Guidelines for Optimization of the Absorber Layer Energy Gap for High Efficiency Cu(In,Ga)Se<sub>2</sub> Solar Cells

This work investigates in-depth the effects of variation of the compositional ratio of the absorber layer in Cu(In,Ga)Se2 (CIGS) thin-film solar cells. Electrical simulations were carried out in order to propose the most suitable gallium double-grading profile for the high efficiency devices. To keep the model as close as possible to the real behavior of the thin film solar cell a trap model was implemented to describe the bulk defects in the absorber layer. The performance of a solar cell with a standard CIGS layer thickness (2 μm) exhibits a strong dependence on the front grading height (decreasing band gap toward the middle of the CIGS layer). An absolute gain in the efficiency (higher than 1%) is observed by a front grading height of 0.22. Moreover, simulation results show that the position of the plateau (the region characterized by the minimum band gap) should be accurately positioned at a compositional ratio of 20% Ga and 80% In, which corresponds to the region where a lower bulk defect density is expected. The developed model demonstrates that the length of the plateau is not playing a relevant role, causing just a slight change in the solar cell performances. Devices with different absorber layer thicknesses were simulated. The highest efficiency is obtained for a CIGS thin film with thicknesses between 0.8 and 1.1 μm.

What makes CIGS an attractive absorber layer compared to silicon, is that it is a direct band gap material characterized by a high absorption coefficient, which allows the decrease of the absorber layer thickness; high stability and high efficiency devices with thicknesses between 1 -2 µm can be readily obtained [2].
CIGS thin film can be grown using different vacuum and non-vacuum techniques (e.g. evaporation, sputtering, electrochemical deposition, nanoparticle printing and ion-beam deposition) [3] [4] [5] [6] [7]. Devices with the highest performances are fabricated by a multi-stage co-evaporation process, known as the "three-stage process" [8]. This deposition technique results in a double-graded composition profile characterized by higher Ga content towards the back and the front of the film, and a plateau of low Ga content in between [9] [10]. Such controlled variable semiconductor composition represents an attractive possibility to tune the semiconductor's band gap, which can be graded over a wide range by varying the [Ga]/([In] + [Ga]) ratio in the thin film layer during the growth process [11] [12] [13].
However, besides its interesting properties, this semiconductor compound results in a complex structure, due to the large number of layers those constitute the final solar cell. In order to allow the selection of the most suitable solar cell structure, which is able to achieve higher conversion efficiencies and to fully understand the fundamental physics behavior of the device, it is needed to develop numerical models which will include the described peculiarities of the material. Simulations based upon these models will reduce the number of technological experiments and enable faster and inexpensive optimization of the devices.
In this paper we analyzed and reviewed the most suitable characteristics of the CIGS absorber layer in order to reach high efficiency devices. In particular an in-depth analysis of gallium double-grading strategy was carried out. Thus, it can provide the support to the technology development.

Simulation Set-Up
In the simulation work SCAPS-1D [14] software was used. Steady-state band diagrams, recombination profiles, and carrier transport were calculated using this software, solving Poisson equation together with hole and electron continuity equations [15]. The device architecture of the simulated CIGS solar cell consists to the most of the solar spectrum. The chemical bath deposited CdS film is employed as buffer layer in the high efficiency CIGS solar cell [16] [17]. This material can uniformly and entirely cover the rough surface of the CIGS film avoiding the formation of shunt paths [18]. Additionally, the use of a buffer layer leads to the creation of an efficient p-n junction in CIGS/CdS/ZnO. A favorable band alignment can be observed when a CdS buffer layer is used [19] [20] [21]. A thin CIGS film, serves as the absorber (photoactive) layer. Mo was used as the back electrode. A part of the Mo layer is converted to MoSe 2 when CIGS layer is deposited at high temperature. The MoSe 2 contributes to the improvement of adhesion at the CIGS/Mo interface and plays a significant role in the formation of a favorable ohmic contact [22]. A summary of the physical parameters used in the model is shown in Table 1. The device architecture of the simulated CIGS solar cell is presented in Figure 1    reported for this parameter [17].
The effects of the change of the Ga content in the absorber layer on the solar cell physical parameters were also considered in the model. Due to the lack of data in literature regarding the effect of the variation of the compositional ratio on the dielectric constant (ε) and electron affinity (χ), ε and χ were assumed to vary linearly with the variation of the Ga composition [24]. On the other side, mobility (µ) was assumed to be independent of the composition [25].  [27], regarding the measured α values for different Ga contents, were implemented in the simulations.
In order to improve the accuracy of the model, the variation of the Ga ratio in the absorber layer and its influence on the CIGS trap concentration was taken into account. A trap model based on the works reported in [25] [28] was used, which considers the dominant (Cu antisite) defects within CIGS composite. The dependence of these defects (traps) concentration on the Ga compositional ratio is shown in Figure 2.
In this model, the trap concentration is around 6 × 10 14 cm −3 for the compositional ratio GGI = 0 and decreases to 1 × 10 14 cm −3 for GGI = 0.2. Above GGI = 0.2 (for Eg higher than 1.14 eV) the trap concentration is characterized by a quick and sharp increase, reaching values around 1 × 10 17 cm −3 at GGI close to 1. This experimental data is based on a standard three stage growth process of the absorber layer. In order to model the traps concentration at GGI = 1, the values reported in [28] were used. These values are based on a single-step co-evaporation process of growth. We can consider this approximation reliable, since the differences of the effects of the defects concentration with the Ga composition for a three-or a one-stage process are worthy of consideration just in the compositional ratio range between GGI = 0.2 and GGI = 0.3 [28]. In this area the trap density is lower when a three stage process is used for the absorber preparation. Using the experimental data reported in [25] [28] bulk traps with an activation energy that was maintained constant for all the different Ga compositions were considered in the model.

