Abstract

In photometric ellipsometry the optical signal is transformed into an electrical signal by a photodetector, and it passes an electronic system to reduce the noise and to amplify the signal. But inherently it will induce a phase shift and an amplitude attenuation of the output signal. Such a specific characteristic of an electronic system depends on the angular frequency of the signal and gives systematic errors to the results of the measurement of rotating-analyzer ellipsometry. We propose a modified method of measurement that enables us to calibrate the electronic system in the ellipsometric measurement configuration.

© 1997 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, “Analysis of systematic errors in rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 1459–1469 (1974).
    [CrossRef]
  2. D. E. Aspnes, “Effect of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 812–819 (1974).
    [CrossRef]
  3. J. M. M. de Nijis, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. Am. A 5, 773–781 (1988).
    [CrossRef]
  4. P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
    [CrossRef]
  5. R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
    [CrossRef]
  6. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [CrossRef] [PubMed]
  7. J. M. M. de Nijis, A. H. M. Holtslag, A. Hoeksta, A. van Silfhout, “Calibration method for rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 5, 1466–1471 (1988).
    [CrossRef]
  8. S. Kawabata, “Improved measurement method in rotating-analyzer ellipsometry,” J. Opt. Soc. Am. A 1, 706–710 (1984).
    [CrossRef]

1990 (1)

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

1988 (2)

1984 (1)

1975 (1)

1974 (2)

1973 (1)

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Aspnes, D. E.

Azzam, R. M. A.

Bashara, N. M.

Collins, R. W.

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

de Nijis, J. M. M.

Dill, F. H.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Hauge, P. S.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Hoeksta, A.

Holtslag, A. H. M.

Kawabata, S.

Studna, A. A.

van Silfhout, A.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the rotating analyzer ellipsometer. A compensator that precedes the polarizer serves to transform the polarization of the laser source into a near circular state to permit an arbitrary polarizer setting.

Fig. 2
Fig. 2

Determination of the correct reference frame of the optical system on the Poincaré sphere. The coordinate system S1 m, S2 m, and S3 m is the apparent reference frame of the measurement. P and Q represent the polarization states of the reflected light at the azimuth of the polarizer χP and χP + 90°, respectively. O represents the p direction of the optical system.

Fig. 3
Fig. 3

Change of the apparent initial azimuth of the analyzer that is due to the capacitor as a noise filter at the various rotation speeds of the analyzer. The curves on the graph represent the capacitance of the capacitors.

Fig. 4
Fig. 4

Measured values of the optical constants of the oxide layer on the silicon wafer at the various rotation speeds of the analyzer that we obtained by taking into account only a phase shift of the output signal: circle, refractive index; triangle, film thickness.

Fig. 5
Fig. 5

Measured values of the attenuation coefficient of the electronic system at the various rotation speeds of the analyzer.

Fig. 6
Fig. 6

Corrected apparent initial azimuth of the analyzer at the various rotation speeds of the analyzer: filled circle, the corrected apparent initial azimuth of the analyzer that we determined by taking into account an amplitude attenuation of the output signal; open circle, the apparent initial azimuth of the analyzer we determined by Eq. (5).

Fig. 7
Fig. 7

Corrected values of the optical constants of the oxide layer on the silicon wafer at the various rotation speeds of the analyzer. We obtained the values by taking into account both the phase shift and the amplitude attenuation of the output signal: circle, refractive index; triangle, film thickness.

Equations (10)

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RP=1-α2-β2=1-η-2+η-22 sin Δ cot Ψ2P-Ps2, ΦP=tan-1β/α/2=As+ϕ/2+cos Δ cot ΨP-Ps,
Vt=K·I01+η·S1 cos2ωt+χA-ϕ+η·S2 sin2ωt+χA-ϕ,
P1=2i=1N Vticos2ωti/i=1NVti=S1 cos2χA-ϕ-S2 sin2χA-ϕ, P2=2 i=1NVtisin2ωti/i=1N Vti=S1 sin2χA-ϕ+S2 cos2χA-ϕ,
Q1=2i=1N Vticos2ωti/i=1NVti=S1 cos2χA-ϕ-S2 sin2χA-ϕ, Q2=2 i=1N Vtisin2ωti/i=1NVti=S1 sin2χA-ϕ+S2 cos2χA-ϕ.
P3=±1-P12-P22, Q3=1-Q12-Q22.
P×Q·O=0.
tan2χA-ϕ=-P21-Q12-Q221/2+Q21-P12-P221/2/P11-Q12-Q221/2+Q11-P12-P221/2.
tan2χA-ϕ=-P2η2-Q12-Q221/2+Q2η2-P12-P221/2/P1η2-Q12-Q221/2+Q1η2-P12-P221/2.
tan2χA-ϕ=-P2η2-Q12-Q221/2+Q2η2-P12-P221/2/P1η2-Q12-Q221/2+Q1η2-P12-P221/2,
S1=P1 cos2χA-ϕ+P2 sin2χA-ϕ, S2=P1 sin2χA-ϕ-P2 cos2χA-ϕ.

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