Near-surface electrons and acoustic phonons: Energy and momentum relaxation

We study energy and momentum relaxation of a two-dimensional (2D) electron channel located at a finite distance $\mathcal{l}$ from a free crystal surface. The interaction with a complete set of bulklike, totally reflected, and Rayleigh acoustic phonon modes is taken into account. In most cases of interest the relaxation rates have the same temperature dependence as for 2D or bulk electrons interacting with bulk phonons. Numerical calculations demonstrate that the presence of a surface results in approximately a 10% modification of scattering rates in the high-temperature region. In the opposite limit (Bloch-Grüneisen regime), the contribution of the surface phonons may dominate over that of bulklike modes. Oscillations of the relaxation rates as a function of the distance $\mathcal{l}$ between the electron channel and the surface are also predicted.