**3. Optimizing material and configuration for typical DSSCs**

Numerous publications and review articles on DSSC have appeared in the literature for certain aspects of the DSSC fabrication or performance during the past three decades [26–30]. Proto-type module cells for manufacturing are actively under development [31–35]. This book reviews systematical parameters via controlled experiments (such as materials preparation, processing, device fabrication and assembly, measurements and device modeling) and the interfacial properties introduced by electrochemical impedance spectroscopy (EIS) for making better solar performance [36–38]. The inherent material properties such as impurity, surface properties in the DSSC are studied from this powerful tool for studying the kinetics of charge transport and electron–hole recombination. Furthermore, this book suggests other ways to improve cell efficiency externally from the photon confinement.

Suppose the complex impedance is the same as its resistance. (*Z* = *R*) *R*<sup>o</sup> represents the ohmic contact resistance from the FTO and the metal. The impedance of the electron transfer at the Pt counter electrode (Z*1*) can be modeled as an RC

(15)

*<sup>Z</sup>*<sup>1</sup> <sup>¼</sup> <sup>1</sup> 1 *rp*<sup>1</sup> þ *iωCp*<sup>1</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *iω <sup>D</sup>*1*=δ*<sup>2</sup> � � <sup>s</sup>

film respectively. *RD* is the DC resistance of impedance of diffusion of tri-iodide. The number of electrons transferred in each reaction, m, is 2 in this case. *A*<sup>v</sup> and *C*\*

Here *n* is the excess electron density in the CB of the TiO2 under illumination, *N* is the excess electron density of the trap sites, *Dcb* describes the diffusion coefficient of an electron in the CB and the function *G* is the generation rate of electrons injected into the TiO2 [40]. By varying the potentials, the excess CB electron

*n x*ð Þ¼ , *t nS*ð Þþ *x*, *t* Δ*n x*ð Þ*e*

*D*eff ¼ *D*cb

Here, *ns* and *Ns* describe the steady state electron densities (Δ*n* and Δ*N* are the amplitudes of the modulated component) in the CB and the trap state, respectively.

> *k*2 *k*2

*k*eff ¼ 2*N*s*k*<sup>r</sup> (22)

*N x*ð Þ¼ , *t NS*ð Þþ *x*, *t* Δ*N x*ð Þ*e*

The impedance *Z***<sup>2</sup>** of the charge transport through diffusion into the mesoporous TiO2 and recombination at the TiO2/dye/electrolyte interface shows in the middle semicircle of the EIS graph. As seen in **Figure 2**, photoexcited electrons in the CB will decay and excite at rate *k***<sup>1</sup>** and *k***<sup>2</sup>** into surface trap states of the TiO2 as well as the back reaction in the iodine electrolyte at a rate of (*k***r**). The charge transfer kinetics for injection, diffusion, collection, trapping, de-trapping and recombination of electrons in the TiO2 of the DSSC can be calculated by

where, *r*p1, *Cp*<sup>1</sup> describes the resistance and capacitance at the Pt coated CE,

*Z3* represents the finite Warburg impedance contributes to the diffusion impedance for the diffusion of tri-iodide ions in the electrolyte at the low frequency region

*where RD* <sup>¼</sup> *kBT*

*<sup>∂</sup>x*<sup>2</sup> � *<sup>k</sup>*1*n x*ð Þþ , *<sup>t</sup> <sup>k</sup>*2ð Þþ *<sup>x</sup>*, *<sup>t</sup> G x*ð Þ , *<sup>t</sup>* (17)

*<sup>∂</sup><sup>t</sup>* ¼ �*k*2*N x*ð Þ� , *<sup>t</sup> <sup>k</sup>*r*N*<sup>2</sup> <sup>þ</sup> *<sup>k</sup>*1*<sup>n</sup>* (18)

*<sup>m</sup>*<sup>2</sup>*q*<sup>2</sup>*AvC*<sup>∗</sup> *<sup>D</sup>*1*<sup>δ</sup>* (16)

� and the thickness of the liquid

� in the bulk, respectively.

