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

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. I n this article, in contrast to preceding ones, we use the dispersion-relate d three-parameter formula E-g(T) = E-g(0) - (alpha Theta /2)[(1 + (pi (2)/6 )(2T/Theta)(2) + (2T/Theta)(4))(1/4)-1], which is a very good approximation in particular for the transition region between the regimes of moderate an d large dispersion. This formula is shown here to be well adapted to the di spersion regime frequently found in hexagonal GaN layers. By means of least -mean-square fittings we have estimated the limiting magnitudes of the slop es, S(T) equivalent to -dE(g)(T)/dT, of the E-g(T) curves published by vari ous experimental groups to be or order alpha equivalent toS(infinity) appro ximate to (5.8 +/-1.0) x 10(-4) eV/K. The effective phonon temperature has been found to be of order Theta approximate to (590 +/- 110) K, which corre sponds to an ensemble-averaged magnitude of about 50 meV for the average ph onon energy. The location of the latter within the energy gap between the l ow- and high-energy subsections of the phonon energy spectrum of h-GaN sugg ests that the weights of contributions made by both subbands to the limitin g slope alpha are nearly the same. This explains the order of Delta approxi mate to0.5-0.6 as being typical for the dispersion coefficient of the h-GaN layers under study, The inadequacies of both the Bose-Einstein model (corr esponding to the limiting regime of vanishing dispersion Delta -->0) and Va rshni's ad hoc formula (corresponding to a physically unrealistic regime of excessively large dispersion Delta approximate to1) are discussed. Unwarra nted applications of these conventional models to numerical fittings, espec ially of unduly restricted data sets (T less than or equal to 300 K), are i dentified as the main cause of the excessively large scatter of parameters quoted for h-GaN in various recent articles. (C) 2001 American Institute of Physics.