Finite element analysis of valence band structures in quantum wires

Abstract

Valence band structures with spin-orbit (SO) coupling of quantum wires (QWRs), are investigated using the multiband effective-mass theory by a calculation procedure based on a finite-element method (FEM). The results are also compared to those obtained by finite difference method (FDM) and obtained by FEM without SO coupling. We expect FEM and FDM methods to give similar results, but the FDM has a limitation in dealing with various quantum wire shapes. In the case of QWR with small strains, the SO coupling effect does not greatly change subband energies and the trends of the subband dispersions. On the other hand, in the case of QWR with large strains, the subband energies of all states including the first state are considerably affected by the SO coupling. The amplitudes of the heavy-hole and light-hole wave functions have nonzero mixings even at the zone center (ky=0) in contrast to the case of quantum wells. It is found that the matrix elements for the TE polarization greatly increase due to the SO coupling effect.