Analytic S-Shaped Temperature Dependence of Peak Positions of the Localized-State Ensemble Luminescence and Application in the Analysis of Luminescence in Non- and Semi-Polar InGaN/GaN Quantum-Wells Micro-Array

Two analytic expressions of temperature-dependent peak positions employing the localized-state ensemble (LSE) luminescence model are deduced for the cases of \Delta E=E_\rm a-E_0 >0 and < 0, respectively, under the first-order approximation of Taylor's expansion. Then, the deduced formulas are applied to examine the experimental variable-temperature photoluminescence data of non- and semi-polar InGaN/GaN quantum-wells (QWs) array by jointly considering the monotonic bandgap shrinking described by Pässler's empirical formula. S-shaped temperature dependence of luminescence peaks of both non- and semi-polar QWs is well reproduced with the analytic formulas. As a result, the localization depths are found to be 31.5 and 32.2 meV, respectively, for non- and semi-polar QWs.