Electrical resistivity model for polycrystalline films: The case of specular reflection at external surfaces

A model is developed for estimating effects due to electron scattering from grain boundaries, occurring simultaneously with background scattering. Since grain-boundary effects are negligible in bulk materials, the model is particularly relevant to polycrystalline metal films in which a very fine-grained structure is often found. It is shown by solution of the appropriate Boltzmann equation, that the total resistivity can be strongly dominated by grain-boundary scattering. If grain size increases with film thickness, a marked dependence of resistivity on thickness exists, even when scattering from external surfaces is negligible or is completely specular. © 1969 The American Institute of Physics.