Construction of stochastic PDEs for feedback control of surface roughness in thin film deposition

Proceedings of the American Control Conference

Volumn 4, Issue , 2005, Pages 2540-2547

  Ni, Dong ^a   Christofides, Panagiotis D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

THIN FILM DEPOSITION;

COMPUTER SIMULATION; DEPOSITION; FEEDBACK CONTROL; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC CONTROL SYSTEMS; SURFACE ROUGHNESS;

THIN FILMS;

EID: 23944453411     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. A. Armaou and P. D. Christofides. Plasma-enhanced chemical vapor deposition: Modeling and control. Chem. Eng. Sci., 54:3305-3314, 1999.
2. A. Armaou, C. I. Siettos, and I. G. Kevrekidis. Time-steppers and 'coarse' control of distributed microscopic processes. Int. J. Robust Nonlin. Control, 14:89-111, 2004.
3. K. J. Åström. Introduction to Stochastic Control Theory. Academic Press, New York, 1970.
4. P. D. Christofides. Nonlinear and Robust Control of Partial Differential Equation Systems: Methods and Applications to Transport-Reaction Processes. Birkhouser, Boston, 2001.
5. S. F. Edwards and D. R. Wilkinson. The surface statistics of a granular aggregate. Proc. R. Soc. Lond. A, 381:17-31, 1982.
6. K. A. Fichthorn and W. H. Weinberg. Theoretical foundations of dynamic Monte Carlo simulations. J. Chem. Phys., 95:1090-1096, 1991.
7. M. A. Gallivan and R. M. Murray. Reduction and identification methods for Markovian control systems, with application to thin film deposition. Int. J. Robust Nonlin. Control, 14:113-132, 2004.
8. P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. Procedures for optimization problems with a mixture of bounds and general linear constraints. ACM Trans. Math. Software, 10:282-298, 1984.
9. D. T. Gillespie. A general method for numerical simulating the stochastic time evolution of coupled chemical reactions. J Camp. Phys., 22:403-434, 1976.
10. M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos. Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. J. Comp. Phys., 186:250-278, 2003.
11. K. B. Lauritsen, R. Cuerno, and H. A. Makse. Noisy Kuramote-Sivashinsky equation for an erosion model. Phys. Rev. E, 54:3577-3580, 2003.
12. Y. Lou and P. D. Christofides. Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models. Chem. Eng. Sci., 58:3115-3129, 2003.
13. Y. Lou and P. D. Christofides. Feedback control of growth rate and surface roughness in thin film growth. A.I.Ch.E J., 49:2099-2113, 2003.
14. Y. Lou and P. D. Christofides. Feedback control of surface roughness of GaAs (001) thin films using kinetic Monte-Carlo models. Comp. & Chem. Eng., 29:225-241, 2004.
15. Y. Lou and P. D. Christofides. Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation. Comp. Chem. Eng., 29:741-759, 2005.
16. Y. Lou and P. D. Christofides. Feedback control of surface roughness using stochastic PDEs. AIChE J., 51:345-352, 2005.
17. M. Marsili, A. Maritan, F. Toigo, and J.R. Banavar. Stochastic growth equations and reparametrization invariance. Rev. Mod. Phys., 68:963-983, 1996.
18. D. Ni and P. D. Christofides. Construction of stochastic PDEs for feedback control of surface roughness in thin film deposition. Int. J. Robust. Nonlin. Control, submitted.
19. D. Ni and P. D. Christofides. Dynamics and control of thin film surface microstructure in a complex deposition process. Chem. Eng. Sci., 60:1603-1617, 2005.
20. D. Ni and P. D. Christofides. Multivariable predictive control of thin film deposition using a stochastic PDE model. Ind. Eng. Chem. Res., to appear, 2005.
21. 2 thin film growth. IEEE Trans. Semiconduct. Manufact., 17:221-230, 2004.
22. S. Park, D. Kim, and J. Park. Derivation of continuum stochastic equations for discrete growth models. Phys. Rev. E, 65:015102(R). 2002.
23. C. I. Siettos, A. Armaou, A. G. Makeev, and I. G. Kevrekidis. Microscopic/stochastic timesteppers and "coarse" control: a KMC example. AIChE J., 49:1922-1926, 2003.
24. M. E. Taylor and H. A. Atwater. Monte Carlo simulations of epitaxial growth: comparison of pulsed laser deposition and molecular beam epitaxy. Appl. Surf. Sci., 127:159-163, 1998.
25. A. Theodoropoulou, R. A. Adomaitis, and E. Zafiriou. Inverse model based real-time control for temperature uniformity of RTCVD. IEEE Trans. Semiconduct. Manufact., 12:87, 1999.
26. D. G. Vlachos. Multiscale integration hybrid algorithms for homogeneous-heterogeneous reactors. AIChE J., 43:3031, 1997.
27. D. D. Vvedensky. Edwards-Wilkinson equation from lattice transition rules. Phys. Rev. E, 67:025102(R), 2003.
28. D. D. Vvedensky, A. Zangwill, C. N. Luse, and M. R. Wilby. Stochastic equations of motion for epitaxial growth. Phys. Rev. E, 48:852-862, 1993.