Effect of Chemical and Physical Parameters on the Electrical Outputs of Cu2Zn1−yFeySnS4-Based Solar Cells by wxAMPS

Cu2Zn1−yFeySnS4-based solar cells with different mole fractions of iron have been analyzed using numerical simulations in this study. The analysis deals with the effect of the iron content on the overall electrical performance of solar cells. Results revealed that the Voc is affected by the increase of the iron content even if it improves the other parameters. We found that the CZFTS solar cell with a mole fraction of iron equal to 1 (CFTS) showed the best results in terms of power conversion efficiency (PCE). Moreover, variations of several structural and physical parameters of the buffer CdS and the best absorber CFTS on the overall electrical characteristics of the cell were investigated. Simulations showed promising results with PCE of 20.35%, Jsc of 26.09mA/cm, Voc of 0.93V, and FF of 83.93%. The results obtained can serve as a basis for the design and manufacture of high-efficiency CZFTS solar cells.


Introduction
Recently, earth-abundant Cu 2 ZnSn(S, Se) 4 nanocrystals are being considered as alternative and ideal absorber materials to CIGS and for thin-film solar cells, thanks to their large absorption coefficients and their tunable direct bandgap energy ranging from 1.0 to 1.5 eV [1][2][3][4][5][6][7][8][9][10]. On the other hand, earth-abundant Cu 2 II-IV-(S, Se) 4 (II = Mn, Fe, Co, Ni, Hg; IV = Si, Ge, Sn) chalcogenide semiconductor nanocrystals have gained broad interest due to their analogous structures to CZT(S, Se), suitable direct bandgaps, and high absorption coefficients; also, quaternary Cu 2 -II-SnS 4 (II = Co 2+ , Fe 2+ , Ni 2+ , Mn 2+ ) compounds are considered to be important potential solar cell materials [11]. The best PCEs for kesterite CZTS and CZTSe-based solar cells have been reported to be 8.4% and 12.6%, respectively [12,13]. The quaternary material CZT(S, Se) can thus lead a new generation of economic and environmentally benign photovoltaic (PV) devices with sufficient availability of their constituent elements. One of the major factors in the success of the synthesis of this kind of solar cell is precise control of secondary phases and deep defect levels as well as the mastery of high-quality phase formation.
Another key factor in optimizing the PCE of CZTS-based solar cells to be mature as its counterpart CIGS-based solar cells is the bandgap grading. It has been shown that the addition of iron in the CZTS lattice can tune its bandgap and hence can improve its PCE [14,15]. The ionic radius of Zn 2+ (0.64 Å) and Fe 2+ (0.66 Å) [16] is almost similar, and iron shows good miscibility in the CZTS lattice. The Fe/Zn alloying is therefore possible and can lead to solid-state materials of the type Cu 2 Zn 1−x Fe x SnS 4 (0 < x < 1). These materials are composed of comparatively cheap, abundant, and environmentally friendly elements. The bandgap can be tuned across the visible range of solar radiation, which makes them potentially useful in a variety of electronic, optoelectronic, and magnetoelectronic applications [17]. One of the best ways to study the role of bandgap grading or iron addition in optimizing the PCE of these solar cells is to use numerical simulations. Numerical simulation is an important step that can allow understanding different ways to improve the PCE of solar cells as well as a better comprehension of the physics involved in their design and their operation. Numerical simulations of CZTS-based solar cells have been reported already [18][19][20][21]. Khattak et al. reported the numerical baseline for high-efficiency CFTS-based solar cells using the SCAPS software and found an optimized simulated solar cell with 19.97% of PCE [22]. Konan et al. found a PCE of 22.33% of an optimized simulated CFTS-based solar cell by SCAPS [23]. But there is a lack of reports on the numerical simulations of CZFTS-based solar cells.
In this study, numerical results were recorded using the Analysis of Microelectronic and Photonic Structures (wxAMPS-1D) program to evaluate and improve CZFTS solar cells' performances. The ZnO:Al/ZnO/CdS/CZFTS/Mo solar cells with different mole fractions of iron were simulated and analyzed. The analysis deals with the effect of the iron content on the overall electrical performance of solar cells. The variations of several structural and physical parameters of the buffer layer CdS and absorber layer CFTS on the overall electrical characteristics of the solar cells were also investigated. The results obtained can serve as a basis for the design and manufacture of high-efficiency CZFTS solar cells. Details of the structure and simulation procedure of the cell are stated in the following sections.

