Classical-to-quantum crossover in 2D TMD field-effect transistors: A first-principles study via sub-10 nm channel scaling beyond Boltzmann tyranny

Scaling field-effect transistors (FETs) into the sub-10-nm regime fundamentally alters the transport mechanism, challenging long-standing design rules. This study investigates monolayer Pt–WSe2–Pt FETs with channel lengths from 12 to 3 nm, quantifying the competition between semiclassical thermionic current and quantum tunneling. We show that quantum transport, as described by the Landauer formula, asymptotically approaches classical thermionic emission in the long-channel and high-temperature limit, in accordance with Richardson's law. In the high-temperature thermionic regime, the slope of log10(J/T) reflects the effective work function. A competition parameter ζ cleanly delineates the semiclassical-to-quantum transition, and two characteristic temperatures emerge: Top (minimizing JOFF), and Tc (thermionic onset). For Lch