Abstract

A new accurate technique for determining the optical constants of thin absorbing films is presented. The configuration used includes a conventional spectrophotometer and a transparent substrate, half of which is covered with an opaque highly reflecting metal layer prior to the deposition of the film to be studied. The normal incidence transmission T of the thin film on the transparent substrate is then combined with a measurement of the near normal reflection Rm of the same film on the metal covered part of the substrate. The combination (T,Rm) yields an accurate and experimentally simple technique for determining the optical constants of thin films. A detailed evaluation of the accuracy of the extracted optical constants n and k of the thin film is obtained from numerical computations using realistic assumptions of various experimental uncertainties. Comparison with conventional techniques shows a greatly improved accuracy of the new technique.

© 1981 Optical Society of America

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  1. H. Mayer, Physik dünner Schichten (Wissenschaftliche, Stuttgart, 1950).
  2. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1950).
  3. P. H. Berning, in Physics of Thin Films, G. Hass, Ed. (Academic, New York, 1963), Vol. 1, p. 6.
  4. E. E. Bell, in Encyclopedia of Physics, L. Genzel, Ed. (Springer, Berlin, 1967), Vol. 25/2a, pp. 1–58.
  5. O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1964), Vol. 2, p. 193.
  6. H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), Vol. 4, pp. 1–96.
  7. F. Abeles, in Physics of Thin Films, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1971), Vol. 6, pp. 151–204.
  8. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [CrossRef]
  9. J. M. Bennett, M. J. Booty, Appl. Opt. 5, 41 (1966).
    [CrossRef] [PubMed]
  10. F. Abeles, M. L. Theye, Surf. Sci. 5, 32 (1966).
    [CrossRef]
  11. L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
    [CrossRef]
  12. L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
    [CrossRef]
  13. P. O. Nilsson, Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  14. K. W. Johnson, E. E. Bell, Phys. Rev. 187, 1044 (1969).
    [CrossRef]
  15. J. E. Nestell, R. W. Christy, Appl. Opt. 11, 643 (1972).
    [CrossRef] [PubMed]
  16. R. F. Miller, A. J. Taylor, J. Phys. D: 4, 1419 (1971).
    [CrossRef]
  17. R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
    [CrossRef]
  18. W. R. Hunter, G. Hass, J. Opt. Soc. Am. 64, 429 (1974).
    [CrossRef]
  19. R. D. Bringans, J. Phys. D: 10, 1855 (1977).
    [CrossRef]
  20. T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
    [CrossRef]
  21. R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
    [CrossRef]
  22. F. T. Ritchie, G. L. Harding, Thin Solid Films 57, 315 (1979), extracted the optical constants of Fe-C films from a regression of the thin film transmission and reflection on glass combined with the reflection on gold. This in fact amounts to a combination of the (T,R) and (T,Rm) methods, although no evaluation or analysis of the method was attempted in this case).
    [CrossRef]
  23. G. Hass, W. R. Hunter, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10.
  24. C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980); A. Hjortsberg, C. G. Granqvist, Appl. Opt. 15, 1694 (1980).
    [CrossRef]
  25. A. Hjortsberg, Thin Solid Films 69, L15 (1980).
    [CrossRef]
  26. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  27. D. E. Aspnes, Opt. Commun. 8, 222 (1973).
    [CrossRef]
  28. F. Stern, in Solid State Physics, F. Seitz, D. Turnbull, Eds. (Academic, New York, 1963), Vol. 15, p. 300.
    [CrossRef]
  29. J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
    [CrossRef]
  30. E. E. Bell, Infrared Phys. 6, 57 (1966).
    [CrossRef]
  31. E. E. Russel, E. E. Bell, Infrared Phys. 6, 75 (1966).
    [CrossRef]
  32. C. Bazin, C. R. Acad. Sci. 260, 83 (1965).
  33. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  34. Landolt-Bernstein, Eigenschaften der Materie in ihren Aggregationszustanden, 8 Teil, Optische Konstanten (Springer, Berlin, 1962).
  35. K. H. Behrndt, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1966), Vol. 3, p. 1.
  36. H. Kiessig, Z. Angew. Phys. 22, 406 (1967).
  37. See, for example, the Alpha-Step Profiler, Tencor Instruments, 2426 Charleston Road, Mountain View, Calif. 94043.
  38. A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960).
  39. G. Hass, J. E. Waylonis, J. Opt. Soc. Am. 51, 719 (1961).
    [CrossRef]
  40. G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1968), p. 95.
  41. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964).
  42. E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
    [CrossRef]
  43. The continuity of the tangential electric field at the metal–thin film interface ensures that the field amplitude is small at the interface, in the film as well as the metal, for normal incidence reflection).
  44. W. A. Pliskin, H. S. Lehman, J. Electrochem. Soc. 112, 1013 (1965).
    [CrossRef]
  45. H. R. Philipp, J. Phys. Chem. Solids 32, 1935 (1971); J. Non-Cryst. Solids 8–10, 627 (1972).
    [CrossRef]
  46. K. Hübner, Phys. Status Solidi A: 42, 50 (1977).
    [CrossRef]
  47. D. E. Aspnes, J. B. Theeten, J. Appl. Phys. 50, 4928 (1979).
    [CrossRef]
  48. G. Hass, C. D. Salzberg, J. Opt. Soc. Am. 44, 181 (1954).
    [CrossRef]
  49. See, for example, B. O. Seraphin, “Solar Energy Conversion,” in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979); A. J. Siewers, in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979).
    [CrossRef]
  50. R. E. Hahn, B. O. Seraphin, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10, p. 1.

