Electronic and optical properties of nonpolara-plane GaN quantum wells

Abstract

In this paper we present a detailed study of the electronic band structure of a series of nonpolar $a$-plane GaN/AlGaN multiple quantum wells (QWs) of varying well width using complementary results from x-ray diffraction, polarization-dependent photoluminescence excitation spectroscopy, and $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory. When excited with unpolarized light, excitonic transitions involving different electron subbands are resolved in the excitation spectra. For linearly polarized $(E\ensuremath{\perp}c,E\ensuremath{\parallel}c)$ excitation, these are shown to consist of overlapping transitions involving different hole subbands. These results are then analyzed in detail using strain data determined by the x-ray diffraction measurements in combination with the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory to calculate the bulk band structure and the relative oscillator strength of an $a$-plane GaN film under strain. The results are compared with those of an unstrained $c$-plane film. This analysis reveals that the experimentally observed polarization anisotropy can be attributed to anisotropic strain in the $c$ plane. Based on the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian, we apply an effective mass approximation, taking into account strain and nonparabolicity effects, to calculate the single-particle states and energies for the different quantum wells. The possible influence of the weak spin-orbit coupling on the results is studied in detail. Starting from the single-particle energies and including excitonic binding energies, the band edge optical transitions are calculated and successfully compared to the experimental data. Our analysis gives an estimate for the conduction- to valence-band offset ratio of 45:55 for nonpolar GaN/AlGaN QW structures. Additionally, our study also allows us to investigate the magnitude of the crystal-field splitting and spin-orbit coupling in GaN systems.