“…We consider only scattering by phonons with wavevector parallel to the surface as was done in the analyses reported earlier [1][2][3]10,14,[22][23][24][25]. Here k, k and q, the phonon wavevector, are in the plane of the surface, E 1 is the effective deformation potential constant and ρ v is the mass density, u l is the average acoustic velocity, d is the width of the layer of lattice atoms with which the electrons can interact.…”