A classical-quantum coupling strategy for a hierarchy of one dimensional models for semiconductors

Clément Jourdana (1) , Paola Pietra (2) , Nicolas Vauchelet (3, 4)

1 EDP - Equations aux Dérivées Partielles
2 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche
3 LJLL - Laboratoire Jacques-Louis Lions
4 MAMBA - Modelling and Analysis for Medical and Biological Applications

We consider one dimensional coupled classical-quantum models for quantum semiconductor device simulations. The coupling occurs in the space variable : the domain of the device is divided into a region with strong quantum effects (quantum zone) and a region where quantum effects are negligible (classical zone). In the classical zone, transport in diffusive approximation is modeled through diffusive limits of the Boltzmann transport equation. This leads to a hierarchy of classical model. The quantum transport is described by the Schrödinger equation. The aim of this work is to focus on the derivation of boundary conditions at the interface between the classical and quantum regions for this hierarchy of models. Numerical simulations are provided for a resonant tunneling diode with an Energy-Transport model.

Mots clés: Schrödinger equation; Boltzmann equation; energy transport system; spherical harmonic expansion system; semiconductors; interface conditions; mixed finite elements.; mixed finite elements

Domaines: Equations aux dérivées partielles [math.AP]

Clément Jourdana, Paola Pietra, Nicolas Vauchelet. A classical-quantum coupling strategy for a hierarchy of one dimensional models for semiconductors. 2014. ⟨hal-01052415v1⟩