In Metal-Oxide-Semiconductor Field Effect Transistors (MOSFETs) with channel length of a few tens of nanometers expected in the next few years [1], a significant fraction of electrons contributing to the drain current traverse the channel without undergoing inelastic scattering. The ``ballistic'' component is expected to increase with further scaling, and to predominate over inelastically scattered electrons in devices with channel length shorter than 30 nm [2,3].
An analytical model for ballistic MOSFETs has been initially proposed by Natori [4], and recent simulations based on semiclassical Monte Carlo codes [5] and on a scattering theory of MOSFETs [6] exhibit significant differences with respect to simulations based on drift-diffusion or energy balance models.
Nanoscale MOSFETs also exhibit a significant degree of quantum confinement
in the channel due to the high electric
field in the
direction perpendicular to the Si/SiO
interface.
A quantum simulation is consequently required to take into account
the 2D subband splitting and the lifting of the six-fold degeneracy of silicon
conduction band. This is especially required to reproduce the
experimental MOSFET threshold voltage 
, since semiclassical simulations
may underestimate by more than 100 mV [7].
We will now focus our attention on ballistic transport in nanoscaled MOSFETs, in which quantum confinement in the channel is properly taken into account, and electrons are assumed to conserve energy and transversal momentum until they reach the drain contact.