A Hybrid Classical-Quantum Transport Model for the Simulation of Carbon Nanotube Transistors

Abstract

In this paper, we propose a hybrid classical-quantum approach to study the electron transport in strongly confined nanostructures. The device domain is made of an active zone (where quantum effects are strong) sandwiched between two electron reservoirs (where the transport is considered highly collisional). A one dimensional effective mass Schrödinger system is coupled with a drift-diffusion model, both taking into account the peculiarities due to the strong confinement and to the two dimensional transversal crystal structure. Interface conditions are built preserving the continuity of the total current. Self-consistent computations are performed coupling the hybrid transport equations with the resolution of a Poisson equation in the whole three dimensional domain. To illustrate this hybrid strategy, we present simulations of a gate-all-around single-walled Carbon Nanotube Field-Effect Transistor.

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

“…that appears in (19). In the sequel, this extremal solution will be called quantum Maxwellian and denoted M n (w n ).…”

“…We obviously notice that the sum over all the bands gives the density N q . Next, as in [9] and [19], the transformation from the one dimensional transport direction to the entire nanostructure is done by means of the quantities g n 's (7). It leads to the definition of a three dimensional density…”

“…Again numerical results are performed for a CNTFET. We compare, analyzing the different current-voltage characteristics, this hybrid approach with the two non hybrid models (effective mass QDD or Schrödinger used in the entire domain) and also with the hybrid DD-Schrödinger strategy described in [19].…”

Hybrid coupling of a one-dimensional energy-transport Schrödinger system

“…Injecting it into the above SHE model and identifying the terms with equal powers of β, we get 27) where DS e (F 0 ) · F 1 denotes the Fréchet derivative of the operator S e at F 0 applied to F 1 . We recall (see e.g.…”

“…Fluid models taking into account localized kinetic effects are obtained and simulated in [17]. Finally, in the framework of strongly confined nanostructures, a hybrid approach [27] has been recently proposed to spatially couple a multiband Schrödinger system [8] with a nanowire drift-diffusion model [28], preserving the continuity of the current.…”