What is an Ellipsometer? An Introduction to Ellipsometry

Ellipsometry is an optical probing technique often used to measure thin films. Ellipsometers measure the change in polarized light after interacting with a sample to determine various physics and optical properties including film thickness, roughness and conductivity. 

Polarization change can be quantified by measuring the amplitude change and the phase shift before and after interacting with a sample. Using this technique, you can probe films that are thinner than the wavelength itself, getting around the diffraction limit. Using ellipsometers, researchers can measure film thickness with sub nanometre accuracy.

Ellipsometers Measure Elliptically Polarized Light

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When we talk about the polarization of light, we are referring to the direction in which the electric field is oscillating. In naturally occurring light, this orientation is random - but in polarized light sources, this orientation is controlled.

Polarized light can be split into two components: the components which are parallel and normal to the plane of incidence, referred to as  p-polarized and s-polarized respectively. Here, we define the plane of incidence the plane containing both the beam path and the surface normal.

The synchronization of the p- and s-components determine the polarization of light:

• If the p- and s-components are synchronized or 180° out of phase, then the light is linearly polarized.
• If the p- and s-components are 90° out of phase and have equal amplitudes, then the light is circularly polarized.
• If the p- and s-components are out of phase by another arbitrary amount, then the light is elliptically polarized.

When a linearly polarized light beam is reflected off a sample, its polarization state will change. This change in polarization can be characterized by the difference in polarization amplitude (ψ) and phase (Δ) between the s-polarized and p-polarized light If the phase shift between the s- and p-polarized light is arbitrary (i.e. not 0°, 90° or 180°), this creates elliptically polarized light, hence the name ellipsometry.

How Does An Ellipsometer Work?

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In spectroscopy ellipsometry, a light source is directed through a polarizer to make linearly polarized light. This linearly polarized light interacts with the sample, usually a substrate with a thin film, or several thin films, deposited on top of it. As polarized light interacts with a layer, its polarization qualities will change.

The new polarization state of this reflected light is measured by an analyzer, before this signal is detected with a detector. These measurements are taken at multiple different angles to accurately measure amplitude difference and phase shift.

Ellipsometers can measure complex reflectance ratio, but this is not very meaningful on its own. You need to apply a model to this data to extract physical information such as film thickness and optical parameters. To do this:

• Measure phase shift and amplitude change at various angles
• Pick your model which relates change in polarization components to physical quantities (such as layer thickness or refractive indexes)
• Computationally vary the parameters in your model until you get amplitude and phase shift constants which match your measured results.
• If your model is appropriate and the fit is good, you can get very reliable measurements of very thin films

Spectroscopic ellipsometry works best for samples that consist of discrete, well defined layers that are optically homogenous and isotropic. Multiangle or immersion ellipsometry can be used to look at inhomogeneous or rough samples. The samples also need to be somewhat specular to be well measured.

Example of Analysis of Ellipsometer Measurement: Thin film on a Substrate

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A great place to start with examining ellipsometer measurements is with the Fresnel equations. Using these, we can relate changes in polarization to physical qunatities. As an example, we will take a look at a very simple analysis of a thin film on a substrate.

The reflection coefficients for p-polarized and s-polarized light reflected at the boundary between materials with reflective indexes n₁ and n₂ can be represented by r^p and r^s respectively.

Where φ is the angle of reflection or refraction, and n_i is the refractive index of the respective medium.

The total reflection coefficients, R^p and R^s combine the reflection coefficients from each layer of the sample. For the above example, the equations become as follows:

Where D is a constant that depends of wavelength (λ) in a vacuum, j=√-1 and d_i is the thickness of film i, as below.

One of the key relationships used in ellipsometry is shown below, where the ratio of total reflectance coefficients are related to phase difference and amplitude change of the polarized wave components.

Where ψ is the change in amplitude, and Δ is the difference in phase. So if you can measure the polarization amplitude and phase change of the reflected light, you can computationally substitute various refractive indexes and film thickness values until you get matching ψ and Δ values.

Benefits and Applications of Ellipsometry

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Benefits of spectroscopic ellipsometry include:

Ellipsometers are used in many different industries to characterize thin film coatings including:

• Polymer science
• Microelectronics
• Flat panel displays
• Biosensors
• Optical Coatings