Wavefunction engineering of layered wurtzite semiconductors grown along arbitrary crystallographic directions

The electronic band structure of wurtzite semiconductor heterostructures is investigated theoretically using the envelope function k⋅P formalism. We use a Lagrangian formulation for the valence bands so that the order of the derivatives appearing in the multiband description is explicitly specified when Schrödinger’s equations for the envelope functions are generated through the application of the principle of least action. The issues of derivative operator ordering and boundary conditions at material interfaces are examined in detail. The theoretical results are presented for arbitrary growth directions and the spin–orbit interaction is taken into account. This is of interest, for example, in treating AA-plane wurtzite heterostructures such as GaN/AlGaN quantum wells grown on RR-plane sapphire. Strain effects are included using a general rotation method that diagonalizes strain and is appropriate for pseudomorphic wurtzite structures in any allowed orientation. It is shown that inversion asymmetry in the valence band leads to shifts in the band-edge energies in the [112¯0]-grown quantum wells. The finite element method is used with the Lagrangian for the composite layered semiconductor structure in order to obtain the energy eigenvalues for multi-quantum well systems. Calculations for quantum wells and superlattices are presented.