Matthienssen’s Rule in Polycrystalline Metallic Nanofilms

Abstract

Matthiessen’s rule has been applied to analyze the simultaneously measured electrical and thermal conductivities of polycrystalline platinum nanofilms. The results show that the greatly reduced conductivities are mainly attributed to the grain boundary scatterings. By taking into account the background scattering and the grain boundary scattering, Mathienssen’s rule slightly underestimates the thermal conductivity, but obviously overestimates the electrical conductivity. By introducing an additional parameter characterizing electron scattering on the grain boundary in Matthiessen’s rule, the agreement between the theoretical predictions and the observed results are greatly improved. Further studies show that when the mean grain size is much smaller than the corresponding mean free path, the electrons’ behavior inside the grains becomes affected by the grain boundaries and the underlying assumption of independent scattering processes for Mathiessen’s rule will become invalid.

Different effects of grain boundary scattering on charge and heat transport in polycrystalline platinum and gold nanofilms

“…As indicated in Ref. [19], grain boundary scattering dominates the combined scattering process for all studied nanofilms in the whole temperature range, while the contribution of surface scattering is rather less important. Hence, in this study, we lay emphasis on the effects of the gain boundary scattering.…”

“…Moreover, the influence of surface scattering can also be neglected due to its little importance compared with grain boundary scattering. [19] The electrons passing through the grain boundary have a relaxation time determined only by the background scattering as…”