Indirect band gap and band alignment for coherently strained ${\mathrm{Si}}_{\mathrm{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ bulk alloys on germanium (001) substrates

Estimates of the fundamental (indirect) band gap and band alignments of coherently strained ${\mathrm{Si}}_{\mathrm{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ alloys for growth on Ge(001) are given for x in the range 0≤x≤1. The present results were obtained by combining phenomenological deformation potential theory with the self-consistent ab initio pseudopotential results of Van de Walle and Martin [J. Vac. Sci. Technol. B 3, 1256 (1985)]. It is found that the band gap of the coherently strained alloy has a maximum value near x=0.15, where the bulk band structure changes from Ge-like to Si-like. The conduction-band discontinuity Δ$E_c$ shows a similar behavior, having a maximum value ≊0.10 eV at x=0.15 and changing sign for x≳0.32 (i.e., type-II alignment with the Ge conduction-band edge lying higher in energy than the alloy conduction-band edge). The present results suggest that electron transfer from the ${\mathrm{Si}}_{\mathrm{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ alloy to the elemental Ge is to be expected if the alloy, having x≊0.15, is selectively n-type doped. Further, hole transfer from the ${\mathrm{Si}}_{\mathrm{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ to the elemental Ge is expected for x≳0.5. It is therefore expected that high-speed complementary logic (implemented with two-dimensional conduction in elemental Ge) may be feasible for growth of (Ge,Si) strained-layer heterostructures on Ge or Ge-rich substrates.