**1. Introduction**

318 Solar Cells – Thin-Film Technologies

Nishimoto, T., Takai, M., Miyahara, H., Kondo, M. & Matsuda, A. (2002). Amorphous silicon

Perrin, J., Takeda, Y., Hirano, N., Takeuchi, Y. & Matsuda, A. (1989). Sticking and

Perrin, J., Leroy, O. & Bordage, M. C. (1996). Cross-sections, rate constants and transport coefficients in silane plasma chemistry. Contrib. Plasma Phys., Vol. 36, pp. 3-49. Roca i Cabarrocas., P. (2000). Plasma enhanced chemical vapor deposition of amorphous,

Shah, A., Torres, P., Tscharner, R., Wyrsch, N. & Keppner, H. (1999). Photovoltaic Technology: The Case for Thin-Film Solar Cells., Science, Vol. 285, pp. 692-698. Shah, A. V., Schade, H., Vanecek, M., Meier, J., Vallat-Sauvain, E., Wyrsch, N., Kroll, U.,

Shimizu, S., Kondo, M. & Matsuda, A. (2005). A highly stabilized hydrogenated amorphous

Shimizu, S., Matsuda, A. & Kondo, M. (2007). The determinants of hydrogen concentrations

Shimizu, S., Matsuda, A. & Kondo, M. (2008). Stability of thin film solar cells having less-

Sonobe, H., Sato, A., Shimizu, S., Matsui, T., Kondo, M. & Matsuda, A. (2006). Highly

Staebler, D. L. & Wronski, C. R. (1977). Reversible conductivity changes in discharge-

Takai, M., Nishimoto, T., Takagi, T., Kondo, M. & Matsuda, A. (2000). Guiding principles for

Toyoshima, Y., Arai, K., Matsuda, A. & Tanaka, K. (1991). In situ characterization of the growing a-Si:H surface by IR spectroscopy. J. Non-Cryst. Solids, Vol. 137-138, pp. 765-770. Yang, J., Banerjee, A. & Guha, S. (1997). Triple-junction amorphous silicon alloy solar cell

produced amorphous Si. Appl. Phys. Lett., Vol. 31, pp. 292-294.

catalytic effect of diborane. Surf. Sci., Vol. 210, pp. 114-128.

1116-1122.

pp. 31-37.

92, pp. 1241-1244.

Vol. 266-269, pp. 90-94.

70, pp. 2975-2977.

Res. Appl., Vol. 12, pp. 113–142.

network. J. Appl. Phys., Vol. 97, pp. 033522 1-4.

system. J. Appl. Phys., Vol. 101, pp. 064911 1-5.

CVD. Thin Solid Films, Vol. 502, pp. 306–310.

solar cells deposited at high growth rate. J. Non-Cryst. Solids, Vol. 299-302, pp.

recombination of the SiH3 radical on hydrogenated amorphous silicon: The

polymorphous and microcrystalline silicon films. J. Non-Cryst. Solids, Vol. 266-269,

Droz, C. & Bailat, J. (2004). Thin-film Silicon Solar Cell Technology. Prog. Photovolt:

silicon film having very low hydrogen concentration and an improved Si bond

in hydrogenated amorphous silicon films prepared using a triode deposition

hydrogenated amorphous silicon i-layers. Solar Energy Mater. & Solar Cells, Vol.

stabilized hydrogenated amorphous silicon solar cells fabricated by triode-plasma

obtaining stabilized amorphous silicon at larger growth rates. J. Non-Cryst. Solids.,

with 14.6% initial and 13.0% stable conversion efficiencies. Appl. Phys. Lett., Vol.

Monograin layer (MGL) solar cell combines the features of a monocrystalline solar cell and a thin film solar cell. The photoactive layer is formed from the kesterite-stannite semiconductor Cu2SnZn(S,Se)4 (CZTSSe) material with the single-crystalline grains embedded into the epoxy resin (Altosaar et al., 2003). With the graphite back contact, cadmium sulphide (CdS) buffer layer, and zinc oxide (ZnO:Al/i-ZnO) window layer, the remainder of the structure resembles a thin film CIS solar cell in the superstrate configuration (Fig. 1).

Fig. 1. The MGL solar cell. The photoactive Cu2SnZnSe4 monograins are covered with CdS, and embedded into the epoxy resin. The thin layer of the intrinsic ZnO serves as the CdS surface passivation and as the barrier for the ZnO:Al impurities. The front contact comprises indium fingers while the back contact is made of the graphite paste.

Analysis of CZTSSe Monograin Layer Solar Cells 321

*T* [K] *J*0 [mA/cm2] *nid* [/] *Rs* [Ωcm2] *Gsh* [mS/cm2]

The ideality factors above 2 deviate from the standard Sah-Noyce-Shockley theory (Sah et al., 1957) and point either to the tunnelling enhanced recombination in the space charge region (SCR) (Dumin & Pearson, 1965) or to the multilevel recombination (Breitenstein et al.,

Fig. 2 shows the Arrhenius plot of the dark saturation current (*J0*) and its extracted activation energy (*EA, J0*). The activation energy is the distance between the Fermi level and the edge of the minority carrier energy band, since these are responsible for the recombination current. In the case of the MGL solar cell, at the CdS/CZTSSe heterointerface the inverted surface makes holes to be the minority carriers, Fig. 8. Thus the *EA, J0* represents the energy distance between the CZTSSe absorber's valence band and the Fermi level near

> Inverse temperature 1000/*T* [1/K] 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Fig. 2. Arrhenius plot of the dark saturation current as obtained from the one-diode model. The slope of the ideality factor weighted logarithm of the dark saturation current versus the inverse absolute temperature, results the activation energy *EA, J0*. *T* is temperature in Kelvin. Comparing the value of the *EA, J0* (Fig. 2) to the absorber's band-gap energy as extracted from the *QE* measurement (Fig. 13, *Eg,CZTSSe* = 1.49 eV), this indicates the position of the recombination peak near the heterointerface and inside the SCR – as depicted in Fig. 8.

fit meas.

310 1.08x10-3 2.68 2.10 0.23 290 4.85x10-4 2.78 2.36 0.17 270 2.50x10-4 2.99 2.66 0.12 250 8.93x10-5 3.19 3.44 0.083 230 3.30x10-5 3.37 4.37 0.061 210 1.44x10-5 3.78 6.65 0.033

2006; Schenk et al., 1995) occurring in the highly defective interfacial regions.

*EA,J0*

= 1.21 eV

Table 1. Parameters of the fitted one-diode model.

the heterointerface.

*nid* x ln(






*J*0) [A/m2

]

The main advantage of this cell over the thin film CIGS solar cell are the low production costs – using a relatively simple powder technology (Altosaar et al., 2005), and the replacement of the expensive indium (In) by the less expensive tin (Sn) and zinc (Zn) metals. The photovoltaic properties of this new structure are very promising: the AM1.5 spectrum conversion efficiency reaches up to 5.9% along with the open-circuit voltage (*Voc*) up to 660 mV and the fill-factor (*FF*) up to 65%. The short-circuit current (*Jsc*) has its maximal value at the room temperature and then decreases with the lowering temperature. Along with the low *FF*, these output parameters point to some specific charge transport properties.

