Numerical Investigation Energy Conversion Performance of Tin-Based Perovskite Solar Cells Using Cell Capacitance Simulator

Abstract

The power conversion efficiency of lead halide perovskite solar cells has been elevated to 25.2%. However, the toxicity of lead and the complex fabrication process of those cells considerably hinder the commercial application of such solar cells. Therefore, lead-free solar cells with comparable power conversion efficiency with a much lower environmental impact have recently attracted enormous attention in both academia and industry. This paper presents a theoretical study to assess the energy conversion capacity of lead-free perovskite solar cells with MASnI₃ perovskite as its absorber layer using solar cell capacitance simulator (SCAPS). In particular, the effects of materials of the perovskite solar cells’ electron transport layers (ETLs) and hole transport layers (HTLs) on their energy conversion performance are elaborated. Our results show that Cd_0.5Zn_0.5S and MASnBr₃ are the most suitable materials for ETL and HTL, respectively. It is also found from that the solar cell performance can be further enhanced through optimizing the thickness and defect density of its absorber layer. Moreover, the effects of defect densities in interface layers are investigated. In addition, the effects of ETL and HTL doping densities as well as influences of the back-contact work function and operating temperature of the tin-based perovskite solar cells are discussed. Finally, a glass substrate/FTO/Cd_0.5Zn_0.5S (ETL)/MASnI₃/MASnBr₃ (HTL)/back-contact solar cell with a power conversion efficiency of 23.86% is recommended for further optimization.

1. Introduction

Perovskites are considered as promising candidate materials for photovoltaic solar energy conversion because of their outstanding photovoltaic properties such as long electron–hole diffusion length, large optical absorption coefficient, small carrier effective mass, low processing temperature, and strong excitonic transition. Among different types of perovskite solar cells (PSCs), the organic–inorganic metal halide PSCs have received significant attention years because they have high power conversion efficiency (PCE) can be fabricated straightforwardly at relatively low cost [1,2].

Methyl ammonium lead tri-iodide (MAPbI₃) has long been considered as a perovskite material and extensively used for PSCs. However, commercial application of the MAPbI₃-based PSCs is considerably hindered because the lead in MAPbI₃ is very toxic [3,4,5], which leads to an appreciation of lead-free PSCs in the field of photovoltaic technology. Normally, a PSC should include an electron transport layer (ETL) and a hole transport layer (HTL) to maximize its power conversion efficiency by extracting and transporting photogenerated electrons, modifying the interface, aligning the interfacial energy level, and minimizing the charge recombination in PSC (for ETL [6]), as well as improving hole extraction and selectively blocking electrons to diminish electron–hole recombination on anode (for HTL [7]). The most commonly used materials for ETL and HTL are titanium dioxide (TiO₂) and Spiro-OMeTAD, respectively. However, the high-temperature deposition of TiO₂ and the high price of Spiro-OMeTAD remain as noticeable barriers that prevent practical applications of those materials in commercializable PSCs. Moreover, Spiro-OMeTAD is an unstable material, which can deteriorate the performance of the PSCs. Therefore, seeking new ETL and HTL materials for the PSCs is crucial for broad application of such devices. Recent studies have proven that inorganic materials are more stable and offer higher carrier mobility than organic materials [8,9,10]. Hence, the application of inorganic charge-transport materials for the PSCs is highly desired.

