Efficiency enhancement of CZTSSe solar cells via screening the absorber layer by examining of different possible defects

This study represents the investigation of earth-abundant and non-toxic CZTSSe absorber materials in kesterite solar cell by using the Finite Element Method (FEM) with (1) electrical, and (2) optical approaches. The simulated results have been validated with the experimental results to define guidelines for boosting the cell performance. For improving the cell efficiency, potential barrier variations in the front contact, and the effect of different lattice defects in the CZTSSe absorber layer have been examined. Controlling the defects and the secondary phases of absorber layer have significant influence on the cell performance improvement. Previous studies have demonstrated that, synthesis of CZTSSe:Na nanocrystals and controlling the S/(S + Se), Cu/(Zn + Sn), and Zn/Sn ratios (stoichiometry) have significant effects on the reduction of trap-assisted recombination (Shockley–Read–Hall recombination model). In this work, a screening-based approach has been employed to study the cell efficiency over a wide range of defect densities. Two categorized defect types including benign defects (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{t}<{10}^{16}$$\end{document}Nt<1016 cm−3 , Nt defines trap density) and harmful defects \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(N}_{t}>{10}^{16}$$\end{document}(Nt>1016 cm−3) in the absorber bandgap in the CZTSSe solar cell, by analyzing their position changes with respect to the electron Fermi level (Efn) and the Valence Band Maximum positions have been identified. It is realized that, the harmful defects are the dominant reason for the low efficiency of the kesterite solar cells, therefore, reducing the number of harmful defects and also total defect densities lead to the power conversion efficiency record of 19.06%. This increment makes the CZTSSe solar cells as a promising candidate for industrial and commercial applications.

Table S1 (supporting information) represents electrical and optical properties of simulated layers in grading mode using for the simulation of the CZTSSe-based solar cell. Likewise, the basic data for defect concentration, the defect properties at the interface of graded CZTSSe/CdS, and for graded absorber layer are available in Tables S2, S3, and S4 in the supporting document, respectively. Scientific Reports | (2020) 10:21813 | https://doi.org/10.1038/s41598-020-75686-2 www.nature.com/scientificreports/

Defects and secondary phases control.
(1) Synthesizing CZTSSe:Na Nanocrystals The presence of undesirable defects in the absorber layer during the deposition process, and formation of secondary phases, limit the cell performance by reducing open-circuit voltage (V OC ). Synthesizing CZTSSe:Na nanocrystals is a method to overcome this problem. In fact, Na ions reduce concentration of deep level recombination, which results enhancement in the carrier concentration and open-circuit voltage (V OC ), as well as the device performance 30,57 .
(2) Controlling the S/(S + Se), Cu/(Zn + Sn) and Zn/Sn ratios (Control Stoichiometry) As we mentioned above, the CZTSSe bandgap is controllable by varying S/(S + Se) ratio from ~ 1.0 eV of CZTSe to ~ 1.5 eV of CZTS. The greater bandgap demonstrates more S/(S + Se) ratio in the film. The graded bandgap implies that different S/(S + Se) ratios of the absorber are formed by different sulfo-selenization temperatures.
Higher sulfo-selenization temperature leads to more S 17 . Moreover, the Cu-poor, Zn-rich, Cu/(Zn + Sn) ≈ 0.80, and Zn/Sn ≈ 1.20, conditions are desirable for higher device performance. The high concentration of defect clusters or complexes results a notable non stoichiometry, which leads to lower device performance. Sulfurization at high temperature during the post-deposition helps to control the stoichiometry 24,36,58 . Numerical modeling. In this work, the CZTSSe solar cell has been investigated using the Finite Element Method (FEM), and validated by the experimental results. The simulation contains (1) electrical, and (2) optical sections, in a two-dimensional cylindrical coordinate based on charge carrier transport equations. In the provided structure, there is no nanoparticle, and due to the morphological properties of the absorber, the Beer-Lambert law has been employed to study the optical properties of the cell. The study of the electrical properties is divided into three parts, in which two parts are based on the Drift-Diffusion equations describing charge carriers with respect to the effect of diffusion and drift carriers, and also recombination rate. Furthermore, the third part is the electrostatic potential based on the Poisson equation [60][61][62][63] . The generation rate is calculated in optical part, which is available in the supporting.
