Evaluation of a proposed barium di-silicide tandem solar cell using TCAD numerical simulation

Barium di-silicide (BaSi2) material has attracted noteworthy interest in photovoltaics, thanks to its stability, abundant nature, and excellent production feasibility. In this current work, a two-terminal (2T) monolithic all-BaSi2 tandem solar cell is proposed and explored through extensive TCAD simulation. A BaSi2 bottom sub-cell with a bandgap of 1.3 eV, and a Ba(CxSi1−x)2 top sub-cell with a tunable bandgap are employed in the design. It was found that a bandgap of 1.8 eV, which corresponds to x = 0.78, is the optimum choice to obtain the maximum initial power conversion efficiency (η) of 30%. Then, the tandem performance is optimized by investigating the impact of doping and the thickness of both absorber layers. Further, the current matching point is monitored whilst altering the thickness of the top cell resulting in η = 32.83%%, and a short-circuit current density (Jsc) of 16.47 mA/cm2. Additionally, we have explored the influence of the defect density in the absorbers, and the work function of contacts on the performance parameters. All TCAD simulations are accomplished using the Silvaco Atlas package under AM1.5G illumination.

replacing some Si atoms with isoelectric C, the corresponding bandgap of Ba(C x Si 1−x ) 2 can steadily increase from 1.3 to 3 eV (Imai and Watanabe 2010). Eventually, BaSi 2 -based TSCs have been demonstrated in association with perovskite and crystalline silicon (Vismara et al. 2016;Tianguo 2019).
In this paper, we investigate a 2T monolithic tandem cell comprising barium di-silicide materials in the top cell as well as the bottom cell. Devices based on barium di-silicide material are regarded as environmentally friendly solar cells besides their low processing cost. A wide bandgap absorber layer is crucial for the top cell to permit a part of visible light and the near-infrared to pass through it and be readily absorbed by the bottom one. Thus, the presented designed TSC is based on combining BaSi 2 (1.3 eV) and Ba(C x Si 1−x ) 2 (1.6-1.9 eV) materials for the bottom and top sub-cells, respectively (Imai and Watanabe 2010;Eperon et al. 2017). Firstly, we investigate the effect of the top cell bandgap on the tandem performance, showing that the best performance is attained at a 1.8 eV bandgap (x = 0.78). Then, the performance of Ba(C 0.78 Si 0.22 ) 2 /BaSi 2 TSC is optimized through various steps including the effect of doping and the thickness of the absorber layers. Further, the current matching point is monitored whilst altering the thickness of the top cell. Finally, the impact of changing the absorber defect density of both cells and the work function of both contacts on the tandem performance is also discussed to highlight the possible routes for boosting the tandem efficiency.

Silvaco Atlas simulation methodology
The simulation study is performed by using the Silvaco Atlas simulation package which is a physics based 2-and 3-dimensional device simulator. The operating basis of this simulator is based on solving transport equations and Poisson's equation through a defined grid, allowing for depicting the physical processes related to device operation and giving reliable estimates about the device operation (Atlas User's Manual 2022). The physical models embedded in the simulation must be appropriately chosen to optimize the TSC. In this study, the principal physical models utilized for the design of a given solar cell structure are included. SRH recombination, the primary recombination mechanism in BaSi 2 , and the Fermi-Dirac statistics have been considered. Carriers' mobility and lifetime values within cell layers have been taken according to available experimental values (Takabe et al. 2014;Deng et al. 2018). In addition, Auger recombination (AUGER), optical recombination (OPTR), and concentration-dependent low-field mobility (CON-MOB) models are enabled. Regarding the TSC, a lumped resistance was specified for the tunnel junction such that the current flows through the cell without considerable limitation (Elbar et al. 2015).
Firstly, our simulation was calibrated against an experimental BaSi 2 /Si heterojunction cell with a structure of indium-doped tin oxide (ITO)/p-BaSi 2 /n-Si/Aluminum (Al) metal back contact (Yachi et al. 2017). Figure 1a, b depict the device design and energy band diagram of the BaSi 2 /Si heterojunction cell. The essential parameters of cell layers derived from previously published studies are summarized in Table 1 Yachi et al. 2017). The work function of the ITO (transparent conducting front contact) is taken as 4.4 eV while that of the back Al metal is set to 4.28 eV. The absorption coefficients of the cell layers are derived from practical data (Toh et al. 2011;Vismara et al. 2016;Green 2022). After applying the listed parameters, the illuminated current density-voltage (J-V) curves for both experimental and simulated cells are presented in Fig. 1c. The simulated cell achieves the following PV parameters: J sc = 35.52 mA/cm 2 , V oc = 0.462 V, FF = 59.40%, and η = 9.74%. These parameters are quite close to the reported parameters,  2.0 × 10 18 -as shown in the inset of Fig. 1c. As a result, an acceptable match between both cells is observed, implying that the simulation model employed in Silvaco Atlas software is validated.

