Abstract

By using accurate prism-coupled optical waveguide refractive-index measurements on cation-doped indium oxide films and a classical polarizability model having adjustable local field weighting factors, estimates have been obtained for the electronic polarizabilities of ten cations and the relative local fields in their respective oxides. Self-consistent results for the ten oxides were obtained for a constant oxygen polarizability of 1.5 (Å)3. The relative local fields were found to be larger at the oxygen than at the cation sites, consistent with the observation that the refractive index is more sensitive to anion than cation changes. The results should be useful for optical applications requiring dopant control of refractive index (e.g., for antireflection coatings and optical waveguides).

© 1981 Optical Society of America

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  1. See, e.g., M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 87ff;A. R. von Hippel, Dielectrics and Waves (MIT Press, Cambridge, 1954), pp. 97ff; orJ. C. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967).
  2. S. Roberts, Phys.Rev. 77, 258 (1950).
    [CrossRef]
  3. J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
    [CrossRef]
  4. A. R. Ruffa, Phys.Rev. 130, 1412 (1963).
    [CrossRef]
  5. A. R. Ruffa, Phys. Rev. A: 133, 1418 (1964).
  6. J. Pirenne, E. Kartheuser, Physica 30, 2005 (1964).
    [CrossRef]
  7. I. M. Boswarva, Phys. Rev. B: 1, 1698 (1970).
    [CrossRef]
  8. S. S. Jaswal, T. B. Sharma, J. Phys. Chem. Solids 34, 509 (1973).
    [CrossRef]
  9. S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
    [CrossRef]
  10. R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
    [CrossRef]
  11. J. W. Medernach, R. C. Martin, J. Vac. Sci. Technol. 312, 63 (1975).
    [CrossRef]
  12. R. Groth, Phys. Status Solidi A: 14, 69 (1966).
    [CrossRef]
  13. H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
    [CrossRef]
  14. The Auger analyses were performed on some samples at the MIT Materials Science Center by T. Garrett-Reed and on other samples at MIT Lincoln Laboratory by M. Finn. It was difficult to arrive at a calibration for the absolute concentrations of the constituent ions. For those samples for which charging effects were absent, the relative concentrations, especially for the cations, were found to agree within ±25% of the x-ray analyses or starting solution concentrations.
  15. B. D. Cullity, Elements of X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1959), pp. 352–353.
  16. L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
    [CrossRef]
  17. See E. M. Levin, H. F. McMurdie, F. P. Hall, Phase Diagrams for Ceramists (American Ceramic Society, Columbus, Ohio, 1956) for the ZnO:In2O3 systems.
  18. See Ref. 16 for the Fe2O3:In2O3 system.
  19. See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
    [CrossRef]
  20. K. Tanaka, Y. Ohtuska, J. Appl. Phys. 49, 6132 (1978).
    [CrossRef]
  21. Model RT-100 Polar Rotator, Ardel Kinamatics, College Point, N.Y.
  22. The ZnSe prism was fabricated from CVD ZnSe (Raytran), kindly donated by J. Pappas of Raytheon Co., Waltham, Mass. The prism was polished by OSTI, Bedford, Mass.
  23. Corning Glass Advanced Products Department Fused Silica Catalog FS7940/9-78(A);CRC Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, 1979); andAmersil Fused Quartz and Fused Silica Catalog.
  24. C. A. Pan, T. P. Ma, J. Electron. Mater. 10, 43 (1981).
    [CrossRef]
  25. L. J. Van der Pauw, Philips Res. 13, 1 (1958).
  26. [See, e.g., R. A. Smith, Semiconductors (Cambridge U. P., London, 1964), pp. 170ff; orR. H. Bube, Electronic Properties of Crystalline Solids (Academic, New York, 1974), p. 241.]
  27. The optical band gap is a reasonably sensitive measure of carrier concentration in degenerate semiconductors such as In2O2 because of the Burstein-Moss shift[see, e.g., Ref. 24 and W. G. Haines, R. H. Bube, J. Appl. Phys. 49, 304 (1978) for recent discussions].
    [CrossRef]
  28. The integrated near IR reflection measurements were made at an angle of ∼20° from normal incidence, using a tungsten lamp with glass envelope, a single crystal germanium filter, and a lead sulfide detector. The weighted reflection was thus determined over a wavelength range of ∼1.8–3.5μm. For heavily reduced samples, the plasma edge readily occurs in this range, and the reflection can easily approach 70–80% of that of copper. The plasma frequency, being proportional to the square root of the free carrier concentration (Bube,26 p. 411), is therefore another measure of the carrier concentration and consequently of oxygen vacancy concentration.
  29. J. H. deWit, “Investigations on the Nonstoichiometry of Indium Sesquioxide,” Ph.D. Thesis, U. Utrecht, The Netherlands (1975).
  30. See Haines and Bube.27
  31. G. M. Samsonov, The Oxide Handbook (Plenum, New York, 1973).
    [CrossRef]
  32. P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  33. V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
    [CrossRef]
  34. P. B. Clapham, Br. J. Appl. Phys. 18, 363 (1967).
    [CrossRef]
  35. K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
    [CrossRef]
  36. L. Pauling, Proc. R. Soc. London Sect. A: 114, 181 (1927).
    [CrossRef]
  37. This was the value found by Ruffa.5 We did not prepare any titanium-doped samples.
  38. This was the value reported by Pandey et al.10 We did not prepare any gallium-doped samples.
  39. Our results suggest that one can use the relative liquid source concentrations as good estimates of the cation concentrations if doped films are pyrolytically deposited from liquid solutions.
  40. R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” in Physics of Thin Films, Vol. 8, G. Hass, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1975), pp. 51–98.

