Spectroscopic Ellipsometry Methodology

The FilmTek™ 2000SE spectroscopic ellipsometer simultaneously solves for refractive index n(l), extinction coefficient k(l), and film thicknesses of multi-layer film structures.  A self-consistent solution is obtained by using SCI’s generalized dispersion formula to model fitted values of the dielectric function e (l).  The SCI dispersion formula is quite general and applies to metallic, amorphous, crystalline, and dielectric materials (Figures 1-3).  This approach allows the user to model complex multi-layer structures with reflection/transmission or ellipsometric data.  Global optimization methods are used to obtain the best solution while avoiding local minima and minimizing sensitivity to the user’s initial guess of fitted parameters (e.g., layer thickness).  The FilmTek™ 2000SE spectroscopic ellipsometer optimizes both the ellipsometric data and power density spectrum (FFT) simultaneously which allows for accurate thickness determination over a wide range of film thickness (1Å to 150µm).

Fig. 1 n and k spectra of Silicon

Fig. 2 n and k spectra of SiO2

Fig. 3 n and k spectra of Tantalum

Related Information

Spectroscopic Ellipsometry Background

Ellipsometry is a versatile and powerful optical technique for the investigation of the dielectric properties (complex refractive index or dielectric function) of thin films. Ellipsometry has applications in many different fields, from semiconductor physics to microelectronics and biology, from basic research to industrial applications. Ellipsometry is a very sensitive measurement technique and provides unequalled capabilities for thin film measurement.  Spectroscopic Ellipsometry is non-destructive and contactless. Ellipsometry can yield information about layers that are thinner than the wavelength of the probing light itself, even down to a single atomic layer or less. Ellipsometry can probe the complex refractive index or dielectric function tensor, which gives access to fundamental physical parameters and is related to a variety of sample properties, including morphology, crystal quality, chemical composition, or electrical conductivity. Ellipsometry is commonly used to characterize film thickness for single layers or complex multilayer stacks ranging from a few angstroms or tenths of a nanometer to several micrometers.

Ellipsometry measures the change of polarization upon reflection or transmission. The name "ellipsometry" stems from the fact that the most general state of polarization is elliptic. The ellipsometry technique has been known for almost a century, and has many standard applications today. Ellipsometry is also becoming more interesting to researchers in other disciplines such as biology and medicine. Typically, ellipsometry is performed in the reflection setup. The exact nature of the polarization change in ellipsometry is determined by the sample's properties (thickness, complex refractive index or dielectric function tensor). Although optical techniques are inherently diffraction limited, ellipsometry exploits phase information and the polarization state of light, and can achieve angstrom resolution. Ellipsometry is applicable to thin films with thickness less than a nanometer to several micrometers. In ellipsometry the sample must be composed of a small number of discrete, well-defined layers that are optically homogeneous and isotropic. Violation of these assumptions will invalidate the standard ellipsometric modeling procedure, and more advanced variants of the ellipsometric technique must be applied.

In ellipsometry, electromagnetic radiation is emitted by a light source and linearly polarized by a polarizer. It can pass through a compensator (retarder, quarter wave plate) and falls onto the sample. After reflection the radiation passes a second polarizer, which is called analyzer, and falls into the detector. Ellipsometry is a specular optical technique (the angle of incidence equals the angle of reflection). The incident and the reflected beam span the plane of incidence. Standard ellipsometry measures two of the four Stokes parameters, which are conventionally denoted by Ψ and Δ. The polarization state of the light incident upon the sample may be decomposed into an s and a p component (the s component is oscillating perpendicular to the plane of incidence and parallel to the sample surface, and the p component is oscillating parallel to the plane of incidence). The amplitudes of the s and p components, after reflection and normalized to their initial value, are denoted by r_s and r_p, respectively. Ellipsometry measures the ratio of r_s and r_p. TanΨ is the amplitude ratio upon reflection, and Δ is the phase shift (difference). Since ellipsometry is measuring the ratio (or difference) of two values (rather than the absolute value of either), ellipsometry is very robust, accurate, and reproducible. For instance, ellipsometry is relatively insensitive to scatter and fluctuations, and requires no standard sample or reference beam.

Ellipsometry is an indirect method.  That is, the measured Ψ and Δ cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed with ellipsometry. Direct inversion of Ψ and Δ is only possible in very simple cases of isotropic, homogeneous and infinitely thick films. In all other ellipsometry cases a layer model must be established, which considers the optical constants (refractive index or dielectric function tensor) and thickness parameters of all individual layers of the sample including the correct layer sequence. Using an iterative procedure (least-squares minimization) unknown optical constants and/or thickness parameters are varied, and Ψ and Δ values are calculated using the Fresnel equations. The calculated Ψ and Δ values, which match the experimental ellipsometric data best, provide the optical constants and thickness parameters of the sample.

Single wavelength ellipsometry uses a monochromatic light source. This is usually a laser in the visible spectral region, for instance, a HeNe laser with a wavelength of 632.8 nm. Therefore, single-wavelength ellipsometry is also called laser ellipsometry. However, the experimental output is restricted to one set of Ψ and Δ values per measurement. Spectroscopic ellipsometry (SE) employs broad band light sources, which cover a certain spectral range in the infrared, visible, or ultraviolet spectral region. With spectroscopic ellipsometry the complex refractive index or the dielectric function tensor in the corresponding spectral region can be obtained, which gives access to a large number of fundamental physical properties.

Standard vs. Generalized Ellipsometry

Standard ellipsometry (or just 'ellipsometry') is applied when no s-polarized light is converted into p-polarized light, nor vice versa.  This is the case for optically isotropic samples such as amorphous materials or crystalline materials with a cubic crystal structure. Standard ellipsometry is also sufficient for optically uniaxial samples when the optical axis is aligned parallel to the surface normal. In all other cases, when s-polarized light is converted into p-polarized light and/or vice versa, the generalized ellipsometry approach must be applied. Examples for generalized ellipsometry are arbitrarily aligned, optically uniaxial samples, or optically biaxial samples.

Spectroscopic Ellipsometry References

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier Science Pub Co (1987).

H. G. Tompkins, A Users's Guide to Ellipsometry, Academic Press Inc, London (1993).

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry, John Wiley & Sons Inc (1999).

H. G. Tompkins and E. A. Irene (Editors), Handbook of Ellipsometry, William Andrews Publications, Norwich, NY (2005).