Abstract

In many technologies a means of characterizing the surfaces of vacuum-deposited metal films would be desirable. Following the first part of this work, which dealt with light scattering, we have assessed ellipsometry as a possible tool. For surfaces with a root-mean-square roughness smaller than 40 nm the influence of roughness on ellipsometric parameters ψ and Δ was observed to be very small (<0.02°/nm) at a wavelength of 632.8 nm. These surfaces however had a different morphology as shown by a scanning electron microscope. Rougher surfaces showed a dominant decrease in ψ and a relatively smaller decrease in Δ with increasing roughness. Besides the influence of surface roughness, the particular morphology of the surface and the constitution of the residual gas atmosphere during evaporation of the Al thin film were shown to be also of significance. For this reason, together with the inability to discriminate between roughness values in the 0–40-nm range, ellipsometry at 632.8 nm wavelength is less suitable for measuring surface roughness of vacuum-deposited films.

© 1986 Optical Society of America

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References

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  1. M. J. Verkerk, I. J. M. M. Raaijmakers, “Topographic Characterization of Vacuum-Deposited Thin Films by Optical Methods,” Thin Solid Films 124, 271 (1985).
    [CrossRef]
  2. M. J. Verkerk, I. J. M. M. Raaijmakers, “Characterization of the Topography of Vacuum-Deposited Films. 1: Light Scattering,” Appl. Opt. 25, 0000 (1986), same issue.
    [CrossRef]
  3. C. F. Fenstermaker, F. L. McCrackin, “Errors arising from Surface Roughness in Ellipsometric Measurement of the Refractive Index of a Surface,” Surf. Sci. 16, 85 (1969).
    [CrossRef]
  4. K. Vedam, M. Malin, “Characterization of Real Surfaces of Vitreous Silica by Ellipsometry,” Mater. Res. Bull. 9, 1053 (1974).
    [CrossRef]
  5. K. Riedling, “Error Effects in the Ellipsometric Investigation of Thin Films,” Thin Solid Films 75, 355 (1981).
    [CrossRef]
  6. E. L. Church, J. M. Zavada, “Effects of Surface Microroughness in Ellipsometry,” J. Opt. Soc. Am. 66, 1136 (1976); “Residual Surface Roughness of Diamond-Turned Optics,” Appl. Opt. 14, 1788 (1975).
    [PubMed]
  7. J. P. Marton, E. C. Chang, “Surface Roughness Interpretation of Ellipsometer Measurements using the Maxwell Garnett Theory,” J. Appl. Phys. 45, 5008 (1974).
    [CrossRef]
  8. D. E. Aspnes, “Optical Properties of Thin Films,” Thin Solid Films 89, 249 (1982).
    [CrossRef]
  9. 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 (1979).
    [CrossRef]
  10. T. V. Vorburger, K. C. Ludema, “Ellipsometry of Rough Surfaces,” Appl. Opt. 19, 561 (1980).
    [CrossRef] [PubMed]
  11. T. Smith, “Effect of Surface Roughness on Ellipsometry of Aluminium,” Surf. Sci. 56, 252 (1976).
    [CrossRef]
  12. I. Ohlidal, F. Lukes, “Ellipsometric Parameters of Rough Surfaces and of a System Substrate—Thin Film with Rough Boundaries,” Opt. Acta 19, 817 (1972); I. Ohlidal, F. Lukes, K. Navratil, “Rough Silicon Surfaces Studied by Optical Methods,” Surf. Sci. 45, 91 (1974).
    [CrossRef]
  13. P. M. Lonardo, “Testing a New Optical Sensor for In-Process Detection of Surface Roughness,” Ann. CIRP 27, 531 (1978).
  14. J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness Measurements by Spectroscopic Ellipsometry,” Appl. Opt. 24, 3773 (1985).
    [CrossRef] [PubMed]
  15. R. M. A. Azzam, H. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  16. M. E. Pedinoff, O. M. Stafsudd, “Multiple Angle Ellipsometric Analysis of Surface Layers and Surface Layer Contaminants,” Appl. Opt. 21, 518 (1982).
    [CrossRef] [PubMed]
  17. 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 (1979).
    [CrossRef]
  18. M. Erman, “Ellipsométrie Spectroscopique du Proche IR au Proche UV: Appareillage et Methodologie,” Thesis, U. Orsay, France (1982).
  19. J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
    [CrossRef]
  20. H. Arwin, D. E. Aspnes, “Unambiguous Determination of Thickness and Dielectric Function of Thin Films by Spectroscopic Ellipsometry,” Thin Solid Films 113, 101 (1984).
    [CrossRef]
  21. D. E. Aspnes, “Studies of Surface, Thin Film and Interface Properties by Automatic Spectroscopic Ellipsometry,” J. Vac. Sci. Technol. 18, 289 (1981).
    [CrossRef]
  22. J. H. Halford, F. K. Chin, J. E. Norman, “Optical Constants of Ultrapure Al Films,” J. Opt. Soc. Am. 63, 786 (1973).
    [CrossRef]
  23. R. W. Fane, W. E. J. Neal, “Optical Constants of Aluminium Films Related to the Vacuum Environment,” J. Opt. Soc. Am. 60, 790 (1970).
    [CrossRef]
  24. A. C. Nyce, L. P. Skolnick, “Optical Constants of Bulk and Thin Film Aluminium at 6328 Å,” J. Opt. Soc. Am. 65, 792 (1975).
    [CrossRef]
  25. H. M. O’Bryan, “The Optical Constants of Several Metals in Vacuum,” J. Opt. Soc. Am. 26, 122 (1936).
    [CrossRef]
  26. J. F. de Torre, T. G. Knorr, D. A. Vaughan, “Application of Ellipsometry to the Study of Phenomena on Surfaces Prepared in Ultra-High Vacuum,” in Proceedings, Symposium on Ellipsometry in the Measurement of Surfaces and Thin Films (National Bureau of Standards, Washington, DC, 1964), pp. 245–254.