In order to discover the origin of the charge transport limiting mechanism we employed the numerical semiconductor simulator Aspin (Topič et al.,1996), based on the drift-diffusion equations (Selberherr, 1984) and coupled to the SRH (Schockley & Read, 1952) recombination statistics. The optical generation rate profile was calculated with the ray tracing simulator Sun*Shine* (Krč et al., 2003), which is able to determine the absorption profile in the illuminated one-dimensional (1D) structure that comprises a stack of layers with flat and/or rough adjacent interfaces. The input semiconductor material parameters were determined from the temperature resolved admittance spectroscopy measurements (Walter et al.,1996): capacitance-voltage (*C-V*) and capacitance-frequency (*C-f*), the van der Pauw measurement (Van der Pauw, 1958) and the dark current density-voltage (*J*-*V*) characteristics measurements (Sah et al., 1957). The numerical model was implemented in a similar way as in (Černivec et al., 2008) where the measured parameters were used as the input and the *J-V* and the external quantum efficiency (*QE*) characteristics were the result of the simulation. By comparing the temperature dependent output characteristics of the AM1.5 illuminated solar cell to the measurements, and additional fine tuning of the input parameters, we assumed the plausible efficiency-limiting mechanism, and by that also revealed the region in the structure that could be responsible for the charge transport limitations.

#### **2. Input parameters measurements**

In order to extract material parameters which will be further on used in the numerical analysis, following measurements were conducted: the dark *J-V* measurement to get insight into the recombination and transport properties of the solar cell, the *C-V* measurement which indicates the width and the shape of the junction, and the *C-f* measurement which results the information of the defect properties of the semiconductor material. The common assumption in the analyses of the measurements is a single-junction model of the solar cell. In the interpretation of the Van der Pauw measurement results we assumed a similar morphology of the annealed tablet of the CZTSSe material as it is one in the solar cell's monograin absorber.

#### **2.1 One-diode model**

Calibration of the parameters of the one-diode model does not yield any input parameters for our numerical model, but it rather gives us initial insight into the transport properties of the MGL solar cell. Table I contains the extracted temperature dependent parameters of the fitted one-diode model (Sze & Ng, 2007). The high ideality factors (*nid*) of the temperature dependent dark *J-V* measurement indicate the CdS/CZTSSe heterointerfacial limited transport.

The main advantage of this cell over the thin film CIGS solar cell are the low production costs – using a relatively simple powder technology (Altosaar et al., 2005), and the replacement of the expensive indium (In) by the less expensive tin (Sn) and zinc (Zn) metals. The photovoltaic properties of this new structure are very promising: the AM1.5 spectrum conversion efficiency reaches up to 5.9% along with the open-circuit voltage (*Voc*) up to 660 mV and the fill-factor (*FF*) up to 65%. The short-circuit current (*Jsc*) has its maximal value at the room temperature and then decreases with the lowering temperature. Along with the

In order to discover the origin of the charge transport limiting mechanism we employed the numerical semiconductor simulator Aspin (Topič et al.,1996), based on the drift-diffusion equations (Selberherr, 1984) and coupled to the SRH (Schockley & Read, 1952) recombination statistics. The optical generation rate profile was calculated with the ray tracing simulator Sun*Shine* (Krč et al., 2003), which is able to determine the absorption profile in the illuminated one-dimensional (1D) structure that comprises a stack of layers with flat and/or rough adjacent interfaces. The input semiconductor material parameters were determined from the temperature resolved admittance spectroscopy measurements (Walter et al.,1996): capacitance-voltage (*C-V*) and capacitance-frequency (*C-f*), the van der Pauw measurement (Van der Pauw, 1958) and the dark current density-voltage (*J*-*V*) characteristics measurements (Sah et al., 1957). The numerical model was implemented in a similar way as in (Černivec et al., 2008) where the measured parameters were used as the input and the *J-V* and the external quantum efficiency (*QE*) characteristics were the result of the simulation. By comparing the temperature dependent output characteristics of the AM1.5 illuminated solar cell to the measurements, and additional fine tuning of the input parameters, we assumed the plausible efficiency-limiting mechanism, and by that also revealed the region in the structure that could be responsible for the charge transport

In order to extract material parameters which will be further on used in the numerical analysis, following measurements were conducted: the dark *J-V* measurement to get insight into the recombination and transport properties of the solar cell, the *C-V* measurement which indicates the width and the shape of the junction, and the *C-f* measurement which results the information of the defect properties of the semiconductor material. The common assumption in the analyses of the measurements is a single-junction model of the solar cell. In the interpretation of the Van der Pauw measurement results we assumed a similar morphology of the annealed tablet of the CZTSSe material as it is one in the solar cell's

Calibration of the parameters of the one-diode model does not yield any input parameters for our numerical model, but it rather gives us initial insight into the transport properties of the MGL solar cell. Table I contains the extracted temperature dependent parameters of the fitted one-diode model (Sze & Ng, 2007). The high ideality factors (*nid*) of the temperature dependent dark *J-V* measurement indicate the CdS/CZTSSe heterointerfacial limited

low *FF*, these output parameters point to some specific charge transport properties.

limitations.

monograin absorber.

**2.1 One-diode model** 

transport.

**2. Input parameters measurements** 


Table 1. Parameters of the fitted one-diode model.

The ideality factors above 2 deviate from the standard Sah-Noyce-Shockley theory (Sah et al., 1957) and point either to the tunnelling enhanced recombination in the space charge region (SCR) (Dumin & Pearson, 1965) or to the multilevel recombination (Breitenstein et al., 2006; Schenk et al., 1995) occurring in the highly defective interfacial regions.

Fig. 2 shows the Arrhenius plot of the dark saturation current (*J0*) and its extracted activation energy (*EA, J0*). The activation energy is the distance between the Fermi level and the edge of the minority carrier energy band, since these are responsible for the recombination current. In the case of the MGL solar cell, at the CdS/CZTSSe heterointerface the inverted surface makes holes to be the minority carriers, Fig. 8. Thus the *EA, J0* represents the energy distance between the CZTSSe absorber's valence band and the Fermi level near the heterointerface.

Fig. 2. Arrhenius plot of the dark saturation current as obtained from the one-diode model. The slope of the ideality factor weighted logarithm of the dark saturation current versus the inverse absolute temperature, results the activation energy *EA, J0*. *T* is temperature in Kelvin.

Comparing the value of the *EA, J0* (Fig. 2) to the absorber's band-gap energy as extracted from the *QE* measurement (Fig. 13, *Eg,CZTSSe* = 1.49 eV), this indicates the position of the recombination peak near the heterointerface and inside the SCR – as depicted in Fig. 8.

Analysis of CZTSSe Monograin Layer Solar Cells 323

*T* = 320 K *T* = 300 K *T* = 280 K *T* = 260 K *T* = 240 K *T* = 220 K *T* = 200 K *V* = 0 V

Apparent doping [cm-3]

1016

Resistivity logarithm [cm]

8

10

12

14

16

1017

Distance from the CdS/CZTSSe heterointerface [m]

Inverse temperature 1000/*T* [1/K] 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Fig. 5. Arrhenius plot of the van der Pauw measurement conducted on the annealed CZTSSe

tablet. *EA,R* is the extracted activation energy. *T* is temperature in Kelvin.

fit meas.

Fig. 4. The apparent doping density *pSCR* obtained from the bias voltage derivative of the Mott-Schottky plot. The distance from the junction is calculated from the space charge

*EA,R* = 0.17 eV

region capacitance. Triangles depict the 0 V bias conditions.

