Abstract

The grating division-of-amplitude photopolarimeter (G-DOAP) is an instrument that exploits the multiple-beam-splitting, polarizing, and dispersive properties of diffraction gratings for the time-resolved measurement of the complete state of polarization of collimated broadband incident light, as represented by the four Stokes parameters as a function of wavelength across the spectrum. It is a compact, high-speed sensor that has no moving parts and is simple to install and operate. These characteristics make the G-DOAP well suited for in situ spectroscopic ellipsometry (SE) applications for monitoring and controlling thin-film processes. The design and performance of a prototype instrument are presented. Precise SE measurements, to ±0.04° in ψ and ±0.1° in Δ, are demonstrated in the 550–940-nm wavelength range.

© 2003 Optical Society of America

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  1. R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
    [CrossRef]
  2. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
    [CrossRef]
  3. S. Krishnan, “Calibration, properties, and applications of the division-of-amplitude photopolarimeter at 632.8 and 1523 nm,” J. Opt. Soc. Am. A 9, 1615–1622 (1992).
    [CrossRef]
  4. K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
    [CrossRef]
  5. E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96, 156–167 (1980).
    [CrossRef]
  6. R. M. A. Azzam, “Division-of-amplitude photopolarimeter based on conical diffraction of light from a metallic grating,” Appl. Opt. 31, 3574–3576 (1992).
    [CrossRef] [PubMed]
  7. R. M. A. Azzam, K. A. Giardina, “Photopolarimeter based on planar grating diffraction,” J. Opt. Soc. Am. A 10, 1190–1196 (1993).
    [CrossRef]
  8. M. A. Azzam, “Diffraction grating photopolarimeters and spectrophotopolarimeters,” U.S. Patent5,337,146 (9August1994).
  9. Y. Cui, R. M. A. Azzam, “Sixteen-beam grating-based division-of-amplitude photopolarimeter,” Opt. Lett. 21, 89–91 (1996).
    [CrossRef] [PubMed]
  10. S. Krishnan, P. C. Nordine, “Mueller-matrix ellipsometry using the division of amplitude photopolarimeter: a study of depolarization effects,” Appl. Opt. 33, 4184–4192 (1994).
    [CrossRef] [PubMed]
  11. S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” in Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
    [CrossRef]
  12. S. Krishnan, “Mueller-matrix ellipsometry on electroformed, rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
    [CrossRef]
  13. R. M. A. Azzam, A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements,” J. Opt. Soc. Am. A 6, 1513–1521 (1989).
    [CrossRef]
  14. See, e.g., C. H. Palmer, F. W. Phelps, “Grating anomalies as local phenomenon,” J. Opt. Soc. Am. 58, 1184–1188 (1968).
    [CrossRef]
  15. R. M. A. Azzam, “Instrument matrix of the four-detector photopolarimeter: physical meaning of its rows and columns and constraints on its elements,” J. Opt. Soc. Am. A 7, 87–91 (1990).
    [CrossRef]

1996 (1)

1995 (1)

S. Krishnan, “Mueller-matrix ellipsometry on electroformed, rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (2)

1991 (1)

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

1990 (1)

1989 (1)

1988 (1)

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

1980 (1)

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

1968 (1)

Azzam, M. A.

M. A. Azzam, “Diffraction grating photopolarimeters and spectrophotopolarimeters,” U.S. Patent5,337,146 (9August1994).

Azzam, R. M. A.

Brudzewski, K.

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

Collett, E.

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

Cui, Y.

Elminyawi, I. M.

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Giardina, K. A.

Grosz, F. B.

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Krishnan, S.

S. Krishnan, “Mueller-matrix ellipsometry on electroformed, rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

S. Krishnan, P. C. Nordine, “Mueller-matrix ellipsometry using the division of amplitude photopolarimeter: a study of depolarization effects,” Appl. Opt. 33, 4184–4192 (1994).
[CrossRef] [PubMed]

S. Krishnan, “Calibration, properties, and applications of the division-of-amplitude photopolarimeter at 632.8 and 1523 nm,” J. Opt. Soc. Am. A 9, 1615–1622 (1992).
[CrossRef]

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” in Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

Lopez, A. G.

Masetti, E.

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Nordine, P. C.

S. Krishnan, P. C. Nordine, “Mueller-matrix ellipsometry using the division of amplitude photopolarimeter: a study of depolarization effects,” Appl. Opt. 33, 4184–4192 (1994).
[CrossRef] [PubMed]

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” in Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

Palmer, C. H.

Phelps, F. W.

