Practical Use of a Hierarchical Linear Solver Concept for 3D MOS Device Simulation

  • O. Heinreichsberger
  • M. Thurner
  • S. Selberherr


Three-dimensional device simulations of sidewall trench-isolated MOSFETs involve linear systems of equations that are extremely ill-conditioned if the geometric channel length exceeds 2µm. Since conventional preconditioned iterative methods tend to fail in such cases we have implemented a robust iterative linear solver using a hierarchy of incomplete factorizations of the coefficient matrix.


Iteration Count Matrix Entry Sparsity Pattern Incomplete Factor Semiconductor Device Simulator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Driessen, H.A.v.d. Vorst, Bi-CGSTAB in Semiconductor Modeling, Proc. SISDEP (1991).Google Scholar
  2. [2]
    O. Heinreichsberger et al., Fast Iterative Solution of Carrier Continuity Equations for Three-Dimensional Device Simulation, SIAM J.Sci.Stat.Comp., Vol. 13, No. 1, pp. 289–306 (1992).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    C. Pommerell, Solution of Large Unsymmetric Systems of Linear Equations, Doctoral Thesis, ETH Z”urich (1992).Google Scholar
  4. [4]
    Y. Saad, Preconditioning Techniques for Nonsymmetric and Indefinite Linear Systems, J.Comp. Appl.Math., Vol. 24, pp. 89–105 (1988).MathSciNetMATHGoogle Scholar
  5. [5]
    S.M. Sze, High-Speed Semiconductor Devices, John Wiley Si Sons, p. 177 (1990).Google Scholar
  6. [6]
    H.A.v.d. Vorst, A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Systems, SIAM J.Sci.Stat.Comp., Vol. 13, No. 2, pp. 631–644 (1992).MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • O. Heinreichsberger
    • 1
  • M. Thurner
    • 2
  • S. Selberherr
    • 1
  1. 1.Institute for MicroelectronicsTU ViennaWienAustria
  2. 2.Campus Based Engineering Center ViennaDigital Equipment CorporationWienAustria

Personalised recommendations