Abstract

Our objective is to develop a method for azimuthal alignment of the polarizer–analyzer in fixed-angle ellipsometry systems in which measurement of the light intensity in the straight-through mode is not possible. An analytical technique has been developed that allows the determination of the reference positions of the polarizer and analyzer through the use of reflection measurements from a dielectric sample at a single angle of incidence. The method was verified by using both a high-temperature unit and a room-temperature reflectometer system. In these cases the real part of the refractive index of the test sample was inferred with accuracy to within 0.5% and 1.7%, respectively. In addition the sensitivity of the technique to the polarizer–analyzer setting was assessed.

© 1992 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. I. Ohlidal, K. Navratil, “Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface,” Thin Solid Films 31, 223–234 (1976).
    [CrossRef]
  3. I. Ohlidal, F. Lukes, “Ellipsometric parameters of rough surfaces and of a system substrate—thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
    [CrossRef]
  4. I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
    [CrossRef]
  5. R. M. Pashley, “Theoretical estimate of errors in ellipsometric measurement of thin films of water on slightly rough quartz surfaces,” Surf. Sci. 71, 139–147 (1978).
    [CrossRef]
  6. O. Hunderi, “Optics of rough surfaces, discontinuous films and heterogeneous materials,” Surf. Sci. 96, 1–31 (1980).
    [CrossRef]
  7. B. J. Stagg, T. T. Charalampopoulos, “Method to minimize the effects of polarizer leakage on reflectivity measurements,” Appl. Opt. 29, 4638–4644 (1990).
    [CrossRef] [PubMed]
  8. B. J. Stagg, T. T. Charalampopoulos, “Surface-roughness effects on the determination of optical properties of materials by the reflection method,” Appl. Opt. 30, 4113–4118 (1991).
    [CrossRef] [PubMed]
  9. M. J. Dignam, M. Moskovits, “Azimuthal misalignment and surface anisotropy as sources of error in ellipsometry,” Appl. Opt. 9, 1868–1873 (1970).
    [PubMed]
  10. M. R. Steel, “Method for azimuthal alignment in ellipsometry,” Appl. Opt. 10, 2370–2371 (1971).
    [CrossRef] [PubMed]
  11. W. A. Shurcliff, Polarized Light—Production and Use (Harvard U. Press, Cambridge, Mass., 1962).
  12. G. K. T. Conn, G. K. Eaton, “On the analysis of elliptically polarized radiation in the infrared region,” J. Opt. Soc. Am. 44, 546–552 (1954).
    [CrossRef]
  13. J. R. Beattie, “Optical constants of metals in the infra-red—experimental methods,” Philos. Mag. 46, 235–245 (1955).

1991 (1)

1990 (1)

1980 (1)

O. Hunderi, “Optics of rough surfaces, discontinuous films and heterogeneous materials,” Surf. Sci. 96, 1–31 (1980).
[CrossRef]

1978 (1)

R. M. Pashley, “Theoretical estimate of errors in ellipsometric measurement of thin films of water on slightly rough quartz surfaces,” Surf. Sci. 71, 139–147 (1978).
[CrossRef]

1976 (1)

I. Ohlidal, K. Navratil, “Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface,” Thin Solid Films 31, 223–234 (1976).
[CrossRef]

1974 (1)

I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

1972 (1)

I. Ohlidal, F. Lukes, “Ellipsometric parameters of rough surfaces and of a system substrate—thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

1971 (1)

1970 (1)

1955 (1)

J. R. Beattie, “Optical constants of metals in the infra-red—experimental methods,” Philos. Mag. 46, 235–245 (1955).

1954 (1)

Azzam, R. M. A.

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

Bashara, N. M.

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

Beattie, J. R.

J. R. Beattie, “Optical constants of metals in the infra-red—experimental methods,” Philos. Mag. 46, 235–245 (1955).

Charalampopoulos, T. T.

Conn, G. K. T.

Dignam, M. J.

Eaton, G. K.

Hunderi, O.

O. Hunderi, “Optics of rough surfaces, discontinuous films and heterogeneous materials,” Surf. Sci. 96, 1–31 (1980).
[CrossRef]

Lukes, F.

I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

I. Ohlidal, F. Lukes, “Ellipsometric parameters of rough surfaces and of a system substrate—thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

Moskovits, M.

Navratil, K.

I. Ohlidal, K. Navratil, “Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface,” Thin Solid Films 31, 223–234 (1976).
[CrossRef]

I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

Ohlidal, I.

I. Ohlidal, K. Navratil, “Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface,” Thin Solid Films 31, 223–234 (1976).
[CrossRef]

I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

I. Ohlidal, F. Lukes, “Ellipsometric parameters of rough surfaces and of a system substrate—thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

Pashley, R. M.

R. M. Pashley, “Theoretical estimate of errors in ellipsometric measurement of thin films of water on slightly rough quartz surfaces,” Surf. Sci. 71, 139–147 (1978).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light—Production and Use (Harvard U. Press, Cambridge, Mass., 1962).

Stagg, B. J.

Steel, M. R.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

I. Ohlidal, F. Lukes, “Ellipsometric parameters of rough surfaces and of a system substrate—thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972).
[CrossRef]

Philos. Mag. (1)

J. R. Beattie, “Optical constants of metals in the infra-red—experimental methods,” Philos. Mag. 46, 235–245 (1955).

Surf. Sci. (3)

I. Ohlidal, F. Lukes, K. Navratil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974).
[CrossRef]

R. M. Pashley, “Theoretical estimate of errors in ellipsometric measurement of thin films of water on slightly rough quartz surfaces,” Surf. Sci. 71, 139–147 (1978).
[CrossRef]

O. Hunderi, “Optics of rough surfaces, discontinuous films and heterogeneous materials,” Surf. Sci. 96, 1–31 (1980).
[CrossRef]

Thin Solid Films (1)

I. Ohlidal, K. Navratil, “Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface,” Thin Solid Films 31, 223–234 (1976).
[CrossRef]

Other (2)

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

W. A. Shurcliff, Polarized Light—Production and Use (Harvard U. Press, Cambridge, Mass., 1962).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a polarizer–sample–analyzer (PSA) ellipsometer centered around a high-temperature furnace. LS is the xenon arc light source, C1 and C2 are the curved first-surface mirrors (200-mm focal length), P1 and P2 are the plane first-surface mirrors, Wl and W2 are the quartz cell windows of the furnace, P and A are the polarizer and analyzer, M is the monochromator, D is the detector, and S is the sample.

Fig. 2
Fig. 2

Error in p, A0, and P0 plotted versus A0 for an error in the polarizer setting (δΔP) of 0.5°, with ρ = 0.3 and ΔA = 35°.

Fig. 3
Fig. 3

Error in ρ, A0, and P0 plotted versus ΔA for an error in the polarizer setting (δΔP) of 0.5°, with ρ = 0.3 and A0 = 15°.

Fig. 4
Fig. 4

Error in p, A0, and P0 plotted versus error in the polarizer setting (δΔP), with ρ = 0.3, A0 = 15°, and ΔA = 35°.

Tables (1)

Tables Icon

Table I Experimental Results

Equations (22)

