Photoemission spectroscopy

Photoelectron spectroscopy (PES) or photoemission spectroscopy is based on the external photoelectric effect can be achieved in the photo-electron by means of electromagnetic radiation from a solid state. In a simplified model of the process of photoemission proceeds in three steps. First, the excitation of the electron is accomplished by the incident photon, and then the transportation of the excited electron from the surface and the third step of the exit of the photoelectron. The exit direction and the kinetic energy of these electrons allows conclusions on the chemical composition and the electronic nature of the investigated solid.

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

Photoelectron spectroscopy is divided into the areas of ultraviolet photoelectron spectroscopy ( UPS, Eng ultraviolet PES. ), X-ray photoelectron spectroscopy (XPS, Eng X -ray PES, . Well ESCA, Eng electron spectroscopy for chemical analysis. ) And angle-resolved photoelectron spectroscopy ( ARPES, Eng. angle -resolved PES). Ultraviolet photoelectron spectroscopy applies mainly statements of chemical compounds and electronic properties of a material. X-ray photoelectron spectroscopy provides information on the elemental composition of the surface and the chemical bonding state of these elements. The depth of information corresponds to the Ausdringtiefe the unscattered or elastically scattered electrons and is usually up to three nanometers. By using angle -resolved photoelectron spectroscopy, the electronic structure of a solid is investigated. This method of measurement is to compare the theoretically calculated with the real course of the spectral function of the electron system.

History

The outer photoelectric effect was discovered experimentally in 1887 by Heinrich Hertz and William Hall wax and later by Albert Einstein explained ( Nobel Prize in Physics 1921).

Hall wax realized that not the intensity of light, but the frequency of which determines whether electrons can be detached from the surface of a photocathode. Einstein introduced the concept of the light quantum ( photon) and showed that the energy of which - such as Max Planck for the thermal radiation discovered before - gives ν directly from the light frequency, at least as large as the work function must be Φ the solid surface. Its photoelectric equation, the kinetic energy Ekin of a photoelectron which is excited by a photon energy EPhoton from a state with the binding energy EB.

Photoelectron spectroscopy was from 1960 by Kai Siegbahn systematically developed in Uppsala to an important experimental method of investigation of 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 state by photoemission excitation in an intensity distribution I ( Ekin ) of photoelectrons with a specific energy Ekin. The kinetic energy of the photoelectrons can then by suitable magnetic or electrostatic analyzers measure ( ray spectra ).

For excitation of the photoelectrons he used two different types of light sources, which are common or in laboratories today, the gas discharge lamp and the x-ray tube. The heat generated in these sources and used for the PES radiation is in the hard ultraviolet range or in the soft X-ray range. According to the energy of the radiation used, a distinction is to present the photoelectron spectroscopy in UPS ( ultraviolet photoelectron spectroscopy) and XPS, according to the English designation X- ray to X-ray radiation. The energy resolution of the first instruments used was typically 1-2 eV in XPS and 100 meV or less the UPS area.

A major discovery of Siegbahn was that the spectra of the core electrons of the chemical environment of the investigated system depend. In the XPS spectra of the same element show, depending on the chemical form it exists differences in the binding energy of a core electron of up to several electron volts, and in many cases, the shape of the spectra provide information on the valence of an element. These observations and the resulting applications, the second name of XPS, ESCA founded ( Electron Spectroscopy for Chemical Analysis).

The method to study molecules in the gas phase by means of ultraviolet light, was developed by David W. Turner and described in a series of publications from 1962 to 1970. As the light source he used a He gas discharge lamp ( E = 21.22 eV) whose emission is in the ultraviolet range. With this source, the group reached to Turner an energy resolution of about 0.02 eV and was thus able energy of molecular orbitals to be determined very accurately and to compare with theoretical values ​​of the then currently developed quantum chemistry. Due to the excitation by UV light, this measurement method was - called UPS - on the basis of XPS.

