Dispersion relations of acoustic phonons on a corrugated surface

Abstract

We present the theory of surface acoustic phonon normal modes and of Brillouin scattering cross section for a shallow grating on the surface of an opaque material. The grating causes the appearing of a surface Brillouin zone and the folding of the surface modes. We study in detail the opening of gaps in the dispersion relations of the folded surface modes and resonances, for a momentum transfer up to the second zone boundary and for a grating profile beyond the simple sinusoidal approximation. The calculations are applied to the Si(001) surface.