1986 (1)

M. J. Verkerk, I. J. M. M. Raaijmakers, “Characterization of the Topography of Vacuum-Deposited Films. 1: Light Scattering,” Appl. Opt. 25, 0000 (1986), same issue.
[CrossRef]

1985 (2)

M. J. Verkerk, I. J. M. M. Raaijmakers, “Topographic Characterization of Vacuum-Deposited Thin Films by Optical Methods,” Thin Solid Films 124, 271 (1985).
[CrossRef]

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness Measurements by Spectroscopic Ellipsometry,” Appl. Opt. 24, 3773 (1985).
[CrossRef] [PubMed]

1984 (1)

H. Arwin, D. E. Aspnes, “Unambiguous Determination of Thickness and Dielectric Function of Thin Films by Spectroscopic Ellipsometry,” Thin Solid Films 113, 101 (1984).
[CrossRef]

1982 (2)

1981 (2)

K. Riedling, “Error Effects in the Ellipsometric Investigation of Thin Films,” Thin Solid Films 75, 355 (1981).
[CrossRef]

D. E. Aspnes, “Studies of Surface, Thin Film and Interface Properties by Automatic Spectroscopic Ellipsometry,” J. Vac. Sci. Technol. 18, 289 (1981).
[CrossRef]

1980 (2)

T. V. Vorburger, K. C. Ludema, “Ellipsometry of Rough Surfaces,” Appl. Opt. 19, 561 (1980).
[CrossRef] [PubMed]

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[CrossRef]

1979 (2)

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 (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 (1979).
[CrossRef]

1978 (1)

P. M. Lonardo, “Testing a New Optical Sensor for In-Process Detection of Surface Roughness,” Ann. CIRP 27, 531 (1978).

1976 (2)

E. L. Church, J. M. Zavada, “Effects of Surface Microroughness in Ellipsometry,” J. Opt. Soc. Am. 66, 1136 (1976); “Residual Surface Roughness of Diamond-Turned Optics,” Appl. Opt. 14, 1788 (1975).
[PubMed]

T. Smith, “Effect of Surface Roughness on Ellipsometry of Aluminium,” Surf. Sci. 56, 252 (1976).
[CrossRef]

1975 (1)

1974 (2)

J. P. Marton, E. C. Chang, “Surface Roughness Interpretation of Ellipsometer Measurements using the Maxwell Garnett Theory,” J. Appl. Phys. 45, 5008 (1974).
[CrossRef]

K. Vedam, M. Malin, “Characterization of Real Surfaces of Vitreous Silica by Ellipsometry,” Mater. Res. Bull. 9, 1053 (1974).
[CrossRef]

1973 (1)

1972 (1)

I. Ohlidal, F. Lukes, “Ellipsometric Parameters of Rough Surfaces and of a System Substrate—Thin Film with Rough Boundaries,” Opt. Acta 19, 817 (1972); I. Ohlidal, F. Lukes, K. Navratil, “Rough Silicon Surfaces Studied by Optical Methods,” Surf. Sci. 45, 91 (1974).
[CrossRef]

1970 (1)

1969 (1)

C. F. Fenstermaker, F. L. McCrackin, “Errors arising from Surface Roughness in Ellipsometric Measurement of the Refractive Index of a Surface,” Surf. Sci. 16, 85 (1969).
[CrossRef]

1936 (1)

Adams, T. E.

