Effective-mass theory for superlattices grown on (11N)-oriented substrates

An effective-mass formulation for superlattices grown on (11N)-oriented substrates is given. It is found that, for GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices, the hole subband structure and related properties are sensitive to the orientation because of the large anisotropy of the valence band. The energy-level positions for the heavy hole and the optical transition matrix elements for the light hole apparently change with orientation. The heavy- and light-hole energy levels at ${\mathbf{k}}_{\mathrm{?}}$=0 can be calculated separately by taking the classical effective mass in the growth direction. Under a uniaxial stress along the growth direction, the energy levels of the heavy and light holes shift down and up, respectively; at a critical stress, the first heavy- and light-hole energy levels cross over. The energy shifts caused by the uniaxial stress are largest for the (111) case and smallest for the (001) case. The optical transition matrix elements change substantially after the crossover of the first heavy- and light-hole energy has occurred.