Band anticrossing in highly mismatchedSnxGe1−xsemiconducting alloys

Abstract

We show that at dilute Sn concentrations $(x<10\%)$, the composition dependence of the direct band gap and spin-orbit splitting energies of ${\mathrm{Sn}}_x{\mathrm{Ge}}_{1-x}$ can be described by a valence band anticrossing model. Hybridization of the extended and localized $p$-like states of the Ge host matrix and the Sn minority atoms, respectively, leads to a restructuring of the valence band into $E_{+}$ and $E_{-}$ subbands. The notably large reduction in the band gap follows from an upward shift in the valence band edge by approximately $22\mathrm{meV}$ per $x=0.01$. These results demonstrate that like III-V and II-VI compound semiconductors, group IV elements may form highly mismatched alloys in which the band anticrossing phenomenon is responsible for their unique properties.