Design and Numerical Analysis of Thin Film Solar Cells Based on Cu 2 ZnSn (S x Se 1-x ) 4 with SnO 2 TCO and ZnS Buffer

— Due to their earth-abundance, direct and adjustable bandgap in the range of visible light, and lower fabrication cost on large areas, Cu 2 ZnSn(S x Se 1-x ) 4 semiconductors, commonly known as kesterite, are gaining recognition as potential materials for affordable, environment‐ friendly, and high‐efficiency thin‐film photovoltaics. In this work, we numerically investigated the performance parameters of a single-heterojunction solar cell using Cu 2 ZnSnS 4 (CZTS) / Cu 2 ZnSnSe 4 (CZTSe) absorber layer and ZnS buffer layer, with SnO 2 transparent conducting oxide (TCO) under a range of operating conditions and cell parameters. Maximum efficiency of 20.68% was obtained for a 5.5 µm absorber layer with 0.01 µm ZnS buffer layer for Cu 2 ZnSnSe 4 solar cell, and 22.86% was obtained for a 6 µm thick Cu 2 ZnSnS 4 absorber layer with 0.03 µm ZnS layer at room temperature and standard irradiance. The increase of irradiance to thrice the standard value led to 1% and 5% increase in efficiency for CZTS and CZTSe cells, respectively. Efficiency increased by 39% and 6.6% when the front surface was textured at an angle of 90° for CZTS and CZTSe cells, respectively. The CZTS and CZTSe based solar cells with optimized thickness and 90° textured front surface with three times the standard irradiation, showed 25.59 % and 21.52 % efficiency with open circuit voltage 1045 mV and 579.4 mV and short circuit current 85.84 mA/cm 2 and 140.7 mA/cm 2 , respectively. The proposed architecture in this study will help produce next-generation solar cells that are both economical and energy-efficient.


I. INTRODUCTION 1
Photovoltaic solar cells have gained popularity over conventional energy sources since it is green, renewable, and sustainable, and the recent development of relatively highefficiency solar cells [1], [2].Solar energy now accounts for 3.74% of all electrical energy generated, a 1,000-fold growth over the last 20 years [3].The efficient operation of a photovoltaic (PV) cell requires three major factors: the absorption of light to generate electron-hole pairs, the separation of charge carriers of opposite polarity, and the collection of charge carriers.Hence, the choice of material for the absorber layer, buffer layer, and charge conduction layer is crucial for highly efficient solar cell design.Based on the technology development stages solar cells are classified as first, second, and third generation solar cells.The first generation of cells is made of crystalline silicon, the PV technology that is most frequently used commercially and Submitted on June 12, 2023.Published on October 11, 2023.N. Sultana, Ahsanullah University of Science and Technology, Bangladesh.(e-mail:naznin_buet.eee@aust.edu)includes elements like polycrystalline and monocrystalline silicon.The second generation of solar cells is thin film solar cells, which uses amorphous silicon, CdTe, and CIGS as photon absorber.They have substantial commercial value in small stand-alone power systems, integrated photovoltaic (PV) buildings, and utility-scale solar power plants.High power conversion efficiency (PCE), direct and adjustable bandgap (Eg), reduced material requirement, and lower fabrication cost on large areas have turned thin film solar cells into one of the emergent fields in photovoltaics (PV) [4].CIGS-based thin film solar cells deliver the highest efficiency of 23.6% [5] in lab environment among second-generation thin film solar cell technologies.However, the limited resources of high-priced Indium (In) and Gallium (Ga) and the complicacy in large-scale fabrication impede the future mass production of CIGS-based solar cells [6].Several thinfilm technologies, or emerging photovoltaics, are included in the third generation of solar cells; most of these technologies have not yet been used commercially and are still in the research or development stages.Earth-abundant kesterite, such as CZTS(Se) is a promising absorber layer of the thirdgeneration thin film technologies, which might be the future of high-efficiency thin film solar cells [7].The Cu2ZnSn(SxSe1-x)4 compounds are rich in nature and inexpensive, thus making them lucrative for future mass production.Moreover, high optical absorption coefficients (~10 4 cm -1 ) and tunable bandgap properties (1eV to 1.5eV) of CZTS(Se) permits direct absorption of incident solar energy using a very thin absorber layer [1], [8]- [10].The availability of the elements Zn and Sn present in CZTS(Se), is far larger than In [11].Additionally, it is feasible to replace CIGS with CZTS(Se) in the CIGS solar cells [12].Although CZTS(Se) based solar cells have great potential for future photovoltaics, the relatively low conversion efficiency compared to CIGSbased solar cells [13] makes it necessary to design an efficient cell structure and to conduct a comprehensive study of the effects of various cell parameters and working conditions on CZTS(Se) based solar cells for optimization purposes.
In this work, we designed thin film solar cells using a kesterite-based absorber layer with bilayers of SnO2:F (FTO) and undoped SnO2 (TO) transparent conducting oxide (TCO) and ZnS as a buffer layer.Due to its non-toxicity and broad band gap (3.69 eV), ZnS can be a potential buffer layer in CZTS(Se)-based solar cells [14].SnO2 is used as the transparent conducting oxide (TCO) due to its thermal and structural stability, availability, and low costs.With a high direct bandgap (>3 eV), the transmittance of SnO2 is near 80% in the visible range [15].The desired material A. Zubair, Bangladesh Universitty of Engineering and Technology, Bangladesh.(e-mail:ahmedzubair@eee.buet.ac.bd)Design and Numerical Analysis of Thin Film Solar Cells Based on Cu 2 ZnSn (S x Se 1-x ) 4 with SnO 2 TCO and ZnS Buffer Naznin Sultana and Ahmed Zubair parameters required for the device simulation are either used from literature or assumed with proper justification to understand the device's performance well.Various electrical performance parameters were studied with the variation of solar irradiance, temperature, front surface texture along absorber and buffer layer thickness for the proposed cell.The results obtained in this work may be helpful for the design and fabrication of high-performance, low-cost CZTS(Se) based solar cells.

