Absorption edge

An absorption edge, absorption discontinuity or absorption limit is a sharp discontinuity in the absorption spectrum of a substance. These discontinuities occur at wavelengths where the energy of an absorbed photon corresponds to an electronic transition or ionization potential. When the quantum energy of the incident radiation becomes smaller than the work required to eject an electron from one or other quantum states in the constituent absorbing atom, the incident radiation ceases to be absorbed by that state. For example, incident radiation on an atom of a wavelength that has a corresponding energy just below the binding energy of the K-shell electron in that atom cannot eject the K-shell electron.[1]

References

1. ^ "The Penguin Dictionary of Physics", 3rd ed., Longman Group Ltd. (2000), p. 3.
Anomalous X-ray scattering

Anomalous X-ray scattering AXRS or XRAS is a non-destructive determination technique within X-ray diffraction that makes use of the anomalous dispersion that occurs when a wavelength is selected that is in the vicinity of an absorption edge of one of the constituent elements of the sample. It is used in materials research to study nanometer sized differences in structure.

Anomalous scattering

In X-ray crystallography, anomalous scattering refers to a change in a diffracting X-ray’s phase that is unique from the rest of the atoms in a crystal due to strong X-ray absorbance. The amount of energy that individual atoms absorb depends on their atomic number. The relatively light atoms found in proteins such as carbon, nitrogen, and oxygen do not contribute to anomalous scattering at normal X-ray wavelengths used for X-ray crystallography. Thus, in order to observe anomalous scattering, a heavy atom must be native to the protein or a heavy atom derivative should be made. In addition, the X-ray’s wavelength should be close to the heavy atom’s absorption edge.

Atomic form factor

In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space (also known as reciprocal space). For an object with spatial density distribution, ${\displaystyle \rho (\mathbf {r} )}$, the form factor, ${\displaystyle f(\mathbf {Q} )}$, is defined as

${\displaystyle f(\mathbf {Q} )=\int \rho (\mathbf {r} )e^{i\mathbf {Q} \cdot \mathbf {r} }\mathrm {d} ^{3}\mathbf {r} }$,

where ${\displaystyle \rho (\mathbf {r} )}$ is the spatial density of the scatterer about its center of mass (${\displaystyle \mathbf {r} =0}$), and ${\displaystyle \mathbf {Q} }$ is the momentum transfer. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer ${\displaystyle \rho }$ in real space ${\displaystyle \mathbf {r} }$, the narrower the distribution of ${\displaystyle f}$ in ${\displaystyle \mathbf {Q} }$; i.e., the faster the decay of the form factor.

For crystals, atomic form factors are used to calculate the structure factor for a given Bragg peak of a crystal.

Electro-absorption modulator

An electro-absorption modulator (EAM) is a semiconductor device which can be used for modulating the intensity of a laser beam via an electric voltage. Its principle of operation is based on the Franz-Keldysh effect, i.e., a change in the absorption spectrum caused by an applied electric field, which changes the bandgap energy (thus the photon energy of an absorption edge) but usually does not involve the excitation of carriers by the electric field.

For modulators in telecommunications, small size and modulation voltages are desired. The EAM is candidate for use in external modulation links in telecommunications. These modulators can be realized using either bulk semiconductor materials or materials with multiple quantum dots or wells.

Most EAMs are made in the form of a waveguide with electrodes for applying an electric field in a direction perpendicular to the modulated light beam. For achieving a high extinction ratio, one usually exploits the Quantum-confined Stark effect (QCSE) in a quantum well structure.

Compared with an Electro-optic modulator (EOM), an EAM can operate with much lower voltages (a few volts instead of ten volts or more). They can be operated at very high speed; a modulation bandwidth of tens of gigahertz can be achieved, which makes these devices useful for optical fiber communication. A convenient feature is that an EAM can be integrated with distributed feedback laser diode on a single chip to form a data transmitter in the form of a photonic integrated circuit. Compared with direct modulation of the laser diode, a higher bandwidth and reduced chirp can be obtained.

Semiconductor quantum well EAM is widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1THz. Here, the NIR absorption of undoped quantum well was modulated by strong electric field with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency-and power- dependent NIR absorption line. The THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quantum coherence may yield new applications for quantum well modulators in optical communications.