Appl. Opt. (2)

J. Mod. Opt. (2)

S. Krishnan, “Mueller-matrix ellipsometry on electroformed, rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. B. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Surf. Sci. (1)

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

Other (2)

M. A. Azzam, “Diffraction grating photopolarimeters and spectrophotopolarimeters,” U.S. Patent5,337,146 (9August1994).

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” in Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

Schematic drawing of G-DOAP showing the grating, incident and diffracted beams, linear array detectors, and polarizers.

Fig. 2
Fig. 2

G-DOAP design implemented in the present research. The first diffraction produces two detected orders while the retroreflected beam produces two additional orders. The location of the arrays with respect to the common plane of incidence is also illustrated.

Fig. 3
Fig. 3

Location of the first and second diffracted orders on the linear array detectors. The wavelength range is 550–940 nm. The location of the order-blocking filter is also shown (see text).

Fig. 4
Fig. 4

Schematic drawing of the system used for G-DOAP calibration, verification, and ellipsometric measurements.

Fig. 5
Fig. 5

Transmittance (right axis) and extinction of the Polarcor (TM) sheet polarizers used in the G-DOAP.

Fig. 6
Fig. 6

Schematic block diagram of the electronics system showing the ADCs, DSP, and serial communications: EPROM, erasable, programmable ROM; UART, universal asynchronous receiver transmitter.

Fig. 7
Fig. 7

Intensity of the four diffracted orders versus wavelength for top, incident parallel p polarization; middle, perpendicular s polarization; and, bottom, right-circular polarization.

Fig. 8
Fig. 8

Detector responses, normalized by the reference detector intensity, for the four diffracted orders versus the polarizer azimuth for a 700-nm wavelength: symbols, measured points in 20° polarizer steps; curves, least-squares fits to the data described by Eq. (4).

Fig. 9
Fig. 9

Elements of the normalized calibration matrix F n versus wavelength for the G-DOAP. Note the strong dispersion in the vicinity of 625 nm, caused by the Wood’s anomaly.

Fig. 10
Fig. 10

Magnitudes of the NPV’s of the G-DOAP.

Fig. 11
Fig. 11

Determinant of the matrix F n as a function of wavelength. The reduced magnitude of the determinant near 625 nm is due to Wood’s anomaly.

Fig. 12
Fig. 12

Measured values of the normalized Stokes parameters (NSP) versus the retarder fast-axis azimuth for the rotating-C test at 700 nm: symbols, measured points in 10° fast-axis steps; curves, predictions for an ideal linear retarder.

Fig. 13
Fig. 13

Deviations of the NSP versus the retarder fast-axis azimuth for the rotating-C test at 700 nm from values predicted for an ideal linear retarder. Note the asymmetry in the deviations across the two 180° segments that are due to imperfections in the retarder. The solid curves are fits to the deviations when the model for the retarder described by Azzam and Lopez13 is used.

Fig. 14
Fig. 14

Calculated retardance as a function of wavelength derived from the model and comparison with the calculated dispersion curve for, dashed line, the BK7 Fresnel rhomb. Solid line, a linear fit, included for clarity.

Fig. 15
Fig. 15

Average deviation of the NSP over a wavelength range of 550–940 nm. The deviations are the residual errors that remain between the model fit and the data in Fig. 13.

Fig. 16
Fig. 16

Measured values of the ellipsometric parameters ψ and Δ as a function of wavelength for a thick SiO2 film on Si at an angle of incidence of 75°. The derived value of the film thickness was 913.5 nm compared with 913.7 nm obtained with a commercial spectroscopic ellipsometer.

Fig. 17
Fig. 17

Distribution of the NSP values derived from a series of 50 measurements for a 700-nm wavelength.

Tables (2)

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Table 1 Polynomial Coefficients for Wavelength Calibration

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Table 2 Relationship between Electrical S/N and ψ and Δ Precision

Equations (15)

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sinθi=sinθ-iλ/g.
I=FS,
S=F-1I.
IP=F0+F1 cos2P+F2 sin2P.
IRCP=F0+F3,  ILCP=F0-F3,
F3=0.5IRCP-ILCP.
F0=0.5IRCP+ILCP.
Fn=1F01F02F031F11F12F131F21F22F231F31F32F33.
S1=0.5+0.5 cos4C, S2=0.5 sin4C, S3=sin2C.
Ψ= 12tan-1S32+S221/2-S1,
Δ=tan-1-S3S2.
D=1x0y0z01x1y1z11x2y2z21x3y3z3.
D=x1-x0y1-y0z1-z0x2-x0y2-y0z2-z0x3-x0y3-y0z3-z0.
D=A · B×C,
Dmax= 1631.5=3.0792.

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