Paper Details

Name: Pooja Kumari
Country: India

Year: 2025
Volume: Volume-12, Issue-2 (July-December)
Page Number: 309-317
DOI: https://doi.org/10.5281/zenodo.17830115

ABSTRACT
As MOS transistors approach sub-5-nm channel lengths, traditional drift–diffusion transport
breaks down, and charge carriers increasingly propagate through the channel via quasiballistic and direct source-to-drain tunnelling pathways. Understanding the ballistic–
tunnelling transition thus becomes essential for predicting device behaviour, assessing scaling
limits, and designing next-generation CMOS technologies. This paper presents a
comprehensive theoretical model describing the continuous evolution of electronic transport
from semi-classical ballistic injection to quantum-mechanical tunnelling in nanoscale MOS
transistors. The analysis is based on a hybrid approach integrating Landauer–Büttiker
formalism, non-equilibrium Green’s functions (NEGF), and Wentzel–Kramers–Brillouin
(WKB) tunnelling approximations. These frameworks collectively capture mode-resolved
carrier injection, transmission probability, quantum confinement, and barrier thinning within
aggressively scaled channels. Analytical derivations reveal that ballistic transport dominates
when the channel length is comparable to or smaller than the mean free path (≈5–15 nm
for Si and ≈20–30 nm for III–V materials), whereas tunnelling becomes prominent when
effective barrier height decreases due to short-channel electrostatics, high-k dielectrics, and
subthreshold drain fields. The model identifies a critical “crossover regime”, typically within
nm, where neither conventional drift–diffusion nor pure tunnelling models adequately
describe current flow. Instead, carrier transmission is governed by combined thermionic–
ballistic injection and direct/phonon-assisted tunnelling across a triangular or trapezoidal
barrier. The proposed analytical expressions for transmission coefficient , quantum
capacitance, and injection velocity are benchmarked against NEGF simulation data and
experimentally measured short-channel transfer characteristics. Results show excellent
agreement in predicting off-state leakage, subthreshold swing degradation, and saturation
current roll-off. The model further highlights how gate oxide thickness, material effective
mass, channel orientation, and dielectric engineering influence the ballistic–tunnelling
balance in nanoscale devices.
Keywords: Ballistic transport; quantum tunneling; nanoscale MOS transistors; Landauer–
Büttiker formalism; WKB approximation; non-equilibrium Green’s function (NEGF); shortchannel effects; electrostatic barrier engineering;