1980 (3)

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980); A. Hjortsberg, C. G. Granqvist, Appl. Opt. 15, 1694 (1980).
[CrossRef]

A. Hjortsberg, Thin Solid Films 69, L15 (1980).
[CrossRef]

R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
[CrossRef]

1979 (2)

F. T. Ritchie, G. L. Harding, Thin Solid Films 57, 315 (1979), extracted the optical constants of Fe-C films from a regression of the thin film transmission and reflection on glass combined with the reflection on gold. This in fact amounts to a combination of the (T,R) and (T,Rm) methods, although no evaluation or analysis of the method was attempted in this case).
[CrossRef]

D. E. Aspnes, J. B. Theeten, J. Appl. Phys. 50, 4928 (1979).
[CrossRef]

1978 (2)

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
[CrossRef]

1977 (2)

K. Hübner, Phys. Status Solidi A: 42, 50 (1977).
[CrossRef]

R. D. Bringans, J. Phys. D: 10, 1855 (1977).
[CrossRef]

1974 (1)

1973 (1)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

1972 (2)

R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
[CrossRef]

J. E. Nestell, R. W. Christy, Appl. Opt. 11, 643 (1972).
[CrossRef] [PubMed]

1971 (2)

R. F. Miller, A. J. Taylor, J. Phys. D: 4, 1419 (1971).
[CrossRef]

H. R. Philipp, J. Phys. Chem. Solids 32, 1935 (1971); J. Non-Cryst. Solids 8–10, 627 (1972).
[CrossRef]

1969 (1)

K. W. Johnson, E. E. Bell, Phys. Rev. 187, 1044 (1969).
[CrossRef]

1968 (1)

1967 (3)

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

H. Kiessig, Z. Angew. Phys. 22, 406 (1967).

1966 (4)

E. E. Bell, Infrared Phys. 6, 57 (1966).
[CrossRef]

E. E. Russel, E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

J. M. Bennett, M. J. Booty, Appl. Opt. 5, 41 (1966).
[CrossRef] [PubMed]

F. Abeles, M. L. Theye, Surf. Sci. 5, 32 (1966).
[CrossRef]

1965 (3)

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[CrossRef]

C. Bazin, C. R. Acad. Sci. 260, 83 (1965).

W. A. Pliskin, H. S. Lehman, J. Electrochem. Soc. 112, 1013 (1965).
[CrossRef]

1963 (1)

J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
[CrossRef]

1961 (1)

1954 (1)

Abeles, F.

F. Abeles, M. L. Theye, Surf. Sci. 5, 32 (1966).
[CrossRef]

F. Abeles, in Physics of Thin Films, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1971), Vol. 6, pp. 151–204.

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, J. Appl. Phys. 50, 4928 (1979).
[CrossRef]

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

Azzam, R. M. A.

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

Bashara, N. M.

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

Bazin, C.

C. Bazin, C. R. Acad. Sci. 260, 83 (1965).

Behrndt, K. H.

K. H. Behrndt, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1966), Vol. 3, p. 1.

Bell, E. E.

K. W. Johnson, E. E. Bell, Phys. Rev. 187, 1044 (1969).
[CrossRef]

E. E. Russel, E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

E. E. Bell, Infrared Phys. 6, 57 (1966).
[CrossRef]

E. E. Bell, in Encyclopedia of Physics, L. Genzel, Ed. (Springer, Berlin, 1967), Vol. 25/2a, pp. 1–58.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), Vol. 4, pp. 1–96.

