Validation of constant mean free path and relaxation time approximations for metal resistivity: explicit treatment of electron-phonon interactions

TL;DR

This study evaluates the validity of constant mean free path and relaxation time approximations in calculating metal resistivity, confirming their applicability even for anisotropic Fermi surfaces through explicit electron-phonon interaction analysis.

Contribution

It provides a first-principles assessment of the constant MFP and CRTA assumptions, validating their use in transport calculations for metals.

Findings

Both approximations are valid for anisotropic Fermi surfaces.

Explicit electron-phonon interactions support the use of these approximations.

Results facilitate practical resistivity predictions without complex calculations.

Abstract

The figure of merit $\rho \lambda$ the product of resistivity and mean free path (MFP) evaluated from first-principles calculations, is widely adopted to screen promising interconnect metals with high electrical conductivity at ultranarrow dimensions. However, the $\rho \lambda$ has been calculated without addressing the validity of the assumption that the MFP is independent of the wavevector $\mathbf{k}$. Here, we assess the validity of the constant MFP approximation, by estimating the $\mathbf{k}$-dependent MFPs for (an)isotropic elemental metals, with explicit treatment of electron-phonon interactions. Additionally, we verify the validity of the constant relaxation time approximation (CRTA) for resistivity calculations. We show that both the constant MFP approximation and CRTA are reasonable even for highly anisotropic Fermi surfaces. Our results support the practical use of those approximations in transport studies, where explicit electron-phonon calculations are not feasible.