The electronic band structure of Ge 1− x Sn x in the full composition range: indirect, direct, and inverted gaps regimes, band offsets, and the Burstein–Moss effect

A comprehensive and detailed study of the composition dependence of lattice constants, band gaps and band offsets has been performed for bulk Ge 1− x Sn x alloy in the full composition range using state-of-the-art density functional theory methods. A spectral weight approach to band unfolding has been applied as a means of distinguishing the indirect and direct band gaps from folded supercell band structures. In this way, four characteristic regions of the band gap character have been identified for Ge 1− x Sn x alloy: an indirect band gap ( x < 6.5%), a direct band gap (6.5% < x < 25%) and an inverse band gap ( x > 25%) with inverse spin–orbit split-off for 45% < x < 85%. In general, it has been observed that the bowing parameters of band edges (Γ and L -point in conduction band (CB Γ and CB L ), valence band (VB), and spin–orbit (SO) band) are rather large ( b CB Γ = 2.43 ± 0.06 eV, b CB L = 0.64 ± 0.04 eV, b VB = −0.59 ± 0.04 eV, and b SO = −0.49 ± 0.05 eV). This indicates that Ge 1− x Sn x behaves like a highly mismatched group IV alloy. The composition dependence of lattice constant shows negligible bowing ( b a = −0.083 Å). Obtained results have been compared with available experimental data. The origin of band gap reduction and large bowing has been analyzed and conclusions have been drawn regarding the relationship between experimental and theoretical results. It is shown that due to the low DOS at the Γ-point, a significant filling of CB by electrons in the direct gap regime may easily take place. Therefore, the Burstein–Moss effect should be considered when comparing experimental data with theoretical predictions as has already been shown for other intrinsic n -type narrow gap semiconductors (e.g. InN).