Modeling surface roughness scattering in metallic nanowires

TL;DR

This paper extends Ando's quantum-mechanical model to better predict surface roughness scattering in metallic nanowires, providing analytical tools for improved resistivity scaling analysis.

Contribution

It introduces surface roughness distribution functions and analytical expressions, extending the model beyond the Prange-Nee approximation for more accurate resistivity predictions.

Findings

Resistivity can be significantly reduced at certain diameters.

The extended model is valid for any roughness size.

Comparison shows improved accuracy over previous methods.

Abstract

Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.