Abstract

We describe a new technique to measure the piezo-optical constants of a material in a frequency region where it is opaque. The technique employs Raman scattering. Using this new method we measure the magnitudes of the piezo-optical constants π11π12 and π44 in silicon at 1.92 eV. Previous measurements were limited to below and near the fundamental edge at 1.1 eV. Using this technique it should be possible to extend the measurements of the piezo-optical constants in a large number of opaque materials.

© 1978 Optical Society of America

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  1. C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
    [Crossref]
  2. P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
    [Crossref]
  3. A. Gavini and M. Cardona, Phys. Rev. 177, 1351 (1969).
    [Crossref]
  4. R. W. Dixon and M. G. Cohen, Appl. Phys. Lett. 8, 205 (1966).
    [Crossref]
  5. Yet-Ful Tsay and B. Bendow, Phys. Rev. B 16, 2663 (1977).
    [Crossref]
  6. J. R. Sandercock, Phys. Rev. Lett. 28, 237 (1972).
    [Crossref]
  7. G. W. Gobeli and E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
    [Crossref]
  8. M. Cardona, Modulation Spectroscopy (Academic, New York, 1969), p. 152.
  9. J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
    [Crossref]
  10. M. Chandrasekhar, M. H. Grimsditch, and M. Cardona (to be published).
  11. H. Vogelmann and T. A. Fjeldly, Rev. Sci. Instrum. 45, 309 (1974).
    [Crossref]
  12. Obtained from Monsanto Chemical Company.
  13. D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
    [Crossref]
  14. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960), p. 253.
  15. R. Loudon, Adv. Phys. 13, 423 (1964).
    [Crossref]
  16. H. R. Philipp, J. Appl. Phys.43, 2835 (1972), and private communication.
    [Crossref]
  17. M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
    [Crossref]

1978 (1)

M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
[Crossref]

1977 (1)

Yet-Ful Tsay and B. Bendow, Phys. Rev. B 16, 2663 (1977).
[Crossref]

1975 (1)

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[Crossref]

1974 (1)

H. Vogelmann and T. A. Fjeldly, Rev. Sci. Instrum. 45, 309 (1974).
[Crossref]

1972 (2)

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[Crossref]

J. R. Sandercock, Phys. Rev. Lett. 28, 237 (1972).
[Crossref]

1971 (1)

P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
[Crossref]

1969 (2)

A. Gavini and M. Cardona, Phys. Rev. 177, 1351 (1969).
[Crossref]

C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
[Crossref]

1966 (1)

R. W. Dixon and M. G. Cohen, Appl. Phys. Lett. 8, 205 (1966).
[Crossref]

1965 (1)

G. W. Gobeli and E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

1964 (1)

R. Loudon, Adv. Phys. 13, 423 (1964).
[Crossref]

Bendow, B.

Yet-Ful Tsay and B. Bendow, Phys. Rev. B 16, 2663 (1977).
[Crossref]

Cardona, M.

M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
[Crossref]

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[Crossref]

P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
[Crossref]

C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
[Crossref]

A. Gavini and M. Cardona, Phys. Rev. 177, 1351 (1969).
[Crossref]

M. Cardona, Modulation Spectroscopy (Academic, New York, 1969), p. 152.

M. Chandrasekhar, M. H. Grimsditch, and M. Cardona (to be published).

Chandrasekhar, M.

M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
[Crossref]

M. Chandrasekhar, M. H. Grimsditch, and M. Cardona (to be published).

Cohen, M. G.

R. W. Dixon and M. G. Cohen, Appl. Phys. Lett. 8, 205 (1966).
[Crossref]

Dixon, R. W.

R. W. Dixon and M. G. Cohen, Appl. Phys. Lett. 8, 205 (1966).
[Crossref]

Fjeldly, T. A.

H. Vogelmann and T. A. Fjeldly, Rev. Sci. Instrum. 45, 309 (1974).
[Crossref]

Gavini, A.

A. Gavini and M. Cardona, Phys. Rev. 177, 1351 (1969).
[Crossref]

Gobeli, G. W.

G. W. Gobeli and E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

Grimsditch, M. H.

M. Chandrasekhar, M. H. Grimsditch, and M. Cardona (to be published).

Higginbotham, C. W.

C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
[Crossref]

Kane, E. O.

G. W. Gobeli and E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

Lax, M.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[Crossref]

Lazay, P. D.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[Crossref]

Loudon, R.

R. Loudon, Adv. Phys. 13, 423 (1964).
[Crossref]

Nelson, D. F.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[Crossref]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960), p. 253.

