Electron transport in isotropic thin metal films

It is shown that, by a suitable choice of the basis states with respect to which the Boltzmann distribution function is defined, the spatial anisotropy of a film can be incorporated into the Boltzmann transport equation for electrons in a thin film by a surface scattering term instead of by a spatial dependence of the distribution function. This scattering term can often be represented by a surface relaxation time, provided that the only fields present are a uniform electric field in the plane of the film and a uniform magnetic field perpendicular to this plane. A functional form for this relaxation time is proposed, and simple analytic formulae are derived for the electrical conductivity and Hall coefficient of a film subjected to such fields. The dependence of these quantities on the thickness of the film is found to be similar to that predicted by the standard Fuchs-Sondheimer theory.