# Ellipsometry
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{{Short description|Optical technique for characterizing thin films}}
[[File:Ellipsometer at LAAS.jpg|thumb|An Ellipsometer at [LAAS-CNRS](/source/Laboratory_for_Analysis_and_Architecture_of_Systems) in Toulouse, France]]
'''Ellipsometry''' is an [optical](/source/optical) technique for investigating the [dielectric](/source/dielectric) properties (complex [refractive index](/source/refractive_index) or [dielectric function](/source/dielectric_function)) of [thin film](/source/thin_film)s. Ellipsometry measures the change of [polarization](/source/Polarization_(waves)) upon reflection or transmission and compares it to a model.
It can be used to characterize [composition](/source/Materials_science), [roughness](/source/Surface_roughness), thickness (depth), [crystalline nature](/source/Crystalline), [doping concentration](/source/Doping_(semiconductor)), [electrical conductivity](/source/electrical_conductivity) and other material properties. It is very sensitive to the change in the optical response of incident radiation that interacts with the material being investigated.
A spectroscopic ellipsometer can be found in most thin film analytical labs. 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.
==Etymology==
The name "ellipsometry" stems from the fact that [elliptical polarization](/source/elliptical_polarization) of light is used. The term "spectroscopic" relates to the fact that the information gained is a function of the light's wavelength or energy (spectra). The technique has been known at least since 1888 by the work of [Paul Drude](/source/Paul_Drude)[P. Drude, Ueber die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbirender Krystalle, Annalen der Physik, Volume 268, Issue 12, 1887, Pages: 584–625, DOI: 10.1002/andp.18872681205; Ueber Oberflächenschichten. I. Theil, Annalen der Physik, Volume 272, Issue 2, 1889, Pages: 532–560, DOI: 10.1002/andp.18892720214; Ueber Oberflächenschichten. II. Theil, Annalen der Physik, Volume 272, Issue 4, 1889, Pages: 865–897, DOI: 10.1002/andp.18892720409 (in German).] and has many applications today.
The first documented use of the term "ellipsometry" was in 1945.[{{Cite journal|last=Rothen|first=Alexandre|date=1945|title=The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films|url=|journal=Review of Scientific Instruments|volume=16|issue=2|pages=26–30|doi=10.1063/1.1770315|bibcode=1945RScI...16...26R |issn=0034-6748}}]{{Primary source inline|date=September 2021}}
==Basic principles==
The measured signal is the change in polarization as the incident radiation (in a known state) interacts with the material structure of interest ([reflected](/source/Reflected_light), [absorbed](/source/Absorption_(electromagnetic_radiation)), [scattered](/source/Scattered_radiation), or [transmitted](/source/Transmitted_light)). The polarization change is quantified by the amplitude ratio, Ψ, and the phase difference, Δ (defined below). Because the signal depends on the thickness as well as the material properties, ellipsometry can be a universal tool for contact free determination of thickness and optical constants of films of all kinds.[{{cite book|author1=Harland Tompkins|author2=Eugene A Irene|title=Handbook of Ellipsometry|url=https://books.google.com/books?id=6PQf1fSzHHEC|date=6 January 2005|publisher=William Andrew|isbn=978-0-8155-1747-4}}]
Upon the analysis of the change of [polarization](/source/Polarization_(waves)) of light, ellipsometry can yield information about layers that are thinner than the [wavelength](/source/wavelength) of the probing light itself, even down to a single [atom](/source/atom)ic layer. Ellipsometry can probe the complex [refractive index](/source/refractive_index) or [dielectric function](/source/dielectric_function) tensor, which gives access to fundamental physical parameters like those listed above. It is commonly used to characterize film thickness for single layers or complex multilayer stacks ranging from a few [angstrom](/source/angstrom)s or tenths of a [nanometer](/source/nanometer) to several [micrometer](/source/micrometre)s with an excellent accuracy.[{{Cite web|url=https://www.jawoollam.com/resources/ellipsometry-tutorial/thin-film-thickness|title=Thin Film Thickness|access-date=29 November 2025|website=J A Woollam|archive-url=https://web.archive.org/web/20250622181517/https://www.jawoollam.com/resources/ellipsometry-tutorial/thin-film-thickness|archive-date=22 June 2025|url-status=live}}]
==Experimental details==
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](/source/refractive_index) or [dielectric function](/source/dielectric_function) tensor). Although optical techniques are inherently [diffraction-limited](/source/Diffraction-limited_system), ellipsometry exploits [phase](/source/phase_(waves)) information (polarization state), and can achieve sub-nanometer resolution. In its simplest form, the technique is applicable to thin films with thickness of less than a nanometer to several micrometers. Most models assume the sample is composed of a small number of discrete, well-defined layers that are optically [homogeneous](/source/Homogeneity_(physics)) and [isotropic](/source/isotropic). Violation of these assumptions requires more advanced variants of the technique (see below).
