Abstract

Rough surfaces of silicon and aluminum have been studied by rotating analyzer spectroscopic ellipsometry (RASE). The roughness of a silicon sample similar to that used for the RASE measurements was also studied by cross-sectional transmission electron microscopy. Total integrated scattering was measured on the aluminum specimens to obtain numerical estimates of the rms roughness. The ellipsometry measurements on these specimens were carried out at a number of angles of incidence in the 30–80° range and at a number of discrete wavelengths in the 300–650-nm spectral range. The RASE results were then analyzed using the Bruggeman effective-medium theory for the Si sample and scalar diffraction theory for the Al samples. This study shows that 70° is the optimum angle of incidence for characterizing the roughness of these Al surfaces using RASE. It also demonstrates the self-consistency of the Bruggeman theory with angular variation for the Si sample. The need for a vector diffraction theory for the interpretation of the rms roughness using ellipsometric angles Δ and Ψ is discussed.

© 1991 Optical Society of America

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  1. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
    [CrossRef]
  2. P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).
  3. O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970).
    [CrossRef]
  4. I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
    [CrossRef]
  5. E. L. Church, J. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [CrossRef] [PubMed]
  8. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [CrossRef]
  9. T. Smith, “Effect of surface roughness on ellipsometry of aluminum,” Surf. Sci. 56, 252–271 (1976).
    [CrossRef]
  10. H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).
  11. T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981).
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  16. C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978).
    [CrossRef]
  17. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,” Ann. Phys. Leipzig 24, 636–670 (1935).
    [CrossRef]
  18. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975); “Methods for drift stabilization and photomultiplier linearization for photometric ellipsometers and polarimeters,” Rev. Sci. Instrum. 49, 291–279 (1978).
    [PubMed]
  19. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
    [CrossRef]
  20. D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982).
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  21. D. E. Aspnes, J. B. Theeten, “Dielectric/semiconductor interface using spectroscopic ellipsometry,” Acta Electron. 24, 217–227 (1981–1982).
  22. D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).
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  24. J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
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  25. P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
    [CrossRef]
  26. S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
    [CrossRef]
  27. K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
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  28. P. J. McMarr, “Characterization of surfaces, thin films, and ion-implanted silicon by spectroscopic ellipsometry,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1985).
  29. I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).
  30. I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973).
    [CrossRef]
  31. I. Ohlídal, K. Navrátil, F. Lukeš, “Reflection of light by a system of nonabsorbing isotropic film-nonabsorbing isotropic substrate with randomly rough boundaries,” J. Opt. Soc. Am. 61, 1630–1639 (1971).
    [CrossRef]
  32. I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
    [CrossRef]
  33. I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).
  34. J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
    [CrossRef] [PubMed]
  35. J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).
  36. F. Varnier, G. Rasigni, J. P. Palmari, A. Llebaria, M. Rasigni, “Influence of some parameters on the surface profile restored from microdensitometer analysis of electron micrographs of surface replicas,” Appl. Opt. 23, 3705–3717 (1984).
    [CrossRef] [PubMed]
  37. B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).
  38. G. Hass, “Über die optischen Konstanten dicker Aluminum und Silberschichten in Vakuum,” Optik 1, 8–10 (1946); G. Hass, J. E. Waylonis, “Optical constants and reflectance and transmittance of evaporated aluminum in the visible and ultraviolet,” J. Opt. Soc. Am. 51, 719–722 (1961).
    [CrossRef]
  39. H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).
  40. O. S. Heavens, Optical Properties of Solid Films (Dover, New York, 1965), p. 200.
  41. R. W. Fane, W. E. J. Neal, “Optical constants of aluminum films related to the vacuum environment,” J. Opt. Soc. Am. 60, 790–793 (1970).
    [CrossRef]
  42. M. Badia, “Ellipsometric analysis of amorphous oxide film growth and crystalline oxide island development during thermal oxidation of aluminum,” Thin Solid Films 13, 329–331 (1972).
    [CrossRef]
  43. T. H. Allen, “Study of Al with a combined auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
    [CrossRef]
  44. E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).
  45. Z. Bodó, G. Gergely, “Intrinsic optical constants of aluminum,” Appl. Opt. 26, 2065–2067 (1987).
    [CrossRef] [PubMed]
  46. J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982).
    [CrossRef]
  47. O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
    [CrossRef]
  48. H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978); P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).
  49. The portable instrument was built by Talandic Research Corp., 2793 East Foothill Ave., Pasadena, Calif. 91107 for the U.S. Army as part of a contract with the Naval Weapons Center (Jean M. Bennett was principal investigator). J. M. Bennett made this set of measurements as part of the demonstration to the Army that the instrument does indeed measure TIS.
  50. J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
    [CrossRef]
  51. H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
    [CrossRef]
  52. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
    [CrossRef] [PubMed]
  53. E. L. Church, J. M. Zavada, “Effects of surface microroughness in mirror absorption,” J. Opt. Soc. Am. 64, 1404A (1974); “Optical effects of surface roughness,” J. Opt. Soc. Am. 64, 574A (1974).
  54. J. L. Stanford, H. E. Bennett, “Enhancement of surface plasma resonance absorption in mirrors by overcoating with dielectrics,” Appl. Opt. 8, 2556–2557 (1969).
    [CrossRef] [PubMed]
  55. H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
    [CrossRef]
  56. J. M. BennettU.S. Naval Weapons Center, Michelson Laboratory, China Lake, CA 93555 (personal communication).

