Extending the Schottky–Mott Rule to Atomic Thickness: Descriptors for Two-Dimensional Semiconductor–Metal Contacts

Ultralow-resistance Ohmic contacts at two-dimensional (2D) semiconductor-metal interfaces are pivotal for advancing next-generation electronics, yet the classical Schottky-Mott rule fails in 2D systems due to quantum confinement and pronounced Fermi-level pinning. Here, we use domain knowledge with machine learning to derive compact, physically interpretable Schottky-barrier descriptors that quantitatively characterize interfacial carrier behavior and accurately predict barrier heights from intrinsic parameters (work function and electronegativity). Applying these descriptors to transition metal dichalcogenides and various metal substrates, we identify 12 promising Ohmic contact electrodes from 1392 heterojunctions. We further introduce a physically grounded Schottky-barrier factor (δ) and reformulate the Schottky-Mott rule by explicitly coupling the interfacial work function difference (Δ<i>W</i>_<i>F</i>) with the electronegativity mismatches (Δχ). The co-modulation of Δ<i>W</i>_<i>F</i> and Δχ governs the Schottky-barrier formation at semiconductor-metal interfaces. This work extends Schottky-Mott physics to the atomic limit and offers practical design rules for engineering low-resistance 2D contacts.