0.10 0.12 0.14 0.16 0.18 0.20 0.22

#### **2.2 Capacitance-voltage measurement**

To obtain the approximate values of the concentration of the uncompensated acceptors (Kosyachenko, 2010) at the edge of the SCR, and the hole mobility (*μh,CZTSSe*) of the CZTSSe absorber layer, we combined the temperature resolved *C-V* and the van der Pauw measurements. Since the concentration of the uncompensated acceptors at the edge of the SCR corresponds to the density of free holes, we will further on introduce this as new parameter called the "apparent doping" – *pSCR*.

Fig. 3 shows the temperature and the bias voltage dependent capacitance plot – the Mott-Schottky plot, where the capacitance results from the admittance measurement at 10 kHz. The nonlinear curves in the Mott-Schottky plot indicate a spatially non-uniform *pSCR*, while their temperature trend points to the temperature decreasing capacitance. The slope of the curves at *V* = 0 V indicates that, in dark conditions, the apparent doping at the edge of the SCR gradually increases with the decreasing temperature.

Fig. 3. The Mott-Schottky plot at 10 kHz. The dashed curve correlates to the temperature at 320 K. Arrow indicates the trend of the temperature decrement. The temperature step equals to 20 K. All curves are measured with a small signal of 10 kHz.

When we observe the 0V bias points as depicted in Fig. 4 by the triangles, we can see that *pSCR* decreases when moving from the quasi-neutral region towards the SCR. However, for the higher temperatures (320 K, 300 K) *pSCR* seems to be increasing towards the heterointerface after it has reached its minimum value. We are not able to explain this trend properly, but since the increasing *pSCR* towards the heterointerface would produce only a poor photovoltaic junction, in the modelling we use the *pSCR* values as obtained at 0 V bias. The trend of the increasing SCR width along with the increasing *pSCR* could results from the influences of the non-ideally asymmetrical *n+*/*p* (CdS/CZTSSe) junction in which the SCR extends also into the *n+* buffer region (CdS).

To obtain the approximate values of the concentration of the uncompensated acceptors (Kosyachenko, 2010) at the edge of the SCR, and the hole mobility (*μh,CZTSSe*) of the CZTSSe absorber layer, we combined the temperature resolved *C-V* and the van der Pauw measurements. Since the concentration of the uncompensated acceptors at the edge of the SCR corresponds to the density of free holes, we will further on introduce this as new

Fig. 3 shows the temperature and the bias voltage dependent capacitance plot – the Mott-Schottky plot, where the capacitance results from the admittance measurement at 10 kHz. The nonlinear curves in the Mott-Schottky plot indicate a spatially non-uniform *pSCR*, while their temperature trend points to the temperature decreasing capacitance. The slope of the curves at *V* = 0 V indicates that, in dark conditions, the apparent doping at the edge of the

> Bias voltage [V] -1.5 -1.0 -0.5 0.0 0.5

Fig. 3. The Mott-Schottky plot at 10 kHz. The dashed curve correlates to the temperature at 320 K. Arrow indicates the trend of the temperature decrement. The temperature step equals

When we observe the 0V bias points as depicted in Fig. 4 by the triangles, we can see that *pSCR* decreases when moving from the quasi-neutral region towards the SCR. However, for the higher temperatures (320 K, 300 K) *pSCR* seems to be increasing towards the heterointerface after it has reached its minimum value. We are not able to explain this trend properly, but since the increasing *pSCR* towards the heterointerface would produce only a poor photovoltaic junction, in the modelling we use the *pSCR* values as obtained at 0 V bias. The trend of the increasing SCR width along with the increasing *pSCR* could results from the influences of the non-ideally asymmetrical *n+*/*p* (CdS/CZTSSe) junction in which the SCR

*f* = 10 kHz

*T* = - 20 K

**2.2 Capacitance-voltage measurement** 

parameter called the "apparent doping" – *pSCR*.

x 10-3

1/

0.0

extends also into the *n+* buffer region (CdS).

0.2

0.4

0.6

0.8

1.0

*C*2 [cm4/nF2

]

SCR gradually increases with the decreasing temperature.

*T* = 320 K *T* = 180 K

to 20 K. All curves are measured with a small signal of 10 kHz.

Fig. 4. The apparent doping density *pSCR* obtained from the bias voltage derivative of the Mott-Schottky plot. The distance from the junction is calculated from the space charge region capacitance. Triangles depict the 0 V bias conditions.

Fig. 5. Arrhenius plot of the van der Pauw measurement conducted on the annealed CZTSSe tablet. *EA,R* is the extracted activation energy. *T* is temperature in Kelvin.

Analysis of CZTSSe Monograin Layer Solar Cells 325

The decreasing capacitance going from the high temperature towards the low temperature indicates the 'freeze out' of the carriers located in the deep traps: the temperature shrinking of the Fermi distribution tail makes the deep trapped charge less sensitive to the small perturbations of the Fermi level (the applied ac signal). The analysis according to (Walter et al.,1996) reveals two trap distributions which are shown in Fig. 7. Measurement at room temperature senses a broad trap distribution extending at least 0.3 eV deep into the energy gap from the valence band, while the measurement at low temperature fingers a very narrow distribution with its maximum at 0.05 eV. Since this maximum remains present also at high reverse biases (not shown here), we believe that this trap extends throughout the whole CZTSSe absorber layer and acts as the intrinsic acceptor doping level. However we can not draw any strong conclusions on the type of the deep trap distribution, but since this could be responsible for the compensating effect; we postulated it to be the donor-like.

Distance to the valence band [eV]

*T* = 100 K *T* = 120 K *T* = 140 K *T* = 300 K *T* = 320 K *T* = 340 K

Deep donor traps (compensating effect)

0.00 0.05 0.10 0.15 0.20 0.25 0.30

In Fig. 7 the pronounced narrow distribution at 0.05 eV above the valence band indicates the shallow acceptor traps responsible for the intrinsic doping, while the deeper and wider

From the measurements we obtained a certain insight into the recombination and transport properties (the dark *J*-*V* and the Van der Pauw measurements), the doping profile (*C-V* measurement) and the indication of the shallow traps (*C-f* measurement). These will be used

Fig. 7. Trap density distributions extracted at 0.2 V of forward bias calculated as the frequency derivative of the space charge region's capacitance. Calibration parameters were chosen according to (Walter et al.,1996): *Ud* = 0.8 V (built-in voltage), *βpNV* = 5x107 Hz (trap emission coefficient), *Efp* = 0.7 eV (the Fermi level position relating the valence band), 1x103 ≤

donor distribution (marked with triangles) results the compensation effect.

as the guidelines to define the numerical model of the CZTSSe MGL solar cell.

Shallow acceptor traps (the intrinsic doping)

Density distribution

1016

*f* ≤ 1x106 Hz (frequency range).

**3. Modelling** 

1017

[cm-3eV-1]

1018

#### **2.3 Van der Pauw measurement**

The van der Pauw measurements were conducted on the tablet of the annealed CZTSSe monograin material. The Arrhenius plot of the resistivity (*ρ*) of the monograin material tablet (Fig. 5) reveals the thermal activation energy (*EA,R*) equal to 0.17 eV, and a very low hole mobility *μh,CZTSSe* equal to 0.02 cm2/Vs at 310 K. The latter was calculated according to (1) and using the *pSCR* as obtained from the *C-V* profiling:

$$
\mu\_{\text{h.CZTSSe}} = \frac{1}{q \cdot p\_{\text{SCR}} \cdot \rho} \,. \tag{1}
$$

#### **2.4 Capacitance-frequency measurement**

Plotting the capacitance as a function of the measurement frequency on a semi-logarithmic scale can reveal some defects present in the energy gap of the CZTSSe absorber layer of the MGL solar cell. A gradually decaying capacitance indicates a defect with a broad energy band, while a steep transition indicates a single level defect (Burgelman & Nollet, 2005). The temperature resolved *C-f* plot shown in Fig. 6 reveals both types of transitions: a gradually decreasing capacitance at the high temperature limit (indicated with triangles), and a characteristic inflection point at the frequency equal to 10 kHz in the low temperature limit (indicated with circles).

