Abstract

A double-beam wavelength-modulated reflectometer utilizing a single detector and without a reflectivity reference has been described. Separate electronic channels are used for the two wavelengths at which the reflectometer alternatively operates. The gain of one of the channels is controlled by feedback to eliminate the instrumental background. The derivative and conventional reflectivity are measured simultaneously. The influence of the photomultiplier dark current and scattered light on the accuracy and of some design parameters on the SNR have been evaluated. The system has been checked by measuring the derivative and conventional reflectivity spectrum of GaAs.

© 1974 Optical Society of America

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References

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  1. See, e.g., M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).
  2. K. L. Shaklee, J. E. Rowe. Appl. Opt. 9, 627 (1970).
    [CrossRef] [PubMed]
  3. M. Welkowsky, R. Braunstein, Rev. Sci. Instrum. 43, 399 (1972).
    [CrossRef]
  4. G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
    [CrossRef]
  5. R. R. L. Zucca, Y. R. Shen, Appl. Opt. 12, 1293 (1973).
    [CrossRef] [PubMed]
  6. R. N. Hager, R. C. Anderson, J. Opt. Soc. Am. 60, 1444 (1970).
    [CrossRef]
  7. F. R. Stauffer, H. Sakai, Appl. Opt. 7, 61 (1968).
    [CrossRef] [PubMed]
  8. I. Balslev, Sol. State Commun. 3, 213 (1965); Phys. Rev. 143, 636 (1966).
    [CrossRef]
  9. R. E. Drews, Bull. Am. Phys. Soc. II 12, 384 (1967).
  10. A. Perregaux, G. Ascarelli, Appl Opt. 7, 2031 (1968).
    [CrossRef] [PubMed]
  11. G. Bonfiglioli, P. Brovetto, Appl. Opt. 3, 1417 (1964).
    [CrossRef]
  12. E. Sutter, Optik 38, 73 (1973).
  13. R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
    [CrossRef]
  14. R. R. L. Zucca, Y. R. Shen, Phys. Rev. 1, 2668 (1970).
    [CrossRef]
  15. R. Braunstein, M. Welkowsky, in Proc. Tenth Intern. Conf. Phys. Semicond. (edited by S. P. Keller, J. C. Hensel, F. Stern, USAEC Division of Technical Information, Oak Ridge, Tennessee, 1970), p. 439.

1973 (3)

G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
[CrossRef]

E. Sutter, Optik 38, 73 (1973).

R. R. L. Zucca, Y. R. Shen, Appl. Opt. 12, 1293 (1973).
[CrossRef] [PubMed]

1972 (1)

M. Welkowsky, R. Braunstein, Rev. Sci. Instrum. 43, 399 (1972).
[CrossRef]

1970 (4)

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

R. R. L. Zucca, Y. R. Shen, Phys. Rev. 1, 2668 (1970).
[CrossRef]

R. N. Hager, R. C. Anderson, J. Opt. Soc. Am. 60, 1444 (1970).
[CrossRef]

K. L. Shaklee, J. E. Rowe. Appl. Opt. 9, 627 (1970).
[CrossRef] [PubMed]

1968 (2)

1967 (1)

R. E. Drews, Bull. Am. Phys. Soc. II 12, 384 (1967).

1965 (1)

I. Balslev, Sol. State Commun. 3, 213 (1965); Phys. Rev. 143, 636 (1966).
[CrossRef]

1964 (1)

Anderson, R. C.

Ascarelli, G.

A. Perregaux, G. Ascarelli, Appl Opt. 7, 2031 (1968).
[CrossRef] [PubMed]

Balslev, I.

I. Balslev, Sol. State Commun. 3, 213 (1965); Phys. Rev. 143, 636 (1966).
[CrossRef]

Bonfiglioli, G.

Braunstein, R.

M. Welkowsky, R. Braunstein, Rev. Sci. Instrum. 43, 399 (1972).
[CrossRef]

R. Braunstein, M. Welkowsky, in Proc. Tenth Intern. Conf. Phys. Semicond. (edited by S. P. Keller, J. C. Hensel, F. Stern, USAEC Division of Technical Information, Oak Ridge, Tennessee, 1970), p. 439.

