Numerical Modeling of High Conversion Efficiency Mo/CZTS/CdS/ZnO/ FTO Thin Film – Based Solar Cells

This article describes in detail the numerical modeling of a CZTS (copper zinc tin sulfide) based kesterite solar cell. The Solar Cell Capacitance Simulator -one-dimension (SCAPS-1D) software was used to simulate MO/CZTS/CdS/ZnO/FTO structured solar cells. The parameters of different photovoltaic thin-film solar cells are estimated and analyzed using numerical modeling. The effects of various parameters on the performance of the photovoltaic cell and the conversion efficiency are discussed. Since the response of the solar cell is also contingent on its internal physical mechanism, J-V characteristic measures are insufficient to characterize the behavior of a device. Different features, as well as different potential conditions, must be considered for simulation, disregarding the belief in the modeling of a solar cell. With a conversion efficiency of 25.72%, a fill factor of 83.75%, a short-circuit current of 32.96436 mA/cm 2 and an open-circuit voltage of 0.64V, promising optimized results have been achieved. The findings will be useful in determining the feasibility of fabricating high-efficiency CZTS-based photovoltaic cells. The efficiency of a CZTS-based experimental solar cell is also discussed. First, the effects of experimentally developed CZTS solar cells are simulated in the SCAPS-1D environment. The experimental results are then compared to the SCAPS-1D simulated results. The conversion efficiency of an optimized system increases after cell parameters are optimized. Using one-dimensional SCAPS-1D software, the effect of system parameters such as the thickness, acceptor and donor carrier concentration densities of absorber and electron transport layers, and the effect of temperature on the efficiency of CZTS-based photovoltaic cells is investigated. The proposed results will greatly assist engineers and researchers in determining the best method for optimizing solar cell efficiency, as well as in the development of efficient CZTS-based solar cells.


Introduction
Solar cells have emerged as a more recent and relatively renewable energy source that is both ecofriendly and cost-effective when produced on a larger scale. In the current scenario, photovoltaic devices with high power conversion efficiency and no material degradation are being developed for the generation of electricity [1]. For several years, silicon-based solar cells dominated the market. Advanced fabrication techniques are required for the manufacturing and production of silicon-based solar cells, which makes the solar panel expensive [2]. Thin film solar cells are becoming more popular as manufacturing capabilities improve. Thin film technology is one of the most cost-effective and efficient methods of producing solar cells, and it is a hot topic of research in the photovoltaic industry. Thin film technology is more cost-effective than other technologies because it uses less material and is based on a range of light-absorbing semiconductor materials [3]. Among these materials, Kesterite solar cells utilizing copper zinc tin sulfide Cu2ZnSnS4 (CZTS) and their alloys are a promising alternative for the chalcopyrite absorbers [4][5][6]. These excellent optical and electrical properties with an optical band gap from1.4eV to 1.5eV along with a large absorption coefficient of (α ˃ 104 cm -1 ) of the CZTS has made it an interesting insight for the community of thin film [7]. By tuning the band gap, a CZTS-based solar cell can theoretically achieve an optimum conversion efficiency of around 28%, according to the Shockley-Queisser limit. However, due to a lack of understanding of device characteristics, it is not experimentally possible to achieve 28 percent conversion efficiency from a solar cell [8]. Numerical modelling can play a major part in a deeper understanding of system characteristics by modelling various device architectures, which can save time and money for the research community. In this work, computational modeling was carried out for estimating and analyzing the effect of physical parameters such as thickness and doping concentration of absorber, buffer and window layers and temperature effect on system output. The simulation program "Solar Cell Capacitance Simulator" was used to model the unit (SCAPS-1D). To begin, a simple heterostructure for CZTS/ CdS/ ZnO thin films with molybdenum (Mo) as the back contact and indium tin oxide (ITO) as the front contact was analyzed. Variations in absorber thickness, doping concentration, and working temperature were found to affect solar cell performance through analysis. First, the effects of experimentally developed CZTS solar cells were simulated in the SCAPS-1D environment. The experimental results were then compared to the SCAPS-1D simulated results. The main goals and objectives of this research are to use computational modelling to improve the performance of thin film solar cells, to suggest new ways to improve the efficiency of experimental solar cells, and to find alternative methods to reduce the cost of thin film solar cells. The effects of the thickness, doping concentration, and working temperature of the absorber, buffer, and window layers, as well as the working temperature, were investigated to analyze their effect on the cell performance.

