A Modeling Study on Utilizing In2S3 as the Bu ﬀ er Layer of Cu(In,Ga)Se2 Based Solar Cell

In Cu(In 1 − x ,Ga x )Se (CIGS)-based solar cells, the cadmium sulde (CdS) layer is conventionally used as a buffer layer. In the current study, the CdS layer was replaced by the Indium sulde (In 2 S 3 ) layer, and the impact of various concentrations of Ga in the CIGS absorber, the band gap of the In 2 S 3 buffer layer, and the band gap of the Na y Cu 1−y In 5 S 8 interfacial layer on the eciency of these CIGS solar cells were investigated. The results indicated that in the absence of Na y Cu 1−y In 5 S 8 , the optimal performance was obtained with an E g−In2S3 value of 3.1 eV and the ratio of Ga/(Ga + In) (GGI) = 1, yielding an eciency of 21.97%. The formation of the Na y Cu 1−y In 5 S 8 interfacial layer deteriorated the eciency of the device, and the highest eciency of the CIGS solar cells with the interfacial layer was 16.33 %.


Introduction
CuIn 1 − x Ga x Se 2 (CIGS) has shown great promise as a solar cell absorber material with excellent properties, such as high absorption coe cient, tunable band gap, and good environmental stability [1][2][3].
In a study, Cu(In, Ga)(S, Se) 2 thin-lm solar cells achieved a power conversion e ciency (η) of 23.35% on a laboratory scale [4]. The structure of CIGS solar cells typically comprises Glass/Mo/CIGS/Buffer layer/i-ZnO/n-ZnO:Al (transparent conductive oxide: TCO). It also includes cadmium sul de (CdS) functioning as a buffer layer between the CIGS absorber and window layers.
However, because of the toxicity of cadmium sul de and its incompatibility with in-line vacuum-based production methods, CdS is not a very reasonable choice as a buffer material in solar cells [5,6].
Furthermore, owing to the low band gap energy (i.e., ~ 2.4 eV) of CdS, the short-wavelength photons of the sunlight spectrum cannot reach the CIGS absorber layer [5,6]. As a result, replacing the CdS buffer layer with other Cd-free buffer layer materials has gained tremendous attention and has been considered one of the major goals in the area of CIGS thin-lm solar cells [5,6].
One of the most in uential parameters in forming buffer layers is conduction band offset (CBO) at the buffer-CIGS absorber interface [7][8][9]. A good alignment of conduction bands reduces recombination at the buffer-CIGS absorber interface [7][8][9]. Thus, it is required to optimally align the conduction band edge of the p-type CIGS absorber layer with that of the n-type buffer layer so as to obtain a good p-n junction [7][8][9]. Extensive research has been carried out on the substitution of alternative buffer materials for CdS [5,[10][11][12][13][14].
Indium sul de (In 2 S 3 ) has emerged as a promising candidate for the buffer layer in CIGS thin-lm solar cells [5,[15][16][17][18][19][20]. In 2 S 3 is superior to CdS as it has a larger band gap (In 2 S 3 ; 2.1-3.2 eV and CdS: 2.4eV)and greater stability [21]. In 2 S 3 thin-lm layers are also deposited via different in-line processing methods, such as atomic layer deposition (ALD) [22], physical vapor deposition (PVD) [15,23], spray ion layer gas reaction (ILGAR) [24], and sputtering [25]. When In 2 S 3 is deposited on the CIGS absorber layer, copper and sodium atoms from the CIGS absorber layer diffuse toward the In 2 S 3 buffer layer, and an interfacial layer with a general formula of Na y Cu 1−y In 5 S 8 is generated [26,27]. This interfacial layer substantially affects the e ciency of CIGS solar cells.
In a study, the In 2 S 3 buffer layer in CIGS-based thin-lm solar cells was deposited through atomic layer deposition (ALD), and a conversion e ciency of 16.4% was reached for these solar cells [16]. The highest power-conversion e ciency reported for CIGS solar cells with the In 2 S 3 buffer layer is 18.2% [26], which is notably lower than that reported for CIGS solar cells with the CdS buffer layer (22.9 %) [27]. Therefore, it is required to optimize CIGS solar cells with In 2 S 3 buffer layers.
In a study, the CIGS solar cells were simulated with In 2 S 3 layers and other Cd-free buffer layers [28].
