The roughness-induced classical size effect in thin films

The authors consider the electronic transport process in thin films with rough surfaces. The approach employed is based on classical concepts and avoids some special assumptions used in earlier papers. Roughness is described in terms of scatterers that are distributed randomly on the surfaces. Their differential scattering cross section yields a generally angle-dependent specularity parameter. A new form of this angle dependence is proposed. They show that the homogeneity of the lateral carrier distribution, as postulated by Fuchs in his well known paper published in 1938, is associated with the time-reversal symmetry of the microscopic scattering cross section. The divergence of the classical surface-dominated conductivity, i.e. for vanishing bulk scattering, is enhanced for angle-dependent specularity parameters in comparison with the constant parameter introduced by Fuchs. They further show how to make contact between classical formulations and quantum-mechanical approaches leading to a stronger dependence of the conductivity on the film thickness. The results are compared with existing classical size-effect theories.