Identifying Direct Bandgap Silicon Structures with High-Throughput Search and Machine Learning Methods

Utilizations of silicon-based luminescent devices are restricted by the indirect-gap nature of diamond silicon. In this study, a high-throughput method is employed to expedite discoveries of direct-gap silicon crystals. The machine learning (ML) potential is utilized to construct a data set comprising 2637 silicon allotropes, which is subsequently screened using an ML Hamiltonian model and density functional theory calculations, resulting in identification of 47 direct-gap Si structures. We calculate transition dipole moments (TDM), energies, and phonon bandstructures of these structures to validate their performance. Additionally, we recalculate bandgaps of these structures employing the HSE06 functional. Twenty-two silicon allotropes are identified as potential photovoltaic materials. Among them, the energy per atom of Si22-Pm, which has a direct bandgap of 1.27 eV, is 0.026 eV/atom higher than that of diamond silicon. Si18-C2/m, which has a direct bandgap of 0.796 eV, exhibits the highest TDM among the identified structures. Si16-P21/c, which has a direct bandgap of 0.907 eV, has a mass density of 2.316 g/cm3, which is the highest among the identified structures and higher than that of diamond silicon. The structure Si12-P1, which possesses a direct bandgap of 1.69 eV, exhibits the highest spectroscopic limited maximum efficiency (SLME) among identified structures at 32.28%, surpassing that of diamond silicon. This study offers insights into the properties of silicon crystals while presenting a systematic high-throughput method for material discovery.