The effect of Se/(S+Se) compositional ratios on the performance of SnS-based solar cell: a numerical simulation

Researchers have currently shown great interest in numerical simulation to study and design materials of solar cell. In our proposed model, the p-type SnS is used as absorber layer in the solar cell simulation. The solar cell configuration was based on the current record device [7], where some of their results and material properties were taking into account as reference for our model. The band gap and electron affinity of this layer were varied in order to obtain SnSSe and evaluate the Se composition on the device performance. The schematic view of the proposed solar cell structure is shown in figure 1(a), where a multilayer planar structured solar cell with thickness values of ITO (300 nm), ZnO (10 nm), Zn(O,S):N (30 nm), SnO₂ (1 nm), SnSSe (500 nm) and Mo (450 nm) was simulated numerically using SCAPS-1D device simulation software. Im et al reported that the CB can be modified by the Se incorporation, while the VB still constant [20]. In figure 1(b) is presented a band energy diagram of Zn(O,S) buffer layer, and the five absorber layers (SnS_xSe_1-x with different Se/(S+Se) CRs) that we used for our simulations (see references in section 2.3).

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Several works have demonstrated the importance of numerical modeling for enhancing the performance of thin-film solar cells, by solving the basic equations of semiconductors, as well as, helping to understand and predict the impacts for each material layer of a solar cell [21–23]. The simulations in this work were carried out by SCAPS-1D, under standard conditions; AM 1.5 solar spectrum at room temperature (300 K). This program resolves three differential equations for J-V characteristics (Poisson, continuity and drift diffusion) at each position throughout the solar cell by taking into account the boundary conditions [24]. Furthermore, the software simulates the device performance by considering the Shockley-Read-Hall recombination.

Poisson equation,

$$\begin{align}\frac{{{\partial ^2}\psi }}{{{\partial ^2}x}} = - \frac{{\partial E}}{{\partial x}} = - \frac{\rho }{{{\varepsilon _s}}} = - \frac{q}{{{\varepsilon _s}}}\left[\, {p - n + {N_D}\left( x \right) - {N_A}\left( x \right) \pm {N_{def}}\left( x \right)} \right].\end{align} \tag{ 1 }$$

This equation relates the electric field $E$ of p-n junction to the space charge density $\rho$. Where, $\psi$ is the electrostatic potential, ${\varepsilon _s}$ is the static material's permittivity, $q$ the elementary charge (1.6 × 10⁻¹⁹ C), $p$ the hole density and $n$ the electron density. Finally, ${N_{D{\text{ }}}}$ and ${N_A}$ are ionized donor and acceptor densities, respectively.

Electron and hole, carrier continuity equations at steady state,

$$\begin{equation}\frac{{\partial {J_n}}}{{\partial x}} + G - {U_n}\left( {n,p} \right) = 0\end{equation} \tag{ 2 }$$

$$\begin{equation} - \frac{{\partial {J_p}}}{{\partial x}} + G - {U_p}\left( {n,p} \right) = 0\end{equation} \tag{ 3 }$$

where ${J_n}$, ${J_p}$ are current density of electron and hole carriers, ${U_n}$, ${U_p}$ are the net recombination rates and $G$ is the electron-hole generation rate.

Drift diffusion (total current density) equations,

$$\begin{equation}{J_n} = qp\,{\mu _n}E + q{D_n}\frac{{\partial n}}{{\partial x}}\end{equation} \tag{ 4 }$$

$$\begin{equation}{J_p} = qp\,{\mu _p}E - q{D_p}\frac{{\partial p}}{{\partial x}}\end{equation} \tag{ 5 }$$

where ${\mu _n}$, ${\mu _p}$ are the electron and hole mobility carrier, $q$ is the elementary charge, and ${D_n}$, ${D_p}$ are the diffusion coefficients of electron and hole, respectively.

