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Null ellipsometer with phase modulation

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Abstract

A new null ellipsometer is described that uses photoelastic modulator (PEM). The phase modulation adds a good signal-to-noise ratio, high sensitivity, and linearity near null positions to the traditional high-precision nulling system. The ellipsometric angles Δ and ψ are obtained by azimuth measurement of the analyzer and the polarizer-PEM system, for which the first and second harmonics of modulator frequency cross the zeros. We show that the null system is insensitive to ellipsometer misadjustment and component imperfections and modulator calibration is not needed. In addition, a fast ellipsometer mode for fine changes measurement of ellipsometric angles is proposed.

©2004 Optical Society of America

1. Introduction

Null ellipsometry [13] is a classical ellipsometric technique based on measurement of azimuth angles of polarizer, compensator, and analyzer for which the detected intensity is extinguished. The null ellipsometer is highly accurate and almost free of systematic errors. The null method does not need intensity calibration and a polarized light source (or a polarization-sensitive detector) does not bring noticeable systematic errors. Moreover, zone averaging, i.e. averaging of obtained ellipsometric angles for different sets of azimuth angles corresponding to nulls, gives measurement insensitive to azimuths misadjustment and polarizing component imperfections. Problems of this method come from a weak signal near nulls and parabolic intensity dependence near null during a polarizer scan due to the Malus’ law. This problem can be solved by including of azimuth modulation in null ellipsometry system. A method with Faraday magnetooptical cells was proposed by Winterbottom [4] and realized afterwords [57] A reason why the azimuth modulation null ellipsometry has not been widespread and commercialized comes probably from relatively low modulation amplitude of the Faraday cells, interference from stray ac magnetic fields, and spurious reflections in the many-component system.

On the other hand, automatic ellipsometers with high sensitivity and high acquisition rate are required for spectral measurements, in situ applications, and fast processes monitoring [8, 9]. Automatic ellipsometers can be divided into two categories: rotating polarizing component ellipsometers and phase-modulation ellipsometers. In the first category, systems with rotating polarizer, analyzer [1012], and compensator [13, 14] are widely used. In the second category, a photoelastic modulator (PEM) with modulation frequency typically 50 kHz is used as a phase modulator [1519]. PEM usually consists of a fused silica bar vibrating with natural resonant frequency sustained by a piezoelectric transducer. The periodic stress creates an optical anisotropy in the silica bar showing a photoelastic effect. The modulator, appearing to be the most critical element in the ellipsometer setup, should be carefully calibrated as a function of wavelength and temperature stabilized [16, 20, 21]. The automatic ellipsometers represent a shift from direct measurement of ellipsometric angles to light intensity measurement, i.e. a shift from ellipsometry to polarimetry [8]. However, intensity based ellipsometers require precise intensity calibration and precise system adjustment. Consequently, small imperfections in calibration or component adjustment can affect precision of measured data.

In this paper, we propose a new ellipsometric configuration based on the null method combined with the phase modulation. The null ellipsometer with phase modulation takes advantages of both configurations: (i) very high precision, insensitivity to component adjustment, and measurement almost free of systematic errors characteristic for null ellipsometry and (ii) high sensitivity, strong linear signal near nulls, and lock-in detection as advantages of modulation ellipsometric methods. Section 2 deals with theoretical description of the new ellipsometric system and its sensitivity to component imperfections. In Section 3 we propose a fast mode of the ellipsometer for measurement of fine changes of ellipsometric angles.

2. New configuration of null ellipsometry with phase modulation

This section deals with description of the new null ellipsometer with phase modulation. Description is based on the Jones matrix formalism. It is shown that the ellipsometric angles ψ and Δ are directly related to the azimuth angles of polarizer and analyzer, which can be obtained by nulling of signals at second- and first-harmonic frequency of the modulator, respectively. In second part of this section we describe possibility of ellipsometric angles averaging for different null positions (zones) and sensitivity of the system to alignment (azimuth angles errors) and modulator and polarizing component imperfections.

