Abstract

We present an algorithm that simultaneously deduces from real-time ellipsometric measurements both the growth rate and the composition of Si1-xGex 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

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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).

1998 (1)

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]

1997 (2)

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]

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]

1996 (4)

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]

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]

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]

D. E. Aspnes, "Optical approaches to determine near-surface compositions during epitaxy," J. Vac. Sci. Technol. A. 14, 960-966 (1996).
[CrossRef]

1994 (3)

C. Pickering and R. T. Carline, "Dielectric function spectra of strained and relaxed Si1−xGex alloys," J. Appl. Phys. 75,4642-4647 (1994).
[CrossRef]

F. Glowacki and Y. Campidelli, "Single wafer epitaxy of Si and SiGe using UHV-CVD," Microelectron. Eng. 25, 161-170 (1994).
[CrossRef]

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]

1993 (2)

1992 (2)

B. Meyerson, "UHV/CVD growth of Si and SiGe alloys: chemistry, physics, and device applications," Proc. IEEE 80, 1592-1608 (1992).
[CrossRef]

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]

1991 (2)

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]

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]

1990 (1)

1989 (1)

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

1988 (1)

B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988).
[CrossRef]

1986 (2)

B. Meyerson, "Low temperature silicon epitaxy by UHV/CVD," Appl. Phys. Lett. 48, 797-799 (1986).
[CrossRef]

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]

1975 (1)

1974 (2)

1971 (1)

E. J. Davison and H. W. Smith, "Pole assignment in linear time-invariant multivariable systems with constant disturbances," Automatica 7, 489-498 (1971).
[CrossRef]

Agarwal, M.

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]

Archer, O.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Archer, R. J.

R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, 1968).

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bajaj, J.

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]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bauer, G.

G. Bauer and W. Richter, Optical Characterization of Epitaxial Semiconductor Layers (Springer-Verlag, 1996).
[CrossRef]

Bigan, E.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Brasil, M. J. S. P.

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]

Bryson, A. E.

A. E. Bryson and Y. Ho, Applied Optimal Control (Hemisphere, 1975).

Campidelli, Y.

F. Glowacki and Y. Campidelli, "Single wafer epitaxy of Si and SiGe using UHV-CVD," Microelectron. Eng. 25, 161-170 (1994).
[CrossRef]

Canale, R. P.

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (McGraw-Hill, 1988).

Carline, R. T.

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]

C. Pickering and R. T. Carline, "Dielectric function spectra of strained and relaxed Si1−xGex alloys," J. Appl. Phys. 75,4642-4647 (1994).
[CrossRef]

Chapra, S. C.

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (McGraw-Hill, 1988).

Chen, W.

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]

Davison, E. J.

E. J. Davison and H. W. Smith, "Pole assignment in linear time-invariant multivariable systems with constant disturbances," Automatica 7, 489-498 (1971).
[CrossRef]

Drevillon, B.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Duncan, W. M.

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]

Eberl, K.

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]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Dover, 1975).

Gelb, A.

A. Gelb, ed., Applied Optimal Estimation (MIT Press, 1974).

Glowacki, F.

F. Glowacki and Y. Campidelli, "Single wafer epitaxy of Si and SiGe using UHV-CVD," Microelectron. Eng. 25, 161-170 (1994).
[CrossRef]

Gregory, S.

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]

Greve, D.

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]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).

Henck, S. A.

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]

Henson, M. A.

M. A. Henson and D. E. Seborg, Nonlinear Process Control (Prentice Hall, 1997).

Ho, Y.

A. E. Bryson and Y. Ho, Applied Optimal Control (Hemisphere, 1975).

Hope, D. A. O.

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]

Horn, R. A.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

Irvine, S. J. C.

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]

Iyer, S. S.

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]

Jacobs, O. L. R.

O. L. R. Jacobs, Introduction to Control Theory (Oxford, U. Press, 1993).

Jellison, G. E.

Johnson, C. R.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

Junge, K. E.

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]

Khargonekar, P. P.

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]

Kuehne, J. W.

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]

Kwakernaak, H.

H. Kwakernaak and R. Sivan, Linear Optimal Control Systems (Wiley, 1972).

Lange, R.

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]

LeGoues, F.

B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988).
[CrossRef]

Leong, W. Y.

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]

Lipson, H.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U. Press, 1995).

Lipson, S. G.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U. Press, 1995).

Lowenstein, L. M.

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]

Maung, S.

