Quantum Corrected Drift-Diffusion Models: Solution Fixed Point Map and Finite Element Approximation

By: Carlo de Falco, Joseph W. Jerome, and Riccardo Sacco

This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM) for the decoupled solution of the Quantum Drift--Diffusion (QDD) model. The solution of the problem is characterized as the fixed point of the GGM, which permits the establishment of a close link between the theoretical existence analysis and the implementation of a numerical tool which was lacking in previous nonconstructive proofs. The finite element approximation of the GGM is illustrated, and the main properties of the numerical fixed point map (discrete maximum principles and order of convergence) are discussed. Numerical results on realistic nanoscale devices are included to support the theoretical conclusions. This paper has appeared in the Journal of Computational Physics: 228 (2009), 1770--1789. Reference doi: 10.1016/j.jcp.2008.11.010. It can be viewed in the following format: