Abstract

We have designed and constructed a new type of spectroscopic ellipsometer to study the optical properties of materials in the 3500–8000-Å wavelength range. In the system, the analyzer and polarizer are driven 104 steps/revolution by two stepping motors that have hollow shafts and rotate synchronously with a speed ratio of 2:1, i.e., A = 2P. Both the polarizer and analyzer are mounted directly on the shafts to avoid mechanical transmission and vibration problems entirely and make the system simple and reliable. An additional source polarizer was placed in the optical path to reduce the slight polarization effects of the light source. The light intensity finally received by the detector contained five components, one dc and four ac, with frequencies of ω0, 2ω0, 3ω0, and 4ω0, respectively. One can independently obtain the ellipsometric parameters of ψ and Δ as well as the optical constants by calculating any one of the two sets of ac signals, with a raw data self-consistency of better than 0.5%. The incident angle, aligned precisely by a laser beam, was continuously variable through a mechanical system with a computer-controlled resolution of 0.001° or a visual resolution of 0.005°. The system operations, including data acquisition and reduction, high-voltage control of the photomultiplier, incident angle, as well as wavelength setting and scanning, were fully and automatically controlled by a 386-based microcomputer. We self-calibrated the system by adjusting and setting precisely the initial azimuthal angles of the prisms. The results from the measured spectra of the complex refractive index for a gold-film sample are presented, and we show that the data obtained at three different incident angles of 65°, 70°, and 75° are remarkably consistent with one another. A comparison of the two results from the ellipsometry and reflectance measurements is given. The experimental skills and system error reduction are discussed in detail.

© 1994 Optical Society of America

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References

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  1. D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8, 222–225 (1973).
    [CrossRef]
  2. D. E. Aspnes, “High precision scanning ellipsometer,” Appl. Opt. 4, 220–228 (1975).
  3. D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), Chap. 15.
  4. L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
    [CrossRef]
  5. A.-R. M. Zaghloul, R. M. Azzam, “Single-element rotating-polarizer ellipsometer: psi meter,” Surf. Sci. 96, 168–173 (1980).
    [CrossRef]
  6. S. Kawabata, “Improved measurement method in rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 1, 706–710 (1984).
    [CrossRef]
  7. L. Y. Chen, D. W. Lynch, “Scanning ellipsometer by rotating polarizer and analyzer,” Appl. Opt. 26, 5221–5228 (1987).
    [CrossRef] [PubMed]
  8. J. A. Woollam, P. G. Snyder, M. C. Rost, “Variable angle spectroscopic ellipsometry: a nondestructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166, 317–323 (1988).
    [CrossRef]
  9. S. Adachi, T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
    [CrossRef]
  10. G. E. Jellison, F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–973 (1990).
    [CrossRef] [PubMed]
  11. C. Wijers, “A one-wavelength in situ alignment method for rotating analyzer ellipsometers,” Appl. Phys. B 27, 5–8 (1982).
    [CrossRef]
  12. D. E. Aspnes, “Effects of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 812–819 (1974).
    [CrossRef]
  13. R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
    [CrossRef]
  14. The motors with hollow shafts were specially ordered at Changzhou General Electric Motors and Appliances Factory, Qi-Shu-Yan, Changzhou, Jiangsu, China. Also, in a quality machine shop it is not difficult to make a shaft hole.
  15. R. W. Hamming, Numerical Methods for Scientists and Engineerings (McGraw-Hill, New York, 1973), Chap. 21.
  16. G. Arfken, Mathematical Methods for Physics (Academic, Orlando, Fla., 1985), Chap. 14.
  17. D. M. Kolb, J. D. E. McIntyre, “Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold,” Surf. Sci. 28, 321–334 (1971).
    [CrossRef]

1991

S. Adachi, T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[CrossRef]

1990

1988

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

1987

1984

S. Kawabata, “Improved measurement method in rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 1, 706–710 (1984).
[CrossRef]

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

1982

C. Wijers, “A one-wavelength in situ alignment method for rotating analyzer ellipsometers,” Appl. Phys. B 27, 5–8 (1982).
[CrossRef]

1980

A.-R. M. Zaghloul, R. M. Azzam, “Single-element rotating-polarizer ellipsometer: psi meter,” Surf. Sci. 96, 168–173 (1980).
[CrossRef]

1978

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

1975

D. E. Aspnes, “High precision scanning ellipsometer,” Appl. Opt. 4, 220–228 (1975).

1974

1973

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

1971

D. M. Kolb, J. D. E. McIntyre, “Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold,” Surf. Sci. 28, 321–334 (1971).
[CrossRef]

Adachi, S.

S. Adachi, T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physics (Academic, Orlando, Fla., 1985), Chap. 14.

Aspnes, D. E.

