Ellipsometry: What is it and Why is it Useful in Optics?

A propagating light beam is commonly known as propagating electromagnetic radiation within the field of physical optics. The direction of propagation is horizontal to the direction of the electric and magnetic field vectors, while the polarizing direction of light is understood to be the direction of the electrical vector component.

As long as the route of the electrical field remains consistent throughout this propagation, light will be polarized directly.

This illustrates that this electric field vector’s perpendicular components are in phase, or there is no instance of phase variation between them (Figure A).

Should a 90° phase difference occur between these perpendicular components, the light will be circularly polarized (Figure B). Where the two components exhibit minimal phase variation, light is often polarized elliptically (Figure C).

Figures A, B, and C provide examples of light polarization.

light polarization

Figures A, B & C: light polarization. Image Credit: Wikipedia

Measured Quantities

Because it is an optical method, ellipsometry is non-contact and does not cause any damage to a sample. Ellipsometry can be used to analyze the thickness and optical purposes of each individual layer present within a multilayer structure.

This method is extremely sensitive because it analyzes a light beam’s phase shift as this is transported through a structure of layers. Phase angle analysis is not reliant on the absolute intensity of light.

It is possible to collect spectral data from the sample by using sources of white light and monochromators. Measurements acquired via each parameter provide information on the layer structure’s physical properties, for example, the thickness of layers and the refractive index.

This information is provided in an unpredictable manner, however.

Measuring the ratio of the complex Fresnel reflection coefficients is one possible solution. Because this number is complex, it may be divided into an amplitude term and a phase shift term. Both of these terms relate to the implied ellipsometric angles, Ψ and Δ.

The Fundamental Equation of Ellipsometry

It is possible to employ precisely measured parameters in order to outline the elliptical polarized reflected light.

semilab

A model-based indirect numerical calculation may facilitate analysis of complex multi-layered structures and their properties.

Here, layer structure is taken into account, with optical functions and thickness serving as parameters.

Relative phase shift is calculated and compared against these measured parameters. This process involves the numerical regression procedure explored below.

Ellipsometry: What is it and Why is it Useful in Optics?

Image Credit: Semilab Semiconductor Physics Laboratory

Numerical Regression Procedure Based on an Optical Model

Ellipsometry: What is it and Why is it Useful in Optics?

Image Credit: Semilab Semiconductor Physics Laboratory

Advanced Formalism

The state of polarization for a completely polarized light beam can be outlined somewhat through the use of Jones vectors; for example, Ex, Ey components.

A 2x2 element referred to as a ‘Jones Matrix’ can be used to illustrate a variation of the Jones vector after reflection from a sample structure has occurred. It is possible to characterize a shift from a linearly polarized state to an orthogonal state via the formula below.

Example: Mueller Matrix of an optically active sample measured vs. stage azimuth rotation. Revealing rotational symmetry of molecular composition.

Example: Mueller Matrix of an optically active sample measured vs. stage azimuth rotation. Revealing rotational symmetry of molecular composition.* (*Example measurement: Monomolecular organic coating on solid substrate—Semilab measurement in cooperation with EPFL). Image Credit: Semilab Semiconductor Physics Laboratory

Mueller Matrix formalism founded on the 4D Stokes vectors is more commonly used to outline moderately polarized light beams.

semilab

In the example shown here, S0 represents the light intensity as a whole, while S1 represents the variation in intensity between the vertical and horizontal polarization. S2 represents the variation in intensity between linearly polarized components in +45° and –45° directions, while S3 represents the variation in intensity between the left and right oriented circularly polarized components.

Multiplying the inbound light’s Stokes vector by the material’s Mueller Matrix results in the Stokes vector illustrating the reflected light:

semilab

Once the Stokes vector of the inbound and reflected light has been measured, the material’s Mueller Matrix can be analyzed. This facilitates the analysis of material properties through the utilization of Mueller Matrix elements.

The material’s optical symmetries are reflected by the symmetry of the Matrix. This approach is more commonly employed as a qualitative means of analyzing an optically active sample because this approach is used without complex optical modeling of the measurement information.

Instrumentation

Image Credit: Semilab Semiconductor Physics Laboratory

 

This information has been sourced, reviewed and adapted from materials provided by Semilab Semiconductor Physics Laboratory.

For more information on this source, please visit Semilab Semiconductor Physics Laboratory.

Citations

Please use one of the following formats to cite this article in your essay, paper or report:

  • APA

    Semilab Semiconductor Physics Laboratory. (2024, June 25). Ellipsometry: What is it and Why is it Useful in Optics?. AZoOptics. Retrieved on October 08, 2024 from https://www.azooptics.com/Article.aspx?ArticleID=1920.

  • MLA

    Semilab Semiconductor Physics Laboratory. "Ellipsometry: What is it and Why is it Useful in Optics?". AZoOptics. 08 October 2024. <https://www.azooptics.com/Article.aspx?ArticleID=1920>.

  • Chicago

    Semilab Semiconductor Physics Laboratory. "Ellipsometry: What is it and Why is it Useful in Optics?". AZoOptics. https://www.azooptics.com/Article.aspx?ArticleID=1920. (accessed October 08, 2024).

  • Harvard

    Semilab Semiconductor Physics Laboratory. 2024. Ellipsometry: What is it and Why is it Useful in Optics?. AZoOptics, viewed 08 October 2024, https://www.azooptics.com/Article.aspx?ArticleID=1920.

Ask A Question

Do you have a question you'd like to ask regarding this article?

Leave your feedback
Your comment type
Submit

While we only use edited and approved content for Azthena answers, it may on occasions provide incorrect responses. Please confirm any data provided with the related suppliers or authors. We do not provide medical advice, if you search for medical information you must always consult a medical professional before acting on any information provided.

Your questions, but not your email details will be shared with OpenAI and retained for 30 days in accordance with their privacy principles.

Please do not ask questions that use sensitive or confidential information.

Read the full Terms & Conditions.