The thin-film solar cells represent a considerable hope in the field of PV solar cells. The goal of current research in thin-film solar cells is to develop low-cost, viable, environmentally-friendly materials which is able to compete with the conventional silicon-based structures. Among the thin-film solar cells, those based on CIGS are very popular because of its very impressive performance. The efficiency of this solar cell has evolved rapidly in recent years due to the maturity of manufacturing techniques. By controlling the benefits of the alkali treatment, the Solar Frontier team achieved a record efficiency of 22.9% . However, CIGS-based solar cells are confronted to serious challenges that could compromise its long-term sustainability. Indium and gallium used in CIGS solar cells and other optoelectronic components are rare . Indium is particularly expensive and it availability can become an issue if the flat panel display industry increases its consumption even more . To overcome this problem, several alternatives are proposed. The replacement of indium and gallium with more abundant, less expensive and more environmentally friendly metals such as zinc and tin has been proposed as an alternative. The best CZTS-based solar cell cells obtained from these substitution metals showed an efficiency of 12.6% , far from the performance of CIGS-based cells. The reduction of the CIGS layer thickness appears to be a viable track. If this thickness could be reduced, the use of indium and gallium will be considerably reduced and therefore the deposition time . However, it was argued that reducing the thickness of the absorber below 1 µm leads to a loss of performances resulting from the increase of free-carrier and defect density   . The most important loss in the electrical parameters is the short-circuit current which reduces the cell efficiency due to the insufficiency CIGS absorption coefficient, the excessive absorption of the molybdenum layer and the stronger impact of the back contact recombination  . In order to develop engineering adapted to ultra-thin absorbers, it is necessary to elucidate the impact of sensitive parameters in the absorber and Mo/CIGS interface properties on the electrical parameters and their evolution with the absorber thickness.
In this paper, SCAPS-1D  simulation software was used to investigate CIGS-based solar cells. Starting from a model that reproduces the experimental results, the simulation allowed us to highlight how band-gap, absorber bulk defect density and the Mo/CIGS interface affect the electrical parameters in relation to the absorber thickness.
2. Device Structure
The structure of the simulated solar cell consists of several layers: (Ni/Al)/MgF2/ZnO:B/i-ZnO/OVC/CIGS/Mo/Substrate. The Mo is sputtered on a subtract, generally soda glass. Several other substrates have been experimented such as stainless steel , industrial steel , aluminum foil , titanium foil , polyimide substrates . However, the best performances have been obtained with soda glass . The importance of the soda glass was discussed in terms of good thermal expansion as well as the leakage of impurities such as Na during the CIGS layer deposition . Then, the CIGS absorber is deposited on the Mo by co-evaporation. A thin CdS layer is deposited by chemical bath deposition (CBD) on the CIGS layer to form the p-n junction. In general, an intermediate composition layer is formed at the CdS/CIGS interface. This layer called surface defect layer (SDL) or ordered vacancy compound (OVC) is related to the atomic inter-diffusion and is supposed to be advantageous to the performance of the solar cell under some conditions . A ZnO intrinsic layer (i-ZnO) and boron-doped ZnO (ZnO:B) layer are deposited on the top of the buffer layer. These two layers are commonly referred to as transparent conductive oxide (TCO), because of their wide band gap which makes them transparent to most of the solar spectrum. The TCO is covered with an antireflection layer MgF2, which increases the absorption of photons in the absorber.
3. Numerical Modeling
The complexity of the solar cell design increases when efficiency enhancement concepts are considered and computer-aided design becomes necessary for novel semiconductor device development and optimization. Using powerful device simulator is an important strategy to better understand the degree of the performance enhancement that can be provided by these new device structures. Computational analysis was performed using the one-dimensional simulation program SCAPS. Given the proper device structure, values of material parameters and initial conditions, SCAPS program calculates the internal electrical parameters of CIGS solar cells by solving the system of semiconductor equation based on Poisson equation, electrons and holes continuity equations by coupled method of Newton-Rapson. Recombination currents are calculated with the Shockley-Read-Hall (SRH) model for bulk defects and an extension of the SHR model for interface defects. A deeper insight into the effect of the material properties such as doping concentration, free carrier mobilities, band-gap, and structural properties such as different layers and layers thicknesses on device performance can be obtained by the simulation. The material parameters used as the inputs are selected based on the values reported in literature   . The semiconductor properties of the intrinsic ZnO:B, i-ZnO, CdS, OVC and CIGS layers used as the input parameters for the simulations are given in Table 1.
