Materialanalytik

Praktikum

Ellipsometry B508

Stand: 05.09.2011

Aims: Measurement of the thickness of different dielectric thin films.

Table of Contents

1. INTRODUCTION 1

2. BASIC CONCEPTS 1

2.1. Polarized light 1

2.2. Reflection of polarized light 3

2.3. Principle of Ellipsometry 4

3. THE EXPERIMENT 7

3.1. Devices / Samples 7

3.2. Performing the experiment 7

4. EVALUATION OF THE EXPERIMENT 7

5. BIBLIOGRAPHY 8

APPENDIX A – REFRACTIVE INDEX FOR SELECTED MATERIALS 8

B508: Ellipsometry

1. Introduction

Ellipsometry is an optical measurement technique which is used to determine the dielectric properties (complex index of refraction) and thickness of thin (a few Å – a few µm) transpar- ent films. It utilizes polarized light and its changing properties upon reflection and transmis- sion at or through dielectric media. Quickness, precision, and the non-destructive nature of this method are strengths of the meth- od. Therefore, ellipsometry is a standard measurement technique used in the industry (e.g. microelectronics, solar cells…), as well as in basic research throughout natural and engineer- ing sciences. This lab course is designed to convey the basic knowledge about the ellipsometry measure- ment technique. It involves a theoretical introduction to the method starting with the theoreti- cal background of polarized light, as well as practical measurements and the required prepara- tions.

2. Basic Concepts

Ellipsometry is based on the use of polarized light. Thus, our theory chapter will start right there and will later be devoted to the method itself. Hence, we will discuss briefly the

• Basics of polarized light. • Basics of ellipsometry.

2.1. Polarized light

Most generally, light can be treated as a transverse electromagnetic wave which consists of sinusoidally oscillating electric (E) and magnetic (H) fields perpendicular to each other and to the propagation direction of the wave. For simplicity the mathematical representation is usual- ly only based on the electric field E. The electric field E of the wave can further be divided into two components, the so-called polarizations, usually called Ep and Es. These polarizations are plane waves, which can be expressed by

ˆ ES = ES exp(iωt) (1) with the amplitude Ês , the angular frequency ω and the time t and

ˆ EP = EP exp(i(ωt − ∆)) (2) where ∆ denotes the phase between both polarizations. If a light wave impinges on a surface, the area which is perpendicular to the surface and which contains the wave, is called the plane of incidence. In this context the meaning of the indices s and p is easy to understand: The p-polarization is the plane wave which is oscillating parallel to the plane of incidence, whereas the s-polarization is oscillating perpendicular (from Ger-

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B508: Ellipsometry man “senkrecht”) to it. Thus, both polarizations are perpendicular to each other and to the propagation direction of wave.

Figure 1: Polarization of light. (a) The light is linearly polarized, i.e. both waves (polariza- tions) are in phase. (b) The light is zircularly polarized, i.e. both polarization amplitudes are the same and both waves are shifted by a phase of 90°. (c) The light is elliptically polarized, i.e. both polarizations’ amplitudes are different and both waves are not in phase.

To calculate the resulting electric field E, the two components (polarizations) simply have to be added (as vectors). This is illustrated in Fig. 1 for three cases:

i) Es and Ep are in phase, Δ = 0 The resulting electrical field E will be a plane wave, the position (angle to Es or Ep) is de- termined by the ratio of the amplitudes Ês/Êp of the polarizations.

ii) Es and Ep are shifted by Δ = 90° and Ês = Êp The resulting wave is circularly polarized, i.e. the wave describes a rotation around the ax- is of propagation. The amplitude of the wave stays constant, since Ês = Êp.

iii) Es and Ep are arbitrarily shifted in phase and Ês ≠ Êp

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B508: Ellipsometry

This case is the most general case for a light wave. The wave is elliptically polarized, i.e. the electric field vector E is rotating around the axis of propagation. Its amplitude however is not constant, as in case ii), therefore the projection of the movement describes an el- lipse. Cases i) and ii) can be seen as special cases of case iii).

