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Proceedings Paper

Transmission ellipsometry on unsupported film/pellicle: closed-form inversion
Author(s): A. R. M. Zaghloul; M. Elshazly-Zaghloul; Y. A. Zaghloul
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Paper Abstract

We present a brief discussion of the transmission ellipsometric function of an unsupported film/pellicle optical structure. We also briefly discuss different ellipsometric techniques that could be used to characterize an unsupported film/pellicle. The current state of data reduction either uses forward curve-fitting techniques or other numerical methods to obtain the refractive index of the optical slab and its thickness. Both methods are dependent on a good starting point and use an iterative approach to minimize a merit function that consumes much valuable time and memory resources. We present closed-form formulas to obtain both the refractive index and thickness. We spare the reader successive and involved transformations and algebraic manipulations to arrive at the closed forms. We provide the reader with an easy-to- follow step-by-step algorithm to obtain the system parameters. Also, we present a closed-form formula for the refractive index using two, and more, sets of measurements. In addition, we discuss the effect of film-thickness multiplicity and its separation. Other technique-specific closed-form formulas are given for different ellipsometric techniques. We also present numerical simulation results that prove the accuracy of the closed-form formulas, and that revealed an interesting and useful characteristic that we utilize. We close by introducing a closed-form formula to calculate the ratio of the unsupported film/pellicle to that of the ambient, which could be used to determine either experimentally. The advantages of closed-form inversion over forward curve fitting and numerical methods are numerous, including: 1) a much higher speed of obtaining the problem solution that allows for real-time applications, 2) it does not require human judgments or intervention, 3) absolute stability, 4) much higher accuracy, 5) no need for close-to-solution starting values of the unknown parameter(s), 6) no errors introduced by the formulas themselves, 7) smart, simple, and concise software programs, 8) use in new material characterization where starting-point-dependent numerical methods fail or require much trial and error.

Paper Details

Date Published: 18 October 2007
PDF: 12 pages
Proc. SPIE 6682, Polarization Science and Remote Sensing III, 66820J (18 October 2007); doi: 10.1117/12.736352
Show Author Affiliations
A. R. M. Zaghloul, ITR Technologies Inc. (United States)
M. Elshazly-Zaghloul, ITR Technologies Inc. (United States)
Y. A. Zaghloul, Georgia Institute of Technology (United States)
ITR Technologies Inc. (United States)

Published in SPIE Proceedings Vol. 6682:
Polarization Science and Remote Sensing III
Joseph A. Shaw; J. Scott Tyo, Editor(s)

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