Material properties are summarized for each layer in table 1. These data were obtained from the literature [4, 7, 21, 25–31]. In the present study, the device parameters such as thickness of active layer were optimized using the SCAPS-1D simulator. Work functions used were 4.4 eV for ITO as front contact and 5.0 eV for Mo as back contact [21] with surface recombination velocity of 1 × 10⁵ cm⁻¹ and 1 ×10⁷cm⁻¹ for electrons and holes, respectively. In the present work, it is assumed that there is no presence of secondary phases in SnS_xSe_1–x absorber, which has been experimentally demonstrated by deposit control [32]. It should be noted that by implementing a compositional change of the SnS_xSe_1–x absorber layer, not only the band gap (${E_g})$, but almost all other materials properties including electron affinity (χ), optical absorption, doping density, transport properties and recombination properties are varied according with the Se contents in the absorber. Nevertheless, in this work, only the ${E_g}$ and χ values from the SnS_xSe_1-x layer was varied as function of the Se content (x), while the other properties are considered constant. This last assumption is due to the scarce of material properties in the literature about the SnS_xSe_1-x thin film. However, Walsh et al has demonstrated that in kesterite, ${E_g}$ decreases almost linear by the Se incorporation from 1.5 eV (CZTS) to 1 eV (CZTSe) [33]. Theoretical and experimental studies have been reported a non-linear behavior of E_g with the composition in SnS_2(1-x)Se_2x alloys [14, 34]. However, for the SnS_xSe_1-x material have been reported a linear behavior with the increasing of Se content, where the optical bowing parameter (b) is very small [35], and even can be considered as zero [36]. Hence, it can be assumed that for SnSSe as well as the kesterites, the band gap (${E_g}$) decreases from 1.35 eV at $x = 1$ to 1 eV at $x = 0$, with a small bowing parameter reported in equation (6) (Vegard´s law). In this work is considered b = 0 and as consequence, a linear dependence of the E_g. as function of $x$. According to this behavior, the ${E_g}{\text{ }}$and χ of SnS_xSe_1-x at different Se concentration are determined by:

$$\begin{equation}{E_g}\left( {Sn{S_x}S{e_{1 - x}}{\text{ }}} \right) = x{E_g}\left( {SnS} \right) + \left( {1 - x} \right){E_g}\left( {SnSe} \right) - bx\left( {1 - x} \right)\end{equation} \tag{ 6 }$$

$$\begin{equation}\chi \left( {Sn{S_x}S{e_{1 - x}}{\text{ }}} \right) = x\chi \left( {SnS} \right) + \left( {1 - x} \right)\chi \left( {SnSe} \right).\end{equation} \tag{ 7 }$$

Table 1. Material layer parameters of the SnSSe solar cell.

Parameters	ITO	ZnO	Zn(O,S):N	SnO2	SnS (reference device)	SnSSe
d (nm)	300	10	30	1	500	500
Eg (eV)	3.65	3.4	2.7	3.6	1.35	Variable
$\chi$ (eV)	4.8	4.6	4.3	4.5	3.9	Variable
${\varepsilon _r}$	8.9	9	10	9	12.5	12.5
${\mu _n}({{c}}{{{m}}^2}\;{{V}}{{{s}}^{ - 1}})$	10	100	4.7	100	100	100
${\mu _p}({{c}}{{{m}}^2}\;{{V}}{{{s}}^{ - 1}})$	10	25	1	25	4	4
${N_D}\left( {{{c}}{{{m}}^{ - 3}}} \right)$	2 × 1019	1017	9.3 × 1016	1020	0	0
${N_A}\left( {{{c}}{{{m}}^{ - 3}}} \right)$	0	0	0	0	5.7 × 1015	5.7 × 1015
α (cm−1)	106	Data file	105	105	104	104
Nt (cm−3)	Data file	Data file	—	—	1015	1015

As shown in figure 1(b), the E_g and χ change depending on the composition. These values are:

E_g = 1.35, 1.26, 1.17, 1.08 1.0 eV and $\chi$ = 3.9, 3.98, 4.07, 4.15, 4.23 eV.

As a starting point, the modeling of SnS solar cell (structure shown in figure 1(a)) was performed by SCAPS. Figures 2(a) (J-V curve) and (b) EQE shows the results of the theoretical simulation. A good approximation with the experimental parameters of record solar cell (Sinsermsuksakul et al) is observed.

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Within the scheme of figure 1(b), was observed that the energy band gap (E_g) and electron affinity (χ) of the SnS layer can be tailored by the Se incorporation. As the E_g and χ of window layer and SnS thin film have different values, there are discontinuity in conduction band and valence band of the window/SnS interfaces. The Se addition modifies the conduction band offset ΔE_c and, as a consequence, the properties of the window layer/SnS heterojunction. Therefore, the effect of the incorporation of Se on the output parameters of the SnS solar cell is shown in figure 3. Furthermore, the output parameters are summarized in table 2.

