Abstract

For stratified samples where material is being uniformly deposited or removed at a known rate, I show that the dielectric function o of the outermost region is determinable exactly and analytically at any given wavelength from the value and the thickness derivative of the complex reflectances for p-polarized, s-polarized, or normally incident light without any knowledge of the underlying structure. This minimal-data approach greatly simplifies analysis compared with the standard procedure, in which dielectric functions are determined sequentially from a combination of new data and previously established sample parameters. It is also robust, eliminating cumulative error and error propagation that can cause conventional analysis to fail. An interferometric method for acquiring complex-reflectance data is proposed, although to achieve the necessary level of accuracy with present technology would be a formidable challenge. For ellipsometric measurements these technical obstacles do not exist, but an equivalent exact solution is not possible. However, I develop a common-pseudosubstrate approximation (CPA) that in applications to semiconductor crystal growth is accurate to better than 0.1%. The minimal-data approach also provides new insights about how sample parameters are determined from measured optical functions. For example, to determine deposition rates one needs to establish the second derivative (curvature) as well, which places additional constraints on measurement accuracy and/or the amount of data required. Also, the small-term expansion of the ellipsometrically determined pseudodielectric function 〈〉, originally derived as a thin-film limit of the three-phase model, is shown to be more generally valid. This result provides a theoretical basis for the direct analysis of several phenomena, including interface mixing, from 〈〉 data obtained during epitaxial growth. Using the CPA, I derive expressions that allow one to assess whether the performance of a given ellipsometer is adequate for growth control. Finally, the influence of selvage layers on determined values of 0 is briefly discussed.

© 1993 Optical Society of America

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  1. F. Hottier, G. Laurence, “Assessment by in situellipsometry of composition profiles of Ga1−xAlxAs–GaAs heterostructures,” Appl. Phys. Lett. 38, 863–865 (1981).
    [CrossRef]
  2. G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
    [CrossRef]
  3. E. Pelletier, “Monitoring of optical thin films during deposition,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 74–82 (1983).
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  4. R. Herrmann, A. Zöller, “Automated control of optical layer fabrication processes,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 83–92 (1983).
    [CrossRef]
  5. D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
    [CrossRef] [PubMed]
  6. B. Drévillon, “In situ analysis of the growth of semiconductor materials by phase modulated ellipsometry from UV to IR,” in Surface and Interface Analysis of Microelectronic Materials Processing and Growth, L. J. Brillson, F. H. Pollak, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1186, 110–121 (1990).
    [CrossRef]
  7. R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
    [CrossRef]
  8. O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
    [CrossRef]
  9. D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
    [CrossRef]
  10. F. Briones, Y. Horikoshi, “Application of reflectance difference spectroscopy (RDS) to migration-enhanced epitaxy (MEE) growth of GaAs,” Jpn. J. Appl. Phys. 29, 1014–1021 (1990).
    [CrossRef]
  11. D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
    [CrossRef]
  12. T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
    [CrossRef]
  13. I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
    [CrossRef]
  14. B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
    [CrossRef]
  15. N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
    [CrossRef]
  16. N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
    [CrossRef]
  17. D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
    [CrossRef]
  18. G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
    [CrossRef]
  19. C. Pickering, “Correlation of in situellipsometric and light scattering data of silicon-based materials with post-deposition diagnostics,” Thin Solid Films 206, 275–282 (1991).
    [CrossRef]
  20. H. Yao, P. G. Snyder, “In situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures,” Thin Solid Films 206, 283–287 (1991).
    [CrossRef]
  21. H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
    [CrossRef]
  22. R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
    [CrossRef]
  23. D. E. Aspnes, W. E. Quinn, M. C. Tamargo, M. A. A. Pudensi, S. A. Schwarz, M. J. S. P. Brasil, R. E. Nahory, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
    [CrossRef]
  24. D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
    [CrossRef]
  25. O. S. Heavens, Thin Film Physics (Methuen, London, 1970).
  26. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  27. D. Y. It. Ko, J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals,” J. Opt. Soc. Am. A 5, 1863–1866 (1988).
    [CrossRef]
  28. C. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13,452–13,465 (1991).
    [CrossRef]
  29. J. W. Brault, “Fourier transform spectrometry in relation to other passive spectrometers,” Phil. Trans. R. Soc. Lond. Ser. A 307, 503–511 (1982).
    [CrossRef]
  30. H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,”J. Phys. E 6, 822–826 (1973).
    [CrossRef]
  31. A. Röseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
    [CrossRef]
  32. K. Leonhardt, “Intensity and polarization of interference systems of a two-beam interferometer,” Opt. Commun. 11, 312 (1974).
    [CrossRef]
  33. D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.
  34. M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
    [CrossRef]
  35. D. E. Aspnes, “Approximate solution of ellipsometric equations for optically biaxial crystals,”J. Opt. Soc. Am. 70, 1275–1277 (1980).
    [CrossRef] [PubMed]
  36. D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,”J. Opt. Soc. Am. 64, 639–646 (1974).
    [CrossRef]
  37. D. E. Aspnes, “Precision bounds to ellipsometer systems,” Appl. Opt. 14, 1131–1136 (1975).
    [CrossRef] [PubMed]
  38. A. Savitzky, M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
    [CrossRef]
  39. I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
    [CrossRef]