Simulation Program and Device Structure
2.1. Simulation Program. In this study, numerical modeling of CZFTS thin-film solar cells was carried out by onedimensional device simulation program wxAMPS. The structural and physical parameters of each layer of the cell were introduced into the program as input parameters to the simulation. Developed by Fonash and his group at the Pennsylvania State University, it was created first as AMPS to examine a variety of device structures such as homojunction and heterojunction p-n and p-i-n, solar cells, detectors, and microelectronic structures, multijunction structures, compositionally graded detectors, Schottky barrier devices with optional back layer, and novel microelectronic, photovoltaic, and optoelectronic structures [24,25]. It was originally developed for crystalline Si, GaAs, and multiple models. Later, standard models for polycrystalline devices at the level of best efficiencies were developed such as CdTe, CIGS, and a-Si [26]. The AMPS simulation program can simulate up to 30 layers, in addition to two layers corresponding to the front and the back contacts [24]. It incorporates all recombinations and charges defect mechanisms compared to other simulation programs. Outputs, such as currentvoltage characteristics under dark and illumination conditions, quantum efficiency, generation and recombination profiles, electric field distribution, free and trapped carrier densities, energy band diagram at equilibrium, and under illumination, can be recorded from a simulation by AMPS. All this information is computed by AMPS based on Poisson's equation and the continuity equation for free electrons and free holes [24]. Several extensions have been implemented in a new shape named wxAMPS by the Angus Rockett group at the University of Illinois. Beyond the original AMPS kernel, wxAMPS incorporates two tunneling models and can simulate an unlimited number of layers and graded solar cells. Five separate input windows are combined into one for quick editing and viewing. The iteration times were reduced, and the convergence has been significantly improved [26][27][28].

Device
Structure and Input Parameters. The CZFTS structure used for our simulations consists essentially of the following layers: a ZnO:Al window layer, ZnO window layer, CdS buffer layer, CZFTS absorber layer, and Mo back layer acting as metal contact. Figure 1 illustrates the vertical cross-section of the cell used in this work. The device is illuminated from the front ZnO:Al to the end of the device with the default AM1.5G illumination spectrum for all simulations. The default working temperature was fixed at 300 K. The basic physical and optoelectronic input parameters used in simulations are listed in Table 1. These parameters were chosen from experimental measurements from AZoM and literature [17,[29][30][31][32][33][34]. The front surface reflectivity and the back surface reflectivity are set to 0.1 and 0.8, respectively, to reflect experimental quantum efficiency data.

Calculation of the CZFTS Bandgap
Energy. The addition of iron in CZTS lattice tunes its bandgap. As the iron content increases in the compound, its bandgap decreases according to the bandgap bowing model described by the following equation and depicted in Figure 2 [34].
where y is the iron content and b is the specific optical bowing constant which describes the degree of nonlinearity and is the result of combined effects  [34,36]. The parabolic trend observed in the bandgap as Fe content increases in Figure 2 could be attributed to both electronegativities of Zn and Fe atoms and the transition from kesterite to stannite phase [34].

Effect of Iron Content on Output
Parameters. The effect of iron content was evaluated by varying its value from 0 to 1 by step of 0.1. Figure 3 As the PCE increases substantially with the Fe content up to the value of 1, this layer (CFTS) has been chosen for the solar cell optimization.

In CdS Buffer Layer.
To study the effect of carrier concentration in the CdS buffer layer on the electrical outputs of the solar cell, its value has been varied from 1 × 10 16 to 1 × 10 17 cm -3 which corresponds to experimental values of Cudoped CdS material [37]. The variations of solar cell electrical parameters for different carrier concentrations can be seen in Figure 4(a). It is seen that the PCE and FF increase when the carrier concentration increases while the Voc and the Jsc slightly decrease. The decrease in the Voc values is probably due to the nonradiative recombination process which starts at the CdS/CFTS interface. This phenomenon increases the saturation current density resulting in a decrease in the value of Voc [38]. When the carrier concentration increases in the CdS buffer layer, the diffusion length of charge carriers decreases, and this contributes to narrow the value of Jsc  3 International Journal of Photoenergy [39]. The increase observed in the PCE values is due to the lowering of the barrier potential at the CdS/CFTS heterojunction interface when the carrier concentration increases, thus leading to an enlargement of the space charge region [40]. This situation allows a good collection of photogenerated carriers and can increase the PCE [41]. The best value of carrier concentration in the CdS buffer layer giving the best PCE is chosen as 1 × 10 17 cm -3 .
The CdS buffer layer thickness was varied from 0.02 to 0.12 μm to find its suitable value in the improvement of PCE. The carrier concentration was fixed at the result of the previous simulation, that is, 1 × 10 17 cm -3 . Figure 4(b) shows the different variations in the solar cell electrical parameters as a function of the thickness. It is observed that all output parameters exhibit the same behavior. They are almost unchanged between 0.02 and 0.047 μm, increasing substantially to 0.05 μm before stabilizing above. The improvement in output parameters with increasing buffer layer thickness is due to the increasing amount of photon absorption outside the hole diffusion length, reducing therefore the recombination rate [42]. At the same time, the values of Voc and Jsc are both affected by the concentration of carriers in the buffer layer which does not allow them to increase further, and thus, they start to stabilize after a certain thickness [40].

