Abstract

From a series of ellipsometric measurements it is now possible to obtain uniquely all of the optical parameters of the system; absorbing substrate+nonabsorbing surface film. The method utilizes the fact that the reflectance of such a system at normal incidence remains essentially constant for a small but finite range of surface-film thicknesses. Furthermore, it hinges on the fact that the ellipsometric parameters Δ and ψ, measured on different film thicknesses grown on the same sample, are compatible with only one choice of the complex refractive index n2+ik2 of the substrate and the refractive index n1 of the film. Measurements on chemically etched samples of silicon yield n2 = 4.052 and k2 = 0.029, in agreement with the results of earlier workers. Measurements on cleaved samples of silicon, on the other hand, reveal that the true values are n2 = 4.140±0.02 and k2 = 0.034±0.01 for 5461 Å.

© 1969 Optical Society of America

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References

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  1. R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962).
    [Crossref]
  2. R. J. Archer, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. Misc. Publ. 256, U. S. Gov’t Printing Off., Washington, 1964.
  3. D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
    [Crossref]
  4. R. J. Archer, J. Electrochem. Soc. 104, 619 (1957); R. J. Archer, Phys. Rev. 110, 354 (1958).
    [Crossref]
  5. K. H. Zaininger and A. G. Revesz, J. Phys. Radium 25, 208 (1964).
  6. K. Vedam, R. Rai, F. Lukes, and R. Srinivasan, J. Opt. Soc. Am. 58, 526 (1968).
    [Crossref]
  7. A. Vašíčicek, Optics of Thin Films (North-Holland Publishing Co., Amsterdam1960); O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth’s Scientific Publications, London, 1955).
  8. S. M. Fainshtein and V. I. Fistul, Sov. Phys.—Tech Phys. 1, 2099 (1957).
  9. A. Many and D. Herlich, Phys. Rev. 107, 404 (1957).
    [Crossref]
  10. G. W. Gobeli and F. G. Allen, J. Phys. Chem. Solids 14, 23 (1960); Phys. Rev. 127, 149 (1962).
    [Crossref]
  11. N. M. Bashara and D. W. Peterson, J. Opt. Soc. Am. 56, 1320 (1966).
    [Crossref]
  12. In Ref. (6) which deals with the refractive index of thin films of SiO2 on silicon, the computations will have to be redone using the new values of the optical constants of silicon reported in this paper. This can influence the value of n1 evaluated as well.
  13. W. C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955).
    [Crossref]
  14. R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
    [Crossref]

1968 (1)

1966 (1)

1964 (2)

D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
[Crossref]

K. H. Zaininger and A. G. Revesz, J. Phys. Radium 25, 208 (1964).

1962 (1)

1960 (1)

G. W. Gobeli and F. G. Allen, J. Phys. Chem. Solids 14, 23 (1960); Phys. Rev. 127, 149 (1962).
[Crossref]

1958 (1)

R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
[Crossref]

1957 (3)

R. J. Archer, J. Electrochem. Soc. 104, 619 (1957); R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

S. M. Fainshtein and V. I. Fistul, Sov. Phys.—Tech Phys. 1, 2099 (1957).

A. Many and D. Herlich, Phys. Rev. 107, 404 (1957).
[Crossref]

1955 (1)

W. C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955).
[Crossref]

Allen, F. G.

G. W. Gobeli and F. G. Allen, J. Phys. Chem. Solids 14, 23 (1960); Phys. Rev. 127, 149 (1962).
[Crossref]

Archer, R. J.

R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962).
[Crossref]

R. J. Archer, J. Electrochem. Soc. 104, 619 (1957); R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

R. J. Archer, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. Misc. Publ. 256, U. S. Gov’t Printing Off., Washington, 1964.

Bashara, N. M.

Bennett, H. E.

Braunstein, R.

R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
[Crossref]

Burge, D. K.

Dash, W. C.

W. C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955).
[Crossref]

Fainshtein, S. M.

S. M. Fainshtein and V. I. Fistul, Sov. Phys.—Tech Phys. 1, 2099 (1957).

Fistul, V. I.

S. M. Fainshtein and V. I. Fistul, Sov. Phys.—Tech Phys. 1, 2099 (1957).

Gobeli, G. W.

G. W. Gobeli and F. G. Allen, J. Phys. Chem. Solids 14, 23 (1960); Phys. Rev. 127, 149 (1962).
[Crossref]

Herlich, D.

A. Many and D. Herlich, Phys. Rev. 107, 404 (1957).
[Crossref]

Herman, F.

R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
[Crossref]

Lukes, F.

Many, A.

A. Many and D. Herlich, Phys. Rev. 107, 404 (1957).
[Crossref]

Moore, A. R.

R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
[Crossref]

Newman, R.

W. C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955).
[Crossref]

Peterson, D. W.

Rai, R.

Revesz, A. G.

K. H. Zaininger and A. G. Revesz, J. Phys. Radium 25, 208 (1964).

Srinivasan, R.

Vašícicek, A.

A. Vašíčicek, Optics of Thin Films (North-Holland Publishing Co., Amsterdam1960); O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth’s Scientific Publications, London, 1955).

Vedam, K.

Zaininger, K. H.