1992 (3)

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

1991 (12)

C. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13,452–13,465 (1991).
[CrossRef]

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
[CrossRef]

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
[CrossRef]

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
[CrossRef]

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

C. Pickering, “Correlation of in situellipsometric and light scattering data of silicon-based materials with post-deposition diagnostics,” Thin Solid Films 206, 275–282 (1991).
[CrossRef]

H. Yao, P. G. Snyder, “In situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures,” Thin Solid Films 206, 283–287 (1991).
[CrossRef]

H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
[CrossRef]

1990 (5)

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
[CrossRef]

F. Briones, Y. Horikoshi, “Application of reflectance difference spectroscopy (RDS) to migration-enhanced epitaxy (MEE) growth of GaAs,” Jpn. J. Appl. Phys. 29, 1014–1021 (1990).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
[CrossRef]

1988 (1)

1987 (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

1982 (2)

J. W. Brault, “Fourier transform spectrometry in relation to other passive spectrometers,” Phil. Trans. R. Soc. Lond. Ser. A 307, 503–511 (1982).
[CrossRef]

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

1981 (3)

F. Hottier, G. Laurence, “Assessment by in situellipsometry of composition profiles of Ga1−xAlxAs–GaAs heterostructures,” Appl. Phys. Lett. 38, 863–865 (1981).
[CrossRef]

G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
[CrossRef]

A. Röseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

1980 (1)

1975 (1)

1974 (2)

D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,”J. Opt. Soc. Am. 64, 639–646 (1974).
[CrossRef]

K. Leonhardt, “Intensity and polarization of interference systems of a two-beam interferometer,” Opt. Commun. 11, 312 (1974).
[CrossRef]

1973 (1)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,”J. Phys. E 6, 822–826 (1973).
[CrossRef]

1964 (1)

A. Savitzky, M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Acher, O.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

Ager, C. D.

C. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13,452–13,465 (1991).
[CrossRef]

An, I.

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

Armstrong, J. V.

T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
[CrossRef]

Armstrong, S.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Aspnes, D. 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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
[CrossRef]

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

D. E. Aspnes, “Approximate solution of ellipsometric equations for optically biaxial crystals,”J. Opt. Soc. Am. 70, 1275–1277 (1980).
[CrossRef] [PubMed]

D. E. Aspnes, “Precision bounds to ellipsometer systems,” Appl. Opt. 14, 1131–1136 (1975).
[CrossRef] [PubMed]

D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,”J. Opt. Soc. Am. 64, 639–646 (1974).
[CrossRef]

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.

Azzam, R. M. A.

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

Bashara, N. M.

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

Brasil, M. J. S. P.

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

Brault, J. W.

J. W. Brault, “Fourier transform spectrometry in relation to other passive spectrometers,” Phil. Trans. R. Soc. Lond. Ser. A 307, 503–511 (1982).
[CrossRef]

Briones, F.

F. Briones, Y. Horikoshi, “Application of reflectance difference spectroscopy (RDS) to migration-enhanced epitaxy (MEE) growth of GaAs,” Jpn. J. Appl. Phys. 29, 1014–1021 (1990).
[CrossRef]

Buskes, H.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Carr, D.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Collins, R.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

Collins, R. W.

