Analytic solution of Ando's surface roughness model with finite domain distribution functions

TL;DR

This paper derives an analytic solution for Ando's surface roughness model in metallic nanowires, improving simulation accuracy by avoiding overlap approximations and revealing how momentum gaps influence resistivity.

Contribution

It extends Ando's model beyond small roughness and infinite barrier limits using finite domain distribution functions for analytic scattering rate calculations.

Findings

Overlap approximations poorly estimate scattering rates.

A critical momentum gap reduces resistivity significantly.

Analytic solutions enable faster, more accurate simulations.

Abstract

Ando's surface roughness model is applied to metallic nanowires and extended beyond small roughness size and infinite barrier limit approximations for the wavefunction overlaps, such as the Prange-Nee approximation. Accurate and fast simulations can still be performed without invoking these overlap approximations by averaging over roughness profiles using finite domain distribution functions to obtain an analytic solution for the scattering rates. The simulations indicate that overlap approximations, while predicting a resistivity that agrees more or less with our novel approach, poorly estimate the underlying scattering rates. All methods show that a momentum gap between left- and right-moving electrons at the Fermi level, surpassing a critical momentum gap, gives rise to a substantial decrease in resistivity.