Modeling and control of film porosity in thin film deposition

Chemical Engineering Science

Volumn 64, Issue 16, 2009, Pages 3668-3682

  Hu, Gangshi ^a   Orkoulas, Gerassimos ^a   Christofides, Panagiotis D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Materials processing; Model predictive control; Process control; Process modeling; Process simulation; Thin films

Indexed keywords

ATOM ADSORPTION; DEPOSITION PROCESS; EXPECTED VALUES; FILM POROSITY; KINETIC MONTE CARLO SIMULATION; LEAST SQUARE METHODS; MATERIALS PROCESSING; MODEL PREDICTIVE CONTROL ALGORITHM; MODELING AND CONTROL; PROCESS MODELING; PROCESS SIMULATION; RUN TO RUN; SIMULATION RESULT; SITE OCCUPANCY; STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS; SUBSTRATE TEMPERATURE; SYSTEMATIC METHODOLOGY; THIN-FILM DEPOSITIONS; TIME EVOLUTIONS; TRIANGULAR LATTICE;

ADSORPTION; ORDINARY DIFFERENTIAL EQUATIONS; POROSITY; PREDICTIVE CONTROL SYSTEMS; QUALITY CONTROL; SIMULATORS; STOCHASTIC MODELS; THIN FILM DEVICES; THIN FILMS;

MODEL PREDICTIVE CONTROL;

EID: 67649784521     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2009.05.008     Document Type: Article

References (43)