All the layers are polycrystalline and therefore contain a large number of different defects. In our model, one type of single level defects is introduced in each layer. These are all compensating defects positioned at the intrinsic level which is close to mid-gap. Neutral interface defects for recombination were also positioned at mid-gap. Neutral cross-sections were selected in the range 10−18 - 10−15 cm2, while attractive ones were selected in the range 10−13 - 10−12 cm2. To pin the Fermi level at the interface level OVC/CdS, donor defects were placed 0.2 eV below the conduction band. These have small capture cross-sections to separate between pinning and the recombination parameters of the OVC layer . The OVC layer parameters are similar to those of bulk CIGS except its band-gap, shallow donor density, and low carrier mobility.
The introduction of Ga into the absorber layer to form the CIGS alloy results in a widening of the band-gap from 1.02 eV to 1.67 eV which are respectively the gap of the CIS and the CGS and Equation (1) is used to adjust the band-gap according to the Ga-content ( ) 
Table 1. Input parameters values for the simulation of CIGS solar cells with SCAPS-1D.
where b is the optical bowing coefficient . The variation in Ga-content in the absorber also affects different material parameters such the conduction band , absorption coefficient  , electron affinity , hole mobility , net carrier concentration  , defect density . All these parameters have been calculated according the Ga-content or taken from the literature  - . The absorption file used in the simulation were calculated over the entire Ga-content using the equation , where the optical contact k as function of Ga-content is extracted over the wavelength (λ) between 300 and 1300 nm from Palson’s and Alonso’s papers   and is shown in Figure 1(b). The band alignment at the interface between the OVC and the 1.15 eV CIGS layers is set at 0.3 eV  , guided by experimental results. The default illumination spectrum is set to the global AM1.5 standard for terrestrial solar cell measurement. The series resistance and shunts resistance have been adjusted according to Ga-content , and the temperature is set at 300 K. The equivalent band diagram calculated in thermodynamic equilibrium condition is given in Figure 1(a). The J-V characteristic and quantum efficiency are represented in Figure 1(c) and Figure 1(d) respectively for x = 0.3 and compared to the experimental results . This step is very important in numerical simulation, since it avoids outliers. There is a good similarity between the simulated results and the experimental results and thus validates our model.
4. Results and Discussion
4.1. Effect of the Absorber Band-Gap
The band-gap of the absorber layer is an important variable to enhance the performance of the solar cells. The effects of the increase in the absorber’s band-gap on the electrical parameters for different thicknesses are shown in Figure 2. The main effects of increasing Ga-content in the absorber are the decrease in short-circuit current density (Jsc) and the increase in open-circuit voltage (Voc)  . It can be seen that the open circuit voltage (Voc) (Figure 2(a)) of the device increases with the Ga-content but not proportionally. For high Ga-contents, although the band-gap increases, the open circuit voltage (Voc) remains relatively constant due to the increase in the recombination rate of charge carriers especially in the space charge region (SCR). The limitation of Voc may be due to defects that increase with the gallium rate . The open circuit voltage is almost independent of the absorber thickness.
The short-circuit current density (Figure2(b)) decreases with the absorber’s band-gap. This decrease is especially important when the absorber thickness is reduced. This decrease can be attributed to the reduction in the generation rate at the p-n junction due to the decrease in absorption  and the increase in recombination at the rear contact when the thickness is significantly reduced . The efficiency (Figure 2(c)) of the solar cell as well as the fill factor (FF) (Figure 2(d)) increase with the band-gap and the best performance is obtained for 1.2 < Eg <1.3 eV. Above this value, the overall performance of the solar cell begins to drop. These results are consistent with the experimental and numerical results obtained from other simulation software   . Experimentally, the best CIGS based solar cells are obtained with a Ga-content around x = 0.3, corresponding to a Eg = 1.2 eV . For a gallium rate x exceeding this value, a drastic decrease in the solar cell’s performance is observed. The theoretical estimation of the optimal band-gap energy to achieve the best performance in the photovoltaic devices is in the range of 1.4 to 1.5 eV for the solar spectrum of AM1.5G . The reason why CIGS-based solar cells are less efficient in this range are still poorly understood but all the evidence suggests that the defect level in the absorber depends on the Ga-content and its position moves to the center of band-gap (mid-gap) with the Ga-content which reduces Voc  (section 4.3). The new record of 22.9% was achieved by reducing the Voc deficit from the reduction of absorber defect density .
Figure 1. (a) Energy band diagram of CIGS solar cell calculated under thermodynamic equilibrium condition. Inset: CIGS cell structure with the OVC layer at the CdS/CIGS interface; (b) Absorption coefficients versus wavelength used for the simulations from  . (c) and (d) J-V characteristic and quantum efficiency compared to experimental results.
Figure 2. Influence of the increase of the band-gap of the absorber on the electrical parameters (Jsc, Voc, FF, Efficiency) according to the thickness of the absorber.
