Double-layer capacitance on a rough metal surface

An expression for the double layer capacitance of rough metal-electrolyte, metal-semiconductor, or semiconductor-electrolyte interfaces is derived which shows the interplay between the Debye length and the lengths characterizing roughness. Different dependencies of the capacitance, as compared to the flat interface, on the concentration of charge carriers in electrolyte or semiconductor are predicted. Examples of the typical roughness spectra are considered. The cases of Euclidean roughness show weak dependence on the particular form of the roughness spectrum, being sensitive only to its main parameters: the random mean square height of roughness and correlation length. A method is proposed for the in situ characterization of surface roughness: the measurement of surface roughness with a ''Debye ruler,'' based on the conventional measurements of the double layer capacitance.