# Photoelectron Spectroscopy

Typical PES system with hemisphere analyzer, X-ray tubes and various preparation methods

The photoelectron spectroscopy (PES) or photoemission spectroscopy is based on the external photoelectric effect , in which photoelectrons by electromagnetic radiation from a solid state to be solved. In a simplified model, the photoemission process takes place in three steps. First, the electron is excited by the incident photon, then the excited electron is transported to the surface and, as a third step, the photoelectron exits. The exit direction and the kinetic energy of these electrons allow conclusions to be drawn about the chemical composition and the electronic properties of the solid body being examined.

In solid-state physics and in related areas such as surface physics , surface chemistry and materials research, photoelectron spectroscopy plays a central role in the investigation of occupied electronic states . The further development of the apparatus since 2000 opened up new fields of basic research for photoelectron spectroscopy.

Photoelectron spectroscopy is divided into the areas of ultraviolet photoelectron spectroscopy ( UPS , ultraviolet PES ), X-ray photoelectron spectroscopy ( XPS , X-ray PES ; also ESCA , English electron spectroscopy for chemical analysis ) and angle-resolved photoelectron spectroscopy ( ARPES , English. angle-resolved PES ). Ultraviolet photoelectron spectroscopy mainly makes statements about chemical compounds and electronic properties of a material. X-ray photoelectron spectroscopy provides information about the elemental composition of the surface and about the chemical bond state of these elements. The information depth corresponds to the penetration depth of the unscattered or elastically scattered electrons and is usually up to three nanometers. The electronic structure of a solid is examined with angle-resolved photoelectron spectroscopy. This measuring method is suitable for comparing the theoretically calculated with the real course of the spectral function of the electron system.

## history

The external photoelectric effect was discovered experimentally in 1887 by Heinrich Hertz and Wilhelm Hallwachs and later explained by Albert Einstein ( Nobel Prize in Physics 1921).

Hallwax realized that it is not the intensity of the light but its frequency that decides whether electrons can be released from the surface of a photocathode. Einstein introduced the term light quantum ( photon ) and showed that its energy, which - as Max Planck had previously discovered for heat radiation - results directly from the light frequency ν, must be at least as large as the work function Φ of the solid surface. Its photoelectric equation gives the kinetic energy of a photoelectron E kin , which is excited by a photon with the energy E photon from a state with the binding energy E B.

Photoelectron spectroscopy was systematically developed from 1960 by Kai Siegbahn in Uppsala into an important experimental investigation method in surface and solid-state physics, for which he received the Nobel Prize in 1981 .

The underlying idea was to convert the energy distribution of the electrons in the solid body into an intensity distribution I ( E kin ) of photoelectrons with a certain energy E kin by means of photoemission excitation . The kinetic energy of the photoelectrons can then be measured (spectroscopically) using suitable magnetic or electrostatic analyzers.

To excite the photoelectrons, he used two different types of light sources, which are still common in laboratories today, the gas discharge lamp and the X-ray tube. The radiation generated in these sources and used for PES is in the hard ultraviolet range or in the soft X-ray range. According to the energy of the radiation used, a distinction is made between photoelectron spectroscopy and UPS (ultraviolet photoelectron spectroscopy) and XPS , after the English name X-ray for X-rays. The energy resolution of the first instruments used was typically between 1 and 2 eV in the XPS range and 100 meV or less in the UPS range.

A major discovery by Siegbahn was that the spectra of the core electrons depend on the chemical environment of the system under investigation. In the XPS spectra of the same element, depending on the chemical form in which it is present, there are differences in the binding energy of a core electron of up to a few electron volts , and in many cases the form of the spectra can also provide information about the valence state of an element. The second name of XPS, ESCA ( Electron Spectroscopy for Chemical Analysis ) is based on these observations and the resulting possible applications .

The method of studying molecules in the gas phase using ultraviolet light was developed by David W. Turner and described in a series of publications from 1962 to 1970. He used a He gas discharge lamp ( E = 21.22 eV) as the light source, the emission of which is in the ultraviolet range. With this source, Turner's group achieved an energy resolution of approx. 0.02 eV and was thus able to determine the energy of molecular orbitals very precisely and to compare it with theoretical values ​​of the quantum chemistry currently developed at the time . Due to the excitation by means of UV light, this measurement method was called UPS, based on XPS.

