Abstract

A new type of ellipsometer using an integrated analyzer composed of 12 sub-analyzers with different azimuth angles was constructed and studied. By using a two-dimensional CCD array camera to measure the light intensity emerging in parallel from each sub-analyzer with the azimuth angles uniformly distributed in the range of about 180°, the ellipsometric parameters were extracted within the data acquisition time less than 1 second. The ellipsometric parameters for the polished bulk Si sample were measured to show good agreement with the results measured by using another two ellipsometric methods. The new method having the merits of high speed and reliability in the optical data measurement can be potentially used in the fields where the in situ data acquisition with high precision is the key issue as required.

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References

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  1. R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976).
    [CrossRef]
  2. R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96(1-3), 108–140 (1980).
    [CrossRef]
  4. J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
    [CrossRef]
  5. R. W. Collins, “Automatic rotating element ellipsometers: Calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61(8), 2029–2062 (1990).
    [CrossRef]
  6. K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314(1-2), 1–9 (1998).
    [CrossRef]
  7. D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
    [CrossRef]
  8. R. H. Muller and J. C. Farmer, “Fast, self-compensating spectral-scanning ellipsometer,” Rev. Sci. Instrum. 55(3), 371–374 (1984).
    [CrossRef]
  9. Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
    [CrossRef]
  10. I. An and R. W. Collins, “Waveform analysis with optical multichannnel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
    [CrossRef]
  11. I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
    [CrossRef]
  12. P. Boher and J. L. Stehle, “In situ spectroscopic ellipsometry: present status and future needs for thin film characterization and process control,” Mater. Sci. Eng. B 37(1-3), 116–120 (1996).
    [CrossRef]
  13. R. M. A. Azzam, “Multichannel polarization state detectors for time-resolved ellipsometry,” Thin Solid Films 234(1-2), 371–374 (1993).
    [CrossRef]
  14. E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96(1-3), 156–167 (1980).
    [CrossRef]
  15. S. N. Japerson and S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40(6), 761–767 (1969).
    [CrossRef]
  16. V. M. Bermudez and V. H. Ritz, “Wavelength-scanning polarization-modulation ellipsometry: some practical considerations,” Appl. Opt. 17(4), 542–552 (1978).
    [CrossRef] [PubMed]
  17. E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
    [CrossRef]
  18. G. E. Jellison and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29(7), 959–974 (1990).
    [CrossRef] [PubMed]
  19. B. D. Cahan and R. F. Spanier, “A high speed precision automatic ellipsometer,” Surf. Sci. 16, 166–176 (1969).
    [CrossRef]
  20. R. W. Stobie, B. Rao, and M. J. Dignam, “Analysis of a novel ellipsometric technique with special advantages for infrared spectroscopy,” J. Opt. Soc. Am. 65(1), 25–28 (1975).
    [CrossRef]
  21. C. V. Kent and J. Lawson, “A Photoelectric Method for the Determination of the Parameters of Elliptically Polarized Light,” J. Opt. Soc. Am. 27(3), 117–119 (1937).
    [CrossRef]
  22. D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8(3), 222–225 (1973).
    [CrossRef]
  23. D. E. Aspnes and A. A. Studna, “High Precision Scanning Ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [PubMed]
  24. M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
    [CrossRef]
  25. R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25(2), 137–140 (1978).
    [CrossRef]
  26. L. Y. Chen and D. W. Lynch, “Scanning ellipsometer by rotating polarizer and analyzer,” Appl. Opt. 26(24), 5221–5228 (1987).
    [CrossRef] [PubMed]
  27. L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, and Y. H. Qian, “Design of a scanning ellipsometer by synchronous rotation of the polarizer and analyzer,” Appl. Opt. 33(7), 1299–1305 (1994).
    [CrossRef] [PubMed]

2004

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

1998

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314(1-2), 1–9 (1998).
[CrossRef]

1996

1994

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, and Y. H. Qian, “Design of a scanning ellipsometer by synchronous rotation of the polarizer and analyzer,” Appl. Opt. 33(7), 1299–1305 (1994).
[CrossRef] [PubMed]

