Magnetophotoluminescence of $\mathrm{GaN}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ quantum wells: Valence band reordering and excitonic binding energies

A reordered valence band in $\mathrm{GaN}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ quantum wells with respect to GaN epilayers has been found as a result of the observation of an enhanced g factor ${(g}^{*}\sim 3)$ in magnetoluminescence spectra in fields up to 55 T. This has been caused by a reversal of the states in the strained ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ barriers thus giving different barrier heights for the different quantum well hole states. From $k-p$ calculations in the quasicubic approximation, a change in the valence band ordering will account for the observed values for the g factors. We have also observed the well-width dependence of the in-plane extent of the excitonic wave function from which we infer an increase in the exciton binding energy with the reduction of the well width in general agreement with theoretical calculations of Bigenwald et al. [Phys. Status Solidi B 216, 371 (1999)] that use a variational approach in the envelope function formalism that includes the effect of the electric field in the wells.