Theory of k ⋅ p electronic structure and effective masses of ultra-wide bandgap wurtzite aluminum nitride

Abstract I develop a k ⃗ · p ⃗ theory of electronic structure for wurtzite(W)-Aluminium Nitride, based on the three uppermost valence bands and the lowest conduction band at the Γ-point. As distinguished from the Chuang-Chang approach [9], where the k ⃗ · p ⃗ Hamiltonian is diagonalised considering all the bands, through an 8 × 8 matrix, I follow a different procedure. In my approach, initially I follow a two-band approximation for the k ⃗ · p ⃗ matrix, where the k ⃗ · p ⃗ Hamiltonian is diagonalised by treating the conduction band and each of the valence bands separately. Thus, I diagonalise three different 4 × 4 matrices, for obtaining the dispersions of the valence bands. The conduction band energy is obtained from the first diagonalization, involving band edge states. Effect of other two valence bands on a given valence band is considered through second order perturbation theory. Details of this procedure are outlined in Appendix A. It gives analytic expressions for the dispersion of the bands. I compare the results obtained for W-AlN with recent calculations and note satisfactory agreements. I also calculate the effective masses of holes in the valence bands both at the Γ-point and also as functions of the wavevector. My results agree fairly well with a recent calculation [3]. The hole effective masses for all the bands show large anisotropy. The effective mass of the electron in the conduction band does not show appreciable anisotropy.