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

1993

R. M. A. Azzam, “Multichannel polarization state detectors for time-resolved ellipsometry,” Thin Solid Films 234(1-2), 371–374 (1993).
[CrossRef]

1991

I. An and R. W. Collins, “Waveform analysis with optical multichannnel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[CrossRef]

1990

Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
[CrossRef]

R. W. Collins, “Automatic rotating element ellipsometers: Calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61(8), 2029–2062 (1990).
[CrossRef]

G. E. Jellison and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29(7), 959–974 (1990).
[CrossRef] [PubMed]

1988

J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
[CrossRef]

1987

1985

E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
[CrossRef]

1984

R. H. Muller and J. C. Farmer, “Fast, self-compensating spectral-scanning ellipsometer,” Rev. Sci. Instrum. 55(3), 371–374 (1984).
[CrossRef]

1980

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96(1-3), 108–140 (1980).
[CrossRef]

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96(1-3), 156–167 (1980).
[CrossRef]

1978

V. M. Bermudez and V. H. Ritz, “Wavelength-scanning polarization-modulation ellipsometry: some practical considerations,” Appl. Opt. 17(4), 542–552 (1978).
[CrossRef] [PubMed]

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25(2), 137–140 (1978).
[CrossRef]

1976

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976).
[CrossRef]

1975

1973

D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8(3), 222–225 (1973).
[CrossRef]

1969

B. D. Cahan and R. F. Spanier, “A high speed precision automatic ellipsometer,” Surf. Sci. 16, 166–176 (1969).
[CrossRef]

S. N. Japerson and S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40(6), 761–767 (1969).
[CrossRef]

1937

An, I.

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

I. An and R. W. Collins, “Waveform analysis with optical multichannnel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[CrossRef]

Aspnes, D. E.

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]

D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8(3), 222–225 (1973).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Multichannel polarization state detectors for time-resolved ellipsometry,” Thin Solid Films 234(1-2), 371–374 (1993).
[CrossRef]

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25(2), 137–140 (1978).
[CrossRef]

Baltzer, N.

E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
[CrossRef]

Bermudez, V. M.

Boher, P.

P. Boher and J. L. Stehle, “In situ spectroscopic ellipsometry: present status and future needs for thin film characterization and process control,” Mater. Sci. Eng. B 37(1-3), 116–120 (1996).
[CrossRef]

Cahan, B. D.

B. D. Cahan and R. F. Spanier, “A high speed precision automatic ellipsometer,” Surf. Sci. 16, 166–176 (1969).
[CrossRef]

Chen, L. Y.

Collett, E.

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96(1-3), 156–167 (1980).
[CrossRef]

Collins, R. W.

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

I. An and R. W. Collins, “Waveform analysis with optical multichannnel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[CrossRef]

Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
[CrossRef]

R. W. Collins, “Automatic rotating element ellipsometers: Calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61(8), 2029–2062 (1990).
[CrossRef]

Dignam, M. J.

Farmer, J. C.

R. H. Muller and J. C. Farmer, “Fast, self-compensating spectral-scanning ellipsometer,” Rev. Sci. Instrum. 55(3), 371–374 (1984).
[CrossRef]

Feng, X. W.

Hauge, P. S.

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96(1-3), 108–140 (1980).
[CrossRef]

Herzinger, C. M.

Heyd, A. R.

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

Huber, E.

E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
[CrossRef]

Japerson, S. N.

S. N. Japerson and S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40(6), 761–767 (1969).
[CrossRef]

Jellison, G. E.

Johs, B.

Kent, C. V.

Kim, Y. T.

Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
[CrossRef]

Lawson, J.

Lynch, D. W.

Ma, H. Z.

Modine, F. A.

Muller, R. H.

R. H. Muller and J. C. Farmer, “Fast, self-compensating spectral-scanning ellipsometer,” Rev. Sci. Instrum. 55(3), 371–374 (1984).
[CrossRef]

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976).
[CrossRef]

Nguyen, H. V.

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

Qian, Y. H.

Rao, B.

Rheinländer, B.

Ritz, V. H.

Rost, M. C.

