From pseudo-direct hexagonal germanium to direct silicon-germanium alloys

Abstract

We present ab initio calculations of the electronic and optical properties of hexagonal ${\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ alloys in the lonsdaleite structure. Lattice constants and electronic band structures in excellent agreement with experiment are obtained using density-functional theory. Hexagonal Si has an indirect band gap, whereas hexagonal Ge has a pseudo-direct gap, i.e., the optical transitions at the minimum direct band gap are very weak. The pseudo-direct character of pure hexagonal Ge is efficiently lifted by alloying. Already for a small admixture of Si, symmetry reduction enhances the oscillator strength of the lowest direct optical transitions. The band gap is direct for a Si content below 45 %. We validate lonsdaleite group-IV alloys to be efficient optical emitters, suitable for integrated optoelectronic applications.