Tin sulphide solar cells: An analysis using a theoretical method for an approximately 24% efficacy path

A solar cell capacitive simulator was utilized to simulate the solar cells by using SnS as the absorber layer (SCAPS-1D) [33]. This software was initially designed at Gent University, and for details of the algorithm and program one can refer to the study of Burgelman et al. [34]. The software’s output relies on solving the continuity and Poisson equations for both electrons and holes as described below. (1) d 2 d x 2 Ψ ( x ) = e ε 0 ε r ( p ( x ) − n ( x ) + N D − N A + ρ P − ρ n ) , \frac{{\text{d}}^{2}}{\text{d}{x}^{2}}\Psi (x)=\frac{e}{{\varepsilon }_{0}{\varepsilon }_{\text{r}}}(p(x)-n(x)+{N}_{\text{D}}-{N}_{\text{A}}+{\rho }_{\text{P}}-{\rho }_{\text{n}}), (2) d J n d x = G − R , \frac{\text{d}{J}_{\text{n}}}{\text{d}x}=G-R, (3) d J p d x = G − R , \frac{\text{d}{J}_{\text{p}}}{\text{d}x}=G-R, where Ψ, ε ₀, ε _r, n, p, ρ _P, and ρ _n are the electrostatic potential, vacuum permittivity, relative permittivity, electron and hole concentrations, and charge densities of p- and n-type, respectively. ND, NA, G, and R represent the donor charge impurity, acceptor impurity, and generation and recombination rates, respectively. Simulation was done under the AM1.5 spectrum at room temperature with 100 mW cm⁻² power density.

The efficiency of a solar cell is sensitive to various parameters like band gap, valence band density of states (VBDOS) or CBDOS, etc. Here, in this study, we varied the SnS band gap from 1.1 to 1.79 eV, VBDOS from 2.4 × 10¹⁸ to 4.6 × 10¹⁹ cm⁻³, CBDOS from 1.17 × 10¹⁸ to 8.846 × 10¹⁸ cm⁻³, work function of back contacts from 4.4 to 5.0 eV, the radiative recombination factor (coefficient) (RRC) from 1 × 10⁻⁴ to 1 × 10⁻¹² cm³ s⁻¹, and the thickness of SnS from 0.7 to 2 µm, respectively. Table 1 displays the values of several parameters used in the simulation of SnS, TiO₂, and ITO layers.

Figure 1a presents the diagram of the solar cell, consisting of SnS as the absorber layer, TiO₂ as the electron transport layer, and ITO as the window layer. Figure 1b depicts the relationship between solar cell parameters and the thickness of the absorber layer, SnS. The thickness of the absorber layer must be in the right range so that it can effectively absorb the light incident on it. The minimum required thickness should be the reciprocal of the absorption coefficient in the visible range to cut 1/e of the incident light. With increasing thickness, J _SC increases and hence the fill factor and efficiency. Efficiency tends to saturate at 2 µm (a slight increase of 9.38–9.99% from 1.5 to 2 µm). By absorbing light, the absorber layer thickens and increases the number of electron–hole pairs, leading to a decrease in defect states due to the increased crystallite size and a smaller ratio of materials exposed to the surrounding environment. A similar trend can be found in the literature [42].

Figure 1

(a) Structural representation of a solar cell device based on SnS, TiO_2, and ITO. (b) Adjustment of solar cell parameters (J _SC, V _OC, ɳ, and fill factor) with the thickness of SnS.

The open circuit voltage depends on the band gap width of the absorber layer, as can be seen in Figure 2a. The Shockley–Queisser model provides information about the efficiency limit of a single-junction device, which operates by carefully balancing the absorption and emission of light. The efficiency of a cell is maximum in the range of 1.1–1.45 eV and decreases on both sides [43]. From Figure 2a, it can be verified that efficiency starts increasing from 1.1 eV and then increases to a maximum at 1.5 eV after which it starts decreasing.

Figure 2

Variations in the parameters of a solar cell (J _SC, V _OC, ɳ, and fill factor) with (a) band gap, (b) radiative recombination coefficient, (c) CBDOS, and (d) VBDOS of SnS.

The band gap of the materials can be tuned by the material synthesis technique [44], doping, and pre- and post-annealing [45]. Shuai and Cheng successfully showed the tuning of the electrical and optical parameters of the thermally evaporated SnS with Cu doping [46]. Herein, we simulated the range of the band gap between 1.11 and 1.79 eV reported for the SnS (thickness-dependent) [15]. The maximum efficiency is attained when the band gap is ∼1.5 eV, which is near the optimized band gap [47]. RRC describes the direct recombination of the carriers from the conduction band (CB) to the VB. It is very low for the indirect band gap materials, while it is high for the direct band gap materials. As the RRC value increases (Figure 2b), the recombination probability increases, leading to a decrease in the collection of carriers. RRC is a function of the carrier concentrations of electrons and holes, as well as temperature [48]. It varies inversely with the carrier concentration and temperature [49]. The efficiency of the cell tends to saturate at the value of 1 × 10⁻¹⁰ cm³ s⁻¹. VBDOS and CBDOS were calculated with the help of the equations given below [50]. N c = 2 × 2 π m n ⁎ K B T h 2 3 , {N}_{\text{c}}=2\times \sqrt[3]{\frac{2\pi {m}_{\text{n}}^{\ast }{K}_{\text{B}}T}{{h}^{2}}}, N V = 2 × 2 π m p ⁎ K B T h 2 3 , {N}_{\text{V}}=2\times \hspace{.25em}{\sqrt[3]{\frac{2\pi {m}_{\text{p}}^{\ast }{K}_{\text{B}}T}{{h}^{2}}}}^{}, where m n ⁎ {m}_{\text{n}}^{\ast } and m p ⁎ {m}_{\text{p}}^{\ast } are the effective mass of DOS in CB and VB, respectively. The effective masses of the hole and electrons along different directions are given by m h a = 1.5 m 0 {m}_{\text{h}}^{\text{a}}=1.5\hspace{.25em}{m}_{0} , m h b = 0.21 m 0 {m}_{\text{h}}^{\text{b}}=0.21\hspace{.25em}{m}_{0} , and m h c = 0.33 m 0 {m}_{\text{h}}^{\text{c}}=0.33\hspace{.25em}{m}_{0} and m e a = 0.5 m 0 {m}_{\text{e}}^{\text{a}}=0.5\hspace{.25em}{m}_{0} , m e b = 0.13 m 0 {m}_{\text{e}}^{\text{b}}=0.13\hspace{.25em}{m}_{0} , and m e c = 0.2 m 0 {m}_{\text{e}}^{\text{c}}=0.2\hspace{.25em}{m}_{0} , respectively, in the VB and CB [13]. Here, m ₀ is the mass of a free electron. Considering the variation of effective mass along different directions, we obtain the VBDOS and CBDOS as 2.4 × 10¹⁸ to 4.6 × 10¹⁹, and 1.17 × 10¹⁸ to 8.846 × 10¹⁸ cm⁻³, respectively.

