Quantum-corrected drift-diffusion models: Solution fixed point map and finite element approximation

Carlo de Falco, Joseph W. Jerome, Riccardo Sacco*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1770-1789
Number of pages20
JournalJournal of Computational Physics
Issue number5
StatePublished - Mar 20 2009


  • Density-gradient
  • Finite element method
  • Functional iterations
  • Nanoscale semiconductor devices
  • Quantum and drift-diffusion models
  • Schrödinger-Poisson
  • Semi-linear elliptic systems

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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