Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Modeling and Simulation for Physical Vapor Deposition: Multiscale Model
Authors: Jürgen Geiser, Robert Röhle
Abstract:
In this paper we present modeling and simulation for physical vapor deposition for metallic bipolar plates. In the models we discuss the application of different models to simulate the transport of chemical reactions of the gas species in the gas chamber. The so called sputter process is an extremely sensitive process to deposit thin layers to metallic plates. We have taken into account lower order models to obtain first results with respect to the gas fluxes and the kinetics in the chamber. The model equations can be treated analytically in some circumstances and complicated multi-dimensional models are solved numerically with a software-package (UG unstructed grids, see [1]). Because of multi-scaling and multi-physical behavior of the models, we discuss adapted schemes to solve more accurate in the different domains and scales. The results are discussed with physical experiments to give a valid model for the assumed growth of thin layers.Keywords: Convection-diffusion equations, multi-scale problem, physical vapor deposition, reaction equations, splitting methods.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332072
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1742References:
[1] P. Bastian, K. Birken, K. Eckstein, K. Johannsen, S. Lang, N. Neuss, and H. Rentz-Reichert. UG - a flexible software toolbox for solving partial differential equations. Computing and Visualization in Science, 1(1):27-40, 1997.
[2] S. Berg and T. Nyberg. Fundamental understanding and modeling of reactive sputtering processes. Thin Solid Films, 476, 215-230, 2005.
[3] D.J. Christie. Target material pathways model for high power pulsed magnetron sputtering. J.Vac.Sci. Technology, 23:2, 330-335, 2005.
[4] P. Csomos, I. Farago and A. Havasi. Weighted sequential splittings and their analysis. Comput. Math. Appl., (to appear)
[5] K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations. Springer, New York, 2000.
[6] I. Farago, and Agnes Havasi. On the convergence and local splitting error of different splitting schemes. E¨otv¨os Lorand University, Budapest, 2004.
[7] I. Farago. Splitting methods for abstract Cauchy problems. Lect. Notes Comp.Sci. 3401, Springer Verlag, Berlin, 2005, pp. 35-45
[8] 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.
[9] 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.
[10] J. Geiser. Gekoppelte Diskretisierungsverfahren f¨ur Systeme von Konvektions-Dispersions-Diffusions-Reaktionsgleichungen. Doktor-Arbeit, Universität Heidelberg, 2003.
[11] J. Geiser. Discretization methods with analytical solutions for convection-diffusiondispersion-reaction-equations and applications. Journal of Engineering Mathematics, published online, Oktober 2006.
[12] J. Geiser. Discretisation and Solver Methods with Analytical Methods for Advection-Diffusion-reaction Equations and 2D Applications. Journal of Porous Media, Begell House Inc., Redding, USA, accepted March, 2008.
[13] J. Geiser. Iterative Operator-Splitting Methods with higher order Time-Integration Methods and Applications for Parabolic Partial Differential Equations. Journal of Computational and Applied Mathematics, Elsevier, Amsterdam, The Netherlands, 217, 227-242, 2008.
[14] J. Geiser. Decomposition Methods for Partial Differential Equations: Theory and Applications in Multiphysics Problems. Habilitation Thesis, Humboldt University of Berlin, Germany, under review, July 2008.
[15] 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.
[16] H.H. Lee. Fundamentals of Microelectronics Processing McGraw- Hill, New York, 1990.
[17] Chr. Lubich. A variational splitting integrator for quantum molecular dynamics. Report, 2003.
[18] S. Middleman and A.K. Hochberg. Process Engineering Analysis in Semiconductor Device Fabrication McGraw-Hill, New York, 1993.
[19] M. Ohring. Materials Science of Thin Films. Academic Press, San Diego, New York, Boston, London, Second edition, 2002.
[20] P.J. Roache. A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids, 12:12591275, 1992.
[21] 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.
[22] J. Stoer and R. Burlisch. Introduction to numerical analysis. Springer verlag, New York, 1993.