Abstract

We describe the design, construction, alignment, and calibration of a photometric ellipsometer of the rotating-analyzer type. Data are obtained by digital sampling of the transmitted flux with an analog-to-digital converter, followed by Fourier transforming of the accumulated data with a dedicated minicomputer. With an operating mechanical rotation frequency of 74 Hz, a data acquisition cycle requires less than 7 msec. The intrinsic precision attainable is high because precision is limited only by shot noise or intrinsic source instabilities, even when relatively weak continuum lamps are used as light sources. Precision may be improved by accumulating the data for consecutive cycles at a fixed wavelength. The system allows complex reflectance ratios to be determined as continuous functions of wavelength from the near infrared to the near ultraviolet spectral range. Data reduction programs can be modified to calculate complex refractive index or dielectric function spectra, or film thicknesses and refractive indices, as well as the usual ellipsometric parameters tanψ, cosΔ.

© 1975 Optical Society of America

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References

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  1. C. V. Kent, J. Lawson, J. Opt. Soc. Am. 27, 117 (1937).
    [CrossRef]
  2. J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).
  3. W. Budde, Appl. Opt. 1, 201 (1962).
    [CrossRef]
  4. N. V. Smith, Phys. Rev. Lett. 21, 96 (1968).
    [CrossRef]
  5. S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, R. C. O’Handley, Surface Sci. 37, 548 (1973).
    [CrossRef]
  6. B. D. Cahan, R. F. Spanier, Surface Sci. 16, 166 (1969).
    [CrossRef]
  7. R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
    [CrossRef]
  8. J. C. Suits, Rev. Sci. Instrum. 42, 19 (1971).
    [CrossRef]
  9. D. E. Aspnes, Opt. Commun. 8, 222 (1973).
    [CrossRef]
  10. P. S. Hauge, F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
    [CrossRef]
  11. D. E. Aspnes, Phys. Rev. Lett. 28, 168 (1972).
    [CrossRef]
  12. D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
    [CrossRef]
  13. E. O. Ammann, G. A. Massey, J. Opt. Soc. Am. 58, 1427 (1968).
    [CrossRef]
  14. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [CrossRef]
  15. Model 9558QB, mfg. by EMI, Gencom Division, Plainview, N.Y. 11803.
  16. Model S2005-3 fiber-optic scanner, mfg. by Skan-A-Matic Corp., Elbridge, N.Y. 13060.
  17. Model 4853 sample-hold amplifier, mfg. by Teledyne Philbrick, Dedham, Mass. 02026. This module has a gain of −1.000.
  18. Model 4106 analog-to-digital converter, mfg. by Teledyne Philbrick, Dedham, Mass. 02026.
  19. Model 2114A computer, mfg. by Hewlett-Packard, Palo Alto, California 94306.
  20. J. S. Bendat, Principles and Applications of Random Noise Theory (Wiley, New York, 1958), p. 15.
  21. D. E. Aspnes, A. A. Studna, Phys. Rev. B7, 4605 (1973).
  22. D. E. Aspnes, J. Opt. Soc. Am. 64, 812 (1974).
    [CrossRef]
  23. U. W. Hochstrasser, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, Eds. (U.S. Nat. Bur. Stds., Appl. Math. Ser. 55, 1964), p. 790-1.
  24. D. E. Aspnes, J. Opt. Soc. Am. 61, 1077 (1971).
    [CrossRef]
  25. R. M. A. Azzam, N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).
    [CrossRef]
  26. R. C. O’Handley, J. Opt. Soc. Am. 63, 523 (1973).
    [CrossRef]
  27. K. L. Shaklee, J. E. Rowe, Appl. Opt. 9, 627 (1970); Y. R. Shen, Surface Sci. 37, 522 (1973) and references therein.
    [CrossRef] [PubMed]
  28. D. D. Sell, Appl. Opt. 9, 1926 (1971).
  29. See, e.g., RCA Photomultiplier Manual (RCA, Harrison, N.J., 1970), p. 68.
  30. W-K. Paik, J. O’M. Bockris, Surface Sci. 28, 61 (1971).
    [CrossRef]

1974 (3)

