A reanalysis of resistive size effects in tungsten

A reanalysis of available data on the influence of surface scattering upon the resistivity of high-purity tungsten is presented. It is shown that some of the data appear to fit quite well to Soffer's model (1967) of surface scattering. From this new analysis values for the product rho infinity lambda infinity (bulk resistivity times bulk mean free path) may be obtained lying in the range 1.0-1.7 f Omega m 2 . Early data, which could not be interpreted using Fuchs' theory (1938) of surface scattering, may now be explained and yield surface roughness ratios (ratio of root mean square height of deviations from the mean surface to the Fermi wavelength) of the order of 0.2-2.5, typical of the value expected for atomically smooth to atomically rough surfaces. However, more recent data violate Soffer's theory in a convincing fashion. They illustrate fully the severe dangers of using a theory to interpret data for which it is not at all applicable. The Fermi surface of tungsten by no means approximates a simple sphere (one of the basic assumptions of the Soffer model). Hence such a naive treatment as Fuchs' leads to meaningless parameters such as quoted above. The authors present a warning to all experimentalists who attempt to interpret data from metals with complex Fermi surfaces in a simple-minded fashion (e.g. using Fuchs' model).