Numerical Modeling and Material Parameters
Numerical modeling is a methodology for evaluating system behavior using complex mathematical models and assisting in the production of analytical solutions. In the manufacturing and fabrication of efficiently operating semiconductor-based photovoltaic modules, numerical analysis can be very useful. Because of seeking the most optimal and effective ways to solve a complex problem, the integration of real-life problems with virtual machine environments is the highest priority task of numerical modeling techniques implementation for design engineers and researchers [9]. Since real-world design problems can be solved in computer-based testing environments without needing physical or functional implementation, academic institutions and universities emphasize computer-based learning techniques. Modeling methods are used to calculate fundamental physical properties including the concentration of holes and electrons, as well as the electrical potential. It also offers more information about how material physical parameters impact system functional parameters or characteristics. Physical material parameters are used as input to simulation software for numerical modeling of solar cells [10]. Experimental data is needed to convert the real or actual device J-V characteristics and functional parameters such as quantum conversion performance, fill factor, open circuit voltage, and short circuit current into device modeling. Numerical simulation allows for a deeper and more straightforward understanding of system behavior. The simulation software that can be used for device modeling must be able to solve semiconductor basic equations like the continuity equation for holes and electrons and the Poisson equation relating charge to electrostatic potential to gain a better understanding of a device's output.

Numerical Modeling
The electrons and holes move in opposite directions is the main cause of current flow. The number of electrons and holes are equal. Hole mobility µp is practically half of the electron mobility μ [11]. The overall flow of current density ( ) is due to electron and hole flow is given by "Eq.1" and are the electron and hole mobilities (cm 2 /Vs), and are free electrons densities in an intrinsic semiconductor (cm -3 ), is the elementary charge (1.6x 10 -19 C), and is the applied electric field (V/m). The conductivity of semiconductor depends on current carriers and the number of current carriers presented per unit volume. From the above equation with an increase in temperature, and increases and the conductivity of intrinsic semiconductor increases, which means resistivity decreases. Shockley's equation explains the general characteristics of forward and reverse biasing regions of diode [12]. The diode current equation is given in "Eq.2": Where is diode current, is reverse saturation current, is diode voltage, is ideality factor, is Boltzmann's constant (1.38 × 10 / ), and is absolute temperature (K). The maximum current flow through the solar cell at zero load condition ( = 0) or short-circuit current ( ) at the voltage of a solar cell will be zero [13]. The flow of is due to the collection and generation of light generated carriers. It mainly depends on the number of incident photons as well as the spectrum, area of solar cell, optical properties and the collection probability of light generated carriers. The short current density (Jsc) can be found by Eq. (3) [14]: Where is the elementary charge, ( ) is the optical transmission, ∅ is the spectral power density, and ∆ is the interval between the two neighboring values of wavelength. The maximum voltage is taken from the solar cell ( is known as open circuit voltage ( ). When a solar cell is an open circuited, and no load is connected across the solar cell then current will be at its minimum (zero) value whereas the voltage will be at maximum value [15]. Energy conversion efficiency is the most frequently used parameter to relate the performance of two solar cells and is termed as . It is defined as the ratio of output power from a solar cell to the input power from the sun [15]. The energy conversion efficiency can be expressed by "Eq. 6"[16] The efficiency, depends on the parameters like incident sunlight intensity, solar cell working temperature and spectrum type. So, to compare two or more solar cells, it is important to carefully control the conditions under which η is measured. The incident light (photons) illumination is AM1.5G spectra through the calculation of the J-V characteristics in this numerical simulation analysis [17] The input power, , from the sun is considered as 1000 W/m 2 , and its properties are summarized in Table (2). The quantum efficiency ( ) is the ratio of the extracted free charge carriers by the solar cell to the number of incident photons. In other words, relates to the response of a solar cell to different wavelengths. It may be given either as a function of energy or wavelength. The will be unity at the precise wavelength if all certain wavelength photons are absorbed and the resulting minority carriers are collected. The spectral response was evaluated based on the quantum efficiency measurements; the QE is defined according to the following Eq.
Where is electrostatic potential, is elementary electrical charge, , are relative and vacuum permittivity, and are hole and electron concentrations, , are charged impurities of donor and acceptor, and are holes and electrons distribution, respectively.
Where and are electron and hole current densities, is the recombination rate, and is the generation rate. Carrier transport occurs by drift and diffusion according to Eq. (10) and Eq. (11), respectively:

