Dispersion-related assessments of temperature dependences for the fundamental band gap of hexagonal GaN

Abstract

We have analyzed a series of data sets available from published literature for the temperature dependence of A and B exciton peak positions associated with the fundamental band gap of hexagonal GaN layers grown on sapphire. In this article, in contrast to preceding ones, we use the dispersion-related three-parameter formula Eg(T)=Eg(0)−(αΘ/2)[(1+(π2/6)(2T/Θ)2+(2T/Θ)4)1/4−1], which is a very good approximation in particular for the transition region between the regimes of moderate and large dispersion. This formula is shown here to be well adapted to the dispersion regime frequently found in hexagonal GaN layers. By means of least-mean-square fittings we have estimated the limiting magnitudes of the slopes, S(T)≡−dEg(T)/dT, of the Eg(T) curves published by various experimental groups to be of order α≡S(∞)≈(5.8±1.0)×10−4 eV/K. The effective phonon temperature has been found to be of order Θ≈(590±110) K, which corresponds to an ensemble-averaged magnitude of about 50 meV for the average phonon energy. The location of the latter within the energy gap between the low- and high-energy subsections of the phonon energy spectrum of h-GaN suggests that the weights of contributions made by both subbands to the limiting slope α are nearly the same. This explains the order of Δ≈0.5–0.6 as being typical for the dispersion coefficient of the h-GaN layers under study. The inadequacies of both the Bose–Einstein model (corresponding to the limiting regime of vanishing dispersion Δ→0) and Varshni’s ad hoc formula (corresponding to a physically unrealistic regime of excessively large dispersion Δ≈1) are discussed. Unwarranted applications of these conventional models to numerical fittings, especially of unduly restricted data sets (T⩽300 K), are identified as the main cause of the excessively large scatter of parameters quoted for h-GaN in various recent articles.