Surface-roughness fractality effects in electrical conductivity of single metallic and semiconducting films

Surface-roughness effects in electrical conductivity of thin metallic and semiconducting films with self-affine fractal surfaces are considered in the framework of the Born approximation. The surface roughness is described by the k-correlation model, and is characterized by the roughness exponent H $(0<~H<~1),$ the in-plane correlation length {ξ}, and the rms roughness amplitude {Δ}. In the case of metallic films the conductivity is shown to increase monotonically with H increasing from $H=0$ to $H=1$ and with decreasing ratio Δ/ξ. For semiconducting quantum wells the conductivity shows a peculiar interplay of quantum-mechanical effects and scattering due to surface roughness.