Similarly, in another study, ZnO/In 2 S 3 /CIGS solar cells were modeled [29]. However, in both cases, the band gaps of CIGS and In 2 S 3 were xed. Two studies [30,31] explored the effect of the properties of the In 2 S 3 buffer layer on the performance of CIGS solar cells using numerical simulation, but variations in the CIGS absorber layer were not neglected in both studies. Sun et al. also examined the effect of the band gap (E g ) of In 2 S 3 and the composition of interfacial layers between In 2 S 3 and CIGS on the e ciency of CIGS solar cells [32] and found that the properties of these interfacial layers exerted a substantial in uence on the performance of the CIGS device. However, they overlooked the possible variation of the band gap of the CIGS absorber layer.
In the present study, the structure of contact/CIGS/In 2 S 3 /i-ZnO/ZnO:Al/contact was analyzed using the Solar Cell Capacitance Simulator (SCAPS) developed by the University of Gent [33,34]. Since the band gap is determined by the GGI ratio, the GGI was calculated for the CuIn 1 − x Ga x Se 2 absorber layer. Then, the impact of the In 2 S 3 band gap and the GGI of the CuIn 1 − x Ga x Se 2 absorber layer on the e ciency of solar cells was examined. After that, the optimum values of the In 2 S 3 band gap and Ga concentrations in the CIGS absorber layer were measured. The role of the band gap of the interfacial layer (Na y Cu 1−y In 5 S 8 ) and the CIGS layer in the performance of CIGS solar cells was also investigated.

Modeling And Simulation Of Cigs Solar Cells
In the current study, two structures, namely, ZnO:Al/i:ZnO/In 2 S 3 /CIGS/Mo and ZnO:Al/i:ZnO/In 2 S 3 /Na y Cu 1y In 5 S 8 /CIGS/Mo, were investigated. The structures are shown in Fig. 1, and their base parameters are provided in Table 1. In Table 1, E g and χ are band gap energy and electron a nity, respectively. N A and N D represent acceptor and donor densities, respectively. N C and N V denote the effective densities of conduction and valence bands, respectively. ε r is relative permittivity, µ p and µ n are the mobility of hole and electron, respectively, and σ h and σ e are hole and electron capture cross sections, respectively. In both structures, the thickness of CIGS, i:ZnO, and ZnO:Al was xed at 2 µm, 80 nm, and 300 nm, respectively. In the rst structure, i.e., ZnO:Al/i:ZnO/In 2 S 3 /CIGS/Mo, the thickness of the In 2 S 3 buffer layer was xed at 40 nm. In the second structure, i.e., ZnO:Al/i:ZnO/In 2 S 3 /Na y Cu 1y In 5 S 8 /CIGS/Mo, the sum of the thickness values of the Na y Cu 1−y In 5 S 8 and In 2 S 3 layers was 40 nm, which indicates that the increase in the thickness of the Na y Cu 1−y In 5 S 8 layer is certainly accompanied by a decrease in that of the In 2 S 3 buffer layer.
It is possible to alter the band gap of the CuIn 1 − x Ga x Se 2 absorber layer by varying the GGI ratio. With an increase in Ga content, the conduction band minimum was augmented, which boosted the band gap of CIGS [7] and declined the electron a nity by the same amount. Figure 2a depicts the band gap variations of the CIGS semiconductor [9]. Variation in Ga fraction yielded different band gaps of CuIn 1 − x Ga x Se 2 .
These bad gaps were calculated through the following equation [7]: where x is Ga fraction. It was found that the bandgap ranged from 1.01 eV for CuInSe2 to 1.67 eV for Variation in the band gap of the In 2 S 3 layer can be attributed to the grain sizes and composition of In 2 S 3 [35,36].
To be more precise, the sodium and oxygen doping of the In 2 S 3 thin lms enlarged the In 2 S 3 band gap [37][38][39]. In this study, it was assumed that shifting the conduction band energy edge toward higher energies widened the band gap of the In 2 S 3 buffer layer. It is worth mentioning that E g−In2S3 varied from 2.1 to 3.2 eV. Figure 2b illustrates a schematic diagram of the band variations for the In 2 S 3 buffer layer.
The main reason why the band gap of the Na y Cu 1−y In 5 S 8 interfacial layer extended with an increase in Na concentration was the shift in the valence band edge toward lower energies. A small shift in the conduction band edge toward higher energies also occurred [40]. Figure 2c shows a schematic diagram of the band variations for the Na y Cu 1−y In 5 S 8 interfacial layer.