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[CrossRef]

Arwin, H.

H. Arwin, D. E. Aspnes, “Unambiguous Determination of Thickness and Dielectric Function of Thin Films by Spectroscopic Ellipsometry,” Thin Solid Films 113, 101 (1984).
[CrossRef]

Aspnes, D. E.

H. Arwin, D. E. Aspnes, “Unambiguous Determination of Thickness and Dielectric Function of Thin Films by Spectroscopic Ellipsometry,” Thin Solid Films 113, 101 (1984).
[CrossRef]

D. E. Aspnes, “Optical Properties of Thin Films,” Thin Solid Films 89, 249 (1982).
[CrossRef]

D. E. Aspnes, “Studies of Surface, Thin Film and Interface Properties by Automatic Spectroscopic Ellipsometry,” J. Vac. Sci. Technol. 18, 289 (1981).
[CrossRef]

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[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 (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 (1979).
[CrossRef]

Azzam, R. M. A.

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

Bashara, H. M.

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

Blanco, J. R.

Chang, E. C.

J. P. Marton, E. C. Chang, “Surface Roughness Interpretation of Ellipsometer Measurements using the Maxwell Garnett Theory,” J. Appl. Phys. 45, 5008 (1974).
[CrossRef]

Chang, R. P. H.

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[CrossRef]

Chin, F. K.

Church, E. L.

E. L. Church, J. M. Zavada, “Effects of Surface Microroughness in Ellipsometry,” J. Opt. Soc. Am. 66, 1136 (1976); “Residual Surface Roughness of Diamond-Turned Optics,” Appl. Opt. 14, 1788 (1975).
[PubMed]

de Torre, J. F.

J. F. de Torre, T. G. Knorr, D. A. Vaughan, “Application of Ellipsometry to the Study of Phenomena on Surfaces Prepared in Ultra-High Vacuum,” in Proceedings, Symposium on Ellipsometry in the Measurement of Surfaces and Thin Films (National Bureau of Standards, Washington, DC, 1964), pp. 245–254.

Erman, M.

M. Erman, “Ellipsométrie Spectroscopique du Proche IR au Proche UV: Appareillage et Methodologie,” Thesis, U. Orsay, France (1982).

Fane, R. W.

Fenstermaker, C. F.

C. F. Fenstermaker, F. L. McCrackin, “Errors arising from Surface Roughness in Ellipsometric Measurement of the Refractive Index of a Surface,” Surf. Sci. 16, 85 (1969).
[CrossRef]

Halford, J. H.

Hottier, F.

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 (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 (1979).
[CrossRef]

Knorr, T. G.

J. F. de Torre, T. G. Knorr, D. A. Vaughan, “Application of Ellipsometry to the Study of Phenomena on Surfaces Prepared in Ultra-High Vacuum,” in Proceedings, Symposium on Ellipsometry in the Measurement of Surfaces and Thin Films (National Bureau of Standards, Washington, DC, 1964), pp. 245–254.

Lonardo, P. M.

P. M. Lonardo, “Testing a New Optical Sensor for In-Process Detection of Surface Roughness,” Ann. CIRP 27, 531 (1978).

Ludema, K. C.

Lukes, F.

I. Ohlidal, F. Lukes, “Ellipsometric Parameters of Rough Surfaces and of a System Substrate—Thin Film with Rough Boundaries,” Opt. Acta 19, 817 (1972); I. Ohlidal, F. Lukes, K. Navratil, “Rough Silicon Surfaces Studied by Optical Methods,” Surf. Sci. 45, 91 (1974).
[CrossRef]

Malin, M.

K. Vedam, M. Malin, “Characterization of Real Surfaces of Vitreous Silica by Ellipsometry,” Mater. Res. Bull. 9, 1053 (1974).
[CrossRef]

Marton, J. P.

J. P. Marton, E. C. Chang, “Surface Roughness Interpretation of Ellipsometer Measurements using the Maxwell Garnett Theory,” J. Appl. Phys. 45, 5008 (1974).
[CrossRef]

McCrackin, F. L.

