## 1 Introduction  
The increasing global demand for energy, beside the depletion of fossil fuel stocks and their irrational use, has led to severe negative effects on the environment, including accelerated global warming. Faced with these challenges, researchers have been actively exploring sustainable solutions [1, 2]. Indeed, renewable energy sources, especially solar energy based on solar cells, have gained significant attention from researchers in the last decades as viable alternatives to the conventional resources of energy. However, enhancing the energy conversion efficiency of solar cells remains a critical challenge for ensuring the optimal performance of these devices. Over time, advances in materials and multi-junction structures, such as indium gallium phosphide (InGaP) and gallium arsenide (GaAs), have played a key role in enhancing solar cell performance. However, the rapid technological progress during recent years, driven by cost reductions and efficiency improvements, has also led to significant advancements in the manufacturing of multi-junction monolithic solar cells based on III-V semiconductor materials. During the last years, experimental investigations on InGaP/GaAs dual-junction solar cells (DJSCs) revealed substantial efficiency gains, where the National Renewable Energy Laboratory (NREL) achieved an efficiency of 32.8% [3]. In the same context, the study presented by [PERSON] and [PERSON] in [4] succeeded in achieving an efficiency of 32.1964% (1 sun) and 36.6781% (1000 suns) in a double-junction InGaP/GaAs solar cell using a BSF InAlGaP layer. Similarly, in [5], [PERSON] et al. experimentally achieved the efficiency of 36.24% by dividing the tunnel zone into six layers on the InGaP/GaAs solar cell. Whereas the highest reported efficiency to date is 40.879%, which is obtained in [6] by [PERSON] et al. through an optimized tandem junction InGaP/GaAs solar cell with a double top back surface field (BSF), where it was proved that the InGaP tunnel junction layer demonstrates high conversion efficiency. Further contributions include the study by [PERSON] et al. [7] and [PERSON] et al. [8], which explored different solar cell configurations and enhancements in double-junction InGaP/GaAs solar cells, incorporating innovations like carbon nanotubes. Other studies were carried out to improve the performance of the aforementioned solar cell, especially on a double-junction structure, such as in [1], [PERSON] et al. introduced a layer of ZnO to optimize GaInP/GaAs tandem solar cells, where the author achieved an efficiency improvement of 5.52%. In [9], [PERSON] et al. developed optimal model variables for InGaP/GaAs solar cells to increase the efficiency, while in [10], [PERSON] et al. proposed a modeling approach for double-junction InGaP/GaAs solar cells. In [11], [PERSON] and [PERSON] proposed an InGaP/GaAs double-junction structure, leveraging 2D codes through Silvaco-Atlas software for optimal design. Further research was presented to improve the multi-junction InGaP/GaAs/InGaAsP/InGaAs solar cells, such as the study published in [12] by [PERSON] et al., where the anti-reflective coating layer is used to increase the efficiency. In [13], [PERSON] et al. optimized four-terminal GaAs/Si tandem solar cells by testing various anti-reflection layers, show-casing technological maturity. In [14], [PERSON] and [PERSON] focused on the optimal shape of InGaP/GaAs solar cells to enhance energy conversion efficiency. In [15], [PERSON] and [PERSON] developed a reliable model for InGaP/GaAs DJSCs, which was validated through comparison with other structures. In [16], [PERSON] and [PERSON] studied the degradation effects on solar cells by examining the triple-junction type-InGaP/InGaAs-GaAsP MQW/InGaAs in the aim to maximize the efficiency. In [17], [PERSON] et al. characterized the effects of fluctuations in the InAs/GaAs solar cell intermediate band to ensure the maximized efficiency and the stability in organometallic solar cells.