Abstract

The thin oxide film present on most metals and semiconductors is difficult to detect and, if uncorrected for, can cause serious errors in the ellipsometric determination of optical constants. The reflectance at normal incidence calculated from these incorrect optical constants will, in general, be higher than that measured experimentally for a film-covered sample. A comparison of the approximate, linear, thin-film relations of Drude and Archer with the exact equations shows that the Drude relations are more inaccurate than are usually reported; in some cases serious errors result for films as thin as 10 Å. Archer’s relations are more accurate than Drude’s in most cases. However, if either of these sets of relations is used to correct measured ellipsometric values to the no-film condition, considerable errors in determining the optical constants may occur even if the film thickness is known. The variation in the ellipsometric parameters ψ and Δ with angle of incidence cannot be used to determine the presence of a thin surface film, since calculations show that the variation of these parameters with angle of incidence for a film-covered surface is practically identical with that for a fictitious film-free surface with appropriate optical constants. Also, the requirement that <i>R<sub>s</sub></i><sup>2</sup>= <i>R<sub>p</sub></i> at 45° angle of incidence is only marginally useful in detecting a surface film.

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  1. P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).
  2. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific Publications Ltd., London, 1955), p. 125.
  3. R. J. Archer, J. Electrochem. Soc. 104, 619 (1957).
  4. A. B. Winterbottom, Kgl. Norske Videnskab. Selskabs, Skrifter 1, 1 (1955).
  5. R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962).
  6. A. Rothen, Rev. Sci. Instr. 16, 26 (1945); 28, 283 (1957).
  7. McCrackin, Passaglia, Stromberg, and Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963).
  8. P. Theroux and R. C. Plumb, J. Opt. Soc. Am. 53, 1451 (1963).
  9. J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).
  10. The formulas as given in A.Vasicek, Optics of Thin Filmns (North-Holland Publishing Company, Amsterdam, 1960), p. 315, are incorrect. The correct expressions are given by L. Tronstad (Ref. 11) with the additional correction that both expressions should be multiplied by n0 as noted by A. B. Winterbottom (Ref. 12). Unfortunately, typographical errors are also present in Winterbottom's published equations. The equations here have been slightly rearranged for greater clarity.
  11. L. Tronstad, Trans. Faraday Soc. 31, 1151 (1935).
  12. See Ref. 4, p. 40.
  13. R. J. Archer (private communication); the equations have been slightly rearranged for greater clarity.
  14. J. R. Partington, An Advanced Treatise on Physical Chemistry (John Wiley & Sons, Inc., New York, 1953), Vol. IV, p. 506. The notation used by Partington differs from that used in this paper.
  15. A. Rothen and M. Hanson, Rev. Sci. Instr. 20, 66 (1949).
  16. I. N. Shklyarevskii and N. A. Nosulenko, Opt. i Spectroskopiya 12, 769 (1962) [English transl.: Opt. Spectry. 12, 435 (1962)].
  17. See Ref. 4, p. 42.
  18. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 617.The notation used by Born and Wolf differs from that used in this paper.
  19. L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).
  20. R. J. Archer, Phys. Rev. 110, 354 (1958).
  21. M. A. Barrett, Norges Tekniske Hogskole, Trondheim, Norway (private communication).

Archer, R. J.

R. J. Archer (private communication); the equations have been slightly rearranged for greater clarity.

R. J. Archer, Phys. Rev. 110, 354 (1958).

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

R. J. Archer, J. Electrochem. Soc. 104, 619 (1957).

Barrett, M. A.

M. A. Barrett, Norges Tekniske Hogskole, Trondheim, Norway (private communication).

Berning, J. A.

J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).

Berning, P. H.

J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).

P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 617.The notation used by Born and Wolf differs from that used in this paper.

Hanson, M.

A. Rothen and M. Hanson, Rev. Sci. Instr. 20, 66 (1949).

Hass, G.

P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific Publications Ltd., London, 1955), p. 125.

