A theoretical description of grain boundary electron scattering by an effective mean free path

A mathematical analysis based on the Mayadas-Shatzkes model indicates that we may define an “effective mean free path” in order to describe electronic conduction in both thin polycrystalline and monocrystalline metallic films. Under this condition a Fuchs-Sondheimer function can be introduced to evaluate the total film resistivity and its temperature coefficient in the presence of external surfaces. A possible extension to other theories derived from the Fuchs theory is mentioned.