Ellipsometry

The ellipsometry is a measurement method of material research and surface science , with the dielectric material properties (complex permittivity , or real and imaginary part of the complex refractive index ) and the layer thickness of thin layers can be determined. Ellipsometry can be used to examine different materials, for example organic or inorganic samples (metals, semiconductors, insulators and also liquid crystals ). The frequency range used covers the spectrum from the microwave range over the terahertz range , the infrared range over the visible frequency range to the range of ultraviolet light (UV, 146 nm).

Measuring station with a phase modulation ellipsometer and automatically adjustable angle arms

Basic principle

Basic structure of an ellipsometer. The angle Φ is variable.

Ellipsometry determines the change in the polarization state of light upon reflection (or transmission) on a sample. As a rule, linear or circularly polarized light is used. As can be seen from the Fresnel equations , this light is generally elliptically polarized when it is reflected at a boundary surface, from which the name ellipsometry is derived.

In the simplest case, the change in the polarization state can be described by the complex ratio of the reflection coefficients and . Here stands for light polarized perpendicular to the plane of incidence and parallel to the plane of incidence. These coefficients are the ratio between incident and reflected amplitude. ${\displaystyle \rho }$ ${\displaystyle r_{\mathrm {s} }}$ ${\displaystyle r_{\mathrm {p} }}$ ${\displaystyle r_{\mathrm {s} }}$ ${\displaystyle r_{\mathrm {p} }}$

${\displaystyle \rho ={\frac {r_{\mathrm {p} }}{r_{\mathrm {s} }}}}$

Another representation uses the ellipsometric parameters and , where is equal to the magnitude of , and corresponds to the change in the phase difference between the s- and p-polarized wave: ${\displaystyle \Psi }$ ${\displaystyle \Delta }$ ${\displaystyle \tan \Psi }$ ${\displaystyle \rho }$ ${\displaystyle \Delta }$

${\displaystyle \rho \equiv {\frac {r_{\mathrm {p} }}{r_{\mathrm {s} }}}=\tan \Psi \exp {i(\Delta _{\mathrm {p} }-\Delta _{\mathrm {s} })}=\tan \Psi \exp {i\Delta }}$.

From the above equation, the following advantages of ellipsometry can be derived compared to pure reflection measurements, in which only the reflectance R is measured:

• No reference measurement necessary, as intensity ratios are determined instead of intensities.
• For the same reason, there is less susceptibility to intensity fluctuations.
• There are always (at least) two parameters ( and ) determined in an experiment. ${\displaystyle \Psi }$ ${\displaystyle \Delta }$

Structure variants and division

The following important information is missing from this article or section:

There is a lack of information on the basic structure of an ellipsometer (best using the example of the zero ellipsometer; light source, polarizer, etc. + graphic). Following this, the construction variants should be briefly explained (zero ellipsometer, rotating analyzer, rotating polarizer, etc.). Explanations of the advantages and disadvantages would be useful here .-- Cepheids 15:19, Feb 13, 2007 (CET)

Help Wikipedia by researching and pasting it .

The ellipsometry can be classified on the one hand according to the wavelength used and on the other hand according to the ellipsometric method used.

wavelength

Different spectral ranges enable the investigation of different properties:

Infrared

Infrared light allows the investigation of lattice vibrations , so-called phonons , and vibrations of the free charge carriers, the plasmons , as well as the dielectric function.

Visible light

In visible light, including near infrared and near ultraviolet light , the refractive index , the absorption index , the properties of band-band transitions and excitons can be investigated.

Ultraviolet

In the ultraviolet radiation range, in addition to the parameters observable in visible light, higher-energy band-band transitions can also be determined.

Single wavelength and spectroscopic ellipsometry

In single- wavelength ellipsometry, a fixed wavelength is used, which is generally predetermined by the use of lasers. With these systems, the angle can often be varied. In contrast, with spectroscopic ellipsometry, the parameters and are determined for a specific spectral range as a function of the wavelength (photon energy). ${\displaystyle \Psi }$ ${\displaystyle \Delta }$

Standard ellipsometry and generalized ellipsometry

The Standardellipsometrie , often short ellipsometry called, used when neither -polarized in converting even reverse-polarized light. This is the case if the samples examined are optically isotropic or optically uniaxial, the optical axis then having to be oriented perpendicular to the surface. In all other cases, generalized ellipsometry must be used. ${\displaystyle {\vec {s}}}$ ${\displaystyle {\vec {p}}}$

Matrix ellipsometry

Jones matrix ellipsometry is used when the samples being examined are not depolarizing. The polarization state of the light is described by the Jones vector and the change in the polarization state by the Jones matrix (2 × 2 matrix with 4 complex elements).

Are the samples depolarizing, e.g. B. Due to layer inhomogeneities or roughness, Müller matrix ellipsometry must be used. The polarization state of the light is described by the Stokes vector and the change in the polarization state by the Müller matrix (4 × 4 matrix with 16 real-valued elements). Due to the increasingly demanding applications, the Müller matrix ellipsometry is becoming increasingly important.

Evaluation of the experimental data

A model analysis is generally used to evaluate the experimental data. The optical constants of the sample can only be determined directly from the experimental data in the special case of a sample that consists of only one layer and is optically infinitely thick. For most samples, these conditions are not met, so that the experimental data must be evaluated by a line shape analysis. For this purpose, a model is created that contains the sequence of the individual layers of the sample, their optical constants and layer thicknesses. The optical constants are either known or are described by a parameterized function ( model dielectric function ). By varying the parameters, the model curves are adapted to the experimental curves.

See also

• Dielectric spectroscopy - electrical measurement of the complex permittivity
• Reflection anisotropy spectroscopy - measurement of optical anisotropies

literature

• RMA Azzam, NM Bashara: Ellipsometry and Polarized Light. Elsevier Science Pub Co., 1987, ISBN 0-444-87016-4 .
• A. Röseler: Infrared Spectroscopic Ellipsometry. Akademie-Verlag, Berlin 1990, ISBN 3-05-500623-2 .
• M. Schubert: Infrared Ellipsometry on semiconductor layer structures: Phonons, Plasmons, and Polaritons (= Springer Tracts in Modern Physics. 209). Springer, Berlin 2004, ISBN 3-540-23249-4 .
• HG Tompkins: A User's Guide to Ellipsometry. Dover Publications Inc., Mineola 2006, ISBN 0-486-45028-7 (Good book for beginners).
• HG Tompkins, EA Irene (Eds.): Handbook of Ellipsometry. William Andrews Publications, Norwich, NY 2005, ISBN 0-8155-1499-9 .
• HG Tompkins, WA McGahan: Spectroscopic Ellipsometry and Reflectometry: A User's Guide. John Wiley & Sons Inc., 1999, ISBN 0-471-18172-2 .
• H. Fujiwara: Spectroscopic Ellipsometry: Principles and Applications. John Wiley & Sons Inc., 2007, ISBN 0-470-01608-6 .

Web links

• German Ellipsometry Forum of the Ellipsometry Working Group (Ellipsometry Working Group - Paul Drude eV)
• Description of the ellipsometry by Karsten Litfin
• Tutorial Ellipsometry, JA Woollam Co, Inc. (English)
• Tutorial Ellipsometry by JE Jellison Jr. (English) (PDF file; 235 kB)

Individual evidence

1. ^ Spectroscopic Ellipsometer Products . JA Woollam, accessed June 1, 2010.
2. ↑ HG Tompkins (ed.), EA Irene (ed.): Handbook of Ellipsometry. William Andrews Publications, Norwich, NY 2005, ISBN 0-8155-1499-9 , p. 77.