Bennett, J. M.

J. M. Bennett, M. J. Booty, Appl. Opt. 5, 41 (1966).
[CrossRef] [PubMed]

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), Vol. 4, pp. 1–96.

Berning, P. H.

P. H. Berning, in Physics of Thin Films, G. Hass, Ed. (Academic, New York, 1963), Vol. 1, p. 6.

Bondar, E. A.

E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
[CrossRef]

Booty, M. J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964).

Bringans, R. D.

R. D. Bringans, J. Phys. D: 10, 1855 (1977).
[CrossRef]

Campbell, R. D.

R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
[CrossRef]

Carey, R.

R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
[CrossRef]

Chamberlain, J. J.

J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
[CrossRef]

Chambers, W. G.

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

Christy, R. W.

Denton, R. E.

R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
[CrossRef]

Ford, J. E.

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1968), p. 95.

Gebbie, H. A.

J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
[CrossRef]

Gibbs, J. E.

J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
[CrossRef]

Granqvist, C. G.

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980); A. Hjortsberg, C. G. Granqvist, Appl. Opt. 15, 1694 (1980).
[CrossRef]

Hahn, R. E.

R. E. Hahn, B. O. Seraphin, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10, p. 1.

Harding, G. L.

F. T. Ritchie, G. L. Harding, Thin Solid Films 57, 315 (1979), extracted the optical constants of Fe-C films from a regression of the thin film transmission and reflection on glass combined with the reflection on gold. This in fact amounts to a combination of the (T,R) and (T,Rm) methods, although no evaluation or analysis of the method was attempted in this case).
[CrossRef]

Hass, G.

Heavens, O. S.

O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1964), Vol. 2, p. 193.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1950).

Hjortsberg, A.

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980); A. Hjortsberg, C. G. Granqvist, Appl. Opt. 15, 1694 (1980).
[CrossRef]

A. Hjortsberg, Thin Solid Films 69, L15 (1980).
[CrossRef]

Hübner, K.

K. Hübner, Phys. Status Solidi A: 42, 50 (1977).
[CrossRef]

Hunter, W. R.

W. R. Hunter, G. Hass, J. Opt. Soc. Am. 64, 429 (1974).
[CrossRef]

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[CrossRef]

G. Hass, W. R. Hunter, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10.

Johnson, K. W.

K. W. Johnson, E. E. Bell, Phys. Rev. 187, 1044 (1969).
[CrossRef]

Kiessig, H.

H. Kiessig, Z. Angew. Phys. 22, 406 (1967).

Kulyupin, Yu. A.

E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
[CrossRef]

Lehman, H. S.

W. A. Pliskin, H. S. Lehman, J. Electrochem. Soc. 112, 1013 (1965).
[CrossRef]

Mayer, H.

H. Mayer, Physik dünner Schichten (Wissenschaftliche, Stuttgart, 1950).

Miller, R. F.

R. F. Miller, A. J. Taylor, J. Phys. D: 4, 1419 (1971).
[CrossRef]

Mok, C. L.

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

Nag, A.

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

Nestell, J. E.

Newman, D. M.

R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
[CrossRef]

Nilsson, P. O.

Parker, T. J.

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

Philipp, H. R.

H. R. Philipp, J. Phys. Chem. Solids 32, 1935 (1971); J. Non-Cryst. Solids 8–10, 627 (1972).
[CrossRef]

Pliskin, W. A.

W. A. Pliskin, H. S. Lehman, J. Electrochem. Soc. 112, 1013 (1965).
[CrossRef]

Popovich, N. N.

E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
[CrossRef]

Ritchie, F. T.

F. T. Ritchie, G. L. Harding, Thin Solid Films 57, 315 (1979), extracted the optical constants of Fe-C films from a regression of the thin film transmission and reflection on glass combined with the reflection on gold. This in fact amounts to a combination of the (T,R) and (T,Rm) methods, although no evaluation or analysis of the method was attempted in this case).
[CrossRef]

Russel, E. E.

E. E. Russel, E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

Salzberg, C. D.

Seraphin, B. O.

See, for example, B. O. Seraphin, “Solar Energy Conversion,” in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979); A. J. Siewers, in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979).
[CrossRef]

R. E. Hahn, B. O. Seraphin, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10, p. 1.

Stern, F.

