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Ellipsometry

Ellipsometry is a very sensitive optical method for the characterization of surfaces and thin film layers. It makes use of the fact that the polarization state of light may change upon reflection from a surface, and that this change carries information about the surface’s properties. Paul Drude published first papers about ellipsometry in 1886. In the 20th century, his basic principles evolved into a powerful technique for optical sample characterization. Today, ellipsometry is an established technology to measure multilayer film thicknesses, refractive index, and absorption.

Paul Drude, Lehrbuch der Optik, Leipzig, 1906

Ellipsometry in short

  • Based on polarization light, ellipsometry is the most sensitive and non-destructive optical method to characterize ultra-thin films.
  • The layer thicknesses of the analyzed samples may be many times smaller than the wavelength of the probing light.
  • Ellipsometers measure two angles, ψ and Δ that describe the sample’s reflectivity and the sample induced phase change for p- and s-polarized light
  • By optical modeling, ψ and Δ transfer into a number of physical parameters like layer thickness, refractive index, absorption, or various other physical parameters.

Ellipsometry in detail

Basic Principles of Ellipsometry

Ellipsometry in general makes use of the fact that the polarization state of light may change when a light beam is reflected from a sample’s surface. Ellipsometry analyzes this change of the state of polarization, and from that, it yields information about thin film layers that are often even thinner than the wavelength of the probing light. A basic ellipsometer consists of a light source, a polarization state generator (PSG) placed in the beam path before the sample, a polarization state analyzer (PSA) placed in the beam path behind the sample, and a photo detector (c. fig. 1). The PSG and PSA control and analyze the polarization states of the probing and the reflected light, respectively. Many different types of PSGs and PSAs exist. Fig. 1 shows a very common design where the PSA consists of a linear polarizer and a quarter-wave plate (λ/4-plate), and the PSA is a sole linear polarizer.

Sketch of a basic setup of an ellipsometer. An objective lens and a camera are only needed for imaging ellipsometry – Image provided by Accuriuon GmbH, Germany.
Figure 1: Sketch of a basic setup of an ellipsometer. An objective lens and a camera are only needed for imaging ellipsometry.

In ellipsometry, the probing beam hits the sample under an oblique angle of incidence. Consequently, the sample’s reflectivity and the phase change induced to the probing beam are different for light with linear polarization within and perpendicular to the plane of incidence, respectively (so-called p- and s- polarisation, c. fig. 2). Ellipsometry measures both the ratio of the reflectivity and the relative phase change of the p- and s-components, and yields these quantities as so-called ellipsometric angles ψ and Δ:
 

tan Ψ = Rp/Rs
 

Δ δpδs
 

(Rp, Rs reflectivity of and δp, δs sample induced phase change on p- and s-components).

If the ellipsometer applies the type of PSG and PSA as shown in fig. 1, the sample’s ellipsometric angles ψ and Δ are measured by altering the rotational angles of polarization optics that are placed in the beam path.

Orientations of p- and s-polarization in an ellipsometric coordinate system. Image provided by Accuriuon GmbH, Germany.
Figure 2: Orientations of p- and s-polarization in an ellipsometric coordinate system.

High Sensitivity for Thin Film Characterization

Ellipsometry is a powerful tool for the characterization of thin film layers as the ellipsometric angles ψ and Δ strongly depend on the film’s properties like its layer thickness, refractive index, and absorption. A simple example is the case of a single thin film layer on a substrate. The outgoing wave is a superposition of the waves reflected from the ambient-film interface (top level interface) and multiple reflection that occur inside the thin film layer (c. fig. 3). Due to this interference, rather small changes of the so-called optical path length of the partial waves caused by variations of the layer thickness, refractive index, or absorption result in relatively large changes of the amplitude (related to the reflectivity R) and the phase (and thus the above mentioned phase change δ) of the outgoing wave.

Contributions to the outgoing wave by multiple reflections in a single thin film layer (N1) placed between an ambient material (N0) and a  thick substrate (N12). – Image provided by Accuriuon GmbH, Germany.
Figure 3: Contributions to the outgoing wave by multiple reflections in a single thin film layer (N1) placed between an ambient material (N0) and a thick substrate (N12).

This picture of superimposing waves holds separately for both p- and s-polarization but the numbers for the reflectivity and phase shifts at the single interfaces are different for the two cases due to Fresnel’s equaitons. The overall result is the strong dependency of ψ and Δ on the thin film layer’s parameters. As an example for the demonstration of layer thickness sensitivity, the calculated dependency of ψ and Δ on layer thickness for a single silicon dioxide film on a silicon substrate is shown in fig. 4.  

Dependency of ellipsometric angles on the change of thin film layer thickness demonstrated by example: ψ and Δ of a single layer of silicon dioxide (SiO2) on a crystalline silicon (c-Si) substrate [calculated with the ACCURION Software 'EP4 Model']. – Image provided by Accuriuon GmbH, Germany.
Figure 4: Dependency of ellipsometric angles on the change of thin film layer thickness demonstrated by example: ψ and Δ of a single layer of silicon dioxide (SiO2) on a crystalline silicon (c-Si) substrate [calculated with the ACCURION Software 'EP4 Model'].

Data Analysis in Ellipsometry

Ellipsometry is an indirect method for thin film characterization as the ellipsometric measurements only yield the sample’s values of ψ and Δ. As illustrated in fig. 5, these values are then put into a computer based model of the sample to calculate layer thicknesses, refractive index, absorption, and a variety of other sample properties, including morphology, crystal quality, chemical composition, or electrical conductivity.

Since the software for data analysis deduces the information of interest - namely the sample’s physical properties - from the measured data set of ψ and Δ, this software is of great importance for the overall performance of an ellipsometric device. One should always have in mind that even a wrong model for the sample might deliver an acceptable fit but of course, the resultant parameters are useless in that case. Both a good-trained user and a powerful, reliable and easy to use modeling software ensure that an appropriate model is applied for fitting and that the data analysis yields the correct results.

Flow chart of ellipsometric measurement and data analysis – Image provided by Accuriuon GmbH, Germany.
Figure 5: Flow chart of ellipsometric measurement and data analysis.
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