There are generally two methods for

As mentioned above, extracting the solar panel I-V curve could be carried out by its output load variation. An easy way is switching of some paralleled resistors to have different loads. If the resistors have been chosen according to Eq. (5), it is possible to have 2n different load

> n n1 <sup>1</sup> R R

The schematic for the proposed switching load is shown in Fig. 8. This method may cause some switching noise in the measurement system. Therefore, a controllable continuous

The schematic diagram for the proposed continuous electronic load is shown in Fig. 9. The drain-source resistor of a MOSFET in linear area of its electrical characteristic curves is used as a load. As we know, the value of this resistor could be controlled by gate-source voltage. Mathematical relationship between the value of this resistor and applied voltage is

gs T

WV V 

ox ds

t L <sup>1</sup> <sup>R</sup> 

<sup>2</sup> (5)

(6)

**Vertical Motor Horizental Motor**

Fig. 6. Block diagram of the proposed measurement system

Fig. 7. Motor driver block diagram

#### **3.1 The I-V curve extractor**

There is an important rule for solar panel's I-V curves in photovoltaic system designing. Although the manufacturers give specifications of their products (cell or panel) generally in the standard condition, behavior of solar cells and panels are more required in non-standard environmental conditions. In order to extract a solar panels' I-V curve, it is sufficient to change the panel current between zero (open-circuit) to its maximum value (short-circuit) continuously or step by step when environmental condition was stable (the incident solar irradiance and panel temperature). Then the characteristic curve could be obtained by measuring the corresponding voltages and currents. Therefore, a variable load is required across the panel output ports.

Since the solar panel's I-V curve is nonlinear, the load variation profile has a significant impact on the precision of the extracted curve. If the load resistance (or conductance) varies linearly, the density of the measured points will be high near Isc or Voc and it is not desired. Hence, the nonlinear electronic load is more suitable. There are generally two methods for implementation a variable load, which will be discussed below.

#### **3.1.1 Discrete method**

208 Solar Cells – Silicon Wafer-Based Technologies

**(Radiation) Solar Panel**

**Control & PWM signals for motors**

**Input Power**

**Temperature Sensor**

> **Control Unit & Electronic Load**

**Motors Driver**

**Amp Volt**

**Power Supply**

**Programming & Monitoring Interface**

**Pyranometer**

There is an important rule for solar panel's I-V curves in photovoltaic system designing. Although the manufacturers give specifications of their products (cell or panel) generally in the standard condition, behavior of solar cells and panels are more required in non-standard

Fig. 6. Block diagram of the proposed measurement system

M

**Horizental Motor**

Fig. 7. Motor driver block diagram

**3.1 The I-V curve extractor** 

M

**Vertical Motor**

As mentioned above, extracting the solar panel I-V curve could be carried out by its output load variation. An easy way is switching of some paralleled resistors to have different loads. If the resistors have been chosen according to Eq. (5), it is possible to have 2n different load values by switching of n resistors.

$$\mathbf{R}\_n = \frac{1}{2}\mathbf{R}\_{n-1} \tag{5}$$

The schematic for the proposed switching load is shown in Fig. 8. This method may cause some switching noise in the measurement system. Therefore, a controllable continuous electronic load is suitable.

Fig. 8. The proposed switching load circuit

#### **3.1.2 Continuous method**

The schematic diagram for the proposed continuous electronic load is shown in Fig. 9. The drain-source resistor of a MOSFET in linear area of its electrical characteristic curves is used as a load. As we know, the value of this resistor could be controlled by gate-source voltage. Mathematical relationship between the value of this resistor and applied voltage is described in Eq. (6).

$$\mathbf{R}\_{\rm ds} = \frac{\mathbf{t}\_{\rm ox} \mathbf{L}}{\mu \varepsilon \mathbf{W} \left(\frac{1}{\mathbf{V}\_{\rm gs} - \mathbf{V}\_{\rm T}}\right)} \tag{6}$$

Evaluation the Accuracy of One-Diode and Two-Diode

R1 10k

C2 100n

LF353/NS

2

3

U1A

+


8

VCC

V+

V-OUT

> R11 47K

1

4


Fig. 11. The schematic diagram of continuous electronic load

R10 1k

R9

1k

Fig. 12. A typical extracted solar panel's I-V curve

models.

**4. The extracted models unknown parameters** 

Models for a Solar Panel Based Open-Air Climate Measurements 211

10k R3

0



4

1

5

7 8

2

3

VCC

0

0

270k R2

LOAD+

LOAD-

U2

6

AD620

Fig. 12 shows a typical extracted I-V and P-V curves by this method in the following conditions; irradiance = 500 w/m2 and temperature = 34.5 °C. It is observed that the

R4 .11

0

To PC

D2

0

D3

R5

+5V

100

R6 1k

The Newton method is chosen to solve the nonlinear equations. A modification is also reported in the Newton's solving approach to attain the best convergence. MATLAB software environment is used to implement the nonlinear equations and their solving method. At first, the main electrical characteristics sc oc mp mp (I , V , V & I ) are extracted for all I-V curves of the solar panel (extracted by the measurement system) which Table 2 shows them. The main electrical characteristics of the solar panel are used in nonlinear equations

proposed electronic load could be suitable to extract the solar panel's I-V curves.

R7 4.7k

R8 1.6k 0

From PC

M2

IRF540

The schematic diagram of the implemented continuous electronic load is shown in Fig. 11.

Fig. 9. The proposed continuous electronic load

In this equation, L is channel length, W is channel width, is electric permittivity, is electron mobility and ox t is oxide thickness in the MOSFET. Implementation of this method is much quicker and easier than the previous one, and doesn't induce any switching noise in the measurement system. Simulation results and the measured data for the proposed electronic load (continuous method) are performed by Orcad/Pspice 9.2. The simulation result and experimental data are shown in Fig. 10. We observed that the simulation result and experimental data have similar electrical behavior. Their difference between curves was raised because of error in measurement and inequality real components with components in the simulation program. Anyway, the proposed electronic load (continuous method) was suitable for our purpose.

Fig. 10. Experimental data and simulation results of continuous electronic load profile

electron mobility and ox t is oxide thickness in the MOSFET. Implementation of this method is much quicker and easier than the previous one, and doesn't induce any switching noise in the measurement system. Simulation results and the measured data for the proposed electronic load (continuous method) are performed by Orcad/Pspice 9.2. The simulation result and experimental data are shown in Fig. 10. We observed that the simulation result and experimental data have similar electrical behavior. Their difference between curves was raised because of error in measurement and inequality real components with components in the simulation program. Anyway, the proposed electronic load (continuous method) was

Fig. 10. Experimental data and simulation results of continuous electronic load profile

is electric permittivity,

is

Fig. 9. The proposed continuous electronic load

suitable for our purpose.

In this equation, L is channel length, W is channel width,

The schematic diagram of the implemented continuous electronic load is shown in Fig. 11.

Fig. 11. The schematic diagram of continuous electronic load

Fig. 12 shows a typical extracted I-V and P-V curves by this method in the following conditions; irradiance = 500 w/m2 and temperature = 34.5 °C. It is observed that the proposed electronic load could be suitable to extract the solar panel's I-V curves.

Fig. 12. A typical extracted solar panel's I-V curve

#### **4. The extracted models unknown parameters**

The Newton method is chosen to solve the nonlinear equations. A modification is also reported in the Newton's solving approach to attain the best convergence. MATLAB software environment is used to implement the nonlinear equations and their solving method. At first, the main electrical characteristics sc oc mp mp (I , V , V & I ) are extracted for all I-V curves of the solar panel (extracted by the measurement system) which Table 2 shows them. The main electrical characteristics of the solar panel are used in nonlinear equations models.

Evaluation the Accuracy of One-Diode and Two-Diode

**(W/m2)** 

**The I-V Curves** 

Models for a Solar Panel Based Open-Air Climate Measurements 213

**Temperature (°C)** 42 633.85 36.20 18.79 2.13 13.39 1.85 43 637.55 35.85 18.84 2.14 13.44 1.86 44 406.40 34.10 18.70 1.59 13.81 1.40 45 412.35 33.00 18.87 1.61 14.10 1.40 46 1006.70 33.05 19.46 2.82 13.30 2.43 47 1014.20 33.20 19.38 2.85 13.22 2.45 48 1014.90 33.95 19.32 2.86 13.19 2.45 49 599.50 44.10 17.86 2.00 12.54 1.73 50 756.85 50.55 17.92 2.23 12.63 1.86 51 776.20 50.35 17.97 2.29 12.37 1.94 52 759.90 50.10 18.06 2.32 12.54 1.93 53 769.55 49.55 18.11 2.33 12.71 1.96 54 590.60 48.20 18.00 1.93 12.94 1.64 55 392.25 45.35 17.94 1.45 13.28 1.27 56 701.00 36.40 19.13 2.17 13.75 1.88 57 822.55 36.55 19.21 2.41 13.53 2.09 58 815.00 36.25 19.21 2.39 13.44 2.07 59 937.35 35.90 19.35 2.61 13.36 2.27 60 948.10 35.40 19.43 2.61 13.73 2.24 61 458.65 37.40 19.60 1.72 14.60 1.52 62 455.65 37.60 19.58 1.72 14.43 1.53 63 602.50 38.40 19.63 1.99 14.34 1.75 64 706.90 38.45 19.66 2.17 14.20 1.90 65 705.40 36.60 19.69 2.16 14.32 1.89 66 703.90 38.70 19.66 2.16 14.37 1.87 67 780.75 37.00 19.86 2.27 14.43 1.96 68 777.75 36.40 19.91 2.25 14.32 1.98 69 777.00 35.80 19.97 2.24 14.57 1.95 70 886.60 44.45 19.38 2.52 13.84 2.14 71 879.15 44.25 19.41 2.43 13.75 2.12 72 830.70 40.05 19.58 2.41 14.03 2.10 73 818.80 40.30 19.60 2.40 14.06 2.07 74 749.45 38.95 19.66 2.26 14.12 1.99 75 746.45 38.70 19.69 2.26 14.23 1.98 76 604.75 45.95 17.75 2.00 12.49 1.73 77 987.30 48.80 17.89 2.71 11.93 2.3 78 981.05 50.00 17.83 2.68 12.09 2.23 79 519.00 33.70 19.29 1.79 14.09 1.59 80 516.00 34.90 19.24 1.79 14.29 1.56 81 615.95 36.35 19.10 2.00 13.95 1.74 82 615.20 36.50 19.07 2.00 13.81 1.74

**(V)** 

**(A) Irradiance** 

**Isc (A)**  **Vmp (V)**  **Imp**

**Environmental Conditions Voc**


**Temperature (°C)** 1 644.30 22.95 20.58 1.90 15.55 1.67 2 657.70 24.00 20.53 1.94 15.52 1.70 3 662.18 24.50 20.50 1.95 15.55 1.70 4 665.16 25.20 20.50 1.97 15.60 1.71 5 668.85 25.20 20.50 1.98 15.40 1.74 6 456.36 15.20 21.10 1.35 16.43 1.21 7 467.55 14.50 21.15 1.39 16.50 1.22 8 478.00 14.15 21.15 1.43 16.50 1.24 9 558.50 17.80 21.00 1.63 16.14 1.47 10 529.50 17.90 20.90 1.57 16.17 1.38 11 575.00 17.40 20.90 1.70 16.10 1.49 12 601.00 18.10 20.90 1.77 16.00 1.55 13 605.50 18.45 20.90 1.78 16.10 1.56 14 474.25 13.65 21.00 1.38 16.40 1.22 15 495.15 14.20 21.00 1.45 16.30 1.27 16 528.00 18.30 20.60 1.53 16.00 1.34 17 528.00 18.45 20.60 1.54 15.95 1.36 18 537.00 18.30 20.58 1.56 15.86 1.37 19 557.80 21.00 20.28 1.61 15.35 1.44 20 548.80 22.00 20.25 1.59 15.47 1.40 21 524.25 21.5 20.22 1.51 15.50 1.36 22 517.50 20.65 20.19 1.47 15.47 1.31 23 533.15 19.85 20.45 1.53 15.92 1.39 24 946.25 40.85 18.95 2.65 13.00 2.29 25 945.50 42.90 18.93 2.64 12.91 2.30 26 778.50 33.40 20.30 2.26 14.60 1.97 27 762.30 33.15 20.22 2.22 14.70 1.94 28 789.00 34.15 20.22 2.28 14.48 2.03 29 782.25 33.80 20.27 2.27 14.60 2.01 30 391.20 41.80 18.34 1.43 13.67 1.26 31 914.95 21.95 20.50 2.56 14.76 2.21 32 917.95 23.85 20.30 2.58 14.42 2.25 33 923.20 27.00 20.00 2.60 14.15 2.25 34 1004.50 34.60 19.10 2.82 13.00 2.42 35 1004.50 35.15 19.07 2.83 12.91 2.43 36 994.75 34.25 19.04 2.80 13.08 2.39 37 900.80 34.90 18.98 2.62 13.05 2.26 38 899.30 35.55 18.98 2.63 13.33 2.22 39 808.30 36.40 18.84 2.45 13.16 2.11 40 811.30 36.80 18.84 2.47 13.08 2.13 41 630.90 36.10 18.73 2.13 13.36 1.85

**(V)** 

**(A) Irradiance** 

**Isc (A)**  **Vmp (V)**  **Imp**

**Environmental Conditions Voc**

**(W/m2)** 

**The I-V Curves** 


Evaluation the Accuracy of One-Diode and Two-Diode

**Temperature** 

**Irradiance (W/m2)** 

Models for a Solar Panel Based Open-Air Climate Measurements 215

4 665.16 25.20 1.9738 9.0465×10-8 1.2164 1.2520 255.1335 5 668.85 25.20 1.9776 1.4502×10-7 1.2513 1.2238 253.4728 6 456.36 15.20 1.3443 2.0084×10-7 1.3468 1.0289 475.3187 7 467.55 14.50 1.3822 5.7962×10-8 1.2489 1.1676 303.7811 8 478.00 14.15 1.4235 5.2113×10-8 1.2401 1.1492 228.1600 9 558.50 17.80 1.6448 1.6758×10-7 1.3089 1.1391 488.4681 10 529.50 17.90 1.5640 1.3622×10-7 1.2908 1.1252 305.8098 11 575.00 17.40 1.6993 1.4140×10-7 1.2872 1.1635 280.1520 12 601.00 18.10 1.7753 1.0810×10-7 1.2614 1.1667 252.2827 13 605.50 18.45 1.7854 1.8325×10-7 1.3034 1.1494 313.9411 14 474.25 13.65 1.3814 2.0780×10-7 1.3435 0.9994 307.3284 15 495.15 14.20 1.4413 2.1472×10-7 1.3430 1.0062 275.3528 16 528.00 18.30 1.5321 2.1087×10-7 1.3087 1.0844 307.3237 17 528.00 18.45 1.54442 1.8252×10-7 1.2961 1.1175 303.6138 18 537.00 18.30 1.5615 9.6833×10-8 1.2447 1.1485 245.5091 19 557.80 21.00 1.6145 3.2875×10-7 1.3193 1.1212 354.5386 20 548.80 22.00 1.5919 2.1440×10-7 1.2835 1.1649 305.2178 21 524.25 21.50 1.5309 5.5771×10-7 1.3667 1.0884 474.5784 22 517.50 20.65 1.4714 3.9398×10-7 1.3375 1.0842 405.6716 23 533.15 19.85 1.5753 2.1603×10-7 1.2953 1.1464 805.5353 24 946.25 40.85 2.6666 8.9271×10-7 1.2757 1.3558 146.2230 25 945.50 42.90 2.6574 1.2424×10-6 1.3030 1.3219 150.3004 26 778.50 33.40 2.1973 3.1128×10-7 1.2892 1.2567 515.2084 27 762.30 33.15 2.2171 5.3812×10-7 1.3316 1.1894 210.1448 28 789.00 34.15 2.2886 3.9798×10-7 1.3028 1.2315 214.3753 29 782.25 33.80 2.2765 5.0119×10-7 1.3266 1.1978 212.4934 30 391.20 41.80 1.4409 2.2284×10-6 1.3744 1.2030 357.0918 31 914.95 21.95 2.5657 2.9407×10-7 1.2866 1.2771 178.6504 32 917.95 23.85 2.5853 4.0314×10-7 1.2993 1.2704 179.9606 33 923.20 27.00 2.6220 5.5929×10-7 1.3065 1.2800 142.9452 34 1004.50 34.60 2.8279 1.2215×10-6 1.3071 1.3467 155.7048 35 1004.50 35.15 2.8362 1.5357×10-6 1.3258 1.3260 151.6557 36 994.75 34.25 2.8140 1.2354×10-6 1.3051 1.3258 141.9868 37 900.80 34.90 2.6385 2.1545×10-6 1.3585 1.3032 170.0669 38 899.30 35.55 2.6449 1.5551×10-6 1.3278 1.3082 152.1797 39 808.30 36.40 2.4663 1.5142×10-6 1.3214 1.3244 186.9949 40 811.30 36.80 2.4866 8.9032×10-7 1.2740 1.3574 152.6324 41 630.90 36.10 2.1335 7.5213×10-7 1.2650 1.3213 179.3817 42 633.85 36.20 2.1493 1.4614×10-6 1.3279 1.2659 172.9979 43 637.55 35.85 2.1526 1.3956×10-6 1.3272 1.2720 181.0577 44 406.40 34.10 1.5971 1.7433×10-6 1.3672 1.1656 253.3236 45 412.35 33.00 1.6220 1.0427×10-6 1.3288 1.1815 221.4351

**(°C) Iph (A) I0 (A) <sup>a</sup> Rs(Ω) Rp(Ω)** 


Table 2. The main electrical characteristic of the panel

Then, the five and the seven nonlinear equations of the models are implemented and the nonlinear least square approach is used to solve them. Tables 3 and 4 show the extracted unknown parameters of the models for environmental conditions.


**Temperature (°C)** 83 648.75 37.90 19.38 2.08 14.23 1.79 84 778.50 35.70 19.80 2.37 14.46 2.02 85 836.70 25.00 20.78 2.4 15.16 2.12 86 850.10 25.40 20.78 2.45 15.24 2.13 87 839.65 23.15 20.90 2.43 15.22 2.14 88 838.16 23.05 20.90 2.42 15.22 2.14 89 844.15 23.35 20.90 2.43 15.22 2.14 90 781.50 20.80 21.07 2.24 15.55 2.00 91 775.50 20.45 21.07 2.23 15.75 1.96 92 612.25 15.55 21.43 1.78 16.54 1.57 93 609.25 15.00 21.46 1.77 16.48 1.57 94 601.75 14.75 21.46 1.75 16.68 1.55 95 240.85 31.40 18.59 1.08 14.46 0.93 96 241.60 31.65 18.48 1.08 14.26 0.94 97 876.20 35.40 19.13 2.42 13.53 2.08 98 873.25 36.45 19.13 2.40 13.56 2.06 99 453.40 34.10 18.90 1.64 14.03 1.44 100 617.40 38.50 19.60 2.00 14.54 1.74 101 620.40 37.40 19.60 2.00 14.43 1.75 102 453.40 37.00 19.35 1.64 14.63 1.48 103 678.60 14.75 21.54 1.91 16.26 1.70 104 718.10 13.15 21.71 2.05 16.43 1.83 105 615.20 33.10 19.77 2.09 14.48 1.79 106 589.10 33.55 19.72 1.95 14.63 1.70 107 649.50 37.85 19.35 2.09 13.92 1.83 108 648.05 37.90 18.79 2.08 13.42 1.82 109 653.95 38.15 18.76 2.08 13.33 1.83 110 665.20 39.20 18.73 2.13 13.19 1.87 111 947.05 42.55 18.90 2.65 13.02 2.28 112 454.90 37.75 18.73 1.64 13.84 1.44 113 458.65 36.10 18.68 1.64 13.92 1.42

**(V)** 

**(A) Irradiance** 

**Isc (A)**  **Vmp (V)**  **Imp**

**Environmental Conditions Voc**

**(W/m2)** 

Table 2. The main electrical characteristic of the panel

**Irradiance (W/m2)** 

unknown parameters of the models for environmental conditions.

**Temperature** 

Then, the five and the seven nonlinear equations of the models are implemented and the nonlinear least square approach is used to solve them. Tables 3 and 4 show the extracted

1 644.30 22.95 1.9054 1.3645×10-7 1.2544 1.2078 279.6413 2 657.70 24.00 1.9406 2.0381×10-7 1.2807 1.1805 287.2463 3 662.18 24.50 1.9579 1.0977×10-7 1.2311 1.2276 252.0760

**(°C) Iph (A) I0 (A) <sup>a</sup> Rs(Ω) Rp(Ω)** 

**The I-V Curves** 


Evaluation the Accuracy of One-Diode and Two-Diode

**Temperature** 

**Irradiance (W/m2)** 

**Irradiance (W/m2)** 

**Temperature** 

Models for a Solar Panel Based Open-Air Climate Measurements 217

88 838.16 23.05 2.4333 1.6491×10-7 1.2697 1.1971 181.9877 89 844.15 23.35 2.4391 1.0187×10-7 1.2337 1.2319 168.4823 90 781.50 20.80 2.2502 2.4789×10-7 1.3180 1.1315 249.5637 91 775.50 20.45 2.2299 1.8167×10-7 1.2934 1.1539 269.1192 92 612.25 15.55 1.7732 1.1189×10-7 1.2958 1.0877 317.2956 93 609.25 15.00 1.7761 2.6497×10-8 1.1944 1.1797 232.1886 94 601.75 14.75 1.7631 5.0466×10-8 1.2390 1.1252 252.8796 95 240.85 31.40 1.0841 2.8277×10-6 1.4522 0.8406 328.3110 96 241.60 31.65 1.0842 2.9811×10-6 1.4494 0.8720 323.0246 97 876.20 35.40 2.4382 5.6696×10-7 1.2564 1.3492 157.0273 98 873.25 36.45 2.4151 1.3653×10-6 1.3337 1.3058 180.0039 99 453.40 34.10 1.6490 1.1006×10-6 1.3337 1.1999 245.1651 100 617.40 38.50 2.0113 3.5727×10-7 1.2650 1.2431 213.8478 101 620.40 37.40 2.0119 4.5098×10-7 1.2847 1.2074 196.3093 102 453.40 37.00 1.6437 1.0425×10-6 1.3602 1.1132 275.7352 103 678.60 14.75 1.8721 1.7176×10-7 1.3306 1.1480 837.2890 104 718.10 13.15 2.0527 7.0015×10-8 1.2647 1.2034 427.2372 105 615.20 33.10 2.0934 1.15866×10-7 1.2124 1.2524 113.7532 106 589.10 33.55 1.9420 3.2678×10-7 1.2673 1.2389 257.1990 107 649.50 37.85 2.1063 6.5590×10-7 1.2966 1.2533 163.5833 108 648.05 37.90 2.0915 1.5511×10-6 1.3355 1.2439 198.8860 109 653.95 38.15 2.0951 1.2615×10-6 1.3138 1.2757 209.6240 110 665.20 39.20 2.1463 1.0031×10-6 1.2899 1.3034 166.9648 111 947.05 42.55 2.6799 1.6611×10-6 1.3274 1.3070 133.4828 112 454.90 37.75 1.6428 2.2538×10-6 1.3913 1.1596 331.7340 113 458.65 36.10 1.6525 2.1133×10-6 1.3810 1.1576 251.5761

Table 3. One-diode model parameters in different environmental conditions

**(°C) Iph (A) I01 (A) a1 I02 (A) a2 Rs (Ω) Rp(Ω)** 

1 644.30 22.95 1.9043 3.0432×10-8 1.1883 1.3697×10-7 1.3197 1.2341 294.5317 2 657.70 24.00 1.9446 2.0588×10-8 1.1240 2.0918×10-7 1.5696 1.3141 254.2053 3 662.18 24.50 1.9536 1.3177×10-7 1.3606 4.0695×10-7 1.3606 1.1380 318.7178 4 665.16 25.20 1.9729 2.9981×10-8 1.1706 1.7914×10-7 1.3537 1.2339 248.5131 5 668.85 25.20 1.9745 2.8887×10-8 1.2215 2.0565×10-7 1.3069 1.2181 281.0450 6 456.36 15.20 1.3453 2.4504×10-8 1.2271 2.6436×10-7 1.4485 1.0603 474.6605 7 467.55 14.50 1.3809 2.7889×10-8 1.2443 1.4274×10-7 1.3800 1.1122 340.2013 8 478.00 14.15 1.4212 2.7554×10-8 1.2449 1.6846×10-7 1.3907 1.0636 250.2702 9 558.50 17.80 1.6464 2.9720×10-8 1.2208 1.6773×10-7 1.3810 1.1662 443.9569 10 529.50 17.90 1.5654 3.4963×10-9 1.0648 7.7917×10-7 1.6272 1.2959 306.1568 11 575.00 17.40 1.7003 2.2433×10-8 1.1666 2.1302×10-7 1.5016 1.2351 268.6247 12 601.00 18.10 1.7728 2.8641×10-8 1.2150 1.8419×10-7 1.3616 1.1607 275.4929

**(°C) Iph (A) I0 (A) <sup>a</sup> Rs(Ω) Rp(Ω)** 


46 1006.70 33.05 2.8445 7.7494×10-7 1.2922 1.3580 132.0408 47 1014.20 33.20 2.8548 9.1903×10-7 1.3001 1.3490 162.1626 48 1014.90 33.95 2.8757 7.7393×10-7 1.2816 1.3650 135.7198 49 599.50 44.10 2.0093 3.2553×10-6 1.3443 1.3202 193.5047 50 756.85 50.55 2.2630 2.0566×10-6 1.2958 1.3584 98.4074 51 776.20 50.35 2.3183 9.4350×10-6 1.4552 1.3151 131.0878 52 759.90 50.10 2.3446 1.3496×10-6 1.2650 1.4109 86.7692 53 769.55 49.55 2.3492 3.1359×10-6 1.3436 1.3764 173.6641 54 590.60 48.20 1.9461 1.7518×10-6 1.2990 1.3753 152.9589 55 392.25 45.35 1.4551 7.3811×10-6 1.4749 1.1449 513.8872 56 701.00 36.40 2.1809 6.3023×10-7 1.2744 1.3197 181.3692 57 822.55 36.55 2.4333 1.4581×10-6 1.3457 1.2695 154.6094 58 815.00 36.25 2.3989 8.6293×10-7 1.2995 1.3051 148.3509 59 937.35 35.90 2.6353 7.8507×10-7 1.2924 1.3333 140.9158 60 948.10 35.40 2.6281 6.5875×10-7 1.2819 1.3362 198.5875 61 458.65 37.40 1.7341 2.3307×10-7 1.2435 1.2222 202.9395 62 455.65 37.60 1.7262 2.9317×10-7 1.2605 1.2122 202.2739 63 602.50 38.40 2.0061 2.2729×10-7 1.2318 1.2910 179.7304 64 706.90 38.45 2.1841 6.2885×10-7 1.3100 1.2227 176.9047 65 705.40 36.60 2.1762 3.4172×10-7 1.2607 1.2898 185.8031 66 703.90 38.70 2.1727 4.4171×10-7 1.2803 1.2778 178.6681 67 780.75 37.00 2.2865 2.7213×10-7 1.2499 1.2911 155.5827 68 777.75 36.40 2.2661 6.4822×10-7 1.3257 1.2351 196.1866 69 777.00 35.80 2.2597 3.5896×10-7 1.2797 1.2661 180.5390 70 886.60 44.45 2.4968 5.9216×10-7 1.2747 1.2546 153.3574 71 879.15 44.25 2.4217 1.7378×10-6 1.3740 1.2205 360.6990 72 830.70 40.05 2.4218 6.8898×10-7 1.3016 1.2563 247.4058 73 818.80 40.30 2.4188 7.9099×10-7 1.3181 1.2113 137.7473 74 749.45 38.95 2.2718 6.9207×10-7 1.3136 1.2329 232.5429 75 746.45 38.70 2.2801 5.1192×10-7 1.2905 1.2244 168.6507 76 604.75 45.95 2.0164 1.5572×10-6 1.2660 1.3880 165.8156 77 987.30 48.80 2.7459 3.1186×10-6 1.3124 1.4018 115.7579 78 981.05 50.00 2.7064 4.3017×10-6 1.3400 1.4091 151.9670 79 519.00 33.70 1.7947 5.8455×10-7 1.2951 1.2475 281.8090 80 516.00 34.90 1.8017 4.0818×10-7 1.2618 1.2594 205.2749 81 615.95 36.35 2.0075 6.1718×10-7 1.2774 1.2940 218.7826 82 615.20 36.50 2.0152 4.5464×10-7 1.2507 1.3113 168.6899 83 648.75 37.90 2.0960 4.6946×10-7 1.2710 1.2501 148.6441 84 778.50 35.70 2.3769 3.8760×10-7 1.2713 1.2666 160.5721 85 836.70 25.00 2.4144 2.1683×10-7 1.2840 1.2112 228.6814 86 850.10 25.40 2.4656 1.6939×10-7 1.2639 1.2282 180.5302 87 839.65 23.15 2.4409 2.2484×10-7 1.2938 1.1793 183.7797

**(°C) Iph (A) I0 (A) <sup>a</sup> Rs(Ω) Rp(Ω)** 

**Irradiance (W/m2)** 

**Temperature** 


Table 3. One-diode model parameters in different environmental conditions


Evaluation the Accuracy of One-Diode and Two-Diode

**Temperature** 

**Irradiance (W/m2)** 

Models for a Solar Panel Based Open-Air Climate Measurements 219

55 392.25 45.35 1.4567 6.3763×10-7 1.3514 2.1097×10-6 1.3685 1.2832 449.1823 56 701.00 36.40 2.1796 5.9120×10-8 1.2659 6.4841×10-7 1.2862 1.3258 185.9257 57 822.55 36.55 2.4292 8.8912×10-8 1.3149 9.5018×10-7 1.3149 1.2908 148.4283 58 815.00 36.25 2.3942 7.8008×10-8 1.3071 8.6383×10-7 1.3071 1.3137 158.4158 59 937.35 35.90 2.6380 5.6508×10-8 1.1643 5.8327×10-7 1.3081 1.3438 125.1391 60 948.10 35.40 2.6253 7.7330×10-8 1.3167 9.1644×10-7 1.3172 1.3343 238.5130 61 458.65 37.40 1.7340 2.0356×10-8 1.0972 4.2763×10-7 1.4106 1.2842 196.2692 62 455.65 37.60 1.7239 3.0959×10-8 1.1392 4.4560×10-7 1.3674 1.2573 216.5685 63 602.50 38.40 2.0035 3.1412 ×10-8 1.1813 4.8461×10-7 1.3212 1.2244 180.2013 64 706.90 38.45 2.1800 5.4562×10-8 1.3504 9.3287×10-7 1.3503 1.2132 194.9991 65 705.40 36.60 2.1695 2.9715×10-8 1.3401 8.3436×10-7 1.3401 1.2273 210.6548 66 703.90 38.70 2.1708 2.9240×10-8 1.3187 6.6092×10-7 1.3187 1.2416 177.3929 67 780.75 37.00 2.2875 1.2985×10-8 1.0604 1.8326×10-6 1.6166 1.3705 151.6619 68 777.75 36.40 2.2669 7.9289×10-8 1.0395 2.0258×10-6 1.6016 1.3944 189.5926 69 777.00 35.80 2.2613 1.0495×10-8 1.0530 2.1107×10-6 1.6648 1.3922 174.3726 70 886.60 44.45 2.4906 5.3519×10-8 1.1734 5.0326×10-7 1.2961 1.2738 151.7814 71 879.15 44.25 2.4246 4.7363×10-8 1.2251 8.2091×10-7 1.3194 1.2895 317.8984 72 830.70 40.05 2.4173 2.0975×10-7 1.3619 1.1345×10-6 1.3619 1.2276 289.4507 73 818.80 40.30 2.4138 4.3268×10-8 1.3130 7.0331×10-7 1.3130 1.2228 141.9730 74 749.45 38.95 2.2701 8.8746×10-8 1.3359 9.5496×10-7 1.3522 1.1952 238.7603 75 746.45 38.70 2.2769 3.4376×10-8 1.3022 6.5867×10-7 1.3174 1.2048 173.1026 76 604.75 45.95 2.0155 2.1057×10-7 1.2517 1.4359×10-6 1.2742 1.3825 166.8131 77 987.30 48.80 2.7327 3.8961×10-6 1.4222 5.1035×10-6 1.4221 1.3555 150.1287 78 981.05 50.00 2.7015 2.1267×10-6 1.3779 4.0844×10-6 1.3779 1.4000 164.3968 79 519.00 33.70 1.7890 3.6873×10-7 1.4160 1.7341×10-6 1.4160 1.1666 388.5935 80 516.00 34.90 1.7966 2.8663×10-7 1.3823 1.2693×10-6 1.3824 1.1770 259.5067 81 615.95 36.35 2.0065 5.4318×10-8 1.2134 5.3810×10-7 1.2844 1.2897 206.7961 82 615.20 36.50 2.0134 5.5856×10-8 1.1890 4.8161×10-7 1.2822 1.3032 171.1018 83 648.75 37.90 2.0925 4.2362×10-8 1.1432 5.3933×10-7 1.3437 1.2704 149.7204 84 778.50 35.70 2.3755 3.8038×10-8 1.1490 4.7462×10-7 1.3515 1.2931 161.9807 85 836.70 25.00 2.4100 3.0253×10-8 1.3337 3.7734×10-7 1.3361 1.1797 260.1578 86 850.10 25.40 2.4609 3.0968×10-8 1.3033 2.4821×10-7 1.3033 1.2173 195.0512 87 839.65 23.15 2.4396 2.5111×10- 1.1490 1.9083×10-7 1.4551 1.2452 169.0755 88 838.16 23.05 2.4322 2.4870×10-8 1.1509 2.0781×10-7 1.4440 1.2393 172.6510 89 844.15 23.35 2.4427 1.2633×10-8 1.0985 1.0025×10-9 1.7022 1.3270 152.1720 90 781.50 20.80 2.2524 9.4105×10-9 1.1001 1.4127×10-6 1.7709 1.2685 219.9114 91 775.50 20.45 2.2298 1.6292×10-8 1.1488 4.3632×10-7 1.4821 1.1884 260.3549 92 612.25 15.55 1.7738 2.4899×10-8 1.1970 1.3638×10-7 1.5022 1.1488 289.5701 93 609.25 15.00 1.7733 2.9613×10-8 1.2056 6.0005×10-8 1.5044 1.1616 247.4696 94 601.75 14.75 1.7590 2.7260×10-8 1.2505 1.9787×10-7 1.3990 1.0152 277.5651 95 240.85 31.40 1.0832 7.6864×10-7 1.4388 1.7435×10-6 1.4391 0.9077 320.8844 96 241.60 31.65 1.0832 1.0096×10-6 1.4575 2.1944×10-6 1.4580 0.8800 315.9751

**(°C) Iph (A) I01 (A) a1 I02 (A) a2 Rs (Ω) Rp(Ω)** 


13 605.50 18.45 1.7850 2.5508×10-8 1.1760 1.8028×10-7 1.4433 1.2442 316.8041 14 474.25 13.65 1.3797 3.0408×10-8 1.3842 2.9990×10-7 1.3846 0.9578 312.5028 15 495.15 14.20 1.4398 2.7505×10-8 1.2616 1.9085×10-7 1.3710 1.0181 268.2193 16 528.00 18.30 1.5321 2.3850×10-8 1.1597 1.9136×10-7 1.4811 1.2332 302.4667 17 528.00 18.45 1.5458 5.7239×10-9 1.0782 6.9380×10-7 1.5793 1.2685 298.4500 18 537.00 18.30 1.5612 2.8985×10-8 1.1918 1.8355×10-7 1.3790 1.1295 254.8772 19 557.80 21.00 1.6153 2.9673×10-8 1.2465 2.6445×10-7 1.3220 1.1547 356.6941 20 548.80 22.00 1.5912 2.9889×10-8 1.1972 1.6498×10-7 1.3094 1.1999 289.9760 21 524.25 21.50 1.5337 2.4210×10-8 1.1624 3.3020×10-7 1.4010 1.1874 396.9221 22 517.50 20.65 1.4707 2.9247×10-8 1.1909 2.4577×10-7 1.3534 1.1742 395.9226 23 533.15 19.85 1.5767 2.9454×10-8 1.1883 1.9557×10-7 1.3592 1.1708 611.9569 24 946.25 40.85 2.6531 2.5017×10-6 1.4644 3.6255×10-6 1.4643 1.2576 222.6724 25 945.50 42.90 2.6524 2.4917×10-7 1.3377 1.5983×10-6 1.3396 1.3038 165.3972 26 778.50 33.40 2.1998 1.1948×10-8 1.0729 1.4190×10-6 1.7427 1.3897 355.8168 27 762.30 33.15 2.2196 2.7598×10-8 1.1455 2.8448×10-7 1.3577 1.2938 200.6356 28 789.00 34.15 2.2859 2.8133×10-8 1.2301 4.0767×10-7 1.3213 1.2504 226.2728 29 782.25 33.80 2.2787 1.9512×10-8 1.1067 4.2830×10-7 1.4745 1.3242 187.2231 30 391.20 41.80 1.4425 2.5260×10-7 1.3334 1.5355×10-6 1.3554 1.2526 350.9833 31 914.95 21.95 2.5641 2.9959×10-8 1.2141 2.4595×10-7 1.2967 1.3091 195.5702 32 917.95 23.85 2.5827 5.4386×10-8 1.3181 5.0320×10-7 1.3275 1.2698 199.2378 33 923.20 27.00 2.6221 9.0452×10-9 1.0543 1.2920×10-6 1.4846 1.3512 137.6304 34 1004.50 34.60 2.8311 6.8694×10-8 1.1262 9.0237×10-7 1.3614 1.4110 152.6305 35 1004.50 35.15 2.8410 6.4888×10-8 1.1394 8.3690×10-7 1.3241 1.3880 142.3507 36 994.75 34.25 2.8144 1.1388×10-7 1.2995 1.0543×10-6 1.2999 1.3414 148.7050 37 900.80 34.90 2.6371 2.5877×10-7 1.3474 1.7108×10-6 1.3502 1.3179 171.1347 38 899.30 35.55 2.6451 7.9309×10-8 1.2414 6.1660×10-7 1.2594 1.3682 150.0456 39 808.30 36.40 2.4660 1.4170×10-7 1.3019 1.1481×10-6 1.3073 1.3361 184.8603 40 811.30 36.80 2.4842 1.8339×10-7 1.3129 1.1981×10-6 1.3128 1.3281 159.9860 41 630.90 36.10 2.1256 2.5422×10-6 1.4743 3.6746×10-6 1.4743 1.1656 248.2853 42 633.85 36.20 2.1413 2.2951×10-6 1.4692 3.4374×10-6 1.4690 1.1719 217.3854 43 637.55 35.85 2.1516 9.4216×10-8 1.3134 1.1090×10-6 1.3134 1.3044 184.2421 44 406.40 34.10 1.5958 2.9422×10-7 1.3599 1.3358×10-6 1.3611 1.1440 237.6602 45 412.35 33.00 1.6175 1.2768×10-6 1.4603 2.4944×10-6 1.4605 1.0597 258.8879 46 1006.70 33.05 2.8442 5.6206×10-8 1.1902 6.3607×10-7 1.3014 1.3825 134.8388 47 1014.20 33.20 2.8506 2.0098×10-7 1.3564 1.5479×10-6 1.3583 1.3247 197.6830 48 1014.90 33.95 2.8735 1.1218×10-7 1.3243 1.1483×10-6 1.3243 1.3351 140.4835 49 599.50 44.10 2.0076 9.6057×10-7 1.3467 2.3573×10-6 1.3467 1.3091 178.8528 50 756.85 50.55 2.2601 1.9992×10-6 1.3906 3.3102×10-6 1.3904 1.3121 108.5623 51 776.20 50.35 2.3243 6.7891×10-7 1.3131 2.3084×10-6 1.3385 1.4005 110.3408 52 759.90 50.10 2.3479 1.6993×10-7 1.1701 5.8437×10-7 1.2368 1.4630 84.6207 53 769.55 49.55 2.3457 2.2463×10-6 1.4075 3.5604×10-6 1.4074 1.3535 201.9657 54 590.60 48.20 1.9409 5.6130×10-7 1.3287 1.8279×10-6 1.3287 1.3952 158.5665

**(°C) Iph (A) I01 (A) a1 I02 (A) a2 Rs (Ω) Rp(Ω)** 

**Irradiance (W/m2)** 

**Temperature** 


Evaluation the Accuracy of One-Diode and Two-Diode

Models for a Solar Panel Based Open-Air Climate Measurements 221

(a)

(b)

Fig. 13. The I-V curves #33 and its one-diode model


Table 4. Two-diode model parameters in different environmental conditions

#### **5. Results and their commentary**

As discussed earlier, Tables 3 and 4 show the models parameters for the poly-crystalline silicon solar panel. It is easily seen any parameters in both models is not equal together. There are many interesting observations that could be made upon examination of the models. Figs. 13 and 14 show the I-V and P-V characteristic curves of #33 and their corresponding one-diode and two-diode models.