2.2. Reflection of polarized light

The two polarizations are not just a theoretical construct, completely s- or p-polarized light shows different behavior in nearly all optical properties. One very distinct difference can be observed in the case of reflection from a material surface, e.g. the reflection at a GaAs sample measured in air, which is presented in Fig. 2. The measured reflectance is plotted versus the incidence angle ρ. The slope of the resulting curve for the s-polarized light Rs is monotonously increasing with increasing angle. In contrast, the curve Rp for p-polarized light decreases to zero between 0° and an angle close to 75°, steeply increasing to unity between that angle and 90°. The angle where Rp = 0 is called “Brewster Angle” ρB. It can be shown, that this angle can be determined by

n2 tan ρ B = , (3) n0 where n2 and n0 are the refractive indices of the measured sample and the medium in which the wave travels, before it impinges on the sample. If a thin layer with refractive index n1 is added to the system, the Brewster angle will be al- tered. On the one hand, Rp will depend on the substrate and the layer, therefore the term “Pseudo-Brewster Angle” is commonly used, on the other hand ρB will shift to

• Lower angles for n1 < n2. • Higher angles for n1 > n2.

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B508: Ellipsometry

0 20 40 60 80 1,0 1,0 0,9 0,9 0,8 0,8 0,7 0,7 RS 0,6 RP 0,6 0,5 0,5

0,4 0,4

Reflactance 0,3 0,3 0,2 0,2 0,1 0,1 0,0 0,0 0 20 40 60 80 ρ Incidence Angle

Figure 2: Reflectance R vs. incidence angle ρ for an air-GaAs interface. The reflectance R differs for the two polarizations. The angle characterized by the minimum in reflectance for Rp is called the “Brewster Angle”.

2.3. Principle of Ellipsometry

In Fig. 3 the basic principle of ellipsometry is illustrated schematically. As light source (here a He-Ne laser with λ = 632.8nm) is used, which emitts unpolarized light. This light is linearly polarized by a polarizer (operated at a fixed azimuth angle of 45°) and can optionally be zircu- larly polarized by a so-called quarterwave plate (compensator). The light beam will hit the sample (simplest case: substrate + dielectric layer on top) at a defined angle ρ. Angles in the vicinity of the Brewster angle are best suited to yield good measurement results, since ellip- sometry is most sensitive to film parameters in this range. The light will penetrate into the layer until it reaches the interface between the layer and the substrate, where it will be reflected parially. Finally the beam leaves the layer under the same exit angle as the incidence angle ρ. If a wave of light travels in a dielectric medium, it will exhibit changes in its properties. The amplitude of both polarization directions (Ês and Êp) will change as will the phase Δ between both polarizations. The beam will then reach a rotat- ing analyzer, which allows to measure the reflectance for all phases Δ. Eventually a photo- detector will measure the intensity of the incoming light beam as a function of the angle of the rotating analyzer. Measurement results are usually expressed in terms of the ellipsometric parameters Δ and Ψ, which are defined by R tanψ e −i∆ = p , (4) Rs where Rs and Rp are the reflectance of the s- and p-polarization. Finally the recorded data is

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B508: Ellipsometry transferred to a computer for the calculation of layer thickness(es) and/or refractive indices.

Figure 3: Schematic illustration of the ellipsometer working principle (after [1]).

One question remains: How are the properties of a wave changed when propagating through a dielectric material? Since answering this question in detail would exceed the time limitations of this lab course, we will give a qualitative description of the processes to give a better un- derstanding of the experiment and to point out how this gained knowledge should influence the execution of our experiments. Fig. 4 shows a schematic view of the light propagation in an ellipsometer experiment. A light wave traveling in a medium of refractive index n0 is impinging on a dielectric layer (n1) on top of a substrate (n2). The light will partially be reflected, illustrated here by the reflection coeffi- cient r01, the remaining fraction will be transmitted, represented by the transmission coeffi- cient t01. The transmitted fraction will penetrate through the dielectric layer to the interface between layer and substrate. There the light will again be partially reflected and transmitted, represented by the coefficients r12 and t12 respectively. This process will be repeated again and again, thus multiple beams will leave the sample and contribute to the measurement result. To calculate the thickness of the layer or its refractive index from the intensities of the reflected light involves a huge amount of straightforward mathematics and therefore is done by special ellipsometer software.

