Effect of weak surface autocorrelation on the size effect in electrical conduction

Correlation between points on a conductor surface may be important in explaining the relatively large specularity parameters attributed to measurements in single-crystal samples. An expression for the size effect in the electrical conductivity is obtained that takes into account the effect of weak surface autocorrelation. The expression shows that, as expected, the correlation increases the electrical conductivity. It also shows that even an angle-dependent specularity parameter may not be an adequate description in the sense of the Fuchs model. Numerical estimates are given for the size effects due to surface roughness and auto correlation. These are explained in terms of the competing effects of flux conservation and surface asperity slopes.