Moderate phonon dispersion shown by the temperature dependence of fundamental band gaps of various elemental and binary semiconductors including wide-band gap materials

Abstract

A recently devised analytical four-parameter model describing the temperature dependence of fundamental band gaps Eg(T) and/or exciton peak positions Egx(T) in semiconductors is used for estimating the material-specific magnitudes of phonon dispersion. A set of four fundamental parameters, the magnitudes of which are essentially independent of various details of the analytical model used, is established by direct connections with the experimentally detectable low-order moments of the electron–phonon spectral function. Numerical fittings of experimental E(T) data sets are performed for a variety of group IV, III–V, and II–VI materials showing a moderate degree of phonon dispersion. The resulting sets of basic parameters are listed. For all materials in question we find that the limiting (T→∞) slopes of the E(T) curves are confined to magnitudes between about 0.2 and 0.9 meV/K. The effective phonon temperatures amount to about 2/3 of the corresponding Debye temperatures. The simultaneous knowledge of both the effective phonon temperature and the associated dispersion coefficient enables a rough estimation of the relative weights of the contributions of various parts of the phonon spectrum to the T→∞ slope of the measured E(T) dependence. From the parameter sets determined recently for zinc chalcogenides we can assume the dominating contributions to the limiting slopes of their E(T) curves are due to short-wavelength longitudinal acoustical phonons. This conclusion is confirmed by a comparison with alternative fittings using a three-oscillator model.