Abstract

By the optical pump-and-probe technique, picosecond acoustic pulses are excited and detected in thin transparent double-layer films of silica and silicon nitride upon opaque chromium substrates. By taking both acoustic and optical multiple reflections into account, one can successfully model the main features of the reflectance variation. The film thicknesses, sound velocities, and photoelastic constants are derived by use of known values of the refractive indices.

© 1995 Optical Society of America

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References

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  1. See, for example,M. R. Hee, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, Opt. Lett. 18, 1107 (1993); K. J. Weingarten, M. J. Rodwell, D. M. Bloom, IEEE J. Quantum Electron. 24, 198 (1988).
    [Crossref] [PubMed]
  2. C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
    [Crossref]
  3. O. B. Wright, K. K. Kawashima, Phys. Rev. Lett. 69, 1668 (1992).
    [Crossref] [PubMed]
  4. O. B. Wright, Phys. Rev. B 49, 9985 (1994).
    [Crossref]
  5. O. B. Wright, T. Hyoguchi, Opt. Lett. 16, 1529 (1991).
    [Crossref] [PubMed]
  6. O. B. Wright, J. Appl. Phys. 71, 1617 (1992).
    [Crossref]
  7. K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
    [Crossref]
  8. H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
    [Crossref]
  9. I assume that θ = 0 in the analysis in this Letter.
  10. The silicon nitride film is thought to be amorphous for the deposition conditions used.
  11. C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
    [Crossref]
  12. These could be separated by frequency-domain analysis.
  13. The beat contribution was calculated with the further simplifying approximation r12 = 0.
  14. The slight smoothing caused by the finite duration of the pump and probe pulses has been neglected. The film and substrate densities and the substrate sound velocity were taken from the literature.
  15. Values ν1 = 5400 ms−1 and ν1 = 5300 ms−1 were used for Figs. 2(a) and 2(b), respectively.
  16. The sound velocity for silica is similar to that previously determined in single-layer films (see Refs. 5 and 6). That for silicon nitride agrees with the data ofT. S. Hickernell, F. M. Fliegel, F. S. Hickernell, in Proceedings of the IEEE Ultrasonics Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), p. 445. From the relation dn/dη = −n3p12/2, dn/dη can be compared with previous measurements of p12, the appropriate photo-elastic tensor element. This gives p12 = 0.28 for silica, in good agreement with; R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).For silicon nitride I obtain p12 = 0.023.
    [Crossref]

1994 (1)

O. B. Wright, Phys. Rev. B 49, 9985 (1994).
[Crossref]

1993 (1)

1992 (2)

O. B. Wright, J. Appl. Phys. 71, 1617 (1992).
[Crossref]

O. B. Wright, K. K. Kawashima, Phys. Rev. Lett. 69, 1668 (1992).
[Crossref] [PubMed]

1991 (1)

1990 (1)

K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
[Crossref]

1988 (1)

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

1986 (2)

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

Abeles, B.

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

Eesley, G. L.

K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
[Crossref]

Fliegel, F. M.

The sound velocity for silica is similar to that previously determined in single-layer films (see Refs. 5 and 6). That for silicon nitride agrees with the data ofT. S. Hickernell, F. M. Fliegel, F. S. Hickernell, in Proceedings of the IEEE Ultrasonics Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), p. 445. From the relation dn/dη = −n3p12/2, dn/dη can be compared with previous measurements of p12, the appropriate photo-elastic tensor element. This gives p12 = 0.28 for silica, in good agreement with; R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).For silicon nitride I obtain p12 = 0.023.
[Crossref]

Fujimoto, J. G.

Grahn, H. J.

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

Grahn, H. T.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

Hee, M. R.

Hickernell, F. S.

The sound velocity for silica is similar to that previously determined in single-layer films (see Refs. 5 and 6). That for silicon nitride agrees with the data ofT. S. Hickernell, F. M. Fliegel, F. S. Hickernell, in Proceedings of the IEEE Ultrasonics Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), p. 445. From the relation dn/dη = −n3p12/2, dn/dη can be compared with previous measurements of p12, the appropriate photo-elastic tensor element. This gives p12 = 0.28 for silica, in good agreement with; R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).For silicon nitride I obtain p12 = 0.023.
[Crossref]

Hickernell, T. S.

