Study of surface roughness using microdensitometer analysis of electron micrographs of surface replicas II: Autocovariance functions

Abstract

Autocovariance functions (ACF’s) for rough surfaces of magnesium and silver deposits are deduced from surface profiles previously determined by using microdensitometer analysis of micrographs of surface-shadowed carbon replicas. It is shown that initial portions of the ACF’s for magnesium and silver surfaces have a Gaussian form, whereas the ACF for a grating is perfectly periodic. The rms roughness height δ and the autocovariance length σ are deduced for each surface. There is a linear relation between δ and σ for rough deposits of magnesium. For this metal, values of δ and σ are compared with corresponding values of Gesell et al. [ Phys. Rev. B7, 5141 ( 1972)], who have fitted their experimental data to a theoretical expression given by Elson and Ritchie [ Phys. Lett.33A, 255 ( 1970)]. Good agreement is obtained. Finally, the ACF’s of the surface slopes are computed, and it is shown that results obtained are consistent with results deduced from ACF’s for surface profiles.