Effects of Homogeneous Deformation on Band Structure of Semiconductors

Abstract

A general scheme to calculate the band structure of the deformed crystal in terms of the solution in the undeformed crystal is presented. A coordinate transformation is introduced to bring the deformed crystal to have the same periodicity as the undeformed crystal. The deformation potential Hamiltonian is defined in the transformed space and its symmetry property is discussed. Energy band of the deformed crystal defined in the deformed 1st Brilloun zone E ( k ) is obtained by substituting (1+ e + ) k for k ' in the solution E '( k ') of the transformed system. This causes a new effect which exists even when the deformation potential effect vanishes ( E '( k ')= E 0 ( k ')). The strain-induced change of the local structure of the energy band is investigated by the k · p perturbation theory and is shown to be separated into two parts; the deformation potential effect at a fixed k point and the “ scaling ” effect. The latter is determined by the band structure of the undeformed crystal and the strain tensor....