is a versatile and powerful optical
technique for the investigation of the dielectric
properties (complex refractive index
or dielectric function
) of thin films. It has applications in many different fields, from semiconductor
physics to microelectronics
, from basic research to industrial applications. Ellipsometry is a very sensitive measurement technique and provides unequalled capabilities for thin film metrology
. As an optical technique, spectroscopic ellipsometry is non-destructive
Upon the analysis of the change of polarization of light, which is reflected off a sample, 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. It 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 with an excellent accuracy.
The name "ellipsometry" stems from the fact that the most general state of polarization is elliptic. The technique has been known for almost a century, and has many standard applications today. However, ellipsometry is also becoming more interesting to researchers in other disciplines such as biology and medicine. These areas pose new challenges to the technique, such as measurements on unstable liquid surfaces and microscopic imaging.
Ellipsometry measures the change of polarization
. Typically, ellipsometry is done only in the reflection setup. The exact nature of the polarization change 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. In its simplest form, the technique is applicable to thin films with thickness less than a nanometer to several micrometers. The sample must be composed of a small number of discrete, well-defined layers that are optically Homogeneity and isotropic.
Violation of these assumptions will invalidate the standard ellipsometric modeling procedure, and more advanced variants of the technique must be applied (see below).
Electromagnetic radiation is emitted by a light source and linearly polarized by a polarizer. It can pass through an optional compensator (retarder, quarter wave plate) and falls onto the sample. After reflection the radiation passes a compensator (optional) and a second polarizer, which is called analyzer, and falls into the detector. Instead of the compensators some ellipsometers use a phase-modulator in the path of the incident light beam. 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. Light, which is polarized parallel or perpendicular to the plane of incidence, is called p or s polarized, respectively.
(Standard) Ellipsometry measures two of the four Stokes parameters
, which are conventionally denoted by
. 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
components, after reflection
and normalized to their initial value, are denoted by
, respectively. Ellipsometry measures the ratio of
, which is described by the fundamental equation of ellipsometry:
is the amplitude ratio upon reflection
is the phase shift (difference). Since ellipsometry is measuring the ratio (or difference) of two values (rather than the absolute value of either), it is very robust, accurate, and reproducible. For instance, it is relatively insensitive to scatter and fluctuations, and requires no standard sample or reference beam.
Ellipsometry is an indirect method, i.e. in general the measured
cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed. Direct inversion of
is only possible in very simple cases of isotropic
and infinitely thick films. In all other 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
values are calculated using the Fresnel equations
. The calculated
values, which match the experimental data best, provide the optical constants and thickness parameters of the sample.
Single-wavelength vs. spectroscopic ellipsometry
Single-wavelength ellipsometry employs 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. The advantage of laser ellipsometry is that laser beams can be focused on a small spot size. Furthermore, lasers have a higher power than broad band light sources. Therefore, laser ellipsometry can be used for imaging (see below). However, the experimental output is restricted to one set of
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. By that 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. Infrared spectroscopic ellipsometry (IRSE) can probe lattice vibrational (phonon
) and free charge carrier
) properties. Spectroscopic ellipsometry in the near infrared, visible up to ultraviolet spectral region studies the refractive index
in the transparency or below-band-gap
region and electronic properties, for instance, band-to-band transitions or excitons
Standard vs. generalized ellipsometry (anisotropy)
Standard ellipsometry (or just short '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, for instance, amorphous
materials or crystalline
materials with a cubic crystal
structure. Standard ellipsometry is also sufficient for optically uniaxial
samples in the special case, 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 are arbitrarily aligned, optically uniaxial
samples, or optically biaxial samples.
Jones matrix vs. Mueller matrix formalism (Depolarisation)
There are two different ways of describing mathematically, how an electromagnetic wave
interacts with a sample, the Jones matrix
and the Mueller matrix
formalism. In the Jones matrix
formalism the electromagnetic wave
before and after interaction is described by Jones vectors
with two complex-valued entries, and their transformation is described by the complex-valued 2x2 Jones matrix
. In the Mueller matrix
formalism the electromagnetic wave
is described by Stokes vectors
with four real-valued entries, and their transformation is described by the real-valued 4x4 Mueller matrix
. When no depolarization
occurs both formalisms are fully consistent. Therefore, for non-depolarizing samples the simpler Jones matrix
formalism is sufficient. If the sample is depolarizing the Mueller matrix
formalism should be used, because it gives additionally access to the amount of depolarization
. Reasons for depolarization
are, for instance, thickness non-uniformity or backside-reflections from a transparent substrate.