2.1. Description of ellipsometer

Figure 1 schematically shows basic components of the null PMSCA ellipsometric system. The system consists of the polarizer, which is mechanically connected to the modulator (PEM) and rotated by 45° from the modulator axis. Both components can slowly rotate and their azimuth angle P can be precisely monitored during the rotation. Note that P denotes the azimuth of the modulator optical axis. We propose to use the photoelastic modulator (PEM), which enables operation with high amplitude of modulation, appropriate modulation frequency, and spectral range. The retardation angle of PEM is the oscillating function of time

φ=φ0+φAsinωt,

where ω=2π f is the angular frequency of the PEM phase oscillation, φA denotes the modulation amplitude, and φ 0 corresponds to the residual birefringence due to PEM internal stress. The modulator is followed by a sample, which is characterized by the amplitude reflection coefficients rss and rpp for s- and p-polarized light, respectively. The ellipsometric angles ψ and Δ are defined using the ratio r pp/rss=tanψexp(iΔ). Polarization state of reflected light from the sample is measured by a quarter-wave compensator (retardation angle ϕ=90° and azimuth C=±45°) and an analyzer with the adjustable azimuth angle A. For spectral measurement the achromatic compensator is needed, we propose to use, for example, the V-shaped Fresnel rhomb, or the zero-order achromatic waveplates [22, 23]. The Jones vector describing polarization of light incident on the detector can be calculated as the matrix product

[ExEy]=E02[1000][cosAsinAsinAcosA]AnalyzeratazimuthA[cos(ϕ2)±sin(ϕ2)±sin(ϕ2)cos(ϕ2)]CompensatorC=±45°×
×[rss00rpp]Sample[cosPsinPsinPcosP]AzimuthofPEMP[exp(iφ2)00exp(iφ2)]Modulator(PEM)[11]Polarizer45°,

where the signs ± correspond to the azimuth angles of the compensator C=±45° and E 0 denotes the amplitude of light wave coming from the polarizer. Detected intensity is obtained from Eq. (2) in the form

I=ExEx*+EyEy*=E02rSS22(I0+ISsinφ+ICcosφ),

where the asterisk ∗ denotes the complex conjugate and using rpp/rss=tanψexp(iΔ)

I0=[1+cos2Acosϕ+(1cos2Acosϕ)tan2ψ]2,
IS=tanψ(sin2AsinΔ±sinϕcos2AcosΔ),
IC=sin2P[1+cos2Acosϕ(1cos2Acosϕ)tan2ψ]2+
+cos2Ptanψ(sin2AcosΔsinϕcos2AcosΔ).
 figure: Fig. 1.

Fig. 1. Schematic description of null PMSCA ellipsometric system consisting of Polarizer-Modulator-Sample-Compensator-Analyzer. Coordinate systems are shown.

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In terms of the Bessel functions of first kind J n, the terms sinφ and cosφ from Eq. (3) can be expanded using Eq. (1) into the series

sinφ=J0(φA)sinφ0+2J1(φA)cosφ0sinωt+2J2(φA)sinφ0cos2ωt+,
cosφ=J0(φA)cosφ02J1(φA)sinφ0sinωt+2J2(φA)cosφ0cos2ωt+.

The main idea of the proposed ellipsometric method is to search for nulls of the first Iω and the second harmonic I 2ω signal. By substitution of Eqs. (7) and (8) into (3) the intensities at the first and second harmonic frequency of the modulator are proportional to Iω∝(IS cosφ 0+IC sinφ 0) and I 2ω∝(IS sinφ 0+IC cosφ 0). Consequently, the signals Iω and I cross simultaneously the zeros for IS=0 and IC=0. In the case of ideal modulators (φ 0=0) IωIS and I 2ωIC, whereas for real modulator (φ 0=0) a coupling between IS and IC arises.

Tables Icon

Table 1. Ideal zone positions for null PMSCA ellipsometer (ϕ=90°). The azimuth of analyzer A is obtained by nulling of the first harmonic signal. The azimuth angle P of the system polarizer-modulator corresponds to the null of the second harmonic.

