## 2 Modeling of InGaP/GaAs Tandem Solar Cells  
### Studied InGaP/GaAs Structure  
This section explores the modeling of InGaP/GaAs tandem photovoltaic solar cells in the main aim to establish the foundation for a novel multi-junction system based on these absorber materials. To ensure an accurate presentation of the proposed structure, this study begins with an in-depth presentation of the cell structure, followed by a detailed examination of the used physical models.  
The studied InGaP/GaAs tandem solar cell in this paper, depicted in Figure 1, emerges as a promising candidate, boasting a double-junction architecture. This intriguing structure features an upper cell crafted from InGaP (\(E_{g}\) = 1.9 eV) and a lower cell composed of GaAs (\(E_{g}\) = 1.42 eV). These cells are intricately intertwined through an AlGaAs/AlGaAs tunnel junction, enabling both electrical and optical connection.  
This solar cell is composed of an upper InGaP cell, which leverages a p-n junction serving as both emitter and base, with AlInGaP acting as the window layer. This ingenious design mitigates thermalization losses inherent to low-gap materials and transmission losses associated with large-gap materials, paving the way for enhanced efficiency. Furthermore, an additional back surface field (BSF) layer is strategically positioned for further performance optimization. However, the bottom cell, a GaAs cell, contains a p-n junction functioning as the emitter/base, accompanied by a p+-type InGaP window layer and an n-type AlInGaP BSF layer. Whereas the inclusion of the tunnel junction composed of the AlGaAs buffer layer beneath these two cells plays a crucial role in boosting overall efficiency.  
Table 1 offers a detailed breakdown of the material composition, thicknesses, and doping concentrations for each region within the studied structures. It is worth noting that gold contacts are employed in the front and back layers to amplify absorption. These meticulously characterized material properties serve as the foundation for developing the geometry of each section in the proposed structure, providing the basis for modeling and configuring the InGaP/GaAs tandem solar cells.  
Table 2 provides a critical reference point, summarizing the key characteristics of each material used in the design of the studied InGaP/GaAs tandem solar cell.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Region Number** & **Materials** & **Thickness (\(\upmu\)m)** & **Doping (cm\({}^{-3}\))** \\ \hline
**1** & AlInGaP & 0.030 & \(2\times 10^{18}\) \\
**2** & InGaP & 0.050 & \(2\times 10^{18}\) \\
**3** & InGaP & 0.550 & \(7\times 10^{18}\) \\
**4** & AlInGaP & 0.120 & \(2\times 10^{17}\) \\
**5** & AlInGaP & 0.050 & \(2\times 10^{18}\) \\
**6** & **AlGaAs** & **0.025** & \(5\times 10^{18}\) \\
**7** & **AlGaAs** & **0.025** & \(3\times 10^{18}\) \\
**8** & InGaP & 0.040 & \(3\times 10^{18}\) \\
**9** & GaAs & 0.5 & \(2\times 10^{18}\) \\
**10** & GaAs & 2.0 & \(2\times 10^{18}\) \\
**11** & AlInGaP & 1.0 & \(2\times 10^{18}\) \\
**12** & **AlGaAs** & 0.05 & \(10^{19}\) \\
**13** & GaAs & 0.2 & \(10^{18}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material composition, thicknesses, and doping profiles in various materials.  
Figure 1: Structure of the studied InGaP/GaAs DJSCs.