Resistivity scaling and electron relaxation times in metallic nanowires

TL;DR

This paper investigates how surface roughness and grain boundaries affect resistivity in metallic nanowires, revealing grain boundaries as the dominant scattering mechanism through an exact calculation of relaxation times.

Contribution

It introduces an exact calculation of relaxation times for each sub-band state in nanowires, improving understanding of resistivity scaling due to surface and grain boundary scattering.

Findings

Grain boundaries dominate resistivity, surpassing surface roughness by a factor of 10.

Relaxation times vary significantly across sub-band states.

Resistivity scaling depends strongly on grain-boundary properties.

Abstract

We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation (RTA) of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxation time strongly depends on the sub-band state, something that remained unclear with the methods of previous work. The resistivity scaling is obtained for different roughness and grain-boundary properties, showing large differences in scaling behavior and relaxation times. Our model clearly indicates that the resistivity is dominated by grain-boundary scattering, easily surpassing the surface roughness contribution by a factor of 10.