Momentum-Resolved Relaxation-Time Approach for Size-Dependent Conductivity in Anisotropic Metallic Films

Abstract

Shrinking CMOS interconnect dimensions to the nanometer scale intensifies electron scattering at surfaces, interfaces, and grain boundaries, causing severe conductivity loss and challenging copper-based designs. Here we present a momentum-resolved relaxation time framework that integrates density functional theory with the semiclassical Boltzmann transport equation to predict size-dependent resistivity in metallic thin films. Electron phonon interactions are computed from first principles, and anisotropic surface and grain boundary scattering is captured through a momentum dependent mean free path, allowing relaxation times to vary spatially and directionally without empirical fitting. Applied to isotropic (Cu, Ag, Au) and anisotropic (W, Ti$_2$GeC) metals, the model achieves excellent agreement with experiments and uncovers the critical role of crystallographic anisotropy in transport. We further identify layered MAX phase compounds as promising ultrathin interconnects. This work provides a predictive, physically rigorous, and computationally efficient route to designing high-performance conductors for next generation nanoelectronics.