Condition IS=0, which relates mainly to null of Iω signal, can be adjusted by rotation of the analyzer [see Eq. (5)]. The analyzer azimuth angle A directly relates to Δ by the formula

tanΔ=sinϕtan2A=sinϕtan[±(2A±π2)],

where the first sign is related to the azimuth of compensator C=±45° and the second sign in the term (2A±π/2) corresponds to the periodicity of the function tangents. Similarly, the condition IC=0, which relates mainly to the null of I 2ω signal, can be adjusted by rotation of the polarizer-PEM system [see Eq. (6)]. The azimuth angle P directly relates to ψ by equations

tanψ=±αtanP,tanψ=±αtan(Pπ2),forC=+45°
tanψ=±α±tanP,tanψ=±α±tan(Pπ2),forC=45°
α±=1cos2ϕcos2Δ±cosϕsinΔsinϕ,α+α=1,α±(ϕ=90°)=1,

where the formula tan2P=2tanP/(1-tan2 P) and Eq. (9) were used. Two solutions and the signs in Eq. (10) correspond to the periodicity of the functions tan 2A and tan 2P. Different signs in Eqs. (9) and (10) correspond to different zones, i. e., different azimuth angles P, A, for which the null intensity is obtained. Table 1 summarizes the different zones obtained by the null ellipsometer with phase modulation in the case of ideal compensator (ϕ=90°).

2.2. Zone averaging and influence of component imperfections

This section deals with description of systematic errors coming from component imperfections and ellipsometer misalignment. We show that the proposed ellipsometer is almost insensitive to the systematic errors, which which is a result of nulling-based measurement and zone averaging.

The main advantage of the null ellipsometer proposed is insensitivity to the PEM modulation amplitude φA according to Eqs. (9)(11). Consequently, intensity calibration is not needed and φA can be roughly adjusted to get maximum modulation. Similarly, one can show that the angle between the polarizer and the PEM axes does not affect the positions of nulls. Its adjustment to 45° only maximizes the signal-to-noise ratio and the adjustment is not critical. Moreover, the proposed nulling system shows insensitivity to the PEM residual birefringence φ 0. Note that for considerable φ 0, the coupling between IS and IC arises and several iterations on A and P azimuth adjustments may be needed in practice to reach ideal null positions.

As a next source of systematic error, compensator retardation error is discussed, which is important mainly in spectral measurements. According to Eqs. (10) and (11) the effect of imperfect compensator retardation ϕ on ψ can be successfully eliminated by averaging of different zones. Influences of the imperfection are opposite in zones 1,2,7,8 and 3,4,5,6 described in Tab. 1. According to Eq. (11) we propose to eliminate completely the compensator imperfection by a geometric averaging of tan ψ from different zones, which is in correlation to the method for standard null ellipsometry proposed by Yamaguchi [24, 25]. On the other hand, the second order (quadratic) influence of the compensator imperfection to Δ can be eliminated using Eq. (9) only if spectral dependence of ϕ is known.

Moreover, zone averaging eliminates the azimuth misadjustment of the compensator, analyzer, and the polarizer-modulator system. One can show that the signs errors of ψ coming from compensator misadjustment are opposite in the zones 1,2,5,6 and 3,4,7,8. We again propose the geometric averaging of tan ψ for complete error compensation. The error of Δ originating from C shows also opposite signs in zones with C=±45°. Consequently, the zone averaging makes the measurement almost insensitive to the compensator azimuth error. Similarly, the azimuth errors of P and A are also eliminated by zone averaging. Despite the measurement is insensitive to the initial azimuth misadjustments, we note that the differences of azimuth angles have to be measured precisely. In some cases of practical interest, the sample shows also imperfections coming from its anisotropy (off diagonal elements of the Jones matrix) and depolarization. The proposed zone averaged measurement is insensitive to small parasitic anisotropy. Using the Mueller matrix [1, 3] or the coherence matrix formalism [26] one can show complete insensitivity of the proposed null method to the sample depolarization.

3. Measurement of fine ellipsometric angles changes

Fast, or in-situ monitoring of fine ψ and Δ changes can be performed in an ellipsometer mode proposed in this section. The ellipsometric angles are described as the sums of unperturbed values and small perturbations: ψ=ψ 0+δψ and Δ=Δ0+δΔ. The measurement can be performed in two steps. (i) the null is adjusted in the same configuration as discussed in previous section by adjusting angles A, P corresponding to Δ0 and ψ 0, respectively. (ii) the fine changes of δψ and δΔ can be monitored using measurement of the first and second harmonic intensity of the modulator. The normalized intensities are in the forms:

ISI0=±δΔsin2ψ0,ICI0=±2δψ.