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

Cong, Y.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

Defour, M.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

Deppert, K.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

Drévillon, B.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

B. Drévillon, “In situ analysis of the growth of semiconductor materials by phase modulated ellipsometry from UV to IR,” in Surface and Interface Analysis of Microelectronic Materials Processing and Growth, L. J. Brillson, F. H. Pollak, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1186, 110–121 (1990).
[CrossRef]

Farrell, T.

T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
[CrossRef]

Florez, L. T.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

Folkard, M. A.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Foxon, C. T.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Golay, M. J. E.

A. Savitzky, M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Gregory, S.

D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
[CrossRef]

Hall, R.

H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
[CrossRef]

Hallais, J.

G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
[CrossRef]

Harbison, J. P.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

Hartley, R. H.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Hazebroek, H. F.

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,”J. Phys. E 6, 822–826 (1973).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Thin Film Physics (Methuen, London, 1970).

Herrmann, R.

R. Herrmann, A. Zöller, “Automated control of optical layer fabrication processes,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 83–92 (1983).
[CrossRef]

Holscher, A. A.

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,”J. Phys. E 6, 822–826 (1973).
[CrossRef]

Horikoshi, Y.

N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
[CrossRef]

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

F. Briones, Y. Horikoshi, “Application of reflectance difference spectroscopy (RDS) to migration-enhanced epitaxy (MEE) growth of GaAs,” Jpn. J. Appl. Phys. 29, 1014–1021 (1990).
[CrossRef]

Hottier, F.

G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
[CrossRef]

F. Hottier, G. Laurence, “Assessment by in situellipsometry of composition profiles of Ga1−xAlxAs–GaAs heterostructures,” Appl. Phys. Lett. 38, 863–865 (1981).
[CrossRef]

Hughes, H. P.

C. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13,452–13,465 (1991).
[CrossRef]

Hwang, D. M.

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Jeppesen, S.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

Jönsson, J.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

Joyce, B. A.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Kightley, P.

T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
[CrossRef]

Ko, D. Y. It.

Kobayashi, N.

N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
[CrossRef]

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

Koch, S. M.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

Kumar, V.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Laurence, G.

F. Hottier, G. Laurence, “Assessment by in situellipsometry of composition profiles of Ga1−xAlxAs–GaAs heterostructures,” Appl. Phys. Lett. 38, 863–865 (1981).
[CrossRef]

G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
[CrossRef]

Lee, J. B.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Leonhardt, K.

K. Leonhardt, “Intensity and polarization of interference systems of a two-beam interferometer,” Opt. Commun. 11, 312 (1974).
[CrossRef]

Li, Y. M.

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

Makimoto, T.

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Neave, J. H.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Nguyen, H. V.

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

Nguyen, N. V.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

Omnes, F.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

Orders, P. J.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Paulsson, G.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

Pelletier, E.

E. Pelletier, “Monitoring of optical thin films during deposition,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 74–82 (1983).
[CrossRef]

Pemble, M. E.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Phillips, B.

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Pickering, C.

C. Pickering, “Correlation of in situellipsometric and light scattering data of silicon-based materials with post-deposition diagnostics,” Thin Solid Films 206, 275–282 (1991).
[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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

Pudliner, B. S.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
[CrossRef]

Razeghi, M.

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

Rees, D.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Röseler, A.

A. Röseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

Sambles, J. R.

Samuelson, L.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

Sankur, H.

H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
[CrossRef]

Savitzky, A.

A. Savitzky, M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Schmidt, P.

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Shen, G.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Shitara, T.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Snyder, P. G.

H. Yao, P. G. Snyder, “In situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures,” Thin Solid Films 206, 283–287 (1991).
[CrossRef]

Southwell, W.

H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
[CrossRef]

Steele, T. A.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Studna, A. A.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

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, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Taylor, A.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Varga, I. K.

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

Wronski, C. R.

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

Yamauchi, Y.

N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
[CrossRef]

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

Yao, H.

H. Yao, P. G. Snyder, “In situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures,” Thin Solid Films 206, 283–287 (1991).
[CrossRef]

Zhang, J.

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

Zöller, A.

