Abstract

We describe a polarizer–compensator–sample–analyzer (PCSA) null ellipsometer in which a variable retarder is used as the compensator and either the polarizer or the analyzer is held at a fixed azimuthal angle. Ellipsometric angles ψ and Δ are determined directly from the azimuth of the rotating component and the compensator delay, respectively. A Soleil–Babinet compensator with quartz plates is used as the variable delay element and the delay at any wavelength is calculated from the independently measured delay at 632.8nm and a knowledge of the dispersion of quartz. The thicknesses of thin silicon di oxide films on a silicon wafer were determined both spectroscopically and at a single wavelength and show excellent agreement with those determined using a traditional single wavelength PCSA null ellipsometer.

© 2010 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  2. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).
  3. R. W. Collins, “Automatic rotating element ellipsometers—calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
    [CrossRef]
  4. D. E. Aspnes, “Precisionbounds to ellipsometer systems,” Appl. Opt. 14, 1131–1136 (1975).
    [CrossRef] [PubMed]
  5. R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
    [CrossRef]
  6. R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
    [CrossRef]
  7. R. M. A. Azzam and N. M. Bashara, “Spacing of the multiple nulls in generalized ellipsometry,” Opt. Commun. 5, 5–9(1972).
    [CrossRef]
  8. L. R. Watkins and S. S. Shamailov, “Variable angle of incidence spectroscopic autocollimating ellipsometer,” Appl. Opt. 49, 3231–3234 (2010).
    [CrossRef] [PubMed]
  9. Thin Film Companion, Semiconsoft, Inc., Southborough, Mass. 01772, USA.

2010 (1)

2000 (1)

1990 (1)

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

1975 (1)

1973 (1)

R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
[CrossRef]

1972 (1)

R. M. A. Azzam and N. M. Bashara, “Spacing of the multiple nulls in generalized ellipsometry,” Opt. Commun. 5, 5–9(1972).
[CrossRef]

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
[CrossRef]

R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, “Spacing of the multiple nulls in generalized ellipsometry,” Opt. Commun. 5, 5–9(1972).
[CrossRef]

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

Bashara, N. M.

R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, “Spacing of the multiple nulls in generalized ellipsometry,” Opt. Commun. 5, 5–9(1972).
[CrossRef]

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

Bundy, T. L.

R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
[CrossRef]

Collins, R. W.

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

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

Shamailov, S. S.

Watkins, L. R.

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

R. M. A. Azzam, T. L. Bundy, and N. M. Bashara, “The fixed-polarizer nulling scheme in generalized ellipsometry,” Opt. Commun. 7, 110–115 (1973).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, “Spacing of the multiple nulls in generalized ellipsometry,” Opt. Commun. 5, 5–9(1972).
[CrossRef]

Rev. Sci. Instrum. (1)

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

Other (3)

Thin Film Companion, Semiconsoft, Inc., Southborough, Mass. 01772, USA.

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

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the variable retarder null ellipsometer. Key: L, laser source; P, polarizer; SBC, Soleil–Babinet compensator; S, sample; G, goniometer; A, analyzer; PD, photodetector.

Fig. 2
Fig. 2

Measured values of ψ and Δ at variable angles of incidence for a 2 nm SiO 2 film on a silicon wafer.

Fig. 3
Fig. 3

Measured values of ψ and Δ at 70 ° and 75 ° AOI for a 100 nm SiO 2 film on a silicon wafer.

Equations (9)

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E out = 1 2 [ 1 0 0 0 ] [ cos A sin A sin A cos A ] [ r p 0 0 r s ] [ 1 0 0 exp ( i δ ) ] [ 1 ± 1 ] = 1 2 [ r p cos A ± r s sin A exp ( i δ ) 0 ] ,
tan ψ exp ( i [ Δ + δ ] ) = tan A ,
I out cos 2 A tan 2 ψ + sin 2 A + 2 sin A cos A tan ψ cos ( Δ + δ ) .
Δ I out = I out max I out min 4 sin 2 ψ cos ( Δ + δ ) .
E out = 1 2 [ 1 0 0 0 ] [ 1 ± 1 1 1 ] [ r p 0 0 r s ] [ 1 0 0 exp ( i δ ) ] [ cos P sin P ] = 1 2 [ r p cos P ± r s sin P exp ( i δ ) 0 ] ,
χ = tan P cot ψ exp ( i [ δ + Δ ] ) ,
tan 2 θ = 2 ( χ ) 1 | χ | 2 = 2 tan ψ tan P cos ( δ + Δ ) tan 2 ψ tan 2 P .
δ 632.8 = 28.641 m 3.299 ,
δ λ = δ 632.8 × 632.8 λ × Δ n λ Δ n 632.8 ,

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