Unveiling Novel Direct Bandgap Allotropes of Germanium: A Computational Exploration

Abstract

Germanium crystallizes in a cubic diamond structure, which restricts its applications in optoelectronics due to its indirect band gap. However, the slight energy difference between the direct and indirect band gaps in germanium presents a promising opportunity to engineer its structure into a direct band gap material, with the hexagonal diamond (lonsdaleite) phase being a notable example. In this study, we conducted an extensive computational search to find germanium allotropes with a direct band gap and low energy using a sensible random structure search approach informed by data-derived interatomic potentials. Among the predicted allotropes, we identified a hexagonal 8H structure with the lowest energy compared to all known germanium allotropes and only 5 meV/atom above the ground state cubic diamond structure. Compared to the cubic diamond phase, which has complete cubicity, the 8H phase consists of 3/4 cubicity and 1/4 hexagonality. This structural motif, coupled with band structure back folding in the hexagonal Brillouin zone, results in a direct band gap of 0.25 eV. Given the prior experimental discovery of 2H and 4H polytypes, the experimental synthesis of the 8H allotrope in germanium is highly feasible. Future research could explore alloying 8H germanium with silicon to optimize the bandgap energy and optical transitions, potentially achieving lifetimes comparable to those of group III-V semiconductors like GaAs.