AFORS-HET is used to analyse and simulate the properties of heterojunction solar cells by solving the one-dimensional semiconductor equation based on Shockley-Read-Hall recombination statistics. In the simulation mode, the energy band electron distributions of solar cells include the valence band, the conduction band extension state, the localized states of valence band tail and the localized states of interval domain. The localized states in the band gap are mainly caused by the dangling bond. The tail domain is mainly caused by strain bond angle. The localized states in the band gap have a double Gaussian function distribution, which were positively correlated. Its distribution equations as follows

g A ( E ) = G A G exp { − 1 / 2 [ ( E − E p k a ) 2 / σ A 2 ] } (1)

g D ( E ) = G D G exp { − 1 / 2 [ ( E − E p k d ) 2 / σ D 2 ] } (2)

where E_pka and E_pkd are the Gaussian peak positions of the acceptor and donor states; σ_A and σ_D are the full width at half maximum (FWHM) of the acceptor and donor states, respectively; G_AG and G_DG are the density of the acceptor state and the density of the donor state.

Density of location state in band tail is described by an exponential function, and its distribution in the forbidden band are shown in equations (3) and (4) respectively.

g A ( E ) = G A 0 exp [ ( E − E c ) / E A ] (3)

g D ( E ) = G D 0 exp [ ( E V − E ) / E D ] (4)

where g_A (E) is conduction band tail defect density of states; g_D (E) is valance band tail defect density of states. E_C is conduction band edge; E_V is the valance band edge. G_A0 and G_D0 are prefactor; E_A and E_D indicate tail characteristics of the energy transfer. These complex states take the role of traps and composite centers. The composite model mainly considers SRH and Auger recombination, which have a decisive influence on the electrical and optical properties of thin film silicon materials.

Sanyo Ltd. has developed a silicon heterojubction solar cell named heterojunction with intrinsic thin layer with an efficiency up to 20%, which makes the HIT structure popular. However continuing to improve the efficiency of HIT solar cell is a big challenge. Owing to the unique electronic characteristics and stronger photoresponsivity in visible light spectrum from 400 nm to 680 nm [11] than Siand GaAs, the monolayer MoS₂ was used as window layer to make up a novel HIT cell. The intrinsic layer and back surface field (BSF) layer adopted to improve the efficiency of solar cell. Transparent conductive film (TCO) and Al back contact are also considered. The structure of solar cell is shown in Figure 1. The main parameters we draft are shown in Table 1, which are taken from various references [10] [12] [13] [14] [15] . For the c-Si, defect density is chosen as oxygen defect at 0.55 eV with a concentration of 1 × 10¹¹ cm⁻³. The surface re-

flectance of the solar cell is 0.1, the backside emissivity is 1. The surface recombination rate of the electrons and holes at the front and rear contact surfaces is 1 × 10⁷ cm/s, these coefficients are given in the AFORS-HET software.

MoS₂ has layered structure, while crystal Si is a diamond-like structure, hence, when MoS₂ film was deposited straight on the Si surface, this would results in large quantities of lattice defects at the interface [16] . So it is necessary to conduct interface modification before deposited MoS₂ on Si [16] . The buffer layer can balance carrier injection and reduce the leakage current. When intrinsic layer is inserted into MoS₂/c-Si interface, the intrinsic instead of the Si surface forms a contact with MoS₂ film. It is good way for MoS₂/Si solar cell to obtain high performance by introducing the intrinsic layer for solar cell. Therefore, in this paper, we compared the performance of TCO/n-type MoS₂/i-layer/p-type c-Si/Al solar cells by using different intrinsic layer, including a-Si: H, nc-Si:H and a-SiGe:H. The results are listed in Table 2.

According to Table 2, it is clear that the cell with a-SiGe:H as intrinsic layer has the best performances with efficiency 21.85%. However, using the a-Si:H as intrinsic layer of cell has the poor performances, which efficiency just is 13.4%. This result is mainly ascribed to the recombination rate in p/i interface.