Recently, advances in crystal growth have triggered the study of self organized quantum dots. Since the EAM requires small size and low modulation voltages, possibility of obtaining quantum dots with enhanced electro-absorption coefficients makes them attractive for such application.

Electro-optic effect

An electro-optic effect is a change in the optical properties of a material in response to an electric field that varies slowly compared with the frequency of light. The term encompasses a number of distinct phenomena, which can be subdivided into

a) change of the absorption

Electroabsorption: general change of the absorption constants

Franz-Keldysh effect: change in the absorption shown in some bulk semiconductors

Quantum-confined Stark effect: change in the absorption in some semiconductor quantum wells

Electrochromic effect: creation of an absorption band at some wavelengths, which gives rise to a change in colour

b) change of the refractive index and permittivity

Pockels effect (or linear electro-optic effect): change in the refractive index linearly proportional to the electric field. Only certain crystalline solids show the Pockels effect, as it requires lack of inversion symmetry

Kerr effect (or quadratic electro-optic effect, QEO effect): change in the refractive index proportional to the square of the electric field. All materials display the Kerr effect, with varying magnitudes, but it is generally much weaker than the Pockels effect

electro-gyration: change in the optical activity.

Electron-refractive effect or EIPMIn December 2015, two further electro-optic effects of type (b) were theoretically predicted to exist but have not, as yet, been experimentally observed.

Changes in absorption can have a strong effect on refractive index for wavelengths near the absorption edge, due to the Kramers–Kronig relation.

Using a less strict definition of the electro-optic effect allowing also electric fields oscillating at optical frequencies, one could also include nonlinear absorption (absorption depends on the light intensity) to category a) and the optical Kerr effect (refractive index depends on the light intensity) to category b). Combined with the photoeffect and photoconductivity, the electro-optic effect gives rise to the photorefractive effect.

The term "electro-optic" is often erroneously used as a synonym for "optoelectronic".

Extended X-ray absorption fine structure

X-ray Absorption Spectroscopy (XAS) includes both Extended X-Ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES). XAS is the measurement of the x-ray absorption coefficient (${\displaystyle \mu (E)}$ in the equations below) of a material as a function of energy. X-rays of a narrow energy resolution are shone on the sample and the incident and transmitted x-ray intensity is recorded as the incident x-ray energy is incremented. The number of x-ray photons that are transmitted through a sample (It) is equal to the number of x-ray photons shone on the sample (I0) multiplied by a decreasing exponential that depends on the type of atoms in the sample, the absorption coefficient ${\displaystyle \mu }$, and the thickness of the sample ${\displaystyle x}$.

${\displaystyle I_{t}=I_{0}e^{-\mu x}}$

The absorption coefficient is obtained by taking the log ratio of the incident x-ray intensity to the transmitted x-ray intensity.

${\displaystyle \mu ={\frac {-\mathrm {ln} ({I}_{t}/{I}_{0})}{x}}}$

When the incident x-ray energy matches the binding energy of an electron of an atom within the sample, the number of x-rays absorbed by the sample increases dramatically, causing a drop in the transmitted x-ray intensity. This results in an absorption edge. Each element on the periodic table has a set of unique absorption edges corresponding to different binding energies of its electrons, giving XAS element selectivity. XAS spectra are most often collected at synchrotrons. Because X-rays are highly penetrating, XAS samples can be gases, solids or liquids. And because of the brilliance of synchrotron X-ray sources the concentration of the absorbing element can be as low as a few ppm.

EXAFS spectra are displayed as graphs of the absorption coefficient of a given material versus energy, typically in a 500 – 1000 eV range beginning before an absorption edge of an element in the sample. The x-ray absorption coefficient is usually normalized to unit step height. This is done by regressing a line to the region before and after the absorption edge, subtracting the pre-edge line from the entire data set and dividing by the absorption step height, which is determined by the difference between the pre-edge and post-edge lines at the value of E0 (on the absorption edge).

The normalized absorption spectra are often called XANES spectra. These spectra can be used to determine the average oxidation state of the element in the sample. The XANES spectra are also sensitive to the coordination environment of the absorbing atom in the sample. Finger printing methods have been used to match the XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate to the amount of each of the known standard spectra within an unknown sample.