II. METHODOLOGY
Numerical simulation was performed by solving onedimensional semiconductor equations in a steady state and setting a variety of boundary conditions for different semiconducting layers and heterojunctions.The potential field was determined by solving the Poisson's equation that is given by: Continuity equations for electrons and holes are given by: Here, ε is the dielectric constant of the material, ψ is the electrostatic voltage, n and p are the electron and hole concentrations in the device, respectively.  + and   − are donor and acceptor concentrations, respectively.G is generation rate of charge, whereas Jn and Jp are electron and hole current density, Rn and Rp are electron and hole recombination rates, respectively.µn and µp are mobilities and Dn and Dp are diffusion coefficients of electron and hole, respectively.
The electrical performance parameters of solar cell are calculated using the equations from (6) to (9).The short circuit current density can be determined from: Here,   = short circuit current density,   = saturation current, kB = Boltzmann constant, V = bias voltage, T = temperature in Kelvin.The open circuit voltage is given by: The fill factor is defined as: and   are the current density and voltage, respectively, at maximum power point.Efficiency is provided by:  =        (9) where   = Power density of incident light.

III. DEVICE STRUCTURE
In our proposed SnO2:F\i-SnO2\ZnS\CZTS(Se)\Mo solar cell, CZTS(Se) was used as the absorber layer that had 1 μm thickness and inherently p-type.ZnS was used as buffer layer and bilayers of SnO2:F (FTO) and intrinsic SnO2 (TO) transparent conducting oxide (TCO) on top were incorporated.A p-n heterojunction was created between ptype CZTS(Se) and n-type ZnS.To avoid toxicity from Cd of the conventional buffer layer CdS [16], ZnS was chosen.SnO2 was used as TCO due to its high transmittance in visible light regime [17].The electrical and optical properties of various layers of the solar cell (i.e.SnO2:F, i-SnO2, ZnS) is given in TABLE I. Various parameter values, which were utilized here, were taken from previous reports [18], [19].Fig. 1. shows the proposed solar cell structure.The electrical and optical properties of absorber layer CZTS and CZTSe considered for the calculations are given in TABLE II [20]- [24].

