Abstract

Picosecond laser pulses are used to excite and detect stress pulses in thin transparent films on opaque substrates. The reflectance variation, measured for silica films, is modeled as a sum of different contributions: an echo contribution from stress-induced modulation of the substrate reflectance, an interference contribution from light reflected by the stress pulse in the transparent film, and a contribution from stress-induced vibrations of the order of 10−3 nm of the film surface, observed for what is to our knowledge the first time. We show how both the thickness and sound velocity of the film can be determined, provided that its refractive index is known.

© 1991 Optical Society of America

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References

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  1. C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
    [CrossRef]
  2. O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
    [CrossRef]
  3. H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
    [CrossRef]
  4. O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
    [CrossRef]
  5. M. Rothenfusser, W. Dietsche, H. Kinder, in Phonon Scattering in Condensed Matter, W. Eisenmenger, K. Lassmann, S. Dottinger, eds. (Springer-Verlag, New York, 1984), p. 419.
    [CrossRef]
  6. The stress-induced displacement of the constrained film–substrate interface is neglected.
  7. In Refs. 2 and 4 the ratio dn1/dη:dκ1/dη = 1.3:2 was derived from the Tauc formula (see Ref. 1) for κ1(λ) in amorphous semiconductors; the ratio −5:2.5 gives a better fit. To give the observed ratio between the interference and displacement contributions, dn/dη = −0.7 ± 0.2. For comparison, in bulk a-SiO2 measured at megahertz frequencies, dn/dη = −n3p12/2 = −0.42, where p12 = 0.27 [see R. W. Dixon, J. Appl. Phys. 38, 5149 (1967)] is the photoelastic tensor coefficient corresponding to the probe light polarization.
    [CrossRef]
  8. G. W C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants (Longman, New York, 1986).
  9. Strain η0 ∼ 10−4 can be approximately determined from the magnitude of δR.

1991 (2)

O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
[CrossRef]

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

1986 (1)

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

1967 (1)

In Refs. 2 and 4 the ratio dn1/dη:dκ1/dη = 1.3:2 was derived from the Tauc formula (see Ref. 1) for κ1(λ) in amorphous semiconductors; the ratio −5:2.5 gives a better fit. To give the observed ratio between the interference and displacement contributions, dn/dη = −0.7 ± 0.2. For comparison, in bulk a-SiO2 measured at megahertz frequencies, dn/dη = −n3p12/2 = −0.42, where p12 = 0.27 [see R. W. Dixon, J. Appl. Phys. 38, 5149 (1967)] is the photoelastic tensor coefficient corresponding to the probe light polarization.
[CrossRef]

Dietsche, W.

M. Rothenfusser, W. Dietsche, H. Kinder, in Phonon Scattering in Condensed Matter, W. Eisenmenger, K. Lassmann, S. Dottinger, eds. (Springer-Verlag, New York, 1984), p. 419.
[CrossRef]

Dixon, R. W.

In Refs. 2 and 4 the ratio dn1/dη:dκ1/dη = 1.3:2 was derived from the Tauc formula (see Ref. 1) for κ1(λ) in amorphous semiconductors; the ratio −5:2.5 gives a better fit. To give the observed ratio between the interference and displacement contributions, dn/dη = −0.7 ± 0.2. For comparison, in bulk a-SiO2 measured at megahertz frequencies, dn/dη = −n3p12/2 = −0.42, where p12 = 0.27 [see R. W. Dixon, J. Appl. Phys. 38, 5149 (1967)] is the photoelastic tensor coefficient corresponding to the probe light polarization.
[CrossRef]

Grahn, H. T.

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

Hyoguchi, T.

O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
[CrossRef]

O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
[CrossRef]

Kawashima, K.

O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
[CrossRef]

O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
[CrossRef]

Kaye, G. W C.

G. W C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants (Longman, New York, 1986).

Kinder, H.

M. Rothenfusser, W. Dietsche, H. Kinder, in Phonon Scattering in Condensed Matter, W. Eisenmenger, K. Lassmann, S. Dottinger, eds. (Springer-Verlag, New York, 1984), p. 419.
[CrossRef]

Laby, T. H.

G. W C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants (Longman, New York, 1986).

Lin, H.-N.

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

Maris, H. J.

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

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

Matsumoto, T.

O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
[CrossRef]

Rothenfusser, M.

