Determination of the sign of δ in spectroscopic ellipsometry without a quarter-wave plate: calculation and applications
| Autor: | J.P. Piel |
|---|---|
| Rok vydání: | 1993 |
| Předmět: |
Chemistry
business.industry Metals and Alloys Surfaces and Interfaces Polarizer Waveplate Surfaces Coatings and Films Electronic Optical and Magnetic Materials law.invention Optical axis Wavelength Optics Optical coating Ellipsometry law Materials Chemistry Transmission coefficient Atomic physics business Sign (mathematics) |
| Zdroj: | Thin Solid Films. 234:447-450 |
| ISSN: | 0040-6090 |
| DOI: | 10.1016/0040-6090(93)90304-8 |
| Popis: | For several years spectroscopic ellipsometry (SE) has been widely used in semiconductor or optical coatings technology to characterize the thicknesses and indices of thin layer deposited or grown on various substrates. In the case of a spectroscopic ellipsometer modulated by mechanical rotation of the polarizer or analyser, it is impossible to determine directly for each wavelength the phase retardation Δ of the signal. Only cos Δ can be measured. Until now, the usual approach to determine the sign of Δ in this configuration has been to introduce in the optical axis a compensator plate (quarter-wave plate). This method has some disadvantages such as the optical alignment of the plate itself, the transmission coefficient and the exact compensation for one wavelength only. To avoid these problems, a mathematical treatment of the measured data can be performed. SE measures the complex ratio R p R s , so it is possible to apply the Kramers-Kronig analysis to this comples function. The measurement of the real part of this ratio tan Ψ cos Δ and the use of this theorem allows the determination of the imaginary part tan Ψ sin Δ and finally the knowledge of the sign of Δ without a compensator. The ability of the method is shown on simulations and its limitation is discussed on a real spectrum. It is interesting to note that this approach is general and without any consideration of the structure of the sample itself. |
| Databáze: | OpenAIRE |
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