## Theoretical description

Simplified scheme of the PES from the photo effect to the measured spectrum. The graph on the left shows the density of states (DOS) of a metal with two trunk level states and a (metallic) band crossing the Fermi level . By measuring at finite temperature and device resolution, the sharp Fermi edge and the discrete body levels are broadened, shown in the right graph as a PES spectrum.
Schematic representation of the relevant energy levels for the measurements of the binding energy using X-ray photoelectron spectroscopy (XPS)

Photoelectron spectroscopy is a measurement method based on the external photoelectric effect. If a gas or a solid body is irradiated with light of the known energy E photon , electrons with the kinetic energy E kin are released. With his photoelectric equation, Einstein was able to establish the connection between the incident photon energy and the kinetic energy of the electrons:

${\ displaystyle E _ {\ mathrm {kin}} = E _ {\ mathrm {Photon}} -E _ {\ mathrm {B}} - \ Phi _ {\ mathrm {spect}}}$

With known photon energy and measured electron energy, statements can be made about the bonding conditions of the electrons in the examined material using this equation. The binding energy E B refers to the chemical potential of the solid body, and (during calibration of the spectrometer determined) work function Φ spectral of the spectrometer. The work function is a characteristic, material or surface-specific variable that can be determined by means of the external photo effect (see Figure 2). In an approximation according to Koopmans it is assumed that the position of the energy levels of an atom or molecule does not change when it is ionized . As a result, the ionization energy for the highest occupied orbital (HOMO: highest occupied molecular orbital ) is equal to the negative orbital energy , i.e. the binding energy. With a closer look at this energy in core level electrons , conclusions can be drawn about the type of atom and the chemical composition ( stoichiometry ) of the sample and, to a certain extent, also the chemical bond conditions in the investigated solid are obtained from the quantitative analysis . In addition, the analysis of the binding energy of the valence band and conduction electrons allows a very detailed investigation of the excitation spectrum of the electron system of crystalline solids. ${\ displaystyle I}$${\ displaystyle \ varepsilon}$

The additional determination of the angle at which the photoelectrons leave a solid allows a more precise investigation of the valence band structures of crystalline solid bodies, whereby the conservation of momentum in the photoemission process is used. Due to the relationship between the momentum of the photoelectron and the wave vector of a Bloch electron , it is possible to infer the dispersion relations of the valence states from the angle dependence of the spectra . This angle-resolved photoelectron spectroscopy is also called ARPES for short ( angular resolved photoelectron spectroscopy ). In the case of metals, the electronic dispersion relations contain information about the shape of the Fermi surface , which can also be determined using a number of other methods, such as B. the De-Haas-van-Alphen , Schubnikow-de-Haas or the anomalous skin effect . The methods mentioned must, however, be carried out on highly pure single crystals at the lowest possible temperatures , whereas ARPES can also be used at room temperature and comparatively defect-rich crystals.

## Measuring methods of photoelectron spectroscopy

### X-ray Photoelectron Spectroscopy (XPS)

XP spectrum of magnetite (Fe 3 O 4 )

X-ray photoelectron spectroscopy (English: X-ray photoelectron spectroscopy , XPS, often electron spectroscopy for chemical analysis , ESCA) is an established method to the chemical composition, especially of solids or its surface to determine non-destructively. You first get an answer to the question of qualitative element analysis, i.e. which chemical elements the solid consists of. Only hydrogen and helium can generally not be detected due to the small cross- sections.

The method uses high - energy X-rays , mostly from an Al -K α or Mg -K α source, to release electrons from the inner orbitals. From the kinetic energy of the photoelectrons, their binding energy E B can then be determined. It is characteristic of the atom (more precisely even for the atomic orbital ) from which the electron originates. The analyzer used for the measurement (usually a hemispherical analyzer ) is set using electrostatic lenses and counter voltages so that only electrons of a certain energy can pass through it. For the XPS measurement, the electrons that still arrive at the end of the analyzer are detected by a secondary electron multiplier, so that a spectrum is created that is usually displayed in a graph by plotting the intensity ( counting rate ) against the kinetic energy of the photoelectrons. The intensity is proportional to the frequency of occurrence of the various elements in the sample. In order to determine the chemical composition of a solid, one has to evaluate the area below the observed lines that are characteristic of the elements. However, there are some measurement-specific features to consider (see main article).

