Indirect band gap of coherently strained ${\mathrm{Ge}}_{\mathrm{x}}$${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ bulk alloys on 〈001〉 silicon substrates

Estimates of the indirect band gap for coherently strained alloys of ${\mathrm{Ge}}_{\mathrm{x}}$ ${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ on Si〈001〉 are given for x in the range 0≤x≤0.75. The present results were obtained by combining x-ray diffraction data with relevant deformation-potential constants and using the phenomenological strain Hamiltonian of Kleiner and Roth. Uniaxial splittings of the sixfold-degenerate valence-band edge were calculated using the 6×6 Hamiltonian of Hasegawa. It is found that the coherency strain generated by lattice mismatch dramatically reduces the indirect gap of the alloy (which approaches the $L_1$-${\Gamma }_{25}^{\mathcal{’}}$ gap of unstrained Ge at x≃0.6).