1973 (4)

R. C. O’Handley, J. Opt. Soc. Am. 63, 523 (1973).
[CrossRef]

D. E. Aspnes, A. A. Studna, Phys. Rev. B7, 4605 (1973).

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

P. S. Hauge, F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
[CrossRef]

1972 (1)

D. E. Aspnes, Phys. Rev. Lett. 28, 168 (1972).
[CrossRef]

1971 (4)

D. E. Aspnes, J. Opt. Soc. Am. 61, 1077 (1971).
[CrossRef]

J. C. Suits, Rev. Sci. Instrum. 42, 19 (1971).
[CrossRef]

D. D. Sell, Appl. Opt. 9, 1926 (1971).

W-K. Paik, J. O’M. Bockris, Surface Sci. 28, 61 (1971).
[CrossRef]

1970 (3)

K. L. Shaklee, J. E. Rowe, Appl. Opt. 9, 627 (1970); Y. R. Shen, Surface Sci. 37, 522 (1973) and references therein.
[CrossRef] [PubMed]

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

1969 (2)

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, R. C. O’Handley, Surface Sci. 37, 548 (1973).
[CrossRef]

B. D. Cahan, R. F. Spanier, Surface Sci. 16, 166 (1969).
[CrossRef]

1968 (2)

1962 (1)

1952 (1)

J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).

1937 (1)

Ammann, E. O.

Archard, J. F.

J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).

Aspnes, D. E.

D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
[CrossRef]

D. E. Aspnes, J. Opt. Soc. Am. 64, 812 (1974).
[CrossRef]

D. E. Aspnes, A. A. Studna, Phys. Rev. B7, 4605 (1973).

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

D. E. Aspnes, Phys. Rev. Lett. 28, 168 (1972).
[CrossRef]

D. E. Aspnes, J. Opt. Soc. Am. 61, 1077 (1971).
[CrossRef]

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

Bendat, J. S.

J. S. Bendat, Principles and Applications of Random Noise Theory (Wiley, New York, 1958), p. 15.

Bockris, J. O’M.

W-K. Paik, J. O’M. Bockris, Surface Sci. 28, 61 (1971).
[CrossRef]

Budde, W.

Cahan, B. D.

B. D. Cahan, R. F. Spanier, Surface Sci. 16, 166 (1969).
[CrossRef]

Clegg, P. L.

J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).

Dill, F. H.

P. S. Hauge, F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
[CrossRef]

Greef, R.

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

Hauge, P. S.

P. S. Hauge, F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
[CrossRef]

Hochstrasser, U. W.

U. W. Hochstrasser, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, Eds. (U.S. Nat. Bur. Stds., Appl. Math. Ser. 55, 1964), p. 790-1.

Jasperson, S. N.

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, R. C. O’Handley, Surface Sci. 37, 548 (1973).
[CrossRef]

Kent, C. V.

Lawson, J.

Massey, G. A.

O’Handley, R. C.

Paik, W-K.

W-K. Paik, J. O’M. Bockris, Surface Sci. 28, 61 (1971).
[CrossRef]

Rowe, J. E.

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, R. C. O’Handley, Surface Sci. 37, 548 (1973).
[CrossRef]

Sell, D. D.

Shaklee, K. L.

Smith, N. V.

N. V. Smith, Phys. Rev. Lett. 21, 96 (1968).
[CrossRef]

Spanier, R. F.

B. D. Cahan, R. F. Spanier, Surface Sci. 16, 166 (1969).
[CrossRef]

Studna, A. A.

D. E. Aspnes, A. A. Studna, Phys. Rev. B7, 4605 (1973).

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

Suits, J. C.

J. C. Suits, Rev. Sci. Instrum. 42, 19 (1971).
[CrossRef]

Taylor, A. M.

J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).