1989 (3)

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

F. Varnier, N. Mayani, G. Rasigni, “Statistical parameters for rough surfaces of thin films of CaF2 and Ag/CaF2,” Appl. Opt. 28, 127–134 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

1986 (1)

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

1985 (4)

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[CrossRef] [PubMed]

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

J. M. Bennett, “Scattering and surface evaluation techniques for the optics of the future,” Opt. News 11(7), 17–27 (1985).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
[CrossRef] [PubMed]

1984 (4)

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

F. Varnier, G. Rasigni, J. P. Palmari, A. Llebaria, M. Rasigni, “Influence of some parameters on the surface profile restored from microdensitometer analysis of electron micrographs of surface replicas,” Appl. Opt. 23, 3705–3717 (1984).
[CrossRef] [PubMed]

P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
[CrossRef]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

1983 (1)

O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
[CrossRef]

1982 (2)

D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982).
[CrossRef]

J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982).
[CrossRef]

1981 (2)

D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981).
[CrossRef]

1980 (3)

B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

1979 (2)

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979).
[CrossRef]

1978 (2)

H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978); P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978).
[CrossRef]

1977 (1)

I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).

1976 (2)

T. H. Allen, “Study of Al with a combined auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

T. Smith, “Effect of surface roughness on ellipsometry of aluminum,” Surf. Sci. 56, 252–271 (1976).
[CrossRef]

1975 (3)

1974 (3)

E. L. Church, J. M. Zavada, “Effects of surface microroughness in mirror absorption,” J. Opt. Soc. Am. 64, 1404A (1974); “Optical effects of surface roughness,” J. Opt. Soc. Am. 64, 574A (1974).

H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).

I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

1973 (1)

I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973).
[CrossRef]

1972 (3)

I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).

M. Badia, “Ellipsometric analysis of amorphous oxide film growth and crystalline oxide island development during thermal oxidation of aluminum,” Thin Solid Films 13, 329–331 (1972).
[CrossRef]

1971 (1)

1970 (2)

R. W. Fane, W. E. J. Neal, “Optical constants of aluminum films related to the vacuum environment,” J. Opt. Soc. Am. 60, 790–793 (1970).
[CrossRef]

O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970).
[CrossRef]

1969 (1)

1968 (1)

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

1967 (1)

H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).

1961 (1)

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

1946 (1)

G. Hass, “Über die optischen Konstanten dicker Aluminum und Silberschichten in Vakuum,” Optik 1, 8–10 (1946); G. Hass, J. E. Waylonis, “Optical constants and reflectance and transmittance of evaporated aluminum in the visible and ultraviolet,” J. Opt. Soc. Am. 51, 719–722 (1961).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,” Ann. Phys. Leipzig 24, 636–670 (1935).
[CrossRef]

Adams, A. C.

B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).

Allen, T. H.

T. H. Allen, “Study of Al with a combined auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

Alterovitz, S. A.

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Appleton, B. R.

O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
[CrossRef]

Ashley, E. J.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).

B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975); “Methods for drift stabilization and photomultiplier linearization for photometric ellipsometers and polarimeters,” Rev. Sci. Instrum. 49, 291–279 (1978).
[PubMed]

D. E. Aspnes, J. B. Theeten, “Dielectric/semiconductor interface using spectroscopic ellipsometry,” Acta Electron. 24, 217–227 (1981–1982).

