Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits

The roughness spectrum $g\left(\overrightarrow{\mathrm{k}}\right)$ (or spectral density function) for surfaces of silver, copper, gold, and magnesium deposits is deduced from surface profiles determined by using microdensitometer analysis of micrographs of shadowed-surface carbon replicas. A process based on computation of autocovariance function via the fast-Fourier-transform algorithm is used. It is shown that the $g\left(\overrightarrow{\mathrm{k}}\right)$ function is not a perfect Gaussian function as is usually assumed. An analytical model is given that provides a rather suitable fit to the computed $g\left(\overrightarrow{\mathrm{k}}\right)$ functions. Results are compared with those obtained from optical experiments (mainly the attenuated-total-reflection method). Discrepancies between the values of $\delta$ (rms roughness) and $\sigma$ (autocorrelation length) determined by the use of our procedure and corresponding values deduced from optical experiments are elucidated.