Theoretical description

Photoelectron spectroscopy is a measurement technique based on the outer photoelectric effect. Irradiation of a gas or a solid with light of known energy EPhoton, so electron kinetic energy Ekin are free. Einstein was able to connect with his photoelectric equation the relationship between the incident photon energy and the kinetic energy of the electrons:

About this equation may contain statements about the bonding of the electrons in the investigated material can be made ​​with a known photon energy and the measured electron energy. The binding energy EB refers to the chemical potential of the solid, and ( when calibrating the spectrometer determined ) work function of the spectrometer Φspek. The work function is a characteristic, material or surface- specific variable, which can be determined by means of the outer photoelectric effect (see Figure 2). In an approximation by Koopmans, it is assumed that the position of the energy levels of an atom or molecule does not change in its ionization. Thus, the ionization energy of the highest occupied molecular orbital (HOMO: highest occupied molecular orbital) is equal to the negative orbital energy ε, ie the binding energy. Upon closer examination of this energy at core level electrons can be closed on the type of atom and can be obtained from the quantitative analysis of the chemical composition (stoichiometry ) of the sample and to a certain extent, the chemical bonding in the investigated solids. In addition, the analysis of the binding energy of the valence band and conduction electrons allows a very detailed study of the excitation spectrum of the electron system of crystalline solids.

The additional determination of the angle at which the photoelectrons leave a solid which allows a closer examination of Valenzbandstrukturen crystalline solids, where one takes the momentum conservation in the photoemission process advantage. Due to the relationship between the momentum of the photoelectron and the wave vector of a Bloch electron it is possible from the angular dependence of the spectra close to the dispersion relations of the valence states. This angle-resolved photoelectron spectroscopy is also called short ARPES ( angular resolved photoelectron spectroscopy ). In metals, the electronic dispersion relations contain the information about the shape of the Fermi surface, which can be determined with a number of other methods, such as the de Haas -van Alphen -, Shubnikov - de Haas or the anomalous skin effect. However, the abovementioned methods must be carried out at very low temperatures of high-purity single crystals, whereas the ARPES can also be applied at room temperature and relatively defect-rich crystals.

Measurement methods of photoelectron spectroscopy

X-ray photoelectron spectroscopy (XPS)

X-ray photoelectron spectroscopy (English: X- ray photoelectron spectroscopy, XPS, electron spectroscopy for often chemical analysis, ESCA ) is an established method to determine the chemical composition, especially of solids and their surface non-destructively. This gives a first answer to the question of the qualitative element analysis, and thus consists of these chemical elements in the solid state. Only hydrogen and helium can not be detected due to low cross sections in general.

The method uses high-energy X-rays, usually of an Al - Ka - or Mg Ka source to release electrons from the inner orbitals. From the kinetic energy of the photoelectrons whose binding energy EB can be determined subsequently. It is characteristic of the atom (specifically, even for the atomic orbital ), from which the electron. The analyzer used for the measurement (generally a hemispherical analyzer ) is adjusted by means of electrostatic lenses, and reverse voltages that may he only electrons of a certain energy to pass. For the XPS measurement, the electrons arriving at the end of the analyzer still detected by a secondary electron multiplier, so that a spectrum is produced, which is usually on a graph by the plot of the intensity ( count rate ) is displayed on the kinetic energy of the photoelectrons. The intensity is proportional to the frequency of occurrence of the various elements in the sample. To determine the chemical composition of a solid, must be below the surface of the observed lines that are characteristic of the elements analyzed. In this case, however, some measurement-specific features are observed (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 is determined (english Density of States, DOS). For this purpose, in the UPS ( the solid area often referred to as Valenzbandspektroskopie ) used ultraviolet light, which is capable only to trigger valence. These energies are, of course, the XPS measurement also available, only the kinetic energy of the photoelectrons as measured with extremely high accuracy by a suitable choice of the light source (typically the He gas discharge lamps ). With UPS also minimal energy differences of molecular orbitals or the physical environment can be resolved (eg, adsorption on surfaces) of spectroscopically molecule. Can be Examines the chemical structure of bonds, adsorption mechanisms of substrates and vibrational energies of various molecular gases.

Angle-resolved measurements ( ARPES )

Using angle-resolved measurements, ARPES ( angle -resolved PES engl. ) and ARUPS (angle -resolved UPS ) called, is not only the energy of the photoelectrons, but also the angle at which they leave the sample measured. In this way a determination of the energy-momentum relation of the electron in the solid state, so the representation of the band structure, or the visualization of the Fermi surface, is possible.

Principle of measurement

All the previously listed methods of PES detect the photoelectrons regardless of the angle at which they leave the sample. Strictly speaking, one selects for these measurements in general, the measurement position of the analyzer such that predominantly electrons can be detected with an exit angle perpendicular to the sample surface. The analyzer settings (specifically, the lens voltages of the electrostatic lens, the electron-optical system ) are set so that a very wide angular acceptance range of about ± 10 ° results. For the measurement method described below, the analyzer settings are changed so that photoelectrons are detected only at a much smaller angle. Modern analyzers achieve this, an angular resolution of less than 0.2 ° without loss of energy resolution of 1-2 meV. Originally high energy and angular resolution were achieved only at low photoelectron energies in the UV range, from which then the name ARUPS derived. Especially in the years 1990-2000, the resolution of the PES analyzers by combining micro- channel plates, phosphorescent plate and CCD camera has been improved such that even at much higher photoelectron energies ( state of the art 2006: Ekin ≈ 10 keV) a determination of the band structure was possible.

Basis of the contingent for the analyzer demand for low photon energies, which, for example, from a He- lamp, ARUPS measurements could only determine the band structure of the near-surface regions of a solid. Along with the improvement of the resolution of the analyzers and the use of high-energy ( Ekin > 500 eV ), extremely monochromatic synchrotron light, it is possible to determine since about 2000 the band structure of the volume of crystalline solids. This is one of the reasons why the ARPES has developed in our time one of the most important spectroscopic methods for the determination of the electronic structure of solids.

Qualitative evaluation of the measurement

An essential condition for the validity of the statement that ARPES can determine the band structure of a crystalline solid, is the applicability of the Bloch theorem to the involved electronic states, that is, that they can be k uniquely characterized by a wave number vector and the corresponding wave function general form:

, said uk is a lattice- periodic function. This condition is not fulfilled in the experiment. Due to the transition from the surface of the sample to the vacuum, the system is not in the vertical direction so that the k and translation invariant component of the measured wave vector is not a good quantum number. However, the K- fraction is obtained, since both the potential of the crystal and the vacuum to remain parallel to the surface grating periodically. Consequently, one can specify the magnitude of the wave number vector in this direction directly:

Ie at not too strong variation of the density of states ( band structure ) of the investigated crystal perpendicular to the surface, it is possible the occupied density of states to measure directly. To allow a comparison with theoretical calculations, it is usually measured in specific high symmetry directions of the Brillouin zone. To the crystal is oriented by LEED often perpendicular to the analyzer, is then rotated along one of the directions and included an energy spectrum of the photoelectrons. By means of a microchannel plate and a CCD camera can even simultaneously under the left the energy and the angle of the electrons, the surface can be measured.

The presentation of the results is carried out usually by representing all the angle dependent spectra in a graph, where the energy and intensity is applied to the coordinate axes. In order to follow the angular dependence of the individual spectra are shifted in intensity, so that the dispersion is observable. An alternative representation of the intensity distribution by means of a color coding, will become more apparent in the angle and energy to the coordinate axes and the intensity gradation.

The almost complete spectroscopy the half-space on a metallic sample in accordance with the above method makes it possible then to determine from the spectra of the Fermi surface of the electron system of the crystal. The Fermi surface is obtained by definition of the concatenation of all points in the momentum space in which an electronic band crosses the Fermi energy ( as in the dispersion relation, it is sufficient to restrict the definition of the Fermi surface in the first Brillouin zone). PES measurements with a constant energy photon, the passage points generally correspond to the emission direction, where in the spectra of the intensity at the Fermi energy is particularly high. Therefore, it is often sufficient to determine the intensity distribution at EF depending on the angle of emission Θ, without having to take account of the exact tape path.