Fig. 6. Frequency dependent space charge region's capacitance measured at 0.2 V of forward bias. Solid curve with circles depicts the relation at 100 K. The arrow indicates the trend of the curves with the increasing temperature. The temperature step equals to 20 K. The curves at lower temperatures exhibit pronounced inflection points thus indicate emission from shallow traps.

The van der Pauw measurements were conducted on the tablet of the annealed CZTSSe monograin material. The Arrhenius plot of the resistivity (*ρ*) of the monograin material tablet (Fig. 5) reveals the thermal activation energy (*EA,R*) equal to 0.17 eV, and a very low hole mobility *μh,CZTSSe* equal to 0.02 cm2/Vs at 310 K. The latter was calculated according to

1

. (1)

*T* = 100 K *T* = 320 K

*SCR q p*

Plotting the capacitance as a function of the measurement frequency on a semi-logarithmic scale can reveal some defects present in the energy gap of the CZTSSe absorber layer of the MGL solar cell. A gradually decaying capacitance indicates a defect with a broad energy band, while a steep transition indicates a single level defect (Burgelman & Nollet, 2005). The temperature resolved *C-f* plot shown in Fig. 6 reveals both types of transitions: a gradually decreasing capacitance at the high temperature limit (indicated with triangles), and a characteristic inflection point at the frequency equal to 10 kHz in the low temperature limit

> Frequency [Hz] 103 104 105 106

Fig. 6. Frequency dependent space charge region's capacitance measured at 0.2 V of forward bias. Solid curve with circles depicts the relation at 100 K. The arrow indicates the trend of the curves with the increasing temperature. The temperature step equals to 20 K. The curves at lower temperatures exhibit pronounced inflection points thus indicate emission from

**2.3 Van der Pauw measurement** 

(1) and using the *pSCR* as obtained from the *C-V* profiling:

**2.4 Capacitance-frequency measurement** 

(indicated with circles).

SCR capacitance [nF/cm2]

shallow traps.

0

20

*T* = 20 K

40

60

80

.

*h CZTSSe*

The decreasing capacitance going from the high temperature towards the low temperature indicates the 'freeze out' of the carriers located in the deep traps: the temperature shrinking of the Fermi distribution tail makes the deep trapped charge less sensitive to the small perturbations of the Fermi level (the applied ac signal). The analysis according to (Walter et al.,1996) reveals two trap distributions which are shown in Fig. 7. Measurement at room temperature senses a broad trap distribution extending at least 0.3 eV deep into the energy gap from the valence band, while the measurement at low temperature fingers a very narrow distribution with its maximum at 0.05 eV. Since this maximum remains present also at high reverse biases (not shown here), we believe that this trap extends throughout the whole CZTSSe absorber layer and acts as the intrinsic acceptor doping level. However we can not draw any strong conclusions on the type of the deep trap distribution, but since this could be responsible for the compensating effect; we postulated it to be the donor-like.

Fig. 7. Trap density distributions extracted at 0.2 V of forward bias calculated as the frequency derivative of the space charge region's capacitance. Calibration parameters were chosen according to (Walter et al.,1996): *Ud* = 0.8 V (built-in voltage), *βpNV* = 5x107 Hz (trap emission coefficient), *Efp* = 0.7 eV (the Fermi level position relating the valence band), 1x103 ≤ *f* ≤ 1x106 Hz (frequency range).

In Fig. 7 the pronounced narrow distribution at 0.05 eV above the valence band indicates the shallow acceptor traps responsible for the intrinsic doping, while the deeper and wider donor distribution (marked with triangles) results the compensation effect.

#### **3. Modelling**

From the measurements we obtained a certain insight into the recombination and transport properties (the dark *J*-*V* and the Van der Pauw measurements), the doping profile (*C-V* measurement) and the indication of the shallow traps (*C-f* measurement). These will be used as the guidelines to define the numerical model of the CZTSSe MGL solar cell.

Analysis of CZTSSe Monograin Layer Solar Cells 327

defect layer (SDL) between the CdS and the CZTSSe to account for the interfacial defects. Because of the degenerate position of the Fermi level in the ZnO:Al, i-ZnO and CdS layers, we assume these will act as the emitter contact, while the graphite at the back acts as the ohmic base contact. Further on in the structure we introduce the SDL which has an increased concentration of the mid-gap defects of the donor (*NtD,SDL*) and the acceptor (*NtA,SDL*) types. *NtD,SDL* will be responsible for the recombination current while the *NtA,SDL*

The van der Pauw measurements of the sole CZTSSe tablets exhibit unusual high resistances, thus we assume that *μh,CZTSSe* will have an important impact to the series resistance – *Rs* (Table I). The Arrhenius plot in Fig. 5 shows the latter's exponential dependence on temperature, revealing the activation energy of 0.17 eV. We believe that the high *Rs* originates from the compensation of the shallow acceptor doping (*NtA,CZTSSe*) by the broader distribution of deeper donor levels (*NtD,CZTSSe*). This agrees well with the *C-f* measurement results shown in Fig. 7. Therefore, rather than calculating the mobility from the van der Pauw measurement, we will use a numerical fitting procedure to calibrate the *μh,CZTSSe* and the *NtD,SDL* for the preselected values of the *NtA,CZTSSe* and the *NtD,CZTSSe*. The initial values for the latter two

Fig. 9 shows the calibration procedure of the measured and the simulated dark *J-V* characteristics at 310 K. By increasing the total concentration of the SDL mid-gap donor defects (*NtD,SDL*) the dark saturation current increases, as shows the inset of Fig. 9. In the voltage range from 0.4 V to 0.6 V a good *J-V* fit can be found for the *NtD,SDL* equal to 1018 cm-3, but still expressing a deviation in the slope as the result of the non-matching ideality factors: with this model it is not possible to obtain such a high ideality factor as yielded the measurement-calibration in Table I. For the lower applied voltages (*V* < 0.4 V) there is a significant deviation in characteristics which can be attributed to the shunt conductance. To compensate this difference the external shunting element can be added in the model, using the value equal to the *Gsh* at 310 K (Table I). A very good fit is found in the voltage range *V* > 0.5 V by setting the value of the *μh,CZTSSe* to 1.5 cm2/Vs – indicated by the solid line in Fig. 9.

> Bias voltage [V] 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Fig. 9. Calibration of the CZTSSe monograin layer's and of the SDL's transport parameters.

will set the Fermi level position in the SDL layer and thus activate the *NtD,SDL*.

measurement

/ Vs

/ Vs

0.0 0.2 0.4 0.6 0.8 1.0

*h,CZTSSe* increasing

*NtD,SDL* increasing

/ Vs

/ Vs

*h* = 0.5 cm<sup>2</sup>

*h* = 1 cm<sup>2</sup>

*h* = 1.5 cm<sup>2</sup>

*<sup>h</sup>* = 3 cm<sup>2</sup>

were calculated from the *C-f* measurement (Fig. 7).