Methods of immersion or multiangular ellipsometry are applied to find the optical constants of the material with rough sample surface or presence of inhomogeneous media. New methodological approaches allow the use of reflection ellipsometry to measure physical and technical characteristics of gradient elements in case the surface layer of the optical detail is inhomogeneous.[{{cite journal|url=http://ntv.ifmo.ru/en/article/13460/primenenie_metoda_ellipsometrii_v_optikeneodnorodnyh_sred.htm|title=Ellipsometry method application in optics of inhomogeneous media. |author1=Gorlyak A.N. |author2=Khramtsovky I.A. |author3=Solonukha V.M. |journal=Scientific and Technical Journal of Information Technologies, Mechanics and Optics|volume=15|issue=3|pages=378–386|year=2015|doi=10.17586/2226-1494-2015-15-3-378-386 |doi-access=free}}]
===Experimental setup===
thumb|right|400px|Schematic setup of an ellipsometry experiment
[Electromagnetic radiation](/source/Electromagnetic_radiation) is emitted by a light source and linearly polarized by a [polarizer](/source/polarizer). It can pass through an optional compensator ([retarder](/source/Wave_plate), [quarter wave plate](/source/wave_plate)) and falls onto the sample. After reflection the radiation passes a compensator (optional) and a second polarizer, which is called an analyzer, and falls into the detector. Instead of the compensators, some ellipsometers use a [phase-modulator](/source/Photoelastic_modulator) in the path of the incident light beam. Ellipsometry is a [specular](/source/Specular_reflection) optical technique (the [angle of incidence](/source/angle_of_incidence_(optics)) equals the angle of reflection). The incident and the reflected beam span the ''plane of incidence''. Light which is polarized parallel to this plane is named ''p-polarized''. A polarization direction perpendicular is called ''s-polarized'' (''s''-polarised), accordingly. The "''s''" is contributed from the German "{{lang|de|senkrecht}}" (perpendicular).
{{See also|Fresnel equations}}
===Data acquisition===
Ellipsometry measures the complex reflectance ratio of a system, which may be parametrized by the amplitude component and the phase difference . 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](/source/Reflection_(physics)) and normalized to their initial value, are denoted by and respectively. The angle of incidence is chosen close to the [Brewster angle](/source/Brewster_angle) of the sample to ensure a maximal difference in and .[Butt, Hans-Jürgen, Kh Graf, and Michael Kappl. "Measurement of Adsorption Isotherms". Physics and Chemistry of Interfaces. Weinheim: Wiley-VCH, 2006. 206-09.] Ellipsometry measures the complex reflectance ratio (a complex quantity), which is the ratio of over :
:
Thus, is the amplitude ratio upon [reflection](/source/Reflection_(physics)), and is the phase shift (difference). It is helpful to note that the right side of the equation is another way to represent a [complex number](/source/complex_number). Since ellipsometry is measuring the ratio (or difference) of two values rather than the absolute value of either, it is less sensitive to variation than other optical techniques, making it robust and reproducible. For instance, it is relatively insensitive to scatter and fluctuations and requires no standard sample or reference beam.
===Data analysis===
Ellipsometry is an indirect method, i.e. in general the measured and cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed, for example the [Forouhi Bloomer model](/source/Forouhi%E2%80%93Bloomer_model). This is one weakness of ellipsometry. Models can be physically based on energy transitions or simply free parameters used to fit the data.
Direct inversion of and is only possible in very simple cases of [isotropic](/source/isotropic), [homogeneous](/source/wiktionary%3AHomogeneity) and infinitely thick films. In all other cases a layer model must be established, which considers the optical constants ([refractive index](/source/refractive_index) or [dielectric function](/source/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 and values are calculated using the [Fresnel equations](/source/Fresnel_equations). The calculated and values which match the experimental data best provide the optical constants and thickness parameters of the sample.[{{Cite book|title=Spectroscopic Ellipsometry: Principles and Applications|last=Fujiwara|first=Hiroyuki|publisher=wiley|year=2007|isbn=9780470060186|pages=147–208|url=https://www.google.com/books/edition/Spectroscopic_Ellipsometry/tTMn0NKcpjsC?hl=en&gbpv=1&dq=Spectroscopic+Ellipsometry&printsec=frontcover}}]
==Definitions==
Modern ellipsometers are complex instruments that incorporate a wide variety of radiation sources, detectors, digital electronics and software. The range of wavelength employed may be far in excess of what is visible to human eyes.
