On the optical polarization properties of semipolar $(20\overline{2}1)$ and $(20\overline{2}\overline{1})$ InGaN/GaN quantum wells

In the framework of $\mathbf{k}·\mathbf{p}$-theory, semipolar $(20\overline{2}1)$ and $(20\overline{2}\overline{1})$ InGaN/GaN quantum wells (QWs) have equivalent band structures and are expected to have identical optical polarization properties. However, $(20\overline{2}1)$ QWs consistently exhibit a lower degree of linear polarization (DLP) than $(20\overline{2}\overline{1})$ QWs. To understand this peculiarity, we investigate the optical properties of $(20\overline{2}1)$ and $(20\overline{2}\overline{1})$ InGaN/GaN single QW light-emitting diodes (LEDs) via resonant polarization-resolved photoluminescence microscopy. LEDs were grown on bulk substrates by metal organic vapor phase epitaxy with different indium concentrations resulting in emission wavelengths between 442 nm and 491 nm. We discuss the origin of their DLP via $\mathbf{k}·\mathbf{p}$ band structure calculations. An analytical expression to estimate the DLP in the Boltzmann-regime is proposed. Measurements of the DLP at 10 K and 300 K are compared to m-plane LEDs and highlight several discrepancies with calculations. We observe a strong correlation between DLPs and spectral widths, which indicates that inhomogeneous broadening affects the optical polarization properties. Considering indium content fluctuations, QW thickness fluctuations, and the localization length of charge carriers, we argue that different broadenings apply to each subband and introduce a formalism using effective masses to account for inhomogeneous broadening in the calculation of the DLP. We conclude that the different DLP of $(20\overline{2}1)$ and $(20\overline{2}\overline{1})$ QWs might be related to different effective broadenings of their valence subbands induced by the rougher upper QW interface in $(20\overline{2}1)$, by the larger sensitivity of holes to this upper interface due to the polarization field in $(20\overline{2}1)$, and/or by the different degrees of localization of holes.