Appl. Opt. (3)

IBM J. Res. Devel. (1)

P. S. Hauge, F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
[CrossRef]

J. Opt. Soc. Am. (7)

Opt. Commun. (1)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[CrossRef]

Phys. Rev. (1)

D. E. Aspnes, A. A. Studna, Phys. Rev. B7, 4605 (1973).

Phys. Rev. Lett. (2)

D. E. Aspnes, Phys. Rev. Lett. 28, 168 (1972).
[CrossRef]

N. V. Smith, Phys. Rev. Lett. 21, 96 (1968).
[CrossRef]

Proc. Phys. Soc. (London) (1)

J. F. Archard, P. L. Clegg, A. M. Taylor, Proc. Phys. Soc. (London) 65B, 758 (1952).

Rev. Sci. Instrum. (4)

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

J. C. Suits, Rev. Sci. Instrum. 42, 19 (1971).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969); S. N. Jasperson, D. K. Burge, R. C. O’Handley, Surface Sci. 37, 548 (1973).
[CrossRef]

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

Surface Sci. (2)

W-K. Paik, J. O’M. Bockris, Surface Sci. 28, 61 (1971).
[CrossRef]

B. D. Cahan, R. F. Spanier, Surface Sci. 16, 166 (1969).
[CrossRef]

Other (8)

Model 9558QB, mfg. by EMI, Gencom Division, Plainview, N.Y. 11803.

Model S2005-3 fiber-optic scanner, mfg. by Skan-A-Matic Corp., Elbridge, N.Y. 13060.

Model 4853 sample-hold amplifier, mfg. by Teledyne Philbrick, Dedham, Mass. 02026. This module has a gain of −1.000.

Model 4106 analog-to-digital converter, mfg. by Teledyne Philbrick, Dedham, Mass. 02026.

Model 2114A computer, mfg. by Hewlett-Packard, Palo Alto, California 94306.

J. S. Bendat, Principles and Applications of Random Noise Theory (Wiley, New York, 1958), p. 15.

See, e.g., RCA Photomultiplier Manual (RCA, Harrison, N.J., 1970), p. 68.

U. W. Hochstrasser, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, Eds. (U.S. Nat. Bur. Stds., Appl. Math. Ser. 55, 1964), p. 790-1.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the optical system of the rotating-analyzer ellipsometer described in the test. The first and last apertures block the deviated beams emerging from the quartz Rochon polarizer and analyzer prisms, respectively. The use of the compensator is optional.

Fig. 2
Fig. 2

Cross-sectional view of the analyzer carrier assembly. The Rochon prism, P, is centered in a cylindrical brass carrier, C, which is pressed into a sealed bearing, B, which is captured in a housing, H. The rotating assembly is driven by a 72-tooth cogged pulley, G. The optical scanners S1 and S2 provide the sample/hold and reference pulses, respectively, for the data acquisition system.

Fig. 3
Fig. 3

Signal processing circuit. The time constant, 510 μsec, of the feedback loop around the current-to-voltage converter amplifier provides the necessary low-pass filtering for the system. The buffer amplifier provides regulation for the photomultiplier power supply as explained in the text. Input points for the output waveforms of the control circuit shown in Fig. 4 are indicated. Numbers on computer input lines refer to bit positions 0–15 of the 16-bit data word.

Fig. 4
Fig. 4

Control circuit. The reference and sample/hold optical scanners provide one and thirty-six output pulses, respectively, per optical cycle. The pulse durations of three monostable multivibrators providing the sample/hold control, delay, and analog/digital reset signals, respectively, are shown explicitly.

Fig. 5
Fig. 5

Timing diagram for control circuit of Fig. 4. The reference signal at the bottom enables bit 15 (logic true) only for the reference reading.

Fig. 6
Fig. 6

Logic flow diagram for data acquisition subroutine. This program accumulates thirty-six double-precision data words for Fourier transform processing by the main program.

Fig. 7
Fig. 7

Residuals and best-fit parabola measured in the calibration procedure to determine the polarizer azimuth reference for an Au film deposited on a glass slide. The arrow indicates the position of the minimum. A portion of the data and best-fit parabola to evaluate the analyzer azimuth reference is also shown.

Fig. 8
Fig. 8

Scatter in data (α,β) and computed quantities (ψ,Δ,1,2) for repeated measurements at λ = 400 nm on a Ni crystal. Other conditions were as stated in the text.

