  In this work we study the quality factor associated with dissipation due to
scattering of shear horizontal surface acoustic waves by random self-affine
roughness. It is shown the quality factor is strongly influenced by both the
surface roughness exponent H, and the roughness amplitude w to lateral
correlation length X ratio. Indeed, quality factors for roughness exponents
H>0.5 are comparable to quality factors due to intrinsic dissipation mechanisms
(e.g., thermoelastic losses and phonon-phonon scattering) especially for wave
vectors <1/X. Our results indicate that this dissipation mechanism should be
carefully considered in the design micro/nanoelectromechanical systems.
