Resistivity scaling model for metals with conduction band anisotropy

TL;DR

This paper develops a resistivity scaling model for metal thin films that incorporates conduction band anisotropy and crystal orientation effects, improving understanding of resistivity behavior in textured films.

Contribution

The paper introduces a novel resistivity scaling model that accounts for band structure anisotropy and crystal orientation, extending beyond traditional models.

Findings

The model accurately predicts resistivity scaling in Cu and Ru thin films.

Calibration with ab initio simulations improves model precision.

Textured Ru films show a renormalized grain boundary reflection coefficient.

Abstract

It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-)isotropic and anisotropic respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru.