  The transport relaxation rate 1/tau of a two-dimensional electron gas due to
scattering by thermally excited surface acoustic phonons is calculated. The
temperature dependence of 1/tau is found to be linear in T for high
temperatures, but decreases like T^alpha as T drops below the Bloch-Gruneisen
temperature for surface sound; alpha=7 (5) for the deformation-potential
(piezoelectric) interaction. The effect of a finite distance between the
crystal surface and the two-dimensional electron gas is discussed. The results
are compared with those that have been calculated for three- and
two-dimensional phonons interacting with a two-dimensional electron gas.