Charge carrier transport equations in two-dimensional symmetrical cylindrical coordinate (3D form with symmetry in the angular direction). The Poisson and charge carrier transport equations were used for validation of the experimental kesterite solar cell case. Three-dimensional form of these equations are represented below: (1) ∇ −D n ∇n + nµ n ∇� + ∇χ  are electron and hole diffusion coefficients. µ n and µ P are electron and hole mobilities, K B is the Boltzmann constant, T is temperature q is electronic charge. �(F = −∇�) is the electrostatic potential, χ is the electron affinity, E g is the bandgap of the semiconductor, N c = m c K B T 2π h 2 1.5 and N v = m v K B T 2π h 2 1.5 are effective density of states of the conduction and the valence band, h is the Planck constant,m c and m v are effective mass of states of the conduction and the valence band. g is the generation rate of charge carriers, λ is wavelength, and U is the recombination rate of charge carriers. Moreover, ε 0 and ε r are vacuum and relative permittivity, C = N D (donordensity) − N A (acceptordensity) is the impurity density.
The U equation depicts the sum of Shockley-Read-Hall, radiative, and the Auger recombination terms which described as: U SRH , U rad , and U aug define as: where τ n and τ p are electron and hole lifetimes, n t and p t are electron and hole concentrations of the trap state. It should be noted that the strongest U SRH occurs when n t = p t = n i . The n i = [N c N V exp(−qE g /K B T)] 1/2 is the intrinsic carrier concentration, B rad is the coefficient of bimolecular radiative recombination , and C ′ n and C ′ p are electron and hole Auger coefficients. The Auger and radiative recombination are neglected due to their low effect on the kesterite cell performance 32,64 . In this study, defect distribution is investigated based on Explicit Trap Distribution (ETD), which is close to Shockley-Read-Hall (SRH) recombination statistics. The equations are written as: where U ETD is the ETD recombination rate, R n and R p are recombination rate of electrons and holes, N t is defect carrier density, g D is degeneracy factor, and C n and C p are electron and hole trap probabilities, which can be derived from following equations: where σ n and σ p are electron and hole trap cross sections, v th n and v th p are thermal velocity of electrons and holes, and as we mentioned above, n and p are concentration of electrons and holes, which can be calculated with the following equations: where γ n and γ p constants are related to the Maxwell-Boltzmann distribution function, and we assume they are equal to one ( γ n = γ p = 1). Also, E fn and E fp are electron and hole Fermi level energy respectively, and n i,eff is the inherent density, which is calculated by: www.nature.com/scientificreports/ also, subscript "i" in Eq. 5 and Eq. 6, is related to the defect's charge, which is categorized in the Table 1 below: It should be noted that, the defect energy difference is calculated by the following equation: where E i is the reference energy, based on our assumption, it is The final changing rate of trapped electrons derived by the following equation: where n 1 and p 1 are calculated by: Experimental validation. We studied the effect of optimization of various parameters for boosting the cell efficiency. Table 2 represents pervious reported performance parameters of Cu 2 ZnSn(S,Se) 4 (CZTSSe) based solar cells with Cu/(Zn + Sn) and Zn/Sn ratios, which have been described as variable chemical components. Furthermore, optimized parameters have been investigated in the following sections. At first, for demonstrating the accuracy of simulated results, the comparison between the reported experimental data and the simulated one has been made. CZTSSe solar cell has been simulated using data listed in Tables S1-S4. The current-voltage characteristics (J-V) of the cell (Fig. 2a) indicates a good agreement between the experimental and simulation results.
The C-V charge densities (N CV ) in the CZTSSe absorber layers at a temperature of 300 K and a frequency of 100 kHz has been measured (Fig. 2b). The depletion width (W d ) at V bias = 0 V was 0.149 µm for CZTSSe cell. By fitting the N CV , carrier density and epsilon of the CZTSSe layer have been extracted from experimental measurement.
