Dispersion of optical and acoustical phonons in the zinc-blende group III-nitride superlattices

Abstract

A comprehensive theoretical study of phonons in cubic GaN, AlN, Ga1−xAlxN, and (GaN)m/(AlN)n superlattices (SLs) is reported using both simple and microscopic models. The new periodicity introduced by the SL structure causes zone folding of the acoustical modes allowing phonons with large q vectors, normally inactive in light scattering, to become Raman active. We predicted the frequencies of such modes in GaN/AlN SLs using elastic continuum, diatomic linear-chain, and rigid-ion models. In the rigid-ion model (RIM), the short range forces are optimized in terms of elastic constants and phonon energies at critical points while the long-range Coulomb forces are evaluated exactly via Ewald summation. The advantage of using RIM is that it permits the construction of a dynamical matrix entering into the secular equation for the SL vibrations of a given wavevector directly from the dynamical matrices of the bulk materials. For short period (GaN)m/(AlN)n SLs, the dependence of phonons on wavevectors both parallel and perpendicular to the growth direction [001] is investigated. Theoretical results for the GaN/AlN superlattices are compared and discussed with the GaAs/AlAs system as well as with the existing model calculation of Grille and Bechstedt. Unlike GaAs/AlAs, the larger optical phonon values and partially changed confinement characteristics in GaN/AlN superlattices are believed to have significant affects on the relaxation properties of electrons in group III-nitride material systems.