D. E. Aspnes, “High precision scanning ellipsometer,” Appl. Opt. 4, 220–228 (1975).

D. E. Aspnes, “Effects of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 812–819 (1974).
[CrossRef]

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

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), Chap. 15.

Azzam, R. M.

A.-R. M. Zaghloul, R. M. Azzam, “Single-element rotating-polarizer ellipsometer: psi meter,” Surf. Sci. 96, 168–173 (1980).
[CrossRef]

Azzam, R. M. A.

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

Cardona, M.

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

Chen, L. Y.

Hamming, R. W.

R. W. Hamming, Numerical Methods for Scientists and Engineerings (McGraw-Hill, New York, 1973), Chap. 21.

Jellison, G. E.

Kawabata, S.

Kolb, D. M.

D. M. Kolb, J. D. E. McIntyre, “Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold,” Surf. Sci. 28, 321–334 (1971).
[CrossRef]

Lynch, D. W.

McIntyre, J. D. E.

D. M. Kolb, J. D. E. McIntyre, “Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold,” Surf. Sci. 28, 321–334 (1971).
[CrossRef]

Modine, F. A.

Rost, M. C.

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

Snyder, P. G.

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

Taguchi, T.

S. Adachi, T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[CrossRef]

Umbach, C.

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

Vina, L.

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

Vodopyanov, L.

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

Wijers, C.

C. Wijers, “A one-wavelength in situ alignment method for rotating analyzer ellipsometers,” Appl. Phys. B 27, 5–8 (1982).
[CrossRef]

Woollam, J. A.

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

Zaghloul, A.-R. M.

A.-R. M. Zaghloul, R. M. Azzam, “Single-element rotating-polarizer ellipsometer: psi meter,” Surf. Sci. 96, 168–173 (1980).
[CrossRef]

Appl. Opt.

Appl. Phys. B

C. Wijers, “A one-wavelength in situ alignment method for rotating analyzer ellipsometers,” Appl. Phys. B 27, 5–8 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8, 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, 137–140 (1978).
[CrossRef]

Phys. Rev. B

L. Vina, C. Umbach, M. Cardona, L. Vodopyanov, “Ellipsometric studies of electric interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752–6760 (1984).
[CrossRef]

S. Adachi, T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[CrossRef]

Surf. Sci.

D. M. Kolb, J. D. E. McIntyre, “Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold,” Surf. Sci. 28, 321–334 (1971).
[CrossRef]

A.-R. M. Zaghloul, R. M. Azzam, “Single-element rotating-polarizer ellipsometer: psi meter,” Surf. Sci. 96, 168–173 (1980).
[CrossRef]

Thin Solid Films

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

Other

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), Chap. 15.

The motors with hollow shafts were specially ordered at Changzhou General Electric Motors and Appliances Factory, Qi-Shu-Yan, Changzhou, Jiangsu, China. Also, in a quality machine shop it is not difficult to make a shaft hole.

R. W. Hamming, Numerical Methods for Scientists and Engineerings (McGraw-Hill, New York, 1973), Chap. 21.

G. Arfken, Mathematical Methods for Physics (Academic, Orlando, Fla., 1985), Chap. 14.

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Figures (6)

Fig. 1
Fig. 1

Configuration of the RPA ellipsometric system. The azimuthal angles of rotating P and A are related clockwise to the s axis along the light-wave propagation direction.

Fig. 2
Fig. 2

Schematic diagram of the optical and controlling system of the RPA ellipsometer: 1, light-collimating lens; 2, the first fixed polarizer P0; 3, 4, rotating analyzer and polarizer, respectively, directly mounted on the shafts of the stepping motors; 5, stepping motors with hollow shafts; 6, light-shielding boxes; 7, sample; 8, mirrors that guide the laser beam for sample alignment; 9, rotating table connected to the arm that holds the analyzer and photomultiplier (P.M.T.); 10, rotating table connected to the sample-mounting stage; 11, fused-silica fiber-optic cable.

Fig. 3
Fig. 3

Diagram illustrating the reduction in error from off centering the incident light. P.M.T. is the photomultiplier tube.

Fig. 4
Fig. 4

Real-test waveform of signals read by the A–D converter for a thick aluminum film sample at a wavelength of 5000 Å with comparison to the waveform calculated by the Fourier transform.

Fig. 5
Fig. 5

Complex refractive index of the gold film sample measured at three different angles of 65°, 70°, and 75°: ñ = n + ik.

Fig. 6
Fig. 6

Comparison of two reflectivity curves for the 3000-Å-thick gold film sample measured by ellipsometry (ϕ = 70°) and the near-normal-reflectance (ϕ = 5°) methods.