Current density [A/m2

10-2

10-1

100

101

102

103

]

The 1D carrier transport model can accurately describe the current flow only in the direction vertical to the layered structure (the direction orthogonal to the solar cell plane) therefore following assumptions are made: i) current flow in the matrix plane between the adjacent monograins is neglected, ii) all the semiconductor parameters are meant as the "effective parameters", thus neglecting the morphology by transforming a single spherical monograin solar cell into the 1D rod, and iii) the "spatial fill-factor" (*SFF*) is introduced, which is the ratio of the grain covered area to the whole contact area. It is important to note that the *SFF* affects only the extensive solar cell parameters (*Jsc*) while the intensive parameters (*Voc*, *FF* and *QE*) remain intact. In our case the *SFF* equals to 0.78.

The most important semiconductor parameters which have to be defined for each layer of the MGL solar cell prior to simulation are the band-gap energy (*Eg*), the electron affinity (*Eχ*), the acceptor and/or donor doping (*NA*, *ND*), the hole and electron low-field mobility (*μh*, *μe*), the hole and electron effective masses (*mh*, *me*), and the parameters of the traps and/or the recombination centres (*Nt* – distribution density, *Et* – distance to the valence band, σ – trap cross section, *et* – characteristic energy). By analyzing the conducted measurements (*C-V*, van der Pauw, *C-f* ) we extracted the initial values of these parameters, relating to the CZTSSe absorber and/or to the CdS/CZTSSe heterointerface. These were further on subjected to the calibration procedure in order to fit the dark structure and the illuminated structure output characteristics to the measurements (*J-V* and *QE*). The rest of the absorber and heterointerface parameters, and those relating to the window (ZnO:Al/ZnO) and buffer (CdS) layers of the MGL solar cell, were taken similar to those used in (Černivec et al., 2008).

#### **3.1 Dark structure** *J-V* **characteristics**

Fig. 8 shows the CZTSSe MGL solar cell structure in its thermodynamic equilibrium. The complete solar cell comprises glass(2 mm)/ZnO:Al(1.6 μm)/i-ZnO(200 nm)/CdS(50 nm)/CZTSSe(60 μm)/graphite(500 nm) layers with the additional 100 nm thick surface

Fig. 8. Energy band diagram of CZTSSe solar cell in thermodynamic equilibrium at 310 K. *EA,J0* indicates the recombination activation energy as obtained from the Arrhenius plot from Fig. 2.

The 1D carrier transport model can accurately describe the current flow only in the direction vertical to the layered structure (the direction orthogonal to the solar cell plane) therefore following assumptions are made: i) current flow in the matrix plane between the adjacent monograins is neglected, ii) all the semiconductor parameters are meant as the "effective parameters", thus neglecting the morphology by transforming a single spherical monograin solar cell into the 1D rod, and iii) the "spatial fill-factor" (*SFF*) is introduced, which is the ratio of the grain covered area to the whole contact area. It is important to note that the *SFF* affects only the extensive solar cell parameters (*Jsc*) while the intensive parameters (*Voc*, *FF*

The most important semiconductor parameters which have to be defined for each layer of the MGL solar cell prior to simulation are the band-gap energy (*Eg*), the electron affinity (*Eχ*), the acceptor and/or donor doping (*NA*, *ND*), the hole and electron low-field mobility (*μh*, *μe*), the hole and electron effective masses (*mh*, *me*), and the parameters of the traps and/or the recombination centres (*Nt* – distribution density, *Et* – distance to the valence band, σ – trap cross section, *et* – characteristic energy). By analyzing the conducted measurements (*C-V*, van der Pauw, *C-f* ) we extracted the initial values of these parameters, relating to the CZTSSe absorber and/or to the CdS/CZTSSe heterointerface. These were further on subjected to the calibration procedure in order to fit the dark structure and the illuminated structure output characteristics to the measurements (*J-V* and *QE*). The rest of the absorber and heterointerface parameters, and those relating to the window (ZnO:Al/ZnO) and buffer (CdS) layers of the MGL solar cell, were taken similar to those used in (Černivec et al., 2008).

Fig. 8 shows the CZTSSe MGL solar cell structure in its thermodynamic equilibrium. The complete solar cell comprises glass(2 mm)/ZnO:Al(1.6 μm)/i-ZnO(200 nm)/CdS(50 nm)/CZTSSe(60 μm)/graphite(500 nm) layers with the additional 100 nm thick surface

> Distance from the top surface [m] 1.0 1.5 2.0 50.0 60.0

Fig. 8. Energy band diagram of CZTSSe solar cell in thermodynamic equilibrium at 310 K. *EA,J0* indicates the recombination activation energy as obtained from the Arrhenius plot from Fig. 2.

CdS

i-ZnO

*EA,J0*

ZnO:Al

CZTSSe

SDL - surface defect layer

conduction band valence band Fermi energy

and *QE*) remain intact. In our case the *SFF* equals to 0.78.

**3.1 Dark structure** *J-V* **characteristics** 

Energy [eV]





0

1

2

defect layer (SDL) between the CdS and the CZTSSe to account for the interfacial defects. Because of the degenerate position of the Fermi level in the ZnO:Al, i-ZnO and CdS layers, we assume these will act as the emitter contact, while the graphite at the back acts as the ohmic base contact. Further on in the structure we introduce the SDL which has an increased concentration of the mid-gap defects of the donor (*NtD,SDL*) and the acceptor (*NtA,SDL*) types. *NtD,SDL* will be responsible for the recombination current while the *NtA,SDL* will set the Fermi level position in the SDL layer and thus activate the *NtD,SDL*.

The van der Pauw measurements of the sole CZTSSe tablets exhibit unusual high resistances, thus we assume that *μh,CZTSSe* will have an important impact to the series resistance – *Rs* (Table I). The Arrhenius plot in Fig. 5 shows the latter's exponential dependence on temperature, revealing the activation energy of 0.17 eV. We believe that the high *Rs* originates from the compensation of the shallow acceptor doping (*NtA,CZTSSe*) by the broader distribution of deeper donor levels (*NtD,CZTSSe*). This agrees well with the *C-f* measurement results shown in Fig. 7. Therefore, rather than calculating the mobility from the van der Pauw measurement, we will use a numerical fitting procedure to calibrate the *μh,CZTSSe* and the *NtD,SDL* for the preselected values of the *NtA,CZTSSe* and the *NtD,CZTSSe*. The initial values for the latter two were calculated from the *C-f* measurement (Fig. 7).

Fig. 9 shows the calibration procedure of the measured and the simulated dark *J-V* characteristics at 310 K. By increasing the total concentration of the SDL mid-gap donor defects (*NtD,SDL*) the dark saturation current increases, as shows the inset of Fig. 9. In the voltage range from 0.4 V to 0.6 V a good *J-V* fit can be found for the *NtD,SDL* equal to 1018 cm-3, but still expressing a deviation in the slope as the result of the non-matching ideality factors: with this model it is not possible to obtain such a high ideality factor as yielded the measurement-calibration in Table I. For the lower applied voltages (*V* < 0.4 V) there is a significant deviation in characteristics which can be attributed to the shunt conductance. To compensate this difference the external shunting element can be added in the model, using the value equal to the *Gsh* at 310 K (Table I). A very good fit is found in the voltage range *V* > 0.5 V by setting the value of the *μh,CZTSSe* to 1.5 cm2/Vs – indicated by the solid line in Fig. 9.

Fig. 9. Calibration of the CZTSSe monograin layer's and of the SDL's transport parameters.

