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 ${\gamma }_{1\mathrm{z}}$=${\gamma }_{1\mathrm{\perp }}$, ${\gamma }_{2\mathrm{z}}$=${\gamma }_{2\mathrm{\perp }}$, and ${\gamma }_{3\mathrm{z}}$=${\gamma }_{3\mathrm{\perp }}$. We establish the relation between two recently proposed 3×3 matrix blocks diagonalizing the full 6×6 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.