DOUBLE-LAYER CAPACITANCE ON A ROUGH METAL-SURFACE

An expression for the double layer capacitance of rough metal-electrol yte, metal-semiconductor, or semiconductor-electrolyte interfaces is d erived which shows the interplay between the Debye length and the leng ths characterizing roughness. Different dependencies of the capacitanc e, as compared to the flat interface, on the concentration of charge c arriers in electrolyte or semiconductor are predicted. Examples of the typical roughness spectra are considered. The cases of Euclidean roug hness show weak dependence on the particular form of the roughness spe ctrum, being sensitive only to its main parameters: the random mean sq uare 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 conventiona l measurements of the double layer capacitance.