X-ray absorption spectra are produced over the range of 200 – 35,000 eV. The dominant physical process is one where the absorbed photon ejects a core photoelectron from the absorbing atom, leaving behind a core hole. The atom with the core hole is now excited. The ejected photoelectron's energy will be equal to that of the absorbed photon minus the binding energy of the initial core state. The ejected photoelectron interacts with electrons in the surrounding non-excited atoms.

If the ejected photoelectron is taken to have a wave-like nature and the surrounding atoms are described as point scatterers, it is possible to imagine the backscattered electron waves interfering with the forward-propagating waves. The resulting interference pattern shows up as a modulation of the measured absorption coefficient, thereby causing the oscillation in the EXAFS spectra. A simplified plane-wave single-scattering theory has been used for interpretation of EXAFS spectra for many years, although modern methods (like FEFF, GNXAS) have shown that curved-wave corrections and multiple-scattering effects can not be neglected. The photelectron scattering amplitude in the low energy range (5-200 eV) of the photoelectron kinetic energy become much larger so that multiple scattering events become dominant in the XANES (or NEXAFS) spectra.

The wavelength of the photoelectron is dependent on the energy and phase of the backscattered wave which exists at the central atom. The wavelength changes as a function of the energy of the incoming photon. The phase and amplitude of the backscattered wave are dependent on the type of atom doing the backscattering and the distance of the backscattering atom from the central atom. The dependence of the scattering on atomic species makes it possible to obtain information pertaining to the chemical coordination environment of the original absorbing (centrally excited) atom by analyzing these EXAFS data.

Franz–Keldysh effect

The Franz–Keldysh effect is a change in optical absorption by a semiconductor when an electric field is applied. The effect is named after the German physicist Walter Franz and Russian physicist Leonid Keldysh (nephew of Mstislav Keldysh).

Karl W. Böer observed first the shift of the optical absorption edge with electric fields during the discovery of high-field domains and named this the Franz-effect. A few months later, when the English translation of the Keldysh paper became available, he corrected this to the Franz–Keldysh effect.As originally conceived, the Franz–Keldysh effect is the result of wavefunctions "leaking" into the band gap. When an electric field is applied, the electron and hole wavefunctions become Airy functions rather than plane waves. The Airy function includes a "tail" which extends into the classically forbidden band gap. According to Fermi's golden rule, the more overlap there is between the wavefunctions of a free electron and a hole, the stronger the optical absorption will be. The Airy tails slightly overlap even if the electron and hole are at slightly different potentials (slightly different physical locations along the field). The absorption spectrum now includes a tail at energies below the band gap and some oscillations above it. This explanation does, however, omit the effects of excitons, which may dominate optical properties near the band gap.

The Franz–Keldysh effect occurs in uniform, bulk semiconductors, unlike the quantum-confined Stark effect, which requires a quantum well. Both are used for electro-absorption modulators. The Franz–Keldysh effect usually requires hundreds of volts, limiting its usefulness with conventional electronics – although this is not the case for commercially available Franz–Keldysh-effect electro-absorption modulators that use a waveguide geometry to guide the optical carrier.

Hafnium disulfide

Hafnium disulfide is an inorganic compound of hafnium and sulfur. It is a layered dichalcogenide with the chemical formula is HfS2. A few atomic layers of this material can be exfoliated using the standard Scotch Tape technique (see graphene) and used for the fabrication of a field-effect transistor. High-yield synthesis of HfS2 has also been demonstrated using liquid phase exfoliation, resulting in the production of stable few-layer HfS2 flakes. Hafnium disulfide powder can be produced by reacting hydrogen sulfide and hafnium oxides at 500–1300 °C.

Johannes Martin Bijvoet

Johannes Martin Bijvoet ForMemRS (23 January 1892, Amsterdam – 4 March 1980, Winterswijk) was a Dutch chemist and crystallographer at the van 't Hoff Laboratory at Utrecht University. He is famous for devising a method of establishing the absolute configuration of molecules. In 1946 he became member of the Royal Netherlands Academy of Arts and Sciences.