IV. RESULTS AND DISCUSSIONS
The effect of varying operating conditions and device parameters on solar cell performance such as open circuit voltage, short circuit current, fill factor and efficiency for our proposed SnO2:F/i-SnO2/ZnS/Cu2ZnSn(SxSe1-x)4/Mo solar cell were comprehensively explored using AFORS-HET simulation package [25].The standard test condition for solar cells was the Air Mass 1.5 spectrum, an incident power density of 1000 Wm -2 , at an ambient temperature of 25 ºC.

A. Current-Voltage Characteristics
The Relationship between current density () and voltage () for both absorber layer CZTS and CZTSe is shown in Fig. 2(a).Cu2ZnSnS4 has a bandgap of 1.5 eV, whereas Cu2ZnSnSe4 has bandgap of 1 eV.Hence, open circuit voltage for absorber layer CZTS is higher than CZTSe, while short circuit current has the reverse relation [26]- [28].Fig. 2(b) illustrates the power output for CZTS and CZTSe solar cells.Although CZTSe solar cell produced lower voltage compared to CZTS solar cell, it generated higher output power since its current density was much higher than that of the CZTS solar cell.The maximum power density for CZTSe and CZTS solar cell were 16.38 mW/cm 2 and 13.67 mW/cm 2 , respectively.For our proposed devices, different electrical performance parameters for solar cell with absorber layer Cu2ZnSnS4 and Cu2ZnSnSe4 are presented in Table III.It is evident that fill factor and efficiency of Cu2ZnSnSe4 was higher than those of Cu2ZnSnS4.

B. Dependence on Solar Irradiance
The solar spectral irradiance can be defined as the intensity of the entire sun at different wavelength of light on a surface.Our proposed solar cell was simulated under the illumination of typical solar intensity to thrice the intensity of 1 sun to observe the effect of solar irradiation on different solar cell performance parameters.Increasing the incident light intensity on a solar cell may increase the possibility of higher efficiency and lower device cost.

1) Effect on Open Circuit Voltage
Increasing light intensity increases open circuit voltage of solar cell logarithmically [29].The open circuit voltage,   ′ for certain irradiance,  is given by: Here,   = open circuit voltage at the standard test condition for solar cell, q=charge of electron.Fig. 3(a We utilized this wavelength range in our simulations.

2) Effect on Short Circuit Current Density
Short circuit current increased linearly with light intensity as the increase of light intensity means more photons availability for generation of additional charge carriers [28].The short circuit photocurrent density,   is expressed as: (11) where, φ (λ) and EQE (λ) are the solar flux concentration and effective quantum efficiency at a particular wavelength, λ.
The   showed linear dependence on spectral intensity for both CZTS and CZTSe as can be seen in Fig. 4 (a).For 3*sun spectral intensity, the short circuit current density reached 57.71 mA/cm 2 and 127.9 mA/cm 2 for CZTS and CZTSe based solar cell, respectively.The short circuit current density tripled with spectral intensity.

3) Effect on Fill Factor and Solar Cell Efficiency
Since   and   both increase with light intensity, fill factor decreases with intensity for CZTS and CZTSe solar cells.Fig. 4 (b) demonstrates the dependence of fill factor on spectral intensity.As the open circuit voltage increased logarithmically and the short circuit current increased linearly with spectral intensity, the efficiency of solar cell also increased.Fig. 4 (c) displays the dependence of efficiency on spectral intensity for the proposed solar cells.The increase in efficiency for CZTSe solar cell was much higher than that for CZTS solar cell because of the higher increment rate in short circuit current.Efficiency increases from 13.67% to 13.8% for CZTS cell with irradiation increases to three times the standard value, and 16.38% to 17.22% for CZTSe cell.The efficiency of the CZTS and CZTSe cells increased by 1% and 5%, respectively, when the irradiance was increased to three times the standard value.However, series resistance, which causes losses in the solar cell and lowers efficiency, was not taken into consideration in our simulation.