### Ultraviolet Photoelectron Spectroscopy (UPS)

The purpose of the UPS is to determine the valence band structure of solids, surfaces and adsorbates. The density of states (DOS) is determined. For this purpose, ultraviolet light is used in UPS (often also referred to as valence band spectroscopy in the solid state area) , which is only capable of triggering valence electrons. These energies are of course also available for XPS measurement, but the kinetic energy of the photoelectrons triggered in this way can be measured with extremely high accuracy by a suitable choice of light source (generally He gas discharge lamps). UPS can also resolve minimal energy differences between molecular orbitals or the physical environment (e.g. adsorption on surfaces) of the spectroscoped molecule. The chemical structure of bonds, adsorption mechanisms on substrates and vibrational energies of various molecular gases can be examined.

### Two-photon photoemission spectroscopy (2PPE)

Two-photon photoemission spectroscopy, or 2PPE spectroscopy for short, is a photoelectron spectroscopy technique that is used to investigate the electronic structure and the dynamics of unoccupied states on surfaces . Femtosecond to picosecond laser pulses are used to photoactivate an electron . After a time delay, the excited electron is emitted into a free electron state by a second pulse. The emitted electron is then detected with special detectors, with which both the energy and the emission angle and thus the momentum of the electron parallel to the surface can be determined.

### Angle-resolved measurements (ARPES)

Principle of angle-resolved measurement

With the help of angle-resolved measurements, ARPES ( angle-resolved PES ) or ARUPS ( angle-resolved UPS ), not only the energy of the photoelectrons, but also the angle at which they leave the sample, is measured. In this way it is possible to determine the energy-momentum relationship of the electron in the solid, i.e. to display the band structure or also to visualize Fermi surfaces.

#### Measuring principle

Energy-resolved detection of electrons from a small angular range.

All of the PES methods listed so far detect the photoelectrons regardless of the angle at which they leave the sample. Strictly speaking, for these measurements, one generally selects the measurement position of the analyzer in such a way that predominantly electrons with an exit angle perpendicular to the sample surface can be detected. The analyzer settings (more precisely the lens voltages of the electrostatic lenses, the electron optics ) are set in such a way that a very wide angle acceptance range of approx. ± 10 ° results. For the measurement method described below, the settings of the analyzer are changed so that photoelectrons are only detected at a significantly smaller angle. Modern analyzers achieve an angular resolution of less than 0.2 ° with a simultaneous energy resolution of 1–2 meV. Originally, high energy and angular resolution were only achieved with low photoelectron energies in the UV range, from which the name ARUPS was derived. Especially in the years 1990–2000 the resolution of the PES analyzers was improved by the combination of microchannel plates , phosphorescent plate and CCD camera so that even with far higher photoelectron energies (state of the art 2006: E kin  ≈ 10 keV) the Band structure became possible.

Due to the requirement for low photon energies for the analyzer, for example from a He lamp, ARUPS measurements could only determine the band structure of the areas of a solid body close to the surface. Together with the improvement of the resolution of the analyzers and the use of high-energy ( E kin  > 500 eV), extremely monochromatic synchrotron light, it has been possible since 2000 to determine the band structure of the volume of crystalline solids. This is one of the reasons why ARPES has developed into one of the most important spectroscopic methods for determining the electronic structure of solids in our time.

#### Qualitative evaluation of the measurement

Momentum relation of an electron in the crystal to an electron released by the photo effect. k and k * are the momentum vectors in the crystal or in a vacuum, k ll is the momentum obtained when the electron passes from the sample to the vacuum.

An essential prerequisite for the validity of the statement that ARPES can determine the band structure of a crystalline solid is the applicability of Bloch's theorem to the electronic states involved, i.e. that they can be uniquely characterized by a wavenumber vector k and the associated wave function the general form:

${\ displaystyle \ Psi ({\ vec {k}}, {\ vec {r}}) = u_ {k} ({\ vec {r}}) \ exp ({\ mbox {i}} {\ vec { k}} {\ vec {r}})}$

where u k is a lattice-periodic function. This requirement cannot be met in the experiment. Due to the transition from the surface of the sample to the vacuum, the system is not translation-invariant in the vertical direction, and therefore the k component of the measured wavenumber vector is not a good quantum number . However, the k part is retained, since both the crystal potential and the vacuum remain lattice-periodic parallel to the surface. Consequently, the magnitude of the wavenumber vector in this direction can be given directly: ${\ displaystyle _ {\ bot}}$${\ displaystyle _ {\ |}}$