Structures of two sub-cells
A homojunction solar cell with the n + -p-p + architecture is introduced based on the practical structure of a BaSi 2 cell (Kodama et al. 2018). Figure 2 depicts the device design and energy band diagrams of the two sub-cells, containing an n + pp + -BaSi 2 bottom cell and an n + pp + -Ba(C x Si 1−x ) 2 top cell. To create a homojunction solar cell, heavily doped n + -and p + -layers were positioned on opposite sides of a lightly doped p-absorber layer to extract photoexcited electron-hole pairs. The thickness of these layers was maintained at 20 nm, which was found experimentally to be the minimum thickness required to cover the entire surface adequately (Yachi et al. 2017). Table 2 summarizes the primary required parameters of the sub-cells layers used to design the tandem solar cell (Tianguo 2019;Yachi et al. 2017;Deng et al. 2020). To model the optical properties, the refractive index n' and extinction coefficient κ as functions of a wavelength of barium di-silicide were extracted

Proposed tandem cell
In this subsection, the suggested structure of the tandem cell design (Ba(C x Si 1−x ) 2 /BaSi 2 ) is displayed in Fig. 3. In this tandem cell, the two cells are coupled through a tunnel junction that performs as a recombination film (Mailoa et al. 2015). The practical design of the tunnel junction is a critical task in order to maintain proper functionality leading to the enhancement of the tandem performance (Shen et al. 2018). The junction has to be transparent, and it should not absorb any part of the input radiation spectrum reaching the bottom cell. Such requirements have been met by fulfilling two design conditions: (1) the tunnel junction has to be heavily doped, and (2) both sides of the junction should be very thin in the nanometer range (Wang et al. 2012). Furthermore, the tandem cell current is controlled by the smaller current transporting through either the top or the bottom sub-cell. Once stacking the two sub-cells, the current matching condition should be maintained to minimize the current loss.

Results and discussion
First, we investigate the effect of the top cell bandgap on the tandem performance to design the tandem device for possible maximum efficiency. Then, the tandem performance of the cell is optimized through various steps including the effect of doping and the thickness of the absorber layers, changing the absorber defect density of both cells, and the work function of both contacts to obtain the maximum available η.

Tandem cell with different bandgap top cell
In this subsection, we investigate the effect of the top cell bandgap on the tandem performance where the compound Ba(C x Si 1−x ) 2 as a top absorber is adopted. The variation of the top cell absorber bandgap depends on the composition (x) (Imai and Watanabe 2010). Here, the Ba(C x Si 1−x ) 2 top cell bandgap is varied from 1.6 to 1.9 eV, which corresponds to x from 0.73 to 0.80. So, the Ba(C x Si 1−x ) 2 /BaSi 2 tandem cells are simulated using Atlas device simulator under 1-sun of AM1.5G spectrum to evaluate its performance parameters. The absorber thickness of the top cell was set to 500 nm, while the bottom BaSi 2 was fixed at 1 μm. Figure 4a, b depict a comparison between the illuminated J-V and EQE curves concerning the Ba(C x Si 1−x ) 2 /BaSi 2 tandem cells. The corresponding performance metrics are listed in Table 3. The results show that the best performance is obtained with a Ba(C 0.78 Si 0.22 ) 2 cell with a 1.8 eV bandgap. These complementary bandgap values agree with those reported in Eperon et al. (2017) to achieve the maximum theoretical η. In the coming simulations, this value will be used for further optimization of the TSC under investigation.

Fig. 3
Schematic representation of a Ba(C x Si 1−x ) 2 /BaSi 2 tandem cell comprising of an n + pp + -Ba(C x Si 1−x ) 2 top sub-cell and an n + pp + -BaSi 2 bottom sub-cell (ETL and HTL represent electron transport and hole transport layer, respectively) 475 Page 8 of 19

Tandem cell optimization
This subsection presents the following optimization steps for a 2T monolithic Ba(C x Si 1−x ) 2 /BaSi 2 TSC. First, the impact of the absorber layers doping on the tandem performance is studied. Then, we investigate the influence of top and bottom absorber thicknesses on TSC working metrics. Furthermore, we inspect the current matching point to get the maximum available η. The effect of top and bottom absorber defect densities on TSC working metrics is then investigated. Finally, we study the impact of front and rear contact work functions on the TSC performance.