J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
[CrossRef]

Schnatterly, S. E.

S. N. Japerson and S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40(6), 761–767 (1969).
[CrossRef]

Schubert, M.

Snyder, P. G.

J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
[CrossRef]

Spanier, R. F.

B. D. Cahan and R. F. Spanier, “A high speed precision automatic ellipsometer,” Surf. Sci. 16, 166–176 (1969).
[CrossRef]

Stehle, J. L.

P. Boher and J. L. Stehle, “In situ spectroscopic ellipsometry: present status and future needs for thin film characterization and process control,” Mater. Sci. Eng. B 37(1-3), 116–120 (1996).
[CrossRef]

Stobie, R. W.

Studna, A. A.

Su, Y.

Vedam, K.

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314(1-2), 1–9 (1998).
[CrossRef]

Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
[CrossRef]

von Allmen, M.

E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
[CrossRef]

Woollam, J. A.

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, B. Johs, and C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2,” J. Opt. Soc. Am. A 13(4), 875–883 (1996).
[CrossRef]

J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Mater. Sci. Eng. B

P. Boher and J. L. Stehle, “In situ spectroscopic ellipsometry: present status and future needs for thin film characterization and process control,” Mater. Sci. Eng. B 37(1-3), 116–120 (1996).
[CrossRef]

Opt. Commun.

D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8(3), 222–225 (1973).
[CrossRef]

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25(2), 137–140 (1978).
[CrossRef]

Rev. Sci. Instrum.

S. N. Japerson and S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40(6), 761–767 (1969).
[CrossRef]

E. Huber, N. Baltzer, and M. von Allmen, “Polarization modulation ellipsometry: A compact and easy handling instrument,” Rev. Sci. Instrum. 56(12), 2222–2227 (1985).
[CrossRef]

I. An and R. W. Collins, “Waveform analysis with optical multichannnel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[CrossRef]

I. An, H. V. Nguyen, A. R. Heyd, and R. W. Collins, “Simultaneous real-time spectroscopic ellipsometry and reflectance for monitoring thin-film preparation,” Rev. Sci. Instrum. 65(11), 3489–3500 (1994).
[CrossRef]

R. W. Collins, “Automatic rotating element ellipsometers: Calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61(8), 2029–2062 (1990).
[CrossRef]

R. H. Muller and J. C. Farmer, “Fast, self-compensating spectral-scanning ellipsometer,” Rev. Sci. Instrum. 55(3), 371–374 (1984).
[CrossRef]

Surf. Sci.

Y. T. Kim, R. W. Collins, and K. Vedam, “Fast scanning spectroelectrochemical ellipsometry: In-situ characterization of gold oxide,” Surf. Sci. 233(3), 341–350 (1990).
[CrossRef]

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976).
[CrossRef]

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96(1-3), 108–140 (1980).
[CrossRef]

B. D. Cahan and R. F. Spanier, “A high speed precision automatic ellipsometer,” Surf. Sci. 16, 166–176 (1969).
[CrossRef]

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96(1-3), 156–167 (1980).
[CrossRef]

Thin Solid Films

R. M. A. Azzam, “Multichannel polarization state detectors for time-resolved ellipsometry,” Thin Solid Films 234(1-2), 371–374 (1993).
[CrossRef]

J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
[CrossRef]

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314(1-2), 1–9 (1998).
[CrossRef]

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

Other

R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

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Figures (7)

Fig. 1
Fig. 1

The ellipsometric configuration with the fixed and integrated analyzer consisting of 12 sub-analyzers. The two-dimensional CCD array camera was used to measure the light intensity emerging from each sub-analyzer.

Fig. 2
Fig. 2

Schematic diagram of the optical and controlling system of the designed ellipsometer: 1. light-collimating lens; 2 and 3. polarizer and integrated analyzer, respectively, directly mounted on the shafts of the stepping motors; 4. stepping motors with hollow shafts; 5. light-shielding boxes; 6. CCD camera; 7. mirrors; 8. sample; 9. rotating table connected to the sample-mounting stage; 10. rotating table connected to the arm that holds the analyzer and CCD camera. The low-power He-Ne Laser was used as an optical indicator to align the sample surface in each measurement precisely.