Inorganic halide perovskites, such as Sn-, Ag-, Sb-, Bi-, Cu-, and Ge-based solar cells, have been investigated as possible replacements of lead [11,12,13]. Due to its optimal bandgap of 1.3 eV, a metal halide perovskite, CH₃NH₃SnI₃, has been considered as a promising alternative for the lead-free PSCs [14]. Other environment-friendly lead-free perovskites, such as Cs₂TiBr₆ [15], Cs₂TiBr₆, Cs₂TiI₆, Cs₂TiF₆, and Cs₂TiCl₆ [16], have also been employed to develop lead-free PSCs by other researchers for the purpose of acquiring optimal solar cell performance. In addition to the perovskites, to achieve desired cell performance, an inorganic charge transport material, Zinc Tin Oxide (ZTO), was used as ETL in the PSCs because of its high charge carrier mobility. PSCs with ZTO as the prime ETL could reach 24.07% PCE with an open circuit voltage (V_oc) of 1.13 eV, a short-circuit current density (J_sc) of 23.18 mA/cm² and a fill factor (FF) of 67.66% [17]. A certain amount of Zn is added to the solution containing Cd and S ions to control the bandgap of the cadmium sulfide (CdS) ETL layer for higher cell performance. As found by Baig et al. [14], the bandgap of the Cd_1-xZn_xS layer heavily depended on the concentration of Zn. Other ETL materials, such as indium gallium zinc oxide (IGZO), Tin (IV) oxide (SnO₂), C60, TiO₂, zinc oxide (ZnO), and phenyl-C61-butyric acid methyl ester (PCBM), were also tested by Lakhdar and Hima [18] to evaluate their effects in improving the cell performance. In terms of HTL, inorganic p-type materials including ZnO, copper (I) thiocyanate (CuSCN), copper (I) oxide (Cu₂O), P₃HT, copper (I) iodide (CuI), and nickel (II) oxide (NiO) have been used as the HTL materials because of their low cost and high performance-degradation resistance [19,20]. For instance, a recent study found that the PSCs with (ZnO) as their HTLs could reach 25.02% PCE [19].

In this study, the performance of the lead-free PSCs with the same configuration, glass/FTO/ETL/IL1/MASnI₃/IL2/HTL/Au (Figure 1), and different ETL and HTL materials are determined and compared. As shown in Figure 1, the proposed lead-free PSCs include a glass substrate, a front electrode layer made of FTO, an ETL made of candidate materials, a MASnI₃ perovskite absorber layer, an HTL made of candidate layers, and a back electrode layer made of gold. IL1 and IL2 are the ETL/perovskite interface layer and the perovskite/HTL interface layer, respectively. Candidate ETL materials include carbon 60 (C60), CdS, Cd_0.5Zn_0.5S, IGZO, PCBM, ZnO, and TiO₂, while the candidate HTL materials are Cu₂O, CuI, CuSCN, MASnBr₃, NiO, poly polystyrene sulfonate (PEDOT:PSS), and Spiro-OMeTAD. In addition, the thickness and defect density of the absorber layer (the MASnI₃ layer) are further optimized. Moreover, the effects of interface layers defect densities are discussed, and the effects of ETL and HTL doping densities as well as the influence of back-contact work function and operating temperature on the cell performance are demonstrated.

2. Materials and Methodology

2.1. Device Structure and Input Parameters

Figure 1 illustrates the structure of a benchmark PSC device first simulated in the present study. In that structure, MASnI₃ is utilized as the perovskite absorption layer, fluorine-doped tin oxide (FTO or SnO₂:F) is chosen as the transparent conducting oxide, and gold (Au) is selected for the back contact. Common materials TiO₂ and Spiro-OMeTAD are initially used as the ETL and HTL, respectively. However, different ETL and HTL materials are tested later to find the best materials that maximize the cell performance. Key simulation parameters for those layers are obtained from previous experimental and theoretical analyses [14,19,21,22] and are summarized in

Table 1. Input parameters for simulation of PSC performance.

Parameters	FTO	TiO2	MASnI3	Spiro-OMeTAD
Thickness (nm)	500	100	500	200
Eg (eV)	3.5	3.2	1.3	3.0
χ (eV)	4.0	3.9	4.17	2.45
εr	9.0	9.0	8.2	3.0
Nc (cm−3)	1 × 1019	1 × 1021	1 × 1018	1 × 1019
Nv (cm−3)	1 × 1019	2 × 1020	1 × 1018	1 × 1019
μn (cm2/Vs)	100	20	1.6	0.0002
μp (cm2/Vs)	25	10	1.6	0.0002
Nd (cm−3)	2 × 1019	1 × 1017	0	0
Na (cm−3)	0	0	1 × 1016	1 × 1018
Nt (cm−3)	1 × 1014	1 × 1015	1 × 1015	1 × 1015