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In figure 3 is observed that the SnS solar cell performance depends on the Se incorporation. All output parameters (V_oc, J_sc, FF and PCE) increased by increasing the CR from 0.0 to 0.75 and decreased at a CR = 1. The figure 3(a) shows that the greatest PCE was achieved at 0.75 CR with a 10.23% value. This implies an increase of 2.35 times compared with the SnS solar cell without Se. Figure 3(b) presents the same behavior on the FF reaching a 69.5% for a CR of 0.75. The figure 3(c) presents as well an increase of V_oc with the Se incorporation, where a 0.499 V was obtained at 0.75 CR. However, the V_oc was reduced to 1.0 CR. The improvement of V_oc indicates a greater separation of fermi quasi levels, which could be attributed to a greater radiation absorption and efficient transfer of electron photogenerated in the absorber. Moreover, the J_sc values are observed in figure 3(d). The greatest value was achieved at 0.75 CR with 29.5 mA cm⁻². The increasement of J_sc by Se incorporation could be due to an absorption improvement by decreasing the E_g (from 1.35 to 1.08 eV), which extended the absorption range at greater wavelength as was observed in EQE (figure 4). The reduction of FF, V_oc and J_sc at 1.0 CR could be attributed to a large barrier at the absorber/buffer layer interface, which affects the transfer of electrons from the absorber to the external circuit. A more detailed discussion of these issues is done below (see discussion of figure 5).

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In figure 4 is presented the EQE for solar cells at different Se/(S + Se) CRs (0.0, 0.25, 0.50, 0.75 and 1.0). It is observed that when the CR increases, the EQE response expands towards greater wavelengths, which corresponds to the decrease of the band gap (from E_g = 1.35 eV (for CR = 0.0) to E_g = 1.0 eV (for CR = 1.0)). It is also observed that the EQE increases in the whole wavelength spectrum, when the CR is increased from 0.0 to 0.75, which could be owing to the fact a greater absorption of the incident radiation. However, the EQE of the solar cell with CR = 1.0 (SnSe) was slightly decreased, which could be because of resistive effects that affect the transport and collection of charge carrier. The results of figure 4 are in good correspondence with the behavior shown in figure 3(d).

The behavior shown in figures 3 and 4 could be explained, based on the understanding that changes in CR produces modifications in the band gap of materials and in the band alignment of heterojunctions. These modifications, impact on processes of radiation absorption, recombination, transport and collection of charge carriers. This scheme has been observed in Zn(O,S)/SnS [6, 37] and other heterojunctions [38–40]. In the present work, the increment of Se/(S + Se) CR produces a reduction of the minimum of the conduction band and the energy band gap of the absorber. The reduction of the minimum of the conduction band generates band alignment changes, which impacts on processes of recombination, transport and collection of charge carriers. The reduction of the energy band gap has an impact on the absorption. In figure 5 are presented the opposite CR cases, SnSe and SnS. Figure 5(a) shows the SnSe as absorber. In this case, the energy band gap is the lowest, which improves the absorption. However, the reduction of the minimum conduction band generates an increment on conduction band offset (ΔE_c). This behavior, implies the presence of a large barrier at Zn(O,S)/SnSe interface that affects the output of electrons from the absorber to the Zn(O,S) buffer layer, and to external electrical circuit. Hence is reflected in a reduction of FF, J_sc and V_oc. This corresponds to that reported by other authors [37], according to which the increase in the barrier at the SnS/Zn(O,S) interface (due to compositional changes in the Zn(O,S) buffer layer) affects the FF, J_sc and V_oc of the cells. On the other hand, figure 5(b) presents the case of the solar cell with SnS as absorber. The SnS has the highest energy band gap and conduction band minimum. In this case, the conduction band offset (ΔE_c) is positive but low, which implies the presence of a small barrier at Zn(O,S)/SnS interface. So, allows the output of electrons from the absorber to the external electrical circuit. Besides, the J_sc is affected by the relative wide energy band gap of the absorber. The opposite analyzed cases (SnSe and SnS) show that a wide energy band gap (SnS case). This implies a minimal barrier to the transport of photogenerated electrons in the absorber, but a poor absorption; while a narrow energy band gap (SnSe case) implies better absorption. Nevertheless, the presence of a high barrier affects the transport. The above explains why a SnSSe structure (with a CR = 0.75) has a better performance as were shown in results above.

3.3.1. Thickness optimization.

Is well known that the absorber thickness has an influence in the device performance. In this section, the influence of the SnSSe thickness (with CR = 0.75) on the solar cell has been studied. This effect is shown in figure 6 and in table 3 the output parameters are presented.

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Table 3. Output parameters of SnSSe solar cell as function of absorber thickness.

