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Ellipsometry is an
optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entitie ...
technique for investigating the
dielectric In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force i ...

dielectric
properties (complex
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
or
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
) of
thin film A thin film is a layer of material ranging from fractions of a nanometer one nanometric Scanning_Tunneling_Microscope.html"_;"title="carbon_nano_tube,_photographed_with_Scanning_Tunneling_Microscope">carbon_nano_tube,_photographed_with_Scannin ...
s. Ellipsometry measures the change of
polarization Polarization or polarisation may refer to: In the physical sciences *Polarization (waves), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of ...
upon reflection or transmission and compares it to a model. It can be used to characterize
composition Composition or Compositions may refer to: Arts * Composition (dance), practice and teaching of choreography * Composition (music), an original piece of music and its creation *Composition (visual arts) The term composition means "putting togethe ...
,
roughness
roughness
, thickness (depth),
crystalline nature
crystalline nature
, doping concentration,
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current An electric current is a stream of charged particle In p ...
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 In electrodynamics Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carri ...
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 Paul Karl Ludwig Drude (; 12 July 1863 – 5 July 1906) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of in ...

Paul Drude
and has many applications today. The first documented use of the term "ellipsometry" was in 1945.


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
reflected
, absorbed, scattered, or transmitted). 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. Upon the analysis of the change of
polarization Polarization or polarisation may refer to: In the physical sciences *Polarization (waves), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of ...
of light, ellipsometry can yield information about layers that are thinner than the
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wavelength
of the probing light itself, even down to a single
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
ic layer. Ellipsometry can probe the complex
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
or
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
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 The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...

angstrom
s or tenths of a
nanometer file:EM Spectrum Properties edit.svg, 330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its derived scales. The nanometre is often used to express dimensions on an atomic scale and mostly in the Mo ...
to several
micrometerMicrometer can mean: * Micrometer (device) A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for Accuracy and precision, accurate measurement of components in mechanical engineeri ...
s with an excellent accuracy.


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 In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
or
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
tensor). Although optical techniques are inherently
diffraction-limited , who approximated the diffraction limit of a microscope as d=\frac, where ''d'' is the resolvable feature size, ''λ'' is the wavelength of light, ''n'' is the index of refraction of the medium being imaged in, and ''θ'' (depicted as ''α'' in the ...
, ellipsometry exploits
phase Phase or phases may refer to: Science * State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter) In the physical sciences, a phase is a region of space (a thermodynamic system A thermodynamic system is a ...
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 Homogeneity and heterogeneity are concepts often used in the sciences Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about th ...
and
isotropic Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
. 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.


Experimental setup

Electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

Electromagnetic radiation
is emitted by a light source and linearly polarized by a
polarizer A polarizer or polariser is an optical filter An optical filter is a device that selectively transmits light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perc ...

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 an 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 Reflections on still water are an example of specular reflection. Specular reflection, or regular reflection, is the mirror Grange, East Yorkshire, UK, from World War I. The mirror magnified the sound of approaching enemy Zeppelins for a ...
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 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 "" (perpendicular).


Data acquisition

Ellipsometry measures the complex reflectance ratio \rho of a system, which may be parametrized by the amplitude component \Psi and the phase difference \Delta. 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
reflectionReflection or reflexion may refer to: Philosophy * Self-reflection Science * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal r ...
and normalized to their initial value, are denoted by r_s and r_p respectively. The angle of incidence is chosen close to the
Brewster angle Brewster's angle (also known as the polarization angle) is an angle of incidence (optics), angle of incidence at which light with a particular Polarization (waves), polarization is perfectly transmitted through a transparent dielectric surface, wi ...

Brewster angle
of the sample to ensure a maximal difference in r_p and r_s. Ellipsometry measures the complex reflectance ratio \rho (a complex quantity), which is the ratio of r_p over r_s: : \rho = \frac = \tan \Psi \cdot e^. Thus, \tan\Psi is the amplitude ratio upon
reflectionReflection or reflexion may refer to: Philosophy * Self-reflection Science * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal r ...
, and \Delta is the phase shift (difference). (Note that the right side of the equation is simply another way to represent a complex number.) 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.


Data analysis

Ellipsometry is an indirect method, i.e. in general the measured \Psi and \Delta cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed, for example the Forouhi Bloomer 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 \Psi and \Delta is only possible in very simple cases of
isotropic Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
,
homogeneous Homogeneity and heterogeneity are concepts often used in the sciences Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about th ...
and infinitely thick films. In all other cases a layer model must be established, which considers the optical constants (
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
or
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
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 \Psi and \Delta values are calculated using the
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perception, percei ...

