Hall effect in thin metal films

Abstract

Hall coefficient R_H and Hall mobility μ have been measured for annealed polycrystalline and epitaxially grown gold, silver, and copper films at 296° and 77°K. At thicknesses above about 600 Å, nearly bulk values are obtained for R_H and μ. Below 600 Å, a film-thickness dependence (size effect) was observed. This dependence is weak for epitaxially grown films, indicating a predominantly specular reflection of conduction electrons. On the other hand, the dependence is marked for polycrystalline films. Results on polycrystalline gold and silver films fit a predominantly diffuse scattering behavior. Data on carefully prepared polycrystalline films of copper agree well with Sondheimer's theory for perfect diffuse scattering so that best fit mean free path values can be calculated. In general, however, contrary to the theoretical predictions, R_H was found to show a slight size effect even for film thicknesses greater than the electron mean free path (t>l). This departure may be the result of an oversimplified theory. The sharper decline of the Hall mobility for t<l in polycrystalline films than is expected theoretically may be attributed to enhanced crystallite-size boundary scattering.