Comparison among the extracted I-V curves show that the both models have high accuracy. It can be seen that the one-diode model with variable diode ideally factor (n) can also models the solar panel accurately. The mentioned approach was repeated for all the curves and similar results were obtained.

Table 5 shows the main characteristics (Pmax, Voc, Isc and Fill Factor) of the solar panel for several measured curves and the corresponding one-diode and two-diode models corresponding parameters. The Fill Factor is described by Equation (7) [1].

$$\text{FF} = \frac{\mathbf{V\_{mp}} \mathbf{I\_{mp}}}{\mathbf{V\_{oc}} \mathbf{I\_{sc}}} \tag{7}$$

In continue dependency of the models parameters over environmental conditions is expressed. Figures 15, 16 and 17 show appropriate sheets fitted on the distribution data (i.e. some of one-diode model parameters) drawn by MATLAB (thin plate smoothing splint fitting). Dependency of the model parameters could be seen from the figures. It could be easily seen that the relation between Iph and irradiance is approximately increasing linear and its dependency with temperature is also the same behavior. Other commentaries could be expressed for other model parameters. Thin plate smoothing splint fitting could be also carried out for two-diode model.

97 876.20 35.40 2.4400 5.9112×10-8 1.1237 6.9247×10-7 1.3634 1.3776 148.9166 98 873.25 36.45 2.4181 5.7254×10-8 1.1237 6.8324×10-7 1.3591 1.3861 154.3058 99 453.40 34.10 1.6455 4.0638×10-7 1.3908 1.5872×10-6 1.3921 1.1546 268.8136 100 617.40 38.50 2.0073 3.2293×10-8 1.2287 4.8840×10-7 1.3040 1.2366 241.8706 101 620.40 37.40 2.0146 2.7671×10-8 1.0959 4.7090×10-7 1.4730 1.3276 181.4589 102 453.40 37.00 1.6427 4.6296×10-8 1.3259 6.7511×10-7 1.3262 1.1444 253.0705 103 678.60 14.75 1.8738 2.7386×10-8 1.2386 1.8163×10-7 1.4012 1.1645 756.5171 104 718.10 13.15 2.0557 1.1487×10-8 1.1480 9.7984×10-7 1.8497 1.2781 404.3674 105 615.20 33.10 2.0924 2.7213×10-8 1.1383 6.1137×10-7 1.3848 1.1947 116.7962 106 589.10 33.55 1.9408 2.9259×10-8 1.1168 3.8318×10-7 1.4000 1.3141 242.0028 107 649.50 37.85 2.1087 3.3872×10-8 1.1031 7.3445×10-7 1.4255 1.3455 152.8020 108 648.05 37.90 2.0881 9.7714×10-7 1.4012 2.0786×10-6 1.4040 1.1869 209.7529 109 653.95 38.15 2.0926 2.2252×10-7 1.3486 1.6059×10-6 1.3486 1.2456 228.6922 110 665.20 39.20 2.1417 2.5978×10-7 1.3349 1.3822×10-6 1.3349 1.2873 185.4866 111 947.05 42.55 2.6777 4.5174×10-7 1.3483 1.7329×10-6 1.3546 1.2946 139.3115 112 454.90 37.75 1.6429 8.0987×10-8 1.3366 1.3234×10-6 1.3447 1.2234 311.6319 113 458.65 36.10 1.6527 1.3443×10-7 1.3189 1.2103×10-6 1.3386 1.2193 244.6175

Table 4. Two-diode model parameters in different environmental conditions

corresponding parameters. The Fill Factor is described by Equation (7) [1].

FF

As discussed earlier, Tables 3 and 4 show the models parameters for the poly-crystalline silicon solar panel. It is easily seen any parameters in both models is not equal together. There are many interesting observations that could be made upon examination of the models. Figs. 13 and 14 show the I-V and P-V characteristic curves of #33 and their

Comparison among the extracted I-V curves show that the both models have high accuracy. It can be seen that the one-diode model with variable diode ideally factor (n) can also models the solar panel accurately. The mentioned approach was repeated for all the curves

Table 5 shows the main characteristics (Pmax, Voc, Isc and Fill Factor) of the solar panel for several measured curves and the corresponding one-diode and two-diode models

> mp mp oc sc

V I (7)

V I

In continue dependency of the models parameters over environmental conditions is expressed. Figures 15, 16 and 17 show appropriate sheets fitted on the distribution data (i.e. some of one-diode model parameters) drawn by MATLAB (thin plate smoothing splint fitting). Dependency of the model parameters could be seen from the figures. It could be easily seen that the relation between Iph and irradiance is approximately increasing linear and its dependency with temperature is also the same behavior. Other commentaries could be expressed for other model parameters. Thin plate smoothing splint fitting could be also

**(°C) Iph (A) I01 (A) a1 I02 (A) a2 Rs (Ω) Rp(Ω)** 

**Irradiance (W/m2)** 

**Temperature** 

**5. Results and their commentary** 

and similar results were obtained.

carried out for two-diode model.

corresponding one-diode and two-diode models.

Fig. 13. The I-V curves #33 and its one-diode model

Evaluation the Accuracy of One-Diode and Two-Diode

Table 5. The main characteristics of the solar panel

**Curve No.** 

*Measurements 1-diode model 2-diode model Measurements 1-*

 *diode model 2-*

33 31.8064 31.8 31.9203 2.5993 2.5929 2.5908 19.9972 19.9972 19.9972 0.6119 0.6134 0.6161

63 25.1194 25.1201 25.0915 1.9918 1.9884 1.9866 19.6316 19.6316 19.6316 0.6424 0.6427 0.6434

79 22.4528 22.4681 22.3444 1.7867 1.7848 1.7822 19.2940 19.2940 19.2940 0.6513 0.6509 0.6498

90 31.0414 31.0373 31.1237 2.2443 2.2371 2.2362 21.066 21.066 21.066 0.6566 0.6582 0.6607

*diode model Measurements 1-diode model 2-diode model Measurements 1-*

 *diode model 2-*

 *diode model* 

**Pmax(W) Isc(A) Voc(V) Fill Factor (FF)** 

Models for a Solar Panel Based Open-Air Climate Measurements 223

Fig. 14. The I-V curves #33 and its two-diode model


Table 5. The main characteristics of the solar panel

(a)

(b)

Fig. 14. The I-V curves #33 and its two-diode model

Evaluation the Accuracy of One-Diode and Two-Diode

Models for a Solar Panel Based Open-Air Climate Measurements 225

Fig. 17. Fitted sheet on shunt resistance of one-diode model by MATLAB.

In this research, a new approach to define one-diode and two-diode models of a solar panel were developed through using outdoor solar panel I-V curves measurement. For one-diode model five nonlinear equations and for two-diode model seven nonlinear equations were introduced. Solving the nonlinear equations lead us to define unknown parameters of the both models respectively. The Newton's method was chosen to solve the models nonlinear equations A modification was also reported in the Newton's solving approach to attain the best convergence. Then, a comprehensive measurement system was developed and implemented to extract solar panel I-V curves in open air climate condition. To evaluate accuracy of the models, output characteristics of the solar panel provided from simulation results were compared with the data provided from experimental results. The comparison showed that the results from simulation are compatible with data form measurement for both models and the both proposed models have the same accuracy in the measurement range of environmental conditions approximately. Finally, it was shown that all parameters of the both models have dependency on environmental conditions which they were extracted by thin plates smoothing splint fitting. Extracting mathematical expression for dependency of the each parameter of the models over environmental conditions will carry

**6. Conclusion** 

out in our future research.

Fig. 15. Fitted sheet on photo-current of one-diode model by MATLAB.

Fig. 16. Fitted sheet on series resistance of one-diode model by MATLAB.

Fig. 17. Fitted sheet on shunt resistance of one-diode model by MATLAB.

#### **6. Conclusion**

224 Solar Cells – Silicon Wafer-Based Technologies

Fig. 15. Fitted sheet on photo-current of one-diode model by MATLAB.

Fig. 16. Fitted sheet on series resistance of one-diode model by MATLAB.

In this research, a new approach to define one-diode and two-diode models of a solar panel were developed through using outdoor solar panel I-V curves measurement. For one-diode model five nonlinear equations and for two-diode model seven nonlinear equations were introduced. Solving the nonlinear equations lead us to define unknown parameters of the both models respectively. The Newton's method was chosen to solve the models nonlinear equations A modification was also reported in the Newton's solving approach to attain the best convergence. Then, a comprehensive measurement system was developed and implemented to extract solar panel I-V curves in open air climate condition. To evaluate accuracy of the models, output characteristics of the solar panel provided from simulation results were compared with the data provided from experimental results. The comparison showed that the results from simulation are compatible with data form measurement for both models and the both proposed models have the same accuracy in the measurement range of environmental conditions approximately. Finally, it was shown that all parameters of the both models have dependency on environmental conditions which they were extracted by thin plates smoothing splint fitting. Extracting mathematical expression for dependency of the each parameter of the models over environmental conditions will carry out in our future research.

Evaluation the Accuracy of One-Diode and Two-Diode

leads to Eq. (15).

proposed coefficient.

**9. References** 

**8. Acknowledgment** 

Science and Technology (IROST).

Spain, June 2007

Sons, ISBN: 0-470-84527-9, England

doi:10.1016/j.apenergy.2006.04.007

dio:10.1016/j.energy.2006.12.006

doi:10.1016/j.solmat.2004.07.019

2004

2005), pp. 78–88, doi:10.1016/j.solener.2005.06.010

appropriate convergence, a modification coefficient (0 1)

Models for a Solar Panel Based Open-Air Climate Measurements 227

new old xx x

Finally, the above iteration is repeated by the new start point (x ) new while the error was less than an acceptable level. The above iterative numerical approach is implemented for the two-diode models with seven nonlinear equations system. It was seen that to have an

> new old xx x

The modified approach has good response to solve the models equations by tuning the

This work was in part supported by a grant from the Iranian Research Organization for

Castaner, L.; Silvestre, S. (2002). *Modeling Photovoltaic Systems using Pspice,* John Wiley &

Sera, D.; Teodorescu, R. & Rodriguez, P. (2007). PV panel model based on datasheet values,

De Soto, W.; Klein, S.A. & Beckman, W.A. (2006). Improvement and validation of a model

Celik, A.N.; Acikgoz, N. (2007). Modeling and experimental verification of the operating

Chenni, R.; Makhlouf, M.; Kerbache, T. & Bouzid, A. (2007). A detailed modeling method for

Gow, J.A. & Manning, C.D. (1999). Development of a Photovoltaic Array Model for Use in

Vol. 146, No. 2, (September 1998), pp. 193-200, doi:10.1049/ip-epa:19990116 Merbah, M.H.; Belhamel, M.; Tobias, I. & Ruiz, J.M. (2005). Extraction and analysis of solar

Xiao, W.; Dunford, W. & Capel, A. (2004). A novel modeling method for photovoltaic cells,

*IEEE International Symposium on Industrial Electronics*, ISBN: 978-1-4244-0754-5,

for photovoltaic array performance, *Elsevier, Solar Energy,* Vol. 80, No. 1, (June

current of mono-crystalline photovoltaic modules using four- and five-parameter models, *Elsevier, Applied Energy,* Vol. 84, No. 1, (June 2006), pp. 1–15,

photovoltaic cells, *Elsevier, Energy,* Vol. 32, No. 9, (Decembere 2006), pp. 1724–1730,

Power-Electronic Simulation Studies, *IEE proceeding, Electrical Power Applications,*

cell parameters from the illuminated current-voltage curve, *Elsevier, Solar Energy Material and Solar Cells,* Vol. 87, No. 1-4, (July 2004), pp. 225-233,

*35th IEEE Power Electronic Specialists Conference*, ISBN: 0-7803-8399-0, Germany, June

(14)

is added to Eq. (14) and it

(15)

#### **7. Appendix**

Equations (8-12) state the one-diode model nonlinear equations for a solar panel. Five unknown parameters; ph 0 s I ,I ,n,R and R should be specified. p

$$\mathbf{I}\_{\rm sc} = \mathbf{I}\_{\rm ph} - \mathbf{I}\_0 \mathbf{e}^{\frac{\mathbf{I}\_{\rm sc} \mathbf{R}\_s}{\mathbf{V}\_\Gamma}} - \frac{\mathbf{I}\_{\rm sc} \mathbf{R}\_s}{\mathbf{R}\_\mathbf{P}} \tag{8}$$

$$\mathbf{I}\_{\rm oc} = \mathbf{0} = \mathbf{I}\_{\rm ph} - \mathbf{I}\_0 \mathbf{e}^{\frac{\mathbf{V}\_{\rm oc}}{\mathbf{V}\_{\rm T}}} - \frac{\mathbf{V}\_{\rm oc}}{\mathbf{R}\_{\rm P}} \tag{9}$$

$$\mathbf{I}\_{\rm mpp} = \mathbf{I}\_{\rm ph} - \mathbf{I}\_0 \mathbf{e} \frac{\mathbf{V}\_{\rm mpp} + \mathbf{I}\_{\rm mpp} \mathbf{R}\_s}{\mathbf{V}\_{\rm T}} - \frac{\mathbf{V}\_{\rm mpp} + \mathbf{I}\_{\rm mpp} \mathbf{R}\_s}{\mathbf{R}\_{\rm p}} \tag{10}$$

$$\mathbf{I}\_{\mathbf{x}} = \mathbf{I}\_{\mathrm{ph}} - \mathbf{I}\_0 \mathbf{e}^{\frac{\mathbf{V}\_{\mathbf{x}} + \mathbf{I}\_{\mathbf{x}} \mathbf{R}\_{\mathbf{x}}}{\mathbf{V}\_{\mathbf{T}}}} - \frac{\mathbf{V}\_{\mathbf{x}} + \mathbf{I}\_{\mathbf{x}} \mathbf{R}\_{\mathbf{s}}}{\mathbf{R}\_{\mathbf{P}}} \tag{11}$$

$$\mathbf{I}\_{\infty} = \mathbf{I}\_{\text{ph}} - \mathbf{I}\_0 \mathbf{e}^{\frac{\mathbf{V}\_{\infty} + \mathbf{I}\_{\infty} \mathbf{R}\_s}{\mathbf{V}\_{\Gamma}}} - \frac{\mathbf{V}\_{\infty} + \mathbf{I}\_{\infty} \mathbf{R}\_s}{\mathbf{R}\_p} \tag{12}$$

Therefore, the five aforementioned nonlinear equations must be solved to define the model. Newton's method is chosen to solve the equations which its foundation is based on using Jacobean matrix. MATLAB software environment is used to express the Jacobean matrix.


To solve the equations, a starting point 0 ph 0 T s p x [I ,I ,V ,R ,R ] must be determined and both matrixes R&J are also examined at that point. Then x is described based on the Eq. (13) and consequently Eq. (14) states the new estimation for the root of the equations.

$$\mathbf{J}^{k}\delta\mathbf{x}^{k} = -\mathbf{R}^{k} \tag{13}$$

$$\mathbf{x}\_{\text{new}} = \mathbf{x}\_{\text{old}} + \delta \mathbf{x} \tag{14}$$

Finally, the above iteration is repeated by the new start point (x ) new while the error was less than an acceptable level. The above iterative numerical approach is implemented for the two-diode models with seven nonlinear equations system. It was seen that to have an appropriate convergence, a modification coefficient (0 1) is added to Eq. (14) and it leads to Eq. (15).

$$\mathbf{x}\_{\text{new}} = \mathbf{x}\_{\text{old}} + \boldsymbol{\alpha} \times \boldsymbol{\delta} \mathbf{x} \tag{15}$$

The modified approach has good response to solve the models equations by tuning the proposed coefficient.

#### **8. Acknowledgment**

This work was in part supported by a grant from the Iranian Research Organization for Science and Technology (IROST).

#### **9. References**

226 Solar Cells – Silicon Wafer-Based Technologies

Equations (8-12) state the one-diode model nonlinear equations for a solar panel. Five

I R I I Ie

<sup>V</sup> oc oc ph 0

<sup>V</sup> I 0 I Ie

mpp mpp s T V IR

x xs T V IR <sup>V</sup> x xs x ph 0

xx xx s T V IR <sup>V</sup> xx xx s xx ph 0

Therefore, the five aforementioned nonlinear equations must be solved to define the model. Newton's method is chosen to solve the equations which its foundation is based on using Jacobean matrix. MATLAB software environment is used to express the Jacobean

> 22222 1 ph 0 T s p <sup>12345</sup> 2 ph 0 T s p

fffff f (I ,I ,V ,R ,R ) 0 xxxxx f (I ,I ,V ,R ,R ) 0

 

To solve the equations, a starting point 0 ph 0 T s p x [I ,I ,V ,R ,R ] must be determined and

kk k Jx R 

(13) and consequently Eq. (14) states the new estimation for the root of the equations.

ffff R f (I ,I ,V ,R ,R ) 0 , J

V IR I I Ie

V IR I I Ie

sc s T I R <sup>V</sup> sc s sc ph 0

> oc T V

p

p

p V IR

(10)

(11)

(12)

11111 12345

fffff xxxxx

 

3333

(13)

44444 12345 55555 12345

fffff xxxxx fffff xxxxx

3 4 5

f x x

is described based on the Eq.

123

xxx

R

p

p

R

R

V mpp mpp s

<sup>R</sup> (8)

<sup>R</sup> (9)

unknown parameters; ph 0 s I ,I ,n,R and R should be specified. p

mpp ph 0

3 ph 0 T s p

4 ph 0 T s p 5 ph 0 T s p

f (I ,I ,V ,R ,R ) 0 f (I ,I ,V ,R ,R ) 0

both matrixes R&J are also examined at that point. Then x

I I Ie

**7. Appendix** 

matrix.


**11** 

*Italy* 

**Non-Idealities in the I-V** 

**Characteristic of the PV Generators:** 

Filippo Spertino, Paolo Di Leo and Fabio Corona *Politecnico di Torino, Dipartimento di Ingegneria Elettrica* 

**Manufacturing Mismatch and Shading Effect** 

A single solar cell can generate an electric power too low for the majority of the applications (2,5 - 4 W at 0,5 V). This is the reason why a group of cells is connected together in series and encapsulated in a panel, known as PhotoVoltaic (PV) module. Moreover, since the output power of a PV module is not so high (few hundreds of watts), then a photovoltaic generator is constituted generally by an array of strings in parallel, each one made by a series of PV

Unfortunately, the current-voltage (I-V) characteristic of each cell, and so also of each PV module, differs nearly from that of the other ones. The causes can be found in the manufacturing tolerance, i.e. the pattern of crystalline domains in poly-silicon cells, or the different aging of each element of the PV generator, or in the presence of not uniformly distributed shade over the PV array. These phenomena can cause important losses in the energy production of the generator, but they could also lead to destructive effects, such as "hot spots", or even the breakdown of single solar cells. The aim of this chapter is to examine the mismatch in all its forms and effects, exposing some experimental works through simulation and real case studies, in order to investigate the solutions which were

Firstly, it will be worthy to explain the I-V mismatch in general for the solar cells, making a classification in series and parallel mismatch. In the first case the effect of the different shortcircuit current (and maximum power point current) of each solar cell is that the total I-V characteristic of a string of series-connected cells can be constructed summing the voltage of each cell at the same current value, fixed by the worst element of the string. This means that the string I-V curve is strongly limited by the short-circuit current of the bad cell, and consequently the total output power is much less than the sum of each cell maximum power. This phenomenon is more relevant in the case of shading than in presence of production tolerance. It will be shown that the bad cell does not perform as an open circuit, but like a low resistance (a few ohms or a few tens of ohms), becoming a load for the other solar cells. In particular, it is subject to an inverse voltage and it dissipates power, then if the power dissipation is too high, it will be possible the formation of some "hot spots", with

modules, in order to obtain the requested electric power.

thought to minimize the effects of the mismatch.

**2. Series/parallel mismatch in the I-V characteristic** 

**1. Introduction** 

Walker, G. R. (2001). Evaluating MPPT converter topologies using a MATLAB PV model, *Journal of Electrical and Electronics Engineering,* Vol. 21, No. 1, (2001), pp. 49–55, ISSN: 0725-2986

### **Non-Idealities in the I-V Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect**

Filippo Spertino, Paolo Di Leo and Fabio Corona *Politecnico di Torino, Dipartimento di Ingegneria Elettrica Italy* 

#### **1. Introduction**

228 Solar Cells – Silicon Wafer-Based Technologies

Walker, G. R. (2001). Evaluating MPPT converter topologies using a MATLAB PV model,

ISSN: 0725-2986

*Journal of Electrical and Electronics Engineering,* Vol. 21, No. 1, (2001), pp. 49–55,

A single solar cell can generate an electric power too low for the majority of the applications (2,5 - 4 W at 0,5 V). This is the reason why a group of cells is connected together in series and encapsulated in a panel, known as PhotoVoltaic (PV) module. Moreover, since the output power of a PV module is not so high (few hundreds of watts), then a photovoltaic generator is constituted generally by an array of strings in parallel, each one made by a series of PV modules, in order to obtain the requested electric power.

Unfortunately, the current-voltage (I-V) characteristic of each cell, and so also of each PV module, differs nearly from that of the other ones. The causes can be found in the manufacturing tolerance, i.e. the pattern of crystalline domains in poly-silicon cells, or the different aging of each element of the PV generator, or in the presence of not uniformly distributed shade over the PV array. These phenomena can cause important losses in the energy production of the generator, but they could also lead to destructive effects, such as "hot spots", or even the breakdown of single solar cells. The aim of this chapter is to examine the mismatch in all its forms and effects, exposing some experimental works through simulation and real case studies, in order to investigate the solutions which were thought to minimize the effects of the mismatch.

#### **2. Series/parallel mismatch in the I-V characteristic**

Firstly, it will be worthy to explain the I-V mismatch in general for the solar cells, making a classification in series and parallel mismatch. In the first case the effect of the different shortcircuit current (and maximum power point current) of each solar cell is that the total I-V characteristic of a string of series-connected cells can be constructed summing the voltage of each cell at the same current value, fixed by the worst element of the string. This means that the string I-V curve is strongly limited by the short-circuit current of the bad cell, and consequently the total output power is much less than the sum of each cell maximum power. This phenomenon is more relevant in the case of shading than in presence of production tolerance. It will be shown that the bad cell does not perform as an open circuit, but like a low resistance (a few ohms or a few tens of ohms), becoming a load for the other solar cells. In particular, it is subject to an inverse voltage and it dissipates power, then if the power dissipation is too high, it will be possible the formation of some "hot spots", with

Non-Idealities in the I-V

Spectral current density [A/m2

m]

g1()

Fig. 1. Comparison of solar spectra in winter and summer.

g2()

Solar spectrum (W/m2

m)

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 231

is noteworthy that between 0.9 and 1m, where S() is high, the winter spectrum exceeds the summer spectrum. Figure 2 shows the quantities S()·g1() and S()·g2(), named spectral current density I1 e I2, which have units of A/(m2m). Not only in this example, but in many cases KS is higher in winter than in summer and the deviations are roughly 5%.

g2(): 7 August ; g1(): 24 February

S()

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Wavelength (m)

i2(): 7 August ; i1(): 24 February

i2()

Fig. 2. Comparison of spectral current density in winter and summer.

*<sup>o</sup> I* and quality factor of junction *m* are the diode parameters to be determined:

*j o IIe*

i1()

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Wavelength (m)

The rated power of the PV devices is defined at Standard Test Conditions (STC), corresponding to the solar spectrum at noon in the spring/autumn equinox, with clear sky. This global irradiance (GSTC = 1000 W/m2) is also referred as Air Mass (AM) equal to 1.5. Then, considering the non linear diode, on the one hand, the first equivalent circuit is based on a single exponential model for the P-N junction, in which the reverse saturation current

1

*j c qV mkT*

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(3)

Spectral response (A/W)

degradation and early aging of the solar cell. Furthermore, if the inverse voltage applied to a shaded cell exceeds its breakdown value, it could be destroyed. The worst situation is with the string in short-circuit, when all the voltage of the irradiated cells is applied to the shaded ones. It is clear that the most dangerous case occurs if the shaded cell is only one, while the experience shows that usually with two shaded cells the heating is still acceptable.

The solution adopted worldwide for this problem is the by-pass diode in anti-parallel connection with a group of solar cell for each module. In this way, the output power decreases only of the contribution of the group of bad cells and the inverse voltage is limited by the diode.

In the case of parallel of strings, it is the voltage mismatch which becomes important. The total I-V characteristic can be constructed summing the current of each string at the same voltage value. The total open-circuit voltage will be very close to that of the bad string. The worst case for the bad or shaded string is that one of the open circuit, because it will become the only load for the other strings. Consequently, it will conduct inverse current with unavoidable over-heating, which can put the string in out of service. In the parallel mismatching a diode in series with the string can avoid the presence of inverse currents.

After this basic introduction to the mismatch, the equivalent circuit of a solar cell with its parameters will be illustrated.

#### **2.1 Solar cell model for I-V curve simulation**

The equivalent circuit of a solar cell with its parameters is a tool to simulate, for whatever irradiance and temperature conditions, the *I-V* characteristics of each PV module within a batch that will constitute an array of parallel-connected strings of series-connected modules. With this aim, the literature gives two typical equivalent circuits, in which a current source I is in parallel with a non linear diode. Iph is directly proportional to the irradiance G and the area of the solar cell A, simulating the photovoltaic effect, according to the formula

$$I\_{ph} = K\_S \cdot G \cdot A \tag{1}$$

Since PV cells and modules are spectrally selective, their conversion efficiency depends on the daily and monthly variations of the solar spectral distribution (Abete et al., 2003) . A way to assess the spectral influence on PV performance is by means of the effective responsivity KS (A/W):

$$K\_S = \frac{\int g(\lambda) \cdot S(\lambda) d\lambda}{\int g(\lambda) d\lambda} \tag{2}$$

where S() is the absolute spectral response of a silicon cell (A/W) and g() the irradiance spectrum (W/m2m).

A suitable software, which calculates the global radiation spectrum on a selected tilted plane, has been used. Apart from month, day and time, the input parameters are meteorological and geographical data: global and diffuse irradiance on horizontal plane (W/m2), ambient temperature (°C), relative humidity (%), atmospheric pressure (Pa); latitude and longitude. Among the output parameters, it is important the global irradiance spectrum (on the tilted plane) versus wavelength. By the spectral response of a typical mono-crystalline silicon cell, it is possible to calculate KS. As an example, Figure 1 shows the quantities S(), g1() and g2() at 12.00 of a clear day in winter and summer, respectively. It

degradation and early aging of the solar cell. Furthermore, if the inverse voltage applied to a shaded cell exceeds its breakdown value, it could be destroyed. The worst situation is with the string in short-circuit, when all the voltage of the irradiated cells is applied to the shaded ones. It is clear that the most dangerous case occurs if the shaded cell is only one, while the

The solution adopted worldwide for this problem is the by-pass diode in anti-parallel connection with a group of solar cell for each module. In this way, the output power decreases only of the contribution of the group of bad cells and the inverse voltage is limited

In the case of parallel of strings, it is the voltage mismatch which becomes important. The total I-V characteristic can be constructed summing the current of each string at the same voltage value. The total open-circuit voltage will be very close to that of the bad string. The worst case for the bad or shaded string is that one of the open circuit, because it will become the only load for the other strings. Consequently, it will conduct inverse current with unavoidable over-heating, which can put the string in out of service. In the parallel mismatching a diode in series with the string can avoid the presence of inverse currents. After this basic introduction to the mismatch, the equivalent circuit of a solar cell with its

The equivalent circuit of a solar cell with its parameters is a tool to simulate, for whatever irradiance and temperature conditions, the *I-V* characteristics of each PV module within a batch that will constitute an array of parallel-connected strings of series-connected modules. With this aim, the literature gives two typical equivalent circuits, in which a current source I is in parallel with a non linear diode. Iph is directly proportional to the irradiance G and the

Since PV cells and modules are spectrally selective, their conversion efficiency depends on the daily and monthly variations of the solar spectral distribution (Abete et al., 2003) . A way to assess the spectral influence on PV performance is by means of the effective responsivity

 

 

 *<sup>S</sup> g Sd <sup>K</sup> g d*

where S() is the absolute spectral response of a silicon cell (A/W) and g() the irradiance

A suitable software, which calculates the global radiation spectrum on a selected tilted plane, has been used. Apart from month, day and time, the input parameters are meteorological and geographical data: global and diffuse irradiance on horizontal plane (W/m2), ambient temperature (°C), relative humidity (%), atmospheric pressure (Pa); latitude and longitude. Among the output parameters, it is important the global irradiance spectrum (on the tilted plane) versus wavelength. By the spectral response of a typical mono-crystalline silicon cell, it is possible to calculate KS. As an example, Figure 1 shows the quantities S(), g1() and g2() at 12.00 of a clear day in winter and summer, respectively. It

*ph S I K GA* (1)

(2)

area of the solar cell A, simulating the photovoltaic effect, according to the formula

experience shows that usually with two shaded cells the heating is still acceptable.

by the diode.

KS (A/W):

spectrum (W/m2m).

parameters will be illustrated.

**2.1 Solar cell model for I-V curve simulation** 

is noteworthy that between 0.9 and 1m, where S() is high, the winter spectrum exceeds the summer spectrum. Figure 2 shows the quantities S()·g1() and S()·g2(), named spectral current density I1 e I2, which have units of A/(m2m). Not only in this example, but in many cases KS is higher in winter than in summer and the deviations are roughly 5%.

Fig. 1. Comparison of solar spectra in winter and summer.

Fig. 2. Comparison of spectral current density in winter and summer.

The rated power of the PV devices is defined at Standard Test Conditions (STC), corresponding to the solar spectrum at noon in the spring/autumn equinox, with clear sky. This global irradiance (GSTC = 1000 W/m2) is also referred as Air Mass (AM) equal to 1.5. Then, considering the non linear diode, on the one hand, the first equivalent circuit is based on a single exponential model for the P-N junction, in which the reverse saturation current *<sup>o</sup> I* and quality factor of junction *m* are the diode parameters to be determined:

$$I\_j = I\_o \cdot \left( e^{\frac{qV\_j}{mkT\_c}} - 1 \right) \tag{3}$$

Non-Idealities in the I-V

on the shaded solar cells.

a. 36 cells totally irradiated; b. 35 cells totally irradiated; c. 1 completely shaded cell; d. 36 cells with 1 shaded cell.

specific program implemented in MATLAB.

**0 0,5 1 1,5 2 2,5 3**

Fig. 4. I-V curves of different number of series-connected solar cells.

the working conditions of the PV module are less dangerous for the solar cells.

**Current (A)**

1 m/s):

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 233

and the irradiance G, according to the NOCT definition valid for modules installed in mounting structures which allow the natural air circulation (maximum wind speed equal to

> 20 *c a NOCT <sup>G</sup> T T NOCT C*

in which *GNOCT* = 800 W/m2. By using the aforementioned model, the PV-array *I*(*V*) characteristic, corresponding to the actual irradiance and cell temperature, is calculated on a

Through this model of a solar cell it is possible to simulate the mismatch due to shading effect on different configurations of a PV generator made of an array of solar panels. Usually the shading effect is studied changing the number of shaded solar cells of a single module for each configuration considered. The current-voltage (I-V) curve is then determined, together with the maximum power available with the shading Pm' (normalized with the power Pm without shades and defined as μ), the power dissipated and the inverse voltage

For example, the following simulation is relative to a series mismatch due to shading. Let us consider a 35 Wp rated power PV module of 36 solar cells in poly-crystalline silicon, with a

**I-V curves at STC**

**-40 -30 -20 -10 0 10 20 30**

In the d) curve the normalized power μ is reduced significantly (nearly 10%) as it is shown in Table 1. In the shaded cell the worst condition, in terms of dissipated power Pc and inverse voltage Uc, occurs when the PV module is in short circuit. Its working point can be obtained from the interception between curve c) and curve b), in figure 1, if the curve b) is reversed respect the current axis. This point gives the dissipated power and inverse voltage on the shaded cell (Uc=18V e Pc=24W). Raising the number of shaded solar cells (Nc) the values of μ, Pc and Uc shown in table 1 are obtained. It is clear that if Nc grows Pc and Uc decrease, namely

**c) d) b) a)**

**Voltage (V)**

short circuit current of 2.4 A in STC. Figure 4 shows the I-V curves of:

*<sup>G</sup>* (7)

**Pm**

**P'm**

where *Vj* is the junction voltage, *k* the Boltzmann constant, *q* the electron charge and *Tc* the cell temperature.

On the other hand, the second model involves a couple of exponential terms, in which the quality factors assume fixed values (1 and 2 usually), whereas *<sup>o</sup>*<sup>1</sup> *I* and *<sup>o</sup>*<sup>2</sup> *I* must be inserted.

$$I\_j = I\_{o1} \cdot \left( e^{\frac{qV\_j}{m\_1kT\_c}} - 1 \right) + I\_{o2} \cdot \left( e^{\frac{qV\_j}{m\_2kT\_c}} - 1 \right) \tag{4}$$

The model with a single exponential is used in this chapter (Fig. 3). In this one, the series resistance *Rs* accounts for the voltage drop in bulk semiconductor, electrodes and contacts, and the shunt resistance *Rsh* represents the lost current in surface paths.

Thus, five parameters are sufficient to determine the behaviour of the solar cell, namely, the current source *ph I* , the saturation current *oI* , the junction quality factor *m*, the series resistance *Rs* , the shunt resistance *Rsh* . If we examine the silicon technologies, monocrystalline (m-Si), poly-crystalline (p-Si) and amorphous (a-Si), the shape of the *I-V* curve is mainly determined by the values of *Rs* and *Rsh* .

Fig. 3. Equivalent circuit of solar cell with one exponential.

Finally, the dependence on the solar irradiance *G*(*t*) and on the cell temperature *Tc*(*t*) is explained for the ideal PV current *Iph* and the reverse saturation current *I*0 in the following expression:

$$I\_{ph} = I\_{SC|STC} \frac{G}{G\_{STC}} \left[1 + \alpha\_T \left(T\_c - 298\right)\right] \tag{5}$$

$$I\_0 = I\_{0\mid \text{STC}} \left(\frac{T\_c}{298}\right)^3 \frac{e^{-\frac{E\_g}{kT\_c}}}{e^{-\frac{E\_g}{k \cdot 298}}}\tag{6}$$

where ISC|STC is the short-circuit current evaluated at STC (TSTC = 25°C = 298 K), *<sup>T</sup>* is the temperature coefficient of *Iph*, *Eg* is the energy gap and *k* is the Boltzmann constant. The cell temperature is evaluated by considering a linear dependence on the ambient temperature Ta

and the irradiance G, according to the NOCT definition valid for modules installed in mounting structures which allow the natural air circulation (maximum wind speed equal to 1 m/s):

$$T\_c = T\_a + \frac{G}{G\_{NOCT}} \left( {NOCT} - 20 {^\circ C} \right) \tag{7}$$

in which *GNOCT* = 800 W/m2. By using the aforementioned model, the PV-array *I*(*V*) characteristic, corresponding to the actual irradiance and cell temperature, is calculated on a specific program implemented in MATLAB.