Azzam, R. M. A.

Badia, M.

M. Badia, “Ellipsometric analysis of amorphous oxide film growth and crystalline oxide island development during thermal oxidation of aluminum,” Thin Solid Films 13, 329–331 (1972).
[CrossRef]

Bagley, B. G.

B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).

Beaglehole, D.

O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970).
[CrossRef]

Beckman, P.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

Bennett, H. E.

H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978); P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

J. L. Stanford, H. E. Bennett, “Enhancement of surface plasma resonance absorption in mirrors by overcoating with dielectrics,” Appl. Opt. 8, 2556–2557 (1969).
[CrossRef] [PubMed]

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).

H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
[CrossRef]

Bennett, J. M.

J. M. Bennett, “Scattering and surface evaluation techniques for the optics of the future,” Opt. News 11(7), 17–27 (1985).
[CrossRef]

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).

J. M. BennettU.S. Naval Weapons Center, Michelson Laboratory, China Lake, CA 93555 (personal communication).

J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).

Blanco, J. R.

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
[CrossRef] [PubMed]

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).

Bodó, Z.

Bohringer, A.

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,” Ann. Phys. Leipzig 24, 636–670 (1935).
[CrossRef]

Cardona, M.

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

Celli, V.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Church, E. L.

E. L. Church, J. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
[CrossRef] [PubMed]

E. L. Church, J. M. Zavada, “Effects of surface microroughness in mirror absorption,” J. Opt. Soc. Am. 64, 1404A (1974); “Optical effects of surface roughness,” J. Opt. Soc. Am. 64, 574A (1974).

Elson, J. M.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

Fane, R. W.

Gergely, G.

Granquist, C.

C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978).
[CrossRef]

Guenther, K. H.

Gundat, W.

H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).

Hagemann, H.-J.

H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).

Hass, G.

G. Hass, “Über die optischen Konstanten dicker Aluminum und Silberschichten in Vakuum,” Optik 1, 8–10 (1946); G. Hass, J. E. Waylonis, “Optical constants and reflectance and transmittance of evaporated aluminum in the visible and ultraviolet,” J. Opt. Soc. Am. 51, 719–722 (1961).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Solid Films (Dover, New York, 1965), p. 200.

Holland, O. W.

O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
[CrossRef]

J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979).
[CrossRef]

Hunderi, O.

C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978).
[CrossRef]

O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970).
[CrossRef]

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

Kunz, C.

H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).

Lin, C.

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

Llebaria, A.

Lukes, F.

I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).

Lukeš, F.

I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).

I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973).
[CrossRef]

I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

I. Ohlídal, K. Navrátil, F. Lukeš, “Reflection of light by a system of nonabsorbing isotropic film-nonabsorbing isotropic substrate with randomly rough boundaries,” J. Opt. Soc. Am. 61, 1630–1639 (1971).
[CrossRef]

Marvin, A.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Mayani, N.

McMarr, P. J.

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
[CrossRef] [PubMed]

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
[CrossRef]

P. J. McMarr, “Characterization of surfaces, thin films, and ion-implanted silicon by spectroscopic ellipsometry,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1985).

J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).

Merkel, K. G.

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Messier, R.

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

Motyka, R. J.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

Narayan, J.

P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
[CrossRef]

O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
[CrossRef]

J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982).
[CrossRef]

Navrátil, K.

I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).

I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

I. Ohlídal, K. Navrátil, F. Lukeš, “Reflection of light by a system of nonabsorbing isotropic film-nonabsorbing isotropic substrate with randomly rough boundaries,” J. Opt. Soc. Am. 61, 1630–1639 (1971).
[CrossRef]

Neal, W. E. J.

Nee, Soe-Mie F.

Ohlidal, I.

I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).

Ohlídal, I.

I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973).
[CrossRef]

I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

I. Ohlídal, K. Navrátil, F. Lukeš, “Reflection of light by a system of nonabsorbing isotropic film-nonabsorbing isotropic substrate with randomly rough boundaries,” J. Opt. Soc. Am. 61, 1630–1639 (1971).
[CrossRef]

Ohlíidal, I.

I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).

Palmari, J. P.

Porteus, J. O.

Rahn, J. P.

Rai, A. K.

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Rasigni, G.

Rasigni, M.

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

Schonherr, E.

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

Smith, D. Y.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

Smith, T.

