Theoretical Analysis of the Effect of the Interfacial MoSe 2 Layer in CIGS-Based Solar Cells

The aim of this work is to analyze the influence of the interfacial MoSe 2 layer on the performance of a /n-ZnO/i-ZnO/n-Zn(O,S)/p-CIGS/p + -MoSe 2 /Mo/SLG solar cell. In this investigation, the numerical simulation software AFORS-HET is used to calculate the electrical characteristics of the cell with and without this MoSe 2 layer. Different reported experimental works have highlighted the presence of a thin-film MoSe 2 layer at the CIGS/Mo contact interface. Under a tunneling effect, this MoSe 2 layer transforms the Schottky CIGS/Mo contact nature into a quasi-ohmic one. Owing to a heavily p-doping, the MoSe 2 thin layer allows better transport of majority carrier, tunneling them from CIGS to Mo. Moreover, the bandgap of MoSe 2 is wider than that of the CIGS absorbing layer, such that an electric field is generated close to the back surface. The presence of this electric field reduces carrier recombination at the interface. Under these conditions, we examined the performance of the cell with and without MoSe 2 layer. When the thickness of the CIGS absorber is in the range from 3.5 μm down to 1.5 μm, the efficiency of the cell with a MoSe 2 interfacial layer remains almost constant, about 24.6%, while that of the MoSe 2 -free solar cell decreases from 24.6% to 23.4%. Besides, a Schottky barrier height larger than 0.45 eV severely affects the fill factor and open circuit voltage of the solar cell with MoSe 2 interface layer compared to the MoSe 2 -free solar cell.


Introduction
High efficiency CIGS-based solar cells have been the focus of several years of theoretical and experimental research. The recent high laboratory efficiency values of 22.9% and 23.4% (Solar Frontier) [1] [2] are close to the efficiency of 25% achieved by crystalline silicon solar cells. These thin-film cells have achieved the best performance of all second-generation cell technologies. The current achieved efficiency is the result of the technological advances which allow the efficiency to be improved empirically by successive tests. In addition to the technological progress observed over the last two decades, significant efforts have been devoted to understanding the physical properties of the key material of these cells, namely the CIGS absorber layer. Indeed, the performance of these cells largely depends on the physical properties of the CIGS alloys which are not yet fully clarified. These include the nature and energy levels of the CIGS absorbing layer defects and the buffer/absorber interface defects [3] [4]. Moreover, data about the material's properties strongly depend on the used growth process and characterization techniques [3] [4]. This entails input parameters of simulation works may vary within wide ranges, imposing some limitation on the accuracy of simulated results. However, CIGS (namely CuIn 1−x Ga x Se 2 ) material remains one of the most promising semiconductor materials for photovoltaic conversion based on polycrystalline thin-films because of several favorable properties: 1) Its bandgap can be varied continuously by changing the gallium content, x, and its value is given by the commonly used formula (all bandgap energies in eV) [5] [6] [7]: ( ) ( ) = and 1.0 eV 4 gCIS E = [5]. All values are given at 300˚K.
2) The commonly referred surface defect layer (SDL), that is present between the absorber and buffer layers increases the absorber bandgap at this interface by lowering the valence band maximum with respect to the Fermi level, and hence reduces the interface recombination rate. In fact, it has been found that this surface defect layer is inverted to n-type such that the photogenerated electrons pass through this region as majority carriers.
3) CIGS is a direct bandgap alloy with an absorption coefficient that can reach 10 5 to 10 7 cm −1 , here too depending on its fabrication process, so that a thin thickness of 0.5 μm is sufficient to absorb 90% of the incident photon flux [3]. 4) Unlike silicon, CIGS materials have exceptional tolerance to structural and chemical defects On the other hand, the high cost and low abundance of indium and gallium Open Journal of Modelling and Simulation remains, in the long term, a major concern as well as the relatively significant degradation of performance observed in case of long-term exposure to the atmosphere, which requires appropriate encapsulation. However, technological progress has made it possible to produce cells with high efficiencies where the usual CdS buffer layer is replaced by cheap and better eco-friendly materials as ZnS, ZnO, and the ternary compound ZnO 1−x S x . This latter is the most promising material with a variable bandgap from 3.6 eV to 3.2 eV [8] [9] [10].
Thin-film cells have nevertheless a small market share compared to their silicon counterparts but, in recent years, they have risen sharply mainly focusing on their particular asset allowing the fabrication of flexible cells. Several routes have been explored to fabricate them on metal and plastic foils jointly enhancing their conversion efficiency by reducing sufficiently the photogenerated carrier recombination caused by the bulk defects. The ultimate goal is affording the flexibility with efficiencies and lifetime comparable to that of rigid cells.
One approach to decrease the raw material cost is to reduce drastically the thickness of the absorber. In that case, the carrier photogeneration rate close to the back contact can no more be negligible and the recombination rate at the back interface is of prime importance. Another approach is to create an electric field within the CIGS absorber by bandgap grading located at appropriate regions. This results in various cell structures with different CIGS composition profiles: the so-called "front grading" which has a higher bandgap towards the buffer layer, "back grading" which has a higher bandgap towards the back contact layer and "double grading" which combines the two first profiles of grading. Thus, front grading reduces recombination at the buffer/absorber junction and back grading does close to the backside pushing back minority carriers towards the collecting junction, then reducing carrier recombination at the absorber backside [11].
Many metals have been studied for contacting the photovoltaic cells to the external circuit. Mention may be made of molybdenum, chromium, tantalum, manganese, gold and silver [12] [13]. Among those, the molybdenum is widely used as back contact metal because of its relative stability at the high temperatures that are encountered during CIGS deposition steps and its low contact resistance with CIGS [14]. Its work function is about 4.53 eV [15]. In addition, the existence of a thin MoSe 2 layer at the CIGS/Mo interface has been clearly dem-  [20]. However, the formation of the thin MoSe 2 layer depends on the fabrication process (deposition technique of CIGS, associated temperatures…) that is used to realize the cell [18].

