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A Scharfetter–Gummel Type Discretization of the Quantum Drift Diffusion Model
Author(s) -
Pinnau René
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310010
Subject(s) - semiclassical physics , discretization , diffusion , quantum , type (biology) , limit (mathematics) , dimension (graph theory) , stochastic drift , statistical physics , physics , mathematics , quantum mechanics , mathematical analysis , ecology , biology , statistics , pure mathematics
We derive a generalized Scharfetter–Gummel discretization of the Quantum Drift Diffusion Model in one space dimension. The scheme relies on the introduction of a generalized potential which identifies the quantum drift term. Further, the new scheme is stable in the semiclassical limit recovering the SG scheme for the classical drift diffusion equations. Numerical results for a ballistic diode are presented.