Effects of strain on the band structure of group-III nitrides

Abstract

We present a systematic study of strain effects on the electronic band structure of the group-III-nitrides (AlN, GaN and InN) in the wurtzite phase. The calculations are based on density functional theory with band-gap-corrected approaches including the Heyd-Scuseria-Ernzerhof hybrid functional (HSE) and quasiparticle ${G}_{0}{W}_{0}$ methods. We study strain effects under realistic strain conditions, hydrostatic pressure, and biaxial stress. The strain-induced modification of the band structures is found to be nonlinear; transition energies and crystal-field splittings show a strong nonlinear behavior under biaxial stress. For the linear regime around the experimental lattice parameters, we present a complete set of deformation potentials (${a}_{\mathrm{cz}}$, ${a}_{\mathrm{ct}}$, ${D}_{1}$, ${D}_{2}$, ${D}_{3}$, ${D}_{4}$, ${D}_{5}$, ${D}_{6}$) that allows us to predict the band positions of group-III nitrides and their alloys (InGaN and AlGaN) under realistic strain conditions. The benchmarking ${G}_{0}{W}_{0}$ results for GaN agree well with the HSE data and indicate that HSE provides an appropriate description for the band structures of nitrides. We present a systematic study of strain effects on the electronic band structure of the group-III nitrides (AlN, GaN, and InN). We quantify the nonlinearity of strain effects by introducing a set of bowing parameters. We apply the calculated deformation potentials to the prediction of strain effects on transition energies and valence-band structures of InGaN alloys and quantum wells (QWs) grown on GaN, in various orientations (including $c$-plane, $m$-plane, and semipolar). The calculated band gap bowing parameters, including the strain effect for $c$-plane InGaN, agree well with the results obtained by hybrid functional alloy calculations. For semipolar InGaN QWs grown in $(20\overline{2}1)$, $(30\overline{3}1)$, and $(30\overline{3}\overline{1})$ orientations, our calculated deformation potentials have provided results for polarization ratios in good agreement with the experimental observations, providing further confidence in the accuracy of our values.