Numerical Simulation
In [3] [4], we reported the optimizing of CIGS-based solar cell including a MoSe 2 layer at the CIGS/Mo interface. The values of front and back contact reflectivity were set to 0% and the front and backside boundaries of the stacked semi-conductors were described by the flat band metal/semi-conductor contact model.
Under those conditions, we demonstrated a maximum conversion efficiency of 26% [3].
Here, we use AFORS-HET to carry out the simulation work [21]. The simulation of the MoSe 2 -free solar cell is based on Fermi level pinning model. The values of the optimized parameters are extracted from our previous papers [3] [4] and take into account the Schottky barrier height at the back contact and the reflectivity on the front (illuminated) side ( Figure 1). The input parameters of AFORS-HET simulation are listed in Table 1 and Table 2.
Contrary to our previously reported simulation, the reflectivity at front side is R = 5% and the back Schottky barrier height E B = 0.3 eV is higher than that pre-  [21]. The metal-semiconductor contact simulation is implemented according to the metal work function. Therefore, the contact can operate either in flat band mode or in band bending mode. AFORS-HET simulator allows the calculation of basic characteristics such as band diagram, generation and recombination rates, carrier densities and cell currents [21]. The simulated cell structures consist of six or seven stacked layers, depending the p-MoSe 2 layer is absent or present, respectively (see Figure 1). These layers are deposited on a soda lime glass (SLG) substrate. Only the front contact boundaries of the solar cells are described by the flat band metal/semiconductor contact model. The solar cell front side is illuminated under AM1.5G solar spectrum corresponding to an incident power density of 100 mW/cm 2 at room temperature (1 Sun). Under these conditions, we calculated the effects of the thickness of the CIGS and MoSe 2 layers that varied from 0.1 μm to 10 μm and from 10 nm to 100 nm respectively. As for the Schottky barrier height at the back MoSe 2 /Mo contact it has been varied from 0.2 eV to 0.65 eV according to the work function Open Journal of Modelling and Simulation of molybdenum that was tuned from 5.16 eV to 5.61 eV.

