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.
has appeared in the Journal of Computational Physics: 228 (2009),
Reference doi: 10.1016/j.jcp.2008.11.010.
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