Philipp, H. R.

H. R. Philipp, J. Appl. Phys.43, 2835 (1972), and private communication.
[Crossref]

Pollak, F. H.

P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
[Crossref]

C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
[Crossref]

Renucci, J. B.

M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
[Crossref]

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[Crossref]

Sandercock, J. R.

J. R. Sandercock, Phys. Rev. Lett. 28, 237 (1972).
[Crossref]

Tsay, Yet-Ful

Yet-Ful Tsay and B. Bendow, Phys. Rev. B 16, 2663 (1977).
[Crossref]

Tyte, R. N.

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[Crossref]

Vogelmann, H.

H. Vogelmann and T. A. Fjeldly, Rev. Sci. Instrum. 45, 309 (1974).
[Crossref]

Yu, P. Y.

P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
[Crossref]

Adv. Phys. (1)

R. Loudon, Adv. Phys. 13, 423 (1964).
[Crossref]

Appl. Phys. Lett. (1)

R. W. Dixon and M. G. Cohen, Appl. Phys. Lett. 8, 205 (1966).
[Crossref]

Phys. Rev. (2)

C. W. Higginbotham, M. Cardona, and F. H. Pollak, Phys. Rev. 184, 821 (1969), and references therein.
[Crossref]

A. Gavini and M. Cardona, Phys. Rev. 177, 1351 (1969).
[Crossref]

Phys. Rev. B (5)

M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17, 1623 (1978).
[Crossref]

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[Crossref]

P. Y. Yu, M. Cardona, and F. H. Pollak, Phys. Rev. B 3, 340 (1971).
[Crossref]

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[Crossref]

Yet-Ful Tsay and B. Bendow, Phys. Rev. B 16, 2663 (1977).
[Crossref]

Phys. Rev. Lett. (2)

J. R. Sandercock, Phys. Rev. Lett. 28, 237 (1972).
[Crossref]

G. W. Gobeli and E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

Rev. Sci. Instrum. (1)

H. Vogelmann and T. A. Fjeldly, Rev. Sci. Instrum. 45, 309 (1974).
[Crossref]

Other (5)

Obtained from Monsanto Chemical Company.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1960), p. 253.

H. R. Philipp, J. Appl. Phys.43, 2835 (1972), and private communication.
[Crossref]

M. Cardona, Modulation Spectroscopy (Academic, New York, 1969), p. 152.

M. Chandrasekhar, M. H. Grimsditch, and M. Cardona (to be published).

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Figures (3)

FIG. 1
FIG. 1

Axes used in the paper. z ˆ is the face used for scattering and ( 1 / 2 ) ( x ˆ + ŷ ) is the direction of stress. The polarization configurations used are at 45° to the stress, z(xx) z ¯ and z(xy) z ¯. ( 1 / 2 ) ( x ˆ + ŷ ) is either the [100] or [110] direction, z ˆ either(001) or (1 1 ¯0).

FIG. 2
FIG. 2

Experimentally obtained intensity ratios β plotted versus stress X for the three cases discussed in the text: case (i) is represented by triangles, case (ii) by circles, and case (iii) by squares. The solid lines are theoretical fits.

FIG. 3
FIG. 3

Birefringence-induced changes in the intensity of the optical phonon for X || [110], measured with an exciting wavelength of 6471 Å. β grows from 1.5% at zero stress to 38% at 18 kbar.

Equations (11)

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e ˆ x = ( 1 / 2 ) [ ( x ˆ + ŷ ) + ( x ˆ - ŷ ) e i ϕ ] , e ˆ y = ( 1 / 2 ) [ ( x ˆ + ŷ ) - ( x ˆ - ŷ ) e i ϕ ] .
ϕ = ( 2 π / λ ) ( n - n ) l ,
I x x ( ϕ ) = i e ˆ x · R i · e ˆ x 2 ,
I x y ( ϕ ) = i e ˆ x · R i · e ˆ y 2 .
I x x = 0 I x x ( ϕ ) e - ( α i + α s ) l d l , I x y = 0 I x y ( ϕ ) e - ( α i + α s ) l d l .
β = 1 1 + 1 / [ 2 ( A X ) 2 ] ,
A = π n 0 3 π 44 λ ( α i + α s ) ,
n - n = n 0 3 2 π 44 X .
β = 1 1 + 1 / [ 2 ( B X ) 2 ] ,
B = π n 0 3 ( π 11 - π 12 ) λ ( α i + α s ) .
n - n = n 0 3 2 ( π 11 - π 12 ) X .