The effects of surface scattering upon resistivity

It is shown how surface scattering may lead to substantial deviations from Matthiessen's rule. Using an angularly dependent surface scattering parameter as modelled by Soffer (1967), limit expressions for surface scattering in foils and wires are presented for both high and low kappa regions, where kappa is the ratio of the foil thickness, d, or wire radius, a, to the bulk electron mean free path, lambda infinity . From considerations for general values of kappa it is shown that surface scattering, at temperatures where the residual resistivity dominates, simply enhances the bulk temperature dependence. For higher temperatures for which the bulk resistivity varies as T 5 the surface scattering can lead to an apparent T 2 dependence. Further, it is shown that only for very thick samples or high temperatures where kappa >>1 is it possible to use a simplifying expression of the form rho - rho infinity = 3 / 8 rho infinity lambda infinity /t, for the resistivity of foils or wires, where t is d or a. For most experiments the full theory is necessary to deduce rho infinity lambda infinity ; consequently virtually all previous determinations of this parameter are erroneous. Moreover, because of the influence of the surface scattering on the apparent temperature dependence of the resistivity, even of relatively thick material, several of the 'bulk' temperature dependences previously deduced for pure materials are almost certainly in error.