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<9 nm, Top<300 K, and JOFF is tunneling-dominated; the 3 nm device remains tunneling-dominated up to 500 K and achieves a subthreshold swing overcoming the Boltzmann tyranny (BT) via the steep slope of τ(E). However, the short-channel effect also generates leakage current and makes the transistor difficult to turn off. For Lch≥9 nm, Top>300 K, and JOFF is thermionic-dominated, and the subthreshold swing approaches (BT/αin). Consequently, the ideal channel length for 2D FETs is Lch≈10 nm. These results provide criteria for selecting the optimal operating temperature and gate-voltage windows in miniaturizing 2D FETs, and pinpoint the crossover at which quantum tunneling current becomes comparable to semiclassical thermionic emission.