What is an Ellipsometer? An Introduction to Ellipsometry

Ellipsometry is an optical technique that can be used to measure the thickness and optical properties of thin films. An ellipsometer measures the change in the polarization state of light after interacting with a sample. This helps determine sample properties (including film thickness, roughness and extinction/absorbance coefficients) at each wavelength of interest.

Changes in the polarization state can be quantified by measuring the amplitude change and the phase shift induced by interaction with a sample. These changes in the polarization state of light can be exploited to study film thickness values that are significantly smaller than the wavelength of the incident light. Ellipsometry can obtain sub-nanometer resolution using visible wavelengths beating the diffraction limit.

Ellipsometers Measure Elliptically Polarized Light

---

When we refer to the polarization state of light, we are referring to the direction in which the electric field is oscillating. In naturally occurring light (sunlight, etc), this orientation is random - but in polarized light sources, this orientation is controlled.

Polarized light can be resolved into two components: one which is parallel (p-polarization) and one which is normal to the plane of incidence (s-polarization. Here, we define the plane of incidence the plane containing both the beam path and the surface normal.

The relative phases and amplitudes of the p- and s-components determine the polarization state 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, or their amplitudes are completely different, then the light is elliptically polarized.

When a linearly polarized light beam is reflected off a thin film sample, its polarization state will change. This is caused by differences in the reflection coefficients for p and s components at each interface that the light encounters. It is also affected by small phase shifts in the two components as the light traverses the medium comprising the film. These changes in polarization can be characterized by the difference in polarization amplitude (ψ) and phase (Δ) between the s-polarized and p-polarized light. The changes in polarization state, caused by interacting with the film, will change the lights ellipticity. For light with a given elliptical polarization, reflection from and interaction with the film can cancel out the phase changes in the incident light and result in linearly polarized light upon reflection from the sample. This is the working principle that underpins ellipsometry.

How Does An Ellipsometer Work?

---

In spectroscopy ellipsometry, a light source is directed through a polarizer to make linearly polarized light. Additional elements are often used to control the ellipticity of incident light. Single wavelength ellipsometers use a polarizer and a quarter waveplate before the sample. For a spectroscopic ellipsometer, you would typically use a polarizer followed by an acousto optic modulator. Indeed, there are many ways that you can do ellipsometry, including rotating polarizer/analyser, rotating compensator, nulling imaging etc.

This 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 state 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 can be taken at multiple different angles of incidence to enable more accurate measurement of the amplitude difference and phase shifts at each incident wavelength.

Ellipsometers measure something called the complex reflectance ratio, but this is not very meaningful on its own. To extract meaningful information about the samples, an optical model need to be applied to this data. This allows users to extract physical information such as film thickness and optical parameters. This is both a strength and a weakness of using ellipsometry. When an appropriate model is used, high quality data can be obtained. Conversely, the use of an inappropriate model can result in misleading and often inaccurate values of the thickness and optical coefficients. A typical ellipsometry study of a thin film sample might look something like following:

To do this:

• Measure phase shift and amplitude change induced by a thin film at various angles of incidence
• Pick a model that accurately represents your sample and which relates change in polarization states to physical quantities (such as layer thickness or refractive indexes). One such example might be a thin film supported on a semi-infinite substrate.
• 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. Ideally, there should not be a lot of specular scattering due to roughness or inhomogeneities in the sample as this can affect subsequent measurements. Multiangle ellipsometry can be used to look at particularly inhomogeneous or rough samples.

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

---

A great place to start with examining ellipsometer measurements is with the Fresnel equations. Using these, we can relate changes in polarization state to physical quantities, such as film thickness and optical coefficients. As an example, we will take a look at a 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 depends of wavelength (λ) of incident light 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 tan(ψ) is the amplitude ratio of the reflection coefficients as defined by the equation, and Δ is the difference in phase between the s and p components. Measurements of the polarization amplitude and phase change of the reflected light can be compared to computationally generated values by substituting refractive indexes and film thickness values into the equations given above. These values are varied until good agreement is obtained between the experimental and computationally determined ψ and Δ values is found.

Benefits and Applications of Ellipsometry

---

There are alternative methods for studying surface topography such as atomic force microscopy, or by using a surface profilometer. However, ellipsometry has some benefits over these other methods including:

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

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

Learn More

---