Equations (44)

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I ( t ) = I 0 ( 1 + α cos 2 A + β sin 2 A ) ,
A = A ( t ) = 2 π f 0 t + θ .
τ 3 Δ t
ω 0 τ = 2 π f 0 τ < tan 1 π / 6 0.58
Δ t = 1 / ( N f 0 ) ,
f 0 1 / ( 33 Δ t ) ,
N 33
a 2 + i b 2 = 2 [ i = 1 36 D n exp ( 2 i A n ) ] / ( i = 1 36 D n ) ,
A n = π ( n 1 ) / 36 .
I = I 0 [ 1 + α cos 2 A + β sin 2 A ]
= k V 0 [ 1 + η a 2 cos 2 ( A + A F ) + η b 2 sin 2 ( A + A F ) ] ,
  α = η [ a 2 cos 2 A F + b 2 sin 2 A F ] ,
β = η [ a 2 sin 2 A F + b 2 cos 2 A F ] ,
r j = 1 a 2 j 2 b 2 j 2 ,
r ( P ) = 1 η 2 ( α 2 + β 2 )
= [ 1 η 2 ] + η 2 R ( P ) ,
R ( P ) = 1 α 2 β 2 .
r min = 1 η 2
r ( P ) = c 0 + c 1 P + c 2 P 2 ,
c 0 = [ r 0 ( p 2 p 4 p 3 2 ) + r 1 ( p 2 p 3 p 1 p 4 ) + r 2 ( p 1 p 3 p 2 2 ) ] / d ,
c 1 = [ r 0 ( p 2 p 3 p 1 p 4 ) + r 1 ( p 0 p 4 p 2 2 ) + r 2 ( p 1 p 2 p 0 p 3 ) ] / d ,
c 2 = [ r 0 ( p 1 p 3 p 2 2 ) + r 1 ( p 1 p 2 p 0 p 3 ) + r 2 ( p 0 p 2 p 1 2 ) ] / d ,
d = p 0 p 2 p 4 + 2 p 1 p 2 p 3 p 2 3 p 0 p 3 2 p 1 2 p 4 ,
p k = N 1 j = 1 N P j k ,
r k = N 1 j = 1 N R j P j k .
P 1 = c 1 / ( 2 c 2 ) ,
η = [ 1 c 0 + c 1 2 / ( 4 c 2 ) ] 1 / 2 .
P s = P 1 ( δ A tan ψ + δ P cos Δ ) / sin Δ | P P s ,
ρ = tan ψ exp ( i Δ )
P 2 = c 1 / ( 2 c 2 ) π / 2 ,
P s = P 2 + ( δ A cot ψ + δ P cos Δ ) / sin Δ | P P s + π / 2 .
( A 1 + A F ) = 1 2 tan 1 ( b 2 / a 2 ) | P ¯ P 1 ,
( A s + A F ) = ( A 1 + A F ) ( δ P cot ψ + δ A cos Δ ) / sin Δ .
( A 2 + A F ) = 1 2 tan 1 ( b 2 / a 2 ) | P = P 2 + π / 2 ,
( A s + A F ) = ( A 2 + A F ) + ( δ P tan ψ + δ A cos Δ ) / sin Δ .
( Q + A F ) = 1 2 tan 1 ( b 2 / a 2 ) + ( π / 2 ) u ( a 2 ) sgn ( b 2 ) ,
a = [ 2 δ A ζ ± ( 1 δ A 2 ) ( 1 ζ ) 1 / 2 ] / [ ( 1 + ζ ) δ A 2 ( 1 ζ ) ] ,
ζ = η [ a 2 2 + b 2 2 ] 1 / 2 ,
ρ = tan ψ exp ( i Δ )
= { cot [ ( Q + A F ) ( A s + A F ) ] i a } [ tan ( P P s ) + i δ P ] { 1 + i a cot [ ( Q + A F ) ( A s + A F ) ] } [ 1 . i δ P tan ( P P s ) ]
= 1 + i 2
= [ ( 1 + ρ ) / ( 1 ρ ) ] 2 sin 2 ϕ tan 2 ϕ + sin 2 ϕ ,
Δ θ 2 π τ Δ f ,
Δ θ = 0.03 °

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