${\ displaystyle \ left | {\ vec {k}} _ {||} \ right | = \ sin {\ Theta} {\ sqrt {2mE _ {\ mathrm {kin}} / \ hbar ^ {2}}}}$

If the density of states (band structure) of the investigated crystal does not vary too much perpendicular to the surface, it is possible to measure the occupied state density directly. To allow comparison with theoretical calculations, measurements are usually made in certain directions of high symmetry of the Brillouin zone . To do this, the crystal is often oriented perpendicular to the analyzer using a LEED , then rotated along one of the directions and an energy spectrum of the photoelectrons is recorded. Using a microchannel plate and a CCD camera, the energy and the angle at which the electrons leave the surface can even be measured simultaneously.

The results are usually presented by showing all the angle-dependent spectra in a graph, with the energy and intensity plotted on the coordinate axes. In order to be able to follow the angle dependence, the individual spectra are shifted in intensity so that the dispersion can be observed. An alternative representation is an intensity distribution by means of color coding , in which the angle and energy on the coordinate axes and the intensity are shown as color gradations.

The almost complete spectroscopy of the half-space over a metallic sample according to the above-mentioned method now allows the Fermi area of ​​the electron system of the crystal to be determined from the spectra. By definition, the Fermi surface results from the joining of all points in momentum space at which an electronic band crosses the Fermi energy (as with the dispersion relation , it is sufficient to limit the definition of the Fermi surface to the first Brillouin zone ) . In PES measurements with constant photon energy, the points of passage generally correspond to emission directions at which the intensity at the Fermi energy is particularly high in the spectra. It is therefore often sufficient to determine the intensity distribution at E F as a function of the emission angle Θ without having to take into account the exact course of the band.

### Photoelectron Diffraction (XPD)

Principle of photoelectron diffraction

Photoelectron diffraction, often abbreviated to PED, PhD or XPD ( X-ray photoelectron diffraction ), is a method to determine the structure of crystalline surfaces or the spatial position of adsorbates on surfaces. The basis of the measurement process is again photoelectron spectroscopy, whereby the intensity of the photoelectrons is determined depending on the emission angle. However, here, as with the angle-dependent PES, the focus is not on the impulse of the photoelectron, but the interference of the wave function of the photoelectron. Depending on the direction of emission and the kinetic energy of the photoelectron, one finds differences in intensity, called modulations. These intensity modulations arise from constructive and destructive interference between the electron wave that reaches the detector directly (reference wave ) and those that arise from waves elastically scattered one or more times around the emitting atom (object waves). The path differences and intensities of the individual waves depend on the geometric arrangement and the type of neighboring atoms. Given a sufficient number of measured intensities, the geometric structure can be determined from the modulations by comparing the experimentally measured modulations with corresponding simulations.

The simplest applications are based on forward focusing by atoms above the photoionized atom. This can be used to determine whether certain atoms are located directly on the surface or deeper, and in the case of adsorbed molecules, whether there are other atoms (and in which direction) above a type of atom. The XPD can be used to determine the crystallographic structure of metal and semiconductor surfaces. In addition, information is obtained about the spatial position of molecules on surfaces, the bond lengths and bond angles.

### Photoemission Electron Microscopy (PEEM)

Another widespread application of PES is photoemission electron microscopy , or PEEM ( photo emission electron microscopy ) for short . Here electrons are released from the sample by the photoelectric effect, but during the detection it is not the number of electrons of a kinetic energy selected by the analyzer that is measured, but rather the intensity distribution of the photoelectrons in a two-dimensional area of ​​the sample. It is therefore, characteristic of microscopes, an imaging measuring technique.

By installing a microanalyser in the beam path that selects the kinetic energy of the photoelectrons (analogous to normal PES) and by using narrow-band and short-wave excitation light sources such as. B. synchrotron radiation, it is possible to carry out laterally resolved XPS (XPS microscope). The term μ-ESCA describes the chemical analysis of a micrometer-sized area of ​​the sample. This enables both the determination of the elemental composition of the sample and the investigation of local differences in the electronic properties.

