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Polarized light

Light is an electromagnetic wave and all its features relevant for ellipsometry can be described within the framework of Maxwell's theory. The relevant material properties are the complex dielectric function epsilon or alternatively the corresponding refractive index n.

An electromagnetic wave consists of an electric field E and a magnetic field B. The field vectors are mutually perpendicular and also perpendicular to the propagation direction as given by the wave vector k. All states of polarization are classified according to the trace of the electrical field vector during one period. Linearly polarized light means the electrical field vector oscillates within a plane, elliptically polarized light means that the trace of the electric field vector during one period is an ellipse. A convenient mathematical representation of a given state of polarization is based on a superposition of two linearly polarized light waves within an arbitrarily chosen orthogonal coordinate system.

The different states of polarization are depicted in the following Fig.:

The Jones representation of polarized light represents any state of polarization as a linear combination of two orthogonal linearly polarized light waves.

Ellipsometry refers to a class of optical experiments which measure changes in the state of polarization upon reflection or transmission on the sample of interest. It is a powerful technique for the characterization of thin films and surfaces. In favorable cases thicknesses of thin films can be measured to within Angstroem accuracy, furthermore it is possible to quantify submonolayer surface coverages with a resolution down to 1/100 of a monolayer or to measure the orientation adopted by the molecules on mesoscopic length scales. The high sensitivity is remarkable if one considers that the wavelength of the probing light is on the order of 500 nm. The data accumulation is fast and allows to monitor the kinetics of adsorption processes. Many samples are suitable for ellipsometry and the only requirement is that they must reflect laser light. Its simplicity and power makes ellipsometry an ideal surface analytical tool for many objects in colloidal and interface science, polymer science for corrosion, metal research or in the filed of bio sensing.

A typical ellipsometric experiment is depicted in the following Figure. Light with a well defined state of polarization is incident on a sample. The reflected light usually differs in its state of polarization and these changes are measured and quantified in an ellipsometric experiment.

The changes in the state of polarization can be expressed by the so-called ellipsometric angles Delta and Psi.

There are various ways for an automatization of an ellipsometer. A good review is presented in the following book chapter.

H. Motschmann, R. Teppner
Ellipsometry in Interface Science,
in Novel methods to Study Interfacial Layers, edited by R. Miller, D. Moebius,
download PDF Elsevier (2001)

A particular successful implementation is Nullellipsometry which eliminates many intrinsic errors due to slight misalignments of the sample or imperfections of the sample. Nullellipsometry means select a setting of the optical components that cancel the light at the detector. The corresponding Nullsetting of the optical components provides the ellipsometric angles Delta and Psi.

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