. Two interface layers are inserted between the ETL and the MASnI₃ perovskite layer (ETL/perovskite interface) and the perovskite layer and HTL (perovskite/HTL interface), respectively. Those interface layers are added because the interfaces play a critical role in capturing electrons and holes. The defects in the perovskite layer are set to be in the neutral Gaussian distribution, with characteristic energy of 0.1 eV and energy above the valence band of 0.6 eV [23]. In contrast, the defects in the ETL/perovskite and perovskite/HTL interfaces are considered to be neutral single defects (as set in SCAPS [23]), with an energy of 0.6 eV above the valence band. The simulation is carried out using solar cell capacitance simulator (SCAPS) software under AM1.5G solar illumination with an incident power density of 100 mW/cm² and the input parameters listed in Table 1. The simulation results are obtained as V_oc = 0.84 V, J_sc = 29.64 mA/cm², FF = 69.27%, and PCE = 17.24%. More details about the numerical method embedded in SCAPS are elaborated in Section 2.2.

To find the best ETL and HTL materials, more simulations are conducted following the same approach with a variety of materials for ETL (C60, CdS, Cd_0.5Zn_0.5S, IGZO, PCBM, and ZnO) and HTL (Cu₂O, CuI, CuSCN, MASnBr₃, NiO, and PEDOT:PSS). To compare the performance of the PSCs with different ETL and HTL materials with the performance of the PSC with the TiO₂ ETL and Spiro-OMeTAD HTL, the thicknesses of all the ETLs and HTLs are maintained at 100 and 200 nm, respectively. Simulation parameters for different ETL and HTL materials are obtained from published articles (see [14,18,19,24,25] (for ETL materials) and [14,19,21,25] (for HTL materials)), as listed in

Table 2. Input parameters for different ETL materials.

Parameters	C60	CdS	Cd0.5Zn0.5S	IGZO	PCBM	ZnO
Eg (eV)	1.7	2.4	2.8	3.05	2	3.3
χ (eV)	3.9	4.2	3.8	4.16	3.9	4.1
εr	4.2	10.0	10.0	10.0	3.9	9.0
Nc (cm−3)	8 × 1019	2.2 × 1018	1 × 1018	5 × 1018	2.5 × 1021	4 × 1018
Nv (cm−3)	8 × 1019	1.8 × 1019	1 × 1018	5 × 1018	2.5 × 1021	1 × 1019
μn (cm2/Vs)	0.08	100	100	15	0.2	100
μp (cm2/Vs)	0.0035	25	25	0.1	0.2	25
Nd (cm−3)	2.6 × 1018	1 × 1017	1 × 1017	1 × 1018	2.93 × 1017	1 × 1018
Na (cm−3)	0	0	0	0	0	0
Nt (cm−3)	1 × 1014	1 × 1017	1 × 1015	1 × 1015	1 × 1015	1 × 1015

and

Table 3. Input parameters for different HTL materials.

Parameters	Cu2O	CuI	CuSCN	MASnBr3	NiO	PEDOT:PSS
Eg (eV)	2.17	2.98	3.4	2.15	3.8	2.2
χ (eV)	3.2	2.1	1.9	3.39	1.46	2.9
εr	6.6	6.5	10.0	8.2	11.7	3.0
Nc (cm−3)	2.5 × 1020	2.8 × 1019	1.7 × 1019	1.0 × 1018	2.5 × 1020	2.2 × 1015
Nv (cm−3)	2.5 × 1020	1.0 × 1019	2.5 × 1021	1.0 × 1018	2.5 × 1020	1.8 × 1018
μn (cm2/Vs)	80	0.00017	0.0001	1.6	2.8	0.02
μp (cm2/Vs)	80	0.0002	0.1	1.6	2.8	0.0002
Nd (cm−3)	0	0	0	0	0	0
Na (cm−3)	1 × 1018	1 × 1018	1 × 1018	1 × 1018	1 × 1018	3.17 × 1014
Nt (cm−3)	1 × 1015	1 × 1015	1 × 1014	1 × 1015	1 × 1015	1 × 1015

, respectively.