*<sup>i</sup>ω<sup>t</sup>* (19)

*<sup>i</sup>*ð Þ *<sup>ω</sup>t*þ*<sup>φ</sup>* (20)

(21)

parallel circuit, and simply expressed as:

*A New Generation of Energy Harvesting Devices DOI: http://dx.doi.org/10.5772/intechopen.94291*

with a frequency maxima of ωz3 [40, 44].

1 ffiffiffiffiffiffiffiffiffiffiffiffi *<sup>i</sup><sup>ω</sup> <sup>D</sup>*1*=δ*<sup>2</sup> ð Þ <sup>q</sup> tanh

*<sup>∂</sup>n x*ð Þ , *<sup>t</sup>*

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> *Dcb*

density *n*(*x,t*) will be expressed as followed [39].

*∂*2 *n x*ð Þ , *t*

*<sup>∂</sup>N x*ð Þ , *<sup>t</sup>*

*D***<sup>1</sup>** and *δ* represent the diffusion coefficient of I3

are the Avogadro number and the concentration of I3

respectively.

[39, 40]:

Defining,

**193**

*Z*<sup>3</sup> ¼ *RD*

### **3.1 Understanding DSSC operation model by EIS**

As mentioned in Section 1. diverse electrochemical processes take place in a DSSC during the cell operation. The I-V curves provide the information on the basic parameters such as short-circuit current (*ISC*), open-circuit potential (*VOC*), Fill factor (*FF*), and cell efficiency (*η*). The impedance spectroscopy measurements are widely used for investigating the properties of a broad class of material system and device. It provides essential information on carrier transport and recombination. In EIS measurement, a direct current (DC) signal is applied to the cell by a small sinusoidal alternating current (AC) perturbation under steady light illumination. From the measured current response, the magnitude of the impedance for amplitude and phase shift is determined as a function of modulation frequency. From the relevant equivalent circuit, the measured data are fitted by some software (such as Zview or Gamry Echem Analyst etc) and the charge transfer kinetics in a DSSC can be estimated.

In this book, for a deep comprehensive understanding of the device operation, Adachi model are employed to figure out the key parameters that control the efficiency of a DSSC [39–42]. **Figure 1** shows the schematic diagram of DSSC structure. In this system, the light comes from the indium or fluorine doped tin oxide (ITO or FTO) coated transparent conductive glass, the sheet resistance as small as 10 Ω/sq. is required, as an anode electrode (left) [43]. An insulating blocking layer and mesoporous metal oxide film (TiO2 ZnO, SnO2 etc.) is deposited on top of bottom electrode. Next, dye molecules are covered by the surface of mesoporous metal oxide and iodine electrolyte is interpenetrated into metal oxide/ dye layer. The platinum coated FTO substrate is used as a catalyst for iodide reduction as the counter electrode (right).

The kinetic behavior of charge trap and de-trap mechanism from electrochemical and photoelectrochemical processes affects the different capacitive and resistive element of faradaic impedance. EIS data generally shows Nyquist and Bode plots. An general plot shows x-axis the real impedance (Z') versus the y-axis the imaginary impedance (Z") in the complex plane. From EIS analysis, the complex impedance *(Z)* of each component express *Z*0, *Z*1, *Z*2, and *Z*3, respectively. (i.e. **Z0** is the contact impedance of conductive glass; **Z1** is the Pt-catalyzed counter electrode impedance; **Z2** is the complex impedance for the interfacial resistivity among metal oxide, dye molecule, and the iodine electrolyte; **Z3** is the Warburg impedance for diffusion of tri-iodide ions). The resulting data from impedance is directly linked to the information on materials quality, internal, interfacial properties of the DSSC.

**3. Optimizing material and configuration for typical DSSCs**

**3.1 Understanding DSSC operation model by EIS**

*Solar Cells - Theory, Materials and Recent Advances*

reduction as the counter electrode (right).

confinement.

be estimated.

of the DSSC.

