k⋅p method for strained wurtzite semiconductors

Abstract

We derive the effective-mass Hamiltonian for wurtzite semiconductors, including the strain effects. This Hamiltonian provides a theoretical groundwork for calculating the electronic band structures and optical constants of bulk and quantum-well wurtzite semiconductors. We apply Kane's model to derive the band-edge energies and the optical momentum-matrix elements for strained wurtzite semiconductors. We then use the k\ensuremath{\cdot}p perturbation method to derive the effective-mass Hamiltonian, which is then checked with that derived using an invariant method based on the Pikus-Bir model. We obtain the band structure ${\mathit{A}}_{\mathit{i}}$ parameters in the group theoretical model explicitly in terms of the momentum-matrix elements. We also find the proper definitions of the important physical quantities used in both models and present analytical expressions for the valence-band dispersions, the effective masses, and the interband optical-transition momentum-matrix elements near the band edges, taking into account the strain effects. \textcopyright{} 1996 The American Physical Society.