Advanced experimental approaches
Ellipsometry can also be done as imaging ellipsometry
by using a CCD
camera as a detector. This provides a real time contrast image of the sample, which provides information about film thickness and refractive index
. Advanced imaging ellipsometer technology operates on the principle of classical null ellipsometry and real-time ellipsometric contrast imaging, using a single-wavelength ellipsometer setup with a laser as light source
. The laser beam gets elliptically polarized after passing a linear polarizer
(P) and a quarter-wave plate (C). The elliptically polarized light is reflected off the sample (S), passes an analyzer (A) and is imaged onto a CCD camera by a long working distance objective. In this PCSA configuration, the orientation of the angles of P and C is chosen in such a way that the elliptically polarized light is completely linearly polarized after it is reflected off the sample. The ellipsometric null condition is obtained when A "crosses" O with respect to the polarization axis of the reflected light, i.e., the state at which the absolute minimum of light flux is detected at the CCD camera. The angles of P, C, and A that obtained the null condition are related to the optical properties of the sample. Analysis of the measured data with computerized optical modeling leads to a deduction of spatially resolved film thickness and complex refractive index values.
In situ ellipsometry
ellipsometry refers to dynamic measurements during the modification process of a sample. This process can be, for instance, the growth of a thin film, etching or cleaning of a sample. By in situ ellipsometry measurements it is possible to determine fundamental process parameters, such as, growth or etch rates, variation of optical properties with time. In situ ellipsometry measurements require a number of additional considerations: The sample spot is usually not as easily accessible as for ex situ measurements outside the process chamber. Therefore, the mechanical setup has to be adjusted, which can include additional optical elements (mirrors, prisms, or lenses) for redirecting or focusing the light beam. Because the environmental conditions during the process can be harsh, the sensitive optical elements of the ellipsometry setup must be separated from the hot zone. In the simplest case this is done by optical view ports, though strain induced birefringence of the (glass-) windows has to be taken into account or minimized. Furthermore, the samples can be at elevated temperatures, which implies different optical properties compared to samples at room temperature. Despite all these problems, in situ ellipsometry becomes more and more important as process control technique for thin film deposition and modification tools. In situ ellipsometers can be of single-wavelength or spectroscopic type. Spectroscopic in situ ellipsometers use multichannel detectors, for instance CCD detectors, which measure the ellipsometric parameters for all wavelength in the studied spectral range simultaneously.
Ellipsometric porosimetry measures the change of the optical properties and thickness of the materials during adsorption and desorption of a volatile species at atmospheric pressure or under reduced pressure depending on the application. The EP technique is unique in its ability to measure porosity of very thin films down to 10nm, its reproducibility and speed of measurement. Compared to traditional porosimeters, Ellipsometer porosimeters are well suited to very thin film pore size and pore size distribution measurement. Film porosity is a key factor in silicon based technology using low-k
materials, organic industry (encapsulated OLED
's) as well as in the coating industry using Sol gel
Magneto-optic generalized ellipsometry
Magneto-optic generalized ellipsometry (MOGE) is an advanced infrared spectroscopic ellipsometry technique for studying free charge carrier properties in conducting
samples. By applying an external magnetic field
it is possible to determine independently the density
, the optical mobility
parameter and the effective mass
parameter of free charge carriers
. Without the magnetic field only two out of the three free charge carrier
parameters can be extracted independently.
Ellipsometry has a number of advantages compared to standard reflection intensity measurements:
- Ellipsometry measures at least two parameters at each wavelength of the spectrum. If generalized ellipsometry is applied up to 16 parameters can be measured at each wavelength.
- Ellipsometry measures an intensity ratio instead of pure intensities. Therefore, ellipsometry is less affected by intensity instabilities of the light source or atmospheric absorption.
- No reference measurement is necessary.
- Both real and imaginary part of the dielectric function (or complex refractive index) can be extracted without the necessity to perform a Kramers–Kronig analysis.
Ellipsometry is especially superior to reflectivity measurements when studying anisotropic samples.
- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier Science Pub Co (1987) ISBN 0-444-87016-4
- A. Roeseler, Infrared Spectroscopic Ellipsometry, Akademie-Verlag, Berlin (1990), ISBN 3-05-500623-2
- H. G. Tompkins, A Users's Guide to Ellipsometry, Academic Press Inc, London (1993), ISBN 0-12-693950-0
- H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry, John Wiley & Sons Inc (1999) ISBN 0-471-18172-2
- I. Ohlidal and D. Franta, Ellipsometry of Thin Film Systems, in Progress in Optics, vol. 41, ed. E. Wolf, Elsevier, Amsterdam, 2000, pp. 181–282
- M. Schubert, Infrared Ellipsometry on semiconductor layer structures: Phonons, Plasmons, and Polaritons, Series: Springer Tracts in Modern Physics, Vol. 209, Springer (2004), ISBN 3-540-23249-4
- H. G. Tompkins and E. A. Irene (Editors), Handbook of Ellipsometry William Andrews Publications, Norwich, NY (2005), ISBN 0-8155-1499-9
- H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications, John Wiley & Sons Inc (2007), ISBN 0-470-01608-6