First-principles investigation of thickness-dependent electrical resistivity for low-dimensional interconnects

The relentless miniaturization of transistors drives the search for alternative metals to copper for low-dimension interconnects. Indeed, some elementary metals, like ruthenium, become less resistive than copper at low dimensions, leading to smaller losses in the connection lines. For most parts, such knowledge is still lacking for binary metals and other alloys. In this work, we carry such an investigation based on first principles, combining electron-phonon and surface scatterings in the relaxation time approximation of Boltzmann's transport equation. We discuss the validity of different proxies of the resistivity at low dimensions (both for thin films and rectangular nanowires), including the so-called $\ensuremath{\rho}\ensuremath{\lambda}$ product, that do not require the computation of the electron-phonon relaxation time. We then identify a few promising binary systems that can in principle compete with copper at low dimensions, namely NiAl, RuAl, and ${\mathrm{Cu}}_{3}\mathrm{Al}$. Finally, we derive on the way the analytical solution of Boltzmann's transport equation for rectangular nanowires.