The concept of tetrahedrally bound carbon in organic compounds stems back to the work by van 't Hoff and Le Bel in 1874. At this time, it was impossible to assign the absolute configuration of a molecule by means other than referring to the projection formula established by Fischer, who had used glyceraldehyde as the prototype and assigned randomly its absolute configuration.

In 1949 Bijvoet outlined his principle, which relies on the anomalous dispersion of X-ray radiation. Instead of the normally observed elastic scattering of X-rays when they hit an atom, which generates a scattered wave of the same energy but with a shift in phase, X-ray radiation near the absorption edge of an atom creates a partial ionisation process. Some new X-ray radiation is generated from the inner electron shells of the atoms. The X-ray radiation already being scattered is interfered with by the new radiation, both amplitude and phase being altered. These additional contributions to the scattering may be written as a real part ${\displaystyle \Delta }$f' and an imaginary one, ${\displaystyle \Delta }$f". Whereas the real part is either positive or negative, the imaginary is always positive, resulting in an addition to the phase angle.

In 1951, using an X-ray tube with a zirconium target, Bijvoet and his coworkers Peerdeman and van Bommel achieved the first experimental determination of the absolute configuration of sodium rubidium tartrate. In this compound, rubidium atoms were the ones close to the absorption edge. In their later publication in Nature,[citation needed] entitled "Determination of the absolute configuration of optically active compounds by means of X-rays", the authors conclude that:

"The result is that Emil Fisher's convention, which assigned the configuration of FIG. 2 to the dextrorotatory acid appears to answer the reality."

thus confirming the preceding decades of stereochemical assignments. The determination of absolute configuration is nowadays achieved using "soft" X-ray radiation, most often generated with a copper target (which generates X-rays with a characteristic wavelength of 154 pm). Shorter wavelengths make the observable differences in measured intensities smaller, thereby making the distinction of absolute configuration more difficult. The measurement of absolute configuration is also facilitated by the presence of atoms heavier than oxygen.

X-ray diffraction is still considered the ultimate proof of absolute structure, but other techniques such as circular dichroism spectroscopy are often used as faster alternatives.

Moss–Burstein effect

The Moss–Burstein effect, also known as the Burstein-Moss shift, is the phenomenon of which the apparent band gap of a semiconductor is increased as the absorption edge is pushed to higher energies as a result of some states close to the conduction band being populated. This is observed for a degenerate electron distribution such as that found in some Degenerate semiconductors and is known as a Moss–Burstein shift.

The effect occurs when the electron carrier concentration exceeds the conduction band edge density of states, which corresponds to degenerate doping in semiconductors. In nominally doped semiconductors, the Fermi level lies between the conduction and valence bands. For example, in n-doped semiconductor, as the doping concentration is increased, electrons populate states within the conduction band which pushes the Fermi level to higher energy. In the case of degenerate level of doping, the Fermi level lies inside the conduction band. The "apparent" band gap of a semiconductor can be measured using transmission/reflection spectroscopy. In the case of a degenerate semiconductor, an electron from the top of the valence band can only be excited into conduction band above the Fermi level (which now lies in conduction band) since all the states below the Fermi level are occupied states. Pauli's exclusion principle forbids excitation into these occupied states. Thus we observe an increase in the apparent band gap. Apparent band gap = Actual band gap + Moss-Burstein shift (as shown in the figure).

Negative Burstein shifts can also occur. These are due to band structure changes due to doping.

Piezochromism

Piezochromism describes the tendency of certain materials to change color with the application of pressure. This effect is closely related to the electronic band gap change, which can be found in plastics, semiconductors (e.g. hybrid perovskites) and hydrocarbons.

Surface-extended X-ray absorption fine structure

Surface-extended X-ray absorption fine structure (SEXAFS) is the surface-sensitive equivalent of the EXAFS technique. This technique involves the illumination of the sample by high-intensity X-ray beams from a synchrotron and monitoring their photoabsorption by detecting in the intensity of Auger electrons as a function of the incident photon energy. Surface sensitivity is achieved by the interpretation of data depending on the intensity of the Auger electrons (which have an escape depth of ~1–2 nm) instead of looking at the relative absorption of the X-rays as in the parent method, EXAFS.

