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.
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.
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 = δp−δs
(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.
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.
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.
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.
More about spectroscopic-ellipsometry.