4.2. Effect of Acceptor Concentration
Many impurities during the growth of the absorber are likely to increase the density of acceptors within it. The most common case is the doping of the absorber with the sodium that diffuses from the soda glass substrate. The increase of the sodium doping in the absorber results in an improvement of the open-circuit voltage (Voc) . In addition, the best cells produced nowadays use an alkali post-treatment such as potassium (K)  , Cs . Several material and device characterizations performed to illuminate the effects of the alkali treatment showed an increased free carrier concentration and reduced carrier recombination throughout the whole absorber film contributed to the improved performance . However, it is recommended to control dopants to optimize the performance of the device since, at high levels, they could reduce mobility and consequently, the lifetime of the charge carriers. In the case of dopants from the substrate, the control is ensured by a barrier (e.g. Al2O3) between the molybdenum and the substrate  .
Figure 3 shows the influence of acceptor density on Voc, Jsc, FF and efficiency, for the various thicknesses of the absorber. The open circuit voltage (Voc) (Figure 3(a)) increases with the acceptor density and reaches a maximal value when the acceptor concentration is 1016 cm−3. Above this value, Voc becomes independent of doping regardless of the absorber thickness. The increase of acceptor concentration of absorber can enhance the built-in electric field of solar cell, which is beneficial to the Voc.
Figure 3. Evolution of the electrical parameters of the solar cell as function of acceptor concentration for different absorber layer thickness.
This increase is in agreement with the experimental results which promote the beneficial effects of impurities such as sodium on Voc. The Short-circuit current density (Jsc) (Figure 3(b)) decreases with increasing the acceptor density, this decrease is particularly important when the absorber is ultra-thin (<1 µm). The increase in the acceptors density affects the charge carrier mobility, enhances the band-to-band recombination of photo-generated carrier and therefore a deficit in the collection of charge carriers. In addition, Mo/CIGS interface recombination is predominant in ultra-thin absorber, which reduces Jsc. The fill factor (Figure 3(c)) is less affected for doping level lower than 1014 cm−3. However, an improvement of FF is obtained between 1015 cm−3 et 1016 cm−3 and reaches a peak at 1016 cm−3. Above this value, the increase of acceptor concentration has a negative effect on FF. Fluctuation in Voc, Jsc and FF affect the cell’s efficiency (Figure 3(d)). The best performance is obtained for doping level around 1016 cm−3. The simulated results show that the increase of acceptor density in the absorber improves CIGS solar cells performance. However, it is necessary to pay attention to the possible decreases of Jsc, FF and efficiency due to enhanced recombination of charge carriers.
4.3. Effect of Absorber Defect Concentration
Defects in the CIGS layer have a crucial role in the cell’s performance. For the improvement of CIGS based solar cells device, it is important to understand the impact of the absorber quality on the cell performance and the critical range of defect density on the electrical parameters. The amount of Ga added to the alloy not only influences the band-gap energy but also the transport mechanism and the defects in the absorber  . Many studies have shown that the quality of the absorber is the origin of the low performance of CIGS with a high Ga-content   . Hanna et al. has established a correlation between the Ga-content, absorber bulk defect densities and the solar cells performances as indicated in Equation (2) .
where q denotes the elementary charge, kT the thermal energy, A the diode ideality factor, jsc the short circuit current and j00 a prefactor proportional to the absorber bulk defect density N. This equation demonstrated that bulk defects limit the open circuit voltage of CIGS solar cells in the hole composition range (x = 0 - 1). The simulation was carried out with all parameters constant to better understand the effects of defects. A Gaussian-shaped donors level have been introduced in the bulk of the absorber at an energy above the valence band edge with a characteristic energy width of 0.1 eV. Table 2 shows the energy level of the defect with respect to the valence band on the electrical parameters. As can be seen, the energetic position of defects has a very important influence on the recombination mechanism. The defects are more harmful at 0.6 eV, i.e. close to mid-gap.
Table 2. Dependence of the absorber defect level on the electrical parameters.
Thereafter, we use this worst scenario to better elucidate the effect of the absorber defect density as shown in Figure 4.
The electrical parameters are less sensitive to defects when they are less than 1014 cm−3 regardless of the thickness of the absorber. Per account, beyond 1014 cm−3, all parameters drop drastically. This suggests that a high defect density may be the origin of the poor performance in CIGS cells with a high Ga content. The record efficiency of 22.9% obtained by the Solar Frontier team was correlated to an improvement of the absorber quality .
