Impact of Dimensional Scaling and Size Effects on Spin Transport in Copper and Aluminum Interconnects

In this paper, compact models of spin-relaxation lengths (SRLs) in copper and aluminum interconnects by incorporating contributions to spin relaxation from phonon-induced and defect-induced scatterings are developed. The proposed models have been exhaustively calibrated with experimental data from mesoscopic lateral spin valves. The compact models are used to predict the SRL in ultrascaled copper and aluminum interconnects with cross-sectional dimensions of only few hundreds of nm². Even though the SRL in bulk copper can be as large as 400 nm, it is predicted that SRL can become sub-100 nm for a 7.5-nm-wide channel in the presence of nominal size effects. It is found that the SRL in aluminum is more than that in copper for the same size effects and interconnect cross-sectional dimensions. The degradation in SRL in aluminum with size effects is slower than that in copper. Using the compact models for SRL in conjunction with spin-diffusion theory, spin injection and transport efficiency (SITE) for metallic interconnects in a conventional spin-valve configuration is quantified in the presence of phonon and defect scatterings.