Analysis of CZTSSe Monograin Layer Solar Cells 329

*Nv* occupation

Distance to the valence band [eV] 0.0 0.1 0.2 0.3 0.4 0.5

Distance from the top surface [m] 1.95 2.00 2.05 2.10 2.15 2.20

*pSCR*[cm-3]

Fig. 11. Space charge region of the CZTSSe layer (*q* is the electron's charge) and its temperature dependence resulting from the occupation function variation (shown in Fig. 10). On the left, the interface to the SDL is indicated. The inset shows the temperature

SDL / CZTSSe

1.95 2.00 2.05 2.10 2.15

*T* = 310 K *T* = 210 K

Fig. 10. Trap distributions of the CZTSSe monograin layer 50 nm deep in the SCR from the

*T* = 310 K *T* = 210 K

*NtA,CZTSSe*

*NtD,CZTSSe*

Occupation function

0.0

0.2

0.4

0.6

0.8

function

1.0

 [/]

Density distribution

1016

Charge [


variation of the apparent doping *pSCR*.







0

x10<sup>3</sup>

*q*]

SDL/CZTSSe heterointerface.

1017

1018

[cm-3eV-1]

In Fig. 9 the calibrated value of the CZTSSe hole mobility equals to 1.5 cm2(Vs)-1 and the corresponding electron mobility equals to 8 cm2(Vs)-1. The inset of Fig 9 shows calibration of the SDL defect concentration. The calibrated defect concentration (*NtD,SDL* = 8x1019 cm-3/eV) corresponds to the solid *J-V* curve of the three simulated characteristics. The *J-V* curve above (dash-dotted) and the *J-V* curve below (dashed) correspond to one order of magnitude higher and to one order of magnitude lower SDL defect concentration, respectively.

To summarize the dark model, this is valid for the bias voltages higher than 0.5 V. When the solar cell is illuminated, this usually happens to be the range at which the recombination current starts to compensate the photogenerated current, and therefore important to match the correct *Voc* value. For the bias voltages lower than 0.5 V the recombination current is rather low and the photogenerated current will dominate the *J-V* characteristics. Thus the external *Gsh* might be of lesser importance when observing the illuminated solar cell structure.

#### **3.2 Illuminated structure characteristics**

In order to calibrate the CZTSSe solar cell model under illumination, we choose to observe the temperature behaviour of the *Jsc*. This is mainly determined by the collection efficiency of the photogenerated carriers in the SCR. The collection efficiency in a large extend depends on the width of the SCR (Fig. 4), determined by the shallow acceptor traps in the CZTSSe *- NtA,CZTSSe*, while its temperature dependence governs the occupation function *F* of the deeper donor traps *NtD,CZTSSe* (Fig. 10). Fig. 10 shows the *NtA,CZTSSe* and *NtD,CZTSSe* distributions similar to the measured trap densities from Fig. 7, and the occupation function *F* at 310 K and 210 K. The peak values of the trap distributions are not the same as the measured traps, but were rather subjected to the calibration procedure of fitting the *J-V* and *QE* measured and simulated characteristics. At the edge of the SCR the apparent doping *pSCR* is a result of the compensatory effect of the density of the occupied *NtA,CZTSSe* and the density of the unoccupied *NtD,CZTSSe* :

$$\mathcal{p}\_{\text{SCR}} = \mathcal{N}\_{t\text{A}, \text{CSZ}\text{SSe}} - \left(1 - F\right) \cdot \mathcal{N}\_{t\text{D,CSZ}\text{SSe}} \cdot \tag{2}$$

When temperature decreases the *Efp* moves towards the valence band, what creates more deep donors unoccupied (*fB* decreases), and lowers the *pSCR*.

In Fig. 10 the trap distributions of the model are calibrated to fit the measured short-circuit current density at 310 K. The distributions correlate well with the calculated distributions shown in Fig. 7. On the right axis the occupation functions at two different temperatures are shown in order to explain the temperature dependent collection efficiency and its influence to the short-circuit current.

The temperature decreasing *pSCR* decreases the SCR width, leading into the lower collection efficiency and lower *Jsc*. Fig. 11 shows the SCR narrowing as the result of the Fermi redistribution according to Fig. 10. The decreased *pSCR* would normally lead into the wider SCR, if the net charge of the SDL remained constant. This would be the case with the ideal asymmetrical *n+*/*p* junction, resulting from the shallow doping levels. But since the net charge in the SDL originates also from the deep defects, these are then affected by the change of the charge in the CZTSSe layer. Therefore in order to satisfy the Poisson's balance, the lower temperature also leads into the charge redistribution in the SDL layer (omitted for clarity in Fig. 11): the decrement of the negative charge resulting from the less occupied acceptor traps in the CZTSSe layer is balanced by the decrement of the positive charge from the deep defects in the SDL. In the SDL the temperature shift of the Fermi level towards the conduction band makes the deep donor defects less ionized and increases the ionization of the deep acceptors.

In Fig. 9 the calibrated value of the CZTSSe hole mobility equals to 1.5 cm2(Vs)-1 and the corresponding electron mobility equals to 8 cm2(Vs)-1. The inset of Fig 9 shows calibration of the SDL defect concentration. The calibrated defect concentration (*NtD,SDL* = 8x1019 cm-3/eV) corresponds to the solid *J-V* curve of the three simulated characteristics. The *J-V* curve above (dash-dotted) and the *J-V* curve below (dashed) correspond to one order of magnitude

To summarize the dark model, this is valid for the bias voltages higher than 0.5 V. When the solar cell is illuminated, this usually happens to be the range at which the recombination current starts to compensate the photogenerated current, and therefore important to match the correct *Voc* value. For the bias voltages lower than 0.5 V the recombination current is rather low and the photogenerated current will dominate the *J-V* characteristics. Thus the external *Gsh*

In order to calibrate the CZTSSe solar cell model under illumination, we choose to observe the temperature behaviour of the *Jsc*. This is mainly determined by the collection efficiency of the photogenerated carriers in the SCR. The collection efficiency in a large extend depends on the width of the SCR (Fig. 4), determined by the shallow acceptor traps in the CZTSSe *- NtA,CZTSSe*, while its temperature dependence governs the occupation function *F* of the deeper donor traps *NtD,CZTSSe* (Fig. 10). Fig. 10 shows the *NtA,CZTSSe* and *NtD,CZTSSe* distributions similar to the measured trap densities from Fig. 7, and the occupation function *F* at 310 K and 210 K. The peak values of the trap distributions are not the same as the measured traps, but were rather subjected to the calibration procedure of fitting the *J-V* and *QE* measured and simulated characteristics. At the edge of the SCR the apparent doping *pSCR* is a result of the compensatory effect of the density of the occupied *NtA,CZTSSe* and the

When temperature decreases the *Efp* moves towards the valence band, what creates more

In Fig. 10 the trap distributions of the model are calibrated to fit the measured short-circuit current density at 310 K. The distributions correlate well with the calculated distributions shown in Fig. 7. On the right axis the occupation functions at two different temperatures are shown in order to explain the temperature dependent collection efficiency and its influence

The temperature decreasing *pSCR* decreases the SCR width, leading into the lower collection efficiency and lower *Jsc*. Fig. 11 shows the SCR narrowing as the result of the Fermi redistribution according to Fig. 10. The decreased *pSCR* would normally lead into the wider SCR, if the net charge of the SDL remained constant. This would be the case with the ideal asymmetrical *n+*/*p* junction, resulting from the shallow doping levels. But since the net charge in the SDL originates also from the deep defects, these are then affected by the change of the charge in the CZTSSe layer. Therefore in order to satisfy the Poisson's balance, the lower temperature also leads into the charge redistribution in the SDL layer (omitted for clarity in Fig. 11): the decrement of the negative charge resulting from the less occupied acceptor traps in the CZTSSe layer is balanced by the decrement of the positive charge from the deep defects in the SDL. In the SDL the temperature shift of the Fermi level towards the conduction band makes the deep donor defects less ionized and increases the ionization of the deep acceptors.