3.3.2.
In CFTS Absorber Layer. The influence of the CFTS absorber layer thickness was studied by varying its value from  International Journal of Photoenergy 0.5 to 5 μm by step of 0.5 μm. The carrier concentration and thickness of the CdS buffer layer were kept constant at 1 × 10 17 cm -3 and 0.05 μm, respectively, as they were found as optimal values by previous simulations. All other parameters were kept unchanged. Figure 5(a) exhibits the effect of CFTS absorber layer thickness on the electrical characteristics of the whole cell. As absorber thickness increases, short current density (Jsc), open-circuit voltage (Voc), and power conversion efficiency (PCE) increase up to an optimal value of 2.6 μm and start stabilizing beyond. The fill factor (FF) decreases following an opposite trend. The increase in Jsc, Voc, and PCE is mainly due to the absorption of a greater number of longer wavelength photons, which in some way can affect the amount of photogenerated carriers [22]. A significant amount of electron-hole pairs is generated by an enhanced absorption of photons, and so, a good number of free carriers can be collected at the front; this improves the Jsc values and therefore the PCE. Consequently, a significant number of photogenerated carriers can affect their mobility and this will foster their recombination before reaching the front contact and be collected. This situation can explain the decrease in FF values.

International Journal of Photoenergy
Carrier concentration in the CFTS absorber layer was varied from 1 × 10 13 to 1 × 10 19 cm -3 as shown in Figure 5(b) to see its variations on electrical outputs of the cell.
It can be seen in Figure 5(b) that Jsc, FF, and PCE are nearly unchanged when carrier concentration varies between 1 × 10 13 and 1 × 10 17 cm -3 and start decreasing above. On the other side, the Voc increases from 1 × 10 13 to 1:5 × 10 17 cm -3 and stabilizes beyond. The decrease in Jsc can be explained by the creation of new recombination centers into the layer as the carrier concentration increases. This situation enhances the recombination process which reduces the ratio of photocarriers to be collected at the front contact. This can also cause a drop in the FF values and therefore the PCE. A higher number of carrier concentrations in the CFTS absorber layer cause a drop of the saturation current of the cell which decreases when the carrier density increases; this decrease leads to an improvement in Voc values according to the simple p-n junction model. Finally, the value 1 × 10 17 cm -3 was found to be the optimal value of the carrier concentration in the absorber layer.

Comparison between the Traditional and the Optimized
CFTS-Based Solar Cell. A thickness of 0.05 μm and a carrier concentration of 1 × 10 17 cm -3 in the buffer layer, as well as a thickness of 2.6 μm and a carrier density of 1 × 10 17 cm -3 in the absorber layer, were found to be the best parameter values of our previous simulations. A simulation using these optimal parameter values has been done to evaluate their contribution to the traditional case. J-V characteristics and quantum efficiencies of the traditional and optimized CFTS solar cells are shown in Figures 6(a) and 6(b), respectively. The optimized values of solar cell parameters for CdS buffer and CFTS absorber layers for this simulation and that of the traditional case are summarized in Table 2. The values are comparable with those of other authors [22,23]. A significant improvement in Voc even if the Jsc decreases slightly is seen in Figure 6(a). A slight increase in photon absorption in the visible range for the optimized structure compared to the traditional case is also seen in Figure 6(b).

Conclusion
In this work, the baselines of ZnO:Al/ZnO/CdS/CZFTS/Mo solar cells have been analyzed via the wxAMPS software. The effect of iron was first evaluated, and CZFTS-based solar cells with a fraction mole value of iron equal to 1 showed the best performance. Then, variations of different parameters of the CdS buffer and CFTS absorber layers on electrical output parameters have been studied. Promising optimized results were achieved with a PCE of 20.35%, a short circuit density (Jsc) of 26.09 mA/cm 2 , an open-circuit voltage (Voc) of 0.93 V, and a fill factor (FF) of 83.93%. These promising results can bring researchers to have a broad interest in the manufacture of high efficient CZFTS-based solar cells. But to better understand this kind of solar cell, it is important and even necessary to conduct several other simulations taking into account other physical or chemical parameters, different other conditions, and different other structure configurations to find the one exhibiting the best performance.

Data Availability
The CZ0F1TS.dev and CZFTS.dev data used to support the findings of this study are available from the corresponding author upon request.