C. Impact of Temperature Variation
Similar to other semiconductor devices, the susceptibility of solar cells to temperature is an important consideration in designing solar cells.Since the temperature increase reduced bandgap of the absorber, it affected the electrical behavior of the cell.

1) Effect on Open Circuit Voltage
Among the cell parameters, open circuit voltage showed the most sensitivity toward temperature variation.The increase in temperature reduces the bandgap of the absorber layer, which results in a decrease of open circuit voltage [30].The rate of change of open circuit voltage with respect to temperature is given by: The larger the open circuit voltage of a solar cell, the lower the negative temperature coefficient.Fig. 5 (a) illustrates the relationship between open circuit voltage and temperature for CZTS and CZTSe solar cells.The negative temperature coefficient for the open-circuit voltage was found to be -1.91 mV/K and -1.87 mV/K for CZTSe and CZTS, respectively, which is lower than Si solar cell [31].

2) Effect on Short Circuit Current Density
The short circuit current density,   increased slightly with temperature since the bandgap energy, Eg decreased, and more photons had enough energy to create electron-hole pairs (EHPs).However, for both CZTS and CZTSe solar cells temperature change had an insignificant effect on short circuit current density.Fig. 5 (b) depicts dependence of short circuit current density on temperature.
3) Effect on Fill Factor Fig. 5 (c) shows dependence of fill factor on temperature.Temperature dependency of fill factor can be approximated by equation ( 13) [31].The change in fill factor is given by: 4) Effect on Solar Cell Efficiency Fig. 5 (d) shows the relation between cell efficiency and temperature for CZTS and CZTSe solar cells.Temperature increase caused the generation of more intrinsic carriers.Therefore, the rate of carrier recombination increased, and efficiency fell with temperature rise [31].The negative temperature coefficient of efficiency for CZTSe was much higher than CZTS, since the band gap of CZTSe was lower than CZTS, and generation of carriers was higher in CZTSe.The negative temperature coefficient of efficiency of CZTS and CZTSe were found to be -0.005%/K and -0.06%/K, respectively, at room temperature.

D. Effect of Front Contact Texture
Light trapping for a high efficiency solar cell can be realized through modifying the angle at which light incidents on the solar cell by using a textured front surface.In plane front surface solar cell, a portion of the incident light is directly reflected, and the rest gets transmitted, a big portion of which gets absorbed in the medium.Fig. 6 (a) shows the mechanism of incident light on a plane surface.In a textured surface the reflected light before escaping the solar cell, again incidents on the angled surface of the cell, and a relatively smaller portion gets reflected.A textured surface also provides a longer optical path length than the physical device thickness of the solar cell, thus increasing the probability of light getting absorbed and increasing charge carrier generation [32] [33].

2) Effect on Short Circuit Current Density
The textured surface increased the probability of incident light getting absorbed in the absorber layer, hence the generation of charge carriers increases with front surface angle.Fig. 7 (b) shows the dependance of textured surface angle on short circuit current density for both CZTS and CZTSe solar cell.The short circuit current density increased with the front surface angle for kesterite solar cell.The increment rate is higher for CZTS solar cell.For 90° surface texture angle, the short circuit current densities were 25.33 mA/cm 2 and 44.14 mA/cm 2 in CZTS and CZTSe solar cell, respectively.
3) Effect on Fill Factor Fig. 7 (c) shows the dependance of textured surface angle on fill factor for both CZTS and CZTSe solar cell.Fill factor increases with the front surface angle.For 90° surface angle the fill factor is 77.38% and 78.06% in CZTS and in CZTSe solar cell, respectively.4) Effect on Efficiency Fig. 7 (d) shows the dependance of textured surface angle on efficiency for both CZTS and CZTSe solar cell.Since short circuit current density increased with surface angle and a slight increment in open circuit voltage with surface angle was observed, efficiency increased with surface texture angle as well.Although for smaller surface angle efficiency was lower in CZTS than CZTSe, CZTS solar cell showed highest efficiency of 18.93 % at 90° surface angle whereas for CZTSe solar cell maximum efficiency was 17.46%, since   for CZTS was much higher at 90°.When the front surface is textured at an angle of 90° degrees for CZTS and CZTSe, respectively, efficiency rises by 39% and 6.6%.

