Discovery of Novel Silicon Allotropes with Optimized Band Gaps to Enhance Solar Cell Efficiency through Evolutionary Algorithms and Machine Learning

In the pursuit of advancing solar energy technologies, this study presents 20 direct and quasi-direct band gap silicon crystalline semiconductors that satisfy the Shockley-Queisser limit, a benchmark for solar cell efficiency. Employing two evolutionary algorithm-based searches, we optimize structures and calculate fitness function using the DFTB method and Gaussian approximation potential. Following the preselection of structures based on energy considerations, we further optimize them using PBEsol DFT. Subsequently, we screen the structures based on their band gap, employing a DFTB method tailored for band gap calculation of silicon crystals. To ensure accurate band gap determination, we employ HSE and GW methods. To validate the structural stability, we employ phonon analysis via linear regression algorithm applied to PBEsol DFT data. Significantly, the structures unveiled in this study are of great importance due to their proven stability from both mechanical and dynamic perspectives. Furthermore, the ductility and low density of certain structures enhance their potential application. We examine the optical properties by studying the imaginary part of the dielectric function by solving the Bethe-Salpeter Equation on top of GW approximation. By calculating the SLME, we achieve an efficiency of 32.7% for Si\(_{22}\) at a thickness of 500 nm. Moreover, the study harnesses various machine learning algorithms to develop a predictive model for the band gap energy of these silicon structures. Input data for machine learning models are derived from structural MBTR and SOAP descriptors, as well as DFT outputs. Notably, the results reveal that features extracted from DFT outperform the MBTR and SOAP descriptors.