Acoustic phonon dynamics in strained cubic and hexagonal GaN/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> superlattices

We study the acoustic-phonon spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from III–V nitride materials (GaN) intercalated by sapphire (Al<Subscript>2</Subscript>O<Subscript>3</Subscript>). Due to the misalignments between the sapphire and the GaN layers that can lead to threading dislocation densities as high as 10<Superscript>8</Superscript>-10<Superscript>10</Superscript> cm<Superscript>-1</Superscript>, 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006