Numerical Investigations and Analysis of Cu2ZnSnS4 Based Solar Cells by SCAPS-1D

This paper reports numerical investigation, using SCAPS-1D program, of the influence of Cu 2 ZnSnS 4 (the so-called CZTS)material features such as thickness, holes, and defects densities on the performances of ZnO:Al/i-ZnO/CdS/CZTS/Mo solar cells structure. We found that the electrical parameters are seriously affected, when the absorber thickness is lower than 600 nm, mainly due to recombination at CZTS/Molybdenum interface that causes the short-circuit current density loss of 3.6mA/cm. An additional source of recombination, inside the absorber layer, affects the short-circuit current density and produces a loss of about 2.1mA/cm above this range of absorber thickness. The J-V characteristic shows that the performance of the device is also limited by a double diode behavior. This effect is reduced when the absorber layer is skinny. Our investigations showed that, for solar cells having a CZTS absorber layer of thin thickness and high-quality materials (defects density ∼10 cm), doping less than 10 cm is especially beneficial. Such CZTS based solar cell devices could lead to conversion efficiencies higher than 15% and to improvement of about 100mV on the open-circuit voltage value. Our results are in conformity with experimental reports existing in the literature.


Introduction
Nowadays, one of the hottest topics in photovoltaic (PV) field is the study of Cu 2 ZnSnS 4 (also known as CZTS) based solar cells.Indeed, thin film of the kesterite compound CZTS is one of the most prospective materials to be used as solar cell absorber layer, due to its excellent optical properties (the band gap varies from 1.4 to 1.5 eV and the absorption coefficient is higher than 10 4 cm −1 [1][2][3][4]), as well as its constituents that are nontoxic and very abundant naturally.However, despite the development of several physical and chemical fabrication techniques of PV devices [5][6][7][8][9], CZTS based thin films solar cells exhibit relatively weak conversion efficiencies (about 8.4% [9]), compared to those of other technological paths of photovoltaic field, like CIGS based solar cells which reach record efficiencies over 20% [10].Several reasons could explain this situation, such as various loss mechanisms due to absorber features.Therefore, a detailed analysis of the effect of thickness, holes, and defects densities of CZTS layer is necessary and has been presented in this work, from computations performed using the one dimensional numerical simulation package SCAPS-1D [11].The results proposed in this study are a useful guideline for design of high performances CZTS based solar cells.

Materials and Methods
2.1.Cell Structure.Figure 1 visualizes our solar cell structure, which reads (Ni/Al)MgF 2 /ZnO:Al/i-ZnO/CdS/CZTS/ Mo/Substrate.As explained in [12], CZTS and CdS, which are, respectively, the absorber and buffer layers, form the p-n junction and constitute the key parts of the device.The intrinsic ZnO (i-ZnO) and ZnO doped with aluminum 2 International Journal of Photoenergy  (ZnO:Al) layers are used as transparent conductive oxide and are covered with an antireflection layer (MgF 2 ).

Numerical Modeling and Material Parameters.
We have used the SCAPS-1D program to simulate the functioning of our solar cell.The baseline parameters used to perform our computations are listed in Table 1.They were borrowed from previous works [9,13,14] or obtained by reasonable estimates in some cases.We have introduced one type of single level defects in each layer and the recombinative defect states have been positioned in the narrow distribution close to the middle of band gap such as recommended by Gloeckler et al. [15].Open-circuit limitation due to interface recombination is a known problem in a wide band gap chalcopyrite solar cell, particularly when the absorber layer conduction band is higher than that of the buffer layer resulting in a "cliff" type band alignment [14].This is the case of CZTS based solar cells, as shown in the band diagram (Figure 2).To take into account recombination at the CZTS/CdS interface, reasonable neutral interface defects for recombination were also positioned at midgap.As mentioned in [4], the front and back surface reflectivity were set to 0.1 and 0.9, respectively.This high reflectivity at back-contact allows photons crossing the absorber to be reflected in order to optimize the absorption in the absorber.For this purpose, the absorption coefficient has been set to 10 5 cm −1 and all SCAPS-1D simulations   were performed under an AM 1.5 light spectrum, while the operating temperature and series resistance have been fixed to 300 K and 4.5 Ω⋅cm −2 , respectively.Figure 3 shows dark and light - curves simulated for our CZTS based solar cell baseline, where the default values of the absorber thickness, the doping, and the defects density are set to 600 nm, 3 × 10 15 cm −3 , and 1 × 10 16 cm −3 , respectively.The resulting performance parameters such as efficiency (), open-circuit voltage ( oc ), short-circuit current density ( sc ), and fill factor (FF) are obtained using - curves.
Our simulated results are presented in Table 2 and compared to experimental data [9].
The short-circuit current density and the efficiency have the same values as those obtained by Shin et al. [9].The experimental CZTS based solar cell shows a low opencircuit voltage, compared to our value.As stated in [16,17], this difference can be explained by either the existence of second phase often present at the absorber/back-contact or absorber/buffer layer interface, which increase interface recombination.It can also be due to the greater value of the defects density in the real samples, as predicted in Section 3.3.According to Table 2, there is a good agreement between the experimental data from the literature [9,14] and our model; therefore, validate our set of parameters as a baseline for simulating the influence of the variation of absorber parameters on the solar cell performance.produce solar cells with high conversion efficiency and very thin absorber layer.Works existing in the literature show that the greater efficiencies of CZTS based solar cells have been obtained with thin CZTS layer [9,14].In order to obtain qualitative information, we have investigated the effects of the absorber layer thickness on the device electrical parameters.This is shown in Figure 4.The other layers properties are kept constant while varying the absorber thickness.The band gap of the absorber layer is also kept constant to 1.45 eV [9].We remark that all device performance parameters such as  oc ,  sc , and FF are nearly constant for thickness beyond 600 nm, corresponding to the zone where the device presents a relatively weak efficiency.This is mainly due to high recombination of the photogenerated electrons in the depth of the absorber, which are recombined before reaching the CZTS/CdS interface, because the estimated electron diffusion length is very short in the CZTS absorber (350 nm) [10].The  sc varies from 21.6 mA/cm 2 (the top value obtained during this simulation) for  = 250 nm to 19.5 mA/cm 2 for  = 600 nm.That is a loss of 2.1 mA/cm 2 , which is not negligible, corresponding to recombination current that occurs inside the CZTS based solar cells device with a thicker absorber layer.Figure 5 shows the generation profile made from our baseline.It appears that the generation rate of photogenerated electron-hole pairs is low for a thick CZTS absorber layer because of a relatively high recombination in the bulk material.