The thin-film solar cell device
The thin-film solar cell device was constructed by glass substrate as a back-supporting slide, molybdenum (Mo) thin layer film was deposited on the glass substrate layer, CZTST (p-type) layer with a thickness of (1200 -3600 nm) was deposited on Molybdenum that is coated the back of substrate glass. The CdS (n-type) used as a buffer layer with a thickness of (10-100 nm), ZnO layer (n-type) with a thickness of (40-280 nm) was used as a window and FTO with a thickness (280 nm) was used as transparent conducting oxides (TCO). The materials for the modeling device were chosen for their efficiency, stability, low cost, and ease of preparation. The illustration for the modeling layers layout is shown in Fig. 1. These essential components of a device are utilized to determine a solar cell's electrical and photoelectric properties.

Material Parameters
In order to solve the basic semiconductor equations, input parameters, also known as physical parameters, are required. Layer thickness, electron-hole mobility, intrinsic carrier concentration, electron affinity, band gap and doping density of absorber, buffer, and window layers, among other physical characteristics utilized in SCAPS 1D software for numerical analysis, are mentioned in " Table 1." All simulations are run with 1.5AM solar radiation and a power density of 100 mW/cm 2 for the lighting source. " Table 2" lists the functional properties of solar cells. The qualities of the back and front contact parameters are provided in " Table 3." The device's construction has two goals in common. The first is analyzing and verifying real-world device behavior, and the second involves simulating a device for certain physical parameters and predicting the results. The behavior of the reference device (s) was effectively simulated, which defines successful device modeling. Physical or input parameters are obtained from referenced device experimental data to create device modeling. Batch simulations are used to monitor and assess predefined physical parameters such as carrier concentration densities and layer thickness. The SCAPS-1D program outputs the J-V characteristics curve, band alignment diagram, spectral response, and other functional parameters including , , , and , which are highly useful for fabricating an efficient photovoltaic device. All measurements are made in both lit and dark circumstances, as well as a function of temperature. Thermal velocity and effective density of states are temperaturedependent quantities, whereas band gap and mobility are temperature-independent parameters.    The major objective of this section is to create a thinner CdTe layer without sacrificing device performance. As a result, the cost of manufacturing solar cells may be reduced by reducing the amount of materials used in the process. The thickness of a device's absorber layer has a direct impact on conversion efficiency ( ). " Table 4 nm, whereas FF declines to a point where the ideal thickness is obtained. The conversion efficiency ( ) will remain constant once the ideal settings are reached. Furthermore, increasing the thickness reduces the . The rise in with increased , is mostly due to increased absorption of longer wavelength photons, which affects the ration of photogenerated carriers. The thickness of the absorber layer that was chosen as the best was 2400 nm. However, one of the major issues with today's large-scale and mass-production CZTS solar cells is the thickness of the absorber layer.
The emission of electron-hole pairs is influenced by the wavelengths of the light. The thickness of the CdTe layer is responsible for these changes since a larger CZTS layer may absorb more photons across a wider wavelength range. Fig 2 (b) shows the influence of CZTS thickness on QE%. The QE% was estimated for a variety of CdTe thicknesses ranging from 1200 to 3600 nm. The QE% rose when the CZTS layer thickness was raised.
The layer thickness of more than 2400 nm has no significant effect on the pace of QE% increases.
This suggests that a thickness of 2400 nm is sufficient to absorb the vast majority of incoming photons. Because the generation zone in thinner CdTe layer cells is close to the high recombination back contact region, the quantity of created electron-hole pairs will be reduced, lowering the quantum efficiency. The generating mechanism happens distant from the rear in thicker CdTe layer cells. Finally, modeling findings indicate that the optimal thickness of the CdTe absorber layer is 2400 nm, with a percent of 23.02%.

