A. Model validation
Figure 4 shows the simulated J–V characteristics and photovoltaic parameters where Jsc, Voc, FF, and η are matched with the measured results at room temperature, AM1.5G spectrum [1]. The quantum efficiency (QE) and integrated current density plots over the visible region. The rear contact resistance (Rc= 0.181 Ω.cm2) is used to emulate the series resistance (Rs). The rear-passivated regions maintain a surface recombination velocity, Spass, of 102 cm/s [1]. The cell characteristics of the investigated model are compared to the experimental outputs [1] and presented in Table 1.
Table 1
Performance parameters of investigated models [1].
PV characteristics | This work Pass. Qf = − 1×1012 | Reference cell [1] Pass. Qf = − 1×1012 |
J0 (mA/cm2) | 3.85×10− 6 | 2.01×10− 6 |
Jsc (mA/cm2) | 26.97 | 26.79 |
Voc (mV) | 632.42 | 661.58 |
Pmax (W/m2) | 250.32 | - |
FF (%) | 73.36 | 71.54 |
η (%) | 12.51 | 12.68 |
B. Influence of Interface Trap Density (Dit)
While in our previous investigation, we demonstrated that the simulations fit well the experimental results, we have not changed the cell configuration. The rear passivation area is the parameter that expresses how much the ultrathin CIGS cell structure emphasizes the cell features. Cell pitch has been found to be important for the performance of the passivated cells. Here, we introduce the Dit in the CIGS/Al2O3 interface using calibrated model configuration. Furthermore, a fixed charge Qf = -1 × 1012 cm-2 [1] was included in the simulated models as a function of Dit and cell pitch. For this, Dit was varied from 1 × 1010 eV-1 cm-2 to 1 × 1013 eV-1 cm-2, where the cell pitch was varied from 0.5 µm to 4 µm for constant Qf and SRVs. Figure 5 illustrates a significant influence of Dit on cell parameters with different cell pitch distances. The figure clearly illustrates a strong dependence of Jsc in cell pitch size. An increase in cell pitch contributes to an increase in the incoming photon absorption, thus current density, and therefore high current density [9]. At good passivation, a smaller interface trap density is better, however, at a high cell pitch, a larger Dit degrades cell performance drastically. The main parameters are Voc and FF, related to carrier recombination. The investigated ultrathin CIGS cell has two main recombination regions: CIGS bulk and rear passivation. This means the bulk doping density influences bulk resistivity (related to FF) and bulk lifetime (related to Voc). It is clearly visible for a given cell pitch; the effect of the rear passivation is dependent on Dit as shown in Fig. 5 [1]. Increasing cell pitch size leads to increase Voc which indicates the recombination is reduced with a larger device pitch. At the highest Dit density (> 1 × 1012 eV-1 cm-2), the cell pitch variation has a very slight effect on Voc due to less field-effect passivation strength compared to Dit, therefore high carrier recombination occurred in the rear side of the cell. The FF decreases with cell pitch size due to an increase in Rs across the investigated cells [7, 25]. Originally, the interface defect is assigned to the imperfect passivation, therefore, a suitable grown process needs to ensure the interface defect density is less than 1011 cm− 2 to maintain high performance. Then, from the cell efficiency plot, it is clearly visible to obtain the cell pitch range for further investigation for the given Dit densities (1–2 µm). Improving chemical passivation is by reducing improving chemical passivation (Dit or SRV).
C. Influence of trap density (Nt)
Another key point to evaluate the cell performances consists of studying the effects of the absorber trap density with different energy levels for the donor trap. Following the previous results, we kept the interface defects density (Dit) constant at about 1011 eV− 1cm− 2 for the rest of the investigation. The thermionic and tunneling mechanisms are enabled at the absorber/buffer interface. In the absorber layer (CIGS, 1.15 eV), donor trapping centers are located at midgap (0.575 eV). They lie in a forbidden gap and exchange charge with the conduction and valence bands through the emission and capture of electrons. These trap levels will capture carriers, slowing the process of any solar cell. The trap centers influence the density of space charge in CIGS bulk and the recombination statistics as illustrated in Fig. 6 and Fig. 7. As depicted in Fig. 6, increasing the Nt results in a change observed in valance/conduction band offset. Additionally, the band bending induced by the defect density influences the free carrier concentrations n, p, and, consequently, also the recombination current. In general, there are three recombination mechanisms that often occur simultaneously in a semiconductor material. They are Shockley–Read–Hall (SRH), Auger, and radiative recombination. The total recombination rate is the sum of all these three recombination rates [7, 11].
$$\frac{1}{{\tau }_{total}}=\frac{1}{{\tau }_{SRH}}+\frac{1}{{\tau }_{Auger}}+\frac{1}{{\tau }_{rad}}$$
Auger electron and hole capture for the CIGS model is taken as 3.7×10− 29 cm6/s and 3.7×10− 29 cm6/s, respectively [7]. The radiative recombination coefficient for the CIGS material is taken as 1.5×10− 10cm3/s [7].