Through this model of a solar cell it is possible to simulate the mismatch due to shading effect on different configurations of a PV generator made of an array of solar panels. Usually the shading effect is studied changing the number of shaded solar cells of a single module for each configuration considered. The current-voltage (I-V) curve is then determined, together with the maximum power available with the shading Pm' (normalized with the power Pm without shades and defined as μ), the power dissipated and the inverse voltage on the shaded solar cells.

For example, the following simulation is relative to a series mismatch due to shading. Let us consider a 35 Wp rated power PV module of 36 solar cells in poly-crystalline silicon, with a short circuit current of 2.4 A in STC. Figure 4 shows the I-V curves of:

a. 36 cells totally irradiated;

232 Solar Cells – Silicon Wafer-Based Technologies

where *Vj* is the junction voltage, *k* the Boltzmann constant, *q* the electron charge and *Tc* the

On the other hand, the second model involves a couple of exponential terms, in which the quality factors assume fixed values (1 and 2 usually), whereas *<sup>o</sup>*<sup>1</sup> *I* and *<sup>o</sup>*<sup>2</sup> *I* must be inserted.

> 1 2 1 2 1 1 *j j c c qV qV m kT m kT*

The model with a single exponential is used in this chapter (Fig. 3). In this one, the series resistance *Rs* accounts for the voltage drop in bulk semiconductor, electrodes and contacts,

Thus, five parameters are sufficient to determine the behaviour of the solar cell, namely, the current source *ph I* , the saturation current *oI* , the junction quality factor *m*, the series resistance *Rs* , the shunt resistance *Rsh* . If we examine the silicon technologies, monocrystalline (m-Si), poly-crystalline (p-Si) and amorphous (a-Si), the shape of the *I-V* curve is

Finally, the dependence on the solar irradiance *G*(*t*) and on the cell temperature *Tc*(*t*) is explained for the ideal PV current *Iph* and the reverse saturation current *I*0 in the following

> *ph* 1 298 *T c SC STC STC <sup>G</sup> I I <sup>T</sup> G*

> > 298

temperature coefficient of *Iph*, *Eg* is the energy gap and *k* is the Boltzmann constant. The cell temperature is evaluated by considering a linear dependence on the ambient temperature Ta

*c STC E*

*<sup>T</sup> <sup>e</sup> I I*

where ISC|STC is the short-circuit current evaluated at STC (TSTC = 25°C = 298 K),

0 0

3

298

*k*

*e*

*g c g*

*E kT*

 

(4)

*Rs*

(5)

(6)

*<sup>T</sup>* is the

*I Vj sh Rsh V*

*I*

*j o <sup>o</sup> II e I e*

and the shunt resistance *Rsh* represents the lost current in surface paths.

*D*

Fig. 3. Equivalent circuit of solar cell with one exponential.

mainly determined by the values of *Rs* and *Rsh* .

*Iph Ij*

cell temperature.

expression:


Fig. 4. I-V curves of different number of series-connected solar cells.

In the d) curve the normalized power μ is reduced significantly (nearly 10%) as it is shown in Table 1. In the shaded cell the worst condition, in terms of dissipated power Pc and inverse voltage Uc, occurs when the PV module is in short circuit. Its working point can be obtained from the interception between curve c) and curve b), in figure 1, if the curve b) is reversed respect the current axis. This point gives the dissipated power and inverse voltage on the shaded cell (Uc=18V e Pc=24W). Raising the number of shaded solar cells (Nc) the values of μ, Pc and Uc shown in table 1 are obtained. It is clear that if Nc grows Pc and Uc decrease, namely the working conditions of the PV module are less dangerous for the solar cells.

Non-Idealities in the I-V

characteristics I2(U) – I1(U).

I(U) dynamic curves of the two modules.

Rs

Rs

Fig. 5. "Series type" bridge measuring circuit.

Fig. 6. "Parallel type" bridge measuring circuit.

PR

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 235

PV modules are parallel connected: in case of mismatch, the voltage output measurement of the unbalanced bridge, for each voltage value, is directly proportional to the difference of the module's currents I. This I vs. voltage U represents the voltage difference

Fig. 5 and Fig. 6 show the series and parallel bridge measuring circuits. Each bridge has two active branches constituted by two modules, PV1 (reference) and PV2 (testing), which are subject to the same irradiance G and cell temperature T. The other two branches of each bridge are two equal resistors, Rs with high resistance in Fig. 5 and Rp with low resistance in Fig. 6, such as to have a negligible loading effect on the I(U) characteristics of PV1 and PV2 modules. C is a capacitor such as to give a suitable du/dt, i.e., not so quick to interfere with the parasitic junction capacitance of the solar cells and not so slow to permit the variation of the ambient conditions. Usually, values around a few millifarad are adequate. The PR devices are Hall-effect probes for accurate and non-intrusive measurement of current. At closing of switch s, the transient charge of the capacitor C provides, in a single sweep, the

+

PR

+

PV <sup>1</sup> (ref.)

s

PV <sup>2</sup> (testing)

RP RP

u ADAS

u2 = K i <sup>2</sup> u1 = K i <sup>1</sup>

u0

+ +

u2 u3 u = Ki <sup>0</sup> ADAS u1

PV <sup>1</sup> (ref.)

C

PV <sup>2</sup> (testing)

s

C

PR


Table 1. Normalized power of the PV module μ, dissipated power Pc and inverse voltage Uc on shaded solar cell, under STC, depending on the number of shaded solar cells.

#### **3. Manufacturing I-V mismatch**

Considering at first the mismatch among PV modules due to production tolerance, a first study is presented in the paper (Abete et al., 1998) in which an experimental set up has been developed to detect the mismatching of the current-voltage characteristics between a reference PV module and another one under test, in the same environmental conditions. Two dual bridge circuits have been set up, one with series and the other one with parallel connected modules, which have produced the direct measurement of the difference characteristic and the mismatching parameters. Therefore it has been achieved a better accuracy as regard to the indirect determination of the difference from the two I-V characteristics. The measuring circuits reported could be profitably employed for optimum module connection in the array, manufacturer quality control, customer acceptance testing and field test on PV array.

#### **3.1 Production tolerance detection**

The optimum performance of a photovoltaic module or array is achieved if the currentvoltage I(U) characteristics of the solar cells in the module or the I(U) characteristics of the modules in the array are identical (matched). Otherwise, that is when an I-U mismatch occurs due to manufacturing tolerance, the electrical output power of the PV array decreases and the increasing internal power losses may cause "hot spots" up to the failure of the module with lower performance. The mismatch of the I(U) curves of PV modules is measured by the difference between two I(U) characteristics, one of a reference module and the other of a testing module, in the same ambient conditions. For the direct measurement of this difference curve (to achieve uncertainty lower than with indirect measurement), two dual measuring circuits are presented, one with series and the other with parallel connected modules.

To obtain this difference between the reference and the testing I(U) curves, it is required to measure the voltage difference of series connected modules, for equal current value, and the current difference of parallel connected modules for equal voltage value. The two measuring circuits can be regarded as a bridge comparing, point by point, the dynamic I(U) characteristics of two PV modules, the reference and the other under test. In the first circuit ("series type") the PV modules are series connected: in case of mismatch, the voltage output measurement of the unbalanced bridge, for each current value, is directly proportional to the difference of the module's voltages U. This U vs. current I represents the difference characteristic U2(I) –U1(I). In the dual circuit ("parallel type") the

*Nc μ Pc [W] Uc [V]*  1 0.11 24 18 2 0.06 4.3 9.2 3 0.04 1.8 6.1 4 0.03 1 4.4 18 0 0 0 36 0 0 0 Table 1. Normalized power of the PV module μ, dissipated power Pc and inverse voltage Uc

Considering at first the mismatch among PV modules due to production tolerance, a first study is presented in the paper (Abete et al., 1998) in which an experimental set up has been developed to detect the mismatching of the current-voltage characteristics between a reference PV module and another one under test, in the same environmental conditions. Two dual bridge circuits have been set up, one with series and the other one with parallel connected modules, which have produced the direct measurement of the difference characteristic and the mismatching parameters. Therefore it has been achieved a better accuracy as regard to the indirect determination of the difference from the two I-V characteristics. The measuring circuits reported could be profitably employed for optimum module connection in the array, manufacturer quality control, customer acceptance testing

The optimum performance of a photovoltaic module or array is achieved if the currentvoltage I(U) characteristics of the solar cells in the module or the I(U) characteristics of the modules in the array are identical (matched). Otherwise, that is when an I-U mismatch occurs due to manufacturing tolerance, the electrical output power of the PV array decreases and the increasing internal power losses may cause "hot spots" up to the failure of the module with lower performance. The mismatch of the I(U) curves of PV modules is measured by the difference between two I(U) characteristics, one of a reference module and the other of a testing module, in the same ambient conditions. For the direct measurement of this difference curve (to achieve uncertainty lower than with indirect measurement), two dual measuring circuits are presented, one with series and the other with parallel connected

To obtain this difference between the reference and the testing I(U) curves, it is required to measure the voltage difference of series connected modules, for equal current value, and the current difference of parallel connected modules for equal voltage value. The two measuring circuits can be regarded as a bridge comparing, point by point, the dynamic I(U) characteristics of two PV modules, the reference and the other under test. In the first circuit ("series type") the PV modules are series connected: in case of mismatch, the voltage output measurement of the unbalanced bridge, for each current value, is directly proportional to the difference of the module's voltages U. This U vs. current I represents the difference characteristic U2(I) –U1(I). In the dual circuit ("parallel type") the

on shaded solar cell, under STC, depending on the number of shaded solar cells.

**3. Manufacturing I-V mismatch** 

and field test on PV array.

modules.

**3.1 Production tolerance detection** 

PV modules are parallel connected: in case of mismatch, the voltage output measurement of the unbalanced bridge, for each voltage value, is directly proportional to the difference of the module's currents I. This I vs. voltage U represents the voltage difference characteristics I2(U) – I1(U).

Fig. 5 and Fig. 6 show the series and parallel bridge measuring circuits. Each bridge has two active branches constituted by two modules, PV1 (reference) and PV2 (testing), which are subject to the same irradiance G and cell temperature T. The other two branches of each bridge are two equal resistors, Rs with high resistance in Fig. 5 and Rp with low resistance in Fig. 6, such as to have a negligible loading effect on the I(U) characteristics of PV1 and PV2 modules. C is a capacitor such as to give a suitable du/dt, i.e., not so quick to interfere with the parasitic junction capacitance of the solar cells and not so slow to permit the variation of the ambient conditions. Usually, values around a few millifarad are adequate. The PR devices are Hall-effect probes for accurate and non-intrusive measurement of current. At closing of switch s, the transient charge of the capacitor C provides, in a single sweep, the I(U) dynamic curves of the two modules.

Fig. 5. "Series type" bridge measuring circuit.

Fig. 6. "Parallel type" bridge measuring circuit.

Non-Idealities in the I-V

the manufacturer flash reports.

**effect in multi-rows PV arrays** 


Current [A]

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 237

, T=25°C IM=0.36 A , P MU=5.2 W

I 2

I 1

<sup>I</sup> IM

0 2 4 6 8 10 12 14 16 18 20 Voltage [V]

G=630W/m <sup>2</sup>

Fig. 8. Experimental results with parallel connected polycrystalline silicon modules.

**3.2 Manufacturing I-V mismatch and reverse currents in large Photovoltaic arrays**  As an example of the consequences of the production tolerance in large PV plants, a brief summary of a study on this topic is reported here. This work has dealt with the currentvoltage mismatch consequent to the production tolerance as a typical factor of losses in large photovoltaic plants (Spertino & Sumaili, 2009). The results have been simulated extracting the parameters of the equivalent circuit of the solar cell for several PV modules from flash reports provided by the manufacturers. The corresponding I-V characteristic of every module has been used to evaluate the behavior of different strings and the interaction among the strings connected for composing PV arrays. Two real crystalline silicon PV systems of 2 MW and 20 kW have been studied. The simulation results have revealed that the impact of the I-V mismatch is negligible with the usual tolerance, and the insertion of the blocking diodes against reverse currents can be avoided with crystalline silicon technology. On the other hand, the experimental results have shown a remarkable power deviation (3%- 4%) with respect to the rated power, mainly due to the lack of measurement uncertainty in

**4. Optimal configuration of module connections for minimizing the shading** 

In another study, the periodic shading among the rows in the morning and in the evening in grid-connected PV systems, installed e.g. on the rooftop of buildings, has been investigated (Spertino et al. 2009). This phenomenon is quite common in large PV plants, in fact often the designer does not take into account this shading when he decides the module connections in the strings, the number of modules per string and the arrangement, according to the longest side of the modules, in horizontal or vertical direction. The study has discussed, by suitable comparisons, various cases of shading pattern in PV arrays from multiple viewpoints: power profiles in clear days with 15-min time step, daily energy as a monthly average value for clear and cloudy days. The simulation results have proved that, with simple structure of the array and important amount of shading, it is better to limit the shading effect within one string rather than to distribute the shading on all the strings: the gains are higher than 10% in the worst month and 1% on yearly basis. Contrary, with more complex structure of the array and low amount of shading, it is practically equivalent to concentrate or to distribute

The circuit analysis proves that:


Therefore, the measurement of the voltage difference U vs. the current I gives the difference curve of the series connected modules; the measurement of the current difference I vs. the voltage U gives the difference curve of the parallel connected modules. For mismatch assessment, besides the difference of open circuit voltages Uoc and of short circuit currents Isc, it is profitable, in the maximum power point PM = (IM,UM) of the reference module, to know the following parameters:


These quantities UM, PMI, IM and PMU can be assumed as "mismatch parameters".

The measuring signals of the circuits in Fig. 5 and Fig. 6 (K current probe constant), with a suitable sampling rate (10-100 kSa/s), are digitized by an Automatic Data Acquisition System (ADAS). This ADAS processes the signals for providing current-voltage curves of the PV modules, the difference characteristics and the mismatch parameters. These experimental results, concerning series and parallel connected polycrystalline silicon modules, are shown respectively in Fig. 7 and Fig. 8. In Fig. 7 the testing module I(U2) curve extends as far as the second quadrant, while the reference module I(U1) curve does not run through all the first quadrant. This proves that the short circuit currents of the two modules are different and consequently the testing module can operate as a load of the reference module. In Fig. 8, likewise, the testing module I2(U) curve extends as far as the fourth quadrant, while the reference module I1(U) curve does not run through all the first quadrant. This proves that the open circuit voltages of the two modules are different and thus the testing one can operate as a load. Once the power reduction are PMI and PMU are measured, it is possible to choose the connection of the modules in the array to achieve the optimum performance. Finally, the presented circuits can be profitably employed in manufacturer quality control and customer acceptance testing.

Fig. 7. Experimental results with series connected polycrystalline silicon modules.

 in the series circuit, for each current value, the voltage output U0 of the unbalanced bridge measures the difference U of the two module's voltages by U = U0(2+Rs/R0); in the parallel circuit, for each voltage values, the voltage output U0 of the unbalanced bridge measures the difference I of the two modules currents by I = U0(1/Rp+2/R0) with R0 input resistance of the instrument which measures the voltage output U0. Therefore, the measurement of the voltage difference U vs. the current I gives the difference curve of the series connected modules; the measurement of the current difference I vs. the voltage U gives the difference curve of the parallel connected modules. For mismatch assessment, besides the difference of open circuit voltages Uoc and of short circuit currents Isc, it is profitable, in the maximum power point PM = (IM,UM) of the

the voltage difference UM and the power reduction PMI = IMUM for series connected

the current difference IM and the power reduction PMU = UMIM for parallel

These quantities UM, PMI, IM and PMU can be assumed as "mismatch parameters". The measuring signals of the circuits in Fig. 5 and Fig. 6 (K current probe constant), with a suitable sampling rate (10-100 kSa/s), are digitized by an Automatic Data Acquisition System (ADAS). This ADAS processes the signals for providing current-voltage curves of the PV modules, the difference characteristics and the mismatch parameters. These experimental results, concerning series and parallel connected polycrystalline silicon modules, are shown respectively in Fig. 7 and Fig. 8. In Fig. 7 the testing module I(U2) curve extends as far as the second quadrant, while the reference module I(U1) curve does not run through all the first quadrant. This proves that the short circuit currents of the two modules are different and consequently the testing module can operate as a load of the reference module. In Fig. 8, likewise, the testing module I2(U) curve extends as far as the fourth quadrant, while the reference module I1(U) curve does not run through all the first quadrant. This proves that the open circuit voltages of the two modules are different and thus the testing one can operate as a load. Once the power reduction are PMI and PMU are measured, it is possible to choose the connection of the modules in the array to achieve the optimum performance. Finally, the presented circuits can be profitably employed in

The circuit analysis proves that:

modules;

connected modules.

reference module, to know the following parameters:

manufacturer quality control and customer acceptance testing.

U

Current [A]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Fig. 7. Experimental results with series connected polycrystalline silicon modules.

U <sup>M</sup>

G = 800 W/m 2 , T = 25 °C U M= 7.7 V , P MI= 12.9 W

U <sup>2</sup> U1

Voltage [V]


Fig. 8. Experimental results with parallel connected polycrystalline silicon modules.

#### **3.2 Manufacturing I-V mismatch and reverse currents in large Photovoltaic arrays**

As an example of the consequences of the production tolerance in large PV plants, a brief summary of a study on this topic is reported here. This work has dealt with the currentvoltage mismatch consequent to the production tolerance as a typical factor of losses in large photovoltaic plants (Spertino & Sumaili, 2009). The results have been simulated extracting the parameters of the equivalent circuit of the solar cell for several PV modules from flash reports provided by the manufacturers. The corresponding I-V characteristic of every module has been used to evaluate the behavior of different strings and the interaction among the strings connected for composing PV arrays. Two real crystalline silicon PV systems of 2 MW and 20 kW have been studied. The simulation results have revealed that the impact of the I-V mismatch is negligible with the usual tolerance, and the insertion of the blocking diodes against reverse currents can be avoided with crystalline silicon technology. On the other hand, the experimental results have shown a remarkable power deviation (3%- 4%) with respect to the rated power, mainly due to the lack of measurement uncertainty in the manufacturer flash reports.

#### **4. Optimal configuration of module connections for minimizing the shading effect in multi-rows PV arrays**

In another study, the periodic shading among the rows in the morning and in the evening in grid-connected PV systems, installed e.g. on the rooftop of buildings, has been investigated (Spertino et al. 2009). This phenomenon is quite common in large PV plants, in fact often the designer does not take into account this shading when he decides the module connections in the strings, the number of modules per string and the arrangement, according to the longest side of the modules, in horizontal or vertical direction. The study has discussed, by suitable comparisons, various cases of shading pattern in PV arrays from multiple viewpoints: power profiles in clear days with 15-min time step, daily energy as a monthly average value for clear and cloudy days. The simulation results have proved that, with simple structure of the array and important amount of shading, it is better to limit the shading effect within one string rather than to distribute the shading on all the strings: the gains are higher than 10% in the worst month and 1% on yearly basis. Contrary, with more complex structure of the array and low amount of shading, it is practically equivalent to concentrate or to distribute

Non-Idealities in the I-V

shaded modules.

*every string* (Conf. 3 of Fig. 11), i.e., the eq. (8) becomes

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 239

On the other hand, in the second array with 6.25%- shading amount the situations are *8 shaded modules in the same string* (half a string in Conf. 4 of Fig. 12) vs. *one shaded module for* 

\_ \_ 1

*P S S N one str N all str N*

with NSsh(one\_str) = 8 and NSsh(all\_str) = 1 corresponding to the minimum number of

*Ssh Ssh*

Fig. 9. Array (NS = 16, NP = 4) with shading patterns - Configuration 1

Fig. 10. Array (NS = 16, NP = 4) with shading patterns - Configuration 2

+ + + +

2

1

12

13

16

1

2

15

16

*N N* (10)

the shading on all the strings. Finally, in the simulation conditions the impact of the shading losses on yearly basis is limited to 1-3%.

#### **4.1 Analysis of some shading patterns**

In order to establish some guidelines for minimising the shading effect in multi-rows PV arrays, a comparison among different configurations of module connections is carried out within simplifying assumptions, i.e., *all the shaded modules are located only in a single string* vs. *the shaded modules are equally distributed in all the strings*. In particular, the shading implies the collection of the diffuse irradiance without the direct or beam irradiance; thus, the parameters which determine the behaviour of the PV arrays in these conditions are:


All the comparisons are performed by satisfying the equation:

$$\frac{N\_{Ssh}\left(one\\_str\right)}{N\_S} = N\_P \cdot \frac{N\_{Ssh}\left(all\\_str\right)}{N\_S} \tag{8}$$

Obviously, the previous parameter NSsh(all\_str) ≥ 1 only if NP ≤ NS.

In our study, the chosen arrays are two, the first one with usual number of modules per string (NS = 16) and low number of parallel strings (NP = 4) concerns a decentralized inverter (Figures 9 and 10), whereas the second one deals with a centralized inverter (NS = 16, NP = 8 in Figures 11 and 12). In order to gain deeper understanding, the pattern of shading (i.e. modules subject to diffuse radiation without beam radiation) can be:


On one hand, in the first array with 25%- shading amount the situations are: *4 shaded modules in every string* (conf. 1 in Figure 9) vs. *all the 16 modules shaded in the same string* (conf. 2 in Fig. 10). The eq. (8) becomes

$$\frac{N\_{Ssh}\left(one\\_str\right)}{N\_S} = N\_P \cdot \frac{N\_{Ssh}\left(all\\_str\right)}{N\_S} = 1\tag{9}$$

with NSsh(one\_str) = 16 and NSsh(all\_str) = 4 corresponding to the maximum number of shaded modules per string in this example. In Figure 9 in every string, even if there are both shaded modules (four) and totally irradiated modules (twelve), it is assumed the same temperature for uniformity reasons and this one is equal to the temperature of the totally irradiated modules. Consequently, the I-V curve can be calculated.

the shading on all the strings. Finally, in the simulation conditions the impact of the shading

In order to establish some guidelines for minimising the shading effect in multi-rows PV arrays, a comparison among different configurations of module connections is carried out within simplifying assumptions, i.e., *all the shaded modules are located only in a single string* vs. *the shaded modules are equally distributed in all the strings*. In particular, the shading implies the collection of the diffuse irradiance without the direct or beam irradiance; thus, the parameters which determine the behaviour of the PV arrays in these

NS: number of series connected modules per string (NS > 1 otherwise the meaning is

NP: number of parallel connected strings per array (NP > 1 otherwise the meaning is

NSsh(one\_str): number of shaded modules in the case of shading concentrated in a single

NSsh(all\_str): number of shaded modules per each string in the case of shading

*Ssh* \_ \_ *Ssh P S S N one str N all str N*

In our study, the chosen arrays are two, the first one with usual number of modules per string (NS = 16) and low number of parallel strings (NP = 4) concerns a decentralized inverter (Figures 9 and 10), whereas the second one deals with a centralized inverter (NS = 16, NP = 8 in Figures 11 and 12). In order to gain deeper understanding, the pattern of

1. either one or a half shaded string in the array, i.e., NSsh(one\_str) = 16 or NSsh(one\_str) =8; 2. whereas only one or more modules with shading for every string of the array, i.e.,

On one hand, in the first array with 25%- shading amount the situations are: *4 shaded modules in every string* (conf. 1 in Figure 9) vs. *all the 16 modules shaded in the same string* (conf. 2 in Fig.

> \_ \_ <sup>1</sup> *Ssh Ssh P S S N one str N all str N*

with NSsh(one\_str) = 16 and NSsh(all\_str) = 4 corresponding to the maximum number of shaded modules per string in this example. In Figure 9 in every string, even if there are both shaded modules (four) and totally irradiated modules (twelve), it is assumed the same temperature for uniformity reasons and this one is equal to the temperature of the totally

shading (i.e. modules subject to diffuse radiation without beam radiation) can be:

*N N* (8)

*N N* (9)

losses on yearly basis is limited to 1-3%.

**4.1 Analysis of some shading patterns** 

conditions are:

vanishing);

vanishing);

distributed in all the strings.

NSsh(all\_str) = 1 or NSsh(all\_str) = 4.

10). The eq. (8) becomes

All the comparisons are performed by satisfying the equation:

Obviously, the previous parameter NSsh(all\_str) ≥ 1 only if NP ≤ NS.

irradiated modules. Consequently, the I-V curve can be calculated.

string;

On the other hand, in the second array with 6.25%- shading amount the situations are *8 shaded modules in the same string* (half a string in Conf. 4 of Fig. 12) vs. *one shaded module for every string* (Conf. 3 of Fig. 11), i.e., the eq. (8) becomes

$$\frac{N\_{Ssh}\left(one\\_str\right)}{N\_S} = N\_P \cdot \frac{N\_{Ssh}\left(all\\_str\right)}{N\_S} = \frac{1}{2} \tag{10}$$

with NSsh(one\_str) = 8 and NSsh(all\_str) = 1 corresponding to the minimum number of shaded modules.

Fig. 9. Array (NS = 16, NP = 4) with shading patterns - Configuration 1

Fig. 10. Array (NS = 16, NP = 4) with shading patterns - Configuration 2

Non-Idealities in the I-V

height angle α).

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 241

The study cannot be limited to the irradiance values in the clear days, but requires the simulation of real-sky conditions by using an average day which takes into account both clear and cloudy days (e.g. Page and Liu-Jordan models). In this case, the PVGIS tool, available on the web-site of JRC of the European Commission, is used. Simulation results are presented in the following with reference to a South-Italy location (latitude ≈ 41.5°, tilt angle β = 15° for maximum installation density and azimuth = 30° W). The installation option is the PV-rooftop array in order to earn higher amount of money within the Italian feed-in tariff (partial building integration). The obstruction which produces the shading effect is the *balustrade* of the building roof: consequently, only the PV-modules of the closest row are subject to the shading because the successive rows are sufficiently separate each other (d > dmin in Figure 13 where dmin is calculated on the Winter solstice at noon with Sun-

*St1 St2 St3 St4*

d>dmin

**4.2 Simulation results of the considered shading patterns** 

Solar beam

m h h

d1

in configuration 2 (Fig. 15) there are all the 16 modules of each string in a single row. The figures 16 and 17 show the two patterns of shading for the second PV array (NS = 16, NP = 8) with 16 rows: in the configuration 3 (Fig. 16) there is only one module per string in each row and in configuration 4 (Fig. 17) there are 8 modules of each string in a single row.

Fig. 14. The row arrangement and the balustrade in the first array - Configuration 1

Fig. 15. The row arrangement and the balustrade in the first array - Configuration 2

*St3*

*St4*

*St1*

*St2*

The figures 14 and 15 show the two patterns of shading for the first PV array (NS=16, NP=4) with 4 rows: in the configuration 1 (Fig. 14) there are 4 modules per string in each row and

Fig. 13. The row arrangement and the balustrade obstruction with height h

Fig. 11. Array (NS = 16, NP = 8) with shading patterns - Configuration 3

Fig. 12. Array (NS = 16, NP = 8) with shading patterns - Configuration 4

#### **4.2 Simulation results of the considered shading patterns**

240 Solar Cells – Silicon Wafer-Based Technologies

1 2 3 7 8

1 2 3 7 8

1

2

3

4

5

12

13

14

15

16

1

2

3

7

8

12

13

14

15

16

Fig. 11. Array (NS = 16, NP = 8) with shading patterns - Configuration 3

Fig. 12. Array (NS = 16, NP = 8) with shading patterns - Configuration 4

**+**

**+**

The study cannot be limited to the irradiance values in the clear days, but requires the simulation of real-sky conditions by using an average day which takes into account both clear and cloudy days (e.g. Page and Liu-Jordan models). In this case, the PVGIS tool, available on the web-site of JRC of the European Commission, is used. Simulation results are presented in the following with reference to a South-Italy location (latitude ≈ 41.5°, tilt angle β = 15° for maximum installation density and azimuth = 30° W). The installation option is the PV-rooftop array in order to earn higher amount of money within the Italian feed-in tariff (partial building integration). The obstruction which produces the shading effect is the *balustrade* of the building roof: consequently, only the PV-modules of the closest row are subject to the shading because the successive rows are sufficiently separate each other (d > dmin in Figure 13 where dmin is calculated on the Winter solstice at noon with Sunheight angle α).

Fig. 13. The row arrangement and the balustrade obstruction with height h

The figures 14 and 15 show the two patterns of shading for the first PV array (NS=16, NP=4) with 4 rows: in the configuration 1 (Fig. 14) there are 4 modules per string in each row and in configuration 2 (Fig. 15) there are all the 16 modules of each string in a single row. The figures 16 and 17 show the two patterns of shading for the second PV array (NS = 16, NP = 8) with 16 rows: in the configuration 3 (Fig. 16) there is only one module per string in each row and in configuration 4 (Fig. 17) there are 8 modules of each string in a single row.

Fig. 14. The row arrangement and the balustrade in the first array - Configuration 1

Fig. 15. The row arrangement and the balustrade in the first array - Configuration 2

Non-Idealities in the I-V

0

0

in a single string, as in the previous case.

1

2

3

power [kW]

4

5

6

2

4

6

8

**current [A]**

10

12

14

16

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 243

**I - V array characteristic**

0 200 400 600

0 200 400 600

configuration 1 configuration 2 without shading

voltage [V]

Furthermore, the simulation outputs provide also the daily power diagrams for both real (Fig. 20) and clear sky (Fig. 21) conditions for the configurations 1 and 2. It is possible to point out that the shading causes power losses in the afternoon, due to the azimuth of the PV array, and the produced energy is higher for configuration 2 with shading concentrated

Fig. 19. The P-V curve at Gg = 395 W/m2, Gd = 131 W/m2 and Ta = 4.1 °C

**voltage [V]**

P - V array characteristic

configuration 1 configuration 2 without shading

Fig. 18. The I-V curve at Gg = 395 W/m2, Gd = 131 W/m2 and Ta = 4.1 °C

Fig. 16. The row arrangement and the balustrade in the second array - Configuration 3

Fig. 17. The row arrangement and the balustrade in the second array - Configuration 4

The selected technology for the PV-module is the conventional poly-crystalline-silicon one with rated power of 215 Wp. The main specifications are presented in Table 2 (rated power Pmax, voltage VMPP and current IMPP at rated power, open circuit voltage VOC, short circuit current ISC, temperature coefficients of VOC, ISC, and normal operating cell temperature NOCT).

Notice that all the PV-modules are equipped with 3 bypass diodes, each protecting a group of 20 cells.


Table 2. Specifications of the PV modules

As an example of the simulation outputs for each time step (15 min), Figure 18 illustrates the I-V curve , while Figure 19 shows the P-V characteristics of the array 1 with rated power Pr = 13.76 kW in the configurations 1, 2, and without shading in particular conditions of global irradiance Gg (direct + diffuse), diffuse irradiance alone Gd, and ambient temperature. It is worth noting that the configuration 2 with shading concentrated on a single string is better that the other configuration with shading equally distributed on all the strings. Moreover, the action of the bypass diodes is clear in the abrupt variation of the derivative in the curve of configuration 1 (blue colour).

Fig. 16. The row arrangement and the balustrade in the second array - Configuration 3

*St7*

Fig. 17. The row arrangement and the balustrade in the second array - Configuration 4

The selected technology for the PV-module is the conventional poly-crystalline-silicon one with rated power of 215 Wp. The main specifications are presented in Table 2 (rated power Pmax, voltage VMPP and current IMPP at rated power, open circuit voltage VOC, short circuit current ISC, temperature coefficients of VOC, ISC, and normal operating cell temperature

Notice that all the PV-modules are equipped with 3 bypass diodes, each protecting a group

Pmax = 215 Wp VMPP = 28.5 V IMPP = 7.55 A

NOCT = 48 ºC

As an example of the simulation outputs for each time step (15 min), Figure 18 illustrates the I-V curve , while Figure 19 shows the P-V characteristics of the array 1 with rated power Pr = 13.76 kW in the configurations 1, 2, and without shading in particular conditions of global irradiance Gg (direct + diffuse), diffuse irradiance alone Gd, and ambient temperature. It is worth noting that the configuration 2 with shading concentrated on a single string is better that the other configuration with shading equally distributed on all the strings. Moreover, the action of the bypass diodes is clear in the abrupt variation of the derivative in

VOC = 36.3 V ISC = 8.2 A βVoc = -0.35%/ºC αIsc = +0.05%/ºC

Row16

*St8*

Row1

*St1*

Table 2. Specifications of the PV modules

the curve of configuration 1 (blue colour).

NOCT).

of 20 cells.

*St2*

*St8 St1.*

Fig. 18. The I-V curve at Gg = 395 W/m2, Gd = 131 W/m2 and Ta = 4.1 °C

Fig. 19. The P-V curve at Gg = 395 W/m2, Gd = 131 W/m2 and Ta = 4.1 °C

Furthermore, the simulation outputs provide also the daily power diagrams for both real (Fig. 20) and clear sky (Fig. 21) conditions for the configurations 1 and 2. It is possible to point out that the shading causes power losses in the afternoon, due to the azimuth of the PV array, and the produced energy is higher for configuration 2 with shading concentrated in a single string, as in the previous case.

Non-Idealities in the I-V

Day

Day

Day

Day

Energy [kWh]

Table 3. Energies and losses in the shading patterns (Real sky)

Energy [kWh]

Table 4. Energies and losses in the shading patterns (Clear sky)

Energy [kWh]

Table 5. Energies and losses in the shading patterns (Real-sky).

Energy [kWh]

Table 6. Energies and losses in the shading patterns (Clear-sky).

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 245

Oct 43.83 41.83 4.30 42.80 2.08 Nov 30.47 27.10 11.06 28.71 5.78 Dec 25.01 20.57 17.76 22.65 9.41 Jan 30.81 26.73 13.23 28.55 7.33 Feb 37.46 34.77 7.19 36.13 3.55

Energy [kWh]

Energy [kWh]

concentrate the shading in a single string or to distribute equally in all the strings.

Energy [kWh]

Energy [kWh]

No shad. Configuration 1 Configuration 2

No shad. Configuration 1 Configuration 2

Oct 61.30 58.65 4.33 59.68 2.65 Nov 47.15 41.81 11.33 43.56 7.61 Dec 40.08 32.75 18.29 35.04 12.54 Jan 44.74 38.66 7.19 40.64 3.55 Feb 56.87 52.70 7.32 54.17 4.75

Now, addressing the focus on the two configurations of the second array, it can be stressed that the simulations on the average day of the months subject to shading effect give slightly greater losses in configuration 3 than in configuration 4 for real-sky days whereas the opposite occurs for clear-sky days with higher values of losses. More in detail, in clear-sky conditions the losses are maximum in December with values of 4.69% (Conf. 3) vs. 6.24% (Conf. 4) but, if we consider the losses on yearly basis (including the months without shading), the mean value of losses is 0.65% (Conf. 3) vs. 0.64% (Conf. 4). Hence, with more complex structure of array and less amount of shading, it is almost equivalent either to

No shad. Configuration 3 Configuration 4

No shad. Configuration 3 Configuration 4

Oct 122.27 121.27 1.09 120.99 1.32 Nov 94.30 91.58 2.88 90.73 3.79 Dec 80.16 76.40 4.69 75.15 6.24 Jan 89.48 86.35 3.51 85.40 4.56 Feb 113.74 111.62 1.86 111.01 2.40

Losses (%)

Oct 87.42 86.46 1.10 86.57 0.98 Nov 60.94 59.23 2.81 59.26 2.76 Dec 50.02 47.75 4.53 47.76 4.50 Jan 61.61 59.54 3.37 59.44 3.53 Feb 74.92 73.55 1.83 73.66 1.68

Losses (%)

Energy [kWh]

Energy [kWh]

Losses [kWh]

Losses [kWh]

Losses (%)

Losses (%)

Energy [kWh]

Energy [kWh]

Losses (%)

Losses (%)

Fig. 20. The daily power diagrams in October for configurations 1 and 2 (Real Sky)

Fig. 21. The daily power diagrams in October for configurations 1 and 2 (Clear-sky)

Concluding the study on the two configurations of the first array, it can be stressed that the simulations on the average day of the months subject to shading effect give greater losses in configuration 1 than in configuration 2, both for real-sky days and clear-sky days. Obviously, the losses are maximum in December with values of 17.8% (Conf. 1) vs. 9.4% (Conf. 2) but, if we consider the losses on yearly basis (including the months without shading), the mean value of losses is 2.5% (Conf. 1) vs. 1.3% (Conf. 2). Hence, in this case it is more profitable to adopt the module connection which allows to concentrate the shading in a single string.

configuration 1 configuration 2 without shading

6 8 10 12 14 16 18

**hours of a day**

6 8 10 12 14 16 18

**hours of a day**

Concluding the study on the two configurations of the first array, it can be stressed that the simulations on the average day of the months subject to shading effect give greater losses in configuration 1 than in configuration 2, both for real-sky days and clear-sky days. Obviously, the losses are maximum in December with values of 17.8% (Conf. 1) vs. 9.4% (Conf. 2) but, if we consider the losses on yearly basis (including the months without shading), the mean value of losses is 2.5% (Conf. 1) vs. 1.3% (Conf. 2). Hence, in this case it is more profitable to adopt

Fig. 21. The daily power diagrams in October for configurations 1 and 2 (Clear-sky)

the module connection which allows to concentrate the shading in a single string.

Fig. 20. The daily power diagrams in October for configurations 1 and 2 (Real Sky)

configuration 1 configuration 2 without shading

0

0

2

4

**power [kW]**

6

8

10

1

2

3

**power [kW]**

4

5

6

7


Table 3. Energies and losses in the shading patterns (Real sky)


Table 4. Energies and losses in the shading patterns (Clear sky)

Now, addressing the focus on the two configurations of the second array, it can be stressed that the simulations on the average day of the months subject to shading effect give slightly greater losses in configuration 3 than in configuration 4 for real-sky days whereas the opposite occurs for clear-sky days with higher values of losses. More in detail, in clear-sky conditions the losses are maximum in December with values of 4.69% (Conf. 3) vs. 6.24% (Conf. 4) but, if we consider the losses on yearly basis (including the months without shading), the mean value of losses is 0.65% (Conf. 3) vs. 0.64% (Conf. 4). Hence, with more complex structure of array and less amount of shading, it is almost equivalent either to concentrate the shading in a single string or to distribute equally in all the strings.


