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Volumn 45, Issue 21, 2006, Pages 7177-7189

Nonlinear feedback control of surface roughness using a stochastic PDE: Design and application to a sputtering process

Author keywords

[No Author keywords available]

Indexed keywords

GALERKIN'S METHOD; LINEARIZATION; NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION;

EID: 33750427024     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie060410h     Document Type: Article
Times cited : (35)

References (43)
  • 1
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • Gillespie, D. T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 1976, 22, 403-434.
    • (1976) J. Comput. Phys. , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 2
    • 36448998595 scopus 로고
    • Theoretical foundations of dynamical Monte Carlo simulations
    • Fichthorn, K. A.; Weinberg, W. H. Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys. 1991, 95, 1090-1096.
    • (1991) J. Chem. Phys. , vol.95 , pp. 1090-1096
    • Fichthorn, K.A.1    Weinberg, W.H.2
  • 3
    • 0000143169 scopus 로고
    • Step-density variations and reflection high-energy electron-diffraction intensity oscillations during epitaxial growth on vicinal GaAs-(001)
    • Shitara, T.; Vvedensky, D. D.; Wilby, M. R.; Zhang, J.; Neave, J. H.; Joyce, B. A. Step-density variations and reflection high-energy electron-diffraction intensity oscillations during epitaxial growth on vicinal GaAs-(001). Phys. Rev. B 1992, 46, 6815-6824.
    • (1992) Phys. Rev. B , vol.46 , pp. 6815-6824
    • Shitara, T.1    Vvedensky, D.D.2    Wilby, M.R.3    Zhang, J.4    Neave, J.H.5    Joyce, B.A.6
  • 4
    • 0035841075 scopus 로고    scopus 로고
    • Monte Carlo algorithms for complex surface reaction mechanisms: Efficiency and accuracy
    • Reese, J. S.; Raimondeau, S.; Vlachos, D. G. Monte Carlo algorithms for complex surface reaction mechanisms: efficiency and accuracy. J. Comput. Phys. 2001, 173, 302-321.
    • (2001) J. Comput. Phys. , vol.173 , pp. 302-321
    • Reese, J.S.1    Raimondeau, S.2    Vlachos, D.G.3
  • 5
    • 0001884774 scopus 로고
    • The surface statistics of a granular aggregate
    • Edwards, S. F.; Wilkinson, D. R. The surface statistics of a granular aggregate. Proc. R. Soc. London A 1982, 381, 17-31.
    • (1982) Proc. R. Soc. London A , vol.381 , pp. 17-31
    • Edwards, S.F.1    Wilkinson, D.R.2
  • 7
    • 0000200873 scopus 로고
    • Stochastic model for surface erosion via ion sputtering: Dynamical evolution from ripple morphology to rough morphology
    • Cuerno, R.; Makse, H. A.; Tomassone, S.; Harrington, S. T.; Stanley, H. E. Stochastic model for surface erosion via ion sputtering: dynamical evolution from ripple morphology to rough morphology. Phys. Rev. Lett. 1995, 75, 4464-4467.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 4464-4467
    • Cuerno, R.1    Makse, H.A.2    Tomassone, S.3    Harrington, S.T.4    Stanley, H.E.5
  • 8
    • 0001149866 scopus 로고    scopus 로고
    • Noisy Kuramote-Sivashinsky equation for an erosion model
    • Lauritsen, K. B.; Cuerno, R.; Makse, H. A. Noisy Kuramote-Sivashinsky equation for an erosion model. Phys. Rev. E 1996, 54, 3577-3580.
    • (1996) Phys. Rev. E , vol.54 , pp. 3577-3580
    • Lauritsen, K.B.1    Cuerno, R.2    Makse, H.A.3
  • 9
    • 0035794374 scopus 로고    scopus 로고
    • Ultraviolet-extended realtime spectroscopic ellipsometry for characterization of phase evolution in BN thin films