Effect of the CZTS Layer Thickness on Solar Cell
In the zone of thin thicknesses, we have selected two domains: (i) For 250 nm <  < 600 nm, the electrical parameters such as  oc ,  sc , and efficiency increase. sc reaches its top value for a thickness of 250 nm.This is mainly due to a good collection of carriers across the entire absorber layer thickness.The quantum efficiency curves for different values of absorber thickness are shown in Figure 6.Since the photons of short wavelengths (300 nm <  < 450 nm) correspond to the absorption in the window ZnO and buffer CdS layers, we have chosen to focus solely on those which are effectively absorbed in the CZTS absorber layer (450 nm <  < 900 nm).The quantum efficiency of cells is higher when the thickness decreases and reaches about 84% for  = 250 nm.Therefore, most photons are absorbed for absorber thickness between 250 nm and 600 nm, which increases the solar cell performance.
(ii) For 100 nm <  < 250 nm,  oc and FF increase.The increase of  oc shows the nondegradation of the junction in the case of ultrathin thickness.In the same condition, the increase of FF indicates the minimization of double diode behavior, observed through the nonsuperposition between the dark and light - characteristics (Figure 3), which reduces the additional recombination occurring in the pn junction. sc decreases rapidly due to the higher recombination of photogenerated electrons close to the back-contact and proves the existence of potential barrier at the CZTS/Molybdenum interface, leading to the removal of the holes to the crossing of this interface.The  sc passes from 21.6 mA/cm 2 for  = 250 nm to 18.5 mA/cm 2 for  = 100 nm, that is, a loss  of 3.6 mA/cm 2 corresponding to the recombination current at the back-contact.
In short, we predict that the optimization of the absorber's thickness in CZTS based solar cells is important to improve its performance.For a good collection of the photogenerated electron-hole pairs, the absorber layer thickness may be chosen below 600 nm.These observations are similar to those of [9,14].

Effect of Absorber Holes
Density. Figure 7 illustrates the influence of the holes density () on  oc ,  sc , FF, and efficiency for different absorber layer thickness.It shows that  oc increases significantly with the increase of absorber doping, while  sc decreases, both in the same way, whatever the absorber layer thickness is.The increase of  oc becomes fast and important for doping beyond  = 10 16 cm −3 .However,  sc decreases very quickly for doping varying from 10 16 to 10 18 cm −3 and becomes almost constant above this range.These phenomena can be explained by Shockley equation in the case of simple p-n junction model: Here, , , and  denote the Boltzmann constant, the operating temperature, and the elementary charge, while  Ph and  0 are, respectively, the photogenerated current density and the saturation current density.The saturation current density is expressed by is the intrinsic carriers concentration;   and  ℎ are the electrons and holes diffusion coefficient, respectively;   and  ℎ are the electrons and holes diffusion length, respectively;   and   are, respectively, the ionized-acceptor atoms and ionized-donor atoms densities;  is the diode quality factor.Since, in the classical p-type semiconductor, we have  ≈   in thermodynamic equilibrium, we have made the approximation that the density of acceptors is equal to holes density in the bulk of absorber.Hence, the saturation current density will reduce when  rises.Therefore,  oc increases (Figure 7(a)).The evolution of  sc as a function of the absorber holes density presents three zones, such as illustrated in Figure 7(b), which influence strongly this electrical parameter: the first zone is 10 12 cm −3 <  < 10 16 cm −3 , the second one corresponds to 10 16 cm −3 <  < 10 18 cm −3 , and the third one is  greater than 10 18 cm −3 .In spite of a slight lowering in the first zone, we observe that the short-circuit current density is larger than 18 mA/cm 2 for the thicker absorber layer and maintains itself up to 20 mA/cm 2 for the thinner thicknesses.This improvement of  sc is due to a better collection of the photogenerated electrons, which enhances the efficiency.The efficiency reaches 10.1% for a 150 nm absorber thickness for weakly doped sample.This is mainly due to the fact that the increase of doping, for the thinner thicknesses, reduces the space charge region width (SCRW) and the absorber thickness may become order of magnitude or smaller than the SCRW.This requirement will be beneficial and crucial when designing the absorber layer thickness of CZTS based solar cells.The reason is that the minority carriers in CZTS materials have a short life time [14].In the second zone,  sc decreases significantly with the increase of absorber doping, because of the fact that this rising enhanced recombination process of photogenerated electrons and reduced the possibility to collect them.On the other hand, the photogenerated electrons undergo Coulomb interactions because of the overpopulation of doping.This leads to more holes' traps and recombination.Hence, CZTS absorber doping strongly produces more effects which are harmful to device performance parameters (Figures 7(b) and 7(d)).The shortcircuit current density, although it is constant, is very low for  > 10 18 cm −3 , whatever the doping is.This is due to various recombination additional mechanisms created by capture centers of photogenerated electrons through the absorber layer which are occasioned by an inhomogeneous distribution of doping in the bulk material.The relative enhancement of efficiency in this range is mainly due to  oc and FF which are affected positively by the rising of doping.