Solar Cell Optimization
The thickness of each layers of the solar cells, including or not the MoSe 2 layer, has been optimized. The conversion efficiency obtained for the MoSe 2 -free solar cell η = 24.6% is equal to that of the cell including a MoSe 2 thin-film layer at the CIGS/Mo contact interface. This value of efficiency has been obtained for a 3 μm-thick CIGS absorber with a front side reflectivity of 5%. The Schottky barrier height is 0.3 eV and 0.18 eV for the solar cells with and without MoSe 2 layer respectively.
The mechanism of carrier transport in metal/semi-conductor contact is intimately related to the energy band structure at the interface under thermodynamic equilibrium conditions. We therefore examined in the next paragraphs the real

Effect of the MoSe2 Layer Thickness on Internal Quantum Efficiency (IQE)
To analyze the effect of the MoSe 2 layer thickness on the IQE (or η), we varied its value from 10 to 100 nm ( Figure 2). We can see that for MoSe 2

Effect of the MoSe2 Layer on the External Quantum Efficiency (EQE)
The EQE expresses the flow of electrons through the external circuit of use For the large absorber thicknesses (t CIGS ≥ 3 μm), the EQE is almost identical for both structures, with and without MoSe 2 layer. On the other hand, for CIGS thicknesses less than 3 μm, the EQE of the solar cell with a MoSe 2 layer is higher.
We have plotted the EQE curves for a solar cell including a 1.5 μm thick CIGS absorbing layer with and without the MoSe 2 layer (30 nm thick). Figure 3 shows that the cell including the MoSe 2 layer offers a higher EQE value in the long wavelength range compared to the MoSe 2 -free cell. layer is more independent on the absorbing layer thickness since it starts to decrease when CIGS thickness is less than 1.5 μm, while that of the MoSe 2 -free cell starts to decrease at approximately 3.5 μm. For CIGS layer thickness less than approximately 0.5 μm, the effciency decreases rapidly in both cases because the carrier generation occurs very close to the back side where the carrier recombination is considerable. It can be seen in Figure 4(d) that the short circuit current presents a similar evolution than efficiency over the whole range of the absorber thickness variation. Looking now at FF in Figure 4(b), we observe that the fill factor of the cell with MoSe 2 layer remains almost unchanged, whatever the

Effet of Schottky Barrier Height at the Back Contact Interface
To investigate the effect of the Schottky barrier height at the CIGS/Mo contact interface, we varied the metal work function from 5.16 to 5.61 eV for MoSe 2 -free and MoSe 2 /Mo contacts ( Figure 6). As far as the metal work function Φ Mo ≥ 5.36 eV, i.e. the Schottky barrier height is less than 0.45 eV (work function of p + -MoSe 2 , eφ SC2 , is 5.8 eV), the electrical characteristics (efficiency, fill factor,

Conclusions
This article focused on the comparative theoretical study, using AFORS-HET software, of two kinds of CIGS-based solar cells performance differentiating by the presence of a MoSe 2 layer at the CIGS/Mo interface. Overall conclusion is that the performance of a cell including such a MoSe 2 layer is better than that of the MoSe 2 -free cell. Its thickness does not seem to be very challenging; 30 nm can be a suitable value. The MoSe 2 layer, firstly, acts as a tunneling barrier providing a quasi-ohmic back contact behavior and, secondly, creates a back surface electric field owing to its wider bandgap than that of CIGS absorber. However, to achieve such a behavior, the molybdenum work function shall be higher than 5.36 eV. These improvements are valid only for absorbing layer thickness less