T. Smith, “Effect of surface roughness on ellipsometry of aluminum,” Surf. Sci. 56, 252–271 (1976).
[CrossRef]

Snyder, P. G.

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Spizzichino, A.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

Stanford, J. L.

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).

D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975); “Methods for drift stabilization and photomultiplier linearization for photometric ellipsometers and polarimeters,” Rev. Sci. Instrum. 49, 291–279 (1978).
[PubMed]

Teague, E. C.

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, “Dielectric/semiconductor interface using spectroscopic ellipsometry,” Acta Electron. 24, 217–227 (1981–1982).

Toigo, F.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Varnier, F.

Vedam, K.

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
[CrossRef] [PubMed]

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).

Vorburger, T. V.

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981).
[CrossRef]

Wierer, P. G.

Woollam, J. A.

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Yehoda, J. E.

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

Zavada, J.

Zavada, J. M.

E. L. Church, J. M. Zavada, “Effects of surface microroughness in mirror absorption,” J. Opt. Soc. Am. 64, 1404A (1974); “Optical effects of surface roughness,” J. Opt. Soc. Am. 64, 574A (1974).

Zollner, S.

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

Acta Electron. (1)

D. E. Aspnes, J. B. Theeten, “Dielectric/semiconductor interface using spectroscopic ellipsometry,” Acta Electron. 24, 217–227 (1981–1982).

Ann. Phys. Leipzig (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,” Ann. Phys. Leipzig 24, 636–670 (1935).
[CrossRef]

Appl. Opt. (10)

D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975); “Methods for drift stabilization and photomultiplier linearization for photometric ellipsometers and polarimeters,” Rev. Sci. Instrum. 49, 291–279 (1978).
[PubMed]

E. L. Church, J. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985).
[CrossRef] [PubMed]

Soe-Mie F. Nee, “Ellipsometric analysis for surface roughness and texture,” Appl. Opt. 27, 2819–2831 (1988).
[CrossRef] [PubMed]

F. Varnier, G. Rasigni, J. P. Palmari, A. Llebaria, M. Rasigni, “Influence of some parameters on the surface profile restored from microdensitometer analysis of electron micrographs of surface replicas,” Appl. Opt. 23, 3705–3717 (1984).
[CrossRef] [PubMed]

F. Varnier, N. Mayani, G. Rasigni, “Statistical parameters for rough surfaces of thin films of CaF2 and Ag/CaF2,” Appl. Opt. 28, 127–134 (1989).
[CrossRef] [PubMed]

J. L. Stanford, H. E. Bennett, “Enhancement of surface plasma resonance absorption in mirrors by overcoating with dielectrics,” Appl. Opt. 8, 2556–2557 (1969).
[CrossRef] [PubMed]

Z. Bodó, G. Gergely, “Intrinsic optical constants of aluminum,” Appl. Opt. 26, 2065–2067 (1987).
[CrossRef] [PubMed]

Bull. Am. Phys. Soc. (1)

B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Deutsches Elektronen-Synchrotron SR-74/7 (1)

H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).

J. Appl. Phys. (2)

O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983).
[CrossRef]

S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Phys. C (1)

I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).

J. Vac. Sci. Technol. (2)

T. H. Allen, “Study of Al with a combined auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982).
[CrossRef]

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

J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (2)

J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985).
[CrossRef]

P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986).
[CrossRef]

Opt. Acta (1)

I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

Opt. Commun. (2)

I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).

I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973).
[CrossRef]

Opt. Eng. (1)

H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978); P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

Opt. Lett. (1)

Opt. News (1)

J. M. Bennett, “Scattering and surface evaluation techniques for the optics of the future,” Opt. News 11(7), 17–27 (1985).
[CrossRef]

Optik (1)

G. Hass, “Über die optischen Konstanten dicker Aluminum und Silberschichten in Vakuum,” Optik 1, 8–10 (1946); G. Hass, J. E. Waylonis, “Optical constants and reflectance and transmittance of evaporated aluminum in the visible and ultraviolet,” J. Opt. Soc. Am. 51, 719–722 (1961).
[CrossRef]

Phys. Rev. (1)

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968).
[CrossRef]

Phys. Rev. A (1)

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).

phys. rev. B (1)

C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978).
[CrossRef]

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979).
[CrossRef]

Phys. Status Solidi A (1)

J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982).
[CrossRef]

Phys. Thin Films (1)

H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).

Precis. Eng. (1)

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).

