Measurement of Elasto-Optic Effect in Absorbing Materials by Ellipsometry*

L. G. Holcomb; N. M. Bashara

doi:10.1364/JOSA.61.000608

Journal of the Optical Society of America
Vol. 61,
Issue 5,
pp. 608-615
(1971)
•https://doi.org/10.1364/JOSA.61.000608

Measurement of Elasto-Optic Effect in Absorbing Materials by Ellipsometry

L. G. Holcomb and N. M. Bashara

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L. G. Holcomb and N. M. Bashara, "Measurement of Elasto-Optic Effect in Absorbing Materials by Ellipsometry*," J. Opt. Soc. Am. 61, 608-615 (1971)

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Abstract

Strain-induced changes in the optical (dielectric) constants of silver films on lead zirconate titanate are determined ellipsometrically. In general, for a contaminant-free surface, the induced changes can be determined directly from the ellipsometer measurements. An additional advantage of the method is that it allows compensation for errors introduced by unavoidable mechanical vibrations. In the development of the theory, four-zone expressions are derived for the general case that includes the effect of extraneous signals caused by mechanical vibration.

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Equations (44)

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Zone	Off-null dynamic relations
1	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (- cot δ A - cot ψ_{n}) \end{array}$
2	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (- cot δ A - cot ψ_{n}) \end{array}$
3	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (cot δ A - cot ψ_{n}) \end{array}$
4	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (cot δ A - cot ψ_{n}) \end{array}$

Zone	Dynamic ellipsometry equations
1	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} + 2 δ D cot 2 ψ_{n} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} - 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [- δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
2	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} + 2 δ D cot 2 ψ_{n} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} - 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [- δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
3	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} - 2 δ D cot 2 ψ_{n} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} + 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
4	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} - 2 δ D cot 2 ψ_{n} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} + 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$

Zone	Off-null dynamic relations
1	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (- cot δ A - cot ψ_{n}) \end{array}$
2	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (- cot δ A - cot ψ_{n}) \end{array}$
3	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (cot δ A - cot ψ_{n}) \end{array}$
4	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} - δ ψ \frac{2}{sin 2 ψ_{n}} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + 2 δ ψ (cot δ A - cot ψ_{n}) \end{array}$

Zone	Dynamic ellipsometry equations
1	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} + 2 δ D cot 2 ψ_{n} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} - 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [- δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
2	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} + 2 δ D cot 2 ψ_{n} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} - 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [- δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
3	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} - 2 δ D cot 2 ψ_{n} - δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} + 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$
4	$\begin{array}{l} S (A_{n}, P) & = \frac{δ R_{p}}{R_{p}} + D - δ ψ \frac{2}{sin 2 ψ_{n}} - 2 δ D cot 2 ψ_{n} + δ Δ cot δ P \\ S (A, P_{n}) & = \frac{δ R_{p}}{R_{p}} + D - 2 δ ψ cot ψ_{n} + 2 δ D cos 2 ψ_{n} cos Δ_{n} + 2 [δ ψ + δ D (1 - cos Δ_{n} sin 2 ψ_{n})] cot δ A \end{array}$

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Equations (44)

Journal of the Optical Society of America