R. Herrmann, A. Zöller, “Automated control of optical layer fabrication processes,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 83–92 (1983).
[CrossRef]

Anal. Chem. (1)

A. Savitzky, M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

D. E. Aspnes, W. E. Quinn, M. C. Tamargo, M. A. A. Pudensi, S. A. Schwarz, M. J. S. P. Brasil, R. E. Nahory, “Growth of AlxGa1−xAs parabolic quantum wells by real-time feedback control of composition,” Appl. Phys. Lett. 60, 1244–1246 (1992).
[CrossRef]

F. Hottier, G. Laurence, “Assessment by in situellipsometry of composition profiles of Ga1−xAlxAs–GaAs heterostructures,” Appl. Phys. Lett. 38, 863–865 (1981).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Optical control of growth of AlxGa1−xAs by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 57, 2707–2709 (1990).
[CrossRef]

T. Farrell, J. V. Armstrong, P. Kightley, “Dynamic optical reflectivity to monitor the real-time metalorganic molecular beam epitaxy growth of AlGaAs layers,” Appl. Phys. Lett. 59, 1203–1205 (1991).
[CrossRef]

I. An, Y. M. Li, C. R. Wronski, H. V. Nguyen, R. W. Collins, “In situdetermination of the dielectric functions and optical gap of ultrathin amorphous silicon by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 59, 2543–2545 (1991).
[CrossRef]

D. E. Aspnes, W. E. Quinn, S. Gregory, “Application of ellipsometry to crystal growth by organometallic molecular beam epitaxy,” Appl. Phys. Lett. 56, 2569–2571 (1990).
[CrossRef]

Infrared Phys. (1)

A. Röseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

J. Appl. Phys. (1)

O. Acher, S. M. Koch, F. Omnes, M. Defour, M. Razeghi, B. Drévillon, “In situinvestigation of the low-pressure metalorganic chemical vapor deposition of lattice-mismatched semiconductors using reflectance anisotropy measurements,” J. Appl. Phys. 68, 3564 (1990).
[CrossRef]

J. Cryst. Growth (5)

G. Paulsson, K. Deppert, S. Jeppesen, J. Jönsson, L. Samuelson, P. Schmidt, “Reflectance-difference probing of surface kinetics of (001) GaAs during vacuum chemical epitaxy,”J. Cryst. Growth 111, 115–119 (1991).
[CrossRef]

B. A. Joyce, J. Zhang, T. Shitara, J. H. Neave, A. Taylor, S. Armstrong, M. E. Pemble, C. T. Foxon, “Dynamics and kinetics of MBE growth,”J. Cryst. Growth 115, 338–347 (1991).
[CrossRef]

N. Kobayashi, Y. Yamauchi, Y. Horikoshi, “In-situoptical monitoring of pyrolysis process on substrate surface in GaAs MOCVD,”J. Cryst. Growth 115, 353–358 (1991).
[CrossRef]

N. Kobayashi, T. Makimoto, Y. Yamauchi, Y. Horikoshi, “In-situmonitoring of GaAs growth process in OMVPE by surface photo-absorption method,”J. Cryst. Growth 107, 62–67 (1991).
[CrossRef]

R. H. Hartley, M. A. Folkard, D. Carr, P. J. Orders, D. Rees, I. K. Varga, V. Kumar, G. Shen, T. A. Steele, H. Buskes, J. B. Lee, “Ellipsometry: a technique for real time monitoring and analysis of MBE-grown CdHgTe and CdTe/HgTe superlattices,”J. Cryst. Growth 117, 166–170 (1992).
[CrossRef]

J. Electron. Mater. (1)

H. Sankur, W. Southwell, R. Hall, “In situoptical monitoring of OMVPE deposition of AlGaAs by laser reflectance,”J. Electron. Mater. 20, 1099–1104 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Phys. E (1)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,”J. Phys. E 6, 822–826 (1973).
[CrossRef]

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

D. E. Aspnes, W. E. Quinn, S. Gregory, “Real-time optical diagnostics for epitaxial growth,”J. Vac. Sci. Technol. A 9, 870–875 (1991).
[CrossRef]

Jpn. J. Appl. Phys. (1)

F. Briones, Y. Horikoshi, “Application of reflectance difference spectroscopy (RDS) to migration-enhanced epitaxy (MEE) growth of GaAs,” Jpn. J. Appl. Phys. 29, 1014–1021 (1990).
[CrossRef]