Table 5. Energies and losses in the shading patterns (Real-sky).


Table 6. Energies and losses in the shading patterns (Clear-sky).

Non-Idealities in the I-V

grid connection is the same as in the previous system.

Fig. 22. PV arrays on the façade of the 1st system.

Fig. 23. PV arrays on the façade of the 2nd system.

The amount of shaded array, the beginning and duration of these conditions, obviously, are depending on the calendar day. As well known, the shading effect, concentrated on

Array 1

Array 2

Array 3

Array 4

Array 5

Array 6

and 6, which are located on the roof, in the second system (Fig. 23).

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 247

supplies a single-phase inverter of the same model as in the first system. Also the scheme of

These PV systems are among the first examples of PV building integration in Italy, even if they are a *retro-fit* work: in fact, their modules behave as saw-tooth curtains (or "sun shields") providing a protection against direct sunlight, principally in summer season. Due to the façade azimuth (25° west), besides the comparative distances among the rows of arrays, a partial shading effect occurs during morning periods from April to September. All the PV fields are involved by this partial shading during these periods except for the array 4, which is entirely located above the last floor in the first system (Fig. 22) and for the arrays 5

#### **4.3 Concluding remarks**

Since the PV-system designer does not take into account possible periodic shading when he decides the connections of the modules in the strings, the paper has discussed, by proper comparisons, various cases of shading pattern in PV arrays from multiple viewpoints: power profiles in clear days with 15-min time step, daily energy as a monthly average value for clear and cloudy days.

The simulation results prove that, with *simple structure* of the array and *important amount of shading*, it is better to limit the shading effect within one string rather than to distribute the shading on all the strings. Contrary, with more complex structure of the array and low amount of shading, it is practically equivalent to concentrate or to distribute the shading on all the strings.

Finally, in the simulation conditions the impact of the shading losses on yearly basis is limited to 1-3%.

### **5. Decrease of inverter performance for shading effect**

The last paragraph of this chapter deals with other consequences of the mismatch, because it has a significant impact also on the inverter performance and the power quality fed into the grid (Abete et al., 2005).

The real case of two systems installed in Italy within the Italian program "PV roofs" is presented. They have been built on the south oriented façades of the headquarters of two different municipal Companies. Due to the façade azimuth, besides the distances among the floors, a partial shading occurs during morning periods from April to September. The shading effect determined an important decrease of the available power. However the attention has been focused on the inverter performance, both at the DC and AC side in these conditions, during which experimental data have been collected. The DC ripples in voltage and current signals can be higher than 30%, with a fundamental frequency within 40-80 Hz; the Maximum Power Point Tracker (MPPT) efficiency resulted around 60%, because the tracking method relied on the wrong assumption that the voltage at maximum power point (MPP) was a constant fraction of the open circuit voltage, while with shading the fraction decreased down to roughly 50%; the Total Harmonic Distortion (THD) of AC current resulted higher than 20% with a great spread and presence of even harmonics, whereas the THD of voltage is slightly influenced by the shading; the power factor was within 0.75-0.95, due to the previous current distortion and the capacitive component, which becomes important in these conditions.

#### **5.1 Two real case PV systems built on façades**

Within an Italian grid connected PV Programme, two systems (20 kWp and 16 kWp, respectively) have been installed in Torino on the south oriented façades of the headquarters of AMIAT (municipal company for the waste-materials management) and of "Provincia di Torino" public administration.

The first system consists of six PV plants, 3.3 kWp each: the array of a single plant counts 30 modules and supplies a single-phase inverter. The low-voltage three-phase grid is fed by two parallel connected inverters per phase (230 V line to neutral wire). The second system consists of six PV plants, 2.6 kWp each: the array of a single plant counts 24 modules and

Since the PV-system designer does not take into account possible periodic shading when he decides the connections of the modules in the strings, the paper has discussed, by proper comparisons, various cases of shading pattern in PV arrays from multiple viewpoints: power profiles in clear days with 15-min time step, daily energy as a monthly average value

The simulation results prove that, with *simple structure* of the array and *important amount of shading*, it is better to limit the shading effect within one string rather than to distribute the shading on all the strings. Contrary, with more complex structure of the array and low amount of shading, it is practically equivalent to concentrate or to distribute the shading on

Finally, in the simulation conditions the impact of the shading losses on yearly basis is

The last paragraph of this chapter deals with other consequences of the mismatch, because it has a significant impact also on the inverter performance and the power quality fed into the

The real case of two systems installed in Italy within the Italian program "PV roofs" is presented. They have been built on the south oriented façades of the headquarters of two different municipal Companies. Due to the façade azimuth, besides the distances among the floors, a partial shading occurs during morning periods from April to September. The shading effect determined an important decrease of the available power. However the attention has been focused on the inverter performance, both at the DC and AC side in these conditions, during which experimental data have been collected. The DC ripples in voltage and current signals can be higher than 30%, with a fundamental frequency within 40-80 Hz; the Maximum Power Point Tracker (MPPT) efficiency resulted around 60%, because the tracking method relied on the wrong assumption that the voltage at maximum power point (MPP) was a constant fraction of the open circuit voltage, while with shading the fraction decreased down to roughly 50%; the Total Harmonic Distortion (THD) of AC current resulted higher than 20% with a great spread and presence of even harmonics, whereas the THD of voltage is slightly influenced by the shading; the power factor was within 0.75-0.95, due to the previous current distortion and the capacitive component, which becomes

Within an Italian grid connected PV Programme, two systems (20 kWp and 16 kWp, respectively) have been installed in Torino on the south oriented façades of the headquarters of AMIAT (municipal company for the waste-materials management) and of "Provincia di

The first system consists of six PV plants, 3.3 kWp each: the array of a single plant counts 30 modules and supplies a single-phase inverter. The low-voltage three-phase grid is fed by two parallel connected inverters per phase (230 V line to neutral wire). The second system consists of six PV plants, 2.6 kWp each: the array of a single plant counts 24 modules and

**5. Decrease of inverter performance for shading effect** 

**4.3 Concluding remarks** 

for clear and cloudy days.

all the strings.

limited to 1-3%.

grid (Abete et al., 2005).

important in these conditions.

Torino" public administration.

**5.1 Two real case PV systems built on façades** 

supplies a single-phase inverter of the same model as in the first system. Also the scheme of grid connection is the same as in the previous system.

These PV systems are among the first examples of PV building integration in Italy, even if they are a *retro-fit* work: in fact, their modules behave as saw-tooth curtains (or "sun shields") providing a protection against direct sunlight, principally in summer season. Due to the façade azimuth (25° west), besides the comparative distances among the rows of arrays, a partial shading effect occurs during morning periods from April to September. All the PV fields are involved by this partial shading during these periods except for the array 4, which is entirely located above the last floor in the first system (Fig. 22) and for the arrays 5 and 6, which are located on the roof, in the second system (Fig. 23).

Fig. 22. PV arrays on the façade of the 1st system.

Fig. 23. PV arrays on the façade of the 2nd system.

The amount of shaded array, the beginning and duration of these conditions, obviously, are depending on the calendar day. As well known, the shading effect, concentrated on

Non-Idealities in the I-V

decreases.

the shading;

so the harmonics decrease the DC power.

distorted and multiple MPPs arise ;

component is low, as in this case.

immediately after the shading;

of inverters of the same model;

**5.4 Experimental tests to detect the inverter behaviour**  The experimental tests, presented in this section, include:

logger in three phase configuration, on the first system.

changes of derivative (bypass diodes action): the power, hence, decreases.

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 249

Vk, Ik represent the r.m.s. values of harmonic voltage and current at the same frequency, whereas k is the phase shift between voltage and current: here every cosk is negative and

A remarkable distortion arises also at the AC side of inverter with reference to the current: even harmonics, which cause that the positive half-wave is different from the negative halfwave, can be noticeable. The even harmonics do not contribute AC active power, since the grid voltage, generally, has only odd harmonics: the DC-AC efficiency, consequently,

 the MPPT efficiency can be lower than 95%, because the tracking method, employed in the inverters under study, relies on the statement that the voltage VMPP at MPP is a constant fraction of the open circuit voltage, but with shading the fraction is lower; the THD of AC current can be higher than 10% with great spread and presence of even harmonics (especially the 2nd one), whereas the THD of voltage is slightly influenced by

 the power factor can be lower than 0.9, due to both the previous distortion of AC current and a capacitive component, which becomes important when the active

1. measurements of DC and AC waveforms by the oscilloscope on the inverters of the most shaded arrays of the first system (array 1 and 2) during the morning period and

2. measurements of AC waveforms by the oscilloscope on the inverters of the second system after the morning shading, in order to compare the behaviour, without shading,

3. daily monitoring of the parameters of inverter performance at the AC side, by the data

Concerning the item 1., the MPPT efficiency is obtained by two tests, carried out as close as possible because of the ambient conditions (irradiance and temperature) must be equal. The first test determines the I(V) characteristics by a suitable method (transient charge of a capacitor. Hence, it is possible to calculate the maximum power PMAX. As an example, Figure 24 shows ten I(V) curves of the array 2 during the morning evolution of the shading (from 9.50 to 11.35 in August). It is possible to note different conditions of irradiance: at 9.50 the shading is complete above all the PV modules (only diffuse radiation gives its contribution) and the I(V) shape is regular; from 10.25 to 10.35 the irradiance is not uniform, some modules begin to be subject to the beam radiation and the I(V) shape has abrupt

Summarizing the previous items, the inverter parameters worsen with shading effect: the DC ripples can be higher than 10% and the waveforms have harmonic content, with a fundamental-harmonic frequency down to 30 Hz, because the I(V) characteristics are

*P V I VI*

1

*n DC mean mean k k k k*

cos

(11)

some cells of a PV array, determines a mismatch of cell current-voltage I(V) characteristics, with an important decrease (only limited by the bypass diodes) of the available power; furthermore, the shaded cells can work as a load and the hot spots can rise. However the attention has been focused on the inverter performance, both at the DC side and at the AC side in shading conditions, during which experimental data have been collected.

#### **5.2 Parameters of inverter performance and their measurement system**

The inverter performance can be defined by the following parameters, besides the DC-AC efficiency:


The measurements have been carried out by a Data Acquisition board (DAQ), integrated into a notebook PC. The real-time sampling has been performed at the sampling rate of 25.6 kSa/s, with a resolution of 12 bits. This rate corresponds to 512 samples per period at grid frequency of 50 Hz, in such a way as to allow the calculation of the harmonics up to 50th. Three voltage probes and three current ones are used as a signal conditioning stage to extend the range of the measured quantities above the voltage range of 10 V. These probes are equipped with operational amplifiers with low output resistance ( 50 ), for obtaining low time constants with the capacitance of the Sample & Hold circuit in the DAQ board, which accepts up to eight input channels by its multiplexer.

A proper software, developed in LabVIEW environment, implements Virtual Instruments behaving as storage oscilloscope and multimeter for measurement of r.m.s. voltage (up to 600 V), current (up to 20 A), active power and power factor. The oscilloscope, in order to obtain the I(V) curves of the PV arrays, is equipped with a trigger system, useful for the capture of the transient charge of a capacitor. The multimeter also performs harmonic analysis for the calculation of THD by the Discrete Fourier Transform (DFT) and operates as data logger with user-selected time interval between two consecutive measurements.

#### **5.3 Distortion of waveforms in case of shading effect**

In case of shading effect, which causes the distortion of the I(V) shape, the ripples at the DC side of inverter increase and cannot be sinusoidal: the waveforms, thus, have harmonic content, as pointed out in (11) for the power, with a fundamental-harmonic frequency different from 100 Hz (double of grid frequency):

some cells of a PV array, determines a mismatch of cell current-voltage I(V) characteristics, with an important decrease (only limited by the bypass diodes) of the available power; furthermore, the shaded cells can work as a load and the hot spots can rise. However the attention has been focused on the inverter performance, both at the DC side and at the AC side in shading conditions, during which experimental data have been

The inverter performance can be defined by the following parameters, besides the DC-AC

*V V <sup>V</sup> V*

MPPT is operating), where PDC is the input power of the inverter and PMAX is the

the power factor *PF P V I AC trms trms* , with PAC active power, Vtrms and Itrms true

The measurements have been carried out by a Data Acquisition board (DAQ), integrated into a notebook PC. The real-time sampling has been performed at the sampling rate of 25.6 kSa/s, with a resolution of 12 bits. This rate corresponds to 512 samples per period at grid frequency of 50 Hz, in such a way as to allow the calculation of the harmonics up to 50th. Three voltage probes and three current ones are used as a signal conditioning stage to extend the range of the measured quantities above the voltage range of 10 V. These probes are equipped with operational amplifiers with low output resistance ( 50 ), for obtaining low time constants with the capacitance of the Sample & Hold circuit in the DAQ board,

A proper software, developed in LabVIEW environment, implements Virtual Instruments behaving as storage oscilloscope and multimeter for measurement of r.m.s. voltage (up to 600 V), current (up to 20 A), active power and power factor. The oscilloscope, in order to obtain the I(V) curves of the PV arrays, is equipped with a trigger system, useful for the capture of the transient charge of a capacitor. The multimeter also performs harmonic analysis for the calculation of THD by the Discrete Fourier Transform (DFT) and operates as data logger with user-selected time interval between two consecutive

In case of shading effect, which causes the distortion of the I(V) shape, the ripples at the DC side of inverter increase and cannot be sinusoidal: the waveforms, thus, have harmonic content, as pointed out in (11) for the power, with a fundamental-harmonic frequency

*mean*

23 1 ... *THD I I I I I n* , where V1 (I1), V2 (I2),…, Vn (In) are the harmonic

and current max min

*MPPT DC MAX P P* (how close to maximum power PMAX the

*pp*

23 1 ... *THD V V V V V n* and AC

*I I <sup>I</sup> I* ;

*mean*

*pp*

**5.2 Parameters of inverter performance and their measurement system** 

maximum power calculated on the current-voltage I(V) characteristic; the total harmonic distortion of grid AC voltage 22 2

the ripple peak factors of DC voltage max min

which accepts up to eight input channels by its multiplexer.

**5.3 Distortion of waveforms in case of shading effect** 

different from 100 Hz (double of grid frequency):

collected.

efficiency:

the MPP Tracker efficiency

r.m.s. values;

measurements.

current 22 2

r.m.s. voltage and current.

$$P\_{\rm DC} = V\_{\rm mean} \cdot I\_{\rm mean} + \sum\_{k=1}^{n} V\_k \cdot I\_k \cdot \cos \varphi\_k \tag{11}$$

Vk, Ik represent the r.m.s. values of harmonic voltage and current at the same frequency, whereas k is the phase shift between voltage and current: here every cosk is negative and so the harmonics decrease the DC power.

A remarkable distortion arises also at the AC side of inverter with reference to the current: even harmonics, which cause that the positive half-wave is different from the negative halfwave, can be noticeable. The even harmonics do not contribute AC active power, since the grid voltage, generally, has only odd harmonics: the DC-AC efficiency, consequently, decreases.

Summarizing the previous items, the inverter parameters worsen with shading effect:


#### **5.4 Experimental tests to detect the inverter behaviour**

The experimental tests, presented in this section, include:


Concerning the item 1., the MPPT efficiency is obtained by two tests, carried out as close as possible because of the ambient conditions (irradiance and temperature) must be equal.

The first test determines the I(V) characteristics by a suitable method (transient charge of a capacitor. Hence, it is possible to calculate the maximum power PMAX. As an example, Figure 24 shows ten I(V) curves of the array 2 during the morning evolution of the shading (from 9.50 to 11.35 in August). It is possible to note different conditions of irradiance: at 9.50 the shading is complete above all the PV modules (only diffuse radiation gives its contribution) and the I(V) shape is regular; from 10.25 to 10.35 the irradiance is not uniform, some modules begin to be subject to the beam radiation and the I(V) shape has abrupt changes of derivative (bypass diodes action): the power, hence, decreases.

Non-Idealities in the I-V

corresponding to 73 V.

Fig. 26. Bad operation of MPPT in the inverter 2.

Table 7. The DC performance parameters (inverter 2)

it occurs for the negative half-waves.

Current (A)

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 251

power point (out of current scale here), due to the algorithm that imposes a voltage vDC equal to 78% of PV open circuit voltage. Moreover in this case PDC is 62% of the local MPP

Table 7 summarizes the experimental results in terms of: the ripple frequency fripple; the

P(V)

0 20 40 60 80 100 120 Voltage (V)

> **Vpp %**

9.50 41 27 38 89 10.15 47 27 33 92 10.25 48 13 69 <54 10.35 53 8.5 59 <49 10.45 50 20 89 <47 10.55 62 16 52 <56 11.05 64 16 51 <57 11.15 73 20 35 <58 11.20 80 9.2 4.5 81 11.35 101 2.9 4.5 94

Concerning the AC measurements of the items 1. and 2., the results show, during the shading, high distortion of current waveforms, which however does not worsen significantly the voltage waveforms (THDV within the range of 2-3%). The positive halfwaves are not all the same (on the time scale of few grid periods) and are very different from the negative half-waves (due to the even harmonics also present at the DC side). A capacitive component, enough remarkable, produces a phase shift with respect to the grid voltage. Figure 27 shows the voltage and current signals at 10.45 for inverter 2: the first positive half-wave has one sharp peak, whereas the last positive half-wave has two peaks, as

The computation of the total harmonic distortion of AC current proves that the values are always higher than 15% (up to 22%). With respect to the individual harmonics, the following

**Ipp %**  **MPPT %** 

I(V)

Power (W)

ripple indices of DC voltage Vpp and current Ipp; the MPPT efficiency MPPT.

**Hours fripple**

**(Hz)** 

Fig. 24. I(V) curves of the array 2 during the shading.

Only after 11.05, when the most of modules are subject to beam radiation, the power begins again to increase; the shading, around 11.35, is vanishing. In Fig. 3 the I(V) curves are not complete because we have preferred to obtain the maximum accuracy of current measurement in the portion of I(V) that is used by the MPPT of the inverter (in this case 66- 120 V is the voltage range of the MPPT).

The second test, for the same ambient conditions, provides the input signals of the inverter: voltage vDC(t), current iDC(t) and power pDC(t) affected by the ripples. It is worth noting that the amplitude and frequency of DC ripple can influence the normal work of the input DC filter and the DC-DC converter. Fig. 25 shows some profiles of DC current ripples, corresponding to the previous I(V) measurements: the waveforms have many changes of derivative with even harmonics, whereas the DC voltage ones have always a slow ascent and a steep descent (not represented here). This behaviour of iDC(t) can be responsible for higher losses in the iron inductor of DC-DC converter.

Fig. 25. DC current ripples during shading (inverter 2).

By combining the results of the two tests (Fig. 24 and Fig. 25), if the functions I(V) and iDC(vDC) are plotted in the same diagram, it is possible to assess the operation of the MPPT in shading condition. As an example, Fig. 26 shows what happens at 10.25 in the inverter 2: the curves are not complete for the previous reason and the voltage VMPP < 47 V (less than 43% of the PV open circuit voltage). The MPPT is not able to work in the absolute maximum power point (out of current scale here), due to the algorithm that imposes a voltage vDC equal to 78% of PV open circuit voltage. Moreover in this case PDC is 62% of the local MPP corresponding to 73 V.

Table 7 summarizes the experimental results in terms of: the ripple frequency fripple; the ripple indices of DC voltage Vpp and current Ipp; the MPPT efficiency MPPT.

Fig. 26. Bad operation of MPPT in the inverter 2.

250 Solar Cells – Silicon Wafer-Based Technologies

9.50 10.15 10.25 10.35 10.45 10.55 11.05 11.15 11.20 11.35

0 20 40 60 80 100 120 Voltage (V)

Only after 11.05, when the most of modules are subject to beam radiation, the power begins again to increase; the shading, around 11.35, is vanishing. In Fig. 3 the I(V) curves are not complete because we have preferred to obtain the maximum accuracy of current measurement in the portion of I(V) that is used by the MPPT of the inverter (in this case 66-

The second test, for the same ambient conditions, provides the input signals of the inverter: voltage vDC(t), current iDC(t) and power pDC(t) affected by the ripples. It is worth noting that the amplitude and frequency of DC ripple can influence the normal work of the input DC filter and the DC-DC converter. Fig. 25 shows some profiles of DC current ripples, corresponding to the previous I(V) measurements: the waveforms have many changes of derivative with even harmonics, whereas the DC voltage ones have always a slow ascent and a steep descent (not represented here). This behaviour of iDC(t) can be responsible for

> -0,01 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 Time (s)

By combining the results of the two tests (Fig. 24 and Fig. 25), if the functions I(V) and iDC(vDC) are plotted in the same diagram, it is possible to assess the operation of the MPPT in shading condition. As an example, Fig. 26 shows what happens at 10.25 in the inverter 2: the curves are not complete for the previous reason and the voltage VMPP < 47 V (less than 43% of the PV open circuit voltage). The MPPT is not able to work in the absolute maximum

9.50

11.15

10.45

10.25

11.05

0

120 V is the voltage range of the MPPT).

Fig. 24. I(V) curves of the array 2 during the shading.

higher losses in the iron inductor of DC-DC converter.

Fig. 25. DC current ripples during shading (inverter 2).

Current (A)

5

10

15

Current (A)

20

25


Table 7. The DC performance parameters (inverter 2)

Concerning the AC measurements of the items 1. and 2., the results show, during the shading, high distortion of current waveforms, which however does not worsen significantly the voltage waveforms (THDV within the range of 2-3%). The positive halfwaves are not all the same (on the time scale of few grid periods) and are very different from the negative half-waves (due to the even harmonics also present at the DC side). A capacitive component, enough remarkable, produces a phase shift with respect to the grid voltage. Figure 27 shows the voltage and current signals at 10.45 for inverter 2: the first positive half-wave has one sharp peak, whereas the last positive half-wave has two peaks, as it occurs for the negative half-waves.

The computation of the total harmonic distortion of AC current proves that the values are always higher than 15% (up to 22%). With respect to the individual harmonics, the following

Non-Idealities in the I-V


Fig. 29. AC waveforms of inverter 5 (2nd system).

also the phase shift between voltage and current.

PF2

0 0,1 0,2 0,3 0,4 0,5 0,6

**5.5 Concluding remarks** 

Fig. 30. Daily monitoring of PF and THD (1st system).

AC sides. The experimental results point out that:

fundamental frequency within 40-80 Hz;

Total Harmonic Distortion

Voltage (V)

Characteristic of the PV Generators: Manufacturing Mismatch and Shading Effect 253


Concerning the item 3., by using the data logger, periodic measurements of r.m.s. voltage, current and power, besides harmonic analysis with THD, have been performed for each phase of the three-phase grid. In the first system, phase 1 supplies the currents of inverter 1 and 2 (the most shaded), phase 2 feeds the currents of inverter 3 and 4 (supplied by the only array without shading) and phase 3 feeds the currents of inverter 5 and 6. In Figure 30, relevant to a data acquisition in May, it is clear the shading effect until 13.00. During the shading, the main results are: the power factors PF1 and PF3 are continuously variable within the range 0.75-0.95, due to not only the high harmonic distortion THDI (15-20%), but

PF3

THDI3

9.30 10.30 11.30 12.30 13.30 14.30 15.30 Time

Concerning two grid connected PV systems, it has been described the negative influence, owing to shading effect of PV arrays, on the inverter performance both at the DC and the

the DC ripples are higher than 30% and the waveforms have harmonic content, with a

 the MPPT efficiency is around 60%, because the tracking method relies on the assumption that the voltage at MPP is a constant fraction of the open circuit voltage, but

THDI2

THDI1

with shading the fraction decreases down to roughly 50%;

PF1


0

0,2

0,4

0,6

Power Factor

0,8

1

Current (A)

remarks can be done: the second harmonic arises up to 8% in the first part (9.50-10.35), then vanishes; the seventh harmonic is the highest (10-14%) for all the duration of the shading; the third harmonic maintains itself nearly constant at 6% until 11.20, when it rises up to 10%, that is the main component after the conclusion of shading; finally the fifth, ninth and eleventh harmonics maintain their selves around the 5% level during the shading. Figure 28 summarizes these results in a histogram.

Fig. 27. AC waveforms of inverter 2 at 10.45.

After the conclusion of the shading, all the six inverters of the first system have values of THD of AC current around 10 %, with the main component given by the third harmonic. In order to check whether this is the behaviour also for the inverters of the second system, the measurements of the AC waveforms, without the shading, have been carried out by the oscilloscope.

Fig. 28. Histogram of the harmonic currents (inverter 2).

As an example for the inverter 5, the waveforms of AC current and voltage are shown in Figure 29, in which it is worth noting that: no phase shift exists between voltage and current; a sharp peak, which causes a THD around 9%, is detected in the current. Also the other inverters have confirmed the same behaviour for the current waveform and the harmonic distortion.

Fig. 29. AC waveforms of inverter 5 (2nd system).

252 Solar Cells – Silicon Wafer-Based Technologies

remarks can be done: the second harmonic arises up to 8% in the first part (9.50-10.35), then vanishes; the seventh harmonic is the highest (10-14%) for all the duration of the shading; the third harmonic maintains itself nearly constant at 6% until 11.20, when it rises up to 10%, that is the main component after the conclusion of shading; finally the fifth, ninth and eleventh harmonics maintain their selves around the 5% level during the shading. Figure 28

> -0,01 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 Time (s)

After the conclusion of the shading, all the six inverters of the first system have values of THD of AC current around 10 %, with the main component given by the third harmonic. In order to check whether this is the behaviour also for the inverters of the second system, the measurements of the AC waveforms, without the shading, have been carried out by the

> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Harmonic order

As an example for the inverter 5, the waveforms of AC current and voltage are shown in Figure 29, in which it is worth noting that: no phase shift exists between voltage and current; a sharp peak, which causes a THD around 9%, is detected in the current. Also the other inverters have confirmed the same behaviour for the current waveform and the harmonic


9:50 10:15 10:25 10:35 10:45 10:55 11:05 11:15 11:20 11:35 Current (A)

summarizes these results in a histogram.

Voltage (V)


Fig. 27. AC waveforms of inverter 2 at 10.45.

Fig. 28. Histogram of the harmonic currents (inverter 2).

Harmonic in % of the fundamental one

oscilloscope.

distortion.

Concerning the item 3., by using the data logger, periodic measurements of r.m.s. voltage, current and power, besides harmonic analysis with THD, have been performed for each phase of the three-phase grid. In the first system, phase 1 supplies the currents of inverter 1 and 2 (the most shaded), phase 2 feeds the currents of inverter 3 and 4 (supplied by the only array without shading) and phase 3 feeds the currents of inverter 5 and 6. In Figure 30, relevant to a data acquisition in May, it is clear the shading effect until 13.00. During the shading, the main results are: the power factors PF1 and PF3 are continuously variable within the range 0.75-0.95, due to not only the high harmonic distortion THDI (15-20%), but also the phase shift between voltage and current.

Fig. 30. Daily monitoring of PF and THD (1st system).

#### **5.5 Concluding remarks**

Concerning two grid connected PV systems, it has been described the negative influence, owing to shading effect of PV arrays, on the inverter performance both at the DC and the AC sides. The experimental results point out that:


**12** 

 *China* 

**Light Trapping Design in** 

**Silicon-Based Solar Cells** 

*Physics science and technology, Wuhan University of Technology* 

When the sunlight illuminates the front surface of solar cell, part of the incident energy reflects from the surface, and part of incident energy transmits to the inside of solar cell and converts into electrical energy. Typically, the reflectivity of bare silicon surface is quite higher; more than 30% of incident sunlight can be reflected. In order to reduce the reflection loss on the surface of solar cell, usually the following methods were adopted. One is to corrode and texture the front surface [Gangopadhyay et al., 2007; Ju et al., 2008; Basu et al., 2010; Li et al., 2011], so that incident light can reflect back and forth between the inclined surfaces, which will increase the interaction between incident light and semiconductor surface. The second is coated with a single-layer or multi-layer antireflection film coating [Chao et al., 2010]. Generally, these coatings are very thin, the optical thickness is nearly quarter or half of incident wavelength. Single-layer antireflection coating only has good anti-reflection effect for a single wavelength, so multi-layer antireflection coating is commonly used in high efficiency solar cells, for it has good anti-reflection effect within the wide spectrum of solar radiation. Third, surface plasmons offer a novel way of light trapping by using metal nanoparticles to enhance absorption or light extraction in thin film solar cell structures [Derkacs et al., 2006; Catchpole et al., 2008; Moulin et al.,2008; Nkayama et al.,2008; Losurdo et al.,2009;]. By manipulating their size, the particles can be used as an efficient scattering layer. One of the benefits of this light trapping approach is that the surface area of silicon and surface passivation layer remain the same for a planar cell, so

The above light tapping methods can be used individually or in combination. In the

Textured solar cells can not only increase the absorption of the incident sunlight, it also has many other advantages [Fesquet et al., 2009]. For solar cells, the higher efficiency and the lower cost are always main topic in scientific research. Because the crystalline silicon is nondirect band gap semiconductor material, the absorption of sunlight is relatively weak, the thickness of the solar cell need to exceed a few millimeters to absorb 99% of the solar spectrum, which increased the weight of materials and the production cost, and increased the recombination probability in the bulk, resulting in reduced anti-radiation performance.

surface recombination losses are not expect to increase.

**2. Principle and preparation of textured surface** 

following section we will introduce them in detail.

**1. Introduction** 

Fengxiang Chen and Lisheng Wang


#### **6. References**


## **Light Trapping Design in Silicon-Based Solar Cells**

Fengxiang Chen and Lisheng Wang *Physics science and technology, Wuhan University of Technology China* 

#### **1. Introduction**

254 Solar Cells – Silicon Wafer-Based Technologies

 the THD of AC current is higher than 20% with a great spread and presence of even harmonics, whereas the THD of voltage is slightly influenced by the shading; the power factor is within 0.75-0.95, due to the previous current distortion and the

Abete, A.; Ferraris, L. & Spertino, F. (1998). Measuring Circuits to detect Mismatching of the

*ADC Modeling and Testing*, pp. 313-315, Naples, Italy, September 17-18, 1998. Abete, A.; Napoli, R. & Spertino, F. (2003). A simulation procedure to predict the monthly

Abete, A.; Napoli, R. & Spertino, F. (2005). Grid connected PV systems on façade "Sun

Spertino, F.; Di Leo, P. & Sumaili Akilimali, J. (2009). Optimal Configuration of module

Spertino, F. & Sumaili Akilimali, J. (2009). Are manufacturing I-V mismatch and reverse

*Electronics*, Vol. 56, No.11, (November 2009), pp. 4520-4531, ISSN 0278-0046.

Photovoltaic cells or modules Current-Voltage Characteristics, *IMEKO TC-4 Symposium on Development in Digital Measuring Instrumentation and 3rd Workshop on* 

energy supplied by grid connected PV systems, *3rd World Conference on Photovoltaic Energy Conversion*, pp. 1-4 (CD ROM), ISBN 4-9901816-3-8, Osaka, Japan, May 11-

Shields": Decrease of inverter performance for shading effect, *20th European Photovoltaic Solar Energy Conference*, pp. 2135-2138, ISBN 3-936338-19-1, Barcelona,

connections for minimizing the shading effect in multi-rows PV arrays, *24th European Photovoltaic Solar Energy Conference*, pp. 4136-4140, ISBN 3-936338-25-6,

currents key factors in large Photovoltaic arrays?, *IEEE Transactions on Industrial* 

capacitive component, which becomes important in shading condition.

**6. References** 

18, 2003.

Spain, June 6-10, 2005.

Hamburg, Germany, September 21-25, 2009.

When the sunlight illuminates the front surface of solar cell, part of the incident energy reflects from the surface, and part of incident energy transmits to the inside of solar cell and converts into electrical energy. Typically, the reflectivity of bare silicon surface is quite higher; more than 30% of incident sunlight can be reflected. In order to reduce the reflection loss on the surface of solar cell, usually the following methods were adopted. One is to corrode and texture the front surface [Gangopadhyay et al., 2007; Ju et al., 2008; Basu et al., 2010; Li et al., 2011], so that incident light can reflect back and forth between the inclined surfaces, which will increase the interaction between incident light and semiconductor surface. The second is coated with a single-layer or multi-layer antireflection film coating [Chao et al., 2010]. Generally, these coatings are very thin, the optical thickness is nearly quarter or half of incident wavelength. Single-layer antireflection coating only has good anti-reflection effect for a single wavelength, so multi-layer antireflection coating is commonly used in high efficiency solar cells, for it has good anti-reflection effect within the wide spectrum of solar radiation. Third, surface plasmons offer a novel way of light trapping by using metal nanoparticles to enhance absorption or light extraction in thin film solar cell structures [Derkacs et al., 2006; Catchpole et al., 2008; Moulin et al.,2008; Nkayama et al.,2008; Losurdo et al.,2009;]. By manipulating their size, the particles can be used as an efficient scattering layer. One of the benefits of this light trapping approach is that the surface area of silicon and surface passivation layer remain the same for a planar cell, so surface recombination losses are not expect to increase.

The above light tapping methods can be used individually or in combination. In the following section we will introduce them in detail.

#### **2. Principle and preparation of textured surface**

Textured solar cells can not only increase the absorption of the incident sunlight, it also has many other advantages [Fesquet et al., 2009]. For solar cells, the higher efficiency and the lower cost are always main topic in scientific research. Because the crystalline silicon is nondirect band gap semiconductor material, the absorption of sunlight is relatively weak, the thickness of the solar cell need to exceed a few millimeters to absorb 99% of the solar spectrum, which increased the weight of materials and the production cost, and increased the recombination probability in the bulk, resulting in reduced anti-radiation performance.

Light Trapping Design in Silicon-Based Solar Cells 257

(a) (b)

(c) (d)

(e) (f)

Fig. 2. The SEM pictures of textured surface with the corrosion time, the corrosion time are:

(a)5min,(b)15min,(c)25min, (d)30min,(e)35min, (f)40min, respectively.[Wang, 2005]

The textured surface can be realized by many methods. These methods are different for mono-crystalline silicon and multi-crystalline silicon material. Next, we will introduce the textured methods for silicon solar cells in detail.

#### **2.1 Textured surface for single crystalline silicon**

Textured surface is fulfilled on mono-crystalline silicon surface by a selective corrosion. At high temperature, the chemical reaction between silicon and alkali occurs as follows:

$$\text{Si} \star \text{2OH} \star \text{H}\_2\text{O=SiO}\_3 \text{2} \star \text{2H}\_2\uparrow$$

Fig. 1. Light trapping by "pyramid" covered at the textured surface.

So hot alkaline solution is usually used to corrode the silicon. For different crystalline faces and crystalline directions, the atoms are arranged differently, so the strength between the atoms is different. According to principles of electrochemical corrosion, their corrosion rate will be different. For {100} planes, the spacing of the adjacent two planes is maximum and the density of covalent bonds is the minimum, so the adjacent layer along the {100} atomic planes are most prone to breakage. On the other hand, atoms within the {111} planes have the minimum distance, and the surface density of covalent bonds is the maximum, which results in that the corrosion rate is the minimum along the <111> direction. Therefore, the corrosion faces revealed by preferential etching solution are (111) planes. After single crystalline silicon material with <100> orientation was corroded preferentially, the pyramids on the surface of mono-crystalline silicon come from the intersection of (111) planes. The "pyramid" structure was shown in Fig. 1.

The low concentrations alkaline solution, such as 1.25% of sodium hydroxide (NaOH) solution is usually used as a selective etching solution, because the corrosion rates of (100) plane and the (111) plane are not the same, the pyramid structure can be obtained on monocrystalline Si surface, which increased light absorption greatly. In the preparation processes, temperature, ethanol content, NaOH content, and corrosion time are the factors which affect the morphology of the pyramids. Fig.2 shows the SEM pictures of textured surfaces with changes of the corrosion time. It can be seen from Fig.2 that the formation of the pyramids with the corrosion time. For example, after 5min, the pyramid began to appear; after 15min, the silicon surface was covered by small pyramids, and a few have begun to grow up; after 30min, the silicon surface covered with pyramids.

The textured surface can be realized by many methods. These methods are different for mono-crystalline silicon and multi-crystalline silicon material. Next, we will introduce the

Textured surface is fulfilled on mono-crystalline silicon surface by a selective corrosion. At

So hot alkaline solution is usually used to corrode the silicon. For different crystalline faces and crystalline directions, the atoms are arranged differently, so the strength between the atoms is different. According to principles of electrochemical corrosion, their corrosion rate will be different. For {100} planes, the spacing of the adjacent two planes is maximum and the density of covalent bonds is the minimum, so the adjacent layer along the {100} atomic planes are most prone to breakage. On the other hand, atoms within the {111} planes have the minimum distance, and the surface density of covalent bonds is the maximum, which results in that the corrosion rate is the minimum along the <111> direction. Therefore, the corrosion faces revealed by preferential etching solution are (111) planes. After single crystalline silicon material with <100> orientation was corroded preferentially, the pyramids on the surface of mono-crystalline silicon come from the intersection of (111) planes. The

The low concentrations alkaline solution, such as 1.25% of sodium hydroxide (NaOH) solution is usually used as a selective etching solution, because the corrosion rates of (100) plane and the (111) plane are not the same, the pyramid structure can be obtained on monocrystalline Si surface, which increased light absorption greatly. In the preparation processes, temperature, ethanol content, NaOH content, and corrosion time are the factors which affect the morphology of the pyramids. Fig.2 shows the SEM pictures of textured surfaces with changes of the corrosion time. It can be seen from Fig.2 that the formation of the pyramids with the corrosion time. For example, after 5min, the pyramid began to appear; after 15min, the silicon surface was covered by small pyramids, and a few have begun to grow up; after

2-+2H2↑

high temperature, the chemical reaction between silicon and alkali occurs as follows:

Si+2OH-+H2O=SiO3

Fig. 1. Light trapping by "pyramid" covered at the textured surface.

