Strain-induced nonlinear energy-band splitting of Si_1-xGe _x alloys coherently grown on (111) and (110) oriented Ge substrates

A multi-band semi-empirical tight-binding method was used to calculate the band structures of Si_1-xGe_x alloys coherently grown on (111) and (110) oriented Si_1-yGe_y substrates. The results show that the lowest conduction band X₅ at point X in the [001] directions of the Si_1-xGe_x alloy is split into two bands with even and odd parities, due to the reduction of symmetry by strain. This is the first calculation that shows a kind of nonlinear band-edge splitting in the coherently grown Si_1-xGe_x alloys. The results here can be approximated by adding a new deformation potential Ξ^'_u to the linear deformation potential formula, which was used earlier for bulk Si under external [111] and [110] uniaxial stress cases. For coherently grown layers with a large lattice mismatch, the nonlinear splittings should not be neglected when analyzing the electronic properties.