Multidimensional Discretization of the Stationary Quantum Drift-Diffusion Model for Ultrasmall MOSFET Structures

Abstract

This paper describes a new approach to construct a multidimensional discretization scheme of quantum drift-diffusion (QDD) model (or density gradient model) arising in MOSFET structures. The discretization is performed for the stationary QDD equations replaced by an equivalent form, employing an exponential transformation of variables. A multidimensional discretization scheme is constructed by making use of an exponential-fitting method in a class of conservative difference schemes, applying the finite-volume method, which leads to a consistent generalization of the Scharfetter-Gummel expression to the nonlinear Sturm-Liouville type equation. The discretization method is evaluated in a variety of MOSFET structures, including a double-gate MOSFET with thin body layer. The discretization method provides numerical stability and accuracy for carrier transport simulations with quantum confinement effects in ultrasmall MOSFET structures.