The photon energies are tuned through the characteristic energy for the onset of core level excitation for surface atoms. The core holes thus created can then be filled by nonradiative decay of a higher-lying electron and communication of energy to yet another electron, which can then escape from the surface (Auger emission). The photoabsorption can therefore be monitored by direct detection of these Auger electrons to the total photoelectron yield. The absorption coefficient versus incident photon energy contains oscillations which are due to the interference of the backscattered Auger electrons with the outward propagating waves. The period of this oscillations depends on the type of the backscattering atom and its distance from the central atom. Thus, this technique enables the investigation of interatomic distances for adsorbates and their coordination chemistry.

This technique benefits from long range order not being required, which sometimes becomes a limitation in the other conventional techniques like LEED (about 10 nm). This method also largely eliminates the background from the signal. It also benefits because it can probe different species in the sample by just tuning the X-ray photon energy to the absorption edge of that species. Joachim Stöhr played a major role in the initial development of this technique.

Synchrotron light source

A synchrotron light source is a source of electromagnetic radiation (EM) usually produced by a storage ring, for scientific and technical purposes. First observed in synchrotrons, synchrotron light is now produced by storage rings and other specialized particle accelerators, typically accelerating electrons. Once the high-energy electron beam has been generated, it is directed into auxiliary components such as bending magnets and insertion devices (undulators or wigglers) in storage rings and free electron lasers.

These supply the strong magnetic fields perpendicular to the beam which are needed to convert high energy electrons into photons.

The major applications of synchrotron light are in condensed matter physics, materials science, biology and medicine. A large fraction of experiments using synchrotron light involve probing the structure of matter from the sub-nanometer level of electronic structure to the micrometer and millimeter level important in medical imaging. An example of a practical industrial application is the manufacturing of microstructures by the LIGA process.

Water window

The water window is a region of the electromagnetic spectrum in which water is transparent to soft x-rays. The window extends from the K-absorption edge of carbon at 282 eV (68 PHz, 4.40 nm wavelength) to the K-edge of oxygen at 533 eV (129 PHz, 2.33 nm wavelength). Water is transparent to these X-rays, but carbon (and thus, organic molecules) is absorbing. These wavelengths could be used in an x-ray microscope for viewing living specimens.

X-ray absorption fine structure

X-ray absorption fine structure (XAFS) is a specific structure observed in X-ray absorption spectroscopy (XAS). By analyzing the XAFS, information can be acquired on the local structure and on the unoccupied local electronic states.

X-ray absorption near edge structure

X-ray absorption near edge structure (XANES), also known as near edge X-ray absorption fine structure (NEXAFS), is a type of absorption spectroscopy that indicates the features in the X-ray absorption spectra (XAS) of condensed matter due to the photoabsorption cross section for electronic transitions from an atomic core level to final states in the energy region of 50–100 eV above the selected atomic core level ionization energy, where the wavelength of the photoelectron is larger than the interatomic distance between the absorbing atom and its first neighbour atoms.

X-ray notation

X-ray notation is a method of labeling atomic orbitals that grew out of X-ray science. Also known as IUPAC notation, it was adopted by the International Union of Pure and Applied Chemistry in 1991 as a simplification of the older Siegbahn notation. In X-ray notation, every principal quantum number is given a letter associated with it. In many areas of physics and chemistry, atomic orbitals are described with spectroscopic notation (1s, 2s, 2p, 3s, 3p, etc.), but the more traditional X-ray notation is still used with most X-ray spectroscopy techniques including AES and XPS.

X-ray scattering techniques

X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an X-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy.

Note that X-ray diffraction is now often considered a sub-set of X-ray scattering, where the scattering is elastic and the scattering object is crystalline, so that the resulting pattern contains sharp spots analyzed by X-ray crystallography (as in the Figure). However, both scattering and diffraction are related general phenomena and the distinction has not always existed. Thus Guinier's classic text from 1963 is titled "X-ray diffraction in Crystals, Imperfect Crystals and Amorphous Bodies" so 'diffraction' was clearly not restricted to crystals at that time.

X-ray spectroscopy

X-ray spectroscopy is a general term for several spectroscopic techniques for characterization of materials by using x-ray excitation.

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