Autocovariance functions, root-mean-square-roughness height, and autocovariance length for rough deposits of copper, silver, and gold

Abstract

Autocovariance functions (ACF's) for rough surfaces of copper, silver, and gold deposits are deduced from surface profiles determined by the use of microdensitometer analysis of surface-shadowed carbon replicas. It is shown that the initial portions of the ACF's have a Gaussian form. The root-mean-square (rms) surface roughness $\ensuremath{\delta}$ and the autocorrelation length $\ensuremath{\sigma}$ are deduced for each surface. Values of $\ensuremath{\sigma}$ agree with corresponding values deduced from the ACF's of the surface slopes. Results of this study are compared with those previously obtained for rough magnesium deposits. We conclude that the Gaussian model is suitable to represent in general the ACF's of rough metallic surfaces. Lastly, it is shown that $\ensuremath{\sigma}$ increases with $\ensuremath{\delta}$, and within the accuracy range of their measurements there is a linear relation between $\ensuremath{\delta}$ and $\ensuremath{\sigma}$.