    • Zapien, J. A.; Messier, R.; Collin, R. W. Ultraviolet-extended realtime spectroscopic ellipsometry for characterization of phase evolution in BN thin films. Appl. Phys. Lett. 2001, 78, 1982-1984.
    • (2001) Appl. Phys. Lett. , vol.78 , pp. 1982-1984
    • Zapien, J.A.1    Messier, R.2    Collin, R.W.3
  • 12
    • 0035449005 scopus 로고    scopus 로고
    • Fundamental processes in Si/Si and Ge/Si studied by scanning tunneling microscopy during growth
    • Voigtländer, B. Fundamental processes in Si/Si and Ge/Si studied by scanning tunneling microscopy during growth. Surf. Sci. Rep. 2001, 43, 127-254.
    • (2001) Surf. Sci. Rep. , vol.43 , pp. 127-254
    • Voigtländer, B.1
  • 13
    • 0037962061 scopus 로고    scopus 로고
    • Estimation and control of surface roughness in thin film growth using kinetic Monte Carlo models
    • Lou, Y.; Christofides, P. D. Estimation and control of surface roughness in thin film growth using kinetic Monte Carlo models. Chem. Eng. Sci. 2003, 58, 3115-3129.
    • (2003) Chem. Eng. Sci. , vol.58 , pp. 3115-3129
    • Lou, Y.1    Christofides, P.D.2
  • 14
    • 0038068807 scopus 로고    scopus 로고
    • Feedback control of growth rate and surface roughness in thin film growth
    • Lou, Y.; Christofides, P. D. Feedback control of growth rate and surface roughness in thin film growth. AIChE J. 2003, 49, 2099-2113.
    • (2003) AIChE J. , vol.49 , pp. 2099-2113
    • Lou, Y.1    Christofides, P.D.2
  • 15
    • 8744309471 scopus 로고    scopus 로고
    • Feedback control of surface roughness of GaAs (001) thin films using kinetic Monte Carlo models
    • Lou, Y.; Christofides, P. D. Feedback control of surface roughness of GaAs (001) thin films using kinetic Monte Carlo models. Comput. Chem. Eng. 2004, 29, 225-241.
    • (2004) Comput. Chem. Eng. , vol.29 , pp. 225-241
    • Lou, Y.1    Christofides, P.D.2
  • 16
    • 13444263244 scopus 로고    scopus 로고
    • Dynamics and control of thin film surface microstructure in a complex deposition process
    • Ni, D.; Christofides, P. D. Dynamics and control of thin film surface microstructure in a complex deposition process. Chem. Eng. Sci. 2005, 60, 1603-1617.
    • (2005) Chem. Eng. Sci. , vol.60 , pp. 1603-1617
    • Ni, D.1    Christofides, P.D.2
  • 17
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and "coarse" control: A kMC example
    • Siettos, C. I.; Armaou, A.; Makeev, A. G.; Kevrekidis, I. G. Microscopic/stochastic timesteppers and "coarse" control: a kMC example. AIChE J. 2003, 49, 1922-1926.
    • (2003) AIChE J. , vol.49 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 18
  • 19
    • 4243979739 scopus 로고
    • Dynamic scaling of growing interfaces
    • Kardar, M.; Parisi, G.; Zhang, Y. C. Dynamic scaling of growing interfaces. Phys. Rev. Lett. 1986, 56, 889-892.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 889-892
    • Kardar, M.1    Parisi, G.2    Zhang, Y.C.3
  • 20
    • 0037095511 scopus 로고    scopus 로고
    • Surface morphology of GaAs during molecular beam epitaxy growth: Comparison of experimental data with simulations based on continuum growth equations
    • Ballestad, A.; Ruck, B. J.; Schmid, J. H.; Adamcyk, M.; Nodwell, E.; Nicoll, C.; Tiedje, T. Surface morphology of GaAs during molecular beam epitaxy growth: comparison of experimental data with simulations based on continuum growth equations. Phys. Rev. B 2002, 65, 205302.
