Finite element based three dimensional Schrödinger solver for nano-scale devices

Abstract

Using a finite element based treatment, the Schrödinger equation is solved in 3D for non-planer devices like FinFETs. Discrete states appearing because of three dimensional geometric and electrostatic confinement in a FinFET are used to calculate the quantum mechanical charge which is solved self-consistently with the Poisson equation in FIELDAY. A hybrid approach is used in which the Schrödinger solver is active in a smaller region and continuum models are used in the remaining simulation domain. The domain is chosen such that it is possible to match the quantum charge and the continuum charge. The methodology and results from this Schrödinger–Poisson solver are presented here and the need to include these effects is highlighted.