Abstract

To extract true optical properties of samples in a chamber with entrance and exit optical windows, oftentimes the windows were approximated as simple retarders where the retardation was small and premeasured under a given condition. The proposed method allows to cope with large birefringent effect of chamber windows thanks to its capability of extracting ellipsometric parameters (Δ, Ψ) of isotropic samples as well as measuring birefringent parameters (δ, θ) of each window separately and simultaneously. This method is, however, not valid for anisotropic samples. Ex situ results and extracted ellipsometric parameters results from in situ measurements of a silicon substrate and a SiO2 film thermally grown on the silicon substrate exhibited excellent agreement and provided significance of this method.

© 2014 Optical Society of America

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References

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2012 (1)

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

2009 (1)

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

2008 (1)

1999 (1)

1993 (1)

G. J. Stagg and T. T. Charlampopoulos, J. Phys. D 26, 2028 (1993).
[CrossRef]

1991 (1)

Y. Z. Hu, J. Joseph, and E. A. Irene, Appl. Phys. Lett. 59, 1353 (1991).
[CrossRef]

1988 (1)

1971 (1)

Aspnes, D. E.

Bakshi, L.

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Broch, L.

Charlampopoulos, T. T.

G. J. Stagg and T. T. Charlampopoulos, J. Phys. D 26, 2028 (1993).
[CrossRef]

de Nijs, J. M. M.

Eliezer, S.

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Hu, Y. Z.

Y. Z. Hu, J. Joseph, and E. A. Irene, Appl. Phys. Lett. 59, 1353 (1991).
[CrossRef]

Irene, E. A.

Y. Z. Hu, J. Joseph, and E. A. Irene, Appl. Phys. Lett. 59, 1353 (1991).
[CrossRef]

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

Jellison, G. E.

Jin, L.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Johann, L.

Joseph, J.

Y. Z. Hu, J. Joseph, and E. A. Irene, Appl. Phys. Lett. 59, 1353 (1991).
[CrossRef]

Kondoh, E.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Moreno, D.

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Naciri, A. E.

Nissim, N.

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Perelmutter, L.

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Sasaki, T.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Stagg, G. J.

G. J. Stagg and T. T. Charlampopoulos, J. Phys. D 26, 2028 (1993).
[CrossRef]

Tamegai, Y.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Tompkins, H. G.

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

Ueno, T.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

van Silfhout, A.

Watanabe, M.

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Z. Hu, J. Joseph, and E. A. Irene, Appl. Phys. Lett. 59, 1353 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. D (1)

G. J. Stagg and T. T. Charlampopoulos, J. Phys. D 26, 2028 (1993).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Sasaki, Y. Tamegai, T. Ueno, M. Watanabe, L. Jin, and E. Kondoh, Jpn. J. Appl. Phys. 51, 05EA02 (2012).
[CrossRef]

Opt. Commun. (1)

N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, and L. Perelmutter, Opt. Commun. 282, 3414 (2009).
[CrossRef]

Opt. Express (1)

Other (1)

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Configuration of an optical arrangement for in situ ellipsometric measurement.

Fig. 2.
Fig. 2.

Ex situ (red line) and in situ (blue line) Muller matrices of a silicon substrate.

Fig. 3.
Fig. 3.

(a) Ellipsometric parameters (Δ, Ψ) of the silicon substrate measured at ex situ and in situ conditions and extracted by using the proposed method. (b) Differences between ex situ and reconstructed in situ spectra for Δ and Ψ.

Fig. 4.
Fig. 4.

Retardation δi and azimuth angle θi of two birefringent chamber windows obtained from in situ measurement.

Fig. 5.
Fig. 5.

(a) Ellipsometric parameters (Δ, Ψ) of the SiO2 film thermally grown on the silicon substrate measured at ex situ and in situ conditions, and extracted by using the proposed method. (b) Differences between ex situ and reconstructed in situ spectra for Δ and Ψ.

Equations (20)

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S=(1N00N10000ScSs00SsSc),N=cos2ΨSc=sin2ΨcosΔSs=sin2ΨsinΔ,
tan(Ψ)exp(Δ)=rprs,
Wi=(10000AiBiCi0BiDiEi0CiEiFi),i=1,2,
Ai=1(1cosδi)sin22θiBi=(1cosδi)sin2θicos2θiCi=sinδisin2θiDi=1(1cosδi)cos22θiEi=sinδicos2θiFi=cosδi,
W2SW1=(1NA1NB1NC1NA2NB2Sub(W2SW1)3×3NC2)
sub(W2SW1)=(A1A2+Sc(B2B1C2C1)+Ss(C2B1+B2C1)B1A2+Sc(B2D1+C2E1)+Ss(C2D1B2E1)C1A2+Sc(B2E1C2F1)+Ss(C2E1+B2F1)A1B2+Sc(D2B1+E2C1)Ss(E2B1D2C1)B1B2+Sc(D2D1E2E1)Ss(E2D1+D2E1)C1B2+Sc(D2E1+E2F1)Ss(E2E1D2F1)A1C2Sc(E2B1F2C1)Ss(F2B1+E2C1)B1C2Sc(E2D1+F2E1)Ss(F2D1E2E1)C1C2Sc(E2E1F2F1)Ss(F2E1+E2F1)).
m13m14=B1C1=1X11+X11Y12=U1.
X1=1Y12U121Y12+U12.
m14m12=C1A1=1X12Y11(1X1)Y12=V1.
Y1=±V12(1+U12)(1+2U12)+2U12[V12(1+U12)(1+2U12)+2U12]2[V12(1+2U12)2+4U12]V12(1+U12)2V12(1+2U12)2+4U12.
δi=arccosXi(0°δi180°)θi=12arcsinYi(90°θi90°).
Bi0,Ci0;Yi0,0°θi45°
Bi<0,Ci>0;Yi0,45°<θi<90°
Bi0,Ci<0;Yi<0,45°θi<0°
Bi>0,Ci<0;Yi<0,90°<θi<45°.
S=W21(W2SW1)W11.
N=m12A1=m21A2,
Sc=(m33B1B2)×(E2E1D2F1)(m34+C1B2)×(E2D1+D2E1)(D2D1E2E1)×(E2E1D2F1)(E2D1+D2E1)×(D2E1+E2F1),
Ss=(m33B1B2)×(D2E1+E2F1)(m34+C1B2)×(D2D1E2E1)(D2D1E2E1)×(E2E1D2F1)(E2D1+D2E1)×(D2E1+E2F1).
Δ=arctanSsSc,Ψ=12arccosN.

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