1981 (1)

C. A. Pan, T. P. Ma, J. Electron. Mater. 10, 43 (1981).
[CrossRef]

1979 (1)

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

1978 (3)

The optical band gap is a reasonably sensitive measure of carrier concentration in degenerate semiconductors such as In2O2 because of the Burstein-Moss shift[see, e.g., Ref. 24 and W. G. Haines, R. H. Bube, J. Appl. Phys. 49, 304 (1978) for recent discussions].
[CrossRef]

V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
[CrossRef]

K. Tanaka, Y. Ohtuska, J. Appl. Phys. 49, 6132 (1978).
[CrossRef]

1977 (2)

R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
[CrossRef]

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

1976 (1)

S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
[CrossRef]

1975 (2)

J. W. Medernach, R. C. Martin, J. Vac. Sci. Technol. 312, 63 (1975).
[CrossRef]

H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
[CrossRef]

1973 (1)

S. S. Jaswal, T. B. Sharma, J. Phys. Chem. Solids 34, 509 (1973).
[CrossRef]

1970 (1)

I. M. Boswarva, Phys. Rev. B: 1, 1698 (1970).
[CrossRef]

1969 (1)

P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

1967 (1)

P. B. Clapham, Br. J. Appl. Phys. 18, 363 (1967).
[CrossRef]

1966 (1)

R. Groth, Phys. Status Solidi A: 14, 69 (1966).
[CrossRef]

1964 (2)

A. R. Ruffa, Phys. Rev. A: 133, 1418 (1964).

J. Pirenne, E. Kartheuser, Physica 30, 2005 (1964).
[CrossRef]

1963 (1)

A. R. Ruffa, Phys.Rev. 130, 1412 (1963).
[CrossRef]

1961 (1)

See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
[CrossRef]

1958 (1)

L. J. Van der Pauw, Philips Res. 13, 1 (1958).

1953 (1)

J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
[CrossRef]

1950 (1)

S. Roberts, Phys.Rev. 77, 258 (1950).
[CrossRef]

1927 (1)

L. Pauling, Proc. R. Soc. London Sect. A: 114, 181 (1927).
[CrossRef]

Arora, N. D.

S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
[CrossRef]

Ben-Dur, L.

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

Born, M.

See, e.g., M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 87ff;A. R. von Hippel, Dielectrics and Waves (MIT Press, Cambridge, 1954), pp. 97ff; orJ. C. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967).

Boswarva, I. M.

I. M. Boswarva, Phys. Rev. B: 1, 1698 (1970).
[CrossRef]

Bube, R. H.