"pyramid" structure was shown in Fig. 1.

30min, the silicon surface covered with pyramids.

textured methods for silicon solar cells in detail.

**2.1 Textured surface for single crystalline silicon** 

Fig. 2. The SEM pictures of textured surface with the corrosion time, the corrosion time are: (a)5min,(b)15min,(c)25min, (d)30min,(e)35min, (f)40min, respectively.[Wang, 2005]

Light Trapping Design in Silicon-Based Solar Cells 259

3 22 3Si+4HNO =3SiO +2H O+4NO

2 26 2 SiO +6HF=H [SiF ]+2H O

+ 2- H [SiF ] 2H +[SiF ] 2 6 <sup>6</sup>

This etching method is isotropic corrosion, which has nothing to do with the orientations of

Fig.4 shows the SEM pictures for polysilicon wafers after alkaline etching, acid etching, and first acid corrosion with the second alkaline etching. From Fig.4(a), we can see that after alkaline corrosion the surface is uneven and has more steps. Fig.4(c) shows the morphology of the first acid corrosion with the second alkaline etching, we can find that the pyramid shape and the surface are uneven. So these two surface conditions are not suitable to the sequent screen printing procedure. And SEM picture for acid corrosion is shown in Fig.4 (b). We can get the required thickness by changing the ratio of acid solution and controlling the

(a) (b) (c) Fig. 4. The SEM pictures for (a)polysilicon with alkaline etching;(b)polysilicon with acid etching; (c)polysilicon with first acid etching and second alkaline etching.[Meng, 2001]

Acid etching method for polysilicon has many advantages: firstly, it can remove surface damage layer and texture surface in a very short period of time, this will save the production time; Secondly, the surface after etching is relatively flat and thin, which is easy to make thin battery; Thirdly, NaOH solution is not used, which avoid the contamination from Na ions; and the wafer after the acid corrosion is flat, which is easy to form a relatively flat pn junction, thereby it help to improve the stability of the solar cells; Finally, the flat surface is suitable for the screen printing process and the electrode contact is not prone to

The reflectance curves of different polysilicon surfaces are shown in Fig.5. We can found the reflectivity with acid etching is no more than 20% in the range 400-1000nm; after the deposition of silicon nitride anti-reflection coating (ARC), the average reflectivity is less than 10%; and the reflectivity reaches 1% at 600nm wavelength. Thus, the reflection loss with acid etching is very small. In contrast, for the alkaline texture, the reflectivity is relatively higher,

while the reflectivity with acid and alkaline double texture is intervenient.

the grains, so it will form a uniform textured surface on the polysilicon surface.

response speed.

break.

Fig. 3. The reflectivity of silicon wafers after different etching time.[Wang, 2005]

Fig.3 shows the reflectivity of mono-crystalline silicon wafer after different corrosion time (5-45min). We can find that in the visible range (450-1000nm), the reflectivity decreases with increasing corrosion time, the minimum reflectivity is 11%. For the corrosion time is in the 25-45min range, the corresponding reflectivity is nearly 11-14%. If etching time is further increased, no significant change happens in reflectivity.

#### **2.2 Textured surface for polycrystalline silicon**

For single crystalline silicon with <100> orientation, the ideal pyramid structure can be etched by NaOH solution. However, for polysilicon, only a very small part of the surface is covered with (100) orientation, so the use of anisotropic etching for textured surface is not feasible. Because the orientations of the grains in polysilicon are arbitrary and alkaline solution such as NaOH or KOH, are anisotropic etching, these can easily result in uneven texture, this alkaline etching method is not suitable for texturing polysilicon. In view of optics, the acid solution (the mixture of HF, HNO3, and H2O) and the RIE (reactive ion etching) method are the isotropic surface texture methods for textured surface of polysilicon.

The acid etching solution for polysilicon is mixture of HF, HNO3 and deionized water mixed by certain percentages, where HNO3 is used as strong oxidant, so that silicon became SiO2 after oxidation. The whole silicon surface is covered by dense SiO2 film after oxidation and this SiO2 film will protect the silicon from further reaction. HF solution is used as complexing agent and this solution can dissolve SiO2 film, the resulting H2[SiF6] complexes is soluble in water. H2[SiF6] is a strong acid, which is stronger than sulfuric acid and easily dissociate in solution. So this reaction is a positive feedback corrosion reaction, with the generation of H2[SiF6], and the dissociation from the H+ concentration increased, then the corrosion rate also increased. If corrosion speed is too fast, the reaction process is difficult to control, leading to poor corrosion. To mitigate the corrosion reaction, by mass action law, reducing the HF concentration can slow the reaction speed. The reaction mechanism is as follows [Yang, 2010]:

258 Solar Cells – Silicon Wafer-Based Technologies

Fig. 3. The reflectivity of silicon wafers after different etching time.[Wang, 2005]

increased, no significant change happens in reflectivity.

**2.2 Textured surface for polycrystalline silicon** 

polysilicon.

follows [Yang, 2010]:

Fig.3 shows the reflectivity of mono-crystalline silicon wafer after different corrosion time (5-45min). We can find that in the visible range (450-1000nm), the reflectivity decreases with increasing corrosion time, the minimum reflectivity is 11%. For the corrosion time is in the 25-45min range, the corresponding reflectivity is nearly 11-14%. If etching time is further

For single crystalline silicon with <100> orientation, the ideal pyramid structure can be etched by NaOH solution. However, for polysilicon, only a very small part of the surface is covered with (100) orientation, so the use of anisotropic etching for textured surface is not feasible. Because the orientations of the grains in polysilicon are arbitrary and alkaline solution such as NaOH or KOH, are anisotropic etching, these can easily result in uneven texture, this alkaline etching method is not suitable for texturing polysilicon. In view of optics, the acid solution (the mixture of HF, HNO3, and H2O) and the RIE (reactive ion etching) method are the isotropic surface texture methods for textured surface of

The acid etching solution for polysilicon is mixture of HF, HNO3 and deionized water mixed by certain percentages, where HNO3 is used as strong oxidant, so that silicon became SiO2 after oxidation. The whole silicon surface is covered by dense SiO2 film after oxidation and this SiO2 film will protect the silicon from further reaction. HF solution is used as complexing agent and this solution can dissolve SiO2 film, the resulting H2[SiF6] complexes is soluble in water. H2[SiF6] is a strong acid, which is stronger than sulfuric acid and easily dissociate in solution. So this reaction is a positive feedback corrosion reaction, with the generation of H2[SiF6], and the dissociation from the H+ concentration increased, then the corrosion rate also increased. If corrosion speed is too fast, the reaction process is difficult to control, leading to poor corrosion. To mitigate the corrosion reaction, by mass action law, reducing the HF concentration can slow the reaction speed. The reaction mechanism is as  3 22 3Si+4HNO =3SiO +2H O+4NO 2 26 2 SiO +6HF=H [SiF ]+2H O + 2- H [SiF ] 2H +[SiF ] 2 6 <sup>6</sup>

This etching method is isotropic corrosion, which has nothing to do with the orientations of the grains, so it will form a uniform textured surface on the polysilicon surface.

Fig.4 shows the SEM pictures for polysilicon wafers after alkaline etching, acid etching, and first acid corrosion with the second alkaline etching. From Fig.4(a), we can see that after alkaline corrosion the surface is uneven and has more steps. Fig.4(c) shows the morphology of the first acid corrosion with the second alkaline etching, we can find that the pyramid shape and the surface are uneven. So these two surface conditions are not suitable to the sequent screen printing procedure. And SEM picture for acid corrosion is shown in Fig.4 (b). We can get the required thickness by changing the ratio of acid solution and controlling the response speed.

Fig. 4. The SEM pictures for (a)polysilicon with alkaline etching;(b)polysilicon with acid etching; (c)polysilicon with first acid etching and second alkaline etching.[Meng, 2001]

Acid etching method for polysilicon has many advantages: firstly, it can remove surface damage layer and texture surface in a very short period of time, this will save the production time; Secondly, the surface after etching is relatively flat and thin, which is easy to make thin battery; Thirdly, NaOH solution is not used, which avoid the contamination from Na ions; and the wafer after the acid corrosion is flat, which is easy to form a relatively flat pn junction, thereby it help to improve the stability of the solar cells; Finally, the flat surface is suitable for the screen printing process and the electrode contact is not prone to break.

The reflectance curves of different polysilicon surfaces are shown in Fig.5. We can found the reflectivity with acid etching is no more than 20% in the range 400-1000nm; after the deposition of silicon nitride anti-reflection coating (ARC), the average reflectivity is less than 10%; and the reflectivity reaches 1% at 600nm wavelength. Thus, the reflection loss with acid etching is very small. In contrast, for the alkaline texture, the reflectivity is relatively higher, while the reflectivity with acid and alkaline double texture is intervenient.

Light Trapping Design in Silicon-Based Solar Cells 261

The following figure shows the basic principles of the anti-reflection film. When the reflection of light on second interface returns to the first interface, and if the phase difference

When the incident light is normally illuminated, and the silicon material covered with a transparent layer with thickness d1, the expression of the reflected energy is [Wang, 2001]:

1 2 cos2

> 2 1 02 2

If the transparent layer has the greatest antireflective effect, the zero reflectivity R = 0 should

index of the antireflective film can be calculated by the above expression. But when the

increase the output of solar cell, the distribution of solar spectrum and the relative spectral response of crystalline silicon should be taken into account, and a reasonable wavelength

will be chosen. The peak energy among the terrestrial solar spectrum occur in 0.5um, while the peak of relative spectrum response of silicon cells is in the range 0.8-0.9um wavelength,

In the actual processes of crystalline silicon solar cells, commonly used anti-reflective materials are TiO2, SiO2, SiNx, MgF2, ZnS, Al2O3, etc. Their refractive indexes were listed in Table 1. Their thicknesses are generally about 60-100nm. Chemical vapor deposition (CVD), plasma chemical vapor deposition (PECVD), spray pyrolysis, sputtering and evaporation

( ) *n nn <sup>R</sup> n nn* 

2*n d*

min 2

4 is fulfilled, the reflectivity has the minimum.

be required. This means *n nn* 1 02 . Thus for the desired wavelength

so the wavelength range of the best anti-reflection is in 0.5-0.7um.

techniques can be used to deposit the different anti-reflection film.

1 1 0

1 02

2 cos2

air n0

dielectric n1

silicon n2

is given by:

(1)

<sup>0</sup> , the reflectivity will increase. Therefore, in order to

<sup>0</sup> , the refractive

*n*

2 2 1 2 12 2 2 1 2 12

*r r rr <sup>R</sup> r r rr*

between the two lights is 180 degrees, the former will offset the latter to some extent.

Fig. 6. The principles of the antireflection coating.

d1

Where r1 and r2 are: 0 1 1 2

When 11 0 *n d*

incident wavelength deviates from

Where ni represents the diffraction index. The

1 2

*r r*

01 12 , *n n n n*

*nn nn* 

Fig. 5. Reflectance curves of polysilicon textured with the chemical etching. (a) Without ARC; (b)With SiN ARC. (a-NaOH texturing; b-NaOH after acidic texturing; c-Acidic texturing). [Meng, 2001]

In the RIE preparation process, the gas species, gas flow, pressure and RF power both will influent the etching result. Combined with the gas plasma etching with chlorine gas (Cl2) and the antireflection coating method, the lower reflectivity can be realized in a wide range of wavelengths. According to [Inomato, 1997], the flow rate of chlorine gas can be easily controlled to adjust the surface aspect ratio, which is helpful to form the similar pyramid structure on the polysilicon surface. The maximum short circuit current and the maximum open circuit voltage can be obtained under the condition the chlorine flow is 4.5sccm. The experimental results show that for the mono-crystalline silicon, the reflectivity is about 1-2% in the 400-1000nm wavelength range. In RIE method, because the chlorine or fluorine was used as etching gas, the influence on the environment should be considered.

The textured structure also has some drawbacks. Firstly, in the production process of pyramids, the acid or alkaline solution is often used, which need to be careful; Secondly, the pyramids on the surface increase the surface area, which reduces the average light intensity. And the multiple reflections on the textured surface will result in the uneven distribution of incident illumination. Both these will affect the open circuit voltage of the solar cell; Thirdly, the textured structure not only decreases the reflectivity, but also increases the absorption of the infrared light. The absorption of infrared light will heat the solar cell and decrease the conversion efficiency of solar cell; seriously it will disable the solar cell.

#### **3. Principle and design of the antireflection coating**

#### **3.1 The basic theory of antireflection coating**

Most solar cells were coated with an antireflection coating layer to reduce light reflection on the front surface [Kuo et al., 2008]. This is why crystalline silicon solar cells appears to be blue or black while silicon material appears to be grey. A set of optimized and well designed anti-reflection coating on the front surface is an effective way to improve the optical absorption of the solar cell. For certain range in sunlight spectrum, reflectivity on the front surface varies from more than 30% down to less than 5% [Geng et al., 2010], which greatly increase the absorption of incident sunlight energy of the solar cell.

(a) (b)

In the RIE preparation process, the gas species, gas flow, pressure and RF power both will influent the etching result. Combined with the gas plasma etching with chlorine gas (Cl2) and the antireflection coating method, the lower reflectivity can be realized in a wide range of wavelengths. According to [Inomato, 1997], the flow rate of chlorine gas can be easily controlled to adjust the surface aspect ratio, which is helpful to form the similar pyramid structure on the polysilicon surface. The maximum short circuit current and the maximum open circuit voltage can be obtained under the condition the chlorine flow is 4.5sccm. The experimental results show that for the mono-crystalline silicon, the reflectivity is about 1-2% in the 400-1000nm wavelength range. In RIE method, because the chlorine or fluorine was used as etching gas, the influence on the environment should

The textured structure also has some drawbacks. Firstly, in the production process of pyramids, the acid or alkaline solution is often used, which need to be careful; Secondly, the pyramids on the surface increase the surface area, which reduces the average light intensity. And the multiple reflections on the textured surface will result in the uneven distribution of incident illumination. Both these will affect the open circuit voltage of the solar cell; Thirdly, the textured structure not only decreases the reflectivity, but also increases the absorption of the infrared light. The absorption of infrared light will heat the solar cell and decrease the

Most solar cells were coated with an antireflection coating layer to reduce light reflection on the front surface [Kuo et al., 2008]. This is why crystalline silicon solar cells appears to be blue or black while silicon material appears to be grey. A set of optimized and well designed anti-reflection coating on the front surface is an effective way to improve the optical absorption of the solar cell. For certain range in sunlight spectrum, reflectivity on the front surface varies from more than 30% down to less than 5% [Geng et al., 2010], which greatly

conversion efficiency of solar cell; seriously it will disable the solar cell.

**3. Principle and design of the antireflection coating** 

increase the absorption of incident sunlight energy of the solar cell.

**3.1 The basic theory of antireflection coating** 

Fig. 5. Reflectance curves of polysilicon textured with the chemical etching. (a) Without ARC; (b)With SiN ARC. (a-NaOH texturing; b-NaOH after acidic texturing; c-Acidic

texturing). [Meng, 2001]

be considered.

The following figure shows the basic principles of the anti-reflection film. When the reflection of light on second interface returns to the first interface, and if the phase difference between the two lights is 180 degrees, the former will offset the latter to some extent.

Fig. 6. The principles of the antireflection coating.

When the incident light is normally illuminated, and the silicon material covered with a transparent layer with thickness d1, the expression of the reflected energy is [Wang, 2001]:

$$R = \frac{r\_1^2 + r\_2^2 + 2r\_1r\_2\cos 2\theta}{1 + r\_1^2r\_2^2 + 2r\_1r\_2\cos 2\theta} \tag{1}$$

Where r1 and r2 are: 0 1 1 2 1 2 01 12 , *n n n n r r nn nn* 

Where ni represents the diffraction index. The is given by:

$$\theta = \frac{2\pi n\_1 d\_1}{\lambda\_0}$$

When 11 0 *n d* 4 is fulfilled, the reflectivity has the minimum.

$$R\_{\min} = (\frac{n\_1^2 - n\_0 n\_2}{n\_1^2 + n\_0 n\_2})^2$$

If the transparent layer has the greatest antireflective effect, the zero reflectivity R = 0 should be required. This means *n nn* 1 02 . Thus for the desired wavelength <sup>0</sup> , the refractive index of the antireflective film can be calculated by the above expression. But when the incident wavelength deviates from <sup>0</sup> , the reflectivity will increase. Therefore, in order to increase the output of solar cell, the distribution of solar spectrum and the relative spectral response of crystalline silicon should be taken into account, and a reasonable wavelength *n* will be chosen. The peak energy among the terrestrial solar spectrum occur in 0.5um, while the peak of relative spectrum response of silicon cells is in the range 0.8-0.9um wavelength, so the wavelength range of the best anti-reflection is in 0.5-0.7um.

In the actual processes of crystalline silicon solar cells, commonly used anti-reflective materials are TiO2, SiO2, SiNx, MgF2, ZnS, Al2O3, etc. Their refractive indexes were listed in Table 1. Their thicknesses are generally about 60-100nm. Chemical vapor deposition (CVD), plasma chemical vapor deposition (PECVD), spray pyrolysis, sputtering and evaporation techniques can be used to deposit the different anti-reflection film.

Light Trapping Design in Silicon-Based Solar Cells 263

from this wavelength, the reflectivity increases very much. While the reflectivity curve for double ARC is W-shape. This means that the reflectivity reaches the minimum in two specific wavelengths, which is helpful to suppress the reflectivity in the range 300-1200nm. It is clear from Fig.7 that the antireflection effect of double layer ARC is better than that of

(a) (b)

Besides the normal incidence, the oblique incidence should also be considered. This is because in the practical application, except for concentrated solar cells, most solar cells are fixed in a certain direction in accordance with local longitude and latitude. In the whole cycle of the sun rising and landing, the antireflection coating is not always perpendicular to the incident light. The incident angle is always changing and this case is known as oblique incidence. When the ARC designed under normal incidence is applied to the oblique incidence, due to the polarization effect, the reflective properties will change dramatically. Therefore, the antireflection coatings used in the wide-angle should be redesigned to meet

In the case of oblique incidence, for a single-layer system, the reflectivity can be obtained by Fresnel formula; for a multi-layer system, each layer can be represented by an equivalent interface. If the equivalent admittance of the interface is obtained, the reflectivity of the

For m layers coating system, the refractive index and thickness of each membrane material are known as , ( 1,2,.... ) *ndk m k k* , respectively. The refractive index of incident medium and

> cos (sin ) sin cos *k kk*

 

> 

*kk k i*

*nd k m* is the phase thickness of the k-layer.

0 . 

(1)

*<sup>k</sup>* is the

whole system can be acquired. The basic calculation is as follows [Lin & Lu, 1990]:

the substrate material are 0 1 *n n*, *<sup>m</sup>* , respectively. The light incident angle is

*i*

optical admittance. The interference matrix for the k-layer is:

where 2 cos ( 0,1... )

 

 *k kk k* 

*k*

*M*

Then the interference matrix for the whole m layers system is:

Fig. 7. The typical reflectivity curves for single and double layer antireflection coating.

single layer ARC.

[Wang et al., 2004]

the needs of all-weather use.


Note: The wavelength 590nm (the corresponding energy is 2.1eV) was used in calibration.

Table 1. The refractive index of common anti-reflective materials [Markvart & Castner, 2009]

Among all antireflection coatings, TiOx(x≤2) is one of commonly used antireflection coatings in preparation of crystalline silicon solar cells. This film is usually used as an ideal antireflection coating (ARC) for its high refractive index, and its transparent band center coincides with visible spectrum of sunlight well. And silicon nitride (SiNx) is another commonly used ARC. Because SiNx film has good insulating ability, density, stability and masking ability for the impurity ions, it has been widely used in semiconductor production as an efficient surface passivation layer. And in the preparation process of SiNx coating, it can be easily achieved that the reflection-passivation dual effect, which will improve the conversion efficiency of silicon solar cells significantly. Therefore, since the 90s of the 20th century, the use of SiNx thin film as antireflection coating has become research and application focus.

#### **3.2 Optimization of the antireflection coating**

When conducting coatings optimization design, generally the following assumptions were assumed [Wang, 2001]: 1) The film is an isotropic optical media, and its dielectric properties can be characterized by the refractive index n, where n is a real number. For metals and semiconductors, their dielectric properties can be represented by the complex refractive index N = n-jk (or optical admittance), where N is a plural, and its real part n still represents refractive index, imaginary part k is the extinction coefficient, j is imaginary unit. 2) Two adjacent media was separated with an interface, and the refractive index occurs on both sides change discontinuously. 3) Except the interface, the variation of the refractive index along the film thickness direction is continuous; 4) Films can be separated by two parallel planes, and it is assumed to be infinite in horizontal direction. The thickness of the film has the same magnitude with the light wavelength; 5) The incident light is a plane wave.

In the design of multi-layer coating, the main parameters of the coating structure are: the thickness of each layer d1, d2, ...,dk; incident media, refractive indexes of each layer and the substrate n0, n1 ... nk; light incidence angle θ and wavelength λ. The optical properties of the coating, such as the reflectivity R, depend on these structural parameters. In general, the spectral distribution of incident light is known, so the desired reflectivity R can be achieved by adjusting the values of ni , di (i = 1,2, ... k) and so on.

Fig.7 shows the typical reflectivity curves for single and double layer antireflection coating under normal incidence. We can find the curve shapes in Fig.7(a) and Fig.7(b) are different. The reflectivity curve for single-layer ARC is V-shape, which means the minimum reflectivity only can be achieved in one specific wavelength. If the incident wavelength is far

Materials Refraction index n

Note: The wavelength 590nm (the corresponding energy is 2.1eV) was used in calibration.

Table 1. The refractive index of common anti-reflective materials [Markvart & Castner, 2009] Among all antireflection coatings, TiOx(x≤2) is one of commonly used antireflection coatings in preparation of crystalline silicon solar cells. This film is usually used as an ideal antireflection coating (ARC) for its high refractive index, and its transparent band center coincides with visible spectrum of sunlight well. And silicon nitride (SiNx) is another commonly used ARC. Because SiNx film has good insulating ability, density, stability and masking ability for the impurity ions, it has been widely used in semiconductor production as an efficient surface passivation layer. And in the preparation process of SiNx coating, it can be easily achieved that the reflection-passivation dual effect, which will improve the conversion efficiency of silicon solar cells significantly. Therefore, since the 90s of the 20th century, the use of SiNx thin film as antireflection coating has become research and

When conducting coatings optimization design, generally the following assumptions were assumed [Wang, 2001]: 1) The film is an isotropic optical media, and its dielectric properties can be characterized by the refractive index n, where n is a real number. For metals and semiconductors, their dielectric properties can be represented by the complex refractive index N = n-jk (or optical admittance), where N is a plural, and its real part n still represents refractive index, imaginary part k is the extinction coefficient, j is imaginary unit. 2) Two adjacent media was separated with an interface, and the refractive index occurs on both sides change discontinuously. 3) Except the interface, the variation of the refractive index along the film thickness direction is continuous; 4) Films can be separated by two parallel planes, and it is assumed to be infinite in horizontal direction. The thickness of the film has

the same magnitude with the light wavelength; 5) The incident light is a plane wave.

In the design of multi-layer coating, the main parameters of the coating structure are: the thickness of each layer d1, d2, ...,dk; incident media, refractive indexes of each layer and the substrate n0, n1 ... nk; light incidence angle θ and wavelength λ. The optical properties of the coating, such as the reflectivity R, depend on these structural parameters. In general, the spectral distribution of incident light is known, so the desired reflectivity R can be achieved

Fig.7 shows the typical reflectivity curves for single and double layer antireflection coating under normal incidence. We can find the curve shapes in Fig.7(a) and Fig.7(b) are different. The reflectivity curve for single-layer ARC is V-shape, which means the minimum reflectivity only can be achieved in one specific wavelength. If the incident wavelength is far

MgF2 1.38 SiO2 1.46 Al2O3 1.76 Si3N4 2.05 Ta2O5 2.2 ZnS 2.36 SiOx 1.8-1.9 TiO2 2.62

**3.2 Optimization of the antireflection coating** 

by adjusting the values of ni , di (i = 1,2, ... k) and so on.

application focus.

from this wavelength, the reflectivity increases very much. While the reflectivity curve for double ARC is W-shape. This means that the reflectivity reaches the minimum in two specific wavelengths, which is helpful to suppress the reflectivity in the range 300-1200nm. It is clear from Fig.7 that the antireflection effect of double layer ARC is better than that of single layer ARC.

Fig. 7. The typical reflectivity curves for single and double layer antireflection coating. [Wang et al., 2004]

Besides the normal incidence, the oblique incidence should also be considered. This is because in the practical application, except for concentrated solar cells, most solar cells are fixed in a certain direction in accordance with local longitude and latitude. In the whole cycle of the sun rising and landing, the antireflection coating is not always perpendicular to the incident light. The incident angle is always changing and this case is known as oblique incidence. When the ARC designed under normal incidence is applied to the oblique incidence, due to the polarization effect, the reflective properties will change dramatically. Therefore, the antireflection coatings used in the wide-angle should be redesigned to meet the needs of all-weather use.

In the case of oblique incidence, for a single-layer system, the reflectivity can be obtained by Fresnel formula; for a multi-layer system, each layer can be represented by an equivalent interface. If the equivalent admittance of the interface is obtained, the reflectivity of the whole system can be acquired. The basic calculation is as follows [Lin & Lu, 1990]:

For m layers coating system, the refractive index and thickness of each membrane material are known as , ( 1,2,.... ) *ndk m k k* , respectively. The refractive index of incident medium and the substrate material are 0 1 *n n*, *<sup>m</sup>* , respectively. The light incident angle is 0 . *<sup>k</sup>* is the optical admittance. The interference matrix for the k-layer is:

$$M\_k = \begin{vmatrix} \cos \delta\_k & i(\sin \delta\_k) / \eta\_k \\ i\eta\_k \sin \delta\_k & \cos \delta\_k \end{vmatrix} \tag{1}$$

where 2 cos ( 0,1... ) *k kk k nd k m* is the phase thickness of the k-layer. Then the interference matrix for the whole m layers system is:

Light Trapping Design in Silicon-Based Solar Cells 265

Fig.8 (a), (b), (c), (d) show the results of SiNx/SiO2 ARC when 15°, 30°, 45°, 60° were selected as the optimal angles, where the angles marked in the figure are the incident angles. It can be seen from Fig.8 (a) that the reflectivity is too high when the incident angle is large, especially for the longer wavelength range. And comparing the results of the case 60° and 15°, we can find that the 60° optimization can significantly reduce the long-wavelength reflectivity within the 10%, but the reflectivity rises in short-wave area inevitably, which inhibits the absorption of high-energy photons in the solar spectrum. While optimization with 30° shows a good antireflection property. Under this case when the incident angles range from 0° to 45°, the reflectivity curve is relatively stable; even for the 60° incident angle, the reflectivities in short wavelength and long wavelength still maintain below 15%. The optimization results of 45° is similar with those of 60°, the reflectivity for long wavelength under large incident angle is lower, but for small angle case, the reflectivity for short

(a) (b)

(c) (d) Fig. 8. Under different optimal angles, the reflectivities of optimal SiNx/SiO2 ARC vary with

the incident angles and wavelength. The different optimal angles equal to

(a) 15°; (b) 30°; (c) 45°; (d) 60°, respectively.[Chen & Wang, 2008]

**3.3 The optimization results** 

wavelength is too high.

$$M = \prod\_{k=1}^{m} M\_k \tag{2}$$

In the case of oblique incidence, the admittance values of s polarization and p polarization are different. For the number k layer, they are:

$$\eta\_k = \begin{cases} n\_k / \cos \theta\_k & p \text{ component} \\ n\_k \cos \theta\_k & s \text{ component} \end{cases} \tag{3}$$

Where *<sup>k</sup>* can be given by the Snell law,

$$n\_0 \sin \theta\_0 = n\_k \sin \theta\_k, k = 1, 2...m, m+1\tag{4}$$

The expression *Y CB* is the admittance for combinations of multi-layer coatings and the substrate, and B, C were determined by:

$$
\begin{bmatrix} B \\ C \end{bmatrix} = M \begin{bmatrix} \mathbf{1} \\ \boldsymbol{\eta}\_{m+1} \end{bmatrix} \tag{5}
$$

Where *<sup>m</sup>*1 is the admittance of the substrate layer. The energy reflectivity *R* of the thin film system is:

$$R = \left| \frac{1 - \chi/\eta\_0}{1 + \chi/\eta\_0} \right|^2 \tag{6}$$

For the *Rs* component, the 0 *Y*, values in above expression should be replaced by 0 , *Ys s* . For the *Rp* component, the corresponding 0 *Y*, should be substituted by 0 , *Yp p* . The total energy reflectivity *R* is:

$$R = \frac{R\_s + R\_p}{2} \tag{7}$$

The reflectivity R of the whole system depends on the structural parameters of each layer. Since the spectral response of silicon ranges from 300 to 1200nm, so only incident light in the 300-1200nm wavelength range is considered. Taking into account the inconsistent between the solar spectrum and the spectral response curve of silicon, the evaluation function is chosen as:

$$F = \frac{\int\_{0.3}^{1.2} S(\lambda) S R(\lambda) R(\lambda) d\lambda}{\int\_{0.3}^{1.2} S(\lambda) S R(\lambda) d\lambda} \tag{8}$$

where *S SR* ( ), ( ) and *R*( ) represent the spectral distribution of the sun, the spectral response of silicon and the reflectivity of the antireflection coating in the specific wavelength, respectively. So the weighted average reflectivity F can be calculated within the entire solar spectrum.

#### **3.3 The optimization results**

264 Solar Cells – Silicon Wafer-Based Technologies

*m*

1

*k M M* 

In the case of oblique incidence, the admittance values of s polarization and p polarization

*k k*

*k k n p n s* 

*k k*

*B*

*C*

The expression *Y CB* is the admittance for combinations of multi-layer coatings and the

*M*

1 1 *<sup>Y</sup> <sup>R</sup> Y* 

1 *m*

 

*k*

 0 0 sin sin , 1,2.... , 1 *n n k mm* 

*<sup>m</sup>*1 is the admittance of the substrate layer.

The energy reflectivity *R* of the thin film system is:

For the *Rp* component, the corresponding 0 *Y*,

 

are different. For the number k layer, they are:

*<sup>k</sup>* can be given by the Snell law,

substrate, and B, C were determined by:

For the *Rs* component, the 0 *Y*,

energy reflectivity *R* is:

chosen as:

where *S SR* ( ), ( ) 

entire solar spectrum.

 and *R*( ) 

Where

Where 

*k*

cos component cos component

1

2 0 0

values in above expression should be replaced by 0 , *Ys s*

should be substituted by 0 , *Yp p*

(7)

(8)

represent the spectral distribution of the sun, the spectral

2 *R R <sup>s</sup> <sup>p</sup> <sup>R</sup>*

() ()()

 

*S SR R d*

() ()

 

*S SR d*

response of silicon and the reflectivity of the antireflection coating in the specific wavelength, respectively. So the weighted average reflectivity F can be calculated within the

The reflectivity R of the whole system depends on the structural parameters of each layer. Since the spectral response of silicon ranges from 300 to 1200nm, so only incident light in the 300-1200nm wavelength range is considered. Taking into account the inconsistent between the solar spectrum and the spectral response curve of silicon, the evaluation function is

> 1.2 0.3 1.2 0.3

*F*

(2)

(4)

(5)

(6)

.

. The total

(3)

Fig.8 (a), (b), (c), (d) show the results of SiNx/SiO2 ARC when 15°, 30°, 45°, 60° were selected as the optimal angles, where the angles marked in the figure are the incident angles. It can be seen from Fig.8 (a) that the reflectivity is too high when the incident angle is large, especially for the longer wavelength range. And comparing the results of the case 60° and 15°, we can find that the 60° optimization can significantly reduce the long-wavelength reflectivity within the 10%, but the reflectivity rises in short-wave area inevitably, which inhibits the absorption of high-energy photons in the solar spectrum. While optimization with 30° shows a good antireflection property. Under this case when the incident angles range from 0° to 45°, the reflectivity curve is relatively stable; even for the 60° incident angle, the reflectivities in short wavelength and long wavelength still maintain below 15%. The optimization results of 45° is similar with those of 60°, the reflectivity for long wavelength under large incident angle is lower, but for small angle case, the reflectivity for short wavelength is too high.

Fig. 8. Under different optimal angles, the reflectivities of optimal SiNx/SiO2 ARC vary with the incident angles and wavelength. The different optimal angles equal to (a) 15°; (b) 30°; (c) 45°; (d) 60°, respectively.[Chen & Wang, 2008]

Light Trapping Design in Silicon-Based Solar Cells 267

absorbed. This is the reason that conventional wafer-based crystalline Si solar cells have a

Fig. 10. AM1.5 solar spectrum, together with a graph that indicates the solar energy absorbed in a 2um-thick crystalline Si film (assuming single-pass absorption and no

Because thin-film solar cells are only a few microns thick, standard methods of increasing the light absorption, which use surface textures that are typically around 10 microns in size, cannot be used. Plasma etching techniques, which can be used to etch submicron-sized feature, can damage the silicon, thereby reducing the cell efficiency. Another alternative to direct texturing of Si is the texturing of the substrate. However, this also results in increased recombination losses through increased surface area. Though in practice it has been experimentally proven to be very difficult to reduce recombination losses beyond a certain limit, theoretically energy conversion efficiency of above 24% even for 1um cells can be achieved. This highlights the need to incorporate better light-trapping mechanisms that do not increase recombination losses in thin-film solar cells to extract the full potential of the cells. A new method of achieving light trapping in thin-film solar cells is the use of plasma

The electromagnetic properties of metal particles have been known for a long time since the work of Wood and Ritchie, but there has been renewed interest in recent years following the development of new nanofabrication techniques which makes it easy to fabricate these nanostructures. Plasmons can exist in bulk, can be in the form of propagating waves on thin metal surface or can be localized to the surface. So the plasmons are termed bulk plasmons, surface plasmon polariton (SPP) and localized surface plasmons (LSP) respectively. Bulk plasmons are studied using electron or x-ray spectroscopy. The excitation of bulk plasmons

Surface Plasmon polaritions (SPPs) are combined excitations of the conduction electrons and a photon, and form a propagating mode bound to the interface between a thin metal and a

much larger thickness of typically 180-300um.

reflection). [Atwater & Polman, 2010]

Spectral intensity (Wm2nm-1)

resonances in metal.

using visible light is difficult.

To further comparing the impact of the optimal angles on the antireflection, combining the intensity distribution of the solar spectrum and spectral response of silicon solar cells, Fig. 9 shows the variation of the weighted average reflectance F with the incident angle. It can be seen from Fig. 9 that if 0° or 15° was selected as an optimal angle, F is just low in small incident angle, with the incident angle increases, F increases rapidly; and if 45° or 60° was used as an optimal angle, although F is low for the large angle, but F is higher in small angle range, especially for 60° case. The value of F is more than 1 percentage point higher than that of 0° in small-angle region. These suggest that if the large angle is selected as the optimal angle, a good anti-reflection effect can't be achieved for the small incident angle. And if 30° is selected, it is clear from the figure that this angle has the minimum average F in this range, so 30°is the best optimization angle.

Fig. 9. Weighted average reflectance of double-layer anti-reflection coatings versus different incident angles.[ Chen & Wang, 2008]

In conclusion, in practical applications, the oblique incidence is a more common situation. In the oblique incidence case, 30° is the best degree for designing and optimizing ARC.

#### **4. Surface Plasmons [Atwater & Polman, 2010; Pillai et al., 2007]**

For thin-film silicon solar cells, the Si absorber has a thickness on the order of only a few micrometers and is deposited on foreign substrates such as glass, ceramics, plastic, or metal for mechanical support. However, the efficiency of such silicon thin-film cells at the moment are low compared to wafer-based silicon cells because of the relatively poor light absorption, as well as high bulk and surface recombination. Fig.10 shows the standard AM1.5 solar spectrum together with a graph that illustrates what fraction of the solar spectrum is absorbed on a single pass through 2-um-thick crystalline Si film. Clearly, a large fraction of the solar spectrum, in particular in the intense 600-1100nm spectral range, is poorly

To further comparing the impact of the optimal angles on the antireflection, combining the intensity distribution of the solar spectrum and spectral response of silicon solar cells, Fig. 9 shows the variation of the weighted average reflectance F with the incident angle. It can be seen from Fig. 9 that if 0° or 15° was selected as an optimal angle, F is just low in small incident angle, with the incident angle increases, F increases rapidly; and if 45° or 60° was used as an optimal angle, although F is low for the large angle, but F is higher in small angle range, especially for 60° case. The value of F is more than 1 percentage point higher than that of 0° in small-angle region. These suggest that if the large angle is selected as the optimal angle, a good anti-reflection effect can't be achieved for the small incident angle. And if 30° is selected, it is clear from the figure that this angle has the minimum average F in

0 10 20 30 40 50 60

Incident Angle

Fig. 9. Weighted average reflectance of double-layer anti-reflection coatings versus different

In conclusion, in practical applications, the oblique incidence is a more common situation. In

For thin-film silicon solar cells, the Si absorber has a thickness on the order of only a few micrometers and is deposited on foreign substrates such as glass, ceramics, plastic, or metal for mechanical support. However, the efficiency of such silicon thin-film cells at the moment are low compared to wafer-based silicon cells because of the relatively poor light absorption, as well as high bulk and surface recombination. Fig.10 shows the standard AM1.5 solar spectrum together with a graph that illustrates what fraction of the solar spectrum is absorbed on a single pass through 2-um-thick crystalline Si film. Clearly, a large fraction of the solar spectrum, in particular in the intense 600-1100nm spectral range, is poorly

the oblique incidence case, 30° is the best degree for designing and optimizing ARC.

**4. Surface Plasmons [Atwater & Polman, 2010; Pillai et al., 2007]** 

this range, so 30°is the best optimization angle.

