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## Ellipsometry

Abstract

Ellipsometry is an optical technique which allows for the properties of thin films to be probed. The most important property is the thickness of the film. This technique utilizes the differential reflectivity between two different linear polarization states in order for a high resolution of the sample in question.

Introduction

Ellipsometry has applications in a variety of fields ranging from semiconductor physics to microelectronics to even the hi-tech industry. This technique is very precise as it provides a great use in the measurement of the thickness of a thin film. It is an optical technique hence the sample only interacts with light. The technique uses two different polarizations of light and once this light is reflected off a sample, detailed information about the different layers of the sample become evident. The amazing thing is that the layers are thinner (or smaller) than the wavelength of the probing light. Although, the main characteristic that is exploited of the sample by the technique is the thickness, other properties are also divisible such as crystal quality, electrical conductivity and chemical composition. The resolution that can be reached by Ellipsometry is around the sub angstrom region hence the details of the sample at the nanometer and micron level are quite detailed. Moreover, the reason why the technique is given the name “Ellipsometry” is due to that fact the general state of polarization of the light is elliptic.

Theory

The optical properties of thin films are devised from the basic laws of reflection and interference. So the basic idea of reflection and transmission is used in this case. When light travels from one medium into another and if both mediums have a different refractive index some of light in transmitted and some of it is reflected. This partial transmission and reflection is a property of the wave-nature of light and this can be exploited. In the figure below a beam of light is travelling from medium 1 (in this case air) with a refractive index of n1 to medium 2 (in this case water) with a refractive index of n2. 2

It should be noted that the reflected beam ( 1’) makes the same angle with the normal as the incident beam. So, at the point of interaction of the light and the surface Snell’s law can be applied to find the angle of the transmitted beam ( 2): This law has information about the direction of the transmitted and reflected beams. But we need to take this a step further and need to know the relative intensities of the electric field vector in order to determine the intensity of the beam. The intensities are given by the Fresnel reflection and transmission coefficients. It should be further noted that the perpendicular (y-axis) component of the reflected beam is a different order of magnitude form the parallel (x-axis) component of the reflect team and the same goes for the transmitted beam. These coefficients are given by:    Since we are armed with these equations we can now consider the situation where a thin film is covers a substrate which is highly reflective. So in this case there will technically be three refractive indices. The initial beam will interact with the thin film surface and there will be some transmission and reflection. The transmitted beam will come into contact with the substrate and once again there will be some transmission and reflection. At this point the beam would have a phase shift 9 hence the amplitude of the electric field must be multiplied by10. To find the total intensity of the electric field that is reflected all the contributions of the electric field amplitude need to be added. After some manipulation, the total reflection coefficient can be written as: Since there are two different linear polarizations of light there will be two Fresnel reflection coefficients. In Ellipsometry the ratio of these two values gives the material properties. Hence this ratio is given by . Since we are dealing with a reflecting substrate this value is complex and is written in the form .
Moreover, the reflection coefficients need to be measured. This is done by nulling Ellipsometry. A light source of HeNe with wavelength 632.8 nm is used. Initially, this light produces a circularly polarized beam so a quarter wave plate is inserted after this initial beam is initiated. A polarizer (P) is inserted onto a rotation stage so the combination of the polarizer and the quarter wave plate is used to produce an elliptic polarization of the light. Hence, this polarization is what interacts with the sample. Now the reflected beam needs to be linearly polarized so the direction of the polarization is found by another polarizer which is given the name analyzer (A). The angle of P and A is what determines the nulling effect. So the angles are related to the and values. Therefore, the P and A are related to and by: Therefore, if the thickness of the film is known, the refractive index of the film is known and the refractive index of the substrate is known then the P and A values can be calculated.

Procedure

The procedure for this experiment can be found in the Physics 360B lab handout, titled “Ellipsometry”.

Results Best fit n value: 1.5847, Outer curve n value: 1.5947, Inner curve n value: 1.5747 The EXACTA 2000 SIM calculated the refractive index of each of the samples. Also, the above picture shows the graph of the ellipse which coincides with theoretical predictions. The error in the thickness can be attributed to the fact that the reflected that was transmitted to the Analyzer was not completely nulled. Moreover, the error in the refractive index can be attributed to the vibrations in the building that would cause the phase shift to deviate. Also, the samples were not a 100% cleaned hence there were some scratches visible on them. However, the main error lies in the calculation of the reflection coefficients. The phase, , can be expanded in a Taylor series to obtain more accurate results.

Conclusion

The technique of Ellipsometry has proved to be a vital one in the modern world of technology. It is also being used by researchers in other disciplines such as medicine. The idea of measuring the change of polarization of light upon reflection and transmission to determine the properties of thing films has proved worthy in its application to everyday life. Moreover, the theoretical predictions of this experiment were in accordance with the measured data making for a sound agreement of theory and experiment.

References

“Experiment #24 Ellipsometry”, University of Waterloo, Physics 360B, 2009|
http://en.wikipedia.org/wiki/Ellipsometry
http://ice.prohosting.com/~jwah/ellipsometry.html