Polarization anisotropy and valence band ordering in semipolar (112¯2) AlInN/GaN heterostructures

Semipolar $(11\overline{2}2)$ AlInN/GaN heterostructures on GaN templates were studied using photoluminescence (PL) spectroscopy both at 15 K and at room temperature. The polarization-resolved PL measurements revealed a dominant polarization along the $[11\overline{2}\overline{3}] {c}^{\ensuremath{'}}$ and a weaker signal along the $[1\overline{1}00] m$-direction, i.e., the two in-plane directions of the semipolar $(11\overline{2}2)$ growth plane. We observed slightly different polarization degrees of $0.34\ifmmode\pm\else\textpm\fi{}0.01, 0.25\ifmmode\pm\else\textpm\fi{}0.02$, and $0.20\ifmmode\pm\else\textpm\fi{}0.01$ at room temperature, respectively, depending on the degree of strain relaxation in the $[1\overline{1}00]$ direction. From a theoretical model based on a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ calculation, we find that the transition from the conduction band (CB) to the uppermost valence band (VB) is C for AlInN similar to AlN, followed by the transition A from the CB to the second VB, for a wide range of compositions. Thus, the in-plane transition matrix elements from the CB to the two topmost VBs near the $\mathrm{\ensuremath{\Gamma}}$ point of the Brillouin zone are dominated by ${M}_{[11\overline{2}\overline{3}]}$ for the C transition and by ${M}_{[1\overline{1}00]}$ for the A transition. For the samples under consideration with an energy splitting of about $18\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{4pt}{0ex}}\mathrm{meV}$, there is sizable thermal occupation of the second VB at room temperature, reasonably explaining the experimental results. The results show that AlInN possesses a band structure similar to AlN, which might explain the strong Stokes shift and the large variation in the band-gap values reported previously.