Opt. Commun. (1)

K. Leonhardt, “Intensity and polarization of interference systems of a two-beam interferometer,” Opt. Commun. 11, 312 (1974).
[CrossRef]

Phil. Trans. R. Soc. Lond. Ser. A (1)

J. W. Brault, “Fourier transform spectrometry in relation to other passive spectrometers,” Phil. Trans. R. Soc. Lond. Ser. A 307, 503–511 (1982).
[CrossRef]

Phys. Rev. B (1)

C. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13,452–13,465 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Optical-reflectance and electron-diffraction studies of molecular-beam-epitaxy growth transients on GaAs(001),” Phys. Rev. Lett. 59, 1687–1690 (1987).
[CrossRef] [PubMed]

Proc. Mater. Res. Soc. (1)

M. C. Tamargo, M. J. S. P. Brasil, R. E. Nahory, D. E. Aspnes, B. Phillips, D. M. Hwang, S. A. Schwarz, “Formation of the interface between InP and arsenic based alloys by chemical beam epitaxy,” Proc. Mater. Res. Soc. 263, 267–272 (1992).
[CrossRef]

Rev. Phys. Appl. (1)

G. Laurence, F. Hottier, J. Hallais, “Qualitative and quantitative assessments of the growth of (Al, Ga)As–GaAs heterostructures by in situellipsometry,” Rev. Phys. Appl. 16, 579–589 (1981).
[CrossRef]

Rev. Sci. Instrum. (1)

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

Thin Solid Films (4)

C. Pickering, “Correlation of in situellipsometric and light scattering data of silicon-based materials with post-deposition diagnostics,” Thin Solid Films 206, 275–282 (1991).
[CrossRef]

H. Yao, P. G. Snyder, “In situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures,” Thin Solid Films 206, 283–287 (1991).
[CrossRef]

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, R. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206, 300–305 (1991).
[CrossRef]

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

Other (6)

O. S. Heavens, Thin Film Physics (Methuen, London, 1970).

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

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.

B. Drévillon, “In situ analysis of the growth of semiconductor materials by phase modulated ellipsometry from UV to IR,” in Surface and Interface Analysis of Microelectronic Materials Processing and Growth, L. J. Brillson, F. H. Pollak, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1186, 110–121 (1990).
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E. Pelletier, “Monitoring of optical thin films during deposition,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 74–82 (1983).
[CrossRef]

R. Herrmann, A. Zöller, “Automated control of optical layer fabrication processes,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 83–92 (1983).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the outer layer of a possibly multilayered sample, shown for s polarization. The dielectric function of the outer layer is assumed to be constant to a depth of at least d.

Fig. 2
Fig. 2

One possible configuration for obtaining amplitude and phase of the complex reflectance at normal incidence.

Fig. 3
Fig. 3

(a) Calculated 〈〉 = 〈〉 trajectory for the fourth pair of Al0.36Ga0.64As/GaAs layers, each layer 25 nm thick, deposited upon a GaAs substrate. The angle of incidence is 71°. The dielectric functions of Al0.36Ga0.64As and GaAs are marked by crosses. The trajectory consists of two segments of approximately exponential spirals whose junctions are marked by the short vertical lines. (b) Like (a) but for the complex reflectances rs, rn, and rp. For these optical functions the Al0.36Ga0.64As cross lies above the GaAs cross. The junctions between segments are shown only for −rp. (c) Differences between 〈p〉 pseudodielectric functions 〈s〉 and 〈p〉 calculated from (b).

Fig. 4
Fig. 4

Differences between values of o, obtained from the calculated 〈ρ〉 trajectory of Fig. 3(a) in the ESA and the CPA. The CPA result has been multiplied by 100 to make it visible on the scale of the figure.

Fig. 5
Fig. 5

Observed uncertainties of 101 points of raw Fourier-coefficient ellipsometric data (α,β) and of the pseudodielectric function derived therefrom. These data were extracted from data obtained during growth of the nominal Al0.3Ga0.7As buffer layer for the 50-nm parabolic quantum well that was grown under closed-loop control as described in Ref. 23.