The solubility of MASnI₃ is different from the solubility of carrier transporting layers proposed in this paper. Generally, the ETL is not affected much by the perovskite layer. The perovskite layer is relatively stable after annealing and the HTL spin coating process is fast, so the HTL has little effect on the perovskite layer. The ETL materials (C60 [26], CdS [27], Cd_0.5Zn_0.5S [14], IGZO [18,19], ZnO [28], and PCBM [18,29]) and HTL materials (Cu₂O [29], CuI [30,31], CuSCN [32,33], MASnBr₃ [14], NiO [34], and PEDOT:PSS [26]) proposed in this paper are feasible and have been verified in the reported articles.

2.2. Numerical Method

Numerical simulations involved in this study are carried out using SCAPS software, an efficient one-dimensional solar cell simulation program developed by researchers at the University of Ghent [24]. Using that software, the spectral response of solar energy, J-V characteristics, and electric field distribution can be obtained by solving the Poisson equation (Equation (1)) and the continuity equation for electrons (Equation (2)) and holes (Equation (3)) that are embedded in SCAPS.

$$\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\mathsf{\epsilon }\left(\mathrm{x}\right)\frac{\mathrm{d}\mathsf{\psi }}{\mathrm{d}\mathrm{x}}\right]=\mathrm{q}\left[\mathrm{p}\left(\mathrm{x}\right)-\mathrm{n}\left(\mathrm{x}\right)+{\mathrm{N}}_{\mathrm{d}}\left(\mathrm{x}\right)-{\mathrm{N}}_{\mathrm{a}}\left(\mathrm{x}\right)+{\mathrm{p}}_{\mathrm{t}}\left(\mathrm{x}\right)-{\mathrm{n}}_{\mathrm{t}}\left(\mathrm{x}\right)\right]$$

(1)

$$-\frac{1}{\mathrm{q}}\frac{\mathrm{d}{\mathrm{J}}_{\mathrm{n}}}{\mathrm{d}\mathrm{x}}+{\mathrm{R}}_{\mathrm{n}}\left(\mathrm{x}\right)-\mathrm{G}\left(\mathrm{x}\right)=0$$

(2)

$$\frac{1}{\mathrm{q}}\frac{\mathrm{d}{\mathrm{J}}_{\mathrm{p}}}{\mathrm{d}\mathrm{x}}+{\mathrm{R}}_{\mathrm{p}}\left(\mathrm{x}\right)-\mathrm{G}\left(\mathrm{x}\right)=0$$

(3)

where ε is the relative permittivity; N_a and N_d are the ionized acceptor concentration and ionized donor concentration, respectively; ψ is the electrostatic potential; x indicates the coordinate position; p and n represent the number of holes and electrons, respectively; p_t and n_t represent the number of trapped holes and electrons; J_p and J_n denote the current density of holes and electrons; R_p(x) and R_n(x) are the recombination rate of holes and electrons; and G(x) denotes the optical generation rate.

3. Results and Discussion

3.1. Effects of ETL Materials on Cell Performance

The simulation results obtained for the PSCs with the proposed ETL materials listed in Table 2 and the benchmark Spiro-OMeTAD HTL are summarized in

Table 4. Responses of PSCs with different ETL materials.

Responses	C60	CdS	Cd0.5Zn0.5S	IGZO	PCBM	ZnO	TiO2
Voc (V)	0.84	0.81	0.93	0.82	0.83	0.83	0.84
Jsc (mA/cm2)	21.73	27.50	29.39	29.27	24.86	29.58	29.64
FF (%)	69.47	62.62	64.73	63.95	67.53	67.72	69.27
PCE (%)	12.66	14.01	17.70	15.32	13.92	16.64	17.24

and the obtained J-V characteristics are plotted in Figure 2. In Table 4, it can be found that the PSC with the C60 ETL yields the lowest PCE while the PSC with the Cd_0.5Zn_0.5S ETL acquires the highest PCE. The performances of the PSCs with the TiO₂ ETL (the benchmark material) and ZnO are also acceptable.