Effect of CdS buffer (donor) layer thickness on the device performance
The effect of buffer layer thickness on solar cell performance is also investigated. One of the major goals of this simulation is to decrease the optical and electrical losses induced by the buffer layer in incoming radiation. The thickness of the buffer (CdS) layer was changed from 10 nm to 100 nm. " Table 5" and " Fig. 3 (a)" illustrate simulated outcomes. and . As a consequence, it was concluded that changing the thickness of the buffer layer had no

Effect of ZnO window layer thickness on the device performance
The incident radiation should pass through the ZnO (window) layer. The bandgap of ZnO is 3.3 eV (absorbs radiation of  < 300nm, UVC area). Visible and IR radiation are entirely transmitted through the ZnO layer, and CZTS may absorb them [27]. Table 6 shows that changing the ZnO layer thickness has no effect on device performance characteristics ( , , , and ). Fig. 4 (a) depicts the relationship between device performance efficiency characteristics and ZnO layer thickness. The use of a very thin layer of ZnO may result in leakage current, while a layer that is too thick may result in a poor carrier separation rate. Finally, 120 nm is chosen as the optimum and recommended layer. As demonstrated in Fig.4 (b), the QE% is unaffected by changes in buffer thickness in the range (40 nm to 280 nm). This may be ascribed to the window layer sharing a little amount of electron-hole pair creation. Finally, the 120 nm layer is chosen as the optimal and preferable layer.   (Table 7). The J-V curves show that as the acceptor charge carrier concentration ( ) of the CdTe layer is increased ( > 1 × 10 ), rises.
This rise implies that the open-circuit voltage ( ) of the CdTe layer is highly influenced by the acceptor charge carrier concentration ( ). The generated electric field in the depletion area is influenced when the acceptor (hole) carrier charge concentration of ( ) of the CdTe layer is high.
As a result, the free charge carrier recombination decreases, increasing the . While lowering the CdTe acceptor carrier charge concentration below 1 × 10 , causes higher optical losses, which might be due to back contact surface recombination.  This section's major goal is to minimize the buffer layer's losses (both optical and electrical). The carrier charge concentration level of the ZnSe layer was altered from 1 x 10 17 cm -3 to 1 x 10 18 cm -3 after that. " Fig. 6 (a)" and " Table 8" illustrate the outcomes of the donor concentration simulation. and are nearly constant as doping concentration increases, as shown in " Table 8."With a rise in doping concentration, the device's conversion efficiency and fill factor have altered marginally. If we increase the doping concentration in a buffer layer beyond the optimal amount (2.5 x 10 17 cm -3 ), the conversion efficiency and fill factor of a device stay steady and begin to drop.
As a result, the buffer layer's final ideal concentration value was 2.5 × 10 17 cm −3 . According to " Fig. 6 (a)," increasing the doping concentration in the buffer layer has no significant effect on the device's operation. As a consequence, it was deduced that a change in buffer layer concentration had no effect on the total output of a photovoltaic device. As the concentration of the buffer layer ( ) decreases, more incoming photons generated by the CdS layer are absorbed, reducing the number of photons that the absorber (CZTS) layer can absorb. As demonstrated in Fig. 6 (b), absorbed photons form fewer electron-hole pairs, resulting in a lower QE%. It can be seen that the QE% increases as the donor carrier charge concentrations rise. Based on the above, it is recommended to have a high buffer layer donner concentration ( ≈ 2.5 × 10 ) in the simulation for thin films.   Heating on solar cells increases as a result of incident light, which has an impact on photovoltaic cell performance. The solar cell panels are functioning at a temperature of above 300 K. The effect of the suggested cell's operating temperature is also explored. The temperature was measured in the range of 280 K to 400 K for research reasons. " Fig. 8 (a)" depicts the simulation findings.
Temperature has a direct effect on open circuit voltage, which has an impact on total photovoltaic cell performance. Photovoltaic cell performance degrades as the temperature rises. The material carrier concentration, band gaps, electron and hole mobility are all influenced by the greater temperature, resulting in a reduced cell conversion efficiency [29]. Because decreases as temperature rises, the reverse saturation current, is temperature dependent. As the temperature rises, the reverse saturation current increases, and this increase in current is the primary source of the drop in , as shown in Eq (12) [30]: where is the photocurrent created by light. The greater operating temperature gives electrons more energy. Because of the greater temperature, these electrons are more likely to recombine with holes before reaching the depletion area. The solar cell efficiency characteristics are shown in " Table 10" which shows that when the temperature rises, the device's conversion efficiency decreases. According to "Eq.12," a rise in operating temperature affects and , whereas climbs marginally to a stable limit with an increase in operating temperature (no significant effect).