Double Graded Band Gap and Its Optimization
When a CIGS layer is produced, it is intrinsic to observe a double-grading of the In order to optimise a double-grading for an enhancement of the CIGS solar cell performance we started with the study of three different grading profiles measured and reported in [16]. The different profiles, experimentally assessed by secondary ion mass spectrometry (SIMS) by Chirilă et al. [16] are shown in The performances of the devices with the described Ga profiles (Figure 4) were analyzed by I-V curve simulations, at the temperature of 300 K with the standard AMG1.5 spectrum and considering CIGS thickness of 2 µm. The simulations showed the best performances for sample C (the "green" line of Ga profile reported in Figure 4), as it was also reported in [16]. These simulation results were obtained considering the trap model for bulk defect density described in Section 2.1, which directly creates a relation between the trap concentration in Figure 4. Ga profiles of three samples (A-C) from reference [16] showing the compositional ratio GGI along the CIGS layer depth (dot lines). Piecewise linear Ga depth profiles (solid lines) based on [16] are implemented in the model. Hence, the front Ga profile does not extend beyond the space charge region.
It is important to confine the front grading in this area, since a rise of Eg in the SCR will generate an additional electric field E that will work against the electric field of the p-n junction retarding the transport of electrons. In principle, this effect could be detrimental for the performances of the device.
Thus, in order to avoid the deterioration of the photo-current, the front grading should be confined to the SCR where the quasi-electric field E, produced by the band-gap variation, should be smaller than the field caused by the p-n junction. This will allow photo-generated electron-hole pairs to be separated without recombination avoiding a sharp decrease of the photo-current caused by the quasi-electric field E.
• Sample C exhibits a plateau at a CIGS layer depth which corresponds to the region where the defects concentration approaches the minimum value ( Figure 2). Therefore a lower bulk defect density is expected in this area.

Effect of Δyf
In order to understand the effect of Δy f on the solar cell performances band diagram simulations at room temperature were carried out. The results are reported in Figure 5.
Band diagram simulations show that a larger front grading height results in a more evident notch in the CB (Sample A) as it is presented in Figure 5. This notch, already visible at T = 300 K, is situated just behind the space charge region. Simulations show that a larger value of Δy f results in larger barrier for electrons. The notch acts like a trap for electrons and its effect will be stronger at   Table 3.
As it can be observed from Table 3  Simulated I-V curves obtained using the different compositional ratio reported in Figure 6(a). Table 3. Solar cells parameters for different front and double grading combinations extracted from simulated I-V curves reported in Figure 6(b).   Table 3. The efficiency of the device with uniform defects distribution is shown to be lower than the efficiency of all presented devices with graded Ga profile. This behavior is mainly caused by the low V OC .

Variation of Low Ga Plateau Length
Starting from the Ga profile of sample number 4 ( Figure 6(a)) which gives the best solar efficiency different lengths of the plateau were tested in order to understand its relevance in the solar cell performances. The different shapes of simulated compositional ratios are reported in Figure 7(a).
The simulated I-V curves obtained using the Ga profiles from Figure 7

Absorber Layer Thickness Variation
Once absorber layer and V OC is almost not affected (a change less than 10 mV has been obtained by simulations). The parameter which is the most influenced by the absorber thickness reduction is J SC , which dramatically deteriorates when reducing CIGS thickness due to reduced absorbance. The simulations results are confirmed by the experimental studies presented in [34].

Conclusion
In this study, we investigated the effects of different Ga profiles on the electrical parameters of the CIGS solar cells. The aim of this work was to propose the most suitable double-grading profile in order to enhance the efficiency of the device.
Our results show that an in-depth control of the front-grading is necessary in order to produce high-performing solar cell. The optimum forward double-grading needs to be confined in the SCR with a height Δy f equal to 0.22.
Higher values of Δy f bring to a deterioration of the cell performances due to the creation of a barrier for electron just behind the space charge region. Moreover, the simulations lead to the conclusion that a good control of the position of the plateau in the Ga profile is more important that the length of the plateau itself.
The plateau needs to be positioned at compositional ratio value of GGI = 0.2, in the area with the lowest defect density according to the trap model considered in the simulations. Furthermore, we showed that higher performances are reached when the CIGS thickness is reduced to 0.8 -1.4 μm. In this thickness range device efficiencies higher than 22.5% were observed. These simulations results are of considerable relevance for the material optimization of the CIGS absorber layer.