For allpying a "simple" theory the substrate should be infinitely thick, in practice this is obvi- ously not possible. If the substrate is a dielectric material (i.e. absorption = 0), e.g. glass, all the light that is transmitted through the n1 / n2 interface can penetrate through the substrate and be reflected from the bottom side. Therefore this fraction of the incident light also "finds a way" through the sample to the detector and can thus influence the measurement. Since this influence is not desired, the backside of transparent substrates is usually blackened to reduce the reflection from the backside of the substrate.

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B508: Ellipsometry

Figure 4: Schematic illustration of the multi-reflection of an incident beam on a thin dielec- tric layer, as in the case of an ellipsometer measurement. The beam is partially reflected at the interface of an incident medium n0 and a thin layer of refractive index n1, the rest of the beam is transmitted to the thin layer. The transmitted beam will undergo further reflections and or transmissions at different interfaces (n0 / n1 interface and between n1 and the substrate n2), resulting in multiple beams leaving the sample towards an detector and therefore influencing the measurement.

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B508: Ellipsometry

3. The experiment

3.1. Devices / Samples

PLASMOS SD2300 Ellipsometer

We will investigate 4 types of thin films on different substrates:

Sample # Thin Film Layer Substrate 1 SiO2 Si 2 Porous Si #1 Si 3 Porous Si #2 Si 4 TiO2 Glass

The complex refractive indices for all layers and substrates can be found in Appendix A. The refractive index n for the porous silicon samples can be estimated according to the simplest case of the Brüggemann approximation by adding the refractive indices for silicon and air weighted by their respective volume fractions. The porosity of the porous silicon (Psi) sample 1 is ≈ 90 %, for sample 2 it is ≈ 40 %. For k the value of bulk silicon can be taken.

3.2. Performing the experiment

• Estimate the refractive index n for the porous silicon samples. • Calculate the Brewster angles for the given sample substrates and estimate the Pseudo- Brewster angles of the samples. • Set up the ellipsometer and the ellipsometer software, the polarizer has to be manually aligned to 45° with the help of the adviser. • Implement the model for the system(s) to be analyzed in the ellipsometer software, i.e. put in values for the number of layers and the complex refractive indices of the layer(s) and the substrate (Important: k-values have to be put in as –k in the software!). • Measure the film thickness d and the refractive index n of the layers at four different angles of incidence ρ (40°, 50°, 60°, and 70°). Perform five measurements at each angle and sam- ple.

4. Evaluation of the experiment

• Plot the layer thickness d and the refractive index n as a function of the incidence angle ρ for the measured samples. • Calculate the statistic error of a regular measurement from the respective 5 measurements per sample and angle (Add error bars into the plots). • Estimate the measurement error induced by changing the incidence angle ρ. • Discuss which measurement contains the most reliable data for each sample based on the

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B508: Ellipsometry

results of the error evaluation. • Discuss possible reasons why the thin layer shows larger errors than the thicker layers.

5. Bibliography

[1] Operating Manual – PLASMOS SD 2300, PLASMOS GmbH, München, 1993

[2] Ellipsometry and polarized light, R.M.A. Azzam and N.M. Bashara, Elsevier Science, Amsterdam, 1987

[3] J.A. Woollam Co., Inc. / www.jawoollam.com

[4] Optics (3rd edition), E. Hecht, Addison Wesley Longman, Reading, 1998

Appendix A – Refractive Index for selected materials

Material n k Si 3.875 0.018 SiO2 1.455 0 TiO2 2.88 0 Glass 1.5 0

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