Surf. Sci. (2)

T. Smith, “Effect of surface roughness on ellipsometry of aluminum,” Surf. Sci. 56, 252–271 (1976).
[CrossRef]

I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

Thin Solid Films (1)

M. Badia, “Ellipsometric analysis of amorphous oxide film growth and crystalline oxide island development during thermal oxidation of aluminum,” Thin Solid Films 13, 329–331 (1972).
[CrossRef]

Other (6)

O. S. Heavens, Optical Properties of Solid Films (Dover, New York, 1965), p. 200.

The portable instrument was built by Talandic Research Corp., 2793 East Foothill Ave., Pasadena, Calif. 91107 for the U.S. Army as part of a contract with the Naval Weapons Center (Jean M. Bennett was principal investigator). J. M. Bennett made this set of measurements as part of the demonstration to the Army that the instrument does indeed measure TIS.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

P. J. McMarr, “Characterization of surfaces, thin films, and ion-implanted silicon by spectroscopic ellipsometry,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1985).

J. M. BennettU.S. Naval Weapons Center, Michelson Laboratory, China Lake, CA 93555 (personal communication).

J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).

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Figures (8)

Fig. 1
Fig. 1

Real (1) and imaginary (2) parts of dielectric function as a function of the photon energy for amorphous silicon (—)37 and the ion-implanted silicon sample (- - - -), this work.

Fig. 2
Fig. 2

Real (1) and imaginary (2) parts of the dielectric function of aluminum evaporated film, sample R-2B, the smoothest of the available samples, with an rms roughness of 1.49 nm.

Fig. 3
Fig. 3

Ellipsometric parameters as a function of wavelength and angle of incidence for the silicon sample: (a) delta and (b) psi. The angle of incidence for both curves is as follows: 30° (—), 40° (- . - .), 50° (- . . -), 60° (- . . . -), 70° (- . . . . -), and 80° (- - - -).

Fig. 4
Fig. 4

(a) Cross-sectional transmission electron micrograph of the silicon sample. The optical penetration depth (OPD) is indicated by the arrow; the start of the arrow also marks the sample surface. (b) Schematic diagram of the effective-medium theory model for the silicon sample.

Fig. 5
Fig. 5

tan β as a function of wavelength as determined by spectroscopic ellipsometry for fourteen aluminum roughness standards for an angle of incidence of 70°. The classification is as follows: (●) R-B, (+) R-3B, (×) R-4B, (○) R-5B, (△) R-6B, (▲) R-7B, (◇) R-8B, (□) R-9B, (▽) R-10B, (−) R-11B, (▼) R-12B, (■) R-13B, (●) R-14B, and (|) R-15B.

Fig. 6
Fig. 6

tan β as a function of wavelength and of angle of incidence for aluminum sample R-4B. The angle of incidence classification is as follows: 30° (×), 40° (□), 50° (◇), 60° (▲), 70° (+), and 80° (●).

Fig. 7
Fig. 7

tan β as a function of wavelength and of angle of incidence for aluminum sample R-8B. The angle of incidence classification is as follows: 30° (×), 40° (□), 50° (◇), 60° (▲), 70° (+), and 80° (●).

Fig. 8
Fig. 8

ln(Rr/Rsm) vs λ−2 for aluminum samples R-4B (■) and R-8B (+).

Tables (4)

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Table I Total Integrated Scattering and rms Roughness Calculated from TIS = 1 − exp[−(πσ/λ)2]a

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Table II Ellipsometric Characterization of the Microroughness of the a-Si sample (Si Single Crystal Implanted with Si lonsa) Using the Bruggeman Effective-Medlum Theory

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Table III Root-Mean-Square Surface Slope (tan β) Derived from Spectroscopic Ellipsometry Measurements at 70° Angle of Incidencea

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Table IV Angles Δ and Ψ (In Degrees) Measured by SE for Al Samples R-2B, R-4B, and R-8B as a Function of Wavelength and Angle of Incidence θ

Equations (3)

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ξ = { 1 ( n - p - 1 ) j = 1 n [ ( cos Δ exp j - cos Δ cal j ) 2 + ( tan Ψ exp j - tan Ψ cal j ) 2 ] } 1 / 2 ,
ρ 0 = tan ( Ψ 0 ) exp ( i Δ 0 ) .
R p , s ( θ ) = R p , s ( θ ) [ 1 - ½ ( 4 π σ cos θ ) 2 f p , s ( θ , T / λ ) + ] ,

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