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S i = [ M ] S 0 ,
[ M ] = [ M N ] [ M N 1 ] [ M N 2 ] [ M 1 ] ,
[ M ] = [ D ] [ A ] [ S ] [ P ] [ S ] ,
I ( P , A ) = C 1 k A k P R [ ρ 2 cos 2 ( P ) cos 2 ( A ) + sin 2 ( P ) sin 2 ( A ) + ( ρ 2 ) cos ( Δ ) sin ( 2 P ) sin ( 2 A ) ] × [ 1 + d 1 , 2 d 1 , 1 cos ( 2 A ) + d 1 , 3 d 1 , 1 sin ( 2 A ) ] × [ 1 + l 2 , 1 l 1 , 1 cos ( 2 P ) + l 3 , 1 l 1 , 1 sin ( 2 P ) ] ,
r p r s = | r p | exp ( i Q p ) | r s | exp ( i Q s ) = ρ exp ( i Δ ) ,
r p , s = ( E r E i ) p , s
I P S A ( P , A ) = C 2 k A k P R [ ρ 2 cos 2 ( P ) cos 2 ( A ) + sin 2 ( P ) sin 2 ( A ) + ( ρ 2 ) cos ( Δ ) sin ( 2 P ) sin ( 2 A ) ] ,
ρ = ± tan ( A ) tan ( P ) ,
ρ = tan ( A 0 + Δ A i ) tan ( P 0 + Δ P i ) , i = 1 , 2 , 3 ,
sin 2 ( 2 A 0 ) = 4 C 3 2 2 ( C 1 C 2 ) ( C 2 + C A ) 4 C 3 2 + ( C 1 C 2 ) 2 sin 2 ( 2 Δ A 1 ) ,
C 1 = a 2 cos 2 ( Δ A 2 + Δ A 1 ) + b 2 cos 2 ( Δ A 3 + Δ A 1 ) 2 a b cos ( Δ P 3 Δ P 2 ) cos ( Δ A 2 + Δ A 1 ) cos ( Δ A 3 + Δ A 1 ) , C 2 = a 2 sin 2 ( Δ A 2 + Δ A 1 ) + b 2 sin 2 ( Δ A 3 + Δ A 1 ) 2 a b cos ( Δ P 3 Δ P 2 ) sin ( Δ A 2 + Δ A 1 ) sin ( Δ A 3 + Δ A 1 ) , C 3 = a 2 2 sin ( 2 Δ A 2 + 2 Δ A 1 ) + b 2 2 sin ( 2 Δ A 3 + 2 Δ A 1 ) ab cos ( Δ P 3 Δ P 2 ) sin ( 2 Δ A 1 + Δ A 2 + Δ A 3 ) , C 4 = sin 2 ( Δ P 3 Δ P 2 ) , a = sin ( Δ P 2 Δ P 1 ) sin ( Δ A 2 Δ A 1 ) , b = sin ( Δ P 3 Δ P 1 ) sin ( Δ A 3 Δ A 1 ) .
sin ( 2 P 0 + Δ P 2 + Δ P 1 ) = a sin ( 2 A 0 + Δ A 2 + Δ A 1 ) .
ρ = tan ( P 0 + Δ P 1 ) tan ( A 0 + Δ A 1 ) .
n = sin ( θ ) [ ( 1 + ρ 1 ρ ) 2 tan 2 ( θ ) + 1 ] 1 / 2 ,
δ A 0 = δ Δ P [ ( A 0 Δ P 1 ) 2 + ( A 0 Δ P 2 ) 2 + ( A 0 Δ P 3 ) 2 ] 1 / 2 ,
δ P 0 = δ Δ P [ ( P 0 Δ P 1 ) 2 + ( P 0 Δ P 2 ) 2 + ( P 0 Δ P 3 ) 2 ] 1 / 2 ,
δρ = δ Δ P [ ( ρ Δ P 1 ) 2 + ( ρ Δ P 2 ) 2 + ( ρ Δ P 3 ) 2 ] 1 / 2 ,
Δ A 1 = Δ A , Δ A 2 = 0 , Δ A 3 = + Δ A ,
[ M ] = [ D ] [ A ] [ S ] [ P ] [ L ] ,
[ P ] = k P 2 [ 1 cos ( 2 P ) sin ( 2 P ) 0 cos ( 2 P ) cos 2 ( 2 P ) sin ( 2 P ) cos ( 2 P ) 0 sin ( 2 P ) sin ( 2 P ) cos ( 2 P ) sin 2 ( 2 P ) 0 0 0 0 0 ] ,
[ A ] = k A 2 [ 1 cos ( 2 A ) sin ( 2 A ) 0 cos ( 2 A ) cos 2 ( 2 A ) sin ( 2 A ) cos ( 2 A ) 0 sin ( 2 A ) sin ( 2 A ) cos ( 2 A ) sin 2 ( 2 A ) 0 0 0 0 0 ] ,
[ S ] = R 2 [ ρ 2 + 1 ρ 2 1 0 0 ρ 2 1 ρ 2 + 1 0 0 0 0 2 ρ cos ( Δ ) 2 ρ sin ( Δ ) 0 0 2 ρ sin ( Δ ) 2 ρ cos ( Δ ) ] ,

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