期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 228, 期 5, 页码 1770-1789出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.11.010
关键词
Quantum and drift-diffusion models; Density-gradient; Schrodinger-Poisson; Functional iterations; Finite element method; Nanoscale semiconductor devices; Semi-linear elliptic systems
资金
- Mathematics Applications Consortium for Science and Industry in Ireland (MACSI)
- Science Foundation Ireland (SFI)
- ONR/Darpa [LLCN00014-05-C-0241]
- M.U.R.S.T. [2006013187-003]
This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM), proposed in [C. de Falco, A.L. Lacaita, E. Gatti, R. Sacco, Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices, J. Comp. Phys. 204 (2) (2005) 533-561] for the decoupled solution of the Quantum Drift-Diffusion (QDD) model. The solution of the problem is characterized as being a 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 non-constructive proofs [N.B. Abdallah, A. Unterreiter, On the stationary quantum drift-diffusion model, Z. Angew. Math. Phys. 49 (1998) 251-275, R. Pinnau, A. Unterreiter, The stationary current-voltage characteristics of the quantum drift-diffusion model, SIAM J. Numer. Anal. 37 (1) (1999) 211-245]. The finite element approximation of the GGM is illustrated, and the main properties of the numerical fixed point map (discrete maximum principle and order of convergence) are discussed. Numerical results on realistic nanoscale devices are included to support the theoretical conclusions. (C) 2008 Elsevier Inc. All rights reserved.
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