Quantum-corrected drift-diffusion models: Solution fixed point map and finite element approximation
- School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9 (Ireland)
- Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730 (United States)
- Dipartimento di Matematica 'F.Brioschi', Politecnico di Milano, via Bonardi 9, 20133 Milano (Italy)
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.
- OSTI ID:
- 21167763
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 5 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Analysis of a Monte Carlo method for nonlinear radiative transfer
Monotone piecewise cubic interpolation: algorithms and software