Brovetto, P.

Cardona, M.

See, e.g., M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).

Cohen, M. L.

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

Drews, R. E.

R. E. Drews, Bull. Am. Phys. Soc. II 12, 384 (1967).

Hager, R. N.

Hart, G. P.

G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
[CrossRef]

Kearney, R. J.

G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
[CrossRef]

Neely, J. A.

G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
[CrossRef]

Perregaux, A.

A. Perregaux, G. Ascarelli, Appl Opt. 7, 2031 (1968).
[CrossRef] [PubMed]

Rowe, J. E.

Sakai, H.

Shaklee, K. L.

Shen, Y. R.

R. R. L. Zucca, Y. R. Shen, Appl. Opt. 12, 1293 (1973).
[CrossRef] [PubMed]

R. R. L. Zucca, Y. R. Shen, Phys. Rev. 1, 2668 (1970).
[CrossRef]

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

Stauffer, F. R.

Sutter, E.

E. Sutter, Optik 38, 73 (1973).

Walter, J. P.

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

Welkowsky, M.

M. Welkowsky, R. Braunstein, Rev. Sci. Instrum. 43, 399 (1972).
[CrossRef]

R. Braunstein, M. Welkowsky, in Proc. Tenth Intern. Conf. Phys. Semicond. (edited by S. P. Keller, J. C. Hensel, F. Stern, USAEC Division of Technical Information, Oak Ridge, Tennessee, 1970), p. 439.

Zucca, R. R. L.

R. R. L. Zucca, Y. R. Shen, Appl. Opt. 12, 1293 (1973).
[CrossRef] [PubMed]

R. R. L. Zucca, Y. R. Shen, Phys. Rev. 1, 2668 (1970).
[CrossRef]

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

Appl Opt. (1)

A. Perregaux, G. Ascarelli, Appl Opt. 7, 2031 (1968).
[CrossRef] [PubMed]

Appl. Opt. (4)

Bull. Am. Phys. Soc. II (1)

R. E. Drews, Bull. Am. Phys. Soc. II 12, 384 (1967).

J. Opt. Soc. Am. (1)

Optik (1)

E. Sutter, Optik 38, 73 (1973).

Phys. Rev. (1)

R. R. L. Zucca, Y. R. Shen, Phys. Rev. 1, 2668 (1970).
[CrossRef]

Rev. Sci. Instrum. (2)

M. Welkowsky, R. Braunstein, Rev. Sci. Instrum. 43, 399 (1972).
[CrossRef]

G. P. Hart, J. A. Neely, R. J. Kearney, Rev. Sci. Instrum. 44, 37 (1973).
[CrossRef]

Sol. State Commun. (2)

I. Balslev, Sol. State Commun. 3, 213 (1965); Phys. Rev. 143, 636 (1966).
[CrossRef]

R. R. L. Zucca, J. P. Walter, Y. R. Shen, M. L. Cohen, Sol. State Commun. 8, 627 (1970).
[CrossRef]

Other (2)

R. Braunstein, M. Welkowsky, in Proc. Tenth Intern. Conf. Phys. Semicond. (edited by S. P. Keller, J. C. Hensel, F. Stern, USAEC Division of Technical Information, Oak Ridge, Tennessee, 1970), p. 439.

See, e.g., M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).

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Figures (4)

Fig. 1
Fig. 1

The wavelength modulation attachment. A is the vibrating plane mirror just before the exit slit of the monochromator, B is the limiter arm, and C the driving spring. The micrometer E, the wedge F, and the two stops G determine the modulation depth.

Fig. 2
Fig. 2

Shown are the exit optics of the monochromator and a block diagram of the electronic system. The system changes from measurement to calibration by shifting a plane mirror from B to B′ and by rotating the plane mirror D over an appropriate angle. BCDB′ constitutes a parallelogram.

