Systematic errors in rotating-compensator ellipsometry

R. Kleim; L. Kuntzler; A. El Ghemmaz

doi:10.1364/JOSAA.11.002550

Journal of the Optical Society of America A
Vol. 11,
Issue 9,
pp. 2550-2559
(1994)
•https://doi.org/10.1364/JOSAA.11.002550

Systematic errors in rotating-compensator ellipsometry

R. Kleim, L. Kuntzler, and A. El Ghemmaz

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R. Kleim, L. Kuntzler, and A. El Ghemmaz, "Systematic errors in rotating-compensator ellipsometry," J. Opt. Soc. Am. A 11, 2550-2559 (1994)

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Abstract

Systematic error sources for the rotating-compensator ellipsometer are discussed. Starting from a general formalism, we derive explicit first-order expressions for the errors δΨ and δΔ caused by azimuthal errors and residual ellipticity introduced by imperfect polarizers or compensators and windows. Comparison is made with measurement results. It is shown that all azimuthal-angle errors can be eliminated by a two-zone measurement and that the natural optical rotation of the rotating quartz compensator has no effect on the measurements.

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Sample	Ψ (deg)	Δ (deg)
Substrate	10.92	168.17
106 nm	44.21	79.09
130 nm	71.15	85.79

Source of Error	δΨ	δΔ
δA	−sgn A sin 2Ψ	0
δP	−sgn A cos Δ	2 sgn A sin Δ cot 2Ψ
δC	2 sgn A cos Δ	−4 sgn A sin Δ cot 2Ψ
γ_A	0	2 sgn A
γ_P	sgn A cos 2P sin Δ cos² 2Ψ − (sin 2P sin 2Δ sin 4Ψ)/4	2(sgn A cos 2P cos Δ cot 2Ψ − cos² Δ sin 2P)
γ_C	0	0
δ(δ_c)	−sin² Δ sin 4Ψ/(4 sin δ_c)	−sin 2Δ/(2 sin δ_c)
δ_{W_a}	(sgn A sin Δ sin 2θ_{W_a})/2	cos 2 θ_{W_a} + sgn A sin 2 θ_{W_a} cos Δ cot 2Ψ
δ_{W_b}	0	cos 2θ_{W_b}

Source of Error	δΨ	δΔ
δA	−sgn P cos Δ;	2 sgn P sin Δ cot 2Ψ
δP	−sgn P sin 2Ψ	0
δC	2 sgn P cos Δ	−4 sgn P sin Δ cot 2Ψ
γ_A	−sgn P cos 2A cos² 2Ψ sin Δ + (sin 2A sin 2Δ sin 4Ψ)/4	2(−sgn P cos 2A cos Δ cot 2Ψ + cos² Δ sin 2A)
γ_P	0	−2 sgn P
γ_C	0	0
δ(δ_c)	−sin² Δ sin 4Ψ/(4 sin δ_c)	−sin 2Δ/2 sin δ_c
δ_{W_a}	0	cos 2θ_{W_a}
δ_{W_b}	(sgn P sin Δ 2θ_{W_a})/2	cos 2θ_{W_b} + sgn P cos Δ cot 2Ψ sin 2θ_{W_b}

Sample	Ψ (deg)	Δ (deg)
Substrate	10.92	168.17
106 nm	44.21	79.09
130 nm	71.15	85.79

Source of Error	δΨ	δΔ
δA	−sgn A sin 2Ψ	0
δP	−sgn A cos Δ	2 sgn A sin Δ cot 2Ψ
δC	2 sgn A cos Δ	−4 sgn A sin Δ cot 2Ψ
γ_A	0	2 sgn A
γ_P	sgn A cos 2P sin Δ cos² 2Ψ − (sin 2P sin 2Δ sin 4Ψ)/4	2(sgn A cos 2P cos Δ cot 2Ψ − cos² Δ sin 2P)
γ_C	0	0
δ(δ_c)	−sin² Δ sin 4Ψ/(4 sin δ_c)	−sin 2Δ/(2 sin δ_c)
δ_{W_a}	(sgn A sin Δ sin 2θ_{W_a})/2	cos 2 θ_{W_a} + sgn A sin 2 θ_{W_a} cos Δ cot 2Ψ
δ_{W_b}	0	cos 2θ_{W_b}

Abstract

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Figures (8)

Tables (3)

Equations (59)

Journal of the Optical Society of America A