Madden, R. P.

P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).

Nosulenko, N. A.

I. N. Shklyarevskii and N. A. Nosulenko, Opt. i Spectroskopiya 12, 769 (1962) [English transl.: Opt. Spectry. 12, 435 (1962)].

Partington, J. R.

J. R. Partington, An Advanced Treatise on Physical Chemistry (John Wiley & Sons, Inc., New York, 1953), Vol. IV, p. 506. The notation used by Partington differs from that used in this paper.

Plumb, R. C.

P. Theroux and R. C. Plumb, J. Opt. Soc. Am. 53, 1451 (1963).

Rothen, A.

A. Rothen and M. Hanson, Rev. Sci. Instr. 20, 66 (1949).

A. Rothen, Rev. Sci. Instr. 16, 26 (1945); 28, 283 (1957).

Schulz, L. G.

L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).

Shklyarevskii, I. N.

I. N. Shklyarevskii and N. A. Nosulenko, Opt. i Spectroskopiya 12, 769 (1962) [English transl.: Opt. Spectry. 12, 435 (1962)].

Tangherlini, F. R.

L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).

Theroux, P.

P. Theroux and R. C. Plumb, J. Opt. Soc. Am. 53, 1451 (1963).

Tronstad, L.

L. Tronstad, Trans. Faraday Soc. 31, 1151 (1935).

Vasicek, A

The formulas as given in A.Vasicek, Optics of Thin Filmns (North-Holland Publishing Company, Amsterdam, 1960), p. 315, are incorrect. The correct expressions are given by L. Tronstad (Ref. 11) with the additional correction that both expressions should be multiplied by n0 as noted by A. B. Winterbottom (Ref. 12). Unfortunately, typographical errors are also present in Winterbottom's published equations. The equations here have been slightly rearranged for greater clarity.

Winterbottom, A. B.

A. B. Winterbottom, Kgl. Norske Videnskab. Selskabs, Skrifter 1, 1 (1955).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 617.The notation used by Born and Wolf differs from that used in this paper.

Other (21)

P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific Publications Ltd., London, 1955), p. 125.

R. J. Archer, J. Electrochem. Soc. 104, 619 (1957).

A. B. Winterbottom, Kgl. Norske Videnskab. Selskabs, Skrifter 1, 1 (1955).

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

A. Rothen, Rev. Sci. Instr. 16, 26 (1945); 28, 283 (1957).

McCrackin, Passaglia, Stromberg, and Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963).

P. Theroux and R. C. Plumb, J. Opt. Soc. Am. 53, 1451 (1963).

J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).

The formulas as given in A.Vasicek, Optics of Thin Filmns (North-Holland Publishing Company, Amsterdam, 1960), p. 315, are incorrect. The correct expressions are given by L. Tronstad (Ref. 11) with the additional correction that both expressions should be multiplied by n0 as noted by A. B. Winterbottom (Ref. 12). Unfortunately, typographical errors are also present in Winterbottom's published equations. The equations here have been slightly rearranged for greater clarity.

L. Tronstad, Trans. Faraday Soc. 31, 1151 (1935).

See Ref. 4, p. 40.

R. J. Archer (private communication); the equations have been slightly rearranged for greater clarity.

J. R. Partington, An Advanced Treatise on Physical Chemistry (John Wiley & Sons, Inc., New York, 1953), Vol. IV, p. 506. The notation used by Partington differs from that used in this paper.

A. Rothen and M. Hanson, Rev. Sci. Instr. 20, 66 (1949).

I. N. Shklyarevskii and N. A. Nosulenko, Opt. i Spectroskopiya 12, 769 (1962) [English transl.: Opt. Spectry. 12, 435 (1962)].

See Ref. 4, p. 42.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 617.The notation used by Born and Wolf differs from that used in this paper.

L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).

R. J. Archer, Phys. Rev. 110, 354 (1958).

M. A. Barrett, Norges Tekniske Hogskole, Trondheim, Norway (private communication).

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