M. Rothenfusser, W. Dietsche, H. Kinder, in Phonon Scattering in Condensed Matter, W. Eisenmenger, K. Lassmann, S. Dottinger, eds. (Springer-Verlag, New York, 1984), p. 419.
[CrossRef]

Stoner, R. J.

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

Tauc, J.

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

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

Thomsen, C.

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

Wright, O. B.

O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
[CrossRef]

O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
[CrossRef]

J. Appl. Phys. (2)

H.-N. Lin, R. J. Stoner, H. J. Maris, J. Tauc, J. Appl. Phys. 69, 3816 (1991).
[CrossRef]

In Refs. 2 and 4 the ratio dn1/dη:dκ1/dη = 1.3:2 was derived from the Tauc formula (see Ref. 1) for κ1(λ) in amorphous semiconductors; the ratio −5:2.5 gives a better fit. To give the observed ratio between the interference and displacement contributions, dn/dη = −0.7 ± 0.2. For comparison, in bulk a-SiO2 measured at megahertz frequencies, dn/dη = −n3p12/2 = −0.42, where p12 = 0.27 [see R. W. Dixon, J. Appl. Phys. 38, 5149 (1967)] is the photoelastic tensor coefficient corresponding to the probe light polarization.
[CrossRef]

Jpn. J. Appl. Phys. (1)

O. B. Wright, T. Hyoguchi, K. Kawashima, Jpn. J. Appl. Phys. 1B, L131 (1991).
[CrossRef]

Phys. Rev. B (1)

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

Other (5)

G. W C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants (Longman, New York, 1986).

Strain η0 ∼ 10−4 can be approximately determined from the magnitude of δR.

O. B. Wright, T. Matsumoto, T. Hyoguchi, K. Kawashima, in Physical Acoustics, O. Leroy, ed. (Plenum, New York, 1991), p. 695.
[CrossRef]

M. Rothenfusser, W. Dietsche, H. Kinder, in Phonon Scattering in Condensed Matter, W. Eisenmenger, K. Lassmann, S. Dottinger, eds. (Springer-Verlag, New York, 1984), p. 419.
[CrossRef]

The stress-induced displacement of the constrained film–substrate interface is neglected.

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Figures (3)

Fig. 1
Fig. 1

(a) Relative reflectance variation for the a-SiO2 (340 nm)/a-Ge (470 nm) sample, (b) Variation with background subtracted (upper curve) and theoretical fit (lower curve). Components of the fit are shown in (c)–(f).

Fig. 2
Fig. 2

Relative reflectance variations with background subtracted for (a) a-SiO2 (1600 nm)/a-Ge, (b) a-SiO2 (350 nm)/Cr, and (c) a-SiO2 (900 nm)/Cr samples (upper curves) with theoretical fits (lower curves).

Fig. 3
Fig. 3

Schematic diagram of the excitation and detection geometry. The vertical dashed–dotted line indicates the stress pulse position (shown localized for clarity) at a given instant. The stress pulse shapes at various times are also shown.

Tables (1)

Tables Icon

Table 1 Experimental Data for the Four Samples Investigated

Equations (7)

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η = η 0 exp [ ( z υ t ) / ζ ] for z υ t d , = 0 for z > υ t ,
r = r 0 + r 1 ( 1 r 0 2 ) exp ( 2 ikd cos θ ) 1 + r 0 r 1 exp ( 2 i k d cos θ ) = r 0 + K r 1 ,
δ R = | r + r r 1 δ r 1 + δ r p + δ r p + r d δ z | 2 | r | 2 ( r * r r 1 δ r 1 + r * δ r p + r * δ r p + r * r d δ z ) + c . c . ,
δ r 1 = i k 0 2 k 1 t 1 t ˜ 1 ( n 1 + i κ 1 ) 0 ( n 1 η + i κ 1 η ) × η ( z , t ) exp ( 2 i k 1 z ) d z ,
δ r p = i K k 0 0 d n η η ( z , t ) exp ( 2 ikz cos θ ) d z ,
δ r p = i K r 1 2 k 0 0 d n η η ( z , t ) exp ( 2 ikz cos θ ) d z ,
δ z = 2 ζ η 0 { exp [ ( d υ t ) / ζ ] 1 } for d υ t 2 d , 0 for 0 < υ t < d ,

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