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]

Meditch, J. S.

J. S. Meditch, Stochastic Optimal Linear Estimation and Control (McGraw-Hill, 1969).

Meyerson, B.

B. Meyerson, "UHV/CVD growth of Si and SiGe alloys: chemistry, physics, and device applications," Proc. IEEE 80, 1592-1608 (1992).
[CrossRef]

B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988).
[CrossRef]

B. Meyerson, "Low temperature silicon epitaxy by UHV/CVD," Appl. Phys. Lett. 48, 797-799 (1986).
[CrossRef]

Middlebrooks, S. A.

S. A. Middlebrooks, "Modelling and control of silicon and germanium thin film chemical vapor deposition," Ph.D. thesis (University of Wisconsin-Madison, 2001).

Modine, F. A.

Morkoc, H.

G. Zhou and H. Morkoc, "Si/SiGe heterostructures and devices," Thin Solid Films 231, 125-142 (1993).
[CrossRef]

Muske, K. R.

K. R. Muske, "Linear model predictive control of chemical processes," Ph.D. thesis (University of Texas at Austin, 1995).

Nahory, R. E.

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]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids III (Academic, 1998).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

E. Palik, Handbook of Optical Constants of Solids II (Academic, 1991).

Pickering, C.

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]

C. Pickering and R. T. Carline, "Dielectric function spectra of strained and relaxed Si1−xGex alloys," J. Appl. Phys. 75,4642-4647 (1994).
[CrossRef]

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]

Powell, A. P.

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]

Pudensi, M. A. A.

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]

Quinn, W. E.

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]

Racanelli, M.

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]

Reif, R.

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]

Richter, W.

G. Bauer and W. Richter, Optical Characterization of Epitaxial Semiconductor Layers (Springer-Verlag, 1996).
[CrossRef]

Rippin, D. W. T.

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]

Robbins, D. J.

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]

Sankur, H. O.

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]

Schwarz, S. A.

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]

Seborg, D. E.

M. A. Henson and D. E. Seborg, Nonlinear Process Control (Prentice Hall, 1997).

Sivan, R.

H. Kwakernaak and R. Sivan, Linear Optimal Control Systems (Wiley, 1972).

Smith, H. W.

E. J. Davison and H. W. Smith, "Pole assignment in linear time-invariant multivariable systems with constant disturbances," Automatica 7, 489-498 (1971).
[CrossRef]

Stengel, R. F.

R. F. Stengel, Stochastic Optimal Control: Theory and Application (Wiley, 1986).

Studna, A. A.

Svoronos, S. A.

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]

Takoudis, C. G.

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]

Tamargo, M. C.

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]

Tannhauser, D. S.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U. Press, 1995).

Terry, F. L.

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]

Turner, K. A.

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]

Uram, K.

B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988).
[CrossRef]

Vincent, T. L.

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]

Welford, W. T.

W. T. Welford, Useful Optics (U. Chicago Press, 1991).

Westhoff, R.

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]

Wilke, T. E.

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]

Wilson, D. I.

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]

Woo, W. W.

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]

Zhou, G.

G. Zhou and H. Morkoc, "Si/SiGe heterostructures and devices," Thin Solid Films 231, 125-142 (1993).
[CrossRef]

Zollner, S.

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]

AIChE J. (1)

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]

Appl. Opt. (2)

Appl. Phys. Lett. (5)

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]

B. Meyerson, K. Uram, and F. LeGoues, "Cooperative growth phenomena in silicon/germanium low-temperature epitaxy," Appl. Phys. Lett. 53, 2555-2557 (1988).
[CrossRef]

B. Meyerson, "Low temperature silicon epitaxy by UHV/CVD," Appl. Phys. Lett. 48, 797-799 (1986).
[CrossRef]

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]

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]

Automatica (1)

E. J. Davison and H. W. Smith, "Pole assignment in linear time-invariant multivariable systems with constant disturbances," Automatica 7, 489-498 (1971).
[CrossRef]

Chem. Eng. Sci. (1)

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]

Comput. Chem. Eng. (1)

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]

J. Appl. Phys. (2)

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]

C. Pickering and R. T. Carline, "Dielectric function spectra of strained and relaxed Si1−xGex alloys," J. Appl. Phys. 75,4642-4647 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. A. (1)

D. E. Aspnes, "Optical approaches to determine near-surface compositions during epitaxy," J. Vac. Sci. Technol. A. 14, 960-966 (1996).
[CrossRef]

