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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 27 — Sep. 20, 2006
  • pp: 7043–7055

State estimation approach for determining composition and growth rate of Si1− x Ge x chemical vapor deposition utilizing real-time ellipsometric measurements

Scott A. Middlebrooks and James B. Rawlings  »View Author Affiliations

Applied Optics, Vol. 45, Issue 27, pp. 7043-7055 (2006)

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We present an algorithm that simultaneously deduces from real-time ellipsometric measurements both the growth rate and the composition of Si 1 - x Ge x films deposited via chemical vapor deposition. The heart of the algorithm is a dynamic, first-principles model of the deposition system and the ellipsometric sensor. The model predicts the ellipsometric parameters Ψ and Δ during film growth. An extended Kalman filter is developed that utilizes the sensor model and infers both the growth rate and the Ge composition of the deposited film in real time. Two simulations demonstrating the effectiveness of the algorithm are evaluated.

© 2006 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(310.1860) Thin films : Deposition and fabrication

Original Manuscript: October 26, 2005
Revised Manuscript: April 4, 2006
Manuscript Accepted: May 12, 2006

Scott A. Middlebrooks and James B. Rawlings, "State estimation approach for determining composition and growth rate of Si1-xGex chemical vapor deposition utilizing real-time ellipsometric measurements," Appl. Opt. 45, 7043-7055 (2006)