===Single-wavelength vs. spectroscopic ellipsometry===
Single-wavelength ellipsometry (SWE) employs a [monochromatic](/source/monochromatic) light source, which is usually a [laser](/source/laser) in the [visible](/source/visible_spectrum) spectral region, for instance, a [HeNe laser](/source/HeNe_laser) with a [wavelength](/source/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, and is more precise than Spectroscopic ellipsometry. 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 only two parameters (one set of and values per measurement).[{{Cite book|title=A practical guide to optical metrology for thin films|last=Quinten|first=Michael|publisher=Wiley-VCH, Weinheim|year=2012|isbn=9783527664344|url=https://www.google.com/books/edition/A_Practical_Guide_to_Optical_Metrology_f/v3Sl6HHmOuUC?hl=en&gbpv=1}}] Due to these limitations, SWE is limited to a single layer system.
By contrast Spectroscopic ellipsometry (SE) employs broad band light sources, which cover the [infrared](/source/infrared), visible and/or [ultraviolet](/source/ultraviolet) spectral region. By that the complex [refractive index](/source/refractive_index) or the [dielectric function](/source/dielectric_function) tensor in the corresponding spectral region can be obtained. Infrared spectroscopic ellipsometry (IRSE) can probe lattice vibrational ([phonon](/source/phonon)) and free [charge carrier](/source/charge_carrier) ([plasmon](/source/plasmon)) properties. Spectroscopic ellipsometry in the near infrared, visible up to ultraviolet spectral region studies the [refractive index](/source/refractive_index) in the transparency or below-[band-gap](/source/Band_gap) region and electronic properties, for instance, band-to-band transitions or [exciton](/source/exciton)s.[{{cite journal | last1=Braeuninger-Weimer | first1=P. | title=Fast, Noncontact, Wafer-Scale, Atomic Layer Resolved Imaging of Two-Dimensional Materials by Ellipsometric Contrast Micrography | journal=ACS Nano | volume=12 | pages=8555–8563 | year=2018 }}][{{cite journal | last1=Albersdörfer | first1=A. | title=High resolution imaging microellipsometry of soft surfaces at 3 µm lateral and 5 Å normal resolution | journal=Applied Physics Letters | volume=72 | page=2930 | year=1998 }}][{{cite journal | last1=Funke | first1=S. | title=Spectroscopic imaging ellipsometry for automated search of flakes of mono- and n-layers of 2D-materials | journal=Applied Surface Science | volume=421 | pages=435–439 | year=2017 }}][{{cite journal | last1=Wurstbauer | first1=U. | title=Imaging ellipsometry of graphene | journal=Applied Physics Letters | volume=97 | page=231901 | year=2010 }}][{{cite journal | last1=Magnozzi | first1=M. | title=Local Optical Properties in CVD-Grown Monolayer WS2 Flakes | journal=The Journal of Physical Chemistry C | volume=125 | pages=16059–16065 | year=2021 }}]
In contrast to classical ellipsometry, IE captures thousands of data points simultaneously, inherently producing two-dimensional data maps. Ψ-Δ or [Mueller matrix](/source/Mueller_calculus) values can be produced for each pixel by applying algorithms for standard or generalized ellipsometry (e.g. nulling or rotating compensator).
These can be converted into physical material properties like film thickness, [refractive index](/source/Refractive_index), [anisotropy](/source/Anisotropy) or [depolarization](/source/Depolarizer_(optics)) using optical modelling software.