Fig. 3
Fig. 3

The schematic diagram of 12 sub-analyzers designed and distributed in the area with the azimuth angle interval of about 15° for each analyzer within the diameter of about 9.4 mm. The specific analyzed orientation of each sub-analyzer was aligned along the direction of the thick line in red color, respectively. Each sub-analyzer was numbered according to its azimuth angle in sequence. The azimuth angle θ o with a negative value corresponds to the real azimuth angle of 180° + θ o.

Fig. 4
Fig. 4

The twelve miniature Glan-Tompson prisms with each size of 1.5 mm × 1.5 mm × 3.5 mm were arranged and fixed on a metal plate as the designed scheme shown in Fig. 3.

Fig. 5
Fig. 5

By rotating the polarizer, the intensities with regard to 12 sub-analyzers changing with the polarizer angle θ P were measured and fitted into 12 normalized cosine curves to show the azimuth angle interval of about 15° in sequence. Each of the cosine curves was numbered in sequence from 1 to 12, respectively, corresponding to the 12 numbered sub-analyzers as indicated in Fig. 3.

Fig. 6
Fig. 6

The image pattern of the light intensity emerging from 12 sub-analyzers at the focal plane was measured by the two-dimensional CCD array camera for the polished bulk Si sample at the wavelength of 546.1 nm and at the incident angle of 60°, showing clearly the intensity variation with the various azimuth angles of the sub-analyzers. The image pattern of the sub-analyzer No. 5 as has been defined in Fig. 3, is virtually dark for its very low output light intensity which agrees well with the result shown in Fig. 7.

Fig. 7
Fig. 7

The measured light intensities changing with the azimuth angle of each sub-analyzer were plotted as 12 blue triangles for the polished bulk Si sample. The number of the azimuth angle of each sub-analyzer in series from 1 to 12 was defined in Figs. 3 and 5. The 12 raw data of the light intensity were fitted into a cosine curve (solid blue line), showing excellent agreement with the result (overlapped and dashed red line) measured by using the RAE for the same sample.

Tables (2)

Tables Icon

Table 1 The actual values of the azimuth angle of each sub-analyzer were measured in calibration and in agreement with the designed ones.

Tables Icon

Table 2 The ellipsometric parameters, ψ and Δ were measured in this work and compared with those measured by the RAE and RPAE for the same polished bulk Si sample.

Equations (29)

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

εsεa=sin2φ+sin2φtan2φ(1ρ1+ρ)2
ρ=ρ0eiΔ=tanψeiΔ
(EsEp)=(cos2θAsinθAcosθAsinθAcosθAsin2θA)(r˜ss00r˜pp)(cosθPE0(θP)sinθPE0(θP))
ρ=r˜ppr˜ss=ρ0eiΔ
(EsEp)=E0(θP)r˜ss(cos2θAsinθAcosθAsinθAcosθAsin2θA)(100ρ0eiΔ)(cosθPsinθP)
I(θA)=ξ(I01+Iccos2θA+Issin2θA)+IB
I(θA)=ξ(I01+Ic2+Is2cos2(θAσ))+IB
tan(2σ)=IsIc
ξ=|E0(θP)r˜ss|2
I01=14[(1+ρ02)+(1ρ02)cos2θP]
Ic=14[(1ρ02)+(1+ρ02)cos2θP]
Is=12sin2θPρ0cosΔ
I01=14(1+ρ02)
Ic=14(1ρ02)
Is=12ρ0cosΔ
I(θA)=b+acos2(θAσ)+IB
b=ξI01
a=ξ(Ic2+Is2)12
tan(2σ)=IsIc
ρ0=(121+Y(1+X2)12)12
cosΔ=1tan2ψ2tanψX
X=tan(2σ)
Y=ba
Ii=I0iTicosθi=I0ηicosθi
Ii=bi+aicos2(θiσ)
bi=ηiξI01+IBi
ai=ηiξ(Ic2+Is2)12
tan(2σ)=IsIc
I(θi)=IiIBiηi=b+acos2(θiσ)

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