  A coupled quantum-classical model describing the transport of electrons
confined in nanoscale semiconductor devices is considered. Using the subband
decomposition approach allows to separate the transport directions from the
confinement direction. The motion of the gas in the transport direction is
assumed to be classical. Then a hierarchy of adiabatic quantum-classical model
is obtained, leading to subband SHE and energy-transport models, with explicit
expression of the diffusion coefficients. The
energy-transport-Schr\"odinger-Poisson model is then used for the numerical
simulation of the transport of the electron gas in an ultra-scaled
Double-Gate-MOSFET.
