Abstract

A method of measurement of the optical absorption coefficient for a semiconductor sample is given, based on the simplified pattern by Rosencwaig and Gersho in the particular case of thick samples. This method allows us to deduce directly the absorption coefficient from photoacoustic amplitude signal measurement, whatever the incident light modulation frequency. The experimental results obtained from thicker sample of GaP (0.2–1 mm) are compared with the results given by classical optical methods.

© 1984 Optical Society of America

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References

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  1. S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
    [CrossRef]
  2. A. Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids,” J. Appl. Phys. 47, 64 (1976).
    [CrossRef]
  3. A. Rosencwaig, “The Generation of Sound Aperiodically Illuminated Solid, an Effect First Discovered 1881, is now being Used to Study the Properties of Materials not Accessible to Optical Spectroscopy,” Phys. Today 28, 23 (1975).
    [CrossRef]
  4. A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).
  5. P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
    [CrossRef]
  6. M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
    [CrossRef]
  7. D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 123 (1983).
    [CrossRef]

1983

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 123 (1983).
[CrossRef]

1981

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

1980

P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
[CrossRef]

1977

M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
[CrossRef]

1976

A. Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids,” J. Appl. Phys. 47, 64 (1976).
[CrossRef]

1975

A. Rosencwaig, “The Generation of Sound Aperiodically Illuminated Solid, an Effect First Discovered 1881, is now being Used to Study the Properties of Materials not Accessible to Optical Spectroscopy,” Phys. Today 28, 23 (1975).
[CrossRef]

Adams, M. J.

M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 123 (1983).
[CrossRef]

Beadle, B. C.

M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
[CrossRef]

Chambron, J.

P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
[CrossRef]

Gersho, A.

A. Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids,” J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Hata, N.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Kirkbright, C. F.

M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
[CrossRef]

Matsuda, A.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Oheda, H.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Okushi, H.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Poulet, P.

P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids,” J. Appl. Phys. 47, 64 (1976).
[CrossRef]

A. Rosencwaig, “The Generation of Sound Aperiodically Illuminated Solid, an Effect First Discovered 1881, is now being Used to Study the Properties of Materials not Accessible to Optical Spectroscopy,” Phys. Today 28, 23 (1975).
[CrossRef]

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 123 (1983).
[CrossRef]

Tanaka, K.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Unterreiner, R.

P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
[CrossRef]

Yamasaki, S.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Analyst London

M. J. Adams, B. C. Beadle, C. F. Kirkbright, “A Double-Beam Optoacoustic Spectrometer for use with Solid and Liquid Samples in the Ultraviolet, Visible and Near-infrared Region of the Spectrum,” Analyst London 102, 569 (1977).
[CrossRef]

J. Appl. Phys.

A. Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids,” J. Appl. Phys. 47, 64 (1976).
[CrossRef]

P. Poulet, J. Chambron, R. Unterreiner, “Quantitative Photoacoustic Spectroscopy Applied to Thermally Thick Samples,” J. Appl. Phys. 51, 456 (1980).
[CrossRef]

Jpn. J. Appl. Phys.

S. Yamasaki, H. Okushi, A. Matsuda, H. Oheda, N. Hata, K. Tanaka, “Determination of the Optical Constants of Thin Films Using Photoacoustic Spectroscopy,” Jpn. J. Appl. Phys. 20, 1665 (1981).
[CrossRef]

Phys. Rev. B

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 123 (1983).
[CrossRef]

Phys. Today

A. Rosencwaig, “The Generation of Sound Aperiodically Illuminated Solid, an Effect First Discovered 1881, is now being Used to Study the Properties of Materials not Accessible to Optical Spectroscopy,” Phys. Today 28, 23 (1975).
[CrossRef]

Other

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

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Figures (7)

Fig. 1
Fig. 1

Q(β) curve (normalized amplitude) for a GaP sample of thickness Ls = 0.3 mm for modulation frequencies between 10 and 1000 Hz.

Fig. 2
Fig. 2

Theoretical q(βμs) (relative amplitude) obtained by Eq. 6.

Fig. 3
Fig. 3

Schematic diagram of automatized photoacoustic spectrometer.

Fig. 4
Fig. 4

Experimental spectra q (normalized amplitude) vs λ for GaP samples 0.3 and 0.7 mm thick.

Fig. 5
Fig. 5

Experimental results corresponding to various modulation frequencies (1–6) agree with the β(λ) curve (plain line) obtained from optical measurement using the ellipsometric technique for wavelength values included between 450 and 550 nm.

Fig. 6
Fig. 6

Comparison of q experimental values of theoretical curve q(βμs) obtained by Eq. (4).

Fig. 7
Fig. 7

Comparison of the application domains of classical optical spectroscopy (transmission measurement) and photoacoustic spectroscopy.

Equations (9)

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I = ( I 0 / 2 ) ( 1 + cos ω t )
Δ P ( t ) = γ P 0 θ μ g 2 L g T 0 · exp [ j ( ω t - π / 4 ) ] ,
θ = β I 0 2 k s ( β 2 - σ s 2 ) [ ( r - 1 ) ( b + 1 ) exp ( σ s L s ) - ( r + 1 ) ( b - 1 ) × exp ( - σ s L s ) + 2 ( b - r ) exp ( - β L s ) ] · [ ( g + 1 ) ( b + 1 ) × exp ( σ s L s ) - ( g - 1 ) ( b - 1 ) exp ( - σ s L s ) ] - 1 .
σ s = 1 + j μ s ,             b = k b μ s k s μ b ,             g = k g μ s k s μ g , and r = ( 1 - j ) 2 β μ s .
Q = A β μ s ω [ ( β μ s + 1 ) 2 + 1 ] 1 / 2 ,
A = γ P 0 I 0 ( α g α s ) 1 / 2 2 L g T 0 k s ,
tan ϕ = β μ s + 1.
q ( β μ s ) = Q ( β μ s ) Q s = β μ s [ 1 + ( 1 + β μ s ) 2 ] 1 / 2 ,
β = 1 μ s · q 2 + q ( 2 - q 2 ) 1 / 2 1 - q 2 ;

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