By varying the band gap of In 2 S 3 (Na y Cu 1−y In 5 S 8 ), a wide range of CBO between the absorber layer and the buffer (as an interfacial layer) was covered; thus, it allowed the offset to be tuned to an optimal value for any GGI ratio in the CIGS absorber layer. Figure  Various short-circuit currents (J SC ) were obtained for different Ga fractions in CIGS as a function of the band gap of the In 2 S 3 buffer layer, as indicated in Fig. 4a. With increasing the band gap of the In 2 S 3 buffer layer, the current was boosted slightly since the wide band gap of In 2 S 3 allowed for greater absorption of short-wavelength photons [8,41]. J SC was not notably changed by varying the GGI ratio.
One possible explanation is that the recombination of the photogenerated carriers does not occur at the interface due to the electric eld generated by the space charge region (SCR) [minemoto 2013]. At low concentrations of gallium, the spike of the TCO-CIGS interface also impedes the photo-generated carrier, which decreases J SC dramatically [8,9,41,42].  One can argue that the incorporation of high Ga content into the SCR increases the barrier height, which facilities band-gap widening in the SCR and reduces the recombination rate [8,43].
As seen in Fig. 3a and Fig. 4b, for a constant GGI ratio, the value of V OC decreased with a reduction in the band gap of the buffer layer so long as the CBO was negative. When the band gap of the buffer layer lessened, its electron a nity (χ) increased and as a result, a larger negative value of CBO was obtained at the absorber/buffer interface. The negative CBO at the absorber-buffer interface acted as a barrier against the injected electrons. This barrier facilitated the recombination of the majority carriers via defects at the absorber-buffer interface. Therefore, the total recombination rate was promoted, and the V OC decreased with increasing the absolute negative value of CBO at the absorber-buffer interface [7]. In a nutshell, the negative CBO at the interface enhanced the interfacial recombination rate, which reduced the V OC [7,8,44]. As also illustrated in Fig. 3a and Fig. 4b, when the CBO at the interface of the absorber and the buffer was positive, the voltage reached its saturation point and became independent of the band gap of In 2 S 3 . When the CBO of the buffer layer was greater than that of the absorber layer, the barrier that was required for the recombination of the majority carriers was not formed; therefore, the V OC remained approximately constant [7]. As mentioned before, these results were observed in all the In 2 S 3 bang gaps except for the higher In 2 S 3 bang gaps. Figure 4c depicts the impact of various Ga fractions in the CIGS absorber layer and different band gap ranges of the buffer layer on the ll factor (FF). For all the GGI ratios, the FF was initially promoted and then reduced with increasing the band gap of the In 2 S 3 buffer layer. Lower GGI ratios triggered more profound changes.
When the CBO value was negative, the FF decreased because of the recombination of the majority carriers including the electrons in the In 2 S 3 buffer and the holes in the CIGS absorber layer at the In 2 S 3 -CIGS interface [7].
When the CBO value was positive, the FF was nearly constant. This value remained the same until the CBO value became so large that the spike of the In 2 S 3 -CIGS interface impeded the photo-generated carrier [7].
E ciency refers to the ratio of the product of J SC , the V OC , and the FF to incident power. The obtained e ciency in this study is plotted in Fig. 4d. As evident in Fig. 4d, the e ciency was promoted as absorber layer was transferred from the pure CIS phase to the pure CGS pure phase. Almost in all the GGI ratios, there was an increase in the e ciency as the E g−In2S3 value was boosted up to 2.9 eV, and then, the

Optimization of
ZnO:Al/i:ZnO/In 2 S 3 /Na y Cu 1−y In 5 S 8 /CIGS/Mo structure The formation of Na y Cu 1−y In 5 S 8 at the CIGS-In 2 S 3 interface strongly affects the performance of CIGS solar cells [32]. This section presents the results obtained for the impact of various E g ranges of the interfacial layer and different GGI ratios in the CIGS layer on the e ciency of the ZnO:Al/i:ZnO/In 2 S 3 /Na y Cu 1−y In 5 S 8 /CIGS/Mo structure.
The variation in J SC as a function of the band gap of the Na y Cu 1−y In 5 S 8 interfacial layer for different Ga fractions in CIGS is displayed in Fig. 5a. With increasing the band gap of the interfacial layer, the current was augmented from about 32.1 to 33.5 mA/cm 2 . It can be interpreted that the larger band gap of the interfacial layer allowed more photons to reach the CIGS absorber and generate more carriers [8,41]. Over all the interfacial band gap ranges, as the GGI ratio increased in the absorber layer the current, J SC , remained nearly constant. One can construe that the recombination of the photogenerated carriers does not occur at the interface due to the electric eld generated by the SCR [7]; consequently, the current remained unchanged.
Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js A boost in the V OC value was observed for all the band gap ranges of the buffer layer as the Ga fraction in the absorber layer increased from 0 to 1 (Fig. 5b). Owing to an increase in the band gap within the SCR, the barrier height was augmented, which diminished the recombination rate, and ultimately promoted the V OC [8,43,[45][46][47].
As demonstrated in Fig. 3b and Fig. 5b, the obtained V OC value was constant when the GGI ratio was xed and the CBO at the Na y Cu 1−y In 5 S 8 -CIGS interface was positive. It was found that for a constant GGI ratio, the V OC value lessened slightly when the band gap of the interfacial layer decreased and the CBO was negative. Based on these results, it can be concluded that using a constant GGI ratio, with increasing the band gap of the interfacial layer a slightly larger negative CBO value is achieved at the absorberbuffer interface. The negative CBO at the interface decreased the energy barrier between the conduction band of the buffer layer and the valence band of the absorber layer across the interface, which induced the carrier recombination via interface defects and eventually lowered the V OC [8]. When the CBO was positive, the barrier triggering the recombination of the majority carriers was not generated and the V OC was nearly constant [7,48]. These results are consistent with those of other studies undertaken on the effect of the CBO of buffer/CIGS layers on solar cell performance [7,48]. The maximum value of V OC was about 0.66 V at E g−NayCu1−yIn5S8 =2.4eV and GGI ≥ 0.5.
The achieved values for the ll factor (FF) over the total range of gallium content in the absorber layer and the band gap of the interfacial layer are shown in Fig. 5c.
The variations of the FF followed the trends in V OC as expected based on the analytical relationship between FF and V OC [49]. For all the E g− NayCu1−yIn5S8 values, the FF increased as the Ga fraction in the absorber layer was boosted, and with an increase in the GGI ratio, this effect lessened. For all GGI ratios, the FF was not under the in uence of the variations in the interfacial band gap.
As illustrated in Fig. 5d, the e ciency rst increased with a boost in the GGI ratio up to 0.4, and then remained approximately constant. The e ciency was nearly unchanged for the GGI ratio less than 0.4 in the full range of E g−NayCu1−yIn5S8 while it promoted for higher GGI ratios than 0.4 with the augmentation of E g−NayCu1−yIn5S8 . The optimal performance was obtained at E g−NayCu1−yIn5S8 =3 eV and GGI = 1, yielding an e ciency of 16.33% (J SC = 33.5 mA/cm 2 , V OC = 655 mV, & FF = 74.4%).
The comparison between Fig. 4d and Fig. 5d revealed that the formation of the Na y Cu 1−y In 5 S 8 interfacial layer deteriorated the e ciency of the device. It seems that the major reason for the decline in the device e ciency is the decrease of the V OC . The highest V OC and e ciency of the CIGS solar cell with no interfacial layer were 0.98 V and 21.97 %, respectively, while those of the cell with an interfacial layer were 0.66 V and 16.33 %, respectively.
The Na y Cu 1−y In 5 S 8 interfacial layer is generated owing to the diffusion of copper from the CIGS layer during In 2 S 3 deposition at substrate temperatures above 250. Thus, it is of crucial importance to deposit In 2 S 3 at temperatures below 250 C and minimize copper diffusion from the CIGS layer.

Conclusion
In the current study, the impact of gallium content in Cu(In,Ga)Se 2 and the variation in the band gap of buffer and interfacial In 2 S 3 and Na y Cu 1−y In 5 S 8 layers on the performance of CIGS solar cells was investigated. The cell parameters were measured for all the ranges of the band gap of In 2 S 3 and Na y Cu 1−y In 5 S 8 layers and the GGI ratios in the CIGS layer were computed.
Based on the results, it can be concluded that in the absence of the Na y Cu 1−y In 5 S 8 interfacial layer, the e ciency of CIGS solar cells enhances for all the GGI ratios when E g−In2S3 increases up to 2.9 eV, and there is a decrease in their e ciency with an E g−In2S3 value above 2.9 eV. The best performance is obtained with an E g−In2S3 value of 3.1 eV and a GGI ratio of 1, which yields an e ciency of 21.97%. The results also reveal that the formation of Na y Cu 1−y In 5 S 8 interfacial layers weakens the performance of the device since it decreases V OC . The highest V OC value obtained for the CIGS solar cell with no interfacial layer was 0.98 V while this value dropped to 0.66 V for the cell with an interfacial layer. The optimum e ciency achieved for the CIGS solar cell with a Na y Cu 1−y In 5 S 8 interfacial layer was 16.33 %.   Calculated conduction band offset for the (a) In2S3/CIGS interface, (b) NayCu1-yIn5S8/CIGS interface.