Fresnel equations
. The calculated \Psi and \Delta values which match the experimental data best provide the optical constants and thickness parameters of the sample.


Definitions

Modern ellipsometers are complex instruments that incorporate a wide variety of radiation sources, detectors, digital electronics and software. The range of wavelength employed is far in excess of what is visible so strictly these are no longer optical instruments.


Single-wavelength vs. spectroscopic ellipsometry

Single-wavelength ellipsometry employs a
monochromatic during the 1889 Exposition Universelle File:Parrot EGA monochrome palette.png, A photograph of a μονόχρωμος.html" ;"title="lightness">values of one color). The term ''monochrome'' comes from the grc">μονόχρωμος">monochrom ...

monochromatic
light source. This is usually a
laser A laser is a device that emits light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as h ...

laser
in the
visible Visibility is in meteorology, a measure of the distance at which an object or light can be seen. Visibility may also refer to: * Visual perception ** Naked-eye visibility * A measure of turbidity in water quality control * Interferometric visibili ...
spectral region, for instance, a
HeNe laser
HeNe laser
with a
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

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 \Psi and \Delta values per measurement. Spectroscopic ellipsometry (SE) employs broad band light sources, which cover a certain spectral range in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior ...

infrared
, visible or
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, ...

ultraviolet
spectral region. By that the complex
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
or the
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
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 In , a phonon is a in a periodic, arrangement of s or s in , specifically in s and some s. Often referred to as a , it is an in the of the for elastic structures of interacting particles. Phonons can be thought of as quantized , similar to ...
) and free
charge carrier In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Phy ...
(
plasmon In physics, a plasmon is a quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity ( physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is refe ...
) properties. Spectroscopic ellipsometry in the near infrared, visible up to ultraviolet spectral region studies the
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
in the transparency or below-
band-gap
band-gap
region and electronic properties, for instance, band-to-band transitions or
exciton An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force. It is an electrically neutral quasiparticle that exists in Electrical insulation, insulators, ...

exciton
s.


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 In condensed matter physics Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science th ...

amorphous
materials or
crystalline A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the least amount of kinet ...

crystalline
materials with a
cubic crystal File:Kubisches_Kristallsystem.jpg, 200px, A network model of a primitive cubic system In crystallography, the cubic (or isometric) crystal system is a crystal system where the Crystal_structure#Unit_cell, unit cell is in the shape of a cube. This i ...
structure. Standard ellipsometry is also sufficient for optically
uniaxial In optics, an index ellipsoid is a diagram of an ellipsoid that depicts the orientation and relative magnitude of refractive index, refractive indices in a crystal . The equation for the ellipsoid is constructed using the electric displacement fie ...

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 (depolarization)

There are typically two different ways of mathematically describing how an electromagnetic wave interacts with the elements within an ellipsometer (including the sample): the Jones matrix and the Mueller matrix formalisms. In the Jones matrix formalism, the electromagnetic wave is described by a Jones vector with two orthogonal complex-valued entries for the electric field (typically E_x and E_y), and the effect that an optical element (or sample) has on it is described by the complex-valued 2×2 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 also gives the amount of depolarization. Reasons for depolarization are, for instance, thickness non-uniformity or backside-reflections from a transparent substrate.


