Effective-mass Hamiltonian for strained wurtzite GaN and analytical solutions

Abstract

We present the effective-mass Hamiltonian for wurtzite crystals including the strain effects and show analytical solutions for the energy band structures. We found that the Hamiltonian can be block-diagonalized in our chosen set of basis functions such that the band structures near the zone center can be conveniently derived with analytical solutions. The constant energy surfaces and the valence-band structures are illustrated graphically. The strain effects on the band structures of the wurtzite GaN are also discussed. This Hamiltonian provides a theoretical foundation for calculating the band structures of the bulk and quantum-well wurtzite crystals under the framework of the effective mass theory.