Doping of absorber layers
The absorber layer doping is crucial in regulating bulk recombination. Its role in controlling the fill factor is also significant as increasing the doping level results in decreasing the series resistance which, in turn, increases the fill factor. However, increasing the doping level beyond a certain value may trigger some other undesirable effects like band gap narrowing and mobility degradation that causes an overall decline in performance. Herein, a parametric analysis study is done by changing the absorber layers doping from 1 × 10 15 to 1 × 10 19 cm −3 to investigate its impact on the tandem performance. Figure 5a, b demonstrate that the η attains its maximum value when the doping density is 1 × 10 17 cm −3 for both cells. To inspect the influence of changing the absorber layers doping on the tandem  performance, the electric field under light illumination before and after optimization is depicted in Fig. 5c, d. The electric field in a depletion region is responsible for separating photogenerated carriers and, in addition, depends on the carrier's doping on both junction sides. As shown in Fig. 5c, d, increasing absorber doping increases the depletion region width and thus increases its electric field for both sub-cells and, consequently, improves their conversion efficiency. Figure 6 represents a contour graph of TSC efficiency dependence on the thickness of both the top and bottom absorber layers. To investigate device performance, the thickness of the top absorber was increased from 0.5 up to 1.6 μm and that of the bottom absorber was increased from 1 to 4 μm while the other parameters remained constant. As obvious from Fig. 6, there is an inconsiderable effect on η as the thickness of the rear absorber grows from 2 to 4 μm and that of the front absorber raises from 0.8 to 1.6 μm. As the bottom absorber thickness falls below 0.8 μm, the efficiency gradually decreases from 32.4 to 30.4%. Furthermore, there is no change in η as the bottom absorber thickness changes from

Current matching point
In this subsection, the absorber thickness (d) of the top cell has been altered from 0.85 to 1.25 μm, while the bottom BaSi 2 was fixed at 3 μm. Figure 7a shows the J sc of the top and bottom sub-cells versus the thickness of the Ba(C 0.78 Si 0.22 ) 2 absorber layer in the top cell, in which significant dependency on d is shown. As d becomes thicker, the J sc of the top cell rises, and the J sc of the bottom cell, in turn, reduces. The reason is that the thicker the top cell is, the more photons are absorbed implying lesser transferred light to the bottom cell. A current matching point occurs at J sc = 16.47 mA/cm 2 and is satisfied at d = 1.05 μm for the absorbing film of the top cell. As displayed in Fig. 7b, η of the tandem cell reaches a maximum value at the current matching point. In this condition, the performance of the Ba(C 0.78 Si 0.22 ) 2 /BaSi 2 tandem cell has been simulated. The J-V characteristics of tandem, top, and bottom cells are drawn in Fig. 7c. The maximum value of J sc of tandem, top, and bottom cells is equal to 16.47 mA/cm 2 with V oc = 2.24 V and η = 32.83% for the tandem cell. The value of V oc = 2.24 V is equal to the sum of those of the top cell (1.37 V) and bottom cell (0.87 V), indicating the efficient operation of the recombination junction. Moreover, the EQE of both cells at the current matching condition is demonstrated in Fig. 7d. The EQE of the bottom BaSi 2 sub-cell surpasses 95% at a wavelength around 800 nm. Figure 8a illustrates the structure of the Ba(C 0.78 Si 0.22 ) 2 /BaSi 2 tandem cell produced by the Atlas simulator at the current matching point. As the bottom BaSi 2 cell is exceedingly thicker than the top sub-cell, the extended view of the red dashed area in Fig. 8a is displayed in Fig. 8b. Figure 8c depicts the electrostatic potential established through the TSC. The built-in potential of the tunnel junction indicates a greater potential in this specific region. Meanwhile, the electrostatic potential decreases as one proceeds in two directions away from the tunnel junction. Additionally, Fig. 8d displays the photogeneration rate inside the different layers. The graph reveals that the top Ba(C 0.78 Si 0.22 ) 2 cell has a greater photogeneration rate  Figure 9 represents contour graphs of TSC performance metrics dependence on the defect concentration of both the top and bottom absorber layers. The defect density ranges from 10 12 to 10 18 cm −3 while preserving the other parameters unchanged to explore the device performance. As clear from Fig. 9a, the J sc significantly decreases as the defect density of the top and bottom absorber layers increases. For example, J sc drops from 16 to 12 mA/ cm 2 as the defect density of the bottom absorber rises from 10 15 to 10 18 cm −3 , and that of the top layer grows from 10 16 to 10 18 cm −3 . Besides, there is no change in J sc as the defect density of the top absorber layer is below 10 16 cm −3 or that of the bottom absorber layer is below 10 15 cm −3 . It has been reported in the literature that V oc is extremely affected by the defect concentration of the absorber layer (Soucase et al. 2016). In this context, it can be shown in Fig. 9b that V oc decreases from 2.10 to 1.55 V when the defect density of the absorber layers raises from 10 15 to 10 18 cm −3 . For absorber layers defect density lower than 10 15 cm −3 , there is no appreciable effect on V oc . Figure 9c shows that the FF gradually declines from 86 to 73% when the defect density of the absorber layers raises from 10 15 to 10 18 cm −3 . Again, for small values of defect density of absorber layers (below 10 15 cm −3 ), there is no significant effect on FF. Theoretically, FF is solely a function of V oc , however, FF is not only related to V oc but in addition, it is strongly correlated to the recombination processes inside the depletion region.