Optimization of the potential barrier effect in front contact. Figure 3 indicates the effect of the potential barrier on performance of the simulated cell, which is derived by: where ϕ B0 is the potential barrier in the front contact, W F is the metal work function of the front contact, and χ SF is the electron affinity of the connected semiconductor layer to the front contact. According to Fig. 3, the lower the value of ϕ B0 , the higher the open-circuit voltage (V OC ) and the short-circuit current density (J SC ), so Table 1. Defect types with respect to i subscript in Eqs. (5) and (6)      Optimization of defect energy and density. The value of 1.02 eV is the maximum value that the bandgap could attain as illustrated in Table 3. So, we ought to choose defects energies less than or equal to this value.   (Fig. 6a), and (2) 0.6 eV to 0.9 eV (Fig. 6b)] on the current density versus voltage (J-V) has been investigated. As indicated in Fig. 6a, acceptor defects with energy of E t = 0.03 eV record higher V OC and J sc , which improve the cell PCE. Therefore, E t,a = 0.03 eV is the optimum energy value for the acceptor defect, and we used that as a defect energy value for simulating our device to find out the optimum value for donor defect energy. Moreover, the investigation of donor defects positions has been done in range of (1) 0.35 eV to 0.55 eV (Fig. 6c), and (2) 0.55 eV to 1.02 eV (Fig. 6d). Consequently, we recorded an increment in open-circuit voltage (V OC ) and Jsc  www.nature.com/scientificreports/ when the donor defect energy is E t,d = 1.02 eV. In a nutshell, we were able to claim that E t,a = 0.03 eV and E t,d = 1.02 eV are optimum energy values for acceptor and donor defects, respectively. As the next step, to find the optimum density value, acceptor densities in the range of 1.0 × 10 12 cm −3 to 1.0 × 10 18 cm −3 and donor defects densities in the range of 1.0 × 10 12 cm −3 to 1.0 × 10 17 cm −3 have been investigated. As seen in Fig. 7a, N t,a = 10 12 cm −3 (acceptor defect density) with higher short-circuit current density (J sc ), and open-circuit voltage (V OC ) is the best density value for the acceptor density. Hence, we have simulated the device with N t,a = 10 12 cm −3 as an optimum defects density value to find the optimum density for donor defects. So, based on our calculations, N t,d = 10 12 cm −3 (donor defect density) is the optimum carrier density of donor defects (Fig. 7b). Subsequently, we can assert that N t,a = N t,d = 10 12 cm −3 are optimum parameters for acceptor and donor defects. Thus, by having optimized values of energies and carrier densities of defects, we are able to simulate a CZTSSe solar cell with higher efficiency (19.06%) than previous works. Also, in Table 4 we present harmful and benign defects for the device performance. As a critical point, closer defects to the electron Fermi level (E fn ) position or ~ Eg/2 (related equations are available in Part S2 in supplementary) cause the absorber electrical conductivity deterioration, which increases the recombination rate, and reduces the opencircuit voltage (V OC ), short-circuit current density (J sc ) and PCE. Also, the increment of acceptor and donor defect densities increases the possibility of electron-trapping in the bandgap, and this leads to a reduction in the absorber electrical conductivity and PCE. Figure 8 represents the final optimized J-V characteristics of the cell in comparison with the experimental data. Obviously, this comparison indicates that the simulation results are in good agreement with experimental data, as it shows an impressive increment in the cell performance.
Investigation of the device performance according to the recombination rate distribution. It is a crucial point to reduce recombination rate for enhancing the cell performance. So, Fig. 9 illustrates the optimized defect energy and density values along the z-component. As shown in Fig. 9, we introduce a 2-D coordinate system, where the x-component depicts optimized defect energy, and the y-component demonstrates optimized defect density. The ( None) value shows the recombination rate without the optimization of the defect energy and the defect density. Optimizing the acceptor defect energy ( E t,a ) with non-optimized acceptor defect density ( N t,a ), causes lower recombination rate than the previous part in ( None) mode. The next step for reducing the recombination rate is optimizing E t,a andE t,d without the optimization of the N t,a . Also, optimization of E t,a andE t,d with N t,a reduces the recombination rate, but the best device performance has been recorded when we optimized the E t,a andE t,d , and the N t,a andN t,d , which shows a dramatic reduction in the recombination rate with the applied voltage of 0.9 V. Benign defects reduce carrier recombination on the grain boundary by their segregation. For example, Zn Sn (as a benign defect) provides deep levels in the CZTSSe absorber by breaking or weakening bonds, and also create barrier for holes and easy transport of electrons through the grain boundaries 30,72,73 . Our evaluation for harmful and benign defects was based on the investigation of available defects in CZTS and CZTSe, and their energy E t (eV) with respect to the Valence Band Maximum (VBM) of the absorber layer. According to the Table 4, benign defects have no negative effect on the cell performance, in contradict, harmful defects cause the cell PCE deterioration. As a crucial point, defects with density ( N t ) higher than 10 16 (1/cm 3 ) are harmful for the cell efficiency, even if they are far from the electron Fermi level (E fn ) energy. It should be noted that, defects with the position higher than the Conduction Band Minimum (CBM) are not considered because they are meaningless (Zn Cu (0/+), Sn Cu (0/+), Cu i (0/+)).

