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Mathematical Problems in Engineering
Volume 2009, Article ID 728105, 34 pages
http://dx.doi.org/10.1155/2009/728105
Research Article

Adaptive Step-Size Control in Simulation of Diffusive CVD Processes

Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

Received 3 September 2008; Revised 5 January 2009; Accepted 28 January 2009

Academic Editor: José Roberto Castilho Piqueira

Copyright © 2009 Jürgen Geiser and Christian Fleck. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Hlavacek, J. Thiart, and D. Orlicki, “Morphology and film growth in CVD reactions,” Journal de Physique IV, vol. 5, pp. 3–44, 1995. View at Publisher · View at Google Scholar
  2. H. Rouch, “MOCVD research reactor simulation,” in Proceedings of the COMSOL Users Conference, pp. 1–7, Paris, France, November 2006.
  3. M. A. Lieberman and A. J. Lichtenberg, Principle of Plasma Discharges and Materials Processing, John Wiley & Sons, New York, NY, USA, 2nd edition, 2005.
  4. M. Ohring, Materials Science of Thin Films, Academic Press, San Diego, Calif, USA, 2nd edition, 2002.
  5. S. Middleman and A. K. Hochberg, Process Engineering Analysis in Semiconductor Device Fabrication, McGraw-Hill, New York, NY, USA, 1993.
  6. M. W. Barsoum and T. El-Raghy, “Synthesis and characterization of a remarkable ceramic: Ti3SiC2,” Journal of the American Ceramic Society, vol. 79, no. 7, pp. 1953–1956, 1996. View at Publisher · View at Google Scholar
  7. C. Lange, M. W. Barsoum, and P. Schaaf, “Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition,” Applied Surface Science, vol. 254, no. 4, pp. 1232–1235, 2007. View at Publisher · View at Google Scholar
  8. P. Eklund, A. Murugaiah, J. Emmerlich et al., “Homoepitaxial growth of Ti-Si-C MAX-phase thin films on bulk Ti3SiC2 substrates,” Journal of Crystal Growth, vol. 304, no. 1, pp. 264–269, 2007. View at Publisher · View at Google Scholar
  9. T. K. Senega and R. P. Brinkmann, “A multi-component transport model for non-equilibrium low-temperature low-pressure plasmas,” Journal of Physics D, vol. 39, no. 8, pp. 1606–1618, 2006. View at Publisher · View at Google Scholar
  10. J. Geiser and M. Arab, “Modelling, Optimzation and Simulation for a Chemical Vapor Deposition,” Journal of Porous Media, Begell House Inc., Redding, USA, June 2008. View at Google Scholar
  11. A. M. P. Valli, G. F. Carey, and A. L. G. A. Coutinho, “Control strategies for timestep selection in simulation of coupled viscous flow and heat transfer,” Communications in Numerical Methods in Engineering, vol. 18, no. 2, pp. 131–139, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. K. L. Chien, J. A. Hrones, and J. B. Reswick, “On the automatic tuning of generalized passive systems,” Transactions of the ASME, vol. 74, pp. 175–185, 1952. View at Google Scholar
  13. M. K. Gobbert and C. A. Ringhofer, “An asymptotic analysis for a model of chemical vapor deposition on a microstructured surface,” SIAM Journal on Applied Mathematics, vol. 58, no. 3, pp. 737–752, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. H. Lee, Fundamentals of Microelectronics Processing, McGraw-Hill, New York, NY, USA, 1990.
  15. N. B. Nichols and J. G. Ziegler, “Optimum settings for automatic controllers,” Transactions of the ASME, vol. 64, pp. 759–768, 1942. View at Google Scholar
  16. H. Lutz and W. Wendt, Taschenbuch der Regelungstechnik, Harri-Deutsch, Frankfurt, Germany, 6th edition, 2005.
  17. P. Bastian, K. Birken, K. Johannsen et al., “UG—a flexible software toolbox for solving partial differential equations,” Computing and Visualization in Science, vol. 1, no. 1, pp. 27–40, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. Geiser, “Discretization methods with embedded analytical solutions for convection-diffusion dispersion-reaction equations and applications,” Journal of Engineering Mathematics, vol. 57, no. 1, pp. 79–98, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2002. View at Zentralblatt MATH · View at MathSciNet
  20. W. Hundsdorfer and J. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, vol. 33 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2003. View at Zentralblatt MATH · View at MathSciNet
  21. J. Lee and Th. F. Edgar, “Continuation method for the modified Ziegler-Nichols tuning of multiloop control systems,” Industrial and Engineering Chemistry Research, vol. 44, no. 19, pp. 7428–7434, 2005. View at Publisher · View at Google Scholar
  22. E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II: Stiff and Differential-Algebraic Problems, vol. 14 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2nd edition, 1996. View at Zentralblatt MATH · View at MathSciNet
  23. I. Faragó and Á. Havasi, “On the convergence and local splitting error of different splitting schemes,” Progress in Computational Fluid Dynamics, vol. 5, no. 8, pp. 495–504, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  24. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, vol. 194 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2000. View at Zentralblatt MATH · View at MathSciNet
  25. T. Yamaguchi and K. Shimizu, “Asymptotic stabilization by PID control: stability analysis based on minimum phase and high-gain feedback,” Electrical Engineering in Japan, vol. 156, no. 1, pp. 44–53, 2006. View at Publisher · View at Google Scholar