The defect density of the absorber layers
Finally, as clarified in Fig. 9d, we noticed an expected changing profile in η due to its dependency on J sc , V oc , and FF. There is an insignificant effect on η as the defect density of the absorber layers is below 10 15 cm −3 . η sharply decreases from 30 to 13% as the defect density of the absorber layers grows from 10 15 to 10 18 cm −3 .

Work functions of the front and rear contacts
Work functions of the front and rear contacts are crucial factors that affect the device's performance as they modulate the metal/semiconductor contact barrier height and therefore the transportation of charge carriers (Anwar et al. 2017). The front Schottky barrier at the metal/n + -Ba(C 0.78 Si 0.22 ) 2 interface is computed using the equation (Liao et al. 2020): where m, front is the front contact work function, and is the electronic affinity of Ba(C 0.78 Si 0.22 ) 2 . while the rear Schottky barrier at the metal/p + -BaSi 2 interface is calculated using the equation (Liao et al. 2020): where and E g are the electronic affinity and the bandgap energy of BaSi 2 , respectively, and m, rear is the rear contact work function. The front contact work function is changed from 3 to 4.8 eV, while that of the rear contact materials is summarized in Table 4. (1) b,front = m,front − (2) b,rear = + E g − m,rear  Figure 10a, b illustrate the energy band diagrams for various work function values of front and rear contacts at the short circuit and dark conditions. As apparent in Fig. 10a, increasing m,front results in increasing the front barrier height b,front , which leads to sufficient bending up of E c close to metal/n + -Ba(C 0.78 Si 0.22 ) 2 interface irrespective of n + -Ba(C 0.78 Si 0.22 ) 2 thickness. This bending impedes the transfer of photo-excited electrons to the front electrode. On the other hand, decreasing m,front leads to a decrease of b,front , and thus, improves the device performance. Similarly, in Fig. 10b, the rear barrier height b, rear produces sufficient bending down of E v adjoining to the p + -BaSi 2 /metal interface and so the series resistance increases at the contact interface which results in impeding the transport of photoexcited holes to the back electrode. In addition, b, rear decreases with increasing m, rear and improves the device performance. Figure 11 exhibits contour graphs of the photovoltaic parameters of Ba(C 0.78 Si 0.22 ) 2 / BaSi 2 tandem solar cells under different values of the work function for both contacts. As apparent in Fig. 11, there is no effect on the performance parameters as m, rear is larger  Fig. 11d, an expected trend in η is observed due to its dependency on J sc , V oc , and FF. There is an insignificant effect on η when m,front is below 3.8 eV, and m, rear remains constant, while it sharply decreases from 31 to 15% as m,front

Fig. 11
Contour graphs of tandem cell performance parameters dependence on front and rear contact work function is increased above 3.8 eV. The optimum efficiency has been attained with a terbium front contact ( terbium = 3 eV) and a silver rear contact, resulting in the following PV parameters: J sc = 16.48 mA/cm 2 , V oc = 2.27 V, FF = 91.45%, and η = 34.25%. Finally, we provide a comparison between our optimized TSC and other tandem candidates, as shown in Table 5. Some of the reported tandem cells are based on experimental investigations, while others are computed numerically, as illustrated in the table. Most tandem cells with lead-based perovskite top cells give higher efficiencies; however, the toxicity of such tandems is a serious issue that limits their use and commercialization. Moreover, our simulated tandem solar cell shows promising properties with a high η and V oc .

Conclusion
In this work, all-BaSi 2 2T monolithic tandem solar cell is presented. In the proposed design, the bottom cell comprises BaSi 2 material with a 1.3 eV bandgap, while for the top cell, Ba(C 0.78 Si 0.22 ) 2 with a 1.8 eV bandgap is employed. After optimizing the doping and the thickness of both absorber layers, and at the designed matching point, the current density and η of the TSC are enhanced up to 16.47 mA/cm 2 and 32.83%, respectively. Additionally, we have inspected the consequence of the absorbers defect density in the range (10 12 -10 18 cm −3 ) and the impact of the work functions of the contacts on the performance parameters of the TSC. It was found that contacts having a work function ≥ 4.5 eV for rear contact and ≤ 3.8 eV for front contact were adequate for better performance. These results can offer possible routes leading in the direction of the advancement of low-cost, environmentally friendly, and efficient TSCs.