J. Vac. Sci. Technol. B. (1)

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]

Mater. Res. Soc. Symp. Proc. (1)

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]

Microelectron. Eng. (1)

F. Glowacki and Y. Campidelli, "Single wafer epitaxy of Si and SiGe using UHV-CVD," Microelectron. Eng. 25, 161-170 (1994).
[CrossRef]

Proc. IEEE (1)

B. Meyerson, "UHV/CVD growth of Si and SiGe alloys: chemistry, physics, and device applications," Proc. IEEE 80, 1592-1608 (1992).
[CrossRef]

Rev. Sci. Instrum. (1)

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Thin Solid Films (3)

G. Zhou and H. Morkoc, "Si/SiGe heterostructures and devices," Thin Solid Films 231, 125-142 (1993).
[CrossRef]

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]

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]

Other (21)

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U. Press, 1995).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, 1968).

S. A. Middlebrooks, "Modelling and control of silicon and germanium thin film chemical vapor deposition," Ph.D. thesis (University of Wisconsin-Madison, 2001).

H. Kwakernaak and R. Sivan, Linear Optimal Control Systems (Wiley, 1972).

K. R. Muske, "Linear model predictive control of chemical processes," Ph.D. thesis (University of Texas at Austin, 1995).

A. E. Bryson and Y. Ho, Applied Optimal Control (Hemisphere, 1975).

A. Gelb, ed., Applied Optimal Estimation (MIT Press, 1974).

O. L. R. Jacobs, Introduction to Control Theory (Oxford, U. Press, 1993).

R. F. Stengel, Stochastic Optimal Control: Theory and Application (Wiley, 1986).

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (McGraw-Hill, 1988).

M. A. Henson and D. E. Seborg, Nonlinear Process Control (Prentice Hall, 1997).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

G. Bauer and W. Richter, Optical Characterization of Epitaxial Semiconductor Layers (Springer-Verlag, 1996).
[CrossRef]

G. R. Fowles, Introduction to Modern Optics (Dover, 1975).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).

W. T. Welford, Useful Optics (U. Chicago Press, 1991).

E. Palik, Handbook of Optical Constants of Solids II (Academic, 1991).

E. Palik, Handbook of Optical Constants of Solids III (Academic, 1998).

J. S. Meditch, Stochastic Optimal Linear Estimation and Control (McGraw-Hill, 1969).

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

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Figures (17)

Fig. 1
Fig. 1

The jth layer of a system of multiple layers.

Fig. 2
Fig. 2

Refractive index and extinction spectra of strained Si 1 - x Ge x alloys grown on Si calculated from Eq. (6).

Fig. 3
Fig. 3

Disilane and germane MFC valve positions and wafer temperature during both simulations.

Fig. 4
Fig. 4

Simulation 1: Δ for λ = 3000   Å and λ = 5520   Å for the first 6 min of the simulation.

Fig. 5
Fig. 5

Simulation 1: State disturbances in the germane MFC valve and wafer temperature for the first 6 min of the simulation.

Fig. 6
Fig. 6

Simulation 1: Film growth rate, composition, and height for the first 6 min of simulation.

Fig. 7
Fig. 7

Simulation 1: Δ for λ = 3000   Å and λ = 5520   Å for the entire simulation.

Fig. 8
Fig. 8

Simulation 1: Observability of the film height and the state disturbances.

Fig. 9
Fig. 9

Simulation 1: Kalman filter gains for the germane MFC valve disturbance state and the wafer temperature disturbance state for the entire simulation.

Fig. 10
Fig. 10

Simulation 1: Film growth rate, composition, and resulting profile for the entire simulation.

Fig. 11
Fig. 11

Simulation 2: Δ for λ = 3000   Å and λ = 5520   Å for the first 6 min of the simulation.

Fig. 12
Fig. 12

Simulation 2: State disturbances in the germane MFC valve and wafer temperature for the first 6 min of the simulation.

Fig. 13
Fig. 13

Simulation 2: Film growth rate, composition, and height for the first 6 min of the simulation.

Fig. 14
Fig. 14

Simulation 2: Δ for λ = 3000   Å and λ = 5520   Å for the entire simulation.

Fig. 15
Fig. 15

Simulation 2: Observability of the film height and the state disturbances.

Fig. 16
Fig. 16

Simulation 2: Kalman filter gains for the germane MFC valve disturbance state and the wafer temperature disturbance state for the entire simulation.