The optical band gap is a reasonably sensitive measure of carrier concentration in degenerate semiconductors such as In2O2 because of the Burstein-Moss shift[see, e.g., Ref. 24 and W. G. Haines, R. H. Bube, J. Appl. Phys. 49, 304 (1978) for recent discussions].
[CrossRef]

Clapham, P. B.

P. B. Clapham, Br. J. Appl. Phys. 18, 363 (1967).
[CrossRef]

Cullity, B. D.

B. D. Cullity, Elements of X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1959), pp. 352–353.

Dayal, B.

R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
[CrossRef]

deWit, J. H.

J. H. deWit, “Investigations on the Nonstoichiometry of Indium Sesquioxide,” Ph.D. Thesis, U. Utrecht, The Netherlands (1975).

Felner, I.

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

Fischbein, E.

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

Groth, R.

R. Groth, Phys. Status Solidi A: 14, 69 (1966).
[CrossRef]

Haines, W. G.

The optical band gap is a reasonably sensitive measure of carrier concentration in degenerate semiconductors such as In2O2 because of the Burstein-Moss shift[see, e.g., Ref. 24 and W. G. Haines, R. H. Bube, J. Appl. Phys. 49, 304 (1978) for recent discussions].
[CrossRef]

Hall, F. P.

See E. M. Levin, H. F. McMurdie, F. P. Hall, Phase Diagrams for Ceramists (American Ceramic Society, Columbus, Ohio, 1956) for the ZnO:In2O3 systems.

Jacobsson, R.

R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” in Physics of Thin Films, Vol. 8, G. Hass, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1975), pp. 51–98.

Jain, S. C.

S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
[CrossRef]

Jaswal, S. S.

S. S. Jaswal, T. B. Sharma, J. Phys. Chem. Solids 34, 509 (1973).
[CrossRef]

Jost, R.

H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
[CrossRef]

Kahn, A. H.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
[CrossRef]

Kalman, Z.

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

Kartheuser, E.

J. Pirenne, E. Kartheuser, Physica 30, 2005 (1964).
[CrossRef]

Knappe, B.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Kostlin, H.

H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
[CrossRef]

Lehmann, J.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Lems, W.

H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
[CrossRef]

Levin, E. M.

See E. M. Levin, H. F. McMurdie, F. P. Hall, Phase Diagrams for Ceramists (American Ceramic Society, Columbus, Ohio, 1956) for the ZnO:In2O3 systems.

Ma, T. P.

C. A. Pan, T. P. Ma, J. Electron. Mater. 10, 43 (1981).
[CrossRef]

Martin, R. C.

J. W. Medernach, R. C. Martin, J. Vac. Sci. Technol. 312, 63 (1975).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

McMurdie, H. F.

See E. M. Levin, H. F. McMurdie, F. P. Hall, Phase Diagrams for Ceramists (American Ceramic Society, Columbus, Ohio, 1956) for the ZnO:In2O3 systems.

Medernach, J. W.

J. W. Medernach, R. C. Martin, J. Vac. Sci. Technol. 312, 63 (1975).
[CrossRef]

Morl, K.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Ohtuska, Y.

K. Tanaka, Y. Ohtuska, J. Appl. Phys. 49, 6132 (1978).
[CrossRef]

Ormond, D. W.

V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
[CrossRef]

Osburn, C. M.

V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
[CrossRef]

Pan, C. A.

C. A. Pan, T. P. Ma, J. Electron. Mater. 10, 43 (1981).
[CrossRef]

Pandey, R. N.

R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
[CrossRef]

Pauling, L.

L. Pauling, Proc. R. Soc. London Sect. A: 114, 181 (1927).
[CrossRef]

Perthel, R.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Pirenne, J.

J. Pirenne, E. Kartheuser, Physica 30, 2005 (1964).
[CrossRef]

Roberts, S.

S. Roberts, Phys.Rev. 77, 258 (1950).
[CrossRef]

Ropke, U.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Roth, R. S.

See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
[CrossRef]

Ruffa, A. R.

A. R. Ruffa, Phys. Rev. A: 133, 1418 (1964).

A. R. Ruffa, Phys.Rev. 130, 1412 (1963).
[CrossRef]

Samsonov, G. M.