1

incident angles.[ Chen & Wang, 2008]

2

3

4

F(%)

5

6

7

absorbed. This is the reason that conventional wafer-based crystalline Si solar cells have a much larger thickness of typically 180-300um.

Fig. 10. AM1.5 solar spectrum, together with a graph that indicates the solar energy absorbed in a 2um-thick crystalline Si film (assuming single-pass absorption and no reflection). [Atwater & Polman, 2010]

Because thin-film solar cells are only a few microns thick, standard methods of increasing the light absorption, which use surface textures that are typically around 10 microns in size, cannot be used. Plasma etching techniques, which can be used to etch submicron-sized feature, can damage the silicon, thereby reducing the cell efficiency. Another alternative to direct texturing of Si is the texturing of the substrate. However, this also results in increased recombination losses through increased surface area. Though in practice it has been experimentally proven to be very difficult to reduce recombination losses beyond a certain limit, theoretically energy conversion efficiency of above 24% even for 1um cells can be achieved. This highlights the need to incorporate better light-trapping mechanisms that do not increase recombination losses in thin-film solar cells to extract the full potential of the cells. A new method of achieving light trapping in thin-film solar cells is the use of plasma resonances in metal.

The electromagnetic properties of metal particles have been known for a long time since the work of Wood and Ritchie, but there has been renewed interest in recent years following the development of new nanofabrication techniques which makes it easy to fabricate these nanostructures. Plasmons can exist in bulk, can be in the form of propagating waves on thin metal surface or can be localized to the surface. So the plasmons are termed bulk plasmons, surface plasmon polariton (SPP) and localized surface plasmons (LSP) respectively. Bulk plasmons are studied using electron or x-ray spectroscopy. The excitation of bulk plasmons using visible light is difficult.

Surface Plasmon polaritions (SPPs) are combined excitations of the conduction electrons and a photon, and form a propagating mode bound to the interface between a thin metal and a

Light Trapping Design in Silicon-Based Solar Cells 269

By proper engineering of this metallodielectric structures, light can be concentrated and "folded" into a thin semiconductor layer, thereby increasing the absorption. Both local surface plasmons excited in metal nanoparticles and surface plasmons polaritions

Plasmonic structures can offer at least three ways of reducing the physical thickness of the photovoltaic absorber layer while keeping their optical thickness constant, as shown in Fig.13. First, metallic nanoparticles can be used as subwavelength scattering elements to couple and trap freely propagating plane waves from the Sun into an absorbing semiconductor thin film, by folding the light into a thin absorber layer. Second, metallic nanoparticles can be used as subwavelength antenna in which the plasmonic near-field is coupled to the semiconductor, increasing its effective absorption cross-section. Third, a corrugated metallic film on the back surface of a thin photovoltaic absorber layer can couple sunlight into SPP modes supported at the metal/semiconductor interface as well as guided modes in the semiconductor slab, whereupon the light is converted to photocarrier in the

Fig. 13. Plasmonic light-trapping geometric for thin-film solar cells.[Atwater & Polman, 2010]

Incident light that is in the region of the resonance wavelength of the particles is strongly scattered or absorbed, depending on the size of the particles. The extinction of the particle is defined as the sum of the scattering and absorption. For small particles in the quasistatic limit, the scattering and absorption cross section are given by [Bohren, 1983; Bohren &

<sup>4</sup> 1 2 <sup>2</sup>

is the

, where

6

 

( 1) <sup>3</sup> ( 2)

*V* 

for a small spherical particle in vacuum, where V is the volume of the particle and

permittivity of the metal. The scattering efficiency *Qsca* is given by <sup>2</sup> *QC r sca sca*

*Csat*

**4.1 Light scattering using particle plasmons** 

and <sup>2</sup> Im[ ] *Cabs*

is the polarizability of the particle, given by

propagating at the metals/semiconductor interface are of interest.

semiconductor.

Huffman, 1998]

Here, 

dielectric travelling perpendicular to the film plane. This phenomenon only occur at the interface between metals and dielectrics where the Re(ε) (where εis the dielectric function) have opposite signs, and decay exponentially with distance from the interface, as shown in Fig.11.

Fig. 11. (a) Schematic of a surface plasmon at the interface of a metal and dielectric showing the exponential dependence of the field E in the z direction along with charges and (b) electromagnetic field of surface plasmons propagating on the surface in the x direction. [Pillai, 2007]

According the theory, the propagating waves can travel up to 10-100um in the visible for silver owing to its low absorption losses and can increase up to 1mm in the near-infrared. Generally the surface plasmon resonant frequency is in the ultra-violet for metals and the infra-red for heavily doped semiconductors.

LSP are collective oscillations of the conduction electrons in metal particles. Movement of the conduction electrons upon excitation with incident light leads to a buildup of polarization charges on the particle surface. This acts as a restoring force, allowing a resonance to occur at a particular frequency, which is termed the dipole surface plasmon resonance frequency. A consequence of surface plasmon excitation in the enhancement of the electromagnetic field around the vicinity of the particles is shown in Fig.12.

Fig. 12. Incident light excites the dipole localized surface Plasmon resonance on a spherical metal nanoparticle. [Pillai, 2007]

dielectric travelling perpendicular to the film plane. This phenomenon only occur at the interface between metals and dielectrics where the Re(ε) (where εis the dielectric function) have opposite signs, and decay exponentially with distance from the interface, as shown in

Fig. 11. (a) Schematic of a surface plasmon at the interface of a metal and dielectric showing the exponential dependence of the field E in the z direction along with charges and (b) electromagnetic field of surface plasmons propagating on the surface in the x direction.

According the theory, the propagating waves can travel up to 10-100um in the visible for silver owing to its low absorption losses and can increase up to 1mm in the near-infrared. Generally the surface plasmon resonant frequency is in the ultra-violet for metals and the

LSP are collective oscillations of the conduction electrons in metal particles. Movement of the conduction electrons upon excitation with incident light leads to a buildup of polarization charges on the particle surface. This acts as a restoring force, allowing a resonance to occur at a particular frequency, which is termed the dipole surface plasmon resonance frequency. A consequence of surface plasmon excitation in the enhancement of

Fig. 12. Incident light excites the dipole localized surface Plasmon resonance on a spherical

the electromagnetic field around the vicinity of the particles is shown in Fig.12.

Fig.11.

[Pillai, 2007]

infra-red for heavily doped semiconductors.

metal nanoparticle. [Pillai, 2007]

By proper engineering of this metallodielectric structures, light can be concentrated and "folded" into a thin semiconductor layer, thereby increasing the absorption. Both local surface plasmons excited in metal nanoparticles and surface plasmons polaritions propagating at the metals/semiconductor interface are of interest.

Plasmonic structures can offer at least three ways of reducing the physical thickness of the photovoltaic absorber layer while keeping their optical thickness constant, as shown in Fig.13. First, metallic nanoparticles can be used as subwavelength scattering elements to couple and trap freely propagating plane waves from the Sun into an absorbing semiconductor thin film, by folding the light into a thin absorber layer. Second, metallic nanoparticles can be used as subwavelength antenna in which the plasmonic near-field is coupled to the semiconductor, increasing its effective absorption cross-section. Third, a corrugated metallic film on the back surface of a thin photovoltaic absorber layer can couple sunlight into SPP modes supported at the metal/semiconductor interface as well as guided modes in the semiconductor slab, whereupon the light is converted to photocarrier in the semiconductor.

Fig. 13. Plasmonic light-trapping geometric for thin-film solar cells.[Atwater & Polman, 2010]

#### **4.1 Light scattering using particle plasmons**

Incident light that is in the region of the resonance wavelength of the particles is strongly scattered or absorbed, depending on the size of the particles. The extinction of the particle is defined as the sum of the scattering and absorption. For small particles in the quasistatic limit, the scattering and absorption cross section are given by [Bohren, 1983; Bohren & Huffman, 1998]

$$\mathbf{C}\_{\rm sat} = \frac{1}{6\pi} \left(\frac{2\pi}{\mathcal{A}}\right)^4 \left|\alpha\right|^2$$

and <sup>2</sup> Im[ ] *Cabs*

Here, is the polarizability of the particle, given by

$$\alpha = 3V \frac{(\varepsilon - 1)}{(\varepsilon + 2)}$$

for a small spherical particle in vacuum, where V is the volume of the particle and is the permittivity of the metal. The scattering efficiency *Qsca* is given by <sup>2</sup> *QC r sca sca* , where

Light Trapping Design in Silicon-Based Solar Cells 271

An alternative use of resonant plasmon excitation in thin-film solar cells is to take advantage of the strong local field enhancement around the metal nanoparticle to increase absorption in a surrounding semiconductor material. The nanoparticles then act as an effective 'antenna' for the incident sunlight that stores the incident energy in a localized surface plasmon mode (Fig.13b). This works particularly well for small (5-20nm diameter) particles for which the albedo is low. These antennas are particularly useful in materials where the carrier diffusion lengths are small, and photocarriers must be generated close to the

Several examples of this concept have recently appeared that demonstrate enhanced photocurrents owing to the plasmonic near-field coupling. Enhanced efficiencies have been demonstrated for ultrathin-film organic solar cells doped with very small (5nm diameter) Ag nanoparticles. An increase in efficiency by a factor of 1.7 has been shown for organic bulk heterojunction solar cells. Dye-sensitized solar cells can also be enhanced by embedding small metal nanoparticles. Also, the increased light absorption and increased photocurrent also reported for inorganic solar cells, such as CdSe/Si heterojunction, Si and so on. The optimization of the coupling between plasmons, excitons and phonons in metalsemiconductor nanostructures is a rich field of research that so far has not received much

In a third plasmonic light-trapping geometry, light is converted into SPPs, which are electromagnetic waves that travel along the interface between a metal back contact and the semiconductor absorber layer, as shown in Fig.13c. Near the Plasmon resonance frequency, the evanescent electromagnetic SPP fields are confined near the interface at dimensions much smaller than the wavelength. SPPs excited at the metal/semiconductor interface can efficiently trap and guide light in the semiconductor layer. In this geometry the incident solar flux is effectively turned by 90°, and light is absorbed along the lateral direction of the solar cell, which has dimensions that are orders of magnitude larger than the optical absorption length. As metal contacts are a standard element in the solar-cell design, this

At frequencies near plasmon resonance frequency (typically in the 350-700nm spectral range, depending on metal and dielectric) SPPs suffer from relatively high losses. Further into the infrared, however, propagation lengths are substantial. For example, for a semiinfinite Ag/SiO2 geometry, SPP propagation lengths range from 10 to 100um in the 800- 1500nm spectral range. By using a thin-film metal geometry the plasmon dispersion can be further engineered. Increased propagation length comes at the expense of reduced optical confinement and optimum metal-film design thus depends on the desired solar-cell geometry. Detailed accounts of plasmon dispersion and loss in metal-dielectric geometries are found in references [Berini, 2000; Berini, 2001; Dionne et al., 2005; Dionne et al., 2006]. The ability to construct optically thick but physically very thin photovoltaic absorbers could revolutionize high-efficiency photovoltaic device designs. This becomes possible by using light trapping through the resonant scattering and concentration of light in arrays of metal nanoparticles, or by coupling light into surface plasmon polaritons and photonic modes that propagate in the plane of the semiconductor layer. In this way extremely thin photovoltaic absorber layers (tens to hundreds of nanometers thick) may absorb the full solar spectrum.

plasmonic coupling concept can be integrated in a natural way.

**4.2 Light concentration using particle plasmons.** 

collection junction area.

attention with photovoltaics in mind.

**4.3 Light trapping using SPPs** 

2 *r* is the geometric cross section of the particle. Near the surface plasmon resonance, light may interact with the particle over a cross-sectional area larger than the geometric cross section of the particle because the polarizability of the particle becomes very high in this frequency range [Bohren, 1983]. Metals exhibit this property due to excitations of surface plasmons at the frequency where 2 .

Both shape and size of metal nanoparticles are key factors determining the incoupling efficiency [Pillai & Green, 2010]. This is illustrated in Fig.14a, which shows that smaller particles, with their effective dipole moment located closer to the semiconductor layer, couple a large fraction of the incident light into the underlying semiconductor because of enhanced near-field coupling. Indeed, in the limit of a point dipole very near to a silicon substrate, 96% of the incident light is scattered into the substrate, demonstrating the power of the particle scattering technique. Fig.14b shows the path-length enhancement in the solar cells derived from Fig.14a using a simple first-order scattering model. For 100-nm-diameter Ag hemispheres on Si, a 30-fold enhancement is found. These light-trapping effects are most pronounced at the peak of the plasmon resonance spectrum, which can be tuned by engineering the dielectric constant of the surrounding medium. For example, small Ag or Au particles in air have plasmon resonances at 350nm and 480nm respectively; they can be redshifted in a controlled way over the entire 500-1500nm spectral range by (partially) embedding them in SiO2, Si3N4 or Si, which are all standard materials in solar cell manufacturing. The scattering cross-sections for metal nanoparticle can be as high as ten times the geometrical area, and a nearly 10% coverage of the solar cell would sufficient to capture most of the incident sunlight into plasmon excitations.

Fig. 14. Light scattering and trapping is very sensitive to particle shape. a. Fraction of light scattered into the substrate, divided by total scattered power, for different sizes and shapes of Ag particles on Si. Also plotted is the scattered fraction for a parallel electric dipole that is 10nm from a Si substrate. b. Maximum path-length enhancement for the same geometries as in left figure at a wavelength of 800nm. Absorption within the particles is neglected for these calculations and an ideal rear reflector is assumed. The line is a guide for eyes. Insets (top left) angular distribution of scattered power for a parallel electric dipole that is 10nm above a Si layer and Lambertian scatter; (bottom-right) geometry considered for calculating the path length enhancement. [Catchpole & Polman, 2008]

*r* is the geometric cross section of the particle. Near the surface plasmon resonance, light may interact with the particle over a cross-sectional area larger than the geometric cross section of the particle because the polarizability of the particle becomes very high in this frequency range [Bohren, 1983]. Metals exhibit this property due to excitations of surface

Both shape and size of metal nanoparticles are key factors determining the incoupling efficiency [Pillai & Green, 2010]. This is illustrated in Fig.14a, which shows that smaller particles, with their effective dipole moment located closer to the semiconductor layer, couple a large fraction of the incident light into the underlying semiconductor because of enhanced near-field coupling. Indeed, in the limit of a point dipole very near to a silicon substrate, 96% of the incident light is scattered into the substrate, demonstrating the power of the particle scattering technique. Fig.14b shows the path-length enhancement in the solar cells derived from Fig.14a using a simple first-order scattering model. For 100-nm-diameter Ag hemispheres on Si, a 30-fold enhancement is found. These light-trapping effects are most pronounced at the peak of the plasmon resonance spectrum, which can be tuned by engineering the dielectric constant of the surrounding medium. For example, small Ag or Au particles in air have plasmon resonances at 350nm and 480nm respectively; they can be redshifted in a controlled way over the entire 500-1500nm spectral range by (partially) embedding them in SiO2, Si3N4 or Si, which are all standard materials in solar cell manufacturing. The scattering cross-sections for metal nanoparticle can be as high as ten times the geometrical area, and a nearly 10% coverage of the solar cell would sufficient to

Fig. 14. Light scattering and trapping is very sensitive to particle shape. a. Fraction of light scattered into the substrate, divided by total scattered power, for different sizes and shapes of Ag particles on Si. Also plotted is the scattered fraction for a parallel electric dipole that is 10nm from a Si substrate. b. Maximum path-length enhancement for the same geometries as in left figure at a wavelength of 800nm. Absorption within the particles is neglected for these calculations and an ideal rear reflector is assumed. The line is a guide for eyes. Insets (top left) angular distribution of scattered power for a parallel electric dipole that is 10nm above a Si layer and Lambertian scatter; (bottom-right) geometry considered for calculating the

2 

plasmons at the frequency where 2

.

capture most of the incident sunlight into plasmon excitations.

path length enhancement. [Catchpole & Polman, 2008]

#### **4.2 Light concentration using particle plasmons.**

An alternative use of resonant plasmon excitation in thin-film solar cells is to take advantage of the strong local field enhancement around the metal nanoparticle to increase absorption in a surrounding semiconductor material. The nanoparticles then act as an effective 'antenna' for the incident sunlight that stores the incident energy in a localized surface plasmon mode (Fig.13b). This works particularly well for small (5-20nm diameter) particles for which the albedo is low. These antennas are particularly useful in materials where the carrier diffusion lengths are small, and photocarriers must be generated close to the collection junction area.

Several examples of this concept have recently appeared that demonstrate enhanced photocurrents owing to the plasmonic near-field coupling. Enhanced efficiencies have been demonstrated for ultrathin-film organic solar cells doped with very small (5nm diameter) Ag nanoparticles. An increase in efficiency by a factor of 1.7 has been shown for organic bulk heterojunction solar cells. Dye-sensitized solar cells can also be enhanced by embedding small metal nanoparticles. Also, the increased light absorption and increased photocurrent also reported for inorganic solar cells, such as CdSe/Si heterojunction, Si and so on. The optimization of the coupling between plasmons, excitons and phonons in metalsemiconductor nanostructures is a rich field of research that so far has not received much attention with photovoltaics in mind.

#### **4.3 Light trapping using SPPs**

In a third plasmonic light-trapping geometry, light is converted into SPPs, which are electromagnetic waves that travel along the interface between a metal back contact and the semiconductor absorber layer, as shown in Fig.13c. Near the Plasmon resonance frequency, the evanescent electromagnetic SPP fields are confined near the interface at dimensions much smaller than the wavelength. SPPs excited at the metal/semiconductor interface can efficiently trap and guide light in the semiconductor layer. In this geometry the incident solar flux is effectively turned by 90°, and light is absorbed along the lateral direction of the solar cell, which has dimensions that are orders of magnitude larger than the optical absorption length. As metal contacts are a standard element in the solar-cell design, this plasmonic coupling concept can be integrated in a natural way.

At frequencies near plasmon resonance frequency (typically in the 350-700nm spectral range, depending on metal and dielectric) SPPs suffer from relatively high losses. Further into the infrared, however, propagation lengths are substantial. For example, for a semiinfinite Ag/SiO2 geometry, SPP propagation lengths range from 10 to 100um in the 800- 1500nm spectral range. By using a thin-film metal geometry the plasmon dispersion can be further engineered. Increased propagation length comes at the expense of reduced optical confinement and optimum metal-film design thus depends on the desired solar-cell geometry. Detailed accounts of plasmon dispersion and loss in metal-dielectric geometries are found in references [Berini, 2000; Berini, 2001; Dionne et al., 2005; Dionne et al., 2006].

The ability to construct optically thick but physically very thin photovoltaic absorbers could revolutionize high-efficiency photovoltaic device designs. This becomes possible by using light trapping through the resonant scattering and concentration of light in arrays of metal nanoparticles, or by coupling light into surface plasmon polaritons and photonic modes that propagate in the plane of the semiconductor layer. In this way extremely thin photovoltaic absorber layers (tens to hundreds of nanometers thick) may absorb the full solar spectrum.

Light Trapping Design in Silicon-Based Solar Cells 273

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Nakayama K., Tanabe K. & Atwater H.A., (2008). Plasmonic nanoparticle enhanced light

Pillai S., (2007). Surface plasmons for enhanced thin-film silicon solar cells and light emitting diodes, *Ph.D thesis,* University of NewSouth Wales, Sydney, Australia Pillai S., Catchpole K. R., Trupke T., et al. (2007). Surface plasmon enhanced silicon solar

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0121


**13** 

*Serbia* 

**Characterization of Thin Films for Solar Cells** 

Faced with an alarming increase of energy consumption on one side, and very limiting amounts of available conventional energy sources on the other, scientists have turned to the most promising, renewable energy sources. Possibilities for the application of solar systems based on photovoltaic conversion of solar energy are very wide, primarily because of their relatively low cost and very important fact that solar energy is most acceptable source of electrical energy from the environmental point of view. Recently, increased investments in the development of PV technology are observed worldwide. Photovoltaic (PV) conversion of solar energy is one of the most up-to-date semiconductor technologies that enables application of PV systems for various purposes. The wider substitution of conventional energies by solar energy lies in the rate of developing solar cell technology. Silicon is still the mostly used element for solar cell production, so efforts are directed to the improvement of physical properties of silicon structures. Silicon solar cells belong to a wide group of semiconductor detector devises, though somewhat specific in its design (larger than most of the detectors). Basic part of solar cell is p-n junction, which active part is less that 0.2μm thick, so it could be treated as thin film. This photosensitive layer have the most important influence on solar cell functioning, primarily on creation of electron-hole pairs under solar irradiation, transport properties in cells, formation of internal field, and finally, output characteristics of the device such as short circuit current, open circuit voltage and efficiency. Furthermore, in order to function as a voltage generator with the best possible performances, beside p-n junction other thin films such as contact, antireflective, protective (oxide) thin films must be applied both on the front and on the back surface of solar cells. Also, in order to improve characteristics of the device, MIS structure (thin oxide layers) and

Since thin films are very important in many fields of modern science (solar cell technology, for example), a large number of methods were developed for their characterization. Characterization of thin films includes investigations of physical processes in them, developing of the methods for measuring major physical and electrical properties and their

**1. Introduction** 

back surface field layers are routinely used.

**and Photodetectors and Possibilities for** 

Aleksandra Vasic1, Milos Vujisic2,

Koviljka Stankovic2 and Predrag Osmokrovic2 *1Faculty of Mechanical Engineering, University of Belgrade 2Faculty of Electrical Engineering, University of Belgrade* 

**Improvement of Solar Cells Characteristics** 


## **Characterization of Thin Films for Solar Cells and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics**

Aleksandra Vasic1, Milos Vujisic2, Koviljka Stankovic2 and Predrag Osmokrovic2 *1Faculty of Mechanical Engineering, University of Belgrade 2Faculty of Electrical Engineering, University of Belgrade Serbia* 

#### **1. Introduction**

274 Solar Cells – Silicon Wafer-Based Technologies

Wang W.H., Li H.B. & Wu D.X., (2004). Design and analysis of anti-reflection coating for

Xiong C., Yao R.H. & Gen K.W., (2010). Two low reflectance of triple-layer broadband

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ISSN 1007-2861

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solar cells, *Journal of Shanghai University (Nature Science)*, vol.10, No.1, pp.39-42,

antireflection coating for silicon solar cells. *Proceeding on 10th IEEE International Conference on Solid-State and Integrated Circuit Technology*, ISBN 978-1-4244-5798-4,

> Faced with an alarming increase of energy consumption on one side, and very limiting amounts of available conventional energy sources on the other, scientists have turned to the most promising, renewable energy sources. Possibilities for the application of solar systems based on photovoltaic conversion of solar energy are very wide, primarily because of their relatively low cost and very important fact that solar energy is most acceptable source of electrical energy from the environmental point of view. Recently, increased investments in the development of PV technology are observed worldwide. Photovoltaic (PV) conversion of solar energy is one of the most up-to-date semiconductor technologies that enables application of PV systems for various purposes. The wider substitution of conventional energies by solar energy lies in the rate of developing solar cell technology. Silicon is still the mostly used element for solar cell production, so efforts are directed to the improvement of physical properties of silicon structures. Silicon solar cells belong to a wide group of semiconductor detector devises, though somewhat specific in its design (larger than most of the detectors). Basic part of solar cell is p-n junction, which active part is less that 0.2μm thick, so it could be treated as thin film. This photosensitive layer have the most important influence on solar cell functioning, primarily on creation of electron-hole pairs under solar irradiation, transport properties in cells, formation of internal field, and finally, output characteristics of the device such as short circuit current, open circuit voltage and efficiency. Furthermore, in order to function as a voltage generator with the best possible performances, beside p-n junction other thin films such as contact, antireflective, protective (oxide) thin films must be applied both on the front and on the back surface of solar cells. Also, in order to improve characteristics of the device, MIS structure (thin oxide layers) and back surface field layers are routinely used.

> Since thin films are very important in many fields of modern science (solar cell technology, for example), a large number of methods were developed for their characterization. Characterization of thin films includes investigations of physical processes in them, developing of the methods for measuring major physical and electrical properties and their

Characterization of Thin Films for Solar Cells

semiconductor barriers including contacts.

phenomenon could occur on the surface of the device also.

Amplitude of the excess current (i.e. burst noise)

the exponential manner:

thermal velocity of the electrons, etc.

where

model current

**2.1 Noise in thin film semiconducting devices** 

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 277

Negative influence of noise on the photodetector characteristics could be observed in widening of the spectral line of the signal as well as in rising of the detection threshold. That is the reason why investigation of physical basis of different types of noises is necessary for their minimizing. Noise level primarily depends on fabrication procedures and is connected to the fundamental physical processes in semiconducting devices, so it could be said that noise appears in every detector regardless to their type or quality. Noise is commonly classified into three categories: thermal noise, frequency dependent noise and shot noise. Also, noise could be classified according to the physical processes as generationrecombination noise, diffusion noise and modulation noise. Low frequency noise, 1/f and burst noise are especially important in semiconducting devices. Various experiments suggests (Jayaweera et al., 2005, 2007) that the origin of this noise is fluctuation of the number free charge carriers connected to existence of the traps located in the vicinity or directly in the junction area, or fluctuation of the mobility of charge carriers. In both cases these fluctuations arise from the interactions of carriers with defects, surface states and impurities, that are either introduced during manufacturing of the device, or as a consequence of the hostile working conditions (radiation, high temperature, humidity). In the case of surface films such as contacts, their electical characteristics modulate potential and electric field in the surface area, controlling in that way transport mechanisms between the surface and bulk area. This is particularly important for photodetectors and metal

Beside 1/f noise, burst noise could also induce discreate fluctuations of current between two or more levels. This type of noise is considered the most limiting factor in the performance of photodetectors. The origin of this noise, as well as its appearance in different voltage regions depends on the type of polarization and on the type of actual device, but it is usually ascribed to the presence of the defects in crystal lattice such as dislocations. Since burst noise is manifested in the presence of the so called excess current, investigations of its origin and factors that influence its amplitude could lead to better understanding of the burst noise. It was supposed that current flowing through the defects is modulated by the change in the charge state of the generation-recombination (GR) centers located near defects in the space charge region. When such GR center captures electron, local increase of the barrier height occurs. Electron flux passing through the barrier in the vicinity of GR center decrease, as a consequence of the barrier height increase, modulating (decreasing) excess current. Vice versa, emmision of the charge carrier from the trap center leads to the local decrease of the barrier height, thus increasing the excess current. Depending on the type of the device, this

*BN*

*Isat* and *nBN*, are saturation current and ideality factor, respectively. Since in this

*n kT*

*IF* is considered to be generation-recombination current, *nBN* > 1, and

FI exp *<sup>F</sup> sat*

depends on the lifetime and concentration of the charge carriers, recombination probability,

*qV <sup>I</sup>*

*IF*, depends on the applied voltage *VF* in

(1)

experimental determination. From the aspect of quality assessment of semiconductor device performance, characterization of the whole device gives best results especially in working conditions.

#### **2. Characterization of thin films for solar cells and photodetectors**

Contemporary trends in microelectronics and electronics in general are oriented to thin films, both from technological and scientific standpoints. Thin film devices as a whole or just a parts of the of devices such as surface, protective, antireflective, contact, or other thin films, have significant advantages over bulk materials. Beside obvious advantage in material and minimization of the device dimensions, methods for obtaining thin films are simpler and less demanded when the quality of the material is concerned than for thicker films. Moreover, characteristics of thin films could be significantly different from the bulk material and could lead to better performances of the device.

Great importance of thin films in modern science, as well as diversity of their characteristics made necessary the development of numerous methods for their research. Investigations of both physical and electrical properties of thin films are necessary primarily in order to determine the best combination for given working conditions (for example, high temperature, exposure to radiation, etc.). On the other hand, ion implantation, laser beams, epitaxial growth in highly controlled environment, etc., are commonly used for structural changes and obtaining better output characteristics of the devices. All of that was made possible by development, availability and improvement of sensitivity of methods for composition and structural characterization of materials. Although also very important in the process of thin film formation, these methods are essential for the quality assessment of the whole device in working conditions. In solar cells, for example, measurement of the output characteristics such as ideality factor, serial and parallel resistance, fill factor and efficiency, could directly or indirectly indicate the possibilities for the improvement of the production technology (from the basic material, formation of thin films, contact films, etc.). The choice of the appropriate method in each case depends on the type of the investigations and expected results. The most commonly used method for characterization of electrical properties of semiconducting devices (such as solar cells) is current-voltage (*I*-*V*) measurement. Versatility of the data obtained in this way gives very important information about the device (solar cell), both from the fundamental standpoint (ideality factor, series and parallel resistance) and from the standpoint of the output characteristics (short-circuit current, open-circuit voltage, fill factor, efficiency).

Also, since contact films have significant influence on the output characteristics of all semiconducting devices, they must possess certain properties such as: low resistivity, good connection to the basic material, temperature stability, and low noise. One of the most important characteristic of detectors such as solar cells is their energy resolution that primarily depends on noise. That is why measuring and lowering noise is important for obtaining good quality detectors. It is known that low frequency noise (1/f and burst noise) is manifested as random fluctuation of the output current or voltage, leading to lowering of the efficiency of the device. Because of the large surface to volume ration, surface effects are expected to be a major cause of 1/f noise, so good quality contacts are of great importance. That is why measurements of 1/f noise and improvement of silicides characteristics by lowering 1/f noise in them leads to the production of reliable contacts.

#### **2.1 Noise in thin film semiconducting devices**

276 Solar Cells – Silicon Wafer-Based Technologies

experimental determination. From the aspect of quality assessment of semiconductor device performance, characterization of the whole device gives best results especially in working

Contemporary trends in microelectronics and electronics in general are oriented to thin films, both from technological and scientific standpoints. Thin film devices as a whole or just a parts of the of devices such as surface, protective, antireflective, contact, or other thin films, have significant advantages over bulk materials. Beside obvious advantage in material and minimization of the device dimensions, methods for obtaining thin films are simpler and less demanded when the quality of the material is concerned than for thicker films. Moreover, characteristics of thin films could be significantly different from the bulk material

Great importance of thin films in modern science, as well as diversity of their characteristics made necessary the development of numerous methods for their research. Investigations of both physical and electrical properties of thin films are necessary primarily in order to determine the best combination for given working conditions (for example, high temperature, exposure to radiation, etc.). On the other hand, ion implantation, laser beams, epitaxial growth in highly controlled environment, etc., are commonly used for structural changes and obtaining better output characteristics of the devices. All of that was made possible by development, availability and improvement of sensitivity of methods for composition and structural characterization of materials. Although also very important in the process of thin film formation, these methods are essential for the quality assessment of the whole device in working conditions. In solar cells, for example, measurement of the output characteristics such as ideality factor, serial and parallel resistance, fill factor and efficiency, could directly or indirectly indicate the possibilities for the improvement of the production technology (from the basic material, formation of thin films, contact films, etc.). The choice of the appropriate method in each case depends on the type of the investigations and expected results. The most commonly used method for characterization of electrical properties of semiconducting devices (such as solar cells) is current-voltage (*I*-*V*) measurement. Versatility of the data obtained in this way gives very important information about the device (solar cell), both from the fundamental standpoint (ideality factor, series and parallel resistance) and from the standpoint of the output characteristics (short-circuit

Also, since contact films have significant influence on the output characteristics of all semiconducting devices, they must possess certain properties such as: low resistivity, good connection to the basic material, temperature stability, and low noise. One of the most important characteristic of detectors such as solar cells is their energy resolution that primarily depends on noise. That is why measuring and lowering noise is important for obtaining good quality detectors. It is known that low frequency noise (1/f and burst noise) is manifested as random fluctuation of the output current or voltage, leading to lowering of the efficiency of the device. Because of the large surface to volume ration, surface effects are expected to be a major cause of 1/f noise, so good quality contacts are of great importance. That is why measurements of 1/f noise and improvement of silicides characteristics by

**2. Characterization of thin films for solar cells and photodetectors** 

and could lead to better performances of the device.

current, open-circuit voltage, fill factor, efficiency).

lowering 1/f noise in them leads to the production of reliable contacts.

conditions.

Negative influence of noise on the photodetector characteristics could be observed in widening of the spectral line of the signal as well as in rising of the detection threshold. That is the reason why investigation of physical basis of different types of noises is necessary for their minimizing. Noise level primarily depends on fabrication procedures and is connected to the fundamental physical processes in semiconducting devices, so it could be said that noise appears in every detector regardless to their type or quality. Noise is commonly classified into three categories: thermal noise, frequency dependent noise and shot noise. Also, noise could be classified according to the physical processes as generationrecombination noise, diffusion noise and modulation noise. Low frequency noise, 1/f and burst noise are especially important in semiconducting devices. Various experiments suggests (Jayaweera et al., 2005, 2007) that the origin of this noise is fluctuation of the number free charge carriers connected to existence of the traps located in the vicinity or directly in the junction area, or fluctuation of the mobility of charge carriers. In both cases these fluctuations arise from the interactions of carriers with defects, surface states and impurities, that are either introduced during manufacturing of the device, or as a consequence of the hostile working conditions (radiation, high temperature, humidity). In the case of surface films such as contacts, their electical characteristics modulate potential and electric field in the surface area, controlling in that way transport mechanisms between the surface and bulk area. This is particularly important for photodetectors and metal semiconductor barriers including contacts.

Beside 1/f noise, burst noise could also induce discreate fluctuations of current between two or more levels. This type of noise is considered the most limiting factor in the performance of photodetectors. The origin of this noise, as well as its appearance in different voltage regions depends on the type of polarization and on the type of actual device, but it is usually ascribed to the presence of the defects in crystal lattice such as dislocations. Since burst noise is manifested in the presence of the so called excess current, investigations of its origin and factors that influence its amplitude could lead to better understanding of the burst noise. It was supposed that current flowing through the defects is modulated by the change in the charge state of the generation-recombination (GR) centers located near defects in the space charge region. When such GR center captures electron, local increase of the barrier height occurs. Electron flux passing through the barrier in the vicinity of GR center decrease, as a consequence of the barrier height increase, modulating (decreasing) excess current. Vice versa, emmision of the charge carrier from the trap center leads to the local decrease of the barrier height, thus increasing the excess current. Depending on the type of the device, this phenomenon could occur on the surface of the device also.

Amplitude of the excess current (i.e. burst noise) *IF*, depends on the applied voltage *VF* in the exponential manner:

$$
\Delta \mathbf{I}\_{\rm F} = \Delta I\_{sat} \exp \frac{qV\_{\rm F}}{n\_{BN}kT} \tag{1}
$$

where *Isat* and *nBN*, are saturation current and ideality factor, respectively. Since in this model current *IF* is considered to be generation-recombination current, *nBN* > 1, and depends on the lifetime and concentration of the charge carriers, recombination probability, thermal velocity of the electrons, etc.

Characterization of Thin Films for Solar Cells

Fig. 1. RBS spectra of TiN/Ti/Si samples (Vasic et al., 2011).

**2.2** *I***-***V* **measurements and the ideality factor** 

Noise pulse height [keV]

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 279

0 50 100 150 200 250 300 350

This influence was confirmed by noise level measurements (all of the samples exhibit similar behaviour). Noise spectra were measured for different time constants *τ* (frequency range *τ* ~ 1/*f*) of the low noise amplifier. Analysis of the results of these measurements shows that implantation could have influence on the noise level (Fig.2), but the main effect depends on the implantation dose. As discussed above, implantation dose of 1x1016 ions/cm2 induces some disorder in the structure that could lead to higher noise level. Ion dose of 5x1015 ions/cm2 shows the best results for the entire measuring range, suggesting that this dose of implantation induce a more homogeneous silicidation and the formation of Ti-Si phase with a lower concentration of crystal defects (after annealing). The lower concentration of point defects and dislocations and a more homogeneous silicide/silicon

Another commonly used and relatively simple method for obtaining output characteristics of photodetectors and solar cells related to the transport processes is current-voltage (*I*-*V*) measurement. Any deviation of the transport mechanism from the ideal model of thermionic emission directly reflexes on the shape of current-voltage characteristics. Main

Fig. 2. Frequency noise level for TiN/Ti/Si samples at 21ºC (Vasic et al., 2011).

interface result in a lower frequency noise level of the analyzed structures.

f [kHz]

T = 21 C U = + 1V

> unimplanted 5 x 10<sup>15</sup> 1 x 10<sup>16</sup>

#### **2.1.1 Minimization of 1/f noise in silicides by ion implantation**

Both burst noise and 1/f noise are considered to be especially important in contact layers, so a large number of investigations are based on measurements of these type of noises in contacts, for example, silicides. Silicides belong to a very promising group of materials with low resistivity and good temperature stability that are used for fabrication of reliable and reproducible contacts. Investigations of this type of contacts include both their experimental development and the development of methods for their characterization such as noise level measurements and RBS analysis. The noise level measurements enable the control of the noise, which is important characteristic of metal-semiconductor electrical contacts (especially 1/f noise). Surface effects such as surface recombination fluctuations in carrier mobility, concentration of surface states, etc., have great influence on frequency dependent noise in silicides. Many authors in their investigation of silicides discuss the problem related to the application of ion beam mixing of As+ ions for the formation of silicides (Stojanovic et al., 1996a). Although introduction of As+ ions and their diffusion could change impurity concentration resulting in an increased noise level (especially for 1/f noise) in the structure, carefull optimization of the implantation dose and subsequent thermal treatment such as annealing could result in the formation of stable contacts with a low noise level. Every step of the silicides fabrication including preparation of Si substartes, deposition of metal layer (Pd, Ti, TiN, for example), As+ ion implantation, and annealing must be taking into consideration in order to achieve the best possible result. It has been found (Stojanovic et al., 1996a, 1996b) that both the implantation dose and ion energy, and annealing have a pronounced influence on the noise level in silicides. When Pd silicides are concerned, structural RBS analysis have shown that Pd2Si phase, which was already formed during preimplantation annealing is not affected by ion implantation. The spectra exibit slight changes in the slopes of the signal, corresponding to the Pd2Si-Si interface. These changes can be attributed to additional intermixing of silicon and palladium atoms due to the presence of radiation-induced defects. It was also found (Stojanovic et al., 1996a) that the sequence of the fabrication steps influence the noise level in the formed silicides. The noise level was lowest in the samples implanted after annealing, so optimized ion implantation concerning implantation energy and dose, and average projected range of As+ ions near Pd-Si interface, does not reorder the silicides formed by annealing (also shown by RBS analysis), and induce more homogenous silicide/silicon interface. This suggests that thermal treatment induce relaxation of crystal lattice and improvement of the crystal structure of the silicides. On the other hand, noise measurements have confirmed that a more homogenous structure of Pdsilicides results in a lower frequency noise level.