Conclusion
Controlling the defects and secondary phases of CZTSSe absorber layer have significant influence on the in kesterite solar cell performance improvement. Previous studies have demonstrated that, synthesis of CZTSSe:Na nanocrystals and controlling the S/(S + Se), Cu/(Zn + Sn), and Zn/Sn ratios (Stoichiometry) have a significant Table 4. Harmful and benign defects based on their influence on the cell performance. www.nature.com/scientificreports/ effect on the reduction of trap-assisted recombination (Shockley-Read-Hall recombination model). Moreover, adding Graphene and Graphyne to the absorber precursors in order to enhance the conductivity might also improve the total mobility and reduces the recombination. In this paper, the CZTSSe absorber materials in kesterite solar cell by using the Finite Element Method (FEM) with (1) electrical, and (2) optical approaches has been investigated and simulation outcomes have been validated by the experimental data. We first optimized the potential barrier effect in the front contact and the connected semiconductor layer. It is found that the lower the value of ϕ B0 = −0.3 eV leads the higher the open-circuit voltage (V OC ) and PCE. In the next step, a screening-based approach has been employed to study the cell efficiency over a wide range of defect densities. Two categorized defect types including benign defects ( N t < 10 16 cm −3 , N t defines trap density) and harmful defects (N t > 10 16 cm −3 ) in the absorber bandgap in the CZTSSe solar cell, by analyzing their position changes with respect to the electron Fermi level (E fn ) and the Valence Band Maximum (VBM) positions have been recognized. The optimum values of E t,a = 0.03 eV, E t,d = 1.02 eV and N t,a = N t,d = 10 12 cm −3 for accepter and donor have been obtained, respectively. Optimization of potential barrier effect in front contact ( ϕ B0 ), classifying the harmful and benign defects, and reduction in defects densities helps us to record the PCE of 19.06%, which is a remarkable increment in comparison with other results and makes the CZTSSe solar cells as a promising candidate for industrial and commercial applications.

Methods
The precursor metal films have been deposited on a Soda Lime Glass (SLG) substrate, which has been coated with a 600 nm-thick Mo. Zn and Sn layers have been consecutively deposited by co-sputtering with the Cu layer. It should be noted that a single layer of Cu was finally deposited to control the Cu composition. Cu/Cu-Sn/ Cu-Zn/Mo/Glass is the stack structure of the deposited precursor. The layers were deposited under sputtering powers of 150 W, 300 W, and 300 W for the Cu, Zn and Sn targets, respectively, at a working pressure of 1 mTorr at Ar atmosphere. It is worth mentioning that, the metal precursors were reacted and annealed in a furnace. The CZTSSe absorption layer was synthesized through a sulfo-selenization process and heat-treated in a Se Shot and Ar/H2S gas atmosphere. Also, 480 °C was the final temperature of the heat treatment, and lasted for 10 min. Cu2ZnSn(S,Se) 4 (CZTSSe) absorber layer was coated with a 50 nm CdS buffer layer by chemical bath deposition www.nature.com/scientificreports/ to fabricate the solar cell,. Afterward, a 50 nm intrinsic ZnO (ZnO(i)) layer and a 300 nm Al-doped ZnO (AZO (ZnO:Al)) layer were deposited by RF sputtering. At last, a 2 µm Al grid, and a 110 nm MgF 2 were deposited by the e-beam evaporator. It should be noted that, the MgF 2 layer was deposited as an antireflection coating layer. Figure S1 in the supporting file illustrates the cross section FESEM image of the cell. It should be noted that, the substrate temperature and deposition time play a crucial role in determining the quality and composition of kesterite films. The current-voltage characteristics were measured under a simulated air mass 1.5 global (AM 1.5 G) spectrum in an illumination of 100 mW/cm 2 (1 sun) using a solar simulator (Newport Co., model 94022A). The grading composition of S/S + Se ratio has been shown in Figure S3.

Data availability
The data that support the findings of this study are available from the corresponding author (M.M. and E.Y.), upon reasonable request.