G. M. Samsonov, The Oxide Handbook (Plenum, New York, 1973).
[CrossRef]

Schneider, S.J.

See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
[CrossRef]

Schroder, H.

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Sharma, T. B.

S. S. Jaswal, T. B. Sharma, J. Phys. Chem. Solids 34, 509 (1973).
[CrossRef]

Sharma, T. P.

R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
[CrossRef]

S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
[CrossRef]

Shockley, W.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
[CrossRef]

Silvestri, V. J.

V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
[CrossRef]

Smith, R. A.

[See, e.g., R. A. Smith, Semiconductors (Cambridge U. P., London, 1964), pp. 170ff; orR. H. Bube, Electronic Properties of Crystalline Solids (Academic, New York, 1974), p. 241.]

Tanaka, K.

K. Tanaka, Y. Ohtuska, J. Appl. Phys. 49, 6132 (1978).
[CrossRef]

Tessman, J. R.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Ultrich, R.

P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Van der Pauw, L. J.

L. J. Van der Pauw, Philips Res. 13, 1 (1958).

Waring, J. L.

See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
[CrossRef]

Wolf, E.

See, e.g., M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 87ff;A. R. von Hippel, Dielectrics and Waves (MIT Press, Cambridge, 1954), pp. 97ff; orJ. C. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967).

Appl. Phys. Lett. (1)

P. K. Tien, R. Ultrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Br. J. Appl. Phys. (1)

P. B. Clapham, Br. J. Appl. Phys. 18, 363 (1967).
[CrossRef]

J. Appl. Phys. (2)

K. Tanaka, Y. Ohtuska, J. Appl. Phys. 49, 6132 (1978).
[CrossRef]

The optical band gap is a reasonably sensitive measure of carrier concentration in degenerate semiconductors such as In2O2 because of the Burstein-Moss shift[see, e.g., Ref. 24 and W. G. Haines, R. H. Bube, J. Appl. Phys. 49, 304 (1978) for recent discussions].
[CrossRef]

J. Electrochem. Soc. (2)

V. J. Silvestri, C. M. Osburn, D. W. Ormond, J. Electrochem. Soc. 125, 903 (1978).
[CrossRef]

L. Ben-Dur, E. Fischbein, I. Felner, Z. Kalman, J. Electrochem. Soc. 124, 451 (1977).
[CrossRef]

J. Electron. Mater. (1)

C. A. Pan, T. P. Ma, J. Electron. Mater. 10, 43 (1981).
[CrossRef]

J. Phys. Chem. Solids (3)

S. S. Jaswal, T. B. Sharma, J. Phys. Chem. Solids 34, 509 (1973).
[CrossRef]

S. C. Jain, T. P. Sharma, N. D. Arora, J. Phys. Chem. Solids 37, 81 (1976).
[CrossRef]

R. N. Pandey, T. P. Sharma, B. Dayal, J. Phys. Chem. Solids 38, 329 (1977).
[CrossRef]

J. Res. Natl. Bur. Stand. Sect. A: (1)

See S.J. Schneider, R. S. Roth, J. L. Waring, J. Res. Natl. Bur. Stand. Sect. A: 65, 345 (1961) for the Al2O3:In2O3 system.
[CrossRef]

J. Vac. Sci. Technol. (1)

J. W. Medernach, R. C. Martin, J. Vac. Sci. Technol. 312, 63 (1975).
[CrossRef]

Philips Res. (1)

L. J. Van der Pauw, Philips Res. 13, 1 (1958).

Phys. Rev. A: (1)

A. R. Ruffa, Phys. Rev. A: 133, 1418 (1964).

Phys. Rev. B: (1)

I. M. Boswarva, Phys. Rev. B: 1, 1698 (1970).
[CrossRef]

Phys. Status Solidi A: (2)

R. Groth, Phys. Status Solidi A: 14, 69 (1966).
[CrossRef]

H. Kostlin, R. Jost, W. Lems, Phys. Status Solidi A: 29, 87 (1975).
[CrossRef]

Phys.Rev. (3)