4.4. Mo/CIGS Interface Optimization
At the Mo/CIGS interface an ohmic contact with a low contact resistance is desired in order to extract efficiently the photo-generated charge carriers from the CIGS absorber . It is generally observed that a MoSe2 layer is formed at the Mo/CIGS interface during the deposition of the CIGS absorber on the Mo by the selenization of Cu-In-Ga precursor. Several factor can be responsible for the MoSe2 layer: the sputtering pressure of Mo , Na content from soda glass   , the selenization temperature . Many studies are unanimous that the MoSe2 layer contributes to the improvement of adhesion at the CIGS/Mo interface  . In addition, the MoSe2 layer at the Mo/CIGS interface acts in a beneficial way by changing the Mo/CIGS hetero-contact from Schottky to an ohmic type contact   .
Generally, the Mo/CIGS interface is a high recombination area, especially for ultra-thin absorbers. The MoSe2 layer with its 1.4 eV band-gap could be a good electron reflector, very important to reduce Mo/CIGS interface recombination  .
However, an optimal MoSe2 layer thickness is required since a very thick MoSe2 limits the current collecting ability of the back electrode due to the high resistivity of MoSe2 (101 - 104 Ωcm) and hence deteriorating the electrical parameters  . An optimization of the MoSe2 layer thickness is therefore required to give it its role as an electron reflector. The MoSe2 layer parameters used in the simulation are represented in Table 3. The equivalent band-diagrams with and without the MoSe2 layer are shown in Figure 5(a) and Figure 5(b) respectively. The comparison of the J-V characteristic and the quantum efficiency in these two configurations are represented by Figure 5(c) and Figure 5(d).
Table 4 shows the electrical parameters extracted from the J-V characteristic. As can be seen, a thin MoSe2 layer at Mo/CIGS improves the electrical parameters.
The open circuit voltage (Voc) increases as a result to the passivation of the Mo/CIGS interface defects as in the case of the Al2O3 layer  . Moreover, there is an improvement in the current density due to a potential barrier at the Mo/CIGS interface that prevents electrons from recombining with the holes. This results in a good collection of charge carriers as shown in Figure 5(d).
To elucidate the advantages or disadvantages of the MoSe2 layer, we performed the simulations by focusing only on its thickness, which seems to be the critical parameters at the Mo/CIGS interface. We have intentionally omitted the open circuit voltage (Voc), since Jsc and FF are the most affected by the recombination at the Mo/CIGS interface. Figure 6(a) shows the effect of the MoSe2 layer thickness on Jsc, FF and the Efficiency as function of the absorber thickness. Jsc and FF are almost unaffected by the increase in the thickness of the MoSe2 layer, however, it depends more to the absorber thickness. When the thickness of the absorber is large, interactions between electrons and holes are reduced, which improves the Jsc. The FF increases with the MoSe2 layer thickness due to the passivation of the Mo/CIGS interface. Nevertheless, ultra-thin absorbers are more advantageous by the MoSe2 layer thickness. The gain of the electrical parameters is shown in Figure 6(b). This gain was obtained by subtracting the electrical parameters with MoSe2 from those without MoSe2. As can be seen, ΔJsc increases with the thickness of the MoSe2 layer but also depends on the thickness of the absorber. For ultra-thin absorbers less than 0.8 µm, a 600 nm MoSe2 layer allows a gain between 1.5 and 2.5 mA/cm2. On the other hand, for absorbers higher than 0.8 µm, the presence of the MoSe2 layer regardless of its thickness becomes critical on the Jsc. In this situation, the beneficial effects on the MoSe2 as an electron reflector are less pronounced and become detrimental to the Jsc. ΔFF decreases almost linearly with absorber thickness.
Figure 4. Calculated impact of absorber thickness and total defect density on the electrical parameters: Voc, Jsc, FF and Efficiency.
Figure 5. Energy band diagram (a) without MoSe2 layer (standard configuration), (b) With MoSe2 layer. (c) J-V and (d) QE characteristics of both configurations.
Figure 6. (a) Electrical parameters according to the MoSe2 layer and CIGS absorber thicknesses; (b) gain due to the presence of the MoSe2 layer.
Table 3. MoSe2 input parameters  .
Table 4. Results from simulation with and without (W/o) MoSe2 layer.
We investigated the requirements to obtain high performance CIGS-based solar cells with SCAPS simulation software. Starting from a baseline model that reproduced the experimental results, we have shown that the achievement of high performance CIGS solar cell requires the optimization of the absorber’s properties but also a careful focus on the Mo/CIGS interface. These requirements in the absorber process can be summarized as follows: 1) control the Ga-content to obtain a band-gap between 1.2 eV and 1.3 eV; 2) the acceptor density should be around 1016 cm−3 and 3) the defect density must be lower than 1014 cm−3. The selenization conditions of Cu-In-Ga precursor on the Mo must be adjusted correctly to obtain ultra-thin MoSe2 layer at the Mo/CIGS.
The authors acknowledge the use of the SCAPS-1D program developed by Marc Burgelman and colleagues at the University of Gent in all the simulations reported in this article.
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