Quantum-corrected drift-diffusion models for transport in semiconductor devices

  • Authors:

  • Carlo de Falco;Emilio Gatti;Andrea L. Lacaita;Riccardo Sacco

  • Affiliations:

  • Dipartimento di Matematica "F.Enriques", Universití degli Studi di Milano, via Saldini 50, 20133 Milano, Italy;DEI - Dipartimento di Elettronica e Informazione, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy;DEI - Dipartimento di Elettronica e Informazione, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, via Bonardi 9, 20133 Milano Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

In this paper, we propose a unified framework for Quantum-corrected drift-diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical drift-diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model named Schrodinger-Poisson-drift-diffusion, and the second one is the quantum-drift-diffusion (QDD) model. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions.