Energy-band structure in strained silicon: A 20-band k⋅p and Bir–Pikus Hamiltonian model

Abstract

A strain Bir–Pikus Hamiltonian Hst, associated with a 20-band sp3s* k⋅p Hamiltonian Hkp, is used to describe the valence band and the first two conduction bands all over the Brillouin zone. Because the local (in k space) deformation potentials Ⅺu and Ⅺd used in pseudopotential method are unusable in k⋅p theory, we show that taking into account the Bir–Pikus parameters (a, b) of the Brillouin zone center in the Hst Hamiltonian allows one to describe the dispersion relation in the whole Brillouin zone. The method is applied to strained Si on a relaxed Si1−xGex alloy. The values of the energy band gap, and of the Δ2−4 conduction band splitting between the four equivalent in-plane valleys Δ4 and the two valleys along the growth direction Δ2 are in very good agreement with those reported in other publications. The small value of the spin-orbit splitting in silicon is taken explicitly into account. We show that the valence band splitting is consequently not proportional to the stress.