The effect of mound roughness on the electrical capacitance of a thin insulating film

We investigate the influence of the roughness at a nanometre scale on the electrical capacitance of thin films. It is shown that the surface roughness causes an increase of the electrical capacitance depending on the details of the roughness characteristics. For mound rough surfaces, the increase of the electrical capacitance depends strongly on the relative magnitude of the average mound separation λ and the system correlation length ζ. A rather complex behaviour develops for ζ > λ, whereas for ζ < λ a smooth decrease of the capacitance as a function of the average mound separation λ occurs due to surface smoothing. Depending on the film thickness, the presence of roughness strongly influences the electrical capacitance as long as ζ < λ, whereas a precise determination of the actual effect requires a detailed knowledge of the thickness dependence of the roughness parameters during film growth.