Influence of surface scattering on the radio-frequency size effect

The surface impedance of a thin metal plate excited by a rf electromagnetic field is calculated as a function of external de magnetic field applied in the plane of the plate under the nonlocal conditions of the anomalous skin effect. A linearized Boltzmann equation in the relaxation time approximation for isotropic bulk scattering is solved by means of a generalized kinetic formulation which (I) describes the surface scattering by means of a specularity function that can depend on the angle of collision of the electron trajectories with the surface, and which 00 contains an ineffectiveness Parameter in the nonlocal form of Ohm's law, thus providing a measure for the possibility that electrons colliding with the boundaries are less effective than bulk electrons in linking the current density at one point of the conductor with the electric field at another point. This generalized path-integral solution of the Boltzmann equation is coupled with Maxwell's equations, and the resulting integrodifferential equation is solved for the spatial distribution of the electric field inside the metal plate using the numerical procedure discussed in an earlier publication by the author. This is done for both the symmetric and antisymmetric modes of excitation of the plate by the rf field in the case of a model cylindrical Fermi surface. The resulting curves for the surface impedance versus the applied dc magnetic field exhibit characteristic features which are greatly influenced by the explicit choice of the specularity function and/or the ineffectiveness parameter. It is suggested that these features can be used in conjunction with experiment to determine the correct parameters for the surface scattering mechanism.