Figure 3 shows the influence of different ETL materials on quantum efficiency (QE) of the PSCs. The figure shows that, when the incident wavelength is greater than 750 nm, the QE values calculated from different PSCs are almost the same. However, if the incident wavelength is less than 750 nm, the QE value yielded from the C60 ETL is the lowest among all calculated QE results, thereby leading to an inadequate photon absorption. In addition, the lowest electron mobility of C60 also restrains charge collection. Therefore, according to our simulation, C60 leads to the lowest J_SC and PCE compared with other ETL materials and should not be selected for designing the lead-free PSCs.

Figure 4 shows that the conduction band (CB) level of almost all tested ETL materials is higher than that of the MASnI₃ perovskite, except for CdS. Conduction band offset (CBO) is defined as the difference between CB level of ETL and that of the perovskite. If the CB level of ETL is lower than that of the perovskite, CBO is negative, and an energy cliff will be formed at the ETL/perovskite interface. Otherwise, CBO is positive, and an energy spike will be formed. Therefore, an energy cliff is formed at the CdS/perovskite interface while energy spikes are generated at the interfaces between other ETL materials and the perovskite. The energy cliff does not hamper photo-generated electron flow. However, the activation energy for carrier recombination (the difference between the bandgap of perovskite and the absolute value of CBO) becomes lower than the bandgap of perovskite [35,36], which may cause the interface recombination to occupy the main position for recombination of the PSC device. V_oc decreases as the recombination rate increases. Therefore, the PCE drops when V_oc decreases and the PCE of the PSC with the CdS ETL is relatively low. For other ETL materials, the energy spike formed at the ETL/perovskite interface acts as a barrier for the photo-generated electrons, but the activation energy for carrier recombination is equal to the bandgap of the perovskite, so the activation energy is more than that calculated by energy cliff, which can certainly enhance the cell performance. It is also proved that energy spike within a small range has less effect on the motion of photo-generated electrons but greater impact on the carrier recombination rate [37]. The PSC with a Cd_0.5Zn_0.5S ETL yields a higher PCE because the CB level of Cd_0.5Zn_0.5S is higher than that of other ETL materials and its mobility is higher. However, as the CBO continues to increase, the performance will decrease due to the double-diode behavior [37]. Thus, Cd_0.5Zn_0.5S is finally selected as the optimal ETL material for the proposed lead-free PSC.

3.2. Effects of HTL Materials on Cell Performance

After selecting the ETL, lead-free PSCs with the Cd_0.5Zn_0.5S ETL and different HTL materials as listed in Table 3 are simulated using SCAPS, and their predicted responses are listed in

Table 5. Responses of PSCs with different HTL materials.

Responses	Cu2O	CuI	CuSCN	MASnBr3	NiO	PEDOT-PSS	Spiro-OMeTAD
Voc (V)	0.92	0.85	0.91	0.94	0.90	0.88	0.93
Jsc (mA/cm2)	28.71	28.18	28.45	30.35	28.32	28.21	29.39
FF (%)	76.49	74.32	75.74	76.65	75.04	73.30	64.73
PCE (%)	20.28	17.79	19.91	21.55	19.04	18.15	17.70

and plotted in Figure 5, Figure 6 and Figure 7. As shown in Figure 5 and Figure 6, the J-V characteristics and the QE values of the PSCs with different HTL materials do not show significant difference. Table 5 shows that the PSC with the MASnBr₃ HTL yields the highest PCE. Since the valence band (VB) level of MASnBr₃ is lower than that of the MASnI₃ perovskite (Figure 7), energy spike is formed at the perovskite/MASnBr₃ interface, and the activation energy for carrier recombination is high, which leads to the high PCE. For the other HTL materials, since their VB levels are higher than that of MASnI₃, energy cliffs will be formed at the perovskite/HTL interface. Similar to the case of the ETL materials, the energy cliffs do not impede the transportation of the photo-generated holes. However, due to the cliffs, the activation energy for carrier recombination becomes lower than the bandgap of the perovskite, which in turn increases the interface recombination and causes a reduction in the cell performance.

