Influence of Size, Shape, and Scattering on Electrical Resistivity of Metal Nanowires

A simple quantitative model has been proposed for exploring the combined effect of size, shape, and electron scattering on the electrical resistivity of metallic nanowires. In the present model, the effect of different cross-sectional shapes of nanowires has been comprised on the surface and grain boundary scattering. For understanding electrical behavior at the nanolevel, the incorporation of specularity parameter (p) with different cross-sectional shapes of nanowires is essential. It is responsible for the reduction in the mean free path of electrons; which generates the favorable condition for enhancing the surface scattering, consequently contributing to increment of electrical resistivity. The applicability of the proposed model has been investigated for copper, nickel, silver, and aluminum metallic nanowires of four different cross-sectional shapes (rectangular, triangular, square, and spherical) along with different values of reflection coefficient (R). Calculated results have been compared with the available experimental data and it is observed that the results are in close agreement, which proves the validity of the proposed model. The proposed model shows the collective effect of size, scattering, and crosssectional shape factor (δ) on electrical resistivity in a very simple and straightforward manner and able to reduce the complexity of existing models up to great extent.