An accelerated monotone iterative method for the quantum-corrected energy transport model

  • Authors:

  • Ren-Chuen Chen;Jinn-Liang Liu

  • Affiliations:

  • Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan;Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

  • Approximations of quantum corrected energy-transport model with non-parabolic energy relaxation time

    MAMECTIS/NOLASC/CONTROL/WAMUS'11 Proceedings of the 13th WSEAS international conference on mathematical methods, computational techniques and intelligent systems, and 10th WSEAS international conference on non-linear analysis, non-linear systems and chaos, and 7th WSEAS international conference on dynamical systems and control, and 11th WSEAS international conference on Wavelet analysis and multirate systems: recent researches in computational techniques, non-linear systems and control

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Abstract

A non-stationary monotone iterative method is proposed and analyzed for the quantum-corrected energy transport model in nanoscale semiconductor device simulation. For the density-gradient equations, it is analytically and numerically shown that the convergence rate of the method is optimal in the sense of Gummel's decoupling iteration. This is a globally convergent method in the sense that the initial guess can be taken as a lower or an upper solution which is independent of applied voltages. The method integrates the monotone parameters, grid sizes, and Scharfetter-Gummel fitting in an adaptive and automatic way to treat the singularly perturbed nature of the model that incurs boundary, junction, and quantum potential layers in the device.