The Conductance of a Perfect Thin Film with Diffuse Surface Scattering

The conductance of thin films with diffusive surface scattering was solved semi-classically by Fuchs and Sondheimer. However, when the intrinsic electron mean free path is very large or infinite their conductance diverges. In this letter a simple diffraction picture is presented. It yields a conductance which corresponds to a limiting mean free path of a2kF /(2π) where a is the film thickness. PACS: 73.50.-h, 73.50.Bk, 73.23.-b, 73.25.+i, B146 The conductivity of a thin film generally decreases considerably when the film thickness is reduced. The main reason is that the surfaces of the film scatter the conduction electrons partially or completely diffusively and reduce their effective mean free path. This phenomenon was first treated by Fuchs [1] and later generalized by Sondheimer [2]. The result of their semi-classical calculation for the conductance G of a square shaped thin film (width equal to length) of thickness a with completely diffusive scattering at the surfaces is