Spin-orbit-coupling effects on the valence-band structure of strained semiconductor quantum wells

Abstract

A unitary transformation is found to diagonalize the 6\ifmmode\times\else\texttimes\fi{}6 Luttinger-Kohn Hamiltonian into two 3\ifmmode\times\else\texttimes\fi{}3 blocks, making it more efficient to calculate the quantum-well subband structure. Using this formulation we study systematically the strain-dependent coupling between the heavy-hole bands, light-hole bands, and the spin-orbit split-off bands for a strained quantum well and its bulk limit. We show how the strain deforms the constant energy surface in k space and compare the subband structure calculated with and without the split-off bands. Our results clearly demonstrate that the spin-orbit coupling has significant effects on the band structure especially for highly strained quantum wells and, therefore, cannot be ignored.