Tables (1)

Tables Icon

Table1 Effect of Sampling Numbers per Data Cycle on the Fourier Coefficientsa

Equations (23)

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I = k 0 + k 1 cos 2 ω 0 t + k 2 sin 2 ω 0 t ,
k 0 = 1 n i = 1 n I i , k 1 = 2 n i = 1 n I i cos 2 A i , k 2 = 2 n i = 1 n I i sin 2 A i .
cos Δ = k 2 ( k 0 2 - k 1 2 ) 1 / 2 , tan ψ = 1 tan P [ ( k 0 - k 1 ) ( k 0 + k 1 ) ] 1 / 2 .
ρ = r ˜ p r ˜ s = r p r s exp ( i Δ ) = ρ 0 exp ( i Δ ) = tan ψ exp ( i Δ ) ,
s a = sin 2 ϕ + sin 2 ϕ tan 2 ϕ [ ( 1 - ρ ) ( 1 + ρ ) ] 2 ,
r ˜ s = r s exp ( i δ s ) ,             r ˜ p = r p exp ( i δ p ) ,             Δ = δ s - δ p ,
k 0 = ( 1 n i = 1 n I i ) - I B ,
k 0 = 1 n i = 1 n ( I i - I B i ) .
I = g 0 + g 1 cos ω 0 t + g 2 cos 2 ω 0 t + g 3 cos 3 ω 0 t ,
cos Δ = g 1 - g 2 - g 3 [ ( g 1 + g 3 ) ( g 1 + g 3 - 2 g 2 ) ] 1 / 2 , tan ψ = ( g 1 + g 3 - 2 g 2 ) 1 / 2 ( g 1 + g 3 ) 1 / 2 .
E f = [ 1 0 ] [ cos A sin A - sin A cos A ] [ r ˜ s 0 0 r ˜ p ] [ cos P - sin P sin P cos P ] × [ 1 0 0 0 ] [ cos P - sin P sin P cos P ] [ 1 0 ] E 0 = ( r ˜ s cos A cos 2 P + r ˜ p sin A cos P sin P ) E 0 .
I E f 2 ~ η ( cos 2 A cos 4 P + ¼ sin 2 A sin 2 2 P ρ 0 2 + ½ sin 2 A sin 2 P cos 2 P ρ 0 cos Δ ) ,
I = I 0 + I 1 cos A + I 2 cos 2 A + I 3 cos 3 A + I 4 cos 4 A = I 0 + I 1 cos ω 0 t + I 2 cos 2 ω 0 t + I 3 cos 3 ω 0 t + I 4 cos 4 ω 0 t ,
I 0 = η ¼ ( 7 + 3 ρ 0 2 + 2 ρ 0 cos Δ ) + I B , I 1 = η ( 3 + ρ 0 cos Δ ) , I 2 = η ( 2 - ρ 0 2 ) , I 3 = η ( 1 - ρ 0 cos Δ ) , I 4 = η ¼ ( 1 + ρ 0 2 - 2 ρ 0 cos Δ ) .
ρ 0 = [ 2 ( I 1 + I 3 - 2 I 2 ) ( I 1 + I 3 ) ] 1 / 2 , cos Δ = ( I 1 - 3 I 3 ) [ 2 ( I 1 + I 3 ) ( I 1 + I 3 - 2 I 2 ) ] 1 / 2
ρ 0 = [ 9 ( I 1 + I 3 - 2 I 2 ) 2 ( 4 I 4 + 2 I 1 + I 2 ) ] 1 / 2 , cos Δ = [ 3 ( I 1 + I 3 ) - 4 ( 4 I 4 + I 2 ) ] [ 8 ( I 1 + I 3 ) ( I 1 + I 3 - 2 I 2 ) ] 1 / 2 .
I k = 2 n i = 1 n I i cos ( k A i ) ,             k = 1 , 2 , 3 , 4 ,
I = I max as A + P = 0 , and I = I min as A = 0 and P = 90 ° or A = 90 ° and P = 0.
x = y ( 2 - 2 ) 0.586 y .
I k = 2 n i = 1 n I i cos [ k ( A i - ϕ k ) ] ,             k = 1 , 2 , 3 , 4 ,
P = ½ A + δ 1 ,             A = A + δ 2 ,
I 1 = - 2 η [ δ 1 ( 1 - ρ 0 cos Δ ) + δ 2 ( 1 + ρ 0 cos Δ ) ] , I 2 = - η [ 2 δ 1 ( 1 - ρ 0 2 ) + δ 2 ( 3 - ρ 0 2 ) ] , I 3 = - 2 η ( δ 1 + δ 2 ) ( 1 - ρ 0 cos Δ ) , I 4 = - η ( δ 1 + ½ δ 2 ) ( 1 + ρ 0 2 - 2 ρ 0 cos Δ ) .
δ s s = 4 ( 1 + cos 2 ϕ ) sin 2 ϕ δ ϕ - 4 1 - ρ 2 δ ρ .

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