**192**

Numerous publications and review articles on DSSC have appeared in the literature for certain aspects of the DSSC fabrication or performance during the past three decades [26–30]. Proto-type module cells for manufacturing are actively under development [31–35]. This book reviews systematical parameters via controlled experiments (such as materials preparation, processing, device fabrication and assembly, measurements and device modeling) and the interfacial properties introduced by electrochemical impedance spectroscopy (EIS) for making better solar performance [36–38]. The inherent material properties such as impurity, surface properties in the DSSC are studied from this powerful tool for studying the kinetics of charge transport and electron–hole recombination. Furthermore, this book suggests other ways to improve cell efficiency externally from the photon

As mentioned in Section 1. diverse electrochemical processes take place in a DSSC during the cell operation. The I-V curves provide the information on the basic parameters such as short-circuit current (*ISC*), open-circuit potential (*VOC*), Fill factor (*FF*), and cell efficiency (*η*). The impedance spectroscopy measurements are widely used for investigating the properties of a broad class of material system and device. It provides essential information on carrier transport and recombination. In EIS measurement, a direct current (DC) signal is applied to the cell by a small sinusoidal alternating current (AC) perturbation under steady light illumination. From the measured current response, the magnitude of the impedance for amplitude and phase shift is determined as a function of modulation frequency. From the relevant equivalent circuit, the measured data are fitted by some software (such as Zview or Gamry Echem Analyst etc) and the charge transfer kinetics in a DSSC can

In this book, for a deep comprehensive understanding of the device operation,

The kinetic behavior of charge trap and de-trap mechanism from electrochemical and photoelectrochemical processes affects the different capacitive and resistive element of faradaic impedance. EIS data generally shows Nyquist and Bode plots. An general plot shows x-axis the real impedance (Z') versus the y-axis the imaginary impedance (Z") in the complex plane. From EIS analysis, the complex impedance *(Z)* of each component express *Z*0, *Z*1, *Z*2, and *Z*3, respectively. (i.e. **Z0** is the contact impedance of conductive glass; **Z1** is the Pt-catalyzed counter electrode impedance; **Z2** is the complex impedance for the interfacial resistivity among metal oxide, dye molecule, and the iodine electrolyte; **Z3** is the Warburg impedance for diffusion of tri-iodide ions). The resulting data from impedance is directly linked to the information on materials quality, internal, interfacial properties

Adachi model are employed to figure out the key parameters that control the efficiency of a DSSC [39–42]. **Figure 1** shows the schematic diagram of DSSC structure. In this system, the light comes from the indium or fluorine doped tin oxide (ITO or FTO) coated transparent conductive glass, the sheet resistance as small as 10 Ω/sq. is required, as an anode electrode (left) [43]. An insulating blocking layer and mesoporous metal oxide film (TiO2 ZnO, SnO2 etc.) is deposited on top of bottom electrode. Next, dye molecules are covered by the surface of mesoporous metal oxide and iodine electrolyte is interpenetrated into metal oxide/ dye layer. The platinum coated FTO substrate is used as a catalyst for iodide

Suppose the complex impedance is the same as its resistance. (*Z* = *R*) *R*<sup>o</sup> represents the ohmic contact resistance from the FTO and the metal. The impedance of the electron transfer at the Pt counter electrode (Z*1*) can be modeled as an RC parallel circuit, and simply expressed as:

$$Z\_1 = \frac{1}{\frac{1}{r\_{p1}} + i\alpha C\_{p1}}\tag{15}$$

where, *r*p1, *Cp*<sup>1</sup> describes the resistance and capacitance at the Pt coated CE, respectively.