    • (2002) Phys. Rev. B , vol.65 , pp. 205302
    • Ballestad, A.1    Ruck, B.J.2    Schmid, J.H.3    Adamcyk, M.4    Nodwell, E.5    Nicoll, C.6    Tiedje, T.7
  • 21
    • 2542427905 scopus 로고    scopus 로고
    • Transient evolution of surface roughness on patterned GaAs(001) during homoepitaxial growth
    • Kan, H. C.; Shah, S.; Tadyyon-Eslami, T.; Phaneuf, R. J. Transient evolution of surface roughness on patterned GaAs(001) during homoepitaxial growth. Phys. Rev. Lett. 2004, 92, 146101.
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 146101
    • Kan, H.C.1    Shah, S.2    Tadyyon-Eslami, T.3    Phaneuf, R.J.4
  • 22
    • 0346685924 scopus 로고    scopus 로고
    • Reduction and identification methods for markovian control systems, with application to thin film deposition
    • Gallivan, M. A.; Murray, R. M. Reduction and identification methods for markovian control systems, with application to thin film deposition. Int. J. Robust Nonlinear Control 2004, 14, 113-132.
    • (2004) Int. J. Robust Nonlinear Control , vol.14 , pp. 113-132
    • Gallivan, M.A.1    Murray, R.M.2
  • 23
    • 29144514832 scopus 로고    scopus 로고
    • Robust nonlinear feedforward-feedback control of a coupled kinetic monte carlo-finite difference simulation
    • Rusli, E.; Drews, T. O.; Ma, D. L.; Alkire, R. C.; Braatz, R. D. Robust nonlinear feedforward-feedback control of a coupled kinetic monte carlo-finite difference simulation. J. Process Control 2006, 16, 409-417.
    • (2006) J. Process Control , vol.16 , pp. 409-417
    • Rusli, E.1    Drews, T.O.2    Ma, D.L.3    Alkire, R.C.4    Braatz, R.D.5
  • 24
    • 0001776828 scopus 로고
    • Continuum models of crystal growth from atomic beams with and without desorption
    • Villain, J. Continuum models of crystal growth from atomic beams with and without desorption. J. Phys. I 1991, 1, 19-42.
    • (1991) J. Phys. I , vol.1 , pp. 19-42
    • Villain, J.1
  • 25
    • 12244249188 scopus 로고    scopus 로고
    • Feedback control of surface roughness using stochastic PDEs
    • Lou, Y.; Christofides, P. D. Feedback control of surface roughness using stochastic PDEs. AIChE J. 2005, 51, 345-352.
    • (2005) AIChE J. , vol.51 , pp. 345-352
    • Lou, Y.1    Christofides, P.D.2
  • 26
    • 13444304351 scopus 로고    scopus 로고
    • Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation
    • Lou, Y.; Christofides, P. D. Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation. Comput. Chem. Eng. 2005, 29, 741-759.
    • (2005) Comput. Chem. Eng. , vol.29 , pp. 741-759
    • Lou, Y.1    Christofides, P.D.2
  • 27
    • 23944453411 scopus 로고    scopus 로고
    • Construction of stochastic PDEs for feedback control of surface roughness in thin film deposition
    • Portland, OR
    • Ni, D.; Christofides, P. D. Construction of stochastic PDEs for feedback control of surface roughness in thin film deposition. In Proceedings of American Control Conference, Portland, OR; 2005; pp 2540-2547.
    • (2005) Proceedings of American Control Conference , pp. 2540-2547
    • Ni, D.1    Christofides, P.D.2
  • 28
    • 13444249983 scopus 로고    scopus 로고
    • Multivariable predictive control of thin film deposition using a stochastic PDE model
    • Ni, D.; Christofides, P. D. Multivariable predictive control of thin film deposition using a stochastic PDE model. Ind. Eng. Chem. Res. 2005, 44, 2416-2427.