1. Åström K.J. Introduction to Stochastic Control Theory (1970), Academic Press, New York
2. Armaou A., Siettos C.I., and Kevrekidis I.G. Time-steppers and 'coarse' control of distributed microscopic processes. International Journal of Robust and Nonlinear Control 14 (2004) 89-111
3. Ballestad A., Ruck B.J., Schmid J.H., Adamcyk M., Nodwell E., Nicoll C., and Tiedje T. Surface morphology of GaAs during molecular beam epitaxy growth: comparison of experimental data with simulations based on continuum growth equations. Physical Review B 65 (2002) 205302
4. Bohlin T., and Graebe S.F. Issues in nonlinear stochastic grey-box identification. International Journal of Adaptive Control and Signal Processing 9 (1995) 465-490
5. Buzea C., and Robbie K. State of the art in thin film thickness and deposition rate monitoring sensors. Reports on Progress in Physics 68 (2005) 385-409
6. Christofides P.D., Armaou A., Lou Y., and Varshney A. Control and Optimization of Multiscale Process Systems (2008), Birkhäuser, Boston
7. Cuerno R., Makse H.A., Tomassone S., Harrington S.T., and Stanley H.E. Stochastic model for surface erosion via ion sputtering: Dynamical evolution from ripple morphology to rough morphology. Physical Review Letters 75 (1995) 4464-4467
8. Edwards S.F., and Wilkinson D.R. The surface statistics of a granular aggregate. Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 381 (1982) 17-31
9. Fichthorn K.A., and Weinberg W.H. Theoretical foundations of dynamical Monte Carlo simulations. Journal of Chemical Physics 95 (1991) 1090-1096
10. Gillespie D.T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22 (1976) 403-434
11. Hu G., Lou Y., and Christofides P.D. Dynamic output feedback covariance control of stochastic dissipative partial differential equations. Chemical Engineering Science 63 (2008) 4531-4542
12. Hu G., Lou Y., and Christofides P.D. Model parameter estimation and feedback control of surface roughness in a sputtering process. Chemical Engineering Science 63 (2008) 1800-1816
13. Kan H.C., Shah S., Tadyyon-Eslami T., and Phaneuf R.J. Transient evolution of surface roughness on patterned GaAs(001) during homoepitaxial growth. Physical Review Letters 92 (2004) 146101
14. Kardar M., Parisi G., and Zhang Y.C. Dynamic scaling of growing interfaces. Physical Review Letters 56 (1986) 889-892
15. Keršulis S., and Mitin V. Monte Carlo simulation of growth and recovery of silicon. Material Science & Engineering B 29 (1995) 34-37
16. Kloster G., Scherban T., Xu G., Blaine J., Sun B., and Zhou Y. Porosity effects on low-k dielectric film strength and interfacial adhesion. Proceedings of the IEEE 2002 International Interconnect Technology Conference (2002) 242-244
17. Kristensen N.R., Madsen H., and Jorgensen S.B. Parameter estimation in stochastic grey-box models. Automatica 40 (2004) 225-237
18. Lauritsen K.B., Cuerno R., and Makse H.A. Noisy Kuramote-Sivashinsky equation for an erosion model. Physical Review E 54 (1996) 3577-3580
19. Levine S.W., and Clancy P. A simple model for the growth of polycrystalline Si using the kinetic Monte Carlo simulation. Modelling and Simulation in Materials Science and Engineering 8 (2000) 751-762
20. Lou Y., and Christofides P.D. Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models. Chemical Engineering Science 58 (2003) 3115-3129
21. Lou Y., and Christofides P.D. Feedback control of growth rate and surface roughness in thin film growth. A.I.Ch.E. Journal 49 (2003) 2099-2113
22. Lou Y., and Christofides P.D. Feedback control of surface roughness of GaAs (001) thin films using kinetic Monte-Carlo models. Computers & Chemical Engineering 29 (2004) 225-241
23. Lou Y., and Christofides P.D. Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation. Computers & Chemical Engineering 29 (2005) 741-759
24. Lou Y., and Christofides P.D. Feedback control of surface roughness using stochastic PDEs. A.I.Ch.E. Journal 51 (2005) 345-352
25. Lou Y., and Christofides P.D. Nonlinear feedback control of surface roughness using a stochastic PDE: design and application to a sputtering process. Industrial & Engineering Chemistry Research 45 (2006) 7177-7189
26. Lou Y., Hu G., and Christofides P.D. Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process. A.I.Ch.E. Journal 54 (2008) 2065-2081
27. Makov G., and Payne M.C. Periodic boundary conditions in ab initio calculations. Physical Review B 51 (1995) 4014-4022
28. Maksym P.B. Fast Monte Carlo simulation of MBE growth. Semiconductor Science and Technology 3 (1988) 594-596
29. Ni D., and Christofides P.D. Dynamics and control of thin film surface microstructure in a complex deposition process. Chemical Engineering Science 60 (2005) 1603-1617
30. Ni D., and Christofides P.D. Multivariable predictive control of thin film deposition using a stochastic PDE model. Industrial & Engineering Chemistry Research 44 (2005) 2416-2427
31. Reese J.S., Raimondeau S., and Vlachos D.G. Monte Carlo algorithms for complex surface reaction mechanisms: efficiency and accuracy. Journal of Computational Physics 173 (2001) 302-321
32. Shitara T., Vvedensky D.D., Wilby M.R., Zhang J., Neave J.H., and Joyce B.A. Step-density variations and reflection high-energy electron-diffraction intensity oscillations during epitaxial growth on vicinal GaAs(001). Physical Review B 46 (1992) 6815-6824
33. Siettos C.I., Armaou A., Makeev A.G., and Kevrekidis I.G. Microscopic/stochastic timesteppers and "coarse" control: a kMC example. A.I.Ch.E. Journal 49 (2003) 1922-1926
34. Varshney A., and Armaou A. Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth. Chemical Engineering Science 60 (2005) 6780-6794
35. Varshney A., and Armaou A. Identification of macroscopic variables for low-order modeling of thin-film growth. Industrial & Engineering Chemistry Research 45 (2006) 8290-8298
36. Villain J. Continuum models of crystal growth from atomic beams with and without desorption. Journal de Physique I 1 (1991) 19-42
37. Vlachos D.G., Schmidt L.D., and Aris R. Kinetics of faceting of crystals in growth, etching, and equilibrium. Physical Review B 47 (1993) 4896-4909
38. Vvedensky D.D., Zangwill A., Luse C.N., and Wilby M.R. Stochastic equations of motion for epitaxial growth. Physical Review E 48 (1993) 852-862
39. Wang L., and Clancy P. A kinetic Monte Carlo study of the growth of Si on Si(100) at varying angles of incident deposition. Surface Science 401 (1998) 112-123
40. Wang L., and Clancy P. Kinetic Monte Carlo simulation of the growth of polycrystalline Cu films. Surface Science 473 (2001) 25-38
41. Yang Y.G., Johnson R.A., and Wadley H.N. A Monte Carlo simulation of the physical vapor deposition of nickel. Acta Materialia 45 (1997) 1455-1468
42. Zhang P., Zheng X., Wu S., Liu J., and He D. Kinetic Monte Carlo simulation of cu thin film growth. Vacuum 72 (2004) 405-410
43. Ziff R.M., Gulari E., and Barshad Y. Kinetic phase transitions in an irreversible surface-reaction model. Physical Review Letters 56 (1986) 2553-2556