*Z3* represents the finite Warburg impedance contributes to the diffusion impedance for the diffusion of tri-iodide ions in the electrolyte at the low frequency region with a frequency maxima of ωz3 [40, 44].

$$Z\_3 = R\_D \frac{1}{\sqrt{\frac{i\nu}{(D\_1/\delta^2)}}} \tanh\sqrt{\frac{i\nu}{(D\_1/\delta^2)}} \text{ where } R\_D = \frac{k\_B T}{m^2 q^2 A v C^\* D\_1 \delta} \tag{16}$$

*D***<sup>1</sup>** and *δ* represent the diffusion coefficient of I3 � and the thickness of the liquid film respectively. *RD* is the DC resistance of impedance of diffusion of tri-iodide. The number of electrons transferred in each reaction, m, is 2 in this case. *A*<sup>v</sup> and *C*\* are the Avogadro number and the concentration of I3 � in the bulk, respectively.

The impedance *Z***<sup>2</sup>** of the charge transport through diffusion into the mesoporous TiO2 and recombination at the TiO2/dye/electrolyte interface shows in the middle semicircle of the EIS graph. As seen in **Figure 2**, photoexcited electrons in the CB will decay and excite at rate *k***<sup>1</sup>** and *k***<sup>2</sup>** into surface trap states of the TiO2 as well as the back reaction in the iodine electrolyte at a rate of (*k***r**). The charge transfer kinetics for injection, diffusion, collection, trapping, de-trapping and recombination of electrons in the TiO2 of the DSSC can be calculated by [39, 40]:

$$\frac{\partial n(\varkappa, t)}{\partial t} = D\_{cb} \frac{\partial^2 n(\varkappa, t)}{\partial \varkappa^2} - k\_1 n(\varkappa, t) + k\_2(\varkappa, t) + G \ (\varkappa, t) \tag{17}$$

$$\frac{\partial N(\mathbf{x},t)}{\partial t} = -k\_2 N(\mathbf{x},t) - k\_1 N^2 + k\_1 n \tag{18}$$

Here *n* is the excess electron density in the CB of the TiO2 under illumination, *N* is the excess electron density of the trap sites, *Dcb* describes the diffusion coefficient of an electron in the CB and the function *G* is the generation rate of electrons injected into the TiO2 [40]. By varying the potentials, the excess CB electron density *n*(*x,t*) will be expressed as followed [39].

$$n(\varkappa, t) = n\_S(\varkappa, t) + \Delta n(\varkappa)e^{i\alpha t} \tag{19}$$

$$N(\mathbf{x}, t) = N\_S(\mathbf{x}, t) + \Delta N(\mathbf{x}) e^{i(\alpha t + \varphi)} \tag{20}$$

Here, *ns* and *Ns* describe the steady state electron densities (Δ*n* and Δ*N* are the amplitudes of the modulated component) in the CB and the trap state, respectively.

Defining,

$$D\_{\rm eff} = D\_{\rm cb} \frac{k\_2}{k\_2} \tag{21}$$

$$k\_{\rm eff} = 2N\_{\rm s}k\_{\rm r} \tag{22}$$

*Solar Cells - Theory, Materials and Recent Advances*

$$\gamma^2 = \frac{k\_{\rm eff}}{D\_{\rm eff}} + \frac{i\nu}{D\_{\rm eff}} \tag{23}$$

and using the following boundary conditions at

$$\text{or} = 0, qD\_{\text{eff}} \left( \frac{\partial \Delta n}{\partial \mathbf{x}} \right) = \frac{\Delta I}{A} = \Delta f \tag{24}$$

$$\boldsymbol{\omega} = \boldsymbol{L}, \frac{\partial \Delta \boldsymbol{n}}{\partial \boldsymbol{\omega}} = \mathbf{0} \tag{25}$$

the impedance *Z*<sup>2</sup> is obtained by Kern et al. as [39].

