Wavefunction engineering for GaN-based quantum wells and superlattices

The electronic band structure of GaN-based heterostructures such as those comprised of AlGaN/GaN epitaxial layers is investigated using envelope function k(.)P theory. We obtain the valence states through minimization of a Lagrangian describing the electronic interaction with the lattice potential including spin-orbit effects. This construction yields transparent derivative operator ordering appropriate for arbitrary allowed crystallographic orientations. The issues of derivative operator ordering and boundary conditions at material interfaces can be significant given the strongly anisotropic character of the wurtzite crystal structure and we explore these effects on the resulting in-plane dispersions in detail. These results are of interest, for example, in treating A-plane wurtzite heterostructures such as GaN/AlGaN quantum wells grown on R-plane sapphire. Numerical examples are obtained using finite-element discretization in order to obtain the valence band electronic; states for quantum wells and superlattices.