Nature of the band gap of Ge:C alloys: Insights from hybrid functional density functional theory calculations

Previous studies have shown that incorporating a small fraction of carbon (C) into germanium (Ge) leads to the lowest conduction state being at the Γ point in small supercell calculations, suggesting that C incorporation can turn Ge into a direct gap semiconductor. We use hybrid functional density functional theory calculations as a function of hydrostatic pressure to investigate the nature (Γ-, X-or L-like) of the lowest conduction states in Ge₁₂₇C₁ and Ge₆₃C₁ supercells. We find in both cases that the lowest conduction state, at Γ in the supercell, has primarily L-like character. Surprisingly, the Ge Γ state mixes with a higher-lying X state, but has almost no interaction with the L-like conduction band edge state. We conclude that the band gap of the here studied Ge:C systems is therefore only quasi-direct, limiting the benefit of this material system for optoelectronic device applications.