In order to explain the results, we investigated the energy band and recombination rate of solar cells. Figure 2(a) and Figure 2(b) are the energy band and the recombination rate of the heterojunction solar cells with different intrinsic layer respectively. As well known, band offset can be observed at interface when two semiconductors with different band gap contact. Therefore, there is different band offset for p region of solar cell with different intrinsic layer. Band offset has

an important impact on the performance of solar cell. According to the Equation (5) [17]

J = J s c − [ ( q D n N d / L n ) exp ( − ( q V D + Δ E c ) / k 0 T )     + ( q D p N A / L P ) exp ( − ( q V D − Δ E V ) / k 0 T ) ] × ( exp ( q v / k 0 T ) − 1 ) (5)

It can be noted that when ΔE_V increases, J will be reduced; this will lead to the decreasing of cell performance. From Figure 2(a), when a-Si: H serving as the intrinsic layer, ΔE_V is larger, according to Equation (5) that will result in J smaller and makes the cell efficiency worse. In addition, From Figure 2(b), it shows that the recombination rate of solar cell with a-Si:H as the intrinsic layer is higher, consequently, the recombination rate of the i/p interface is increased, and resulting in the open circuit voltage has a low value, so using a-Si:H as the intrinsic layer of heterojunction solar cell, the efficiency is lower than the other materials. For a-SiGe:H, ΔE_V is small so that the efficiency of the TCO/n-type MoS₂/i-layer/p-type c-Si/Al solar cells with a-SiGe:H as intrinsic layer is higher, reaching 21.85%. For the solar cell with nc-Si:H as the intrinsic layer, it can be seen from Figure 2(a) that the conduction band offset is large that equals to 0.25 eV. Conduction band offset suppresses the surface recombination and makes the cell efficiency up to 21.83%.

For MoS₂/c-Si heterojunction solar cells, the density of defect states of MoS₂/c-Si interface is the important influencing factor that determines the transport properties of the cell. Here, in this paper, the TCO/n-type MoS₂/i-type nc-Si:H/p-type c-Si solar cell is studied. Because the bandgap adjusted of a-Si: H is less convenient than nc-Si:H. The bandgap of a-SiGe:H is small, though its bandgap is adjustable. Hence, we select the nc-Si:H as intrinsic layer in TCO/n-type MoS₂/i-type/p-type c-Si solar cell. The performances of the solar cell with TCO/n-type MoS₂/i-layer nc-Si:H/p-type c-Si/Al structure as a function of MoS₂/c-Si interface defect states show in Figure 3.

From Figures 3(a)-(d), we can see that the larger density of defect state of MoS₂/c-Si interface leads to the decreasing of V_oc, J_sc, FF and Eff. Initially V_oc and J_sc slightly decrease with the increasing density of defect state of MoS₂/c-Si interface. However, V_oc and J_sc obviously decrease when value larger than 1 × 10¹¹ cm⁻²∙eV⁻¹. FF and E_ff almost keep at constant initially with increasing density of

defect state of MoS₂/c-Si interface, but greater than 1 × 10¹² cm⁻²∙eV⁻¹, they visibly reduce. The results indicate that the density of defect states of interface is less than 1 × 10¹¹ cm⁻²∙eV⁻¹, the performances of solar cell decrease slowly, however, the performances of solar cell reduce rapidly when the defect states of MoS₂/c-Si interface higher than 1 × 10¹¹ cm⁻²∙eV⁻¹. Therefore, the density of defect states of interface should be under1 × 10¹¹ cm⁻²∙eV⁻¹ in order to obtain good performance, and the better performances can be obtained due to the larger J_sc when the density of interface defect states is lower than 1 × 10¹¹ cm⁻²∙eV⁻¹. It is because that defect states of interface and monolayer MoS₂ works as charge carriers traps that provide the channel for carriers recombination.

The photo-generated carriers come mainly from p-type c-Si layer in n-type MoS₂/p-type c-Si heterojunction solar cells. And there is a potential barrier resulting from the valence band offset at n-type MoS₂/p-type c-Si interface, which hinders the photo-generated minority carrier holes from being collected by front electrode. As a result, the valence band offset strongly affects the interface transport properties of photogenerated holes. As well known, the influence of ΔE_V on the interface transport properties and performances of solar cells can be got by changing the electron affinity of n type MoS₂layer and p-type c-Si layer [10] . The performances of TCO/n-type MoS₂/i-layer nc-Si:H/p-type c-Si/Al solar cell as a function of ΔE_V are given in Figure 4.

As we can see from Figure 4(a), initially the V_oc keeps at constant with the increasing of ΔE_V from 0.55 eV to 0.7 eV, then decreases when ΔE_V larger than 0.7 eV, however, when ΔE_V greater than 0.76 eV the value of V_oc keeps at constant again. From Figure 4(b), the J_sc almost remains at a constant with increasing of ΔE_V. In case of the fill factor, it slightly reduces from 83.64% to 83.58% with increasing of ΔE_V from 0.56 eV to 0.76 eV. However, the value keeps at constant when ΔE_V greater than 0.86 eV. E_ff decreases continuously with the increasing of ΔE_V. It is found that when ΔE_V is under 0.762 eV, ΔE_V has little impact on J_sc and FF, with the increasing of ΔE_V, J_sc stands at fixed value, but FF and V_oc decrease. It indicates that an appropriate high minority carrier band offset can lead to an effective suppression of interface recombination at MoS₂/c-Si hetero-interface, but too high band offset may enhance the interface recombination. So it is evident that ΔE_V should be kept lower than 0.762 eV in order to obtain good performance of solar cell. For this result, we studied the energy band structure with different ΔE_V, the results display in Figure 5.

