Ab initio transfer length method simulations of tunneling limits in 2D semiconductors

As semiconductor devices approach the sub-2 nm technology node, identifying the fundamental quantum limits of contact-resistance scaling becomes imperative; however, the transition from thermionic emission to direct tunneling remains experimentally inaccessible and theoretically ill-defined. Herein, based on multi-space constrained-search density functional theory, which self-consistently treats carrier injection and diffusive transport physics under finite bias, we perform ab initio transfer length method analyses for monolayer MoS₂ contacted by Sc, Ag, Au, and Pd electrodes in both top-contact and edge-contact geometries. We find a robust crossover in resistance scaling from metal-induced-gap-states-mediated direct tunneling in the sub-10 nm regime to thermionic emission at longer channel lengths. The extracted transition length provides a rigorous first-principles measure of the critical tunneling length, establishing a physically grounded metric for contact quality and the source-to-drain tunneling limit of 2D transistors. The method further identifies optimal contact strategies: low-work-function metal top contacts for n-type operation and high-work-function metal edge contacts for p-type operation, providing practical guidelines for scalable low-resistance contact engineering.