The total recombination is proportional to the defect density near the CdS/CIGS interface as shown in Fig. 7. It is shown that, with the trap density and capture cross-section of electrons, increasing in the cross-section area and trap density of electrons, current density decreases and thus the cell efficiency due to more minority carriers are trapped for large cross-section area and trap density. However, the increase in bulk defect density leads to a deterioration of the cell efficiencies that depends very much on the assumed capture cross sections and the energy level of the trap. Figure 8 illustrates the impact of defect density (Nt) of the absorber layer varied between 1013 cm− 3 to 1017 cm− 3 with different energy levels on cell performance. At the lowest energy levels (shallow trap, < 0.3eV), the defect density of the absorber has no significant effect on cell characteristics. Figure 9 shows the electric field distribution in ultrathin CIGS cells. Two potential spikes can be seen at the hetero junctions. One is at the CdS/CIGS junction and the other is at CIGS/Al2O3 interface. The presence of the spike at the CIGS/Al2O3 interface is due to the negative charges implemented in the rear-passivation layer preventing the minority carriers (electrons) to be recombined with the CIGS/Molybdenum interface traps. It is observed clearly the effect of the trap density on the electric field magnitude at the CdS/CIGS interface. The maximum electric field intensity observed is 0.118 MV/cm and 0.107 MV/cm for 1013 cm− 3 and 1017 cm− 3, respectively. The defect density of 1014 cm− 3 was taken as in the reviewed literature [1, 7]. Table 2 illustrates the PV characteristics with different trap densities. As shown in Fig. 8, Jsc remains constant when the energy level of the trap lies between 0.1–0.4 eV. As shown also in the figure, defect density at higher energy levels has a strong impact on the open-circuit voltage, fill factor and conversion efficiency. Inefficient charge transport and collection at higher Nt and large energy level of the trap. Efficient transport is achieved if electrons are transported from CIGS to ZnO:Al without significant energy loss.
Table 2
PV characteristics with two different defect densities at fixed energy level (0.4 eV)
PV characteristics | 1×1013 cm− 3 | 1×1016 cm− 3 | 5×1016 cm− 3 | 1×1017 cm− 3 |
Jsc (mA/cm2) | 26.97 | 25.57 | 24.74 | 23.91 |
Voc (mV) | 632.40 | 512.65 | 429.67 | 395.48 |
Pmax (W/m2) | 249.77 | 167.81 | 125.28 | 95.34 |
FF (%) | 73.22 | 63.99 | 58.91 | 50.40 |
η (%) | 12.48 | 8.39 | 6.26 | 4.76 |
D. Influence of absorber doping density
For the passivated u-CIGS solar cell, the photovoltaic parameters such as Jsc, Voc, FF, and η are strongly influenced by the doping concentration of the absorber and cell pitch. To obtain the optimum values, the doping concentration and cell pitch size were varied from 1014 to 1018 cm− 3 and from 0.5 to 4 µm, respectively. We present in Fig. 10 the four PV parameters for a passivated cell with different cell pitches and doping concentrations of the absorber layer at fixed opening width (W = 200 nm) with contact resistance (Rc = 0.181 Ωcm2) at Mo/CIGS interface within the opening. Moreover, for the passivated layer with a specific Qf value − 1×1012 cm− 2 at CIGS/Al2O3 interface for a fixed SRV of 102 cm/s [1]. It is well known that a thin absorber layer with a high doping concentration is not beneficial for a solar cell as poor light absorption entails lower η values. Similarly, a thicker absorber is also not suitable as it introduces a more significant route to transfer the photo-generated charge carriers that lead to high recombination. Therefore, optimum u-CIGS absorber doping concentration selection is necessary for an efficient u-CIGS solar cell. Figure 11 illustrates the effect of absorber layer doping density on the built-in electric field and total recombination rate using the 1×1014 cm− 3, 1×1016 cm− 3, and 1×1018 cm− 3 u-CIGS absorber layer doping density. As compared to the 1×1016 cm− 3, the 1×1014 cm− 3 doping density produces a weaker electric field, which reduces the charge separation ability of the u-CIGS and causes increased charge recombination. From Fig. 11, when the doping density is lower and the cell pitch size is less than 2 µm, the Jsc of the passivated cells is improved. By increasing the cell area, a significant impact of the field-effect passivation compared to the bulk defect effect on cell performance is observed. However, we find that its value increases till it reaches a certain level where from 2.5 µm become almost constant. An increase in Jsc is due to a decrease of effective recombination with cell pitch with a fixed contact area (opening width). Voc follows the same trend as the cell pitch increases for the low doping densities of the absorber because of the elevation of charge separation. From the figure, when increasing the doping density, the cell pitch effect starts reducing and the Voc value reaches a high magnitude of 656 mV. FF follows the opposite trend of Jsc and Voc due to increasing in series resistance across the cell as the cell pitch size increases. A loss in FF is observed while increasing the acceptor carrier concentration. The resulting cell conversion efficiency is a combination of Jsc, Voc, and FF parameters, the first increase from small cell pitch, where the cell pitch has a high effect on cell performance, passes by an optimum value and then decreases when the cell pitch sizes are further increased. These results are very important when designing an ultrathin solar cell for less difficulties and less costly to produce. Figure 12 shows the effect of the absorber doping density on cell efficiency at 1.5 µm cell pitch. The PEC reaches a maximum value of 13.07% at 1×1016 cm− 3, even though it starts decreasing afterward. A magnesium fluoride (MgF2, 120 nm) has been used as an anti-reflective coating to reduce the light reflection for investigated model (1.5 µm cell pitch), thus enhancing the efficiency [9]. Figure 13 illustrates a comparison of the J–V characteristics of the proposed u-CIGS models with and without ARC layers. Table 3 presents a comparison between simulated and fabricated model results at room temperature, AM1.5G spectrum [10, 12].
