Abstract

A novel single-beam interferometric measurement of a thermal bump produced by an intensity modulated and focused laser beam is described. The effects of the ac change in optical reflectivity and the displacement of the surface are determined independently by fitting data to a phenomenological theory. This technique is insensitive to sample vibrations and variations in optical path resulting from thermal fluctuations.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Royer, E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
    [CrossRef]
  2. H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).
  3. M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
    [CrossRef]
  4. A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
    [CrossRef]
  5. J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
    [CrossRef]
  6. L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: Theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, Eds. Vol. 8A, 635–640, (Plenum Press, New York, 1989).

1986 (3)

D. Royer, E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[CrossRef]

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
[CrossRef]

1983 (2)

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Ash, E. A.

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Dieulesaint, E.

D. Royer, E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[CrossRef]

Favro, L. D.

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: Theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, Eds. Vol. 8A, 635–640, (Plenum Press, New York, 1989).

Fournier, D.

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Hartikainen, J.

J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
[CrossRef]

Jaarinen, J.

J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
[CrossRef]

Kohan, S. E.

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Luukkala, M.

J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
[CrossRef]

Martin, Y.

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

Munidasa, M.

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: Theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, Eds. Vol. 8A, 635–640, (Plenum Press, New York, 1989).

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Opsal, J.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

Royer, D.

D. Royer, E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[CrossRef]

Smith, W. L.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

Spear, D. A. H.

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

Wickramasinghe, H. K.

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

Willenborg, D. L.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

Appl. Phys. A (1)

M. A. Olmstead, N. M. Amer, S. E. Kohan, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: An optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

D. Royer, E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[CrossRef]

Can. J. Phys. (1)

J. Hartikainen, J. Jaarinen, M. Luukkala, “Deformation of a liquid surface by laser heating: laser-beam self-focusing and generation of capillary waves,” Can. J. Phys. 64, 1341–1344 (1986).
[CrossRef]

J. Appl. Phys. (1)

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of thermal waves through modulated optical transmittance and modulated optical scattering,” J. Appl. Phys. 59, 1392–1394 (1986).
[CrossRef]

J. Phys. Paris Coll. C6 (1)

H. K. Wickramasinghe, Y. Martin, D. A. H. Spear, E. A. Ash, “Optical heterodyne techniques for photoacoustic and photo-thermal Detection,” J. Phys. Paris Coll. C6 44, 191–196 (1983).

Other (1)

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: Theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, Eds. Vol. 8A, 635–640, (Plenum Press, New York, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Interference of the reflected probe beam.

Fig. 2
Fig. 2

Propagation of a Gaussian beam.

Fig. 3
Fig. 3

Position of the probe beam and the heating beam on the sample surface.

Fig. 4
Fig. 4

Experimental arrangement.

Fig. 5
Fig. 5

Experimental data and the theoretical fit of the inphase signal for five different heating beam positions within the probe beam.

Fig. 6
Fig. 6

Interference signal in air and in a vacuum.

Fig. 7
Fig. 7

Experimental data and the theoretical fit of inphase and quadrature signal for a Si wafer with a heating beam power of 0.1 mW and a modulation frequency of 1 kHz. The bump height calculated from the fit is 3 × 10−3 Å.

Fig. 8
Fig. 8

Plot of bump height vs frequency of the unimplanted region and an implanted region (50-keV B+, 1016 ions/cm2) of a p-type Si wafer.

Fig. 9
Fig. 9

Interference signal for silicon at 300 Hz and 100 kHz.

Fig. 10
Fig. 10

Theoretical plot of the interference signal where the reflectivity change dominates bump height.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

h ( x , y , t ) = δ h cos ( Ω t + θ h ) exp [ - ( x 2 + y 2 ) / r b 2 ] ,
E ( x , y , z , t ) = E 0 - i z 0 z - z 1 - i z 0 exp i k [ z + x 2 + y 2 2 ( z - z 1 - i z 0 ) ] ,
z 0 = w 0 2 k / 2.
E ( x , y , z , t ) = E 0 exp ( i k ρ ) / ρ ,
ρ = x 2 + y 2 + ( z - z 1 - i z 0 ) 2 ,
R ( x , y , t ) = R 0 + δ R cos ( Ω t + θ R ) exp [ - ( x 2 + y 2 ) / r b 2 ] ,
R ( x - x 1 , y , t ) exp [ - 2 i k h ( x - x 1 , y , t ) ] ,
exp [ - 2 i k h ( x - x 1 , y , t ) ] = 1 - 2 i k h ( x - x 1 , y , t ) .
exp ( a + r x + p x 2 ) cos ( b + t x + s x 2 ) ,
a + i b = 1 2 ln 2 π i k + ln ( I 0 z 0 2 ) + ln z 1 - i z 0 z 1 - i z 0 + ln ( δ R R 0 cos θ R - 2 i k δ h cos θ h ) - ½ ln { [ ( z 1 - z 1 ) - i ( z 0 + z 0 ) ] ( z 1 + d + i z 0 ) ( z 1 + d - i z 0 ) } - i k x 1 2 2 [ ( z 1 - z 1 ) - i ( z 0 - z 0 ) ] ( z 1 + d - i z 0 ) ( z 1 + d - i z 0 ) ( z 1 - i z 0 ) 2 ,
r + i t = i k x 1 [ ( z 1 - z 1 ) - i ( z 0 - z 0 ) ] ( z 1 + d - i z 0 ) ( z 1 - z 0 ) ,
p + i s = - i k 2 [ ( z 1 - z 1 ) - i ( z 0 + z 0 ) ] ( z 1 + d - i z 0 ) ( z 1 + d + i z 0 ) ,
1 z 1 - i z 0 - 1 z 1 - i z 0 = 2 i k r b 2 .
δ R R 0 cos θ R - 2 i k δ h cos θ h .
signal with vacuum signal with atm . air - signal with vacuum = 4.85

Metrics