C. F. Fenstermaker, F. L. McCrackin, “Errors arising from Surface Roughness in Ellipsometric Measurement of the Refractive Index of a Surface,” Surf. Sci. 16, 85 (1969).
[CrossRef]

McMarr, P. J.

Neal, W. E. J.

Norman, J. E.

Nyce, A. C.

O’Bryan, H. M.

Ohlidal, I.

I. Ohlidal, F. Lukes, “Ellipsometric Parameters of Rough Surfaces and of a System Substrate—Thin Film with Rough Boundaries,” Opt. Acta 19, 817 (1972); I. Ohlidal, F. Lukes, K. Navratil, “Rough Silicon Surfaces Studied by Optical Methods,” Surf. Sci. 45, 91 (1974).
[CrossRef]

Pedinoff, M. E.

Raaijmakers, I. J. M. M.

M. J. Verkerk, I. J. M. M. Raaijmakers, “Characterization of the Topography of Vacuum-Deposited Films. 1: Light Scattering,” Appl. Opt. 25, 0000 (1986), same issue.
[CrossRef]

M. J. Verkerk, I. J. M. M. Raaijmakers, “Topographic Characterization of Vacuum-Deposited Thin Films by Optical Methods,” Thin Solid Films 124, 271 (1985).
[CrossRef]

Riedling, K.

K. Riedling, “Error Effects in the Ellipsometric Investigation of Thin Films,” Thin Solid Films 75, 355 (1981).
[CrossRef]

Skolnick, L. P.

Smith, T.

T. Smith, “Effect of Surface Roughness on Ellipsometry of Aluminium,” Surf. Sci. 56, 252 (1976).
[CrossRef]

Stafsudd, O. M.

Theeten, J. B.

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[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 (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 (1979).
[CrossRef]

Vaughan, D. A.

J. F. de Torre, T. G. Knorr, D. A. Vaughan, “Application of Ellipsometry to the Study of Phenomena on Surfaces Prepared in Ultra-High Vacuum,” in Proceedings, Symposium on Ellipsometry in the Measurement of Surfaces and Thin Films (National Bureau of Standards, Washington, DC, 1964), pp. 245–254.

Vedam, K.

J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness Measurements by Spectroscopic Ellipsometry,” Appl. Opt. 24, 3773 (1985).
[CrossRef] [PubMed]

K. Vedam, M. Malin, “Characterization of Real Surfaces of Vitreous Silica by Ellipsometry,” Mater. Res. Bull. 9, 1053 (1974).
[CrossRef]

Verkerk, M. J.

M. J. Verkerk, I. J. M. M. Raaijmakers, “Characterization of the Topography of Vacuum-Deposited Films. 1: Light Scattering,” Appl. Opt. 25, 0000 (1986), same issue.
[CrossRef]

M. J. Verkerk, I. J. M. M. Raaijmakers, “Topographic Characterization of Vacuum-Deposited Thin Films by Optical Methods,” Thin Solid Films 124, 271 (1985).
[CrossRef]

Vorburger, T. V.

Zavada, J. M.

E. L. Church, J. M. Zavada, “Effects of Surface Microroughness in Ellipsometry,” J. Opt. Soc. Am. 66, 1136 (1976); “Residual Surface Roughness of Diamond-Turned Optics,” Appl. Opt. 14, 1788 (1975).
[PubMed]

Ann. CIRP (1)

P. M. Lonardo, “Testing a New Optical Sensor for In-Process Detection of Surface Roughness,” Ann. CIRP 27, 531 (1978).

Appl. Opt. (4)

J. Appl. Phys. (1)

J. P. Marton, E. C. Chang, “Surface Roughness Interpretation of Ellipsometer Measurements using the Maxwell Garnett Theory,” J. Appl. Phys. 45, 5008 (1974).
[CrossRef]

J. Electrochem. Soc. (1)

J. B. Theeten, R. P. H. Chang, D. E. Aspnes, T. E. Adams, “In Situ Measurement and Analysis of Plasma Grown GaAs Oxides with Spectroscopic Ellipsometry,” J. Electrochem. Soc. 127, 378 (1980).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Vac. Sci. Technol. (1)

D. E. Aspnes, “Studies of Surface, Thin Film and Interface Properties by Automatic Spectroscopic Ellipsometry,” J. Vac. Sci. Technol. 18, 289 (1981).
[CrossRef]

Mater. Res. Bull. (1)

K. Vedam, M. Malin, “Characterization of Real Surfaces of Vitreous Silica by Ellipsometry,” Mater. Res. Bull. 9, 1053 (1974).
[CrossRef]

