AMaSiS 2018 Workshop: Abstracts

A quantum drift diffusion model for strongly confined nanostructures: Modeling, numerics and hybrid strategy

Clément Jourdana${}^{\mathbf{\text{(1)}}}$ and Paola Pietra${}^{\mathbf{\text{(2)}}}$

(1) Université Grenoble Alpes, Laboratoire Jean Kuntzmann

(2) Istituto di Matematica Applicata e Tecnologie Informatiche - CNR

In strongly confined nanostructures, such as carbon nanotubes, the electron transport occurs in the longitudinal direction only, with effect on the characteristic physical quantities of the material under consideration. The crystal lattice can be considered as periodic in the one dimensional longitudinal direction only, keeping an atomistic description of the entire cross-section. Starting from this point of view, in [1] it is obtained an effective mass model, consisting 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. A Quantum-Drift-Diffusion is then derived in [2], following the entropy maximization approach of [3], incorporating the effective quantity of the Schrödinger approach into the definition of the entropy. In order to simulate the electron transport in a gate-all-around Carbon Nanotube Field Effect Transistor, a hybrid strategy coupling the QDD model in the source-drain regions and the Schrödinger equations in the channel is used. Moreover, self-consistent computations include the resolution of a Poisson equation in the whole 3D domain.