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Ellipsometry
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==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]] light source. This is usually a [[laser]] in the [[visible spectrum|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 <math>\Psi</math> and <math>\Delta</math> 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]] ([[plasmon]]) properties. Spectroscopic ellipsometry in the near infrared, visible up to ultraviolet spectral region studies the [[refractive index]] in the transparency or below-[[Band gap|band-gap]] region and electronic properties, for instance, band-to-band transitions or [[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]] 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 (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 <math>E_x</math> and <math>E_y</math>), and the effect that an optical element (or sample) has on it is described by the complex-valued 2Γ2 Jones matrix. In the Mueller matrix formalism, the electromagnetic wave is described by [[Stokes vector]]s 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.
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