When an energy cliff is formed, the activation energy for carrier recombination (E_a) is defined by

$${\mathrm{E}}_{\mathrm{a}}={\mathrm{E}}_{\mathrm{g},\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r}}-\left|{\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r}}-{\mathrm{E}}_{\mathrm{v},\mathrm{H}\mathrm{T}\mathrm{L}}\right|$$

(4)

where E_g,absorber is the bandgap of the perovskite and E_v,absorber and E_v,HTL represent the VB levels of the perovskite and HTL, respectively. The values of E_a calculated for Cu₂O, CuSCN, NiO, and CuI are 1.2, 1.13, 1.09, and 1.03 eV, respectively. The PCE values calculated from the PSCs with those HTL materials are ordered as: CuI < NiO < CuSCN < Cu₂O. Obviously, there is a positive correlation between the E_a and PCE results. However, the PCE of the PSC with the Spiro-OMeTAD HTL is lower than those of the PSCs with other HTL materials despite the higher E_a (1.28 eV). This is because of the very low hole mobility of Spiro-OMeTAD. In summary, MASnBr₃ is selected as the HTL material because it leads to the highest PCE. Thus, the optimized PSC with a Cd_0.5Zn_0.5S ETL and MASnBr₃ HTL is used for the following simulations to find how other key parameters affect its performance.

3.3. Effect of Absorber Layer Thickness

The active perovskite absorber layer has a considerable influence on the cell performance. The effect of perovskite layer thickness on the cell performance is also inspected through numerical simulations, in which the thickness is assumed to vary from 100 to 10,000 nm. The simulation results are plotted in Figure 8. The figure shows that, as the absorber layer thickness increases, the V_oc, J_sc, and PCE values rise while the FF keeps decreasing. The J_sc value increases because, as the absorber layer thickness increases, more photons will be absorbed by the layer. As a result, the elevation of the excess carrier concentration causes the J_sc to increase. On the other hand, as the absorber layer thickness increases, series resistance value in the solar cell and the internal power depletion would increase as well, leading to a continuous drop in FF. As depicted in Figure 8, when the thickness reaches and exceeds 500 nm, all those results become saturated.

V_oc can be calculated by

$${\mathrm{V}}_{\mathrm{o}\mathrm{c}}=\frac{\mathrm{n}\mathrm{k}\mathrm{T}}{\mathrm{q}}\mathrm{l}\mathrm{n}\left(\frac{{\mathrm{I}}_{\mathrm{L}}}{{\mathrm{I}}_0}+1\right)$$

(5)

where n is a factor, nkT/q is the thermal voltage, I_L represents the light generated current, and I₀ is the dark saturation current. When the absorber layer gets thinner, the recombination of electrons and holes becomes weaker, causing I₀ to decrease. On the other side, the concentration of excess carriers becomes higher as the increasing of thickness, causing I_L to increase and therefore leading to an enhanced V_oc (Equation (5)) [38].

PCE can be jointly determined by V_oc, J_SC, and FF as

$$\mathrm{P}\mathrm{C}\mathrm{E}=\frac{{\mathrm{J}}_{\mathrm{s}\mathrm{c}}{\mathrm{V}}_{\mathrm{o}\mathrm{c}}\mathrm{F}\mathrm{F}}{{\mathrm{P}}_{\mathrm{s}}}$$

(6)

where P_s is the irradiance from the Sun to the Earth. It can be readily deduced that PCE increases as the thickness increases by extracting J_sc, V_oc, and FF values from the results in Figure 8 and substituting them into Equation (6).

3.4. Effect of Absorber Layer Defect Density

Photo-generated electrons are primarily generated in the perovskite absorber layer. Hence, the cell performance is significantly determined by the properties of perovskite absorption films. Defect density is an important indicator of the quality of the absorption films. A perovskite absorber layer with a higher defect density has lower quality and its carrier recombination rate is stronger than its carrier generation rate [39]. In this paper, the performances of PSCs with different absorption layer defect densities are simulated to determine the influence of the layer defect density on the cell performance. Defect density values involved in this study range from 10¹³ to 10¹⁸ cm⁻³. As illustrated in Figure 9, when the defect density is below 10¹⁵ cm⁻³, the J-V characteristics of the PSC almost remain unchanged. The J-V characteristics start to deteriorate when the defect density continues to increase.