Opt. Acta (1)

I. Ohlidal, F. Lukes, “Ellipsometric Parameters of Rough Surfaces and of a System Substrate—Thin Film with Rough Boundaries,” Opt. Acta 19, 817 (1972); I. Ohlidal, F. Lukes, K. Navratil, “Rough Silicon Surfaces Studied by Optical Methods,” Surf. Sci. 45, 91 (1974).
[CrossRef]

Phys. Rev. B (2)

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 (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 (1979).
[CrossRef]

Surf. Sci. (2)

T. Smith, “Effect of Surface Roughness on Ellipsometry of Aluminium,” Surf. Sci. 56, 252 (1976).
[CrossRef]

C. F. Fenstermaker, F. L. McCrackin, “Errors arising from Surface Roughness in Ellipsometric Measurement of the Refractive Index of a Surface,” Surf. Sci. 16, 85 (1969).
[CrossRef]

Thin Solid Films (4)

K. Riedling, “Error Effects in the Ellipsometric Investigation of Thin Films,” Thin Solid Films 75, 355 (1981).
[CrossRef]

M. J. Verkerk, I. J. M. M. Raaijmakers, “Topographic Characterization of Vacuum-Deposited Thin Films by Optical Methods,” Thin Solid Films 124, 271 (1985).
[CrossRef]

D. E. Aspnes, “Optical Properties of Thin Films,” Thin Solid Films 89, 249 (1982).
[CrossRef]

H. Arwin, D. E. Aspnes, “Unambiguous Determination of Thickness and Dielectric Function of Thin Films by Spectroscopic Ellipsometry,” Thin Solid Films 113, 101 (1984).
[CrossRef]

Other (3)

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

J. F. de Torre, T. G. Knorr, D. A. Vaughan, “Application of Ellipsometry to the Study of Phenomena on Surfaces Prepared in Ultra-High Vacuum,” in Proceedings, Symposium on Ellipsometry in the Measurement of Surfaces and Thin Films (National Bureau of Standards, Washington, DC, 1964), pp. 245–254.

M. Erman, “Ellipsométrie Spectroscopique du Proche IR au Proche UV: Appareillage et Methodologie,” Thesis, U. Orsay, France (1982).

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Figures (7)

Fig. 1
Fig. 1

Effective medium theories depicted in the complex plane. The arrows indicate increasing void percentage. The absolute limits for are given by the Wiener bounds (1 and 2). In this case (Al and air as constitutents) they nearly coincide with the Maxwell-Garnett lines (3 and 4). In the figure the difference is exaggerated for the sake of clarity. The inconsistency in the Maxwell-Garnett approach is solved by the EMA (5). If a deviation from 3-D isotropy is present one obtains a curve similar to (6). Note that a very small deviation of q from 1 drastically decreases the width between the upper and lower bounds of .

Fig. 2
Fig. 2

ψ-Δ values for samples with different surface roughnesses.

Fig. 3
Fig. 3

SEM photographs of two samples with σ < 40 nm which yield equal results with ellipsometry: (a) σ = 13 nm, (b) σ = 25 nm.

Fig. 4
Fig. 4

Measured vs calculated ψ and Δ values as a function of the angle of incidence. The calculated values are obtained by assuming that the sample consists of a new substrate with different optical constants covered with a 4-nm oxide layer. (a) Δ; (b) ψ.

Fig. 5
Fig. 5

Values of the effective dielectric constants of the rough surface plotted in the complex plane. The same symbols for different samples were used as in Fig. 4.

Fig. 6
Fig. 6

ψ-Δ loci for samples deposited with increased water partial pressure. The × refers to measured points. The curve marked dox (○) represents calculated ψ,Δ values for an aluminum surface with an increased native oxide thickness (2.5 nm increase/dot); the curve marked fAl2O3 (□) represents aluminum contaminated with Al2O3. Each square represents an increase of 5% in the volume fraction of Al2O3.

Fig. 7
Fig. 7

SEM photographs of two samples with the same roughness according to light scattering but yielding different ellipsometric angles ψ and Δ (Table I): (a) Sample A, (b) Sample B from Table I.

Tables (1)

Tables Icon

Table I Two Samples, Evaporated in Different Conditions but Having Approximately the Same Roughness as Measured by Light Scattering, Show Very Different ψ,Δ Values

Equations (3)

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

ρ = R p R s = tan ψ exp i Δ ,
eff = a b + ( f a a + f b b ) + ( f b a + f a b ) ,
= 1 - q q h ,

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