Table 3
PV characteristics of different u-CIGS models
PV characteristics | Optimized cell with ARC | Optimized cell without ARC | Optimized Pass. without Qf | Ref. [1] Pass. Qf = -1×1012 | Ref. [10] pss. Qf = -1×1012 |
Jsc (mA/cm2) | 30.47 | 28.44 | 27.17 | 26.79 | 28.56 |
Voc (mV) | 615.04 | 613.22 | 584.63 | 661.58 | 625.5 |
Pmax (W/m2) | 209.81 | 196.09 | 170.81 | - | - |
FF (%) | 74.62 | 74.95 | 71.66 | 71.54 | 74.85 |
η (%) | 14 | 13.07 | 11.38 | 12.68 | 13.37 |
E. Strategies to improve the efficiency of u-CIGS solar cell
In this section, we investigate different ways to improve the cells performance by optimizing their spectral responses. Band gap profile grading and tandem structure configuration are considered as very promising approaches for achieving maximum efficiencies.
1) Impact of Ga-concentration in u-CIGS solar cells
For the passivated u-CIGS solar cell, the photovoltaic parameters such as Jsc, Voc, FF, and η are strongly influenced by the Ga/(In + Ga) ratio in CuIn1 − xGaxS2 based solar cells. CIGS alloy has both bandgap and electron affinity depending on the gallium content [9]. The optical and electrical properties of the absorber layer change, if the Ga-concentration is varied. Previous modeling research has suggested that forward Ga composition grading is the most effective way to boost the efficiency of the next CIGS generation [3, 27]. For the investigation cell, the energy bandgap is varied due to the change in Ga/(In + Ga) ratios. The initial efficiency increase is primarily due to an increase in Ga content in the absorber layer and consequently, an increase in Voc, and to a lesser extent due to a small increase in Jsc. The increase of Jsc is believed to be due to a reduction of the conduction band offset at the CdS/CIGS interface. Figure 14 presents the cell characteristics' dependence on Ga content grading from 12–77%. At the ultrathin CIGS layer (< 1µm), an increase in Ga/(In + Ga) ratio towards the back contact has a beneficial impact on the cell performance, thus improving the cell efficiency as illustrated in Fig. 14 [6, 9]. The efficiency reaches a maximum value when the Ga concentration at the junction reaches 77% (1.6 eV). The material properties are certainly very significant for future tandem structures where bandgap matching with the optical spectrum can be further exploited to increase efficiency when applied to the future tandem structure.
