Hybrid coupling of a one-dimensional Energy-Transport Schrödinger system

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. It can lead to an Energy-Transport model, obtained using a Spherical Harmonic Expansion model as intermediate step. 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. Numerical simulations are provided for a resonant tunneling diode with the Energy-Transport model.

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

Domaines: Equations aux dérivées partielles [math.AP]

Clément Jourdana, Paola Pietra, Nicolas Vauchelet. Hybrid coupling of a one-dimensional Energy-Transport Schrödinger system. Monatshefte für Mathematik, 2017, 184 (4), pp.563-596. ⟨10.1007/s00605-016-1008-8⟩. ⟨hal-01052415v2⟩