Structural, electronic, and optical properties of hexagonal GeSn from density functional theory

Abstract

Unlike cubic GeSn, which requires a high Sn concentration to undergo an indirect-to-direct bandgap transition, lonsdaleite (2H) germanium is an intrinsic direct-gap semiconductor. We employ first-principles density functional theory to investigate the structural, electronic, and optical properties of 2H-Ge$_{1-x}$Sn$_{x}$ random alloys in the dilute Sn regime ($x \le 0.10$). The extended alloy disorder is modeled using 48-atom special quasirandom structure (SQS) supercells, and the coherent effective band structure is recovered via spectral band unfolding. We show that 2H-Ge$_{1-x}$Sn$_{x}$ maintains a direct bandgap at the $\Gamma$ point across the studied composition range, exhibiting a strong bandgap bowing that shifts the fundamental absorption edge into the mid-infrared. Evaluation of the optical transition matrix elements reveals a giant polarization anisotropy dictated by spin-orbit coupling. The fundamental transition is strongly dipole-allowed for light polarized perpendicular to the crystal $c$-axis, an optical selection rule that is robustly preserved despite the random alloy disorder breaking the symmetry. These results demonstrate that hexagonal GeSn bypasses the compositional threshold limitations of the cubic phase, providing a highly tunable direct-gap system for infrared optoelectronics.