Thomas-Fermi impurity potential for metallic thin films

With the treatment of the metallic thin film as a bounded free-electron gas, the effective potential energy of an electron due to a positive point-charge impurity is derived. The formulation is based on the Thomas-Fermi approximation and the Fourier-transform technique. The Boltzmann transport equation is solved with the above-mentioned impurity potential incorporated in the collision term. The resistivity ratio for an aluminum thin film is computed and compared with those already published. There is good agreement between theory and experiment.