$$Z = -\mathcal{S} \frac{1}{qA} \frac{1}{D\_{\rm eff} \mathcal{Y} \sqrt{\frac{1}{k\_{\rm eff}}}} \frac{1 + e^{2\gamma L}}{1 - e^{2\gamma L}} \tag{26}$$

$$\mathcal{S} = \frac{K\_B T}{qn\_s} \sqrt{\frac{1}{k\_{\text{eff}}}} \tag{27}$$

volume, Parr Instrument Co.) and heated at 240°C for 12 h. The resulting powders are dried at �80°C in a conventional drying oven for 24 hour (**Figure 4(b)**). The pure Anatase colloidal TiO2 nanoparticle was obtained by autoclaving the low-pH

*(a) A electrical equivalent and (b) an illustrative Nyquist plot of a DSSC with R0, R1, R2, and R3, and each*

For photosensitization studies, the calcined TiO2 nanoparticle electrode were immersed in the ethanol solution containing purified 3x10�<sup>4</sup> M cis-di(thiocynato)-

ruthenium (II) (N719, Solaronix) for 18 h at room temperature [46]. Commercial N719 dye may not produce high efficiency because of impurities. Therefore, purifi-

*Scheme showing a typical procedure for highly crystalline TiO2 nanoparticle based DSSC. Reprinted from [26].*

cation is required. The N719 complex is firstly dissolved in water with


titanate suspension at 240°C for 12h (**Figure (4c)**) [45].

*peak frequency maxima of* ω*Z1,* ω*Z2, and* ω*Z3, respectively. Reprinted from [26, 51].*


*3.2.2 Photosensitizer (purifed N719 dye)*

*A New Generation of Energy Harvesting Devices DOI: http://dx.doi.org/10.5772/intechopen.94291*

N,N<sup>0</sup>

**Figure 4.**

**195**

**Figure 3.**


By defining

$$
\rho\_{\rm d} = \frac{D\_{\rm eff}}{L^2}, \rho\_{\rm k} = k\_{\rm eff} \text{ and } \chi L = \sqrt{\frac{\rho\_{\rm k}}{\rho\_{\rm d}} + \frac{i\rho}{\rho\_{\rm d}}} \tag{28}
$$

The equivalent impedance Z2 of Bisquert [39] is obtained as follows:

$$Z\_2 = R\_0 \left(\frac{1}{(a\flat\_\mathbf{k}/a\flat\_\mathbf{d})(\mathbf{1}+i\alpha/a\flat\_\mathbf{k})}\right)^{1/2} \coth\left[ (a\flat\_\mathbf{k}/a\flat\_\mathbf{d})(\mathbf{1}+i\alpha/a\flat\_\mathbf{k}) \right]^{1/2} \tag{29}$$

$$R\_w = \frac{k\_B T}{q^2 A n\_\text{s}} \frac{L}{D\_{\text{eff}}} = \text{Con} \frac{L}{D\_{\text{eff}}},\\ R\_k = \frac{a \nu\_\text{d}}{a \nu\_\text{k}} \times R\_w = \text{Con} \frac{1}{L k\_{\text{eff}}} \tag{30}$$

Here, *ω* is modulation frequency (s�<sup>1</sup> ) (with *ω*<sup>k</sup> *= k*eff), *R***<sup>w</sup>** is the electron transport resistance, and *R***<sup>k</sup>** is the charge transfer resistance related to recombination of electrons at the TiO2/electrolyte interface. The relation can be expressed by *R*<sup>k</sup> = (*ω*d/*ω*k)� *R*w.

The total impedance (*Z***s**) of the DSSC can be calculated by the summation of *Z*1, *Z*2, *Z*3, and the external resistance, *Z*0,

$$\mathbf{Z}\mathbf{s} = \mathbf{Z}\_0 + \mathbf{Z}\_1 + \mathbf{Z}\_2 + \mathbf{Z}\_3. \tag{31}$$

From experimental (*L*, *A*, *δ*) and EIS data (the maxima values of *ω*Z1, *ω*Z2, *ω*Z3 of the semi-circle diameters along the *Z*' axis), necessary information on charge transport kinetics can be determined (**Figure 3**).

#### **3.2 Materials preparation**