Fig. 17
Fig. 17

Simulation 2: Film growth rate, composition, and resulting profile for the entire simulation.

Equations (51)

Equations on this page are rendered with MathJax. Learn more.

[ E j + 1 H j + 1 ] = [ cos ( ϰ j d j ) i sin ( ϰ j d j ) η j i sin ( ϰ j d j ) η j cos ( ϰ j d j ) ] [ E j H j ] .
η pj = n ˜ j cos φ j ,
η sj = n ˜ j cos φ j .
ϰ j = 2 π n ˜ j cos ( φ j ) λ .
n ˜ = n - i κ ,
ϵ ( x , E ) = ϵ ( 0 , E + 0.4805 x ) + 10.575 x ( 3.050 - 0.6556 x ) 2 - E 2 + i 0.5028 E .
n ˜ 0 sin ( φ 0 ) = n ˜ j sin ( φ j ) ,
ϒ H tangential E tangential .
ϒ p j - 1 = η p j ϒ p j cos ϰ j d j + i η p j sin ϰ j d j η p j cos ϰ j d j + i ϒ p j sin ϰ j d j ,
ϒ s j - 1 = η s j ϒ s j cos ϰ j d j + i η s j sin ϰ j d j η s j cos ϰ j d j + i ϒ s j sin ϰ j d j .
d ϒ p d t = i η p ϰ ( ϒ p 2 η p 2 - 1 ) G ,
d ϒ s d t = i η s ϰ ( ϒ s 2 η s 2 - 1 ) G ,
R p ( t ) = ϒ p ( t ) - η p ( t ) η p ( t ) + ϒ p ( t ) ,
R s ( t ) = η s ( t ) - ϒ s ( t ) η s ( t ) + ϒ s ( t ) .
ρ ( t ) R p ( t ) R s ( t ) ,
Ψ ( t ) = arctan [ | ρ ( t ) | ] ,
Δ ( t ) = arg [ ρ ( t ) ] .
d = λ 4 πκ ,
d x d t = f ( x , u , t ) ,
y = g ( x ) ,
z = h ( x ) ,
x = ( ϒ p ( λ 1 ) ϒ s ( λ 1 ) ϒ p ( λ 2 ) ϒ s ( λ 2 ) ) .
y = ( Δ ( λ 1 ) Δ ( λ 2 ) ) .
z = ( G x ) .
p k + 1 = p k + ξ k ,
x k + 1 = f ( x k , u k , p k , k ) + ω k ,
y k = g ( x k ) + ν k ,
z k = h ( x k ) ,
x k + 1 = f ( x ^ k | k , u k ) + A k x k + B k u k ,
y k = g ( x ^ k | k ) + C k m x k ,
z k = h ( x ^ k | k ) + C k c x k ,
A k = f ( x , u ) x | x = x ^ k | k , u = u k ,
B k = f ( x , u ) u | x = x ^ k | k , u = u k ,
C k m = g ( x ) x | x = x ^ k | k - 1 , u = u k ,
C k c = h ( x ) x | x = x ^ k | k - 1 , u = u k .
x ^ k | k = x ^ k | k - 1 + K k [ y k - g ( x ^ k | k - 1 , k ) ] ,
P ^ k | k = ( I - K k C k m ) P ^ k | k - 1 ,
x ^ k + 1 | k = f ( x ^ k | k , u k , k ) ,
P ^ k + 1 | k = A k P ^ k | k A k T + Q ω ,
K k = P ^ k | k - 1 C k mT ( C k m P ^ k | k - 1 C k mT + R ν ) - 1 .
x ^ k | k = x ^ k | k - 1 + K k [ y k - g ( x ^ k | k - 1 , k ) ] ,
P ^ k | k = ( I - K k C k m ) P ^ k | k - 1 .
x k + 1 | k = f ( x ^ k | k , u k ) ,
P ^ k + 1 | k = A k P ^ k | k A k T + Q ω .
K k + 1 = P ^ k + 1 | k C k + 1 mT ( C k + 1 m P ^ k + 1 | k C k + 1 mT + R ν ) - 1 .
z k | k = h ( x ^ k | k ) .
x k + 1 = A k x k ,
y k = C k m x k
M d = i = 1 N Φ T ( i , 0 ) C mT ( i ) C m ( i ) Φ ( i , 0 )
Φ ( i , 0 ) = A ( i ) A ( i - 1 ) A ( 1 ) , i = 1 , , N
M d = V T ,

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