The DOS in both VB and CB talks about the available states to the carriers. The higher the density, the higher the state’s availability. Hence, a higher density triggers the recombination mechanism in the materials, which leads to lower efficiency. A similar trend in Figure 2c and d can be seen with increasing DOS in both VB and CB, respectively.

The back electrode contact gathers the holes at the interface, necessitating a proper band alignment for efficient collection. If the work function of the metal is greater than the work function of the absorber layer (p-type) [51], it results in the formation of ohmic contacts, which facilitates the efficient collection of carriers [52]. CBO also governs efficiency optimization. Ikuno et al. studied the detailed CBO in SnS/Zn_1−x Mg _x O (ZMO). The doping concentration of Mg in zinc oxide controls the band gap of ZMO and hence the conduction band minima. They demonstrated the optimal efficiency for this structure at nearly zero CBO [53]. Sinsermsuksakul et al. also conducted a CBO study for the SnS/Zn(O, S) solar cell [22]. The magnitude of the CBO is positive or negative depending on the position of the CB levels at the interface. Here, electrons are transported from SnS to the TiO₂ layer, and if the CBO is positive from the SnS to the TiO₂ side, then it impedes the transportation of the electrons. If the CBO is negative, it provides an easier path for electron transfer (Figure 3).

Figure 3

(a) Variations in parameters of solar cells with the work function of back contacts and (b) CBO.

Herein, the electron affinities of SnS and TiO₂ are 3.52 and 4.2 eV, respectively. CBO is studied in the range of −0.12 to 0.68 eV. The efficiency of the cell reached its maximum (14.77%) for the CBO at 0.48 eV. There is slightly less efficiency for the CBO at 0.28 eV (14.66%). The current density shows a tiny variation, while the open circuit voltage varies from 0.74 to 0.83 V for the CBO at −0.12 to 0.5 eV. Temperature distribution throughout the globe varies from near freezing point of water to 50°C. This operating temperature affects the performance of the solar cell. With increasing operating temperatures, the band gap of the material varies as per the following relation [54]. E g ( T ) = E g ( 0 ) − α T 2 T + β , {E}_{\text{g }}(T)={E}_{\text{g}}(0)-\frac{\alpha {T}^{2}}{T+\beta }, where α and β are the temperature fitting parameters of the given material.Variation in I _sc and V _OC can be related to the variation in the material’s band gap with temperature. I _sc increases, while V _OC decreases with increasing temperature due to the decreasing band gap of the material [54]. Hence, the overall efficiency of the cell is hampered by the increased recombination rates of carriers. Variation in the cell parameters with temperature is shown in Figure 4a.

Figure 4

Variation in the cell parameters with (a) operating temperature and (b) without and with BSF layers.

The cell is tested for the back-surface layer (BSF layer) by inserting different BSF layers. Inserting the BSF improves the cell efficiency by introducing the barriers to the minority carrier’s flow to the rear surface and reducing the misalignment between the back contact and the absorber layer. The BSF layer always consists of a higher doping concentration than the absorber layer, and this constitutes the electric field due to the p⁺/p region. Cells with NiO, WS_2, and WSe₂ BSF layers and without BSF layers are simulated, and output parameters are shown in Figure 4b, where parameters are chosen from studies of Ghori et al. and Alok and Brahma [55,56].

Later, the thickness of the NiO BSF layer and absorber layer will be optimized for the cell. After selecting NiO as the BSF layer for this cell, various thicknesses of NiO (30–100 nm) were tested, but there was no significant variation in the cell parameters. The BSF layer generally enhances the values of V _OC and I _sc due to reduced recombination of the minority carriers at the surface of the rear absorber layer [57]. Here, the values of V _OC and I _sc increase from 0.8405 (without BSF) to 0.8466 V (for NiO), while J _SC increases from 28.90 to 31.17 mA cm⁻². The metal having work function >4.8 eV is enough to form the ohmic contacts, which can be achieved using Ni, Co, Pt, Au, etc.

With optimized parameters, the solar cell showed efficiencies of 24.00% at 300 K operating temperature and 24.05% at 275 K (Figure 5a and b). Quantum efficiency seems to reach 100% for the visible region (550–750 nm) for this structure (Figure 5c), and energy band alignment is shown in Figure 5d. A list of optimized parameters is shown in Table 2.

Figure 5

J–V curves of the output panel at operating temperatures of (a) 300 K and (b) 275 K, (c) quantum efficiency of the cell, and (d) energy band alignment for the cell.