The influence of the implantation dose on the noise level could clearly be seen for the Ti-TiN silicides example (Vasic et al., 2011). Structural RBS analysis has shown that ion implantation did not induce redistribution of components for lower implantation doses (Fig. 1). The spectra indicate that the entire titanium layer has interdiffused with the silicon substrate.

The presence of the TiSi2 and TiSi2 phase in the implanted samples was observed. In all cases top TiN layer remains unaffected, but for higher doses of implantation (1x1016 ions/cm2) a disordered structure was registered. This corresponds to the amorphization of silicon substrate, which is moving deeper with the ion dose, showing that the physical properties of TiN/Ti/Si are influenced by the implantation.

Both burst noise and 1/f noise are considered to be especially important in contact layers, so a large number of investigations are based on measurements of these type of noises in contacts, for example, silicides. Silicides belong to a very promising group of materials with low resistivity and good temperature stability that are used for fabrication of reliable and reproducible contacts. Investigations of this type of contacts include both their experimental development and the development of methods for their characterization such as noise level measurements and RBS analysis. The noise level measurements enable the control of the noise, which is important characteristic of metal-semiconductor electrical contacts (especially 1/f noise). Surface effects such as surface recombination fluctuations in carrier mobility, concentration of surface states, etc., have great influence on frequency dependent noise in silicides. Many authors in their investigation of silicides discuss the problem related to the application of ion beam mixing of As+ ions for the formation of silicides (Stojanovic et al., 1996a). Although introduction of As+ ions and their diffusion could change impurity concentration resulting in an increased noise level (especially for 1/f noise) in the structure, carefull optimization of the implantation dose and subsequent thermal treatment such as annealing could result in the formation of stable contacts with a low noise level. Every step of the silicides fabrication including preparation of Si substartes, deposition of metal layer (Pd, Ti, TiN, for example), As+ ion implantation, and annealing must be taking into consideration in order to achieve the best possible result. It has been found (Stojanovic et al., 1996a, 1996b) that both the implantation dose and ion energy, and annealing have a pronounced influence on the noise level in silicides. When Pd silicides are concerned, structural RBS analysis have shown that Pd2Si phase, which was already formed during preimplantation annealing is not affected by ion implantation. The spectra exibit slight changes in the slopes of the signal, corresponding to the Pd2Si-Si interface. These changes can be attributed to additional intermixing of silicon and palladium atoms due to the presence of radiation-induced defects. It was also found (Stojanovic et al., 1996a) that the sequence of the fabrication steps influence the noise level in the formed silicides. The noise level was lowest in the samples implanted after annealing, so optimized ion implantation concerning implantation energy and dose, and average projected range of As+ ions near Pd-Si interface, does not reorder the silicides formed by annealing (also shown by RBS analysis), and induce more homogenous silicide/silicon interface. This suggests that thermal treatment induce relaxation of crystal lattice and improvement of the crystal structure of the silicides. On the other hand, noise measurements have confirmed that a more homogenous structure of Pd-

The influence of the implantation dose on the noise level could clearly be seen for the Ti-TiN silicides example (Vasic et al., 2011). Structural RBS analysis has shown that ion implantation did not induce redistribution of components for lower implantation doses (Fig. 1). The spectra indicate that the entire titanium layer has interdiffused with the silicon

The presence of the TiSi2 and TiSi2 phase in the implanted samples was observed. In all cases top TiN layer remains unaffected, but for higher doses of implantation (1x1016 ions/cm2) a disordered structure was registered. This corresponds to the amorphization of silicon substrate, which is moving deeper with the ion dose, showing that the physical

**2.1.1 Minimization of 1/f noise in silicides by ion implantation** 

silicides results in a lower frequency noise level.

properties of TiN/Ti/Si are influenced by the implantation.

substrate.

Fig. 1. RBS spectra of TiN/Ti/Si samples (Vasic et al., 2011).

Fig. 2. Frequency noise level for TiN/Ti/Si samples at 21ºC (Vasic et al., 2011).

This influence was confirmed by noise level measurements (all of the samples exhibit similar behaviour). Noise spectra were measured for different time constants *τ* (frequency range *τ* ~ 1/*f*) of the low noise amplifier. Analysis of the results of these measurements shows that implantation could have influence on the noise level (Fig.2), but the main effect depends on the implantation dose. As discussed above, implantation dose of 1x1016 ions/cm2 induces some disorder in the structure that could lead to higher noise level. Ion dose of 5x1015 ions/cm2 shows the best results for the entire measuring range, suggesting that this dose of implantation induce a more homogeneous silicidation and the formation of Ti-Si phase with a lower concentration of crystal defects (after annealing). The lower concentration of point defects and dislocations and a more homogeneous silicide/silicon interface result in a lower frequency noise level of the analyzed structures.

#### **2.2** *I***-***V* **measurements and the ideality factor**

Another commonly used and relatively simple method for obtaining output characteristics of photodetectors and solar cells related to the transport processes is current-voltage (*I*-*V*) measurement. Any deviation of the transport mechanism from the ideal model of thermionic emission directly reflexes on the shape of current-voltage characteristics. Main

Characterization of Thin Films for Solar Cells

following dependence:

series resistance, *Rs* for higher voltages.

functions based on some physical parameters are introduced.

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 281

spatial inhomogenities, etc.), and frequently is a function of the applied voltage (Vasic et al., 2005). Parameters *n* and *Is* are direct indicators of the output characteristics of the semiconducting devices on the electric transport processes in the junction. Deviations of the ideal (Shockley) case of the carrier transport are mostly the result of the combined influence of following factors: surface effects, generation and recombination of the cerriers in the depletion region, tunneling between states in the energy gap, series resistance, etc. For homo-junctions with homogenous distribution of recombination centers, two limiting values for the ideality factor are usually taken into consideration: *n* = 1 for the injection and diffusion in the depletion layer, and *n* = 2 in the case of the domination of the generation-recombination current in the depletion layer (due to the recombination of the electron-hole pairs in the recombination centers - traps). Very rarely values of the ideality factor are exactly 1 or 2, and they usually depend on the applied voltage also. Variations from the predicted values are the consequence of many factors. On the microscopic level impurities and defects induced during manufacture could form regions of low carrier lifetime, and that could have influence on the *I*-*V* characteristics, and hence the ideality factor also. Beside that, surface states could act as a recombination centers as well, and in that case ideality factor depends on the energy states of that recombination centers. If the space distribution of the recombination centers within the

depletion region is nonuniform, the ideality factor could have values greater than 2.

All of these factors make the extraction of the diode parameters very complicated since, usually, the first step in extraction of the diode parameters is the linear approximation of the ln*I*-*V* plot. Determination of the ideality factor value could be used as a measure of the validity of such a method. Namely, if the value of *n* is approximately 1, such approximation could be considered accurate enough, but if *n* > 1.4, transport mechanisms that produce the deviation from the ideal model and non-linearity of the ln*I*-*V* plot should also be considered. Even when the type of the transport mechanism could be more or less preciselly determined, series and parallel resistance of the device should also be taken into consideration. Introduction of these parameters in the *I-V* characteristic (eq.2) gives

> <sup>1</sup> exp 1exp 1 *s s <sup>s</sup> <sup>s</sup> sn*

 

*q V IR q V IR V IR I I <sup>I</sup>*

In this case, ln*I*-*V* plot is clearly not linear, because depending on the applied voltage, there could exsist one or more linear regions. The decrease of the ln*I*-*V* slope, i.e. increase of the ideality factor for lower voltage is a result of the presence of parallel resistance, *Rsh* (due to ''leakage'' current across the junction). The same effect on the values of the ideality factor has

Since in the real semiconductiong device (solar cell, photodetector) many unpredictable factors (concentration of defects and impurities, exsistance of the energy states in the forbidden zone, etc.) influence their parameters (*n*, *Is*, *Rs*), determination of the ideality factor as a macroscopic quantity, could give accurate information about the quality of each device. The basis of most of methods for obtaining the diode parameters from *I*-*V* curves (Vasic et al., 2005) is the correction of the experimentaly obtained data due to the presence of the series resistance *Rs*, but some of them also treat the diode parameters (especially *n* and *Is*) as voltage dependent. Analysis of the linear part of ln*I* vs *V* plot and fitting of the experimental results is used in the so called numerical methods, whereas in other methods auxiliary

*kT nkT R*

*sh*

(3)

parameter that could be extracted from *I*-*V* data is the ideality factor (*n*), direct indicator of the output parameter dependence on the electrical transport properties of the junction. Output characteristic of all semiconductor devices are primarily defined by fundamental parameters (resistance, lifetime and mobility of charge carriers, diffusion length etc.), and processes in them. Analytical connections between fundamental and output characteristics of solar cells are matter of theoretical analysis, but experimentally obtained results are more complex than theoretical suppositions. Both in production process of solar cells, and during their performance, the distribution of dopants, impurities and especially defects is usually not uniform and predictable, and could directly influence the processes in the cells. Factors that influence internal parameters of solar cells such as series and parallel resistance lead to changes in efficiency and maximum generated power in solar cell. Capability of solar cell to convert solar energy into electrical, depends on various fundamental and technological parameters (Stojanovic et al., 1998). Empirically obtained influence of fundamental parameters is usually mathematically defined by formal introduction of the ideality factor, *n*, in the exponent of current – voltage characteristics of solar cells. Ideality factor combines all variations of current flow from the ideal case, induced by various internal and external influences of physical parameters during the manufacturing process or as a consequence of aging. The non-ideal behavior of the device is reflected in the values of *n* greater than 1, and that is the result of the presence of different transport mechanisms that can contribute to the diode current. Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depends on various parameters, such as density of the interface states, concentration of the impurities and defects, height of the potential barrier, device voltage, and device temperature (Vasic et al., 2004). Obtaining of the ideality factor from *I*-*V* measurements is simple, non-invasive and effective way to evaluate possible degradation of output characteristics of solar cells and photodetectors in general in working conditions.

#### **2.2.1 Extraction of parameters from** *I***-***V* **measurements**

Characteristic parameters of the semiconducting devices are often very difficult to determine and their values could depend on the used measurement methods. Currentvoltage measurements are widely used to characterize the barrier height, carrier transport mechanisms and interface states both in Schotky barriers and p-n junctions. This relatively simple method provides reliable and reproducible results, but the extraction of the diode parameters could be influenced by their voltage dependence and the presence of series resistance (Vasic et al., 2000, 2005).

In an ideal case of thermionic emmision as a dominant trasport mechanism of charge carriers, current flow across the junction diode under forward bias and in the case when *VIRs* >> 3*kT*/*q*, is usually represented by the equation:

$$I = I\_s \left[ \exp \frac{q \left( V - IR\_s \right)}{nkT} \right] \tag{2}$$

where *I* is diode current, *Is* the saturation current, *V* the applied bias voltage, *Rs* the series resistance, *n* the ideality factor, *T* the temperature, *q* the electron charge and *k* the Boltzman constant. The saturation current *Is* depends on the carrier transport mechanism across the junction, and the formally introduced ideality factor *n* reflects the influence of various parameters (presence of the interface states, generation-recombination current, tunneling,

parameter that could be extracted from *I*-*V* data is the ideality factor (*n*), direct indicator of the output parameter dependence on the electrical transport properties of the junction. Output characteristic of all semiconductor devices are primarily defined by fundamental parameters (resistance, lifetime and mobility of charge carriers, diffusion length etc.), and processes in them. Analytical connections between fundamental and output characteristics of solar cells are matter of theoretical analysis, but experimentally obtained results are more complex than theoretical suppositions. Both in production process of solar cells, and during their performance, the distribution of dopants, impurities and especially defects is usually not uniform and predictable, and could directly influence the processes in the cells. Factors that influence internal parameters of solar cells such as series and parallel resistance lead to changes in efficiency and maximum generated power in solar cell. Capability of solar cell to convert solar energy into electrical, depends on various fundamental and technological parameters (Stojanovic et al., 1998). Empirically obtained influence of fundamental parameters is usually mathematically defined by formal introduction of the ideality factor, *n*, in the exponent of current – voltage characteristics of solar cells. Ideality factor combines all variations of current flow from the ideal case, induced by various internal and external influences of physical parameters during the manufacturing process or as a consequence of aging. The non-ideal behavior of the device is reflected in the values of *n* greater than 1, and that is the result of the presence of different transport mechanisms that can contribute to the diode current. Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depends on various parameters, such as density of the interface states, concentration of the impurities and defects, height of the potential barrier, device voltage, and device temperature (Vasic et al., 2004). Obtaining of the ideality factor from *I*-*V* measurements is simple, non-invasive and effective way to evaluate possible degradation of output characteristics of solar cells and photodetectors in general in working

Characteristic parameters of the semiconducting devices are often very difficult to determine and their values could depend on the used measurement methods. Currentvoltage measurements are widely used to characterize the barrier height, carrier transport mechanisms and interface states both in Schotky barriers and p-n junctions. This relatively simple method provides reliable and reproducible results, but the extraction of the diode parameters could be influenced by their voltage dependence and the presence of series

In an ideal case of thermionic emmision as a dominant trasport mechanism of charge carriers, current flow across the junction diode under forward bias and in the case when

exp *<sup>s</sup>*

*nkT* 

(2)

*q V IR I I*

where *I* is diode current, *Is* the saturation current, *V* the applied bias voltage, *Rs* the series resistance, *n* the ideality factor, *T* the temperature, *q* the electron charge and *k* the Boltzman constant. The saturation current *Is* depends on the carrier transport mechanism across the junction, and the formally introduced ideality factor *n* reflects the influence of various parameters (presence of the interface states, generation-recombination current, tunneling,

*s*

conditions.

*V*

**2.2.1 Extraction of parameters from** *I***-***V* **measurements** 

*IRs* >> 3*kT*/*q*, is usually represented by the equation:

resistance (Vasic et al., 2000, 2005).

spatial inhomogenities, etc.), and frequently is a function of the applied voltage (Vasic et al., 2005). Parameters *n* and *Is* are direct indicators of the output characteristics of the semiconducting devices on the electric transport processes in the junction. Deviations of the ideal (Shockley) case of the carrier transport are mostly the result of the combined influence of following factors: surface effects, generation and recombination of the cerriers in the depletion region, tunneling between states in the energy gap, series resistance, etc. For homo-junctions with homogenous distribution of recombination centers, two limiting values for the ideality factor are usually taken into consideration: *n* = 1 for the injection and diffusion in the depletion layer, and *n* = 2 in the case of the domination of the generation-recombination current in the depletion layer (due to the recombination of the electron-hole pairs in the recombination centers - traps). Very rarely values of the ideality factor are exactly 1 or 2, and they usually depend on the applied voltage also. Variations from the predicted values are the consequence of many factors. On the microscopic level impurities and defects induced during manufacture could form regions of low carrier lifetime, and that could have influence on the *I*-*V* characteristics, and hence the ideality factor also. Beside that, surface states could act as a recombination centers as well, and in that case ideality factor depends on the energy states of that recombination centers. If the space distribution of the recombination centers within the depletion region is nonuniform, the ideality factor could have values greater than 2.

All of these factors make the extraction of the diode parameters very complicated since, usually, the first step in extraction of the diode parameters is the linear approximation of the ln*I*-*V* plot. Determination of the ideality factor value could be used as a measure of the validity of such a method. Namely, if the value of *n* is approximately 1, such approximation could be considered accurate enough, but if *n* > 1.4, transport mechanisms that produce the deviation from the ideal model and non-linearity of the ln*I*-*V* plot should also be considered. Even when the type of the transport mechanism could be more or less preciselly determined, series and parallel resistance of the device should also be taken into consideration. Introduction of these parameters in the *I-V* characteristic (eq.2) gives following dependence:

$$I = I\_{s1} \left[ \exp\frac{q\left(V - IR\_s\right)}{kT} - 1 \right] + I\_{sn} \left[ \exp\frac{q\left(V - IR\_s\right)}{nkT} - 1 \right] + \frac{V - IR\_s}{R\_{sh}} \tag{3}$$

In this case, ln*I*-*V* plot is clearly not linear, because depending on the applied voltage, there could exsist one or more linear regions. The decrease of the ln*I*-*V* slope, i.e. increase of the ideality factor for lower voltage is a result of the presence of parallel resistance, *Rsh* (due to ''leakage'' current across the junction). The same effect on the values of the ideality factor has series resistance, *Rs* for higher voltages.

Since in the real semiconductiong device (solar cell, photodetector) many unpredictable factors (concentration of defects and impurities, exsistance of the energy states in the forbidden zone, etc.) influence their parameters (*n*, *Is*, *Rs*), determination of the ideality factor as a macroscopic quantity, could give accurate information about the quality of each device. The basis of most of methods for obtaining the diode parameters from *I*-*V* curves (Vasic et al., 2005) is the correction of the experimentaly obtained data due to the presence of the series resistance *Rs*, but some of them also treat the diode parameters (especially *n* and *Is*) as voltage dependent. Analysis of the linear part of ln*I* vs *V* plot and fitting of the experimental results is used in the so called numerical methods, whereas in other methods auxiliary functions based on some physical parameters are introduced.

Characterization of Thin Films for Solar Cells

give unreliable results.

factor *n*(*V*),

point by point) using equation:

with the influence of the series resistance,

a. conventional *I*-*V* measurements, and

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 283

also the fact that at high bias voltages series resistance could significantly influence the shape of the *I*-*V* plot, making the linear fit for the whole voltage region impossible. Nevertheless, these methods usually treat such problems separately. Namely, most of the methods do not take into account that the diode parameters (*n*, *Is*) are voltage-dependent. On the other hand, methods that analyze voltage-dependent parameters produce correct results only under assumption that the influence of the series resistance is negligible. However, generally speaking, for real diodes neither series resistance nor voltage dependence are negligible, so most of the proposed methods have limited application and

There are several approaches for determination of the voltage-dependent ideality factor:

 <sup>1</sup> ln *kT <sup>I</sup> nV q V*

2. calculation of the function *n*(*V*) at each point of the experimental *I*-*V* data (method

ln 1

*qV <sup>I</sup> n V kT I* 

3. method of adding an external resistance, based on two consecutive measurements:

 ln ln *s s <sup>q</sup> I I V IR n V kT*

 ln ln *s s ex <sup>q</sup> I I I V I IR R n V kT*

> ln *s ex ex ex <sup>I</sup> <sup>q</sup> <sup>I</sup> RR I*

*R n V kT R* 

Equations (10) and (12) form the system of two equations with three unknown diode parameters (*Rs*, *Is* and *n*), so some relationship must be established between any two of the unknown parameters. There are two methods of eliminating one unknown parameter; first method (A) is based on establishing the relationship between the ideality factor and

b. *I*-*V* measurement with external resistance *Rex* in series with the diode.

*s*

with the assumption that the saturation current is previously determined in accordance

From the equation (2) and after adding *Rex*, following set of equations were obtained:

where *I* is the change in *I* produced by adding *Rex*. From those equations follows:

(8)

(10)

(11)

(9)

(12)

but numerical differentiation is, in effect, a total (complete) and not partial differentiation, so the obtained result is some function f(*n*), and not the true ideality

1. differentiation of the simplified expression of equation (2):

#### **Standard linearization method**

This method is based on the analysis of the linear part of ln*I* = f(*V*) plot using equation (2) when diode parameters are voltage independent - *Is* is calculated from the extrapolated intercept with the y (current) axis, and *n* is deduced from the slope. However, when measured plot deviates from straight line shape (in the presence of *Rs*), calculated parameters are significantly different from the values obtained using other methods. This is very distinct when *Rs* is high and the shape of the *I*-*V* curve is not the same in different voltage regions (especially for high forward bias).

#### **Numerical method**

Enhanced version of the standard method also includes presence of the series reistance, but the diode parameters could be determined without linearization of the *I*-*V* curve (Vasic et al., 2005). Method is based on a least square method of fitting the experimentally obtained results in order to yield optimal values of *Is*, *n*, and *Rs*.

When an applied voltage *VA* is provided across the device terminals, actual barrier (junction) voltage *V* is given by:

$$V = V\_A - I\_E R\_s \tag{4}$$

(*IE* is experimentally measured diode current). Then, from the equation (2) and using equation (4), applied voltage is given by:

$$V\_A = I\_E R\_s + a \ln I\_E + b \tag{5}$$

where:

$$a = nkT/q \quad \text{and } b = -a \ln l\_s \tag{6}$$

Thus if *Rs*, *a*, and *b* could be determined, then *n* and *Is* could also be obtained. One of the ways for optimization of *Rs*, *a*, and *b* is method of least squares, and for this purpose function S is defined as:

$$S = \sum\_{i=1}^{m} \left\{ I\_{Ei} R\_s + a \ln I\_{Ei} + b - V\_{Ei} \right\}^2 \tag{7}$$

where *m* is the number of diode pairs of experimentally determined *IE* and *VE*. The optimal combination of parameters would result in a minimum value of S, and from the set of matrix equations values of *Rs*, *a*, and *b* could be calculated. Then, using equation (6) *n* and *Is* are easilly obtained.

It has been shown (Vasic et al., 2005) that the agreement between experimental data and numerical simulation is very good, especially when parasitic series resistance effects are present, and when the measured ln*I* = f(*V*) plot shows no linear regime. However, since this method is not based on any physical model of current transport, there are no sufficient indications of the validity of these results.

#### **Methods based on the physical models**

Physical parameters such as differential conductance and resistance, for example, are the basis of some methods that use auxiliary functions or parameters for the determination of real diode parameters. Novel methods take into account that for the real diodes *n* 1, and

This method is based on the analysis of the linear part of ln*I* = f(*V*) plot using equation (2) when diode parameters are voltage independent - *Is* is calculated from the extrapolated intercept with the y (current) axis, and *n* is deduced from the slope. However, when measured plot deviates from straight line shape (in the presence of *Rs*), calculated parameters are significantly different from the values obtained using other methods. This is very distinct when *Rs* is high and the shape of the *I*-*V* curve is not the same in different

Enhanced version of the standard method also includes presence of the series reistance, but the diode parameters could be determined without linearization of the *I*-*V* curve (Vasic et al., 2005). Method is based on a least square method of fitting the experimentally obtained

When an applied voltage *VA* is provided across the device terminals, actual barrier

 *V* = *VA IERs* (4) (*IE* is experimentally measured diode current). Then, from the equation (2) and using

 *a* = *nkT*/*q* and *b* = *a*ln*Is* (6) Thus if *Rs*, *a*, and *b* could be determined, then *n* and *Is* could also be obtained. One of the ways for optimization of *Rs*, *a*, and *b* is method of least squares, and for this purpose

<sup>2</sup>

*Ei s Ei Ei*

ln

where *m* is the number of diode pairs of experimentally determined *IE* and *VE*. The optimal combination of parameters would result in a minimum value of S, and from the set of matrix equations values of *Rs*, *a*, and *b* could be calculated. Then, using equation (6) *n* and *Is* are

It has been shown (Vasic et al., 2005) that the agreement between experimental data and numerical simulation is very good, especially when parasitic series resistance effects are present, and when the measured ln*I* = f(*V*) plot shows no linear regime. However, since this method is not based on any physical model of current transport, there are no sufficient

Physical parameters such as differential conductance and resistance, for example, are the basis of some methods that use auxiliary functions or parameters for the determination of real diode parameters. Novel methods take into account that for the real diodes *n* 1, and

*S IR a I b V*

1

*i*

*m*

*V IR a I b A Es E* ln (5)

(7)

**Standard linearization method** 

(junction) voltage *V* is given by:

equation (4), applied voltage is given by:

indications of the validity of these results. **Methods based on the physical models** 

**Numerical method** 

where:

function S is defined as:

easilly obtained.

voltage regions (especially for high forward bias).

results in order to yield optimal values of *Is*, *n*, and *Rs*.

shape of the *I*-*V* plot, making the linear fit for the whole voltage region impossible. Nevertheless, these methods usually treat such problems separately. Namely, most of the methods do not take into account that the diode parameters (*n*, *Is*) are voltage-dependent. On the other hand, methods that analyze voltage-dependent parameters produce correct results only under assumption that the influence of the series resistance is negligible. However, generally speaking, for real diodes neither series resistance nor voltage dependence are negligible, so most of the proposed methods have limited application and give unreliable results.

There are several approaches for determination of the voltage-dependent ideality factor:

1. differentiation of the simplified expression of equation (2):

$$\frac{1}{\ln(V)} = \frac{kT}{q} \frac{\mathcal{\partial}}{\mathcal{\partial}V} (\ln I) \tag{8}$$

but numerical differentiation is, in effect, a total (complete) and not partial differentiation, so the obtained result is some function f(*n*), and not the true ideality factor *n*(*V*),

2. calculation of the function *n*(*V*) at each point of the experimental *I*-*V* data (method point by point) using equation:

$$\ln\left(V\right) = \frac{qV}{kT}\ln\left(\frac{I}{I\_s} + 1\right) \tag{9}$$

with the assumption that the saturation current is previously determined in accordance with the influence of the series resistance,

	- a. conventional *I*-*V* measurements, and
	- b. *I*-*V* measurement with external resistance *Rex* in series with the diode. From the equation (2) and after adding *Rex*, following set of equations were obtained:

$$
\ln I = \ln I\_s + \frac{q}{n(V)kT}(V - IR\_s) \tag{10}
$$

$$\ln\left(I+\Delta I\right) = \ln I\_s + \frac{q}{n\left(V\right)kT} \left[V - \left(I+\Delta I\right)\left(R\_s + R\_{ex}\right)\right] \tag{11}$$

where *I* is the change in *I* produced by adding *Rex*. From those equations follows:

$$\frac{\Delta\left(\ln I\right)}{R\_{ex}} = -\frac{q}{n\left(V\right)kT} \left[ \left(R\_s + R\_{ex}\right)\frac{\Delta I}{R\_{ex}} + I \right] \tag{12}$$

Equations (10) and (12) form the system of two equations with three unknown diode parameters (*Rs*, *Is* and *n*), so some relationship must be established between any two of the unknown parameters. There are two methods of eliminating one unknown parameter; first method (A) is based on establishing the relationship between the ideality factor and

Characterization of Thin Films for Solar Cells

procedure and experiment requirements.

1096.63316 exper. 3 BPW 43 standard

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

V [V]

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

f 1 (V)


a) b)

the local ideality factor *nloc* (i.e., determination of the *n*(*V*) dependence) necessary.

0.04979 0.13534 0.36788 1 2.71828 7.38906 20.08554 54.59815 148.41316 403.42879

al., 2005).


et al., 2005).

f

2

I [A]

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 285

standard method and method A for one sample, 3 BPW 43 (dots represent experimental data, and lines – calculated characteristics). Correlation factor for all three used methods was good (r > 0.99), so the choice of the exact method depends on the complexity of the

I [A]

Fig. 3. Agreement: experimental and calculated data for a) standard, b) method A (Vasic et

In order to test the assumption that the ideality factor is voltage-independent and that the determination of only one, summary ideality factor is sufficient, diagrams of f2 = f(f1) dependence were plotted (two characteristic examples are shown in Fig. 4). Correlation factor for those functions for the sample 3 BPW 43 was the highest (*r* = 0.99751), and that, together with the obvious good linearity of the f2 = f(f1) diagram, shows that for this sample ideality factor has approximately constant value for whole voltage range. However, although the agreement between experimental and calculated data for both shown samples were good, from Fig. 4b) could be seen that f2 = f(f1) dependence for sample 9 BPW 34 was not linear, so junction parameters are voltage dependent. This makes the determination of

> -18 -16 -14 -12 -10 -8

(V) a) b)

f

Fig. 4. Diagram of the f2 = f(f1) dependence for samples a) 3 BPW 43 and b) 9 BPW 34 (Vasic

2

0.04979 0.13534 0.36788 1 2.71828 7.38906 20.08554 54.59815 148.41316

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

V [V]

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

f 1


403.42879 3 BPW 43 exper. "A"

saturation current by eliminating series resistance from the equation (10), and obtaining from the equation (11):

$$f\_2\left(I, \Delta I\right) = \ln I\_s + \frac{q}{n\left(V\right)kT} f\_1\left(V, I\_\prime \Delta I\_\prime R\_{\rm ex}\right) \tag{13}$$

$$f\_2\left(I,\Delta I\right) = \ln I - \frac{\Delta I}{I}\ln\left(1 + \frac{\Delta I}{I}\right) \qquad \text{and} \qquad f\_1\left(V, I\_\prime \Delta I\_\prime R\_{ex}\right) = V + R\_{ex}I\left(1 + \frac{I}{\Delta I}\right)$$

Using the f2 = f(f1) dependence, saturation current *Is* and ideality factor *n* could be obtained from the slope and the vertical axis intercept of the plot, independently of the series resistance (*Rs* could be calculated from the equation (2), afterwards).

However, in the case of voltage-dependent *n*, dependence f2 = f(f1) is not a straight line, so second method (B) that allows determination of all parameters in the case of non-linearity, must be used. The ideality factor *n* is, at the beginning, eliminated from the equations (11) and (12), thus establishing the relationship between *Is* and *Rs*:

$$R\_s = -\frac{1}{\Delta I} \left[ \frac{f\_1}{f\_2 - \ln I\_s} \ln \left( 1 + \frac{\Delta I}{I} \right) + R\_{ex} \left( I + \Delta I \right) \right] \tag{14}$$

assuming that both *Is* and *Rs* are voltage independent over the range of interest. Saturation current could be determined by fitting in such a way that series resistance would have approximately constant value. The obtained values of *Is* and *Rs* could then be used to extract the voltage-dependent *n*(*V*) from the equation (2).

It was shown that both of these methods that use the auxiliary function f1 and f2 give reliable and reproducible results. First one (A) is limited on the cases of voltage independent parameters, but gives good results in the presence of noise, while method B provides the possibility of analyzing the general case of voltage-dependent ideality factor in the presence of series resistance and experimental noise.

#### **Verification of the presented methods**

The validity of the above-described methods was examined by analyzing *I*-*V* characteristics (primarily obtaining the values of the ideality factor) of real photodiodes (Vasic et al., 2005). Samples used in the experiment were commercially available p-i-n and p-n silicon photodiodes (trademarks BPW 34, BPW 43, SFH 205, and BP 104). Forward bias dark *I*-*V* characteristics of the diodes were measured using standard configuration for the *I*-*V* measurements. In all samples presence of the series resistance was detected (calculated range of *Rs* was from 2030 for BPW 34 and SFH 205 p-i-n type, to 100200 for BPW 43 p-n type of photodiodes). Values of the ideality factor calculated using standard method were in the range of 1.21.6, depending on the type of the samples. Similar range of values was obtained by numerical method, while application of the auxiliary functions (method A) results in lower values of *n* (1.051.5). Considering physical meaning of the ideality factor (measure of non-ideality of the junction), the only way to verify the validity of a given method is evaluation of the agreement between experimentally measured data and numerically calculated *I*-*V* curves (with calculated diode parameters), i.e., determination of the correlation factor *r*. For standard and numerical method correlation factor was higher than 0.99, but the best values of *r* were for the method A. Figure 3 shows agreement for

saturation current by eliminating series resistance from the equation (10), and obtaining

 2 1 , ln ,, , *s ex <sup>q</sup> f I I I f VI IR n V kT*

Using the f2 = f(f1) dependence, saturation current *Is* and ideality factor *n* could be obtained from the slope and the vertical axis intercept of the plot, independently of the series

However, in the case of voltage-dependent *n*, dependence f2 = f(f1) is not a straight line, so second method (B) that allows determination of all parameters in the case of non-linearity, must be used. The ideality factor *n* is, at the beginning, eliminated from the equations (11)

assuming that both *Is* and *Rs* are voltage independent over the range of interest. Saturation current could be determined by fitting in such a way that series resistance would have approximately constant value. The obtained values of *Is* and *Rs* could then be used to extract

It was shown that both of these methods that use the auxiliary function f1 and f2 give reliable and reproducible results. First one (A) is limited on the cases of voltage independent parameters, but gives good results in the presence of noise, while method B provides the possibility of analyzing the general case of voltage-dependent ideality factor in the presence

The validity of the above-described methods was examined by analyzing *I*-*V* characteristics (primarily obtaining the values of the ideality factor) of real photodiodes (Vasic et al., 2005). Samples used in the experiment were commercially available p-i-n and p-n silicon photodiodes (trademarks BPW 34, BPW 43, SFH 205, and BP 104). Forward bias dark *I*-*V* characteristics of the diodes were measured using standard configuration for the *I*-*V* measurements. In all samples presence of the series resistance was detected (calculated range of *Rs* was from 2030 for BPW 34 and SFH 205 p-i-n type, to 100200 for BPW 43 p-n type of photodiodes). Values of the ideality factor calculated using standard method were in the range of 1.21.6, depending on the type of the samples. Similar range of values was obtained by numerical method, while application of the auxiliary functions (method A) results in lower values of *n* (1.051.5). Considering physical meaning of the ideality factor (measure of non-ideality of the junction), the only way to verify the validity of a given method is evaluation of the agreement between experimentally measured data and numerically calculated *I*-*V* curves (with calculated diode parameters), i.e., determination of the correlation factor *r*. For standard and numerical method correlation factor was higher than 0.99, but the best values of *r* were for the method A. Figure 3 shows agreement for

<sup>1</sup>

2 1 , ln ln 1 ,, , 1 *ex ex I I <sup>I</sup> fII I and f V I I R V R I I I <sup>I</sup>* 

resistance (*Rs* could be calculated from the equation (2), afterwards).

2

<sup>1</sup> ln 1 ln *s ex s <sup>f</sup> <sup>I</sup> <sup>R</sup> RI I If I I*

and (12), thus establishing the relationship between *Is* and *Rs*:

the voltage-dependent *n*(*V*) from the equation (2).

of series resistance and experimental noise. **Verification of the presented methods** 

(13)

(14)

from the equation (11):

standard method and method A for one sample, 3 BPW 43 (dots represent experimental data, and lines – calculated characteristics). Correlation factor for all three used methods was good (r > 0.99), so the choice of the exact method depends on the complexity of the procedure and experiment requirements.

Fig. 3. Agreement: experimental and calculated data for a) standard, b) method A (Vasic et al., 2005).

In order to test the assumption that the ideality factor is voltage-independent and that the determination of only one, summary ideality factor is sufficient, diagrams of f2 = f(f1) dependence were plotted (two characteristic examples are shown in Fig. 4). Correlation factor for those functions for the sample 3 BPW 43 was the highest (*r* = 0.99751), and that, together with the obvious good linearity of the f2 = f(f1) diagram, shows that for this sample ideality factor has approximately constant value for whole voltage range. However, although the agreement between experimental and calculated data for both shown samples were good, from Fig. 4b) could be seen that f2 = f(f1) dependence for sample 9 BPW 34 was not linear, so junction parameters are voltage dependent. This makes the determination of the local ideality factor *nloc* (i.e., determination of the *n*(*V*) dependence) necessary.

Fig. 4. Diagram of the f2 = f(f1) dependence for samples a) 3 BPW 43 and b) 9 BPW 34 (Vasic et al., 2005).

Characterization of Thin Films for Solar Cells

and this could be done by any of the proposed methods.

for quick extraction of diode parameters.

**characteristics** 

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 287

precision of the obtained results, the complexity of the method presents in some cases, the major limiting factor for its application. Adding an external resistance, together with the problem of selection of an optimal value for Rex, makes these methods (both A and B) inappropriate in the field conditions for example, or when a quick evaluation of the *I*-*V* data is necessary. In this case, method based on the calculation of the *n*(*V*) at each point of the experimental *I*-*V* data – method point by point, should be used (equation (9)). In Fig. 6, bias dependent ideality factor calculated using method B (filled circles) and point by point (asterisk) for one sample (1 BPW 34) is presented. It could be seen that both methods give similar values of *n*, as well as the same *n*(*V*) behavior (high values of *nloc* at low bias, decrease for medium, and slight increase for higher bias). For the comparison, in the same figure 1/f(*n*) dependence was also plotted (triangles). The only condition that should be fulfilled for using equation (9) is to determine the value of the saturation current previously,

The extraction of diode parameters is difficult due to the presence of the series resistance, and values of *Is*, *n*, and *Rs* usually depend on the methods used for their calculation. The choise of the exact method depends both on the complexity of the method and on the experimental demands (conditions). Methods of using auxiliary functions (methods A and B) demand adding (optimal) external resistance and additional measurements. Also, calculation of the diode parameters is more complex than for other methods due to the extended numerical procedure. In laboratory conditions, these methods undoubtedly give the best results, but in the field conditions both of these methods are very complex and the extraction of the parameters is slow. This is more emphasized if the devices are exposed to the severe working conditions when quick assessment of their performance is needed. Even in the laboratory conditions, when the relative change of the diode parameters is measured for the estimation of the worst-case scenario, both standard and numerical method gave good results for voltage-independent parameters, and point by point method for voltagedependent parameters. Based on the experimental verification, it could be concluded that, although the results obtained by the methods of adding an external resistance have the best agreement with the experimental data, standard and numerical methods are more suitable

**3. Radiation effects and possibilities of improvement of solar cells** 

Beside the diversity of the device technologies used for designing of the optical and other detectors, there are a variety of radiation environments in which they are used (natural space and atmospheric, as well as military and civil nuclear environments, etc.). Reliability of electrical devices in a radiation environment is very important, and extensive studies concerning the development of semiconductor devices that can operate normally in such conditions have been seriously undertaken. Possible degradation of the electrical performance of solar cells and photodetectors induced by irradiation means that very strict conditions for their application must be predetermined for the worst case scenario. Performance failure in such conditions could have negative impact both on the financial and environmental aspects of the device application. Therefore, from the technological point of view, it is important to study the variations induced by irradiation of semiconductor

Differentiation of the equation (2) leads to as previously explained, some function f(*n*), due to the presence of *Rs*:

$$f(n) = \frac{kT}{q} \frac{d}{dV} (\ln I) = \frac{1}{n} - \frac{V}{n^2} \frac{dn}{dV} \tag{15}$$

Except in cases when d*n*/d*V* << *n*(*V*)/*V* at the same bias, second term in the right hand side of the equation (15) cannot be neglected. Therefore, the exact values of the ideality factor could be obtained by integration of the equation (15), which is difficult, due to the unknown initial conditions.