S. Roberts, Phys.Rev. 77, 258 (1950).
[CrossRef]

J. R. Tessman, A. H. Kahn, W. Shockley, Phys.Rev. 92, 890 (1953).
[CrossRef]

A. R. Ruffa, Phys.Rev. 130, 1412 (1963).
[CrossRef]

Physica (1)

J. Pirenne, E. Kartheuser, Physica 30, 2005 (1964).
[CrossRef]

Proc. R. Soc. London Sect. A: (1)

L. Pauling, Proc. R. Soc. London Sect. A: 114, 181 (1927).
[CrossRef]

Thin Solid Films (1)

K. Morl, U. Ropke, B. Knappe, J. Lehmann, R. Perthel, H. Schroder, Thin Solid Films 60, 49 (1979).
[CrossRef]

Other (17)

This was the value found by Ruffa.5 We did not prepare any titanium-doped samples.

This was the value reported by Pandey et al.10 We did not prepare any gallium-doped samples.

Our results suggest that one can use the relative liquid source concentrations as good estimates of the cation concentrations if doped films are pyrolytically deposited from liquid solutions.

R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” in Physics of Thin Films, Vol. 8, G. Hass, M. H. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1975), pp. 51–98.

[See, e.g., R. A. Smith, Semiconductors (Cambridge U. P., London, 1964), pp. 170ff; orR. H. Bube, Electronic Properties of Crystalline Solids (Academic, New York, 1974), p. 241.]

The integrated near IR reflection measurements were made at an angle of ∼20° from normal incidence, using a tungsten lamp with glass envelope, a single crystal germanium filter, and a lead sulfide detector. The weighted reflection was thus determined over a wavelength range of ∼1.8–3.5μm. For heavily reduced samples, the plasma edge readily occurs in this range, and the reflection can easily approach 70–80% of that of copper. The plasma frequency, being proportional to the square root of the free carrier concentration (Bube,26 p. 411), is therefore another measure of the carrier concentration and consequently of oxygen vacancy concentration.

J. H. deWit, “Investigations on the Nonstoichiometry of Indium Sesquioxide,” Ph.D. Thesis, U. Utrecht, The Netherlands (1975).

See Haines and Bube.27

G. M. Samsonov, The Oxide Handbook (Plenum, New York, 1973).
[CrossRef]

Model RT-100 Polar Rotator, Ardel Kinamatics, College Point, N.Y.

The ZnSe prism was fabricated from CVD ZnSe (Raytran), kindly donated by J. Pappas of Raytheon Co., Waltham, Mass. The prism was polished by OSTI, Bedford, Mass.

Corning Glass Advanced Products Department Fused Silica Catalog FS7940/9-78(A);CRC Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, 1979); andAmersil Fused Quartz and Fused Silica Catalog.

See, e.g., M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 87ff;A. R. von Hippel, Dielectrics and Waves (MIT Press, Cambridge, 1954), pp. 97ff; orJ. C. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967).

See E. M. Levin, H. F. McMurdie, F. P. Hall, Phase Diagrams for Ceramists (American Ceramic Society, Columbus, Ohio, 1956) for the ZnO:In2O3 systems.

See Ref. 16 for the Fe2O3:In2O3 system.

The Auger analyses were performed on some samples at the MIT Materials Science Center by T. Garrett-Reed and on other samples at MIT Lincoln Laboratory by M. Finn. It was difficult to arrive at a calibration for the absolute concentrations of the constituent ions. For those samples for which charging effects were absent, the relative concentrations, especially for the cations, were found to agree within ±25% of the x-ray analyses or starting solution concentrations.

B. D. Cullity, Elements of X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1959), pp. 352–353.

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Table I Estimates of Cation Polarizabilities (αD) and Local Field Weighting Factors (wD) in Dopant Oxides Obtained from Refractive Index (nDIO) Measurements of Doped Indium Oxide (DIO) Films. Oxygen Polarizability. α0 = 1.5 (Å)3.a

Equations (3)

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α m = w c α c + w o α o ,
n 2 1 n 2 + 2 = ( 4 π N m 3 ) α m ,
( n 2 1 n 2 + 2 ) doped In 2 O 3 = ( 4 π N m 3 ) { w c [ γ α D + ( 1 γ ) α In ] + w 0 α 0 } ,

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