## 3 Results and Discussions
### GalInP Single Junction Solar Cell with Double Back Surface Field  
In general, III-V composite materials are found to be the most suitable for optoelectronic devices that have been extensively studied in several previous research experiments [2; 17], allowing the achievement of optimal efficiency of multi-junction solar cells. Figure 2 illustrates the optimized BSF layer with a double back surface field integrated into the p+/n+ type \(GaInP\) single junction solar cell. The use of \(GaInP\)-based pn-junction solar cells (with a bandgap energy of \(E_{g}\) = 1.9 eV) represents a promising choice for ensuring thermal stability in the top cell of a double or dual-junction solar cell (DJSC). As shown in Figure 2, there are two types of composite materials, such as the one based on \((In,Ga,P)\), which is called ternary type, and the one based on \((In,Al,Ga,P)\), which is called quaternary type. Indeed, the lattice constant (\(\alpha\)) for both types can be calculated using Vegard's law, which approximates the lattice constant of an alloy as a weighted average of its components. The quaternary compound \(In_{x}(Al_{y}Ga_{1-y})_{1-x}P\) is calculated using [PERSON]'s law, which approximates the lattice constant of an alloy as a weighted average of its constituent binaries:  
* Ternary type:  
For ternary-type composed by \((In,Al,P)\), it is presented by the composition \(In_{x}Al_{1-x}P\); hence, based on [PERSON]'s law, the lattice constant can be calculated from the following equation:  
\[\alpha_{In_{x}Al_{1-x}P}=x.\alpha_{InP}+(1-x)\alpha_{AlP} \tag{7}\]  
Figure 2: Silvaco-Atlas of p+/n+ GalnP single junction with double BSF layer. For ternary-type composed by \((In,Ga,P)\), it is presented by the composition \(In_{x}Ga_{1-x}P\); hence, based on [PERSON]'s law, the lattice constant can be calculated from the following equation:  
\[\alpha_{In_{x}Ga_{1-x}P}=x.\alpha_{InP}+(1-x)\alpha_{GaP} \tag{8}\]  
* Quaternary type: The lattice constant for the quaternary type composed by \((In,Al,Ga,P)\) and which is presented by \(In_{x}(Al_{y}Ga_{1-y})_{1-x}P\) can be calculated based on [PERSON]'s law from the following equation: \[\alpha_{In_{x}(Al_{y}Ga_{1-y})_{1-x}P}=y.\alpha_{InAlP}+(1-y)\alpha_{GaP}\] (9) where \(x\) and \(y\) are molar fractions defining the composition of each component and shown in their presentation. Similarly, the refractive index \((n)\) of such compound materials can be modeled as a weighted sum of the refractive indices of the corresponding components, following the same compositional dependence. In this study, the quaternary compound material \((In,Al,Ga,P)\) is introduced as a double or dual-back surface field (BSF) layer into the single-junction solar cell compound \((In,Ga,P)\). It is important to mention that the BSF layer's lattice constant must align with the substrate and adjacent layers to balance electrical performance (carrier confinement) and structural quality (defect suppression). This synergy is critical for achieving reliable, high-efficiency tandem solar cells. In Figure 3, the short circuit current density as a function of open circuit voltage \((V_{OC})\) is observed for two different single and double or dual-back surface field (BSF) thicknesses in the buffer. It can be noted clearly that for thicknesses of 50 \(\upmu\)m, the cathode current densities \((J_{SC})\) versus the slight increase in the anode voltage exhibit higher values for both single and double back surface field (BSF) compared to those of 30 \(\upmu\)m thickness, where the optimal values for the current density and conversion efficiency obtained at short circuit are 17.170 mA/cm\({}^{2}\) and 18.540% and 19.384 mA/cm\({}^{2}\) and 21.088% for single and double BSF, respectively. Figure 3: I–V characteristics of \(InGaP\) single junction with different double BSF thicknesses.