Hole scattering and optical transitions in wide-band-gap nitrides: Wurtzite and zinc-blende structures

The energy spectrum and transitions of valence-band carriers in wurtzite materials are studied theoretically using cubic crystals for comparison. We correct the commonly used cubic approximation and propose notations for Luttinger-like parameters in wurtzite structures that simplify the cubic approximation to gamma(1z)=gamma(1 perpendicular to), gamma(2z)=gamma(2 perpendicular to), and gamma(3z)=gamma(3 perpendicular to). We establish the relation between two recently proposed 3x3 matrix blocks diagonalizing the full 6x6 Hamiltonian and provide geometric interpretation in three-dimensional Bloch space. The formalism is used then to derive transition matrix elements for three types of processes: (i) macrofield hole scattering, described by the Bloch overlap factor; (ii) optical transitions between conduction and valence bands; and (iii) intervalence band optical transitions. Finally, we discuss the set of material parameters for group-III nitrides and present the numerical results.