Note that in this mode the system calibration and precise adjustment is needed. For easy calibration we propose to adjust the modulation amplitude φA=137.79° for which J 0=0, J 1=0.51915, and J 2=0.43175. Moreover, if the measured process can be repeated, measurements in different zones increases precision and insensitivity to imperfections. This measurement mode can be used, for example, in magneto-optical ellipsometry, where the transverse Kerr effect can be represented as small deviation of ψ and Δ

4. Conclusion

New null ellipsometer with PEM has been proposed. Two mode of ellipsometer operation have been discussed: (i) high precision null measurement insensitive to component imperfection and misadjustment and (ii) fast intensity based monitoring of fine ψ and Δ changes.

Acknowledgments

This work has been done in the frame of the Marie Curie Host Fellowships for Transfer of Knowledge - the NANOMAG-LAB project (2004-003177). Partial support from the Grant Agency of the Czech Republic (202/03/0776) is acknowledged.

References and links

1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

2. I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282. [CrossRef]  

3. S.-M. F. Nee, “Error analysis of null ellipsometry with depolarization,” Appl. Opt. 38, 5388–5398 (1999). [CrossRef]  

4. A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.

5. H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974). [CrossRef]  

6. M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003). [CrossRef]  

7. H. Zhu, L. Liu, Y. Wen, Z. Lü, and B. Zhang, “High-precision system for automatic null ellipsometric measurement,” Appl. Opt. 41, 4536–4540 (2002). [CrossRef]   [PubMed]  

8. D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004). [CrossRef]  

9. T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

10. D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975). [PubMed]  

11. J. M. M. de Nijs and A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. Am. A 5, 773–781 (1988). [CrossRef]  

12. J. M. M. de Nijs, A. H. M. Holtslag, A. Hoeksta, and A. van Silfhout, “Calibration method for rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 5, 1466–1471 (1988). [CrossRef]  

13. C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004). [CrossRef]  

14. T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004). [CrossRef]  

15. J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977). [CrossRef]  

16. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989). [CrossRef]  

17. C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992). [CrossRef]  

18. G. E. Jellison Jr. and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003). [CrossRef]  

19. K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981). [CrossRef]  

20. M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004). [CrossRef]  

21. G. E. Jellison Jr. and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

22. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express 9, 225–235 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-225. [CrossRef]   [PubMed]  

23. G. P. Nordin and P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (1999). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163. [CrossRef]   [PubMed]  

24. T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.

25. R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

26. K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002). [CrossRef]   [PubMed]  

References

  • View by:

  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).
  2. I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
    [Crossref]
  3. S.-M. F. Nee, “Error analysis of null ellipsometry with depolarization,” Appl. Opt. 38, 5388–5398 (1999).
    [Crossref]
  4. A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.
  5. H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
    [Crossref]
  6. M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
    [Crossref]
  7. H. Zhu, L. Liu, Y. Wen, Z. Lü, and B. Zhang, “High-precision system for automatic null ellipsometric measurement,” Appl. Opt. 41, 4536–4540 (2002).
    [Crossref] [PubMed]
  8. D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
    [Crossref]
  9. T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).
  10. D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [PubMed]
  11. J. M. M. de Nijs and A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. Am. A 5, 773–781 (1988).
    [Crossref]
  12. J. M. M. de Nijs, A. H. M. Holtslag, A. Hoeksta, and A. van Silfhout, “Calibration method for rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 5, 1466–1471 (1988).
    [Crossref]
  13. C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
    [Crossref]
  14. T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
    [Crossref]
  15. J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
    [Crossref]
  16. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
    [Crossref]
  17. C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
    [Crossref]
  18. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
    [Crossref]
  19. K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
    [Crossref]
  20. M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
    [Crossref]
  21. G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).
  22. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express 9, 225–235 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-225.
    [Crossref] [PubMed]
  23. G. P. Nordin and P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (1999). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163.
    [Crossref] [PubMed]
  24. T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.
  25. R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).
  26. K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
    [Crossref] [PubMed]

2004 (4)

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

2003 (1)

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

2002 (2)

2001 (1)

1999 (2)

1992 (1)

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

1989 (1)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

1988 (2)

1981 (1)

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

1977 (1)

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

1975 (1)

1974 (1)

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

1967 (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

Acher, O.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

An, I.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Antos, R.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Aspnes, D. E.

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
[PubMed]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Badoz, J.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Bigan, E.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

Billardon, M.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Boulbry, B.

Bousquet, B.

Canit, J.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Chao, Y.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Chen, C.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Chen, S.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Collins, R. W.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

de Nijs, J. M. M.

Deguzman, P. C.

