Communications in Mathematical Sciences

Volume 12 (2014)

Number 1

Numerical simulations of an energy-transport model for partially quantized particles

Pages: 99 – 123



Paola Pietra (Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”, CNR, Pavia, Italy)

Nicolas Vauchelet (Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, Paris, France)


A coupled quantum-classical model describing the transport of electrons confined in nanoscale semiconductor devices is considered. Using the subband decomposition approach allows us 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 models is obtained, leading to subband SHE and energy-transport models with explicit expression of the diffusion coefficients. The energy-transport-Schrödinger-Poisson model is then used for the numerical simulation of the transport of the electron gas in an ultra-scaled Double-Gate-MOSFET.


Schrödinger equation, energy-transport system, subband model, nanotransistor, gummel iterations, mixed finite elements

2010 Mathematics Subject Classification

35J10, 65M60, 65Z05, 76P05, 82D37, 82D80

Published 20 August 2013