The electrical conductivity of very thin metal films

The solution of the Boltzmann transport equation to calculate the electrical conductivity of very thin metal films is a difficult mathematical problem. However, on physical grounds one expects this conductivity to depend on the total rate of scattering of the electrons, and not on the scattering rate weighted in favour of large-angle scattering as is the case for bulk crystals. This hypothesis has been confirmed by analysis of the results of previous calculations, and by calculations using a new technique that the authors have developed. Thus, it is found that the standard Fuchs-Sondheimer results are applicable to films whose thickness is less than 1/100 of the electron mean free path l_b, provided that one inserts in this theory the value, l _b⁰, appropriate to the total scattering rate. In practice, the use of l_b in place of l_b⁰ usually introduces only a small error.