*SCR tA CSZSSe* , , 1 *tD CSZSSe p N F N* . (2)

higher and to one order of magnitude lower SDL defect concentration, respectively.

might be of lesser importance when observing the illuminated solar cell structure.

**3.2 Illuminated structure characteristics** 

density of the unoccupied *NtD,CZTSSe* :

to the short-circuit current.

deep donors unoccupied (*fB* decreases), and lowers the *pSCR*.

Fig. 10. Trap distributions of the CZTSSe monograin layer 50 nm deep in the SCR from the SDL/CZTSSe heterointerface.

Fig. 11. Space charge region of the CZTSSe layer (*q* is the electron's charge) and its temperature dependence resulting from the occupation function variation (shown in Fig. 10). On the left, the interface to the SDL is indicated. The inset shows the temperature variation of the apparent doping *pSCR*.

Analysis of CZTSSe Monograin Layer Solar Cells 331

Fig. 12 shows the measured and simulated *J-V* characteristics of the CZTSSe MGL solar cell. The measured characteristics were obtained from the *I-V* characteristics normalized to the contacting area of the solar cell equal to *A* = 4.81 mm2. Here we used the assumptions i) and ii) as defined in 3. Since the CZTSSe monograins shape in the spherical forms this means that the real current density varies throughout the structure. In the simulated *J-V* characteristics at 310 K we also took into account the *SFF* as the assumption iii). This means that the *Jsc* obtained by using the parameters from Table 2 would in fact be larger by this

In Fig. 12 we can observe a very good agreement of the measured and simulated *J-V* characteristics at 310 K while the simulation at 210 K exhibits a discrepancy in all solar cell output parameters. A possible reason for the non-matched *Jsc* at 210 K could be that in the modelling we did not account for the temperature dependent mobility, which could be the

> Bias voltage [V] 0.0 0.2 0.4 0.6 0.8

Dashed lines in Fig. 12 represent the simulation and the arrow indicates temperature decrement. The short-circuit current and the open-circuit voltage trends are well correlated while their absolute value deviation at the low temperature indicate the necessity to include the temperature dependent mobility and the tunnelling enhanced recombination, respectively. At 210 K a significant mismatch also occurs with the *Voc*. This leads us to the conclusion that it is not merely the SRH recombination (Sze & Ng, 2007) in the SDL layer that limits the *Voc*, but there should also be present other recombination mechanisms which are less thermodynamically affected, namely the tunnelling enhanced recombination (Dumin & Pearson, 1965). The tunnelling enhanced recombination would reduce the rate of

Fig. 12. Comparison of the measured and simulated *J-V* characteristics of the AM1.5

case as seen from the van der Pauw measurement of the monograin tablet (Fig. 5).

meas., *T* = 310 K sim., *T* = 310 K meas., *T* = 210 K sim., *T* = 210 K

Decreasing *T*

**4. Analysis of the model** 

Current density [A/m2

the *Voc-T* change.


illuminated CZTSSe monograin solar cell.





0

]

factor.

The modelled SCR width of approximately 0.2 μm and the *pSCR* concentration of 1016 cm-3 at 310 K agree well with the respective measured values which equal to 0.18 μm and 2.6x1016 cm-3, as observed from Fig. 4. Similarly well agrees the temperature correlation between the *pSCR* and the SCR width: with the increasing *pSCR* also the increasing SCR width is observed. In the measurement this correlation is indicated with the triangles (Fig. 4). However the corresponding temperatures do not comply: in the measurement the 320 K triangle corresponds to the lowest *pSCR* and the 220 K triangle corresponds to the highest *pSCR*. One should indeed always take care about the width of the SCR calculated in the apparent doping density analysis. There, the following formula is used to calculate the SCR width:

$$\mathcal{W}\_{\text{SCR}} = \frac{\mathcal{E}}{\mathcal{C}} \,' \,. \tag{3}$$

where *ε* is the permittivity and *C* is the capacitance. This formula however only holds if the capacitance is governed by the depletion, and not by filling and emptying of deep states. As can be seen in Fig. 6 the capacitance is indeed governed by defects rather than depletion at *f*=10kHz.

Table 2 summarizes the calibrated material parameters. The parameters which were the subject of calibration are denoted bold, while the dash corresponds to the parameter for which we used the value 0. In the reality this would correspond to a very low value. Other material parameters are similar as in (Černivec et al., 2008). The effective density of states is calculated from the corresponding effective masses (Sze & Ng, 2007).


Table 2. Material parameters of the CZTSSe MGL monograin layer solar cell.

#### **4. Analysis of the model**

330 Solar Cells – Thin-Film Technologies

The modelled SCR width of approximately 0.2 μm and the *pSCR* concentration of 1016 cm-3 at 310 K agree well with the respective measured values which equal to 0.18 μm and 2.6x1016 cm-3, as observed from Fig. 4. Similarly well agrees the temperature correlation between the *pSCR* and the SCR width: with the increasing *pSCR* also the increasing SCR width is observed. In the measurement this correlation is indicated with the triangles (Fig. 4). However the corresponding temperatures do not comply: in the measurement the 320 K triangle corresponds to the lowest *pSCR* and the 220 K triangle corresponds to the highest *pSCR*. One should indeed always take care about the width of the SCR calculated in the apparent doping density analysis. There, the following formula is used to calculate the SCR width:

> *WSCR <sup>C</sup>*

where *ε* is the permittivity and *C* is the capacitance. This formula however only holds if the capacitance is governed by the depletion, and not by filling and emptying of deep states. As can be seen in Fig. 6 the capacitance is indeed governed by defects rather than depletion at

Table 2 summarizes the calibrated material parameters. The parameters which were the subject of calibration are denoted bold, while the dash corresponds to the parameter for which we used the value 0. In the reality this would correspond to a very low value. Other material parameters are similar as in (Černivec et al., 2008). The effective density of states is

ZnO:Al i-ZnO CdS SDL CZTSSe

calculated from the corresponding effective masses (Sze & Ng, 2007).

*W* [μm] 1.6 0.2 0.05 0.1 60 *me* [*m0*] 0.27 0.27 0.27 0.09 0.09 *mh* [*m0*] 0.78 0.78 0.78 0.73 0.73 *ND* [cm-3] 1018 1018 1018 - - *NA* [cm-3] - - - - - *Eg* [eV] 3.3 3.1 2.4 1.4 1.4 *Eχ* [eV] 4.0 4.0 4.0 4.0 4.0 *Ε* [*ε*0] 9.0 9.0 9.0 13.6 13.6 *μe* [cm2/Vs] 100 100 100 **40 8** *μh* [cm2/Vs] 25 25 25 **15 1.5** *NtA* [cm-3/eV] - - - **4x1017 8x1016** *EtA* [eV] - - - **0.7 0.05**  *σnA* [cm2] - - - **2x10-15 2x10-15** *σpA* [cm2] - - - **8x10-13 8x10-13** *etA* [eV] - - - **0.1 (step) 0.02 (gauss)** *NtD* [cm-3/eV] - - - **8x1019 7x1017** *EtD* [eV] - - - **0.7 0.15**  *σnD* [cm2] - - - **8x10-14 10-14** *σpD* [cm2] - - - **2x10-15 10-15** *etD* [eV] - - - **0.1 (step) 0.3 (step)**

Table 2. Material parameters of the CZTSSe MGL monograin layer solar cell.

