Hexagonal Si_xGe_1-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 150text{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}-{8mathrm{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 xleq 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.