A Quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures

Clément Jourdana (1) , Paola Pietra (2)

1 EDP - Equations aux Dérivées Partielles
2 IMATI - Istituto di Matematica Applicata e Tecnologie Informatiche

In this paper we derive by an entropy minimization technique a local Quantum Drift-Diffusion (QDD) model that allows to describe with accuracy the transport of electrons in confined nanostructures. The starting point is an effective mass model, obtained by considering the crystal lattice as periodic only in the one dimensional longitudinal direction and keeping an atomistic description of the entire two dimensional cross-section. It consists of a sequence of one dimensional device dependent Schrödinger equations, one for each energy band, in which quantities retaining the effects of the confinement and of the transversal crystal structure are inserted. These quantities are incorporating into the definition of the entropy and consequently the QDD model that we obtain has a peculiar quantum correction that includes the contributions of the different energy bands. Next, in order to simulate the electron transport in a gate-all-around Carbon Nanotube Field Effect Transistor, we propose a spatial hybrid strategy coupling the QDD model in the Source/Drain regions and the Schrödinger equations in the channel. Self-consistent computations are performed coupling the hybrid transport equations with the resolution of a Poisson equation in the whole three dimensional domain.

Mots clés: entropy minimization; hybrid coupling; confined nanostructures; Schrödinger equation; carbon nanotube FETs; Quantum Drift-Diffusion model

Domaines: Equations aux dérivées partielles [math.AP]

Clément Jourdana, Paola Pietra. A Quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures. Kinetic and Related Models , 2019, 12 (1), pp.217-242. ⟨10.3934/krm.2019010⟩. ⟨hal-01452393v2⟩