Statistical Model for the Size Effect in Electrical Conduction

Abstract

A statistical model for the reflection of scalar plane waves from a rough surface leads to a plane wave in the direction of specular reflection and to a contribution with a finite angular spread about that direction, depending on the tangential correlation of the surface asperities. Based upon on this result, a new semiclassical model, which satisfies the requirement of flux conservation, is proposed for the boundary condition for the distribution function of the size effect in the electrical conductivity. In the absence of correlation, the resultant expression replaces the constant specularity parameter p of Fuchs by the function exp[−(4π(h/λ) cosθ0)2] with θ0 the angle of the electron wave vector with the surface normal. Correlation produces an additional forward component within the diffuse contribution. Numerical results of the size effect for zero correlation are compared to the Fuchs model as well as a more recent model, and show a different thickness dependence for thin samples. The effect of correlation is to add to the conductivity, as a result of the diffuse contribution whose velocity has a finite expectation value in the direction of the current.

Spin-dependent transport in Fe andFe∕Aumultilayers

“…The variations in height translate into variations in the electron path lengths of those electrons reflected from the surface. Ziman 34 and Soffer 35 have shown that this is analogous to the surface diffraction problem.…”

“…As discussed in Ref. 35, in order to formulate surface diffraction for electron transport using an Ewald construction, the electron wave packet was assumed to be large enough so as to have a nearly monochromatic wavelength. From the STM pictures in Fig.…”

Nanolink-based thermal devices : integration of ALD tin thin films

“…For both sets of data, the same trend of increasing resistivity with decreasing layer thicknesses is observed. For extremely thin films the mean free path (L mfp ) of electrons becomes larger than the film thickness, resulting in increased scattering at the thin film interface and hence a higher resistivity [84,85]. The higher ρ-values for thin films for our measurements with respect to literature results can be due to differences in the metrology.…”

Impact of High-<I>κ</I> Gate Stacks on Transport and Variability in Nano-CMOS Devices

“…Equation (6) may be found from a solution of the Lippmann-Schwinger equation, for a wave packet elastically scattering of a rough interface as a boundary condition, in the far-field approximation employed here and then normalizing the average flux density to unity. 29 Further details maybe found in the following two references. 32 …”