As we can see form Figure 5, the degree of band bending at interface between MoS₂ and c-Si increases when ΔE_V is larger, which will lead to the higher valence

band barrier for holes and enhancing the build-in potential. From Equation (5), it is easy to note that J will decrease with the increasing of ΔE_V, and then the performance of the solar cell will go bad. The offsets between the band edges, ΔE_C and ΔE_V of the MoS₂/c-Si junction influence strongly the carrier transporting across the hetero-interface, so setting the suitable carrier band offset is necessary. Above all, the defect state of MoS₂/c-Si interface should be under 1 × 10¹¹ cm⁻²∙eV⁻¹, and the ΔE_V should be under 0.762 eV so that we can get the good performance for solar cell. It implies that the monolayer MoS₂ is a potential material for solar cell if we deal well the MoS₂/c-Si interface.

It is known that BSF working as passivation plays an important role in improving the performance of solar cell [18] . In order to improve the performances of solar cell, the effect of BSF on the performance of the cell was studied by TCO/n-type MoS₂/i-typenc-Si:H/p-type c-Si/BSF/Al cell structure in this paper. We choose p + -μc-Si:H as back surface layer. On one hand, the band gap of p + -a-Si:H is about 1.74 eV, and it has a large ΔE_c because of its large band gap which has a good effect on the reflection of electrons. On the other hand, nevertheless, ΔE_V also increases resulting in the holes difficultly reach to the back electrode. Compared with p + -a-Si:H, the bandgap of p + -μc-Si:H is about 1.45 eV, that is to say, the ΔE_c is relatively low which can lessen the reflection of the effective electrons. Furthermore, the electrons of the back surface field are collected, therefore, using p + -μc-Si:H as the back surface layer can transport enough of the majority of carriers [18] . The optimizing result is shown in Figure 6.

Figure 6 is the J-V curve of TCO/n-typeMoS₂/i-layer nc-Si:H/p-type c-Si/BSF/Al solar cells. According to Figure 6, the result reveals that the open circuit voltage of solar cell increases from 652.7 mV to 771.1 mV, in case of short-circuit current density, it increases from 39.97 mA/cm² to 42.46 mA/cm² and cell efficiency increases from 21.83% to 26.99%. It is obvious that the

performances of the solar cell with BSF are obviously improved. It means that BSF is a good way to improve the performance of solar cell. BSF can collect the photogenic minority carrier in back surface, improving the internal quantum efficiency of solar cell. In addition, BSF layer can introduce barrier for minority carriers, which can reduce the recombination of the photons on the surface.

Figures 10(a)-(d) show the cell performance of solar cells with the different MoS2 thickness. From Figure 10(a), it is evident that Voc indicates that the thickness of MoS₂ has no effect on Voc. However, Figure 10(b) shows that the short-circuit current density decreases gradually from 42.49 mA/cm² to 42.16 mA/cm² with the increasing MoS₂ thickness from 0.65 nm to 9.75 nm. For Figure 10(c), we can see that the value of fill factor follows oscillating behaviour with increasing the thickness of MoS₂ but it continuously reduces from 82.49% to 82.43% in the thickness range 1.95 to 7.15 nm, and it reaches a maximum of 82.49% for the thickness at 8.45 nm. From Figure 10(d), we can note that the efficiency of solar cell decreases from 27.22% to 26.8% with increasing the thickness of MoS₂. The reduction of Jsc may be ascribed to the increase in absorption losses at the surface layer and the larger series resistance in solar cell. The monolayer MoS₂ is a direct gap which is beneficial to electron jumping. Hence, we can achieve the best performance of the cell up to 27.22% at the thickness of MoS₂ is 0.65 nm. But the efficiency reduces with increasing the thickness of MoS₂ due to it is indirect gap for multilayer MoS₂.

From the above work we did, we finally obtained the best performance of solar cell which efficiency is up to 27.22% with the density of defect states and band offset of MoS₂/c-Si interface lower than 1 × 10¹¹ cm⁻²∙eV⁻¹ and 0.762 eV respectively, MoS₂ thickness of 0.65 nm, intrinsic layer thickness of 2 nm and the band gap is 1.7 eV. The J-V curve of solar cell is shown in Figure 11.