Thickness (nm)	Voc (V)	Jsc (mA cm−2)	FF (%)	PCE (%)
100	0.359	18.37	56.1	3.69
200	0.42	21.2	62.5	5.56
300	0.486	26.8	66.3	8.63
400	0.495	28.9	68.7	9.82
500	0.499	29.5	69.5	10.23
600	0.52	29.99	70.43	10.98
700	0.528	30.36	70.81	11.35
800	0.537	30.797	71.28	11.78
900	0.537	30.54	71.05	11.65
1000	0.537	30.28	70.79	11.51

The thickness of the absorber was varied over a wide range (from 100 to 1000 nm). In figure 6 and table 3 it is observed that the V_oc experiences a significant increase with increasing thickness of the absorber, going from 0.359 V (for 100 nm) to 0.537 V (for 800 nm). The V_oc is kept constant for higher thicknesses. For its part, the J_sc increases by the increment of the absorber thickness (which could be due to a greater radiation absorption), reaches a maximum of 30.797 mA cm⁻² for a thickness of 800 nm, and decreases slightly for greater thicknesses (which corresponds to the fact that an excessively thick absorber affects the carriers transport and collection). The FF shows a behavior similar to the J_sc. The PCE, on the other hand, increases with the increment of the absorber thickness, reaching a maximum for 800 nm, and decreases slightly for greater. With a thickness of 200 nm of the ternary absorber (CR = 0.75), an efficiency of 5.56% is obtained. This value is superior to the record efficiency of the SnS solar cell (4.36%), obtained with a thickness of 500 nm of the binary absorber material. It is observed, thus, that ternary material enhances the use of thinner films in solar cells. With 500 nm of ternary absorber (SnSSe) at CR = 0.75, an efficiency of 10.23% was obtained (which is more than double the record efficiency mentioned above). The greatest PCE is 11.78% and was achieved for an absorber thickness of 800 nm. This PCE means an increase of 2.7 times with respect to the record efficiency of the SnS solar cell. The previous results show that the use of SnS_xSe_1-x ternary type as an absorber material constitutes a very interesting way to increase the efficiency of solar cells with respect to binary type absorber (SnS).

3.3.2. Work function in back contact.

There are two types of metal-semiconductor contacts: the rectifying and the nonrectifying or ohmic types. In the contact rectifier, there is a potential barrier that affect the charge carrier collection. On contrary, an ohmic contact has a negligible contact resistance relative to the bulk or series resistance of the semiconductor, thus an enhancement on internal collection processes on the solar cell is produced. There are several reports about the work function (WF) of the contacts (back and front), which has an influence on these processes [17, 41, 42]. For SnS solar cell, the record efficiency was obtained by using Mo (5.0 eV) as back contact. In this work, we varied the WF of the back contact from 4.7 to 5.7 eV in order to study this influence on the output parameters of solar cell (with a CR = 0.75 and an absorber thickness of 800 nm). In figure 7 is shown the effect of different WF of back contact on SnSSe solar cell performance.

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In figure 7 is observed that all electrical parameters increase with increasing the WF. This suggests the formation of a less resistive contact (a barrier reduction) and greater carrier collection. It is observed that the maximum PCE (14.65%) was obtained for a value of 5.4 eV and keeping constant for higher values. However, a decrease on the efficiency for lower WF values was perceived. The observed behavior reveals the importance of finding new materials with greater WFs than Mo for this type of device.

3.3.3. Bulk defect density on the absorber.

The defect in bulk material usually act as recombination (Shockley-Read-Hall non-radiative) centers for photo-generated carriers, resulting in the decrease of the FF, J_sc and V_oc. In this sense, a simulation under different defect densities (10¹¹–10¹⁷ cm⁻³) was carried out in order to evaluate the impact of the defect density on the SnS_xSe_1-x solar cell performance. For this study was employed the device with the greatest PCE (14.65%), which has a defect density of 10¹⁵ cm⁻³. This effect is presented in figure 8.

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Figure 8 shows the effect of bulk absorber defect density on solar cell performance. It is observed that the J_sc, FF, V_oc and PCE of the solar cells show a stable behavior, with relatively high values, for a defect density between 10¹¹ and 10¹⁴ cm⁻³. The performance of the devices is observed to get worse for N_t ≥ 10¹⁵ cm⁻³. The greatest efficiency was 17.56% at 10¹⁴cm⁻³ of bulk defect density, while the lowest was of 0.26% for defect density of 10¹⁷ cm⁻³. The previous results indicate, on the one hand, that the performance of these devices has a certain tolerance to the defects of the absorber layer. On the other hand, in order to obtain high efficiencies, these defects must not exceed the critical value (∼10¹⁴ cm⁻³).