3.3.
Effect of Absorber Defects Density.Chen et al. [18] have studied the defect properties of CZTS using first-principle calculations.Their study has shown that the formation energy acceptor defects were lower than donor ones.This reason influences our choice to introduce only single acceptor (−/0) like defects state in the CZTS absorber layer.Figure 8 presents the defects density effects on the solar cell performance parameters.We see that the solar cell performance does not change when the defects density is below 10 14 cm −3 .
Once the defects density exceeds this value, the electrical performance parameters are strongly affected although there is a slight increase of FF when it reaches 10 17 cm −3 .The use of a bad quality of CZTS material results in the multiplication of carriers' traps and drives to produce weak efficiency solar cells.Besides, Wang et al. [16] have shown that the activation energy of CZTS absorber is lower than its band gap (1.45 eV).Hence, close to deep defect levels, the increase of defect density also contributes to recombination loss mechanism commonly ascribed to dominant recombination at the buffer/absorber interface.Associated with other recombinations mentioned above, these could explain the stronger loss undergone by the electrical parameters for the defects density up to 10 16 cm −3 .The  oc curve (Figure 8(a)) shows that a source of open-circuit voltage loss in the CZTS based thin film solar cells device also would be the strong concentration of defects that, beyond a density of 3.10 16 cm −3 , brought down  oc under 700 mV. Figure 8(d) shows that the development of CZTS absorber materials with a high quality (defects density ∼10 15 cm −3 ) is very beneficial for the CZTS based solar cells devices.We predict conversion efficiencies over 15%.

Conclusion
Using SCAP-1D package, we analyzed the variations of absorber layer thickness, absorber holes, and defects densities on CZTS based solar cells.We have shown the following facts: (i) The electrical parameters are affected significantly by increase of absorber thickness.This produces a loss of about 2.1 mA/cm 2 on short-circuit current density due to the recombination inside the absorber layer.Besides, the effect of the double diode phenomenon is much reduced when thickness is thinner and leads to minimization of additional recombination at the p-n junction that causes an important loss of fill factor.We predict that, for a development of the CZTS based solar cells with high conversion efficiency, the absorber layer thickness must be chosen below 600 nm, because of the short electrons diffusion length in the CZTS compounds.The recombination current density at the back-contact estimated at 3.6 mA/cm 2 shows that a strong potential barrier exists at CZTS/Molybdenum interface.
(ii) The open-circuit voltage and the fill factor are affected positively by the increase of holes density.A doping less than 10 16 cm −3 is beneficial for the CZTS based solar cells and especially for the absorber thickness lower than 600 nm.Above this range of doping, the increase of the population of holes creates supplementary centers of recombination of the photogenerated carriers.
(iii) The performance parameters are seriously affected by the defects.Wave length : Absorber layer thickness : Layerswidth.

Figure 2 :
Figure 2: Band diagram obtained from our CZTS solar cell baseline.

Figure 7 :
Figure 7: The simulated performance of holes density on  oc ,  sc , FF, and efficiency as a function of the CZTS absorber thickness.

Figure 8 :
Figure 8: The simulation of defect density effects on the CZTS solar cell performance parameters.
The development of high-quality CZTS materials can allow achievement of the devices having conversion efficiencies up to 15% and could also improve about 100 mV of open-circuit voltage value.  ,  ℎ : Electron and hole mobility   ,  V : States effective densities in the conductor and valence band :   ,  ℎ : Electron and hole capture cross section   ,  ℎ : Electron and hole surface recombination velocity ]  , ] ℎ : Electron and hole thermal velocity :