[{{cite journal | last1=Meng | first1=Y. H. | last2=Jin | first2=G. | title=Rotating compensator sampling for spectroscopic imaging ellipsometry | journal=Thin Solid Films | volume=519 | pages=2742–2745 | year=2011 }}][{{cite journal | last1=Käseberg | first1=T. | title=Imaging Mueller matrix ellipsometry setup for optical nanoform metrology | journal=EPJ Web of Conferences | volume=238 | pages=06006 | year=2020 }}][{{cite journal | last1=Duwe | first1=M. | title=Thin-film metrology of tilted and curved surfaces by imaging Mueller-matrix ellipsometry | journal=Journal of Vacuum Science & Technology B | volume=37 | pages=062908 | year=2019 }}][{{cite journal | last1=Funke | first1=S. | title=Determining the Dielectric Tensor of Microtextured Organic Thin Films by Imaging Mueller Matrix Ellipsometry | journal=The Journal of Physical Chemistry Letters | pages=3053–3058 | year=2021 | doi=10.1021/acs.jpclett.1c00317 | pmc=8041376 }}]
A wide variety of suitable light sources is routinely used with IE. These range from monochromatic [laser](/source/Laser) devices, to multi-wavelength assemblies of high-power light-emitting diodes ([LEDs](/source/Light-emitting_diode)), to continuously tunable sources. Imaging Spectroscopic Ellipsometry (ISE) combines the features of IE with the advantages of [spectroscopic](/source/Spectroscopy) optical characterization. ISE is typically employed in the spectral range between 190 nm and 1700 nm, due to technological restrictions of imaging components and sensors. It has become a powerful tool in many disciplines of modern science and technology, particularly in 2D material research, [MEMS](/source/MEMS) applications, and display inspection.[{{cite journal | last1=Meng | first1=Y. | title=Spectroscopic imaging ellipsometry for characterization of nanofilm pattern on Si substrate | journal=Chinese Optics Letters | volume=8 | page=114 | year=2010 }}][{{cite journal | last1=Funke | first1=S. | title=Imaging spectroscopic ellipsometry of MoS2 | journal=Journal of Physics: Condensed Matter | volume=28 | page=385301 | year=2016 }}][{{cite journal | last1=Matković | first1=A. | title=Spectroscopic imaging ellipsometry and Fano resonance modeling of graphene | journal=Journal of Applied Physics | volume=112 | page=123523 | year=2012 }}][{{cite journal | last1=Ermolaev | first1=G. A. | title=Giant optical anisotropy in transition metal dichalcogenides for next-generation photonics | journal=Nature Communications | volume=12 | page=854 | year=2021 }}]
===In situ ellipsometry===
[In situ](/source/In_situ) ellipsometry refers to dynamic measurements during the modification process of a sample. This process can be used to study, for instance, the growth of a thin film,[P. Koirala, D. Attygalle, P. Aryal, P. Pradhan, J. Chen, S. Marsillac, A.S. Ferlauto, N.J. Podraza, R.W. Collins, "Real time spectroscopic ellipsometry for analysis and control of thin film
polycrystalline semiconductor deposition in photovoltaics"] including calcium phosphate mineralization at the air-liquid interface,[R. Shahlori, A. R. J. Nelson, G. I. N. Waterhouse, D. J. McGillivray, "Morphological, chemical and kinetic characterisation of zein protein-induced biomimetic calcium phosphate films"] 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 wavelengths in the studied spectral range simultaneously.
===Ellipsometric porosimetry===
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.[{{Cite web|url=https://semilab.com/category/products/ellipsometric-porosimetry-rd|title=Semilab | Products|website=semilab.com}}] The EP technique is unique in its ability to measure porosity of very thin films down to 10 nm, 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-κ](/source/low-%CE%BA_dielectric) materials, organic industry (encapsulated [organic light-emitting diode](/source/organic_light-emitting_diode)s) as well as in the coating industry using [sol gel](/source/sol_gel) techniques.
=== Magneto-optic generalized ellipsometry ===
Magneto-optic generalized ellipsometry (MOGE) is an advanced infrared spectroscopic ellipsometry technique for studying free charge carrier properties in [conducting](/source/electrical_conductor) samples. By applying an external [magnetic field](/source/magnetic_field) it is possible to determine independently the [density](/source/electron_density), the optical [mobility](/source/electron_mobility) parameter and the [effective mass](/source/effective_mass_(solid-state_physics)) parameter of [free charge carrier](/source/charge_carrier)s. Without the magnetic field only two out of the three [free charge carrier](/source/charge_carrier) parameters can be extracted independently.
=== Ellipsometry in semiconductor manufacturing ===
Using spectroscopic ellipsometry an analysis method first developed for semiconductors has been adopted more widely. In this method complex multi-layers stacks made of multiple mediums are capable of being measured at the same time if each layer has known optical properties. Because of the optical properties are known, all of the unknowns are wavelength independent. In this case, a linear regression can be applied to and , from which one can extract the thickness of all layers, as well as the volume fractions.[{{Cite journal|url=https://pubs.acs.org/doi/10.1021/ac00216a721|title=Ellipsometry for Thin-Film and Surface Analysis|last=Collins|first=Robert W.|journal=Analytical Chemistry|issue=17|volume=62|date=1990-09-01|last2=Kim|first2=Yeon-Taik|url-access=subscription}}]
This method works well in semiconductor manufacturing because a library of known [Refractive index (n)](/source/Refractive_index) and [Extinction coefficient (k)](/source/Optical_extinction_coefficient) for the materials used during manufacturing can be developed. In the case of semiconductor development where the material properties are unknown, this process can be used in reverse, and it is possible to extract the n and k values by measuring the thickness of the sample using another technique such as TEM. These material properties can then be used to measure the thickness of future samples of the same material.