Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31824
Simulation of a Multi-Component Transport Model for the Chemical Reaction of a CVD-Process

Authors: J. Geiser, R. Röhle


In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1240


[1] U.M. Ascher, St.J. Ruuth and R.J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Applied Numerical Mathematics, vol. 25, no. 2-3, 151-167, 1997.
[2] P. Buchner, A. Datz, K. Dennerlein, S. Lang and M. Waidhas. Low-cost air-cooled PEFC stacks. Journal of Power Sources, vol. 105, iss. 2, 243- 249, 2002.
[3] J.C. Butcher. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons Ltd, Chichester, 2003.
[4] D.J. Christie. Target material pathways model for high power pulsed magnetron sputtering. J. Vac. Sci. Technol., A 23 (2), 330-335, 2005.
[5] P. Csom'os, I. Farag'o and A. Havasi. Weighted sequential splittings and their analysis. Comput. Math. Appl., (to appear)
[6] K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations. Springer, New York, 2000.
[7] I. Farago, and Agnes Havasi. On the convergence and local splitting error of different splitting schemes. Eötvös Lorand University, Budapest, 2004.
[8] I. Farago. Splitting methods for abstract Cauchy problems. Lect. Notes Comp.Sci. 3401, Springer Verlag, Berlin, 2005, pp. 35-45
[9] I. Farago, J. Geiser. Iterative Operator-Splitting methods for Linear Problems. Preprint No. 1043 of theWeierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany, June 2005.
[10] P. Frolkoviˇc and H. De Schepper. Numerical modelling of convection dominated transport coupled with density driven flow in porous media. Advances in Water Resources, 24:63-72, 2001.
[11] J. Geiser. Numerical Simulation of a Model for Transport and Reaction of Radionuclides. Proceedings of the Large Scale Scientific Computations of Engineering and Environmental Problems, Sozopol, Bulgaria, 2001.
[12] J. Geiser. Gekoppelte Diskretisierungsverfahren für Systeme von Konvektions- Dispersions-Diffusions-Reaktionsgleichungen. Doktor- Arbeit, Universit¨at Heidelberg, 2003.
[13] J.Geiser.R3T: Radioactive-Retardation-Reaction-Transport-Program for the Simulation of radioactive waste disposals. Proceedings: Computing, Communications and Control Technologies: CCCT 2004, The University of Texas at Austin and The International Institute of Informatics and Systemics (IIIS), to appear, 2004.
[14] 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, 58, 737-752, 1998.
[15] J. Jansen. Acceleration of waveform relaxation methods for linear ordinary and partial differential equations PhD-thesis, Department of Computer Science, K.U.Leuven, Belgium, 1999.
[16] D. Keffer, H.T. Davis and A.V. McCormick, The effect of nanopore shape on the structure and isotherms of adsorbed fluids, Springer Netherlands, Vol. 2, No. 1, 1996
[17] R.J. Kaye and A.Sangiovanni-Vincentelli. Solution of piecewiese-linear ordinary differential equations using waveform relaxation and laplace transform. IEEE Transaction on systems, MAN, and Cybernetics, Vol. SMC-13, No. 4, 1983.
[18] M.A. Lieberman and A.J. Lichtenberg. Principle of Plasma Discharges and Materials Processing. Wiley-Interscience, AA John Wiley & Sons, Inc Publication, Second edition, 2005.
[19] Chr. Lubich. A variational splitting integrator for quantum molecular dynamics. Report, 2003.
[20] M. Ohring. Materials Science of Thin Films. Academic Press, San Diego, New York, Boston, London, Second edition, 2002.
[21] A.E. Scheidegger. General theory of dispersion in porous media. Journal of Geophysical Research, 66:32-73, 1961.
[22] T.K. Senega and R.P. Brinkmann. A multi-component transport model for nonequilibrium low-temperature low-pressure plasmas. J. Phys. D: Appl.Phys., 39, 1606-1618, 2006.
[23] S. Vandewalle. Parallel Multigrid Waveform Relaxation for Parabolic Problems. B.G. Teubner, Stuttgart, 1993.
[24] K.R. Westerterp, W.P.M. van Swaaij and A.A.C.M. Beenackers. Chemical Reactor Design and Operation. John Wiley and Sons, New York, Brisbane, Toronto, Singapore, 1984.