Classical-to-Quantum Crossover in 2D TMD Field-Effect Transistors: A First-Principles Study via Sub-10 nm Channel Scaling Beyond the 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 TMD FETs with channel lengths from 12 nm 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 law. A competition parameter $\zeta$ cleanly delineates the semiclassical-to-quantum transition, and two characteristic temperatures emerge: $T_{op}$ (minimizing $J_{OFF}$ and $T_{c}$ (thermionic onset). For $L_{ch}<9$ nm, $T_{op}<300$ K and $J_{OFF}$ is tunneling-dominated; the 3 nm device remains tunneling-dominated up to 500 K and achieves a subthreshold swing overcoming Boltzmann tyranny via the steep slope of $\tau(E)$. However, the short-channel effect also generates leakage current and makes the transistor difficult to turn off. For $L_{ch} \geq 9$ nm, $T_{op}>300$ K and $J_{OFF}$ is thermionic-dominated, and the subthreshold swing approaches Boltzmann tyranny scaled by $\alpha_{in}}$. Consequently, the ideal channel length for 2D FETs is $L_{ch} \approx 10$ 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.