F. Stern, in Solid State Physics, F. Seitz, D. Turnbull, Eds. (Academic, New York, 1963), Vol. 15, p. 300.
[CrossRef]

Taylor, A. J.

R. F. Miller, A. J. Taylor, J. Phys. D: 4, 1419 (1971).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, J. Appl. Phys. 50, 4928 (1979).
[CrossRef]

Theye, M. L.

F. Abeles, M. L. Theye, Surf. Sci. 5, 32 (1966).
[CrossRef]

Thomas, B. W. J.

R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
[CrossRef]

Tomlin, S. G.

R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
[CrossRef]

Vasicek, A.

A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960).

Ward, L.

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

Waylonis, J. E.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980); A. Hjortsberg, C. G. Granqvist, Appl. Opt. 15, 1694 (1980).
[CrossRef]

Br. J. Appl. Phys. (2)

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

C. R. Acad. Sci. (1)

C. Bazin, C. R. Acad. Sci. 260, 83 (1965).

Infrared Phys. (3)

E. E. Bell, Infrared Phys. 6, 57 (1966).
[CrossRef]

E. E. Russel, E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

T. J. Parker, W. G. Chambers, J. E. Ford, C. L. Mok, Infrared Phys. 18, 571 (1978).
[CrossRef]

J. Appl. Phys. (1)

D. E. Aspnes, J. B. Theeten, J. Appl. Phys. 50, 4928 (1979).
[CrossRef]

J. Electrochem. Soc. (1)

W. A. Pliskin, H. S. Lehman, J. Electrochem. Soc. 112, 1013 (1965).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Phys. Chem. Solids (1)

H. R. Philipp, J. Phys. Chem. Solids 32, 1935 (1971); J. Non-Cryst. Solids 8–10, 627 (1972).
[CrossRef]

J. Phys. D (3)

R. D. Bringans, J. Phys. D: 10, 1855 (1977).
[CrossRef]

R. F. Miller, A. J. Taylor, J. Phys. D: 4, 1419 (1971).
[CrossRef]

R. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D: 5, 852 (1972).
[CrossRef]

Nature London (1)

J. J. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature London 198, 874 (1963); Infrared Phys. 9, 185 (1969).
[CrossRef]

Opt. Commun. (1)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

Phys. Rev. (1)

K. W. Johnson, E. E. Bell, Phys. Rev. 187, 1044 (1969).
[CrossRef]

Phys. Status Solidi A (1)

K. Hübner, Phys. Status Solidi A: 42, 50 (1977).
[CrossRef]

Surf. Sci. (1)

F. Abeles, M. L. Theye, Surf. Sci. 5, 32 (1966).
[CrossRef]

Thin Solid Films (4)

R. Carey, B. W. J. Thomas, D. M. Newman, Thin Solid Films 66, 139 (1980).
[CrossRef]

F. T. Ritchie, G. L. Harding, Thin Solid Films 57, 315 (1979), extracted the optical constants of Fe-C films from a regression of the thin film transmission and reflection on glass combined with the reflection on gold. This in fact amounts to a combination of the (T,R) and (T,Rm) methods, although no evaluation or analysis of the method was attempted in this case).
[CrossRef]

A. Hjortsberg, Thin Solid Films 69, L15 (1980).
[CrossRef]

E. A. Bondar, Yu. A. Kulyupin, N. N. Popovich, Thin Solid Films 55, 201 (1978).
[CrossRef]

Z. Angew. Phys. (1)

H. Kiessig, Z. Angew. Phys. 22, 406 (1967).

Other (20)

See, for example, the Alpha-Step Profiler, Tencor Instruments, 2426 Charleston Road, Mountain View, Calif. 94043.

A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960).

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

Landolt-Bernstein, Eigenschaften der Materie in ihren Aggregationszustanden, 8 Teil, Optische Konstanten (Springer, Berlin, 1962).

K. H. Behrndt, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1966), Vol. 3, p. 1.

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

F. Stern, in Solid State Physics, F. Seitz, D. Turnbull, Eds. (Academic, New York, 1963), Vol. 15, p. 300.
[CrossRef]

G. Hass, W. R. Hunter, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10.

H. Mayer, Physik dünner Schichten (Wissenschaftliche, Stuttgart, 1950).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1950).