E. Effect of Material Layer Thickness
Optimum thickness indicates the absorber layer thickness for which best performance is achieved.Larger absorber layer thickness helps reduce reflection of the incident light and according to Beer-Lambert's law, greater thickness increases amount of light getting absorbed, resulting in more EHPs generation, which guarantees high efficiency solar cell.However, greater thickness also increases the probability of charge trapping and recombination of generated charges.Consequently, selecting optimum absorption layer thickness is crucial for superior performance of solar cell.Therefore, the light got absorbed at a smaller thickness and for lesser layer thickness saturation is achieved.

2) Effect on Short Circuit Current Density
Figs. 8 (c) and (d) demonstrate the dependency of the short circuit current density on the CZTS(Se) layer thickness and ZnS layer thickness for CZTS(Se) solar cell.For CZTS, saturation for short circuit current density of 26.67 mA/cm 2 occurred when the thickness was greater than 6 µm.For CZTSe, short circuit current density reached peak 46.4 mA/cm 2 at 4.9 µm.For both solar cells, reaching the saturation of   required higher thickness compared to open circuit voltage.3) Effect on Fill Factor Figs. 9 (a) and (b) show the dependance of the fill factor on the absorber layer and buffer layer thickness for CZTS and CZTSe solar cell, respectively.For CZTS, saturation for fill factor occurred when thickness was 1.5 µm.For CZTSe saturation for fill factor occurred when thickness is 6 µm.4) Effect on Efficiency Fig. 9 (c) shows the dependance of the efficiency on the absorber layer and ZnS layer thickness for CZTS solar cell.For CZTS saturation for efficiency occurred when the thickness was 6 µm with 0.03 µm buffer layer 22.86%.Fig. 9 (d) shows the dependance of the efficiency on the absorber layer and ZnS layer thickness for CZTSe solar cell.For CZTSe, saturation for efficiency occurred when the thickness is 5.5 µm with ZnS thickness of 0.01 µm and efficiency is 20.68%.V. CONCLUSION The urgent demand for large scale sustainable and green energy source to solve imminent global warming threat as well as providing world energy security, caused the emergence of third-generation thin film solar cells.Natural origin, non-toxicity and possessing optical and electrical properties suitable for solar cells make kesterite one of the potential candidates for third-generation solar cells.In this work, design and numerical analysis of a CZTS(Se)-based solar cell with ZnS buffer layer and SnO2 transparent conducting oxide layer operating under AM.1.5Gsolar spectrum at room temperature was performed.Performance analyses were conducted for different cell parameters and operating conditions for both CZTS and CZTSe solar cells.At 25 °C temperature and 1000 W/m 2 light intensity, the efficiency achieved for 1 µm Cu2ZnSnS4 is 13.67% with open circuit voltage 957.6 mV and short circuit current density 19.23 mA/cm 2 .For Cu2ZnSnSe4 with 1 µm absorber layer thickness, the efficiency was 16.38% with open circuit voltage 505.2 mV and short circuit current density 42.63 mA/cm 2 .The performance was enhanced by implementing a textured front surface and by increasing intensity of incident light.We obtained optimum thickness for which maximum efficiency occurred.Maximum efficiency of 25.59% was achieved for a 6 µm thick CZTS absorber with 0.03 µm of ZnS layer, whereas maximum efficiency of 21.52% was achieved for a 5.5 µm thick CZTSe absorber with 0.01 µm of considering drift and diffusion of electrons and holes are provided by:  = µ   +   (4)  = µ   −   .

Fig. 1 .
Fig. 1.Structure of the proposed kesterite solar cell consisted of SnO2:F, i-SnO2, ZnS, CZTS(Se), and Mo.The substrate of the cell was glass.
Fig. 2. (a) J-V characteristics of CZTS (magenta dashed line) and CZTSe (blue dotted line) based solar cells.(b) Power density vs voltage curves for CZTS (magenta dashed line) and CZTSe (blue dotted line) based solar cells.