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  1. F. Glowacki and Y. Campidelli, "Single wafer epitaxy of Si and SiGe using UHV-CVD," Microelectron. Eng. 25, 161-170 (1994). [CrossRef]
  2. B. Meyerson, "UHV/CVD growth of Si and SiGe alloys: chemistry, physics, and device applications," Proc. IEEE 80, 1592-1608 (1992). [CrossRef]
  3. B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988). [CrossRef]
  4. B. Meyerson, "Low temperature silicon epitaxy by UHV/CVD," Appl. Phys. Lett. 48, 797-799 (1986). [CrossRef]
  5. M. Racanelli and D. Greve, "Low-temperature selective epitaxy by ultrahigh-vacuum chemical vapor deposition from SiH4 and GeH4/H2," Appl. Phys. Lett. 58, 2096-2098 (1991). [CrossRef]
  6. T. E. Wilke, K. A. Turner, and C. G. Takoudis, "Chemical vapor deposition of silicon under reduced pressure in hot-wall reactors," Chem. Eng. Sci. 41, 643-650 (1986). [CrossRef]
  7. G. Zhou and H. Morkoc, "Si/SiGe heterostructures and devices," Thin Solid Films 231, 125-142 (1993). [CrossRef]
  8. O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989). [CrossRef]
  9. D. E. Aspnes, "Effects of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers," J. Opt. Soc. Am. 64, 812-819 (1974). [CrossRef]
  10. D. E. Aspnes, "Optimizing precision of rotating-analyzer ellipsometers," J. Opt. Soc. Am. 64, 639-646 (1974). [CrossRef]
  11. D. E. Aspnes and A. A. Studna, "High precision scanning ellipsometer," Appl. Opt. 14, 220-228 (1975). [PubMed]
  12. W. M. Duncan, S. A. Henck, J. W. Kuehne, L. M. Lowenstein, and S. Maung, "High-speed spectral ellipsometry for in situ diagnostics and process control," J. Vac. Sci. Technol. B. 12, 2779-2784 (1994). [CrossRef]
  13. G. E. Jellison and F. A. Modine, "Two-channel polarization modulation ellipsometer," Appl. Opt. 29, 959-974 (1990). [CrossRef] [PubMed]
  14. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  15. G. Bauer and W. Richter, Optical Characterization of Epitaxial Semiconductor Layers (Springer-Verlag, 1996). [CrossRef]
  16. W. Chen, R. Westhoff, and R. Reif, "Determination of optical constants of strained Si1−xGex epitaxial layers in the spectral range of 0.75-2.75 eV," Appl. Phys. Lett. 71, 1525-1527 (1997). [CrossRef]
  17. R. Lange, K. E. Junge, S. Zollner, S. S. Iyer, A. P. Powell, and K. Eberl, "Dielectric response of strained and relaxed Si1−x−yGexCy alloys grown by molecular beam epitaxy on Si(001)," J. Appl. Phys. 80, 4578-4586 (1996). [CrossRef]
  18. E. Palik, Handbook of Optical Constants of Solids II (Academic, 1991).
  19. E. Palik, Handbook of Optical Constants of Solids III (Academic, 1998).
  20. C. Pickering and R. T. Carline, "Dielectric function spectra of strained and relaxed Si1−xGex alloys," J. Appl. Phys. 75,4642-4647 (1994). [CrossRef]
  21. G. R. Fowles, Introduction to Modern Optics (Dover, 1975).
  22. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).
  23. W. T. Welford, Useful Optics (U. Chicago Press, 1991).
  24. D. E. Aspnes, "Minimal-data approaches for determining outer-layer dielectric responses of films from kinetic reflectometric and ellipsometric measurements," J. Opt. Soc. Am. A 10, 974-983 (1993). [CrossRef]
  25. D. E. Aspnes, "Optical approaches to determine near-surface compositions during epitaxy," J. Vac. Sci. Technol. A. 14, 960-966 (1996). [CrossRef]
  26. D. E. Aspnes, W. E. Quinn, M. C. Tamargo, M. A. A. Pudensi, S. A. Schwarz, M. J. S. P. Brasil, R. E. Nahory, and S. Gregory, "Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition," Appl. Phys. Lett. 60, 1244-1246 (1992). [CrossRef]
  27. D. A. O. Hope, C. Pickering, R. T. Carline, W. Y. Leong, and D. J. Robbins, "Real-time control of layer thickness in LPCVD Si0.88Ge0.12 HBT structures," Thin Solid Films 294, 18-21 (1997). [CrossRef]
  28. C. Pickering, "Correlation of in situ ellipsometric and light scattering data of silicon-based materials with post-deposition diagnostics," Thin Solid Films 206, 275-282 (1991). [CrossRef]
  29. T. L. Vincent, P. P. Khargonekar, and F. L. Terry, "An extended Kalman filter based method for fast in situ etch rate measurements," Mater. Res. Soc. Symp. Proc. 406, 87-93 (1996). [CrossRef]
  30. W. W. Woo, S. A. Svoronos, H. O. Sankur, J. Bajaj, and S. J. C. Irvine, "In-situ estimation of MOCVD growth rate via a modified Kalman filter," AIChE J. 42, 1319-1325 (1996). [CrossRef]
  31. S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U. Press, 1995).
  32. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  33. R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, 1968).
  34. S. A. Middlebrooks, "Modelling and control of silicon and germanium thin film chemical vapor deposition," Ph.D. thesis (University of Wisconsin-Madison, 2001).
  35. E. J. Davison and H. W. Smith, "Pole assignment in linear time-invariant multivariable systems with constant disturbances," Automatica 7, 489-498 (1971). [CrossRef]
  36. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems (Wiley, 1972).
  37. K. R. Muske, "Linear model predictive control of chemical processes," Ph.D. thesis (University of Texas at Austin, 1995).
  38. A. E. Bryson and Y. Ho, Applied Optimal Control (Hemisphere, 1975).
  39. A. Gelb, ed., Applied Optimal Estimation (MIT Press, 1974).
  40. O. L. R. Jacobs, Introduction to Control Theory (Oxford, U. Press, 1993).
  41. R. F. Stengel, Stochastic Optimal Control: Theory and Application (Wiley, 1986).
  42. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (McGraw-Hill, 1988).
  43. M. A. Henson and D. E. Seborg, Nonlinear Process Control (Prentice Hall, 1997).
  44. D. I. Wilson, M. Agarwal, and D. W. T. Rippin, "Experiences implementing the extended Kalman filter on an industrial batch reactor," Comput. Chem. Eng. 22, 1653-1672 (1998). [CrossRef]
  45. J. S. Meditch, Stochastic Optimal Linear Estimation and Control (McGraw-Hill, 1969).
  46. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

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