Editing Ellipsometry (section)

==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]] or [[dielectric function]] tensor). Although optical techniques are inherently [[Diffraction-limited system|diffraction-limited]], ellipsometry exploits [[phase (waves)|phase]] 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 [[Homogeneity (physics)|homogeneous]] and [[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.<ref>{{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}}</ref>

===Experimental setup===
[[Image:Ellipsometry setup.svg|thumb|right|400px|Schematic setup of an ellipsometry experiment]]
[[Electromagnetic radiation]] is emitted by a light source and linearly polarized by a [[polarizer]]. It can pass through an optional compensator ([[Wave plate|retarder]], [[wave plate|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 [[Photoelastic modulator|phase-modulator]] in the path of the incident light beam. Ellipsometry is a [[Specular reflection|specular]] optical technique (the [[angle of incidence (optics)|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 "{{lang|de|senkrecht}}" (perpendicular).

{{See also|Fresnel equations}}

===Data acquisition===
Ellipsometry measures the complex reflectance ratio <math>\rho</math> of a system, which may be parametrized by the amplitude component <math>\Psi</math> and the phase difference <math>\Delta</math>. 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 (physics)|reflection]] and normalized to their initial value, are denoted by <math>r_s</math> and <math>r_p</math> respectively. The angle of incidence is chosen close to the [[Brewster angle]] of the sample to ensure a maximal difference in <math>r_p</math> and <math>r_s</math>.<ref>Butt, Hans-Jürgen, Kh Graf, and Michael Kappl. "Measurement of Adsorption Isotherms". Physics and Chemistry of Interfaces. Weinheim: Wiley-VCH, 2006. 206-09.</ref> Ellipsometry measures the complex reflectance ratio <math>\rho</math> (a complex quantity), which is the ratio of  <math>r_p</math> over <math>r_s</math>:
: <math>\rho = \frac{r_p}{r_s} = \tan \Psi \cdot e^{i\Delta}.</math>
Thus, <math>\tan\Psi</math> is the amplitude ratio upon [[Reflection (physics)|reflection]], and <math>\Delta</math> 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 <math>\Psi</math> and <math>\Delta</math> cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed, for example the [[Forouhi–Bloomer model|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 <math>\Psi</math> and <math>\Delta</math> is only possible in very simple cases of [[isotropic]], [[wiktionary:Homogeneity|homogeneous]] 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 <math>\Psi</math> and <math>\Delta</math> values are calculated using the [[Fresnel equations]]. The calculated <math>\Psi</math> and <math>\Delta</math> values which match the experimental data best provide the optical constants and thickness parameters of the sample.