## 3 Results and Discussions
### Optimization of the \(InGaP/GaAs\) DjSCs with Buffer and New Top BSF Layers
#### 3.3.2 Double-Junction Solar Cell (DJSC) with Optimized New Top BSF Layer Thickness  
The incorporation of the quaternary-type compound \(AlInGaP\) as a BSF in the n-p \(InGaP\) top cell has a significant impact on the device's performance, as depicted in Table 6 and Figures 8 and 9. Indeed, adjusting the BSF thickness from 0.01 \(\upmu\)m to 0.16 \(\upmu\)m demonstrates significant changes in the key parameters of the investigated solar cell, particularly \(J_{\text{SC}}\) and \(\eta\).  
It is clear from Figure 8 that the \(J_{\rm SC}\) exhibits a sharp rise as the new top BSF thickness increases from 0.01 \(\upmu\)m to 0.12 \(\upmu\)m, reaching a maximum value of 21.65 mA/cm\({}^{2}\) at 0.12 \(\upmu\)m before gradually declining, as shown in Figure 8. Similarly, the efficiency follows this trend, reaching a maximum of 41.585% at 0.12 \(\upmu\)m, as shown in Figure 9, after which it begins to decrease. Based on this, the optimal new top BSF thickness is determined to be approximately 0.12 \(\upmu\)m, at which the solar cell achieves its highest conversion efficiency of 41.585%. Furthermore, the observed maximum value of Jsc at BSF thickness of 0.12 \(\upmu\)m is 0.001 \(\upmu\)m, which is consistent with the observed maximum value of Jsc at BSF thickness of 0.12 \(\upmu\)m.  
Figure 8: Variations in Jsc of the InGaP/GaAs DJSCs as a function of the new top BSF layer thickness.  
Figure 9: Effect of the new top BSF layer thickness variation on the \(\eta\) of \(\mathit{InGaP/GaAs}\) DJSCs.  
reflects an optimal balance between the following three critical factors: (1) suppression of carrier recombination through an enhanced built-in electric field, (2) minimization of resistive and optical losses, and (3) maximization of carrier collection efficiency within the minority carrier diffusion length. It can be said that below this BSF thickness (less than 0.12 \(\upmu\)m), insufficient field strength fails to fully confine carriers, leading to elevated surface recombination. Whereas beyond this BSF thickness (greater than 0.12 \(\upmu\)m), diminishing returns in field strength and the onset of parasitic effects--such as increased series resistance and absorption losses in the BSF layer--degrade performance, reducing \(J_{SC}\) and overall efficiency. This behavior aligns with experimental and simulation studies on III-V tandem solar cells, where precise BSF thickness optimization is essential to harmonize carrier dynamics with optical and electrical constraints. For instance, in [8], [PERSON] et al. demonstrated that a double BSF configuration in \(InGaP/GaAs\) cells enhances \(J_{SC}\) by 12% compared to single BSF designs, validating the critical role of thickness-dependent electric field tailoring in suppressing recombination while maintaining low resistive losses.  
A double or dual-back surface field (BSF) with varying thicknesses outperforms a single BSF by creating a graded electric field, which optimizes carriers' confinement and reduces recombination. The thinner layer generates a strong initial field to repel minority carriers from defect-prone surfaces, while the thicker layer extends this field to improve carriers' collection. This dual structure minimizes surface recombination velocity, lowers series resistance, and balances optical transparency, leading to the enhancement of both \(V_{OC}\) and \(J_{SC}\). It can be deduced that by spatially decoupling carriers' confinement and defect management, the double BSF resolves the trade-offs of single BSFs, leading to higher efficiency in tandem solar cells.