Eur. Phys. J. B 51, 583-591 (2006)
https://doi.org/10.1140/epjb/e2006-00256-0

Acoustic phonon dynamics in strained cubic and hexagonal GaN/Al₂O₃ superlattices

¹ Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil
² Departamento de Ciências Exatas, Centro Federal de Educação Tecnológica do Maranhão, 65025-001 São Luís, MA, Brazil
³ Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-970 Fortaleza, CE, Brazil

Corresponding author: ^a eudenilson@dfte.ufrn.br

Received: 21 December 2005
Revised: 24 February 2006
Published online: 28 June 2006

Abstract

We study the acoustic-phonon spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from III–V nitride materials (GaN) intercalated by sapphire (Al₂O₃). Due to the misalignments between the sapphire and the GaN layers that can lead to threading dislocation densities as high as 10⁸-10¹⁰ cm^-1, and a significant lattice mismatch (~14%), the phonon dynamics is described beyond the continuum elastic model using coupled elastic and electromagnetic equations, stressing the importance of the piezoelectric polarization field in a strained condition. We use a transfer-matrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expressions for the phonon dispersion relation. Furthermore, a quantitative analysis of the localization and magnitude of the allowed band widths in the phonon's spectra, as well as their scale law and the parametric spectrum of singularities f(α), are presented and discussed.