This is owing to the temperate-affected drop in band-gap energy [31]. As a result, more farreaching radiation photons will be able to form electron-hole pairs. , on the other hand, decreases significantly when the temperature rises. The reverse saturation current ( ), which is temperature sensitive, is responsible for the reduction in levels with increasing temperature [32]. The inherent carrier concentration [33] is another important component that causes the decrease in with increasing operating temperature. The absorber layer's bandgap is usually rather small. The electron-hole pair recombination may be aided by the narrower bandgaps. The interatomic spacing rises as the amplitude of the atomic vibrations increases owing to increased thermal energy [34]. This behavior may be better understood if one thinks that the interatomic spacing grows when the amplitude of the atomic vibrations increases. The linear expansion coefficient of a material is used to quantify this impact. The potential observed by electrons in the material decreases as interatomic separation increases, reducing the energy bandgap. With increasing temperature, the FF percent decreases until it reaches a steady-state temperature limit.
Finally, when the temperature rises, the device's conversion efficiency decreases.
Quantum efficiency percent (QE%) profiles at different temperature values are shown in Figure   8(b). The QE% profiles were calculated based on the SCAPS-1D software program. The QE% profiles show a peak response to illumination wavelength. The QE% was ranged (80-90%) in the wavelength range (520-800 nm) and started lowering to 45% in the range below (300 -520) nm.
The lowering is due to the recombination and absorption in the absorber and buffer layer. The quantum efficiency was slightly affected with an increase in temperature that falls in the range of 2800-400 K. The QE% profile shows absorption maxima at ≈530 nm, this value is consistent with the input CZTS value ( =1.45eV). Fig. 8 (b) shows an absorption edge at 800 nm, which can be attributed to vacancy levels in the energy gap, which can be produced by doping. In addition, a minor effect in quantum efficiency with temperature was observed, which can be attributed to the short period in the studied temperature range (280-400), which meant that the range couldn't cause a noticeable effect on the semiconductor construction, and thus only a minor change in quantum efficiency was observed [35].    μm to 2.825 μm is FTO layer ( = 3.5). When the conduction band of the absorber layer is higher than the conduction band of the buffer layer, that leads to a "cliff" type band alignment [37]. This is the case of CZTS as the absorber of thin film, as shown in Fig. 10 (b). It can be shown that the absorber, buffer, and window layers have acceptable band alignment. Four recombination zones may be seen in the band diagram. Recombination at the back contact (region R1), bulk (Quasi-Neutral) recombination in the absorber layer (region R2), space charge (region R3), and absorber/buffer interface recombination (region R4) are the four areas. The thin absorber layer will maintain the back-contact close to the depletion zone, resulting in a considerable increase in back contact recombination. Reasonable neutral interface defects for recombination were also evaluated at mid-gap to accommodate recombination at the CZTS/CdS and CdS/ZnO interfaces [38]. The reflectance of the rear and front contact surfaces was tuned to 0.1 and 0.9, respectively ( Table 3).
Photons that traverse the absorber are reflected by this high reflectivity upon return contact, which improves absorption in the absorber.

Conclusion
The SCAPS program was used to model and analyze a kesterite MO/CZTS/CdS/ZnO/FTO-based solar cell. Researchers, designers, and engineers will find this work extremely valuable in studying and constructing CZTS-based systems. It should be emphasized that using J-V characteristics to explain the device's behavior is insufficient to fully comprehend the solar cell, which is due to the fact that the solar cell's reaction is also influenced by its internal physical mechanism. Several variables, as well as various alternative simulation situations, must be addressed to improve the confidence in the modeling of a solar cell. This work achieved encouraging optimized results with a conversion efficiency of 25.72% and (FF ≈ 83.75 %, Jsc ≈ 32.96436 mA/cm 2 and Voc ≈ 0.9315 V). The findings will provide crucial information for the production of high-efficiency thin-film solar cells. The development of enhanced numerical modeling performance of solar cells plays a vital role, as evidenced by the findings.
Knowlagent: The authors would like to acknowledge the University of Gent, Belgium for providing the SCAPS simulator. Furthermore, we are grateful to Ajman University for supporting this study.