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

The figure of meritρλ-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, theρλhas been calculated without addressing the validity of the assumption that the MFP is independent of the wavevectork. Here, we assess the validity of the constant MFP approximation, by estimating thek-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.