Transport properties of thin metallic films

Abstract

ABSTRACTIn using the Boltzmann equation to calculate the transport properties of thin metallic films, it is usually assumed that a time of relaxation exists for the scattering in the film which is the same as for the bulk metal, although this is only strictly justified in the ideal case of isotropic scattering. The correct Boltzmann equation in the case of elastic scattering, when the cross-section depends on the angle of scatter, is set up and possible methods of solution are discussed.The equation is solved for a simple anisotropic scattering law and the electrical resistivity and thermo-electric power are found to depend upon two parameters which are measures respectively of the thickness of the film and the anisotropy of the scattering mechanism. The numerical results for the electrical resistivity, however, differ only slightly from those given by the one-parameter formula obtained when a time of relaxation is assumed to exist.