Drévillon, B.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

Ferreira, G. M.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Franta, D.

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

Gerland, J.W.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Guern, Y.

Hoeksta, A.

Holtslag, A. H. M.

Horie, M.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Hotta, Y.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Jellison, G. E.

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

Kantor, R.

Kim, C. C.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Le Jeune, B.

Leou, K.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Lin, T.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Liu, L.

Liu, Y.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Lotrian, J.

Lü, Z.

Mathieu, H. J.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

McClure, D. E.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Mistrik, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Modine, F. A.

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

Mori, T.

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

Muller, R. H.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Nee, S.-M. F.

Nordin, G. P.

Ohlidal, I.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Ohlídal, I.

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

Pistora, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Podraza, N. J.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Postava, K.

K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
[Crossref] [PubMed]

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Raccah, P. M.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Russel, M. F.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Sato, K.

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

Sato, M.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Studna, A. A.

Tsai, F.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

van Silfhout, A.

Visnovsky, S.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Wang, M.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Wen, Y.

Winterbottom, A. B.

A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.

Yamaguchi, T.

K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
[Crossref] [PubMed]

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.

Yamamoto, M.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Zapien, J. A.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Zhang, B.

Zhu, H.

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

J. Optics (Paris) (1)

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Jap. J. Appl. Phys. (2)

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Opt. Express (2)

Rev. Sci. Instrum. (3)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Science of Light (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

Thin Solid Films (4)

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

Other (7)

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

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Figures (1)

Fig. 1.
Fig. 1. Schematic description of null PMSCA ellipsometric system consisting of Polarizer-Modulator-Sample-Compensator-Analyzer. Coordinate systems are shown.

Tables (1)

Tables Icon

Table 1. Ideal zone positions for null PMSCA ellipsometer (ϕ=90°). The azimuth of analyzer A is obtained by nulling of the first harmonic signal. The azimuth angle P of the system polarizer-modulator corresponds to the null of the second harmonic.

Equations (15)

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

φ = φ 0 + φ A sin ω t ,
[ E x E y ] = E 0 2 [ 1 0 0 0 ] [ cos A sin A sin A cos A ] Analyzer at azimuth A [ cos ( ϕ 2 ) ± sin ( ϕ 2 ) ± sin ( ϕ 2 ) cos ( ϕ 2 ) ] Compensator C = ± 45 ° ×
× [ r ss 0 0 r pp ] Sample [ cos P sin P sin P cos P ] Azimuth of PEM P [ exp ( i φ 2 ) 0 0 exp ( i φ 2 ) ] Modulator ( PEM ) [ 1 1 ] Polarizer 45 ° ,
I = E x E x * + E y E y * = E 0 2 r SS 2 2 ( I 0 + I S sin φ + I C cos φ ) ,
I 0 = [ 1 + cos 2 A cos ϕ + ( 1 cos 2 A cos ϕ ) tan 2 ψ ] 2 ,
I S = tan ψ ( sin 2 A sin Δ ± sin ϕ cos 2 A cos Δ ) ,
I C = sin 2 P [ 1 + cos 2 A cos ϕ ( 1 cos 2 A cos ϕ ) tan 2 ψ ] 2 +
+ cos 2 P tan ψ ( sin 2 A cos Δ sin ϕ cos 2 A cos Δ ) .
sin φ = J 0 ( φ A ) sin φ 0 + 2 J 1 ( φ A ) cos φ 0 sin ω t + 2 J 2 ( φ A ) sin φ 0 cos 2 ω t + ,
cos φ = J 0 ( φ A ) cos φ 0 2 J 1 ( φ A ) sin φ 0 sin ω t + 2 J 2 ( φ A ) cos φ 0 cos 2 ω t + .
tan Δ = sin ϕ tan 2 A = sin ϕ tan [ ± ( 2 A ± π 2 ) ] ,
tan ψ = ± α tan P , tan ψ = ± α tan ( P π 2 ) , for C = + 45 °
tan ψ = ± α ± tan P , tan ψ = ± α ± tan ( P π 2 ) , for C = 45 °
α ± = 1 cos 2 ϕ cos 2 Δ ± cos ϕ sin Δ sin ϕ , α + α = 1 , α ± ( ϕ = 90 ° ) = 1 ,
I S I 0 = ± δ Δ sin 2 ψ 0 , I C I 0 = ± 2 δ ψ .

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