K. H. Zaininger and A. G. Revesz, J. Phys. Radium 25, 208 (1964).

J. Electrochem. Soc. (1)

R. J. Archer, J. Electrochem. Soc. 104, 619 (1957); R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

J. Opt. Soc. Am. (4)

J. Phys. Chem. Solids (1)

G. W. Gobeli and F. G. Allen, J. Phys. Chem. Solids 14, 23 (1960); Phys. Rev. 127, 149 (1962).
[Crossref]

J. Phys. Radium (1)

K. H. Zaininger and A. G. Revesz, J. Phys. Radium 25, 208 (1964).

Phys. Rev. (3)

W. C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955).
[Crossref]

R. Braunstein, A. R. Moore, and F. Herman, Phys. Rev. 109, 695 (1958).
[Crossref]

A. Many and D. Herlich, Phys. Rev. 107, 404 (1957).
[Crossref]

Sov. Phys.—Tech Phys. (1)

S. M. Fainshtein and V. I. Fistul, Sov. Phys.—Tech Phys. 1, 2099 (1957).

Other (3)

R. J. Archer, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. Misc. Publ. 256, U. S. Gov’t Printing Off., Washington, 1964.

A. Vašíčicek, Optics of Thin Films (North-Holland Publishing Co., Amsterdam1960); O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth’s Scientific Publications, London, 1955).

In Ref. (6) which deals with the refractive index of thin films of SiO2 on silicon, the computations will have to be redone using the new values of the optical constants of silicon reported in this paper. This can influence the value of n1 evaluated as well.

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Figures (10)

Fig. 1
Fig. 1

Variation of n ¯ 2 , k ¯ 2, and R as a function of δ (and hence the film thickness d1). The initial parameters assumed are n2 = 4.050, k2 = 0.028, n1 = 1.460, ϕ = 70° and λ = 5461 Å.

Fig. 2
Fig. 2

The permissible sets of n2, k2 for the given reflectance R ¯ = 36.495% (solid line). The hatched lines indicate the permissible range of sets of n2, k2 for a ±0.1% possible error in determination of R.

Fig. 3
Fig. 3

Silicon, ideal case: Calculated values of n1 vs n2 for various values of film thickness δ for the silicon ideal case. n2 = 4.0517 and k2 = 0.028 were assumed in the calculation of n1 vs n2.

Fig. 4
Fig. 4

GaAs, ideal case: Calculated values of n1 vs n2 for various values of film thickness δ for the gallium arsenide ideal case. n2 = 3.923 and k2 = 0.304 were assumed in the calculation of n1 vs n2.

Fig. 5
Fig. 5

Ge, ideal case: Calculated values of n1 vs n2 for various value of film thickness δ for the germanium ideal case. n2 = 5.30 and k2 = 1.983 were assumed in the calculation of n1 vs n2.

Fig. 6
Fig. 6

Tungsten, ideal case: Calculated values of n1 vs n2 for various values of film thickness δ for the tungsten ideal case. n2 = 3.46 and k2 = 3.250 were assumed in the calculation of n1 vs n2.

Fig. 7
Fig. 7

Si, etched sample: Calculated values of n1 vs n2 for various values of film thickness δ for the case of chemically etched silicon. Experimental data were used and no values of the optical parameters were assumed.

Fig. 8
Fig. 8

Silicon, ideal case: Three groups of calculated values of n1 vs n2 corresponding to three different reflectances R for various values of film thickness in the silicon ideal case. The intersections of the curves for various pairs of thickness values are connected by the thin straight lines; they all intersect in a point which defines the true (and in this case assumed) optical parameters of the system. Dashed interconnecting lines indicate regions where there is no longer an intersection between the curves for a particular pair of δ values for real values of k2.

Fig. 9
Fig. 9

Silicon, cleaved sample: Three groups of calculated values of n1 vs n2 corresponding to three different reflectances R for various values of film thickness δ in the case of a cleaved silicon sample. The intersections of the curves for various pairs of δ values are connected by the thin straight lines; they all intersect in a point which defines the true optical parameters of the system. Dashed interconnecting lines indicate regions where there is no longer an intersection between the curves for a particular pair of δ values for real values of k2.

Fig. 10
Fig. 10

Silicon, cleaved sample: Calculated values of n1 vs n2 for various values of film thickness δ in the case of cleaved silicon (experimental). The calculation was performed for that value of R ¯ which was determined by the intersections of Fig. 9.

Tables (3)

Tables Icon

Table I Calculated values of Δ and ψ for various thicknesses of film of refractive index 1.460 on a substrate of refractive index n2 = 4.050 and k2 = 0.028. The values of n ¯ 2 , k ¯ 2 and R computed from these Δ and ψ are also given in the table.

Tables Icon

Table II Silicon, chemically polished sample: Possible values of (n2,k2) for R ¯ = 36.495%.

Tables Icon

Table III Optical constants of silicon for 5461 Å.

Equations (4)

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n ¯ 2 2 - k ¯ 2 2 = n 0 2 sin 2 ϕ + n 0 2 sin 2 ϕ tan 2 ϕ cos 2 2 ψ - sin 2 2 ψ sin 2 Δ ( 1 + sin 2 ψ cos Δ ) 2
2 n ¯ 2 k ¯ 2 = n 0 2 sin 2 ϕ tan 2 ϕ sin 4 ψ sin Δ ( 1 + sin 2 ψ cos Δ ) 2
R = [ ( n ¯ 2 - n 0 ) 2 + k ¯ 2 2 ] / [ ( n ¯ 2 + n 0 ) 2 + k ¯ 2 2 ] .
k 2 = { 2 ( 1 + R ¯ 1 - R ¯ ) n 2 n 0 - [ ( n 2 ) 2 + n 0 2 ] } 1 2 .