A deep energy level defect acts as Shockley–Read–Hall nonradiative recombination center. Hence, as the defect density in the absorber layer increases, the short minority carrier lifetime will decrease while the charge recombination will increase, leading to a drop in V_oc and J_sc. Furthermore, when the doping density is comparable to or lower than the defect density in the absorber, the PSC becomes semi-insulating and a desired p-n junction will not be formed [40], resulting in an inferior cell performance. Thus, to achieve an ideal PSC performance, the defect density in the absorber layer has to be minimized or even eliminated. However, it is still very difficult to significantly reduce the defect density with the present manufacturing advances. According to our results, to achieve a desired cell performance, the defect density in the absorber layer should be less than 10¹⁵ cm⁻³.

3.5. Effect of Interface Layer Defect Density

The properties of the interface layers have a critical impact on solar cell performance. A higher defect density decreases the layer quality and increases the recombination rate [40]. To discuss the effect of the interface layer defect density on the PSC performance, we assume that the defect densities of IL1 and IL2 vary from 10¹¹ to 10²¹ cm⁻³.

Figure 10 and Figure 11 show the J-V characteristics of PSCs with different defect densities in IL1 and IL2, respectively. Figure 12 shows the effect of interface layer defect density on PCE. These figures show that a lower defect density in the interface layer will enhance V_oc and J_sc, thereby promoting the PCE. Obviously, when the defect density of IL1 is below 10¹⁵ cm⁻³ and the defect density of IL2 is below 10¹⁷ cm⁻³, the effect of the defect density on the J-V characteristics becomes weak. However, if the interface layer defect density continues to increase, the PSC performance will deteriorate because higher defect densities in IL1 and IL2 will lead to more traps and recombination centers [38].

Compared with IL2, it is evident that the defect density of IL1 has a stronger influence on the PCE. This is because the number of electron–hole pairs generated at IL1 are much larger than IL2, and the higher excess carrier density will result in a higher recombination rate. According to our simulation results, the defect densities of IL1 and IL2 should be less than 10¹⁵ and 10¹⁷ cm⁻³, respectively, to achieve desired PSC performance.

3.6. Effect of Doping Density in ETL and HTL

The effects of the doping density in ETL and HTL on the PCE of PSC are displayed in Figure 13 and Figure 14, respectively. The curves in those figures show a similar trend, which is that the PCE rises gradually with the increasing of the doping density. This is because the increase in ETL donor doping concentration will lead to an improvement in conductivity of the ETL and a decrease in the reverse saturation current, both of which in turn leading to the growth of the PCE. An increase in HTL acceptor doping concentration will reduce resistivity of the HTL and therefore will enhance the current in the solar cell, which will cause the PCE to increase [25].

Taking N-type doping as an example, the conductivity (σ) can be determined as σ = nqμ_n, where n is the electron concentration, μ_n is the electron mobility, and q is the electric charge. In the case of light doping, we have n ≈ N_d, where N_d is the ionized donor concentration. Then, we obtain σ ≈ N_dqμ_n. The mobility does not change much with N_d in the case of light doping, so there is a positive correlation between σ and N_d. This is similar for the P-type doping.

It can also be observed in these figures that the PCE grows slowly when the doping density exceeds 10¹⁷ cm⁻³. This is because, if the doping density continues to increase to a certain extent, high doping effects will appear due to the Moss–Burstein effect [41], which will impede the PSC performance.

3.7. Effect of Back-Contact Work Function

Figure 15 depicts the PCE results calculated from different back-contact work functions, which range from 4.6 to 5.1 eV. The figure shows that, when the back-contact work function decreases, the built-in voltage in solar cell decays, resulting a drop in V_oc and an inefficient collection of photo-generated carriers, which therefore causes the J_sc to decrease. When the back-contact work function is below 4.9 eV, the cell performance deteriorates steeply due to the formation of a Schottky junction [24] at the MASnBr₃/back-contact interface. The Schottky junction leads to S-shaped J-V characteristics and is a barrier for the hole movements. The Schottky barrier increases as the back-contact work function decreases, which impedes the hole transportation and causes the FF to decrease and PCE to deteriorate.