### Coincident photoelectron spectroscopy

In addition to the emission of a single electron per incident photon, there is also the possibility that two or more electrons are released. On the one hand, this can take place as part of a secondary electron cascade, but also through the coherent emission of two electrons by a photon. The coincident measurement of the emitted electrons allows conclusions to be drawn about the underlying coupling mechanisms. Typically no electrostatic analyzers are used for experimental detection, but rather time-of-flight spectrometers. Due to the small opening angle of an electrostatic analyzer, only very low coincidence rates can be achieved in this way. Time-of-flight projection systems enable significantly higher detection efficiency. The electrons emitted by a pulsed photon beam are projected onto spatially resolving detectors. The initial impulses or angles and kinetic energy can be determined from the flight time and location.

### Measurements in resonance (ResPES)

In principle, the course of the photoemission spectrum, especially that of the valence band, depends on the photon energy used for excitation. If the photon energy sweeps over the area of ​​an X-ray absorption edge, the changes are generally particularly pronounced. The reason for this are resonance effects, which arise from the interaction of two or more different end states, more precisely from continuum states with discrete levels, and thus influence the overall photoemission cross section. If the photoemission intensity of a selected spectral structure is plotted against the photon energy, asymmetrical excitation profiles, so-called Fano resonances , are generally obtained . The shape and intensity of these profiles can provide information about the elementary character of the spectral structure, about details of the chemical bond and about the interactions between the states involved. This will help in resonant photoemission spectroscopy ( resonant photoemission spectroscopy exploited ResPES).

### Inverse Photoelectron Spectroscopy (IPES)

In contrast to PES, with inverse photoelectron spectroscopy (IPS, IPES), often also called inverse photoemission spectroscopy, electrons of known energy are accelerated onto the sample and the photons emitted are detected as bremsstrahlung . The two measurement methods PES and IPES can complement each other very well, as the IPES is well suited for determining the unoccupied density of states (above the Fermi energy ) (more details on determining the unoccupied density of states with UPS above). Analogous to the angle-integrated measurements just mentioned, IPES also enables the experimental determination of the band structure above the chemical potential (above the Fermi energy) for angle-resolved measurements . Analogous to ARUPS, with IPES in the UV range to determine the band structure, k information is obtained from the direction of incidence of the exciting electrons.

In terms of equipment, an IPES spectrometer consists of a simple electron gun and a photon detector with a bandpass filter or monochromator . In laboratory measurements, the kinetic energy (primary energy) of the electrons is usually varied and the photon energy is kept constant during detection. In this case, one speaks of isochromatic mode , from which the designation BIS , bremsstrahlung isochromatic spectroscopy , is derived. Bandpass filters of the Geiger-Müller type are most frequently used for energies in the UV range , in which an alkaline earth fluoride window is used as a low pass (e.g. CaF 2 or SrF 2 ) and a suitable counting gas (e.g. I 2 or CS 2 ) can be combined as a high pass . The detection energy and bandpass width result from the transmission threshold of the window material or from the molecular photoionization barrier of the counting gas (approx. 9.5 eV). The bandwidth of the bandwidth essentially determines the spectrometer resolution. Other types of detectors combine the alkaline earth fluoride window with a suitably coated channel electron multiplier (e.g. with sodium chloride or potassium bromide ).

Because of the small cross-section of the inverse photoemission process, the typical count rate is very small compared to photoelectron spectroscopy. Therefore, with the IPES, no comparable energy resolutions can be achieved, since the signal decreases linearly with the bandwidth. Typical values ​​for the resolution are a few hundred milli-electron volts , which is two orders of magnitude worse than with UPS. Detectors with grating monochromators in principle achieve significantly better values ​​and can be used much more flexibly because of their tunable photon energy, but are much more expensive and larger than the other types of detectors.

### ZEKE spectroscopy

In the ZEKE spectroscopy (ZEKE short for English zero-electron kinetic energy or even zero kinetic energy ) in particular electrons are detected at the ionization limit. The gas to be examined is irradiated with a short laser pulse. After this laser pulse has subsided, the time is waited. During this time, all electrons move out of the examination area. With the help of an electric field all remaining electrons are sucked out and measured after the expiration of . ${\ displaystyle \ tau}$${\ displaystyle E> E_ {c}}$${\ displaystyle \ tau}$

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