Multidimensional Nanoscale device modeling: the Finite Element Method applied to the Non-Equilibrium Green’s Function formalism

This work deals with the modeling and the numerical simulation of quantum transport in multidimensional open nanoscale devices. The electron transport in the device is described using the Non-Equilibrium Green’s Functions (NEGF) formalism and the variational form of the problem is solved using the finite element method (FEM). In this approach, the derivation of the boundary conditions at the interfaces of the device with the reservoirs, is used to calculate the self-energy functions. The FEM allows us to consider very complex geometries and nonuniform mesh, while the NEGF is a powerful formalism which will allow to include scattering in the problem. The simulations are performed by solving self-consistently the NEGF (equivalent to the open Schrödinger equation in ballistic regime) for the transport problem and the Poisson equation to account for the space charge effects.