Equations (39)

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c 2 k o 2 / ω 2 = o ,
c k j z / ω = n j z = ( j - a sin 2 ϕ ) 1 / 2 ,
E + o ( - d , t ) = y ^ E + o exp ( - i ω t ) ,
E - o ( - d , t ) = y ^ E - o exp ( - i ω t ) ,
E + o ( 0 , t ) = y ^ E + o exp ( - i k o z d ) exp ( - i ω t ) ,
E - o ( 0 , t ) = y ^ E + o exp ( i k o z d ) exp ( - i ω t ) .
r ( d ) = Z r v + r o a 1 + Z r v r o a ,
Z = exp ( 2 i k o z d ) ,
r o a r o a , s = ( n a z - n o z ) / ( n a z + n o z )
r o a r o a , p = ( o n a z - a n o z ) / ( o n a z + a n o z ) .
r v r v o , s = ( n o z - n v z ) / ( n o z + n v z ) .
r v r v o , p = ( v p n o z - o n v z ) / ( u p n o z + o n v z ) .
r = r v + r o a 1 + r v r o a .
r r s = ( n a z - n s z ) / ( n a z + n s z )
r r p = ( p n a z - a n p z ) / ( p n a z + a n p z ) .
s = a ( 1 + r s 2 - 2 r s cos 2 ϕ ) ( 1 + r s ) 2 ,
p = ξ ± [ ξ 2 - a 2 sin 2 ( 2 ϕ ) ( 1 - r p 2 ) 2 ] 1 / 2 2 ( cos 2 ϕ ) ( 1 - r p ) 2 ,
ξ = a ( 1 + r p ) 2 .
o = a [ ( 1 + r s 2 - 2 r s cos ( 2 ϕ ) ] - i λ n a z r s / π ( 1 + r s ) 2 ,
o = ξ ± [ ξ 2 - a 2 sin 2 ( 2 ϕ ) ( 1 - r p 2 ) 2 ] 1 / 2 2 ( cos 2 ϕ ) ( 1 - r p ) 2 ,
ξ = a ( 1 + r p ) 2 + i λ n a z r p / π .
ρ = sin 2 ϕ + ( sin 2 ϕ ) ( tan 2 ϕ ) [ ( 1 - ρ ) 2 / ( 1 + ρ ) 2 ] .
ρ = ( Z r v p + r o a , p ) ( 1 + Z r v s r o a , s ) ( 1 + Z r v p r o a , p ) ( Z r v s + r o a , s ) ,
ρ = ,
= 4 π i n z ( - o ) ( o - a ) λ o ( - a ) ,
o = ξ ± ( ξ 2 - a ) 1 / 2 ,
ξ = 1 2 ( + a ) + i λ ( - a ) 8 π n z .
r ( d ) r o a + [ r ( 0 ) - r o a ] exp ( 2 i k o z d ) .
( d ) o + [ ( 0 ) - o ] exp ( 2 i k o z d ) .
r s = n a z - n z n a z + n z ( 1 + 4 π i d x n a z λ - x - a ) ,
r s d o = 4 π i n a z ( o - ) λ ( n a z + n z ) 2 ( 1 + 4 π i d x λ n x z 2 + n z n o z n a z + n z ) ,
˜ o = o - 4 π i d x λ ( n a z + n z ) [ ( - o ) ( n x z 2 + n z n o z ) - ( - x ) ( n o z 2 + n z n a z ) ] .
¯ k , ¯ k = j = - ( N - 1 ) / 2 ( N - 1 ) / 2 c j j + k ,
δ ¯ k , δ ¯ k = [ j = - ( N - 1 ) / 2 ( N - 1 ) / 2 c j 2 ] 1 / 2 δ .
δ = N - 1 / 2 δ ,
δ = 2 ( 3 ) 1 / 2 δ Δ d [ N ( N 2 - 1 ) ] 1 / 2 ,
δ o = ( δ 2 + | λ δ 4 π n o | 2 ) 1 / 2
= δ N { 1 + [ ( 3 ) 1 / 2 λ 2 π n o Δ d ( N 2 - 1 ) 1 / 2 ] 2 } 1 / 2
( 3 ) 1 / 2 λ δ 2 π Δ d n o [ N ( N 2 - 1 ) ] 1 / 2 .

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