P. H. Berning, in Physics of Thin Films, G. Hass, Ed. (Academic, New York, 1963), Vol. 1, p. 6.

E. E. Bell, in Encyclopedia of Physics, L. Genzel, Ed. (Springer, Berlin, 1967), Vol. 25/2a, pp. 1–58.

O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1964), Vol. 2, p. 193.

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), Vol. 4, pp. 1–96.

F. Abeles, in Physics of Thin Films, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1971), Vol. 6, pp. 151–204.

The continuity of the tangential electric field at the metal–thin film interface ensures that the field amplitude is small at the interface, in the film as well as the metal, for normal incidence reflection).

G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1968), p. 95.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964).

See, for example, B. O. Seraphin, “Solar Energy Conversion,” in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979); A. J. Siewers, in Topics in Applied Physics, B. O. Seraphin, Ed. (Springer, New York, 1979).
[CrossRef]

R. E. Hahn, B. O. Seraphin, in Physics of Thin Films, G. Hass, M. H. Francombe, Eds. (Academic, New York, 1978), Vol. 10, p. 1.

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Figures (9)

Fig. 1
Fig. 1

Experimental configuration for the (T,Rm) method. Reflection measurements are performed at an angle of incidence of 10–15°.

Fig. 2
Fig. 2

Plot of the contours of constant normal transmission T and reflection R of a thin film, d/λ = 0.1 on a transparent substrate, ns = 1.5. Thin film refractive index Ñ = n + ik.

Fig. 3
Fig. 3

Plot of regions (shaded) in which the contour tangency problem in the (T,R) combination contributes an absolute error Δn larger than 0.5 for d/λ = 0.1 and 0.05, respectively. The uncertainties in T and R are set to 0.01.

Fig. 4
Fig. 4

Plot of the contours of constant normal transmission T and reflection Rm of a thin film, d/λ = 0.1, on a partly metallized substrate. Thin film refractive index Ñ = n + ik, transparent substrate index ns = 1.5, and metal substrate index Ñm = 20 + i70.

Fig. 5
Fig. 5

Plot of T and Rm as in Fig. 4, except a reduction of d/λ to 0.05. Note that the scales on the n and k axes are different from those in Fig. 4.

Fig. 6
Fig. 6

Computed absolute error |Δn| in the real part of the refractive index of a thin film, d/λ = 0.1, as determined with the (T,R) method (left) and the (T,Rm) method (right). Computations assume experimental uncertainties in T, R, and Rm of 0.01. Solid lines show |Δn| as a function of k with constant n for values of n and k in the range (0,2). Dark horizontal area obtained by truncating |Δn| at 0.5 indicates regions of poor sensitivity.

Fig. 7
Fig. 7

Cross sections of Fig. 6 showing the computed error |Δn| as a function of k for n = 1.0, 1.4, and 1.8: (a) (T,R) method; (b) (T,Rm) method. All parameters are identical in the two cases.

Fig. 8
Fig. 8

Upper part: Change of reflected intensity Rm in the (T,Rm) configuration as a result of a 10% uncertainty of the metal dielectric function m = m + i m for wavelengths λ = 0.5, 2, and 10 μm, respectively, and k values ranging from 0 to 2; n = 1.4. Lower part: Corresponding error in the determined optical constants of the thin film using the (T,Rm) method.

Fig. 9
Fig. 9

Solid lines represent the optical constants n and k of evaporated SiO determined with the (T,Rm) method. Shaded regions indicate the computed uncertainty in n for the (T,Rm) and (T,R) methods, respectively, assuming an experimental uncertainty in T, R, and Rm of 0.01 (see HG, Ref. 24).

Equations (8)

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F ( n , k ) = | T calc T | + | R calc R m |
r m = n + i k ( n m + i k m ) n + i k + ( n m + i k m ) .
Δ ϕ = ϕ 0 ϕ 1 + 2 π · 2 n ( d / λ ) ,
Δ T = T ( n , k ) T ( n 0 , k 0 ) = ( T n ) Δ n + ( T k ) Δ k ,
Δ R = R ( n , k ) R ( n 0 , k 0 ) = ( R n ) Δ n + ( R k ) Δ k ,
Δ R m = R m ( n , k ) R m ( n 0 , k 0 ) = ( R m n ) Δ n + ( R m k ) Δ k ,
( Δ T Δ R m ) = M R m ( n 0 , k 0 ) ( Δ n Δ k ) ,
( Δ n Δ k ) = M R m 1 ( n 0 , k 0 ) ( Δ T Δ R m ) ,

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