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The variation of the resistivity with thickness d and bulk electron mean free path Aof thin metal films with unlike surfaces is calculated using Soffer's angularly dependent surface scattering model. Tabular values for the resistivity enhancement due to a range of surface roughness combinations are presented. It is shown that in the limit of one very smooth and one very rough surface, the effect, as expected, is simply an apparent doubling in the sample thickness. This contrasts with the much more likely situation of one relatively rough surface and one smooth surface. For this case it is shown that at high K values ( K = diA,) the dependence of the resistivity on K varies approximately as the rougher surface limit, while at low Kvalues the variation approaches the limit of a sample of double thickness having, on both surfaces, the higher roughness. The overall effect in this case is that the resistivity appears to vary in the manner expected from an intermediate value of surface roughness with a changed p& value, p , being the bulk resistivity. It is demonstrated that only in the limit of identical surfaces, or one very smooth and one very rough surface, with in either case no, or at least known and quantifiable, grain boundary scattering, will the determination of p d , values be meaningful. Consequently p A values determined in the past from the measurement of the variation with thickness of the resistivity of thin films are often substantially in error. t Present address:

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