Fig. 5. Method B (Vasic et al, 2005).

Fig. 6. Comparison for *nloc* (Vasic et al., 2005).

Above-mentioned deviations of the f2 = f(f1) plot from the linearity are ascribed to the bias dependence of the ideality factor. Reliable and accurate method for obtaining the local ideality factor directly, is method B. For the sample 9 BPW 34 (f2 = f(f1) significantly deviates from the linearity, Fig. 4 b)), bias dependent *nloc* was calculated using proposed method, and the result is shown in Fig. 5. From this figure it could be seen that the ideality factor is constant only in the very narrow voltage region (from 0.32 to 0.42 V). The correlation factor for method B was very good (near 1). However, beside very high

Differentiation of the equation (2) leads to as previously explained, some function f(*n*), due

<sup>1</sup> ( ) ln *kT d V dn f n <sup>I</sup>*

Except in cases when d*n*/d*V* << *n*(*V*)/*V* at the same bias, second term in the right hand side of the equation (15) cannot be neglected. Therefore, the exact values of the ideality factor could be obtained by integration of the equation (15), which is difficult, due to the unknown

1.8 9 BPW 34 nloc - "B"

1.8 1 BPW 34

<sup>2</sup>

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

V [V]

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

V [V]

Above-mentioned deviations of the f2 = f(f1) plot from the linearity are ascribed to the bias dependence of the ideality factor. Reliable and accurate method for obtaining the local ideality factor directly, is method B. For the sample 9 BPW 34 (f2 = f(f1) significantly deviates from the linearity, Fig. 4 b)), bias dependent *nloc* was calculated using proposed method, and the result is shown in Fig. 5. From this figure it could be seen that the ideality factor is constant only in the very narrow voltage region (from 0.32 to 0.42 V). The correlation factor for method B was very good (near 1). However, beside very high

 n(V) nloc-"B" 1/f(n)

*q dV n dV <sup>n</sup>* (15)

to the presence of *Rs*:

initial conditions.

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

> 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

n

Fig. 6. Comparison for *nloc* (Vasic et al., 2005).

loc , 1/f(n)

n

Fig. 5. Method B (Vasic et al, 2005).

loc

precision of the obtained results, the complexity of the method presents in some cases, the major limiting factor for its application. Adding an external resistance, together with the problem of selection of an optimal value for Rex, makes these methods (both A and B) inappropriate in the field conditions for example, or when a quick evaluation of the *I*-*V* data is necessary. In this case, method based on the calculation of the *n*(*V*) at each point of the experimental *I*-*V* data – method point by point, should be used (equation (9)). In Fig. 6, bias dependent ideality factor calculated using method B (filled circles) and point by point (asterisk) for one sample (1 BPW 34) is presented. It could be seen that both methods give similar values of *n*, as well as the same *n*(*V*) behavior (high values of *nloc* at low bias, decrease for medium, and slight increase for higher bias). For the comparison, in the same figure 1/f(*n*) dependence was also plotted (triangles). The only condition that should be fulfilled for using equation (9) is to determine the value of the saturation current previously, and this could be done by any of the proposed methods.

The extraction of diode parameters is difficult due to the presence of the series resistance, and values of *Is*, *n*, and *Rs* usually depend on the methods used for their calculation. The choise of the exact method depends both on the complexity of the method and on the experimental demands (conditions). Methods of using auxiliary functions (methods A and B) demand adding (optimal) external resistance and additional measurements. Also, calculation of the diode parameters is more complex than for other methods due to the extended numerical procedure. In laboratory conditions, these methods undoubtedly give the best results, but in the field conditions both of these methods are very complex and the extraction of the parameters is slow. This is more emphasized if the devices are exposed to the severe working conditions when quick assessment of their performance is needed. Even in the laboratory conditions, when the relative change of the diode parameters is measured for the estimation of the worst-case scenario, both standard and numerical method gave good results for voltage-independent parameters, and point by point method for voltagedependent parameters. Based on the experimental verification, it could be concluded that, although the results obtained by the methods of adding an external resistance have the best agreement with the experimental data, standard and numerical methods are more suitable for quick extraction of diode parameters.

#### **3. Radiation effects and possibilities of improvement of solar cells characteristics**

Beside the diversity of the device technologies used for designing of the optical and other detectors, there are a variety of radiation environments in which they are used (natural space and atmospheric, as well as military and civil nuclear environments, etc.). Reliability of electrical devices in a radiation environment is very important, and extensive studies concerning the development of semiconductor devices that can operate normally in such conditions have been seriously undertaken. Possible degradation of the electrical performance of solar cells and photodetectors induced by irradiation means that very strict conditions for their application must be predetermined for the worst case scenario. Performance failure in such conditions could have negative impact both on the financial and environmental aspects of the device application. Therefore, from the technological point of view, it is important to study the variations induced by irradiation of semiconductor

Characterization of Thin Films for Solar Cells

properties of photodiodes.

et al., 2003).

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 289

characteristics before and after irradiation reveals the extent of degradation of electrical

Although polycrystalline and monocrystalline solar cells are more reliable than amorphous, inherent presence of defects and impurities in the basic material could, during time, produce some negative effects. This is specially emphasized if those states are located within the energy gap and are activated during work. In such a case they become traps for optically produced electron-hole pairs, and thus decrease the number of collected charge carriers. Macroscopically, this effect could be observed as a decrease of the output current and voltage, and ultimately could lead to the decrease of the efficiency of solar cell. Lower values of short-circuit current indicate the existence of the recombination centers that decrease the mobility and diffusion length of the charge carriers, making the recombination in the depletion region dominant transport in such solar cells (Vasic et al., 2000, 2003). The lifetime of the solar cell is restricted by the degree of radiation damage that the cell receives. This is an important factor that affects the performance of the solar cell in practical applications. The permanent damage in the solar cells materials is caused by collisions of the incident radiation particles with the atoms in the crystalline lattice, which are displaced from their positions. These defects degrade the transport properties of the material and particularly the minority carrier lifetime (Alurralde et al., 2004, Horiushi et al., 2000, Zhenyu et al., 2004). This lifetime decrease produces degradation of the parameters of the cell ultimately leading to an increase of the noise level. The interaction between vacancies, selfinterstitials, impurities, and dopants in Si leads to the formation of undesirable point defects such as recombination and compensator centers which affects performance of the solar cells, especially in space. Introduction of radiation-induced recombination centers reduce the minority carrier lifetime in the base layer of the p-n junction increasing series resistance. After very high doses of radiation series resistance of the base layer could be so high that most of the power generated by the device is dissipated by its own internal resistance (Khan

0.0 0.1 0.2 0.3 0.4 0.5 0.6

V [V]

Fig. 7. Simulation of the dependence of *P*-*V* characteristics on *n* (Vasic et al., 2011).

 2l, n=1.38 5l, n=1.65 10l, n=1.73 8l, n=1.87 7l, n=1.99

P [mW/cm 2]

junction characteristic parameters (ideality factor, saturation current, etc.), that affect the performance of the photodiodes and solar cells.

Investigations of radiation effects in solids are primarily based on the study of the characteristics based on structure. Since radiation unduced deffects are connetcted to the defects in the crystal lattice, physical evidence of such a damage must br found through those characteristics that are most sensitive to the unperfections of the lattice. Due to the microscopic nature of such a defects, measurements of variations in those charcateristics are almost the only method of evaluation of radiation influence (Loncar et al., 2005, 2006, 2007). In semiconductor devices, radiation induced defects are connected to the localized energy states that could change concentration and mobility of the charge carriers. Namely, the main charactersitics of semiconducting devices is precisely the change (in a large range) of the charge carriers concentration, weather because of the defects and impurities, or under the influence of the raised temperature. When the equilibrium concentration of electrons and holes is disturbed by the radiation, for example, their mutual anihillation is possible only in the localized energy states in the crystal. These are, so called, recombination centers, and radiation induced defects represent very good example of such a centers.

Interaction of radiation with the semiconducting devices basically produses three effects: permenent ionization damage in insulator layers, ionization effects in semiconductors, and dislocation damage. During interction of γ radiarion with the device, and depending on the radiation energy, primarilly three effects could occur: photoelectric effect, Compton effect, and electron-hole creation. In all of these processe, absorbed photon energy couses ionization and excitation of the created electrons, with the electron-hole creation. These effects lead to the generation of parasitic charge (noise) collected in the depletion region. Also, ionization effects could produce recombination centers in the energy gap. In silicon, all of these effects could be permenent or quasi-permenent.

On the other hand, dislocation damage usually arise after the interaction of the particled such as protons, neutrons and electrons. Processes that could happen during those collisions depend on the type of particles and their energy. Collision of the particles with the atoms of crystal lattice could produce vacances, interstities, and other types of defects. These defects could be traped in the impurity centers, for example, and could form active defects leading to the changes in the characteristics of the photodetectros, primarilly the decrease of the minority carrier lifetime. Radiation damage due to neutrons (heavy particles) is, as mentioned above, primarily connected to the displacement of silicon atoms from their lattice sites in the crystalline silicon solar cells, leading to destruction and distortion of local lattice structure and formation of defects. If, under the influence of neutrons, stable defects are made, they could, together with impurity atoms, donors and for example implanted atoms, form complex defects acting as recombination sites or traps, significantly decreasing minority carrier lifetime.

#### **3.1 Radiation damage in solar cells and photodiodes**

The main effect of radiation on photodiodes and solar cells is an increase in the dark current generated within or at the surface of the depletion region. Generation of electron–hole pairs due to ionization effects and displacement damage induced by neutrons, result in the generation and increase of the noise and the minimum signal that can be detected. Since presence of the noise could be connected to the excess current, measurement of the *I-V*

junction characteristic parameters (ideality factor, saturation current, etc.), that affect the

Investigations of radiation effects in solids are primarily based on the study of the characteristics based on structure. Since radiation unduced deffects are connetcted to the defects in the crystal lattice, physical evidence of such a damage must br found through those characteristics that are most sensitive to the unperfections of the lattice. Due to the microscopic nature of such a defects, measurements of variations in those charcateristics are almost the only method of evaluation of radiation influence (Loncar et al., 2005, 2006, 2007). In semiconductor devices, radiation induced defects are connected to the localized energy states that could change concentration and mobility of the charge carriers. Namely, the main charactersitics of semiconducting devices is precisely the change (in a large range) of the charge carriers concentration, weather because of the defects and impurities, or under the influence of the raised temperature. When the equilibrium concentration of electrons and holes is disturbed by the radiation, for example, their mutual anihillation is possible only in the localized energy states in the crystal. These are, so called, recombination centers, and

Interaction of radiation with the semiconducting devices basically produses three effects: permenent ionization damage in insulator layers, ionization effects in semiconductors, and dislocation damage. During interction of γ radiarion with the device, and depending on the radiation energy, primarilly three effects could occur: photoelectric effect, Compton effect, and electron-hole creation. In all of these processe, absorbed photon energy couses ionization and excitation of the created electrons, with the electron-hole creation. These effects lead to the generation of parasitic charge (noise) collected in the depletion region. Also, ionization effects could produce recombination centers in the energy gap. In silicon, all

On the other hand, dislocation damage usually arise after the interaction of the particled such as protons, neutrons and electrons. Processes that could happen during those collisions depend on the type of particles and their energy. Collision of the particles with the atoms of crystal lattice could produce vacances, interstities, and other types of defects. These defects could be traped in the impurity centers, for example, and could form active defects leading to the changes in the characteristics of the photodetectros, primarilly the decrease of the minority carrier lifetime. Radiation damage due to neutrons (heavy particles) is, as mentioned above, primarily connected to the displacement of silicon atoms from their lattice sites in the crystalline silicon solar cells, leading to destruction and distortion of local lattice structure and formation of defects. If, under the influence of neutrons, stable defects are made, they could, together with impurity atoms, donors and for example implanted atoms, form complex defects acting as recombination sites or traps, significantly decreasing

The main effect of radiation on photodiodes and solar cells is an increase in the dark current generated within or at the surface of the depletion region. Generation of electron–hole pairs due to ionization effects and displacement damage induced by neutrons, result in the generation and increase of the noise and the minimum signal that can be detected. Since presence of the noise could be connected to the excess current, measurement of the *I-V*

radiation induced defects represent very good example of such a centers.

of these effects could be permenent or quasi-permenent.

**3.1 Radiation damage in solar cells and photodiodes** 

minority carrier lifetime.

performance of the photodiodes and solar cells.

characteristics before and after irradiation reveals the extent of degradation of electrical properties of photodiodes.

Although polycrystalline and monocrystalline solar cells are more reliable than amorphous, inherent presence of defects and impurities in the basic material could, during time, produce some negative effects. This is specially emphasized if those states are located within the energy gap and are activated during work. In such a case they become traps for optically produced electron-hole pairs, and thus decrease the number of collected charge carriers. Macroscopically, this effect could be observed as a decrease of the output current and voltage, and ultimately could lead to the decrease of the efficiency of solar cell. Lower values of short-circuit current indicate the existence of the recombination centers that decrease the mobility and diffusion length of the charge carriers, making the recombination in the depletion region dominant transport in such solar cells (Vasic et al., 2000, 2003). The lifetime of the solar cell is restricted by the degree of radiation damage that the cell receives. This is an important factor that affects the performance of the solar cell in practical applications. The permanent damage in the solar cells materials is caused by collisions of the incident radiation particles with the atoms in the crystalline lattice, which are displaced from their positions. These defects degrade the transport properties of the material and particularly the minority carrier lifetime (Alurralde et al., 2004, Horiushi et al., 2000, Zhenyu et al., 2004). This lifetime decrease produces degradation of the parameters of the cell ultimately leading to an increase of the noise level. The interaction between vacancies, selfinterstitials, impurities, and dopants in Si leads to the formation of undesirable point defects such as recombination and compensator centers which affects performance of the solar cells, especially in space. Introduction of radiation-induced recombination centers reduce the minority carrier lifetime in the base layer of the p-n junction increasing series resistance. After very high doses of radiation series resistance of the base layer could be so high that most of the power generated by the device is dissipated by its own internal resistance (Khan et al., 2003).

Fig. 7. Simulation of the dependence of *P*-*V* characteristics on *n* (Vasic et al., 2011).

Characterization of Thin Films for Solar Cells

(for different types of solar cells).

1E-10

1E-9

1p 1c

1E-8

*J0* [A/cm2

]

1E-7

1E-6

centers.

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 291

contribute to the diode current. Since the ideality factor is the direct indicator of the output parameter dependence on the electrical transport properties, measurements of the *n*(*V*) dependence along with the *I*-*V* measurements at different irradiation doses, could narrow down possibilities of the dominant current component. Also, values of the ideality factor could indicate not only the transport mechanism, but indirectly, the presence and possible activation of the defects and impurities, acting as recombination and/or tunneling

The influence of the ideality factor on the solar cell efficiency is predominantly through the voltage, i.e. the decrease of the efficiency with the increase of the ideality factor is the result of the voltage decrease in the maximum power point. Physical basis of such dependence lies in the connection between the ideality factor and saturation current density shown in Fig. 9

1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

*n*

Direct connection between *J0* and *n* (nearly exponential increase of saturation current density with the increase of *n*) produces the decrease of the efficiency with the increase of either of these parameters. In the radiation environment, such an increase is usually the result of induced defects and/or activation of the existent impurities that could act as a recombination centers for the charge carriers, altering the dominant current transport. Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depend on various parameters such as, density of the interface states, concentration of the impurity defects, and also devises operating voltage. Existence of the *n*(*V*) dependence is the result of such a junction imperfections, leading to domination of different transport mechanisms in different voltage regions. Therefore, measuring and monitoring the *n*(*V*) dependence which is possible even in working conditions, could reveal not only the degree of degradation, but also, possible instabilities of the device in certain voltage regions. This is especially important if those instabilities occur in the voltage region where maximum power is transferred to the load. Although still in working condition, performances of such solar cells (efficiency, for most) are considerably degraded, so that monitoring of the device characteristics should be performed

5l

4p

Fig. 9. Saturation current dencity dependence on ideality factor (Vasic et al., 2000).

10l

7l

Capability of solar cell to convert solar energy into electrical, depends on various fundamental and technological parameters. Variations from the ideal case of current transport could be represented by the ideality factor that could be easily obtained from *I*-*V* characteristics of solar cells. The non-ideal behaviour of the device is reflected in the values of *n* greater than 1, and that is the result of the presence of different transport mechanisms that can contribute to the diode current.

Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depends on various parameters, such as density of the interface states, concentration of the impurities and defects, height of the potential barrier, device voltage, and device temperature. The dependence of the maximum power on the ideality factor could be seen in Fig. 7.

Considering the fact that maximum power point depends on the resistance (and ideality factor as well), series and parallel resistance should be maintained at such a values to obtain maximum efficiency. Also, voltage decrease in the maximum power point (*Pm*) has great influence on the efficiency. One of the main reasons for this decrease is the increase of the ideality factor, so it could be said that the influence of the ideality factor on the solar cell efficiency is through the voltage. Set of the experimentally obtained = f(*n*) dependencies for different solar cells is shown in Fig. 8 (Vasic et al., 2000).

Fig. 8. Efficiency dependence on the ideality factor (Vasic et al., 2000).

Regardless to the type of radiation used, damage to even a small portion of the individual solar cell results in an increase in saturation (leakage) current for whole cell. The cell diode saturation current (or more commonly used its density) *J0*, increases with the decreased minority carrier lifetime. On the other hand, the minority carrier lifetime decreases due to the ionization effects and displacement damage in the depletion region, caused by the incident radiation. In consequence, this reduces the cell open circuit voltage *Voc*. Since forward-biased cell diode current increases for all diode voltages, the current available to the load decreases, so that the maximum power delivered to the load, *Pmax*, will also decrease, leading to the substantial drop of the cell efficiency . Such non-ideal behavior of the device is usually reflected in the values of the ideality factor *n* greater than 1, as the result of the presence of different transport mechanisms in different voltage regions that can

Capability of solar cell to convert solar energy into electrical, depends on various fundamental and technological parameters. Variations from the ideal case of current transport could be represented by the ideality factor that could be easily obtained from *I*-*V* characteristics of solar cells. The non-ideal behaviour of the device is reflected in the values of *n* greater than 1, and that is the result of the presence of different transport mechanisms

Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depends on various parameters, such as density of the interface states, concentration of the impurities and defects, height of the potential barrier, device voltage, and device temperature. The dependence of the maximum power on the

Considering the fact that maximum power point depends on the resistance (and ideality factor as well), series and parallel resistance should be maintained at such a values to obtain maximum efficiency. Also, voltage decrease in the maximum power point (*Pm*) has great influence on the efficiency. One of the main reasons for this decrease is the increase of the ideality factor, so it could be said that the influence of the ideality factor on the solar cell

1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

*n*

Regardless to the type of radiation used, damage to even a small portion of the individual solar cell results in an increase in saturation (leakage) current for whole cell. The cell diode saturation current (or more commonly used its density) *J0*, increases with the decreased minority carrier lifetime. On the other hand, the minority carrier lifetime decreases due to the ionization effects and displacement damage in the depletion region, caused by the incident radiation. In consequence, this reduces the cell open circuit voltage *Voc*. Since forward-biased cell diode current increases for all diode voltages, the current available to the load decreases, so that the maximum power delivered to the load, *Pmax*, will also

the device is usually reflected in the values of the ideality factor *n* greater than 1, as the result of the presence of different transport mechanisms in different voltage regions that can

5l

4p

10l

7l

. Such non-ideal behavior of

= f(*n*) dependencies

efficiency is through the voltage. Set of the experimentally obtained

1c 1p

Fig. 8. Efficiency dependence on the ideality factor (Vasic et al., 2000).

decrease, leading to the substantial drop of the cell efficiency

for different solar cells is shown in Fig. 8 (Vasic et al., 2000).

10

11

12

13

*Efficiency* [%]

14

15

16

that can contribute to the diode current.

ideality factor could be seen in Fig. 7.

contribute to the diode current. Since the ideality factor is the direct indicator of the output parameter dependence on the electrical transport properties, measurements of the *n*(*V*) dependence along with the *I*-*V* measurements at different irradiation doses, could narrow down possibilities of the dominant current component. Also, values of the ideality factor could indicate not only the transport mechanism, but indirectly, the presence and possible activation of the defects and impurities, acting as recombination and/or tunneling centers.

The influence of the ideality factor on the solar cell efficiency is predominantly through the voltage, i.e. the decrease of the efficiency with the increase of the ideality factor is the result of the voltage decrease in the maximum power point. Physical basis of such dependence lies in the connection between the ideality factor and saturation current density shown in Fig. 9 (for different types of solar cells).

Fig. 9. Saturation current dencity dependence on ideality factor (Vasic et al., 2000).

Direct connection between *J0* and *n* (nearly exponential increase of saturation current density with the increase of *n*) produces the decrease of the efficiency with the increase of either of these parameters. In the radiation environment, such an increase is usually the result of induced defects and/or activation of the existent impurities that could act as a recombination centers for the charge carriers, altering the dominant current transport.

Determination of the dominant current mechanism is very difficult because the relative magnitude of these components depend on various parameters such as, density of the interface states, concentration of the impurity defects, and also devises operating voltage. Existence of the *n*(*V*) dependence is the result of such a junction imperfections, leading to domination of different transport mechanisms in different voltage regions. Therefore, measuring and monitoring the *n*(*V*) dependence which is possible even in working conditions, could reveal not only the degree of degradation, but also, possible instabilities of the device in certain voltage regions. This is especially important if those instabilities occur in the voltage region where maximum power is transferred to the load. Although still in working condition, performances of such solar cells (efficiency, for most) are considerably degraded, so that monitoring of the device characteristics should be performed

Characterization of Thin Films for Solar Cells

initial *Jsc*.

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 293

correspond to deep energy level in the silicon energy gap, they act as efficient surface recombination centers for charge carriers. Generation of electron-hole pairs due to ionization effects usually result in the generation and an increase of the noise and minimum signal that can be detected. All of these effects lead to the decrease of output current. Steeper decrease of the *Jsc* for higher illumination levels indicates that recombination centers could be both optically activated and activated by irradiation. Therefore, solar cells exposed to the higher values of solar irradiation during their performance could exhibit greater decrease in the

Additionally, if solar cells are polycrystalline, so presence of grain boundaries, characteristic for the polycrystalline material, has great influence on the collection of the photogenerated carriers. Presence of the recombination centers, small diffusion length and minority carrier lifetime, as a result of either irradiation or aging, finally leads to the decrease of the efficiency of solar cells. As could be seen in Fig. 12, this decrease is very pronounced, regardless of the illumination level. Although initial efficiencies were slightly different for different illumination levels, after irradiation they became almost equal, indicating that radiation gas greater influence on production and transport of charge carriers than illumination. That, from the standpoint of solar cells, could be very limiting factor for their performance. Combined influence of the increased 1/f and burst noise due to radiation induced damage has significant negative influence on major solar cells characteristics.

0 1000 2000 3000 4000 5000 6000

Dose [kGy]

All of this inevitably leads to the decrease of the resolution of the photodetector devices, lowering solar cells efficiency and for this reason, monitoring of the device characteristics should be performed continuously, especially when solar cells are exposed to the severe

The lifetime decrease of the charge carriers due to the radiation damage induced by neutrons, produces degradation of electrical parameters of the cell, such as series resistance (*Rs*), output current and finally efficiency (*η*). High level of series resistance usually indicate

working conditions.

Fig. 12. Dependence of the efficiency on doses (Vasic et al., 2007).

**3.2 Possibilities of the improvement of solar cells and photodetectors** 

Efficiency [%]

continuously, especially if solar cells are exposed to severe working conditions, such as radiation environment.

Although effects of gamma irradiation on the solar cells are known to be primarily through ionization effects, increase of series resistance could also be observed, Fig. 10 (Vasic et al., 2007, 2010).

Fig. 10. Dependence of *Rs* on doses for polycrystalline solar cells (Vasic et al., 2007).

Almost linear dependence of series resistance on the absorbed irradiation dose indicates that some changes in the collection of the charge carriers have occurred. This behaviour of *Rs* is reflected mostly on the short-circuit current density *Jsc*, since radiation induced activation of defects and impurities mainly affects the transport mechanisms in the device. Dependence of the *Jsc* on the absorbed dose for different illumination levels was shown in Fig. 11.

Fig. 11. Dependence of the Jsc on doses for polycrystalline solar cells (Vasic et al., 2007).

Due to the inevitable presence of surface energy states (as a result of lattice defects, dislocations, impurities, etc.), after silicon is irradiated with gamma photons, both the surface recombination velocity and the density of surface states increase. If those states

continuously, especially if solar cells are exposed to severe working conditions, such as

Although effects of gamma irradiation on the solar cells are known to be primarily through ionization effects, increase of series resistance could also be observed, Fig. 10 (Vasic et al.,

0 1000 2000 3000 4000 5000 6000

0 1000 2000 3000 4000 5000 6000

Dose [kGy]

Due to the inevitable presence of surface energy states (as a result of lattice defects, dislocations, impurities, etc.), after silicon is irradiated with gamma photons, both the surface recombination velocity and the density of surface states increase. If those states

Fig. 11. Dependence of the Jsc on doses for polycrystalline solar cells (Vasic et al., 2007).

Dose [kGy]

Almost linear dependence of series resistance on the absorbed irradiation dose indicates that some changes in the collection of the charge carriers have occurred. This behaviour of *Rs* is reflected mostly on the short-circuit current density *Jsc*, since radiation induced activation of defects and impurities mainly affects the transport mechanisms in the device. Dependence of the *Jsc* on the absorbed dose for different illumination levels was shown in

Fig. 10. Dependence of *Rs* on doses for polycrystalline solar cells (Vasic et al., 2007).

*J*

*sc* [mA/cm2

]

*Rs* [Ohm]

radiation environment.

2007, 2010).

Fig. 11.

correspond to deep energy level in the silicon energy gap, they act as efficient surface recombination centers for charge carriers. Generation of electron-hole pairs due to ionization effects usually result in the generation and an increase of the noise and minimum signal that can be detected. All of these effects lead to the decrease of output current. Steeper decrease of the *Jsc* for higher illumination levels indicates that recombination centers could be both optically activated and activated by irradiation. Therefore, solar cells exposed to the higher values of solar irradiation during their performance could exhibit greater decrease in the initial *Jsc*.

Additionally, if solar cells are polycrystalline, so presence of grain boundaries, characteristic for the polycrystalline material, has great influence on the collection of the photogenerated carriers. Presence of the recombination centers, small diffusion length and minority carrier lifetime, as a result of either irradiation or aging, finally leads to the decrease of the efficiency of solar cells. As could be seen in Fig. 12, this decrease is very pronounced, regardless of the illumination level. Although initial efficiencies were slightly different for different illumination levels, after irradiation they became almost equal, indicating that radiation gas greater influence on production and transport of charge carriers than illumination. That, from the standpoint of solar cells, could be very limiting factor for their performance. Combined influence of the increased 1/f and burst noise due to radiation induced damage has significant negative influence on major solar cells characteristics.

Fig. 12. Dependence of the efficiency on doses (Vasic et al., 2007).

All of this inevitably leads to the decrease of the resolution of the photodetector devices, lowering solar cells efficiency and for this reason, monitoring of the device characteristics should be performed continuously, especially when solar cells are exposed to the severe working conditions.

#### **3.2 Possibilities of the improvement of solar cells and photodetectors**

The lifetime decrease of the charge carriers due to the radiation damage induced by neutrons, produces degradation of electrical parameters of the cell, such as series resistance (*Rs*), output current and finally efficiency (*η*). High level of series resistance usually indicate

Characterization of Thin Films for Solar Cells

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Fig. 14. Dependence of the *Jm* on doses (Vasic et al., 2008).

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

Fig. 15. Dependence of the efficiency on doses (Vasic et al., 2008).

Efficiency [%]

quality.

*Jm* [mA/cm2

]

and Photodetectors and Possibilities for Improvement of Solar Cells Characteristics 295

 32 W/m<sup>2</sup> 58 W/m<sup>2</sup>

 32 W/m<sup>2</sup> 58 W/m<sup>2</sup>

0 50 100 150 200

0 50 100 150 200

Though commonly referred to as a source of noise in semiconducting devices, radiation induced effects (interaction of neutrons with Si solar cells, in particular) could have in some cases positive effect on main electrical characteristics (*Rs*, *Jm*, *η*). Initial improvement of the characteristics observed for small doses of neutron radiation and low illumination level, indicates that there is a possibility of using irradiation for enhancement of the solar cells

Dose [mGy]

Dose [mGy]

the presence of impurity atoms and defects localized in the depletion region acting as traps for recombination or tunneling effects, increasing dark current of the cell (Alexander, 2003, Holwes-Siedle & Adams, 2002). Moreover, shallow recombination centers in the vicinity of conducting zone enhance tunneling effect, further degrading output characteristics of the cell by increasing noise level (especially burst noise that is connected to the presence of excess current).

Such negative impact of neutron radiation was observed higher illumination level, as could be seen in Fig. 13 (Vasic et al., 2008). But interesting phenomena – the decrease of series resistance, was observed for lower values of illumination. (Different behavior for different illumination level is due to the presence of finite series and parallel resistance in the cell.) This decrease is very significant from the solar cell design standpoint because it indicates possible beneficent influence of low doses of irradiation, even with neutrons. It could be explained by the fact that during fabrication process of any semiconducting device, structural defects and impurities that were unavoidably made, produce tension in the crystal lattice. Low doses of radiation could act similarly to annealing, relaxing lattice structure and decreasing series resistance. Subsequently, this leads to lowering of noise level and an increase of the output current as shown in Fig.14 (*Jm* – current in the maximum power point).

Fig. 13. Dependence of *Rs* on doses for two illumination levels (Vasic et al., 2008).

Other parameters of solar cells (voltage in the maximum power point *Vm* , fill factor *ff* and efficiency) have shown the similar tendencies, which is not surprising since, as it is well known, high series resistance of the solar cell is one of the main limiting factors of the efficiency. So, it could be expected that all the main output parameters of the solar cell should exhibit the same behavior as series resistance in the relation to the irradiation dose.

Finally, improvement of output characteristics after the first irradiation step for low illumination level is registered for the efficiency also, Fig. 15. Although higher doses of neutron radiation undoubtedly have negative impact on the performance of solar cells, observed phenomena give possibilities for using radiation as a method for the improvement of solar cell characteristics.

the presence of impurity atoms and defects localized in the depletion region acting as traps for recombination or tunneling effects, increasing dark current of the cell (Alexander, 2003, Holwes-Siedle & Adams, 2002). Moreover, shallow recombination centers in the vicinity of conducting zone enhance tunneling effect, further degrading output characteristics of the cell by increasing noise level (especially burst noise that is connected to the presence of

Such negative impact of neutron radiation was observed higher illumination level, as could be seen in Fig. 13 (Vasic et al., 2008). But interesting phenomena – the decrease of series resistance, was observed for lower values of illumination. (Different behavior for different illumination level is due to the presence of finite series and parallel resistance in the cell.) This decrease is very significant from the solar cell design standpoint because it indicates possible beneficent influence of low doses of irradiation, even with neutrons. It could be explained by the fact that during fabrication process of any semiconducting device, structural defects and impurities that were unavoidably made, produce tension in the crystal lattice. Low doses of radiation could act similarly to annealing, relaxing lattice structure and decreasing series resistance. Subsequently, this leads to lowering of noise level and an increase of the output current as shown in Fig.14 (*Jm* – current in the maximum

0 50 100 150 200

Other parameters of solar cells (voltage in the maximum power point *Vm* , fill factor *ff* and efficiency) have shown the similar tendencies, which is not surprising since, as it is well known, high series resistance of the solar cell is one of the main limiting factors of the efficiency. So, it could be expected that all the main output parameters of the solar cell should exhibit the same behavior as series resistance in the relation to the irradiation dose. Finally, improvement of output characteristics after the first irradiation step for low illumination level is registered for the efficiency also, Fig. 15. Although higher doses of neutron radiation undoubtedly have negative impact on the performance of solar cells, observed phenomena give possibilities for using radiation as a method for the improvement

Fig. 13. Dependence of *Rs* on doses for two illumination levels (Vasic et al., 2008).

Dose [mGy]

 32 W/m<sup>2</sup> 58 W/m<sup>2</sup>

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

of solar cell characteristics.

*Rs* [Ohm]

excess current).

power point).

Fig. 14. Dependence of the *Jm* on doses (Vasic et al., 2008).

Fig. 15. Dependence of the efficiency on doses (Vasic et al., 2008).

Though commonly referred to as a source of noise in semiconducting devices, radiation induced effects (interaction of neutrons with Si solar cells, in particular) could have in some cases positive effect on main electrical characteristics (*Rs*, *Jm*, *η*). Initial improvement of the characteristics observed for small doses of neutron radiation and low illumination level, indicates that there is a possibility of using irradiation for enhancement of the solar cells quality.

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### **4. Conclusion**

Single element optical detectors such as solar cells and photodiodes are the final component needed for a communications or optical information processing systems. Due to wide area of application, they are often exposed to the variety of radiation effects (natural space environment, atmospheric environment, military and civil nuclear environment). Therefore, the extensive studies concerning the development of semiconductor devices that can operate normally in a radiation environment have been undertaken. Although proven to be reliable in terrestrial applications, solar systems are (like other semiconductor devices) sensitive to variety of radiation environments in which they are used. Performance failure could have negative impact both on the financial and environmental aspects of the device application. From a technological point of view, it is important to study the variations induced by irradiation of semiconductor junction characteristic parameters (reverse saturation current, ideality factor etc.), that affect the performance of the solar cells and photodiodes.

#### **5. Acknowledgment**

The Ministry of Science and Technological Development of the Republic of Serbia supported this work under contract 171007.

#### **6. References**


Single element optical detectors such as solar cells and photodiodes are the final component needed for a communications or optical information processing systems. Due to wide area of application, they are often exposed to the variety of radiation effects (natural space environment, atmospheric environment, military and civil nuclear environment). Therefore, the extensive studies concerning the development of semiconductor devices that can operate normally in a radiation environment have been undertaken. Although proven to be reliable in terrestrial applications, solar systems are (like other semiconductor devices) sensitive to variety of radiation environments in which they are used. Performance failure could have negative impact both on the financial and environmental aspects of the device application. From a technological point of view, it is important to study the variations induced by irradiation of semiconductor junction characteristic parameters (reverse saturation current,

ideality factor etc.), that affect the performance of the solar cells and photodiodes.

The Ministry of Science and Technological Development of the Republic of Serbia supported

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**4. Conclusion** 

**5. Acknowledgment** 

**6. References** 

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**14** 

 *Moldova* 

**Solar Cells on the** 

**Base of Semiconductor-**

*Institute of Applied Physics, Academy of Sciences,* 

**Insulator-Semiconductor Structures** 

Alexei Simaschevici, Dormidont Serban and Leonid Bruc

The conventional energy production is not based on sustainable methods, hence exhausting the existing natural resources of oil, gas, coal, nuclear fuel. The conventional energy systems also cause the majority of environmental problems. Only renewable energy systems can meet, in a sustainable way, the growing energy demands without detriment to the

The photovoltaic conversion of solar energy, which is a direct conversion of radiation energy into electricity, is one of the main ways to solve the above-mentioned problem. The first PV cells were fabricated in 1954 at Bell Telephone Laboratories (Chapin et al., 1954); the first applications for space exploration were made in the USA and the former USSR in 1956. The first commercial applications for terrestrial use of PV cells were ten years later. The oil crisis of 1972 stimulated the research programs on PV all over the word and in 1975 the terrestrial market exceeds the spatial one 10 times. Besides classical solar cells (SC) based on p-n junctions new types of SC were elaborated and investigated: photoelectrochemical cells, SC based on Schottky diodes or MIS structures and semiconductor-insulator-semiconductor (SIS) structures, SC for concentrated radiation, bifacial SC. Currently, researchers are focusing their attention on lowering the cost of electrical energy produced by PV modules. In this regard, SC on the base of SIS structures are very promising, and recently the SIS structures have been recommended as low cost photovoltaic solar energy converters. For their fabrication, it is not necessary to obtain a p-n junction because the separation of the charge carriers generated by solar radiation is realized by an electric field at the insulatorsemiconductor interface. Such SIS structures are obtained by the deposition of thin films of transparent conductor oxides (TCO) on the oxidized silicon surface. A overview on this

Basic investigations of the ITO/Si SIS structures have been carried out and published in the USA (DuBow et al., 1976; Mizrah et al., 1976; Shewchun et al., 1978; Shewchun et al, 1979) Theoretical and experimental aspects of the processes that take place in these structures are examined in those papers. Later on the investigations of SC based on SIS structures using, as an absorber component, Si, InP and other semiconductor materials have been continued in Japan (Nagatomo et al., 1982; Kobayashi, et al., 1991), India (Vasu & Subrahmanyam, 1992; Vasu et al., 1993), France (Manifacier & Szepessy, 1977; Caldererer et al., 1979), Ukraine

**1. Introduction** 

environment.

subject was presented in (Malik et al., 2009).

Vasic,A., Loncar, B., Vujisic, M., Stankovic, K., & Osmokrovic, P. (2010). Aging of the Photovoltaic Solar Cells, Proceedings of 27th IEEE International Conference on Microelectronics, pp. 487-490, ISBN 1-4244-0116-x, Nis, Serbia, May 2010