*f*=10kHz.

, (3)

Fig. 12 shows the measured and simulated *J-V* characteristics of the CZTSSe MGL solar cell. The measured characteristics were obtained from the *I-V* characteristics normalized to the contacting area of the solar cell equal to *A* = 4.81 mm2. Here we used the assumptions i) and ii) as defined in 3. Since the CZTSSe monograins shape in the spherical forms this means that the real current density varies throughout the structure. In the simulated *J-V* characteristics at 310 K we also took into account the *SFF* as the assumption iii). This means that the *Jsc* obtained by using the parameters from Table 2 would in fact be larger by this factor.

In Fig. 12 we can observe a very good agreement of the measured and simulated *J-V* characteristics at 310 K while the simulation at 210 K exhibits a discrepancy in all solar cell output parameters. A possible reason for the non-matched *Jsc* at 210 K could be that in the modelling we did not account for the temperature dependent mobility, which could be the case as seen from the van der Pauw measurement of the monograin tablet (Fig. 5).

Fig. 12. Comparison of the measured and simulated *J-V* characteristics of the AM1.5 illuminated CZTSSe monograin solar cell.

Dashed lines in Fig. 12 represent the simulation and the arrow indicates temperature decrement. The short-circuit current and the open-circuit voltage trends are well correlated while their absolute value deviation at the low temperature indicate the necessity to include the temperature dependent mobility and the tunnelling enhanced recombination, respectively. At 210 K a significant mismatch also occurs with the *Voc*. This leads us to the conclusion that it is not merely the SRH recombination (Sze & Ng, 2007) in the SDL layer that limits the *Voc*, but there should also be present other recombination mechanisms which are less thermodynamically affected, namely the tunnelling enhanced recombination (Dumin & Pearson, 1965). The tunnelling enhanced recombination would reduce the rate of the *Voc-T* change.

Analysis of CZTSSe Monograin Layer Solar Cells 333

is still about 3 times larger than the measured (simulated) *Jsc* at 310 K, showing tremendous possibilities in improvement of the collection efficiency of the monograin CZTSSe absorber.

We have set up the baseline model of the Cu2SnZn(Se,S)4 monograin layer solar cell, which is able to predict the *J-V* characteristics and the external *QE* of the AM1.5 illuminated MGL solar cell in the temperature range from 310 K to 210 K. The model comprises following

i) in between the CdS and CZTSSe layers, the highly defective region called the surface defect layer – SDL, comprising a high concentrations of the mid-gap donor defects and a

ii) in the CZTSSe monograin layer the narrow Gaussian distribution of shallow acceptor traps at 0.05 eV above the valence band and the wider distribution of the compensatory donor traps extending at least 0.3 eV deep into the energy band, relative to the valence band; iii) energy gap of the CZTSSe monograin material equals to 1.4 eV, width of the SCR at 310 K equals to 180–200 nm and the concentration of the apparent doping *pSCR* is in the range

Low *FF* can be attributed to the low CZTSSe hole mobility, which equals to 1.5 cm2/Vs, and to the low apparent doping *pSCR*, which originates from the compensatory effect of the shallow acceptors and deeper donors. Comparison of the flux absorbed in the CZTSSe monograin absorber and the three times lower actual current density of the extracted carriers shows us that further possibilities may reside in the shaping of the collection efficiency of the monograin absorber and/or in the additional passivation of the CdS/CZTSSe interface. Since the former is mainly attributed to the SCR this might not be an easy technological task. Whether these limiting properties are the result of the necessary surface engineering prior to the formation of the CdS/CZTSSe monograin heterojunction or they simply originate from the physical properties of the structure's materials, we were be

Authors would like to thank prof. dr. Jüri Krustok, Tallinn University of Technology, for his objective criticism which helped to improve the quality of this work. We also thank prof. dr. Marko Topič, University of Ljubljana, for his approval on the use of the simulation software

Altosaar, M.; Jagomägi, A.; Kauk, M.; Krunks, M.; Krustok, J.; Mellikov, E.; Raudoja, A. &

Altosaar, M.; Danilson, M.; Kauk, M.; Krustok, J.; Mellikov, E.; Raudoja, J.; Timmo, K. &

Varema, T. (2003). Monograin layer solar cells. *Thin Solid Films*, Vol. 431-432, pp.

Varema, T. (2005). Further development in CIS monograin layer solar cells technology. *Solar Energy Materials & Solar Cells*, Vol. 87, pp. 25-32, ISSN 0927.0248 Breitenstein, O.; Altermatt, P.; Ramspeck, K. & Schenk, A. (2006). The origin of ideality

factors N>2 of shunt and surfaces in the dark I-V curves of SI solar cells, *Proceedings* 

**5. Conclusion** 

material properties:

from 1x1016 cm-3 to 2x1016 cm-3.

not able to determine at this point.

466-469, ISSN 0040.6090

**6. Acknowledgments** 

Aspin2 and Sun*Shine*.

**7. References** 

lower concentration of the mid-gap acceptor defects;

The optical simulations were performed using the Sun*Shine* simulator (Krč et al., 2003) which takes as an input a layered structure with the wavelength dependent complex refraction index coefficients, which comprise the real part *n*(*λ*), called refractive index, and the complex part *k*(*λ*) known as the extinction coefficient. Both are defined in for each layer. For the monograin material we used the complex refraction index coefficients as obtained by Paulson (Paulson et al., 2003) for the thin film Cu(In1-*x*Ga*x*)Se2 alloy with the *x* = 0.66. This corresponds to the energy gap of 1.41 eV. The layer's interfaces were described using the roughness coefficient – *σrms*. In our case we set the *σrms* equal to 100 nm at all interfaces. Simulation of the external quantum efficiency (Fig. 13) shows a good agreement between the measured *QE* and the simulated *QE* in the shorter wavelengths region, while in the middle wavelengths there seems to exist some discrepancy – most probably due to the discrepancy between the measured and modelled *μh,CZTSSe*. The cut-off wavelengths are well pronounced at both temperatures and correspond to the band-gap of 1.4 eV. In the long wavelength region (*λ* > 900 nm) the non-vanishing plateau of the simulated *QE* points to a mismatch in the absorption properties of the thin film CIGS and the monograin layer CZTSSe materials.

Fig. 13. Comparison of the measured and simulated external quantum efficiency of the AM1.5 illuminated CZTSSe monograin solar cell.

In Fig. 13 dashed lines represent the simulation and the arrow indicates temperature decrement. The non-vanishing plateau of the simulation originates from the mismatch in the absorption properties of the thin film CIGS (used in the simulation) and the monograin layer CZTSSe materials.

Both, measured and simulated *QE* show that the temperature change does not affect their shape, which inclines us to a conclusion that most of the photogenerated carriers recombine in the SDL and at the SDL/CZTSSe interface. This fact can as well be observed from the cumulative recombination profile (not shown here).

The absorptance simulations show that if all photogenerated carriers originating from the photon flux absorbed in the CZTSSe layer were extracted, the *Jsc* would equal to 37.7 mA/cm2. Taking into account the *SFF* the latter would reduce to a 29.4 mA/cm2. This value is still about 3 times larger than the measured (simulated) *Jsc* at 310 K, showing tremendous possibilities in improvement of the collection efficiency of the monograin CZTSSe absorber.
