# Ellipsometry

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The characterization of the optical constants and thickness of organic thin films is a major part of our research, and ellipsometry is the primary method of determining these quantities.  The instrument used is a Variable Angle Spectroscopic Ellipsometer (VASE©) ellipsometer made by J.A. Woollam Co.  Ellipsometry is sensitive to several material characteristics, such as

• Layer thickness
• Optical constants (refractive index and extinction coefficient)
• Surface roughness
• Composition
• Optical anisotropy

For the purposes of our research we are most interested in determining film thickness, optical constants, and optical anisotropy.  The information that is obtained from the ellipsometry data is used to analyze the results from other experiments such as Maker fringe experiment, and waveguide coupling.

## Basics

There are three types of data typically acquired with the ellipsometer, transmission and reflection intensity and of course ellipsometry.

### Transmission and Reflection

An illustration of the transmitted, reflected, and incident beams is shown in Fig. 1.  A beam of light is incident on a sample at at some arbitrary angle of incidence , the angle of incidence is defined as the angle between the input beam direction and the direction normal to the sample surface.  At the boundary of the medium, part of the light will be reflected at angle while the other part will be transmitted through the sample at angle . Snell's law requires that all three beams be in the plane of incidence (shaded green in Fig. 1).  The plane of incidence is defined as that plane which contains the input beam, the output beam, and the direction normal to the sample surface.

Fig. 1 Schematic showing the showing the incident, reflected, and transmitted light.

The transmission and reflection measurements acquire the intensity ratios, T and R respectively, over a given range of wavelengths.  T and R are defined as the ratio of the light intensity being transmitted or reflected over the incident light intensity on the sample, as shown in Eqs. (1) and (2)

 (1)
 (2)

### Ellipsometry

Ellipsometry measures the change in polarization state of light reflected from the surface of a sample. The measured values are expressed as and . These values are related to the ratio of Fresnel reflection coefficients, and for p and s-polarized light, respectively.

 (3)

Because ellipsometry measures the ratio of two values, it can be highly accurate and very reproducible.  From Eq. (3) the ratio is seen to be a complex number, thus it contains “phase” information contained in , which makes the measurement very sensitive.  In the Fig. 2, a linearly polarized input beam is converted to an elliptically polarized reflected beam. For any angle of incidence greater than 0° and less than 90°, p-polarized light and s-polarized will be reflected differently.

Fig. 2 Schematic of the geometry of an ellipsometry experiment.

The coordinate system used to describe the ellipse of polarization is the p-s coordinate system.  The s-direction is taken to be perpendicular to the direction of propagation and parallel to the sample surface. The p-direction is taken to be perpendicular to the direction of propagation and contained in the plane of incidence.

• ### Measures a ratio of two values

• Highly accurate and reproducible (even in low light levels)
• No reference sample necessary
• Not as susceptible to scatter, lamp or purge fluctuations
• ### Measures a "phase"

• Increased sensitivity, especially to ultrathin films (<10nm)
• ### Spectroscopic Ellipsometry (SE)

• Data at wavelengths of interest (157nm, 193nm, 248nm, 1550nm, etc.)
• Variable Angle Spectroscopic Ellipsometry (VASE)
• New information (different path length), optimize sensitivity
• ### Spectroscopic ellipsometry, like all other optical metrology techniques, requires:

• Acquiring data ( and ). Data is typically acquired versus wavelength and angle of incidence.
• Building an optical model that describes the sample structure using as much information about the sample as possible. It is important to account for all layers in the sample structure.
• Generating theoretical data from the optical model that corresponds to the experimental data.
• Comparing generated data to experimental data. Unknown parameters in the optical model, such as thin film thickness or optical constants or both, are varied to try and produce a "best fit" to experimental data. Regression algorithms are used to vary unknown parameters and minimize the difference between the generated and experimental data.
• Physical parameters of the sample such as film thickness, optical constants, composition, surface roughness, etc. are obtained once a good "fit" to the experimental data is achieved.

## Optical Constants

The optical constants define how light interacts with a material.  The complex refractive index is a representation of the optical constants of a material, it is represented by

 (4)

The real part or index of refraction, n, defines the phase velocity of light in material:

 (5)

where v is the speed of light in the material and c is the speed of light in vacuum.  The imaginary part or extinction coefficient, k, determines how fast the amplitude of the wave decreases.  The extinction coefficient is directly related to the absorption of a material and is related to the absorption coefficient by:

 (5)

were is the absorption coefficient and is the wavelength of light.

#### Related Pages

[ISAM Films] [Maker Fringe Experiment] [Ellipsometry] [Atomic Force Microscopy] [Anisotropic Theory] [Waveguide Coupling] [Equipment] [Materials]

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