2) Impact of stepped band gap profile and Ga-concentration in u-CIGS solar cells
We investigate the effect of the thickness of the sub-layers on cell performance. The first and third u-CIGS sub-layers are varying from 50 nm to 300 nm by fixing the u-CIGS thickness around 500 nm. Figure 15 presents clearly the three sub-layers on the u-CIGS structure. The initial bandgap of these three layers is 1.6 eV, 1.32 eV, and 1.15 eV, respectively. Figure 16 illustrates the impact of the sub-absorber thickness on cell performance. Numerous research works have attributed that reducing absorber thickness causes a decrease in the photon absorption rate and consequently less amount of the generated carriers [3–7]. A decrease in the photocurrent density results inevitably to in drop in the yields of solar cell devices. A strong impact is appearing from 200 nm thick for both devices. The sub-layer thicknesses were optimized with the following configuration CIGS 1 (300 nm)/ CIGS 2 (150 nm)/ CIGS 3 (50 nm) which induce to increase in conversion efficiency from 13.07–15.82%. After optimizing the thickness of the sub-layers, it is very important to optimize the bandgap of the second sublayer (CIGS 2). Figure 17 presents the cell characteristics dependence on Ga content in CIGS 2 from 12–77%. An improvement in Jsc and FF was clearly visible while increasing the Ga content due to conduction band offset reduction at CIGS 1/CIGS 2 interface, η follows the same trend until at a certain concentration level and then becoming approximately constant from 60% of Ga/(In + Ga) ratio. It shows also a significant improvement in Voc in the range of 30%-60%. From Fig. 17, the Ga content ratio would be optimized between 50–77%. The ratio of 57% (1.46 eV) is chosen for the next studies. Figure 18 illustrates the electric field distribution, electron velocity, electron concentration inside the investigated structure, and I-V characteristics with two different absorber configurations. The electric field levels are clearly visible at the heterojunction CdS/CIGS. For Eg1<Eg1<Eg1 absorber configuration, an increase in the current density is observed due to high electric field distribution across the junction. On the other hand, For Eg1>Eg1>Eg1, shows high electron velocity and concentration that cause a loss in short circuit current due to less electric field strength at higher Eg. Grading Eg toward the junction causes carrier recombination within the absorber layer.
3) Optimization of u-CIGS/C-Si PERT tandem solar cell
The numerical simulations were performed to model a two-terminal u-CIGS/silicon tandem cell targeting the high efficiency and stability of devices [8, 26]. The proposed C-Si PERT model was inspired by Benick’s works [27]. The PERT cell model was calibrated with the reported experimental data. In their study, Benick et. al. applied ion implantation for the realization of both the emitter and the BSF of high efficiency PERT and PERL structures. For the C-Si model, good agreement between simulated and reference quantities is observed [26]. Figure 19 represents the investigated u-CIGS/C-Si PERT tandem cell with the following configuration: MgF2/ ZnO:Al/ ZnO/ CdS/ u-CIGS/ ITO (25 nm)/ FSF (1.5 µm)/ Bulk (180 µm)/ BSF (1.5 µm)/ Al2O3 (10 nm)/Silver /glass-substrate (250 µm cell pitch). The thermionic emission and tunneling mechanisms are activated at the CdS/CIGS interface. Aluminum oxide (Al2O3) material of 10 nm-thick has been used for the rear passivation. Al2O3 has been used to reduce the recombination losses at the rear contact Silicon/Silver, hence surface passivation properties. The front and rear contacts are assumed to be Schottky (4.7 eV) and ohmic contact according to the literature, respectively. The interface trap density (Dit) is inserted into the model by donor-type Gaussian defect distribution at Silicon/Al2O3 interface [1]. The J–V curves of the studied cell models are shown in Fig. 20. An efficiency of 29.93% can be obtained with the optimized 2T u-CIGS/Silicon tandem cell [28]. Table 4 summarizes the PV cell performance of the studied cells in comparison to recently published work [8, 26].
Table 4
PV characteristics of different ultrathin CIGS cells
Cell | Absorber thickness | Eg (eV) | Jsc (mA/cm2) | Voc (V) | FF (%) | η (%) |
Optimized pass. u-CIGS cell | 500 nm | 1.15 | 30.47 | 0.615 | 74.62 | 14 |
Optimized pass. u-CIGS cell (Thickness for graded Bandgap) | 500 nm | 1.6eV/1.3eV/1.15eV | 21.56 | 1.012 | 70.74 | 15.45 |
Optimized pass. u-CIGS cell (Graded Bandgap Eg1 > Eg2 > Eg3) | 500 nm | 1.6eV/1.46eV/1.15eV | 22.22 | 1026 | 72.95 | 16.63 |
Optimized pass. u-CIGS cell (Graded Bandgap Eg1<Eg2<Eg3) | 500 nm | 1.15eV/1.46eV/1.6eV | 29.11 | 733.95 | 75.74 | 16.18 |
C-Si PERT cell untextured | 180 µm | 1.124 | 36.45 | 0.693 | 83.36 | 21.07 |
C-Si PERT cell textured [27] | ~ 180 µm | - | 40.9 | 0.691 | 83.8 | 22.7 |
u-CIGS top cell | 500 nm | 1.6 | 29.65 | 1.070 | 79.58 | 25.27 |
C-Si PERT filtered by top cell | 100 µm | 1.124 | 9.05 | 0.633 | 25.04 | 1.43 |
Our previous work [26] Perovskite/u-CIGS Tandem cell | 500 nm/600 nm | 1.6/1.15 | 20.89 | 1.708 | 85.05 | 30.36 |
u-CIGS/C-Si Tandem cell | 500 nm/180 µm | 1.6/1.124 | 19.98 | 1.749 | 85.57 | 29.93 |