Modeling and Simulation for Physical Vapor Deposition: Multiscale Model
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53447", author = "Jürgen Geiser and Robert Röhle", title = "Modeling and Simulation for Physical Vapor Deposition: Multiscale Model", 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.", volume = "2", number = "11", pages = "799-9", }