3.8. Effect of Operating Temperature

In general, the operating temperature of solar cells is higher than 300 K. Therefore, in our simulation, the domain of the operating temperature is set from 300 to 500 K to study how the operating temperature influences the cell performance. Figure 16 plots the J-V characteristics of the PSC. As exhibited in that figure, the PSC performance deteriorates as the operating temperature increases. This might be because the increase of operating temperature will cause a decrease in V_oc (Equation (7)), and consequently will hurt the PSC performance.

$$\frac{\mathrm{d}\left({\mathrm{V}}_{\mathrm{o}\mathrm{c}}\right)}{\mathrm{d}\mathrm{T}}=\frac{\left({\mathrm{V}}_{\mathrm{o}\mathrm{c}}-\frac{{\mathrm{E}}_{\mathrm{g}}}{\mathrm{q}}\right)}{\mathrm{T}}$$

(7)

where T is the operating temperature and E_g and q are the bandgap and electric charge, respectively.

As shown in Equation (7), when the operating temperature increases, V_oc drops, the reverse saturation current increases, and the PCE decreases. As declared by Devi et al. [40], electron and hole mobility, carrier concentration, and bandgap will change at high temperatures; therefore, the ambient temperature has a critical impact on the cell performance, as also confirmed by our simulation results.

Based on the simulation results, Cd_0.5Zn_0.5S and MASnBr₃ are chosen for the ETL and HTL materials, respectively. It is also found that the PSC will achieve optimal performance when the absorber layer thickness is 500 nm; the defect density is maintained below 10¹⁵ cm⁻³; the defect densities of IL1 and IL2 are 10¹⁵ and 10¹⁷ cm⁻³, respectively; the ETL and HTL doping densities are 10¹⁷ cm⁻³; and the back-contact work function is 5.1 eV. Figure 17 compares the J-V characteristics before and after the optimization. The optimal PSC performance is indicated with V_oc = 0.96 V, J_sc = 32.48 mA/cm², FF = 76.40%, and PCE = 23.86%.

4. Conclusions

In this paper, lead-free PSCs with the MASnI₃ perovskite as the absorber layer are investigated through SCAPS simulation. At first, optimal materials for the ETL and HTL are determined, which are Cd_0.5Zn_0.5S and MASnBr₃, respectively. The suitability of those materials is shown by the appropriate band alignment between the CB level of Cd_0.5Zn_0.5S and MASnI₃ and between the VB level of MASnI₃ and MASnBr₃. Next, the effects of absorber layer thickness, defect density in the absorber layer, defect density in interface layers, doping density in ETL and HTL, back-contact work function, and operation temperature on the PSC performance are discussed. The configuration of the PSC is glass substrate/FTO/Cd_0.5Zn_0.5S/MASnI₃/MASnBr₃/Au. Simulation results reveal that the optimal absorber layer thickness is 500 nm and a thinner absorber layer will lead to poor cell performance due to the insufficient photon absorption. An optimal defect density (10¹⁵ cm⁻³) in the absorber layer is found from the simulations, and any defect densities higher than that level will lead to the reduction of the solar cell performance due to the creation of additional recombination centers. It is confirmed that the defect densities in IL1 and IL2 should be less than 10¹⁵ and 10¹⁷ cm⁻³, respectively. Simulation results also indicate that the conductivities of ETL and HTL will improve when their doping densities increase. Finally, it is found that the solar cell performance will be impeded if the back-contact work function is less than 4.9 eV and the operating temperature is higher than 300 K. The results obtained from this study will facilitate the design of lead-free and efficient PSCs, therefore promoting the application of solar power as a form of sustainable energy along with wave energy [42,43] and wind energy [44,45]. Other factors that impact PSC performance such as the mobility and bandgap of perovskites will be investigated in the next phase of this project.