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

Abstract

I develop a 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 Hamiltonian is diagonalised considering all the bands, through an matrix, I follow a different procedure. In my approach, initially I follow a two-band approximation for the matrix, where the Hamiltonian is diagonalised by treating the conduction band and each of the valence bands separately. Thus, I diagonalise three different 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.