The sound velocity for silica is similar to that previously determined in single-layer films (see Refs. 5 and 6). That for silicon nitride agrees with the data ofT. S. Hickernell, F. M. Fliegel, F. S. Hickernell, in Proceedings of the IEEE Ultrasonics Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), p. 445. From the relation dn/dη = −n3p12/2, dn/dη can be compared with previous measurements of p12, the appropriate photo-elastic tensor element. This gives p12 = 0.28 for silica, in good agreement with; R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).For silicon nitride I obtain p12 = 0.023.
[Crossref]

Hyoguchi, T.

Izatt, J. A.

Kawashima, K. K.

O. B. Wright, K. K. Kawashima, Phys. Rev. Lett. 69, 1668 (1992).
[Crossref] [PubMed]

Maris, H. J.

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

Meng, W. J.

K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
[Crossref]

Svinarich, K. A.

K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
[Crossref]

Swanson, E. A.

Tauc, J.

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

Thomsen, C.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

Wright, O. B.

O. B. Wright, Phys. Rev. B 49, 9985 (1994).
[Crossref]

O. B. Wright, J. Appl. Phys. 71, 1617 (1992).
[Crossref]

O. B. Wright, K. K. Kawashima, Phys. Rev. Lett. 69, 1668 (1992).
[Crossref] [PubMed]

O. B. Wright, T. Hyoguchi, Opt. Lett. 16, 1529 (1991).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

K. A. Svinarich, W. J. Meng, G. L. Eesley, Appl. Phys. Lett. 57, 1185 (1990).
[Crossref]

J. Appl. Phys. (1)

O. B. Wright, J. Appl. Phys. 71, 1617 (1992).
[Crossref]

Opt. Commun. (1)

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

Opt. Lett. (2)

Phys. Rev. B (3)

O. B. Wright, Phys. Rev. B 49, 9985 (1994).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 643, 4129 (1986).
[Crossref]

H. J. Grahn, H. J. Maris, J. Tauc, B. Abeles, Phys. Rev. B 38, 6606 (1988); P. Basseras, S. M. Gracewski, G. W. Wicks, R. J. D. Miller, J. Appl. Phys. 75, 2761 (1994).
[Crossref]

Phys. Rev. Lett. (1)

O. B. Wright, K. K. Kawashima, Phys. Rev. Lett. 69, 1668 (1992).
[Crossref] [PubMed]

Other (7)

I assume that θ = 0 in the analysis in this Letter.

The silicon nitride film is thought to be amorphous for the deposition conditions used.

These could be separated by frequency-domain analysis.

The beat contribution was calculated with the further simplifying approximation r12 = 0.

The slight smoothing caused by the finite duration of the pump and probe pulses has been neglected. The film and substrate densities and the substrate sound velocity were taken from the literature.

Values ν1 = 5400 ms−1 and ν1 = 5300 ms−1 were used for Figs. 2(a) and 2(b), respectively.

The sound velocity for silica is similar to that previously determined in single-layer films (see Refs. 5 and 6). That for silicon nitride agrees with the data ofT. S. Hickernell, F. M. Fliegel, F. S. Hickernell, in Proceedings of the IEEE Ultrasonics Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), p. 445. From the relation dn/dη = −n3p12/2, dn/dη can be compared with previous measurements of p12, the appropriate photo-elastic tensor element. This gives p12 = 0.28 for silica, in good agreement with; R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).For silicon nitride I obtain p12 = 0.023.
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the excitation and detection geometry. The vertical dashed lines indicate the strain pulse positions (shown localized for simplicity) at a delay time d1/ν1 + d2/ν2 > t > d1/ν1. The strain pulse shapes and polarity at this time are also shown. The probe beam angle has been exaggerated for clarity.

Fig. 2
Fig. 2

Relative reflectance variation for double-layer films of silicon nitride upon silica with nominal thicknesses (a) 500 nm and (b) 300 nm. Upper curves: Experiment. Lower curves: Theory. The total heights of the vertical scales in (a) and (b) correspond to δR/R ≈ 8 × 10−3 and 4 × 10−3, respectively.

Equations (3)

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η = η 0 exp [ ( z ν 1 t ) / ζ 1 ] for z ν 1 t d 1 , = 0 for z > ν 1 t ,
δ R = i r * δ r i + c . c . ,
r r 0 + r exp ( i q ) 1 + r 0 r exp ( i q ) + r 21 ( 1 r 0 2 ) exp ( i q ) [ exp ( i q 1 ) r 1 r exp ( i q 1 ) ] [ 1 + r 0 r exp ( i q ) ] 2 ,

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