Fig. 3
Fig. 3

(a) A part of the derivative emission spectrum of a Philips type 7023 100-W tungsten halogen lamp containing a bromide compound additive. An EMI 9658Q photomultiplier was used as the detector. (b) An exploded view of a part of the same spectrum showing the emission lines attributed to tungsten bromide complexes.

Fig. 4
Fig. 4

As a typical measuring result, a derivative and conventional reflectivity spectrum of an etched {111} surface of GaAs at room temperature are shown together with the calculated reflectivity spectrum obtained by numerical integration of the derivative spectrum. The zero of the ordinate of the measured spectrum is shifted by 3% for reasons of clarity.

Equations (18)

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g ( λ λ 0 ) = 1 | λ λ 0 | / a for | λ λ 0 | a , g ( λ λ 0 ) = 0 for | λ λ 0 | > a ,
ψ ( λ ) = 2 n = 0 ( δ / 2 ) 2 n + 1 ( 2 n + 1 ) ! d 2 n + 1 ψ 0 ( λ ) d λ 2 n + 1
ψ ( λ ) = ψ 0 ( λ δ / 2 ) ψ 0 ( λ + δ / 2 ) .
ψ ( λ δ / 2 ) + γ α 0 [ ψ ( λ + δ / 2 ) + γ ] = 0.
R ( λ δ / 2 ) ψ ( λ δ / 2 ) + γ α 0 [ R ( λ + δ / 2 ) ψ ( λ + δ / 2 ) + γ ] .
[ R ( λ δ / 2 ) ψ ( λ δ / 2 ) + R ( λ + δ / 2 ) ψ ( λ + δ / 2 ] / 2 ,
δ R R [ 1 δ 2 ψ ψ δ 2 4 ( R ψ R ψ 1 6 R R ) ] + δ ( 1 R R ) ψ ψ γ ψ + higher order contributions .
1 2 ( ψ 1 + α ψ 2 ) + 2 π ( ψ 1 α ψ 2 ) n = 0 sin ( 2 n + 1 ) Ω t 2 n + 1 .
1 2 ( R 1 ψ 1 + α 0 R 2 ψ 2 ) + 2 π ( R 1 ψ 1 α 0 R 2 ψ 2 ) n = 0 sin ( 2 n + 1 ) Ω t 2 n + 1 .
ψ i ( t ) = ψ i 0 + 0 [ a i ( ω ) cos ω t + b i ( ω ) sin ω t ] d ω ,
{ 2 π Δ R ψ 1 0 + Δ R [ 2 π a 1 ( 0 ) + 1 2 b 1 ( Ω ) 2 π n = 1 a 1 ( 2 n Ω ) ( 2 n 1 ) ( 2 n + 1 ) ] d ω } sin Ω t ,
t t + τ 0 Δ ω [ a i ( ω ) cos ω t + b i ( ω ) sin ω t ] d ω d t
2 π R 2 { [ a 1 m ( 0 ) a 1 c ( 0 ) ] ( 1 + Δ ψ 0 ψ 2 0 ) [ a 2 m ( 0 ) a 2 c ( 0 ) ] } Δ ω .
8 π R δ 0 γ/ τ sin 2 ω τ / 2 ω { [ a ( λ , ω ) λ + 1 ψ 0 d ψ 0 d λ a ( λ , ω ) ] sin ω t + [ b ( λ , ω ) λ + 1 ψ 0 d ψ 0 d λ b ( λ , ω ) ] cos ω t } d ω .
R δ 0 γ/ τ sin 2 ω τ / 2 ω · K d ω , where K = { [ a ( λ , ω ) λ + 1 ψ 0 d ψ 0 d λ b ( λ , ω ) ] 2 + [ a ( λ , ω ) λ + 1 ψ 0 d ψ 0 d λ b ( λ , ω ) ] 2 } 1 / 2 .
R δ 0 γ n / T ( 1 ) n + 1 ω tan ω T 2 n sin ω T · K d ω .
0 γ / 2 ( 1 ) n + 1 x tan x sin 2 n x d x ,
( T n ) 1 / 2 0 γ / 2 ( 1 ) n + 1 x 3 / 2 tan x sin 2 n x d x .

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