    • (2005) Ind. Eng. Chem. Res. , vol.44 , pp. 2416-2427
    • Ni, D.1    Christofides, P.D.2
  • 31
    • 0034616305 scopus 로고    scopus 로고
    • Wave suppression by nonlinear finite-dimensional control
    • Armaou, A.; Christofides, P. D. Wave suppression by nonlinear finite-dimensional control. Chem. Eng. Sci. 2000, 55, 2627-2640.
    • (2000) Chem. Eng. Sci. , vol.55 , pp. 2627-2640
    • Armaou, A.1    Christofides, P.D.2
  • 32
    • 0001841018 scopus 로고    scopus 로고
    • Feedback control of the Kuramoto-Sivashinsky equation
    • Armaou, A.; Christofides, P. D. Feedback control of the Kuramoto-Sivashinsky equation. Physica D 2000, 137, 49-61.
    • (2000) Physica D , vol.137 , pp. 49-61
    • Armaou, A.1    Christofides, P.D.2
  • 33
    • 0000411924 scopus 로고    scopus 로고
    • Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control
    • Christofides, P. D.; Armaou, A. Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control. Syst. Control Lett. 2000, 39, 283-294.
    • (2000) Syst. Control Lett. , vol.39 , pp. 283-294
    • Christofides, P.D.1    Armaou, A.2
  • 34
    • 0141638523 scopus 로고    scopus 로고
    • Optimal actuator/sensor placement for nonlinear control of the Kuramoto-Sivashinsky equation
    • Lou, Y.; Christofides, P. D. Optimal actuator/sensor placement for nonlinear control of the Kuramoto-Sivashinsky equation. IEEE Trans. Control Syst. Technol. 2003, 11, 737-745.
    • (2003) IEEE Trans. Control Syst. Technol. , vol.11 , pp. 737-745
    • Lou, Y.1    Christofides, P.D.2
  • 36
    • 20644451605 scopus 로고    scopus 로고
    • Development of a spatially controllable chemical vapor deposition reactor with combinatorial processing capabilities
    • Choo, J. O.; Adomaitis, R. A.; Henn-Lecordier, L.; Cai, Y.; Rubloff, G. W. Development of a spatially controllable chemical vapor deposition reactor with combinatorial processing capabilities. Rev. Sci. Instrum. 2005, 76, 062217.
    • (2005) Rev. Sci. Instrum. , vol.76 , pp. 062217
    • Choo, J.O.1    Adomaitis, R.A.2    Henn-Lecordier, L.3    Cai, Y.4    Rubloff, G.W.5
  • 37
    • 4143138757 scopus 로고    scopus 로고
    • Edwards-Wilkinson equation from lattice transition rules
    • 025102R
    • Vvedensky, D. D. Edwards-Wilkinson equation from lattice transition rules. Phys. Rev. E 2003, 67, 025102(R).
    • (2003) Phys. Rev. E , vol.67
    • Vvedensky, D.D.1
  • 39
    • 0031366767 scopus 로고    scopus 로고
    • Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds
    • Christofides, P. D.; Daoutidis, P. Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds. J. Math. Anal. Appl. 1997, 216, 398-420.
    • (1997) J. Math. Anal. Appl. , vol.216 , pp. 398-420
    • Christofides, P.D.1    Daoutidis, P.2
  • 40
    • 0035254396 scopus 로고    scopus 로고
    • Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation
    • Liu, W. J.; Krstić, M. Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation. Nonlinear Anal: Theory, Methods Appl. 2001, 43, 485-507.
    • (2001) Nonlinear Anal: Theory, Methods Appl. , vol.43 , pp. 485-507
    • Liu, W.J.1    Krstić, M.2
  • 41
    • 4243683853 scopus 로고
    • Solid-on-solid models of molecular-beam epitaxy
    • Siegert, M.; Plischke, M. Solid-on-solid models of molecular-beam epitaxy. Phys. Rev. E 1994, 50, 917-931.
    • (1994) Phys. Rev. E , vol.50 , pp. 917-931
    • Siegert, M.1    Plischke, M.2


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