Advanced experimental approaches


Imaging ellipsometry

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 In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
. Advanced imaging ellipsometer technology operates on the principle of classical null ellipsometry and real-time ellipsometric contrast imaging. Imaging ellipsometry is based on the concept of nulling. In ellipsometry, the film under investigation is placed onto a reflective substrate. The film and the substrate have different refractive indexes. In order to obtain data about film thickness, the light reflecting off of the substrate must be nulled. Nulling is achieved by adjusting the analyzer and polarizer so that all reflected light off of the substrate is extinguished. Due to the difference in refractive indexes, this will allow the sample to become very bright and clearly visible. The
light source Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nano ...
consists of a monochromatic laser of the desired wavelength. A common wavelength that is used is 532 nm green laser light. Since only intensity of light measurements are needed, almost any type of camera can be implemented as the CCD, which is useful if building an ellipsometer from parts. Typically, imaging ellipsometers are configured in such a way so that the laser (L) fires a beam of light which immediately passes through a linear polarizer (P). The linearly polarized light then passes through a quarter wavelength compensator (C) which transforms the light into elliptically polarized light. This elliptically polarized light then reflects off the sample (S), passes through the analyzer (A) and is imaged onto a CCD camera by a long working distance objective. The analyzer here is another polarizer identical to the P, however, this polarizer serves to help quantify the change in polarization and is thus given the name analyzer. This design is commonly referred to as a LPCSA configuration. The orientation of the angles of P and C are chosen in such a way that the elliptically polarized light is completely linearly polarized after it is reflected off the sample. For simplification of future calculations, the compensator can be fixed at a 45 degree angle relative to the plane of incidence of the laser beam. This set up requires the rotation of the analyzer and polarizer in order to achieve null conditions. The ellipsometric null condition is obtained when A is perpendicular with respect to the polarization axis of the reflected light achieving complete destructive interference, 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 obtained are used to determine the Ψ and Δ values of the material. : \Psi = A and \Delta = 2P + \pi/2, where ''A'' and ''P'' are the angles of the analyzer and polarizer under null conditions respectively. By rotating the analyzer and polarizer and measuring the change in intensities of light over the image, analysis of the measured data by use of computerized optical modeling can lead to a deduction of spatially resolved film thickness and complex refractive index values. Due to the fact that the imaging is done at an angle, only a small line of the entire field of view is actually in focus. The line in focus can be moved along the field of view by adjusting the focus. In order to analyze the entire region of interest, the focus must be incrementally moved along the region of interest with a photo taken at each position. All of the images are then compiled into a single, in focus image of the sample.


In situ ellipsometry

In situ ''In situ'' (; often not italicized in English) is a Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicar ...

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, including calcium phosphate mineralization at the air-liquid interface, 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. 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 materials, organic industry (encapsulated
organic light-emitting diode An organic light-emitting diode (OLED or organic LED), also known as organic electroluminescent (organic EL) diode, is a light-emitting diode A light-emitting diode (LED) is a semiconductor A semiconductor material has an v ...
s) as well as in the coating industry using 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 Conducting is the art of directing a musical performance, such as an orchestral or Choir, choral concert. It has been defined as "the art of directing the simultaneous performance of several players or singers by the use of gesture." The primar ...
samples. By applying an external
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

magnetic field
it is possible to determine independently the
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...
, the optical
mobility Mobility may refer to: Social sciences and humanities * Economic mobility, ability of individuals or families to improve their economic status * Geographic mobility, the measure of how populations and goods move over time * Mobilities, a contempo ...
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.


Applications

This technique has found applications in many different fields, from
semiconductor A semiconductor material has an electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric curre ...
physics to
microelectronics Microelectronics is a subfield of electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electron is a subatomic particle In physica ...
and
biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms, Development ...

biology
, from basic research to industrial applications. Ellipsometry is a very sensitive measurement technique and provides unequaled capabilities for thin film
metrology Metrology is the scientific study of measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events ...

metrology
. As an optical technique, spectroscopic ellipsometry is non-destructive and contactless. Because the incident radiation can be focused, small sample sizes can be imaged and desired characteristics can be mapped over a larger area (m2).


Advantages

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. * By using polarized light, normal ambient unpolarized
stray lightStray light is light in an optical system, which was not intended in the design. The light may be from the intended source, but follow paths other than intended, or it may be from a source other than the intended source. This light will often set a w ...
does not significantly influence the measurement, no dark box is necessary. * No reference measurement is necessary. * Both real and imaginary part of the
dielectric function In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
(or complex
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

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.


See also

* Photo-reflectance *
Petrographic microscope Leica DMRX incident light microscope with mechanical stage and Swift F automated point counter for analysis of organic composition of coal and rock samples A petrographic microscope is a type of optical microscope The optical microsco ...
*
Polarimetry Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interac ...

Polarimetry
*
Spectroscopy Spectroscopy is the study of the interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way ...

Spectroscopy


References


Further reading

* R. M. A. Azzam and N. M. Bashara, ''Ellipsometry and Polarized Light'', Elsevier Science Pub Co (1987) * A. Roeseler, ''Infrared Spectroscopic Ellipsometry'', Akademie-Verlag, Berlin (1990), * 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) * 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), * H. G. Tompkins and E. A. Irene (Editors), ''Handbook of Ellipsometry'' William Andrews Publications, Norwich, NY (2005), * H. Fujiwara, '' Spectroscopic Ellipsometry: Principles and Applications'', John Wiley & Sons Inc (2007), * M. Losurdo and K. Hingerl (Editors), ''Ellipsometry at the Nanoscale'', Springer (2013), * K. Hinrichs and K.-J. Eichhorn (Editors), ''Ellipsometry of Functional Organic Surfaces and Films'', Springer (2014), {{ISBN, 978-3-642-40128-2 Optical metrology Radiometry Spectroscopy