Fig. 3 .
) and Fig. 3(b) show logarithmic dependence of open circuit voltage on spectral intensity for CZTS and CZTSe based cells, respectively.For 3*sun irradiances, the open circuit voltages attained were 986.1 mV and 533.9 mV for CZTS and CZTSe solar cells, respectively, which were 3% and 5.7%, respectively, higher than the open circuit voltage obtained at typical solar intensity.Open circuit voltage as a function of spectral intensity for (a) CZTS and (b) CZTSe absorber layer.Inset shows the solar irradiance per unit time per unit area for different wavelengths ranging from 300 nm to 1200 nm.

Fig. 4 .
Relationship between different electrical parameters and spectral intensity for CZTS (magenta dashed line) and CZTSe (blue dotted line) absorber layer.

Fig. 5 .
Dependence of various electrical performance parameters on temperature for CZTS (magenta dashed line) and CZTSe (blue dotted line) based solar cells.

Fig. 6 (Fig. 6 . 1 )
b), shows the mechanism of incident light on a textured front surface.Mechanism of incident light on (a) plane and (b) textured front surface.Effect on Open Circuit Voltage Fig. 7 (a) shows the dependance of textured surface angle on open circuit voltage for both CZTS and CZTSe solar cell.It is apparent that the front surface angle does not have a substantial effect on the open circuit voltage for kesterite solar cell.The open circuit voltage reached 960 mV and 506 mV for CZTS and CZTSe solar cell, respectively, when textured angle is 90 °.

Fig. 7 .
Relation between electrical performance parameters-(a) open circuit voltage, (b) short circuit current, (c) fill factor, and (d) efficiency of solar cell and front surface angle for both CZTS (red dashed line) and CZTSe (blue dotted line) solar cells.

Fig. 8 (
a) shows the dependance of the open circuit voltage on the absorber layer and ZnS layer thickness for CZTS solar cell.With increase of absorber layer thickness, EHPs generation increased which resulted in photocurrent increase.Hence, the open circuit voltage increased for CZTS, and reached saturation when thickness was 3.8 µm.The maximum open circuit voltage was 1014 mV.When the thickness was further increased the opposite effect could be seen.ZnS layer thickness did not affect the open circuit voltage as apparent from Fig. 8 (a).Fig. 8 (b) shows the relationship between the open circuit voltage and the absorber layer and buffer layer thickness for CZTSe solar cell.For CZTSe, saturation for open circuit voltage occurred when thickness was 1.5 µm and maximum open circuit voltage was 553 mV.Since, bandgap of CZTSe was lower compared to CZTS, the probability of EHPs generation was higher.

Fig. 8 .
Relation between open circuit voltage and short circuit current density with layer thickness for (a), (c) CZTS and (b), (d) CZTSe solar cells.

F
. Optimization of CZTS / CZTSe Solar Cell The optimized thicknesses 6 µm for CZTS absorber layerwith 0.03 µm ZnS layer and 5.5 µm for CZTSe absorber layer with 0.01 µm ZnS layer were used to design efficient CZTS and CZTSe based solar cells.The irradiation intensity was three times the standard intensity and the front surface was textured at 90°.The open circuit voltage of CZTS and CZTSe solar cell were 1045 mV and 579.4 mV, respectively.The short circuit current density of CZTS and CZTSe solar cell were achieved at 85.84 mA/cm 2 and 140.7 mA/cm 2 , respectively.Optimized CZTS solar cell achieved an efficiency of 25.59% and CZTSe solar cell obtained an efficiency of 21.52%.

TABLE I :
THE MATERIAL PROPERTIES OF BUFFER LAYER AND TCO

TABLE II :
THE MATERIAL PROPERTIES OF CZTS AND CZTSE

TABLE III :
THE COMPARISON OF SOLAR CELL PERFORMANCE OF CZTS TABLE IV lists the electrical parameters of optimized CZTS and CZTSe solar cells.