Electron-fluid model for dc size effect

Abstract

The ensemble of conduction electrons is treated as a fluid whose collective motion is described by the Navier-Stokes and Maxwell equations. Under simplifying conditions, Ohm's law is generalized for the stationary case. The profile of the current density is shown. Geometry-dependent effective conductivities are derived for circular cylinders and plates with rectangular and square cross sections, in good agreement with size effect experiments. A compilation of the fitting parameters, bulk resistivity, and adherence length used for Cu, Ga, and CoSi2 is presented in the temperature range 300→0 K for dimensions between 1 nm and 2 mm.