Strain and crystallographic orientation effects on the valence subbands of wurtzite quantum wells

We present a derivation of the 6x6 valence band Hamiltonian valid for general [h0il] oriented m-V wurtzite strained substrates. The derivation is performed within the exact envelope function theory approach in which the I; operators are written in an ordered form when the Hamiltonian is applied to wurtzite superlattices. The choice of suitable basis functions for the (h0il) growth direction, written in terms of those for the typical (0001) case. allows us to define the heavy-, light-, and split-off-hole states in a transparent way and without ambiguities. The Hamiltonian for the (10 (1) over bar 0) oriented crystals is provided explicitly. The main differences between the hulk and superlattice ((k) over cap-ordered) Hamiltonians are contrasted. As an application, numerical calculations of the subband dispersion of GaN/InxAl(1-x)N quantum wells for various directions an presented and discussed. We show that inclusion of strain effects and the properly (k) over cap-ordered Hamiltonian are essential in an accurate description of the valence subbands of quantum wells in these systems.