Transport relaxation rate of a two-dimensional electron gas: Surface acoustic-phonon contribution

The transport relaxation rate 1/τ of a two-dimensional electron gas due to scattering by thermally excited surface acoustic phonons is calculated. The temperature dependence of 1/τ is found to be linear in T for high temperatures, but decreases like ${\mathrm{T}}^{\mathrm{\alpha }}$ as T drops below the Bloch-Grüneisen temperature for surface sound; α=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.