Hexagonal SixGe1-xas a direct-gap semiconductor

The band gap of germanium (Ge) is “weakly” indirect, with the $\mathrm{L}_{6c}$ conduction band (CB) minimum lying only $\approx 150\text{meV}$ below the zone-center $\Gamma_{7c}$ CB edge in energy. This has stimulated significant interest in engineering the band structure of Ge, with the aim of realizing a direct-gap group-IV semiconductor compatible with established complementary metal-oxide-semiconductor fabrication and processing infrastructure. Recent advances in nanowire fabrication now allow growth of Ge in the metastable lonsdaleite (“hexagonal diamond”) phase, reproducibly and with high crystalline quality. In its lonsdaleite allotrope Ge is a direct- and narrow-gap semiconductor, in which the zone-center $\mathrm{T}_{8\mathrm{c}}$ CB minimum originates via back-folding of the $\mathrm{L}_{6c}$ CB minimum of the conventional cubic (diamond) phase. Here, we analyze the electronic structure evolution in direct-gap lonsdaleite SixGe1-x alloys from first principles, using a combination of alloy supercell calculations and zone unfolding. We confirm the Si composition range $x\leq$ 25 % across which SixGe1-x possesses a direct band gap, quantify the impact of alloy-induced band hybridization on the inter-band optical matrix elements, and describe qualitatively the consequences of the alloy band structure for carrier recombination.