Stabilized mixed finite elements for fluid models in semiconductors

Abstract

In this article we deal with the numerical simulation of semiconductor devices using the Energy-Balance (EB) transport model. This accounts for hot electrons behaviour and nonlocal effects which are of utmost relevance in the simulation of submicron devices. We propose an efficient and accurate solver for the EB equations based on the well-known Gummel’s decoupled algorithm to handle iteratively the full system, while the discretization employs cell-centred Mixed Finite Volume (MFV) methods. These are derived from the standard Raviart-Thomas (RT) finite elements of lowest degree through a suitable quadrature formula which diagonalizes the element mass matrix. Numerical results to validate the newly proposed stabilized method are reported including the simulation of a model curved p-n diode, a one-dimensional p-n diode and a realistic state-of-the-art 1 μm-channel nMOS transistor.