Photoelectron diffraction (XPD )

The photoelectron diffraction, often with PED, PhD or XPD ( engl. X - ray photoelectron diffraction ) abbreviated, is a method to determine the structure of crystalline surfaces or the spatial position of adsorbates on surfaces. Basis of the measurement process is in turn the photo- electron spectroscopy, the intensity of the photoelectrons is determined depending on the emission angle. However, this is not like the angle-dependent PES, the focus on the momentum of the photoelectron, but the interference of the wave function of the photoelectron. In response to the emission direction and the photoelectron kinetic energy can be found differences in intensity called modulations. These intensity modulations caused by constructive and destructive interference between the electron wave that reaches the detector in a direct way ( reference wave ), and those obtained from one or more times in the vicinity of the emitting atom elastically scattered wave (object wave ) occur. The speed differences of the individual waves and intensities depend on the geometric arrangement and the type of the neighboring atoms. With a sufficient number of measured intensities can be calculated from the modulations of the geometric structure determined by the experimentally measured modulations with corresponding simulations are compared.

The simplest applications are based on the forward - focusing by atoms above the photoionized atom. This makes it possible to determine whether certain atoms sit directly on the surface or deeper, and adsorbed molecules, whether above a type of atom other atoms ( and in what direction) sit. By means of XPD, the crystallographic structure of metal and semiconductor surfaces can be determined. In addition, we obtain information about the spatial location of molecules on surfaces, the bond lengths and bond angles.

Photoemission electron microscopy ( PEEM )

Another common application of the PES is the photoemission electron microscopy PEEM short (English photoemission electron microscopy) called. Here, by the photo- electron effect of the sample dissolved, but at the detection of the number of electrons of a selected by the analyzer kinetic energy is not measured, but rather, one is interested in for the intensity distribution of the photoelectrons a two-dimensional area of the sample. This is therefore characteristic of microscopes to an imaging metrology.

By installing a microanalyzer in the beam path, which selects the kinetic energy of the photoelectrons (analogous to the normal PES) as well as by the use of narrow band and the short-wave excitation light sources, such as synchrotron radiation, it is possible to perform also laterally resolved XPS (XPS microscope ). The term μ - ESCA describes the chemical analysis of a micron -sized area of the sample. So that both the determination of the elemental composition of the sample as well as the investigation of local differences in the electronic properties is possible.

Coincident photoelectron spectroscopy

In addition to the emission of a single incident photon per electron, it is also possible that two or more electrons are released. This can be done on the one hand as part of a secondary electron cascade, but also by the coherent emission of two electrons by a photon. By coincidence measurements of the emitted electrons can be concluded that the underlying coupling mechanisms. Typically come no electrostatic analyzers used but flight time spectrometer for the experimental proof. Due to the small opening angle of an electrostatic analyzer, very low coincidence rates can thus be achieved. A much higher detection efficiency allow flight time projection systems. Here, the light emitted by a pulsed photon beam electrons are projected onto position-sensitive detectors. From flight time and place as the initial impetus or angular and kinetic energy can be determined.

Measurements in resonance ( ResPES )

Basically, the variation of the photon emission spectrum, in particular the the valence band, depending on the photon energy used for excitation. About one Paints the area of X-ray absorption edge with the photon energy, the changes are generally particularly strong. This is due to resonance effects. Due to the interaction of two or more different final states, more of continuum states with discrete levels occur and thus affect the total photoemission cross section Plotting the photoemission intensity of a selected spectral structure against the photon energy, the result is generally asymmetric excitation profiles, so-called Fano resonances. Shape and intensity of these profiles can provide information about the elementary character of the spectral structure over details of chemical bonding and on the interactions of the states involved. This is exploited in the resonant photoemission spectroscopy ( resonant photoemission spectroscopy, ResPES ).

Inverse photoelectron spectroscopy ( IPES )

In contrast to the PEs in the inverse photoemission spectroscopy ( IPS IPES ), often referred to as inverse photoemission spectroscopy, electron energy accelerated to the known sample, and detecting the photons emitted thereby as bremsstrahlung. The two measurement methods PES and IPES can complement each other very well, because the IPES well for the determination of the unoccupied density of states (above the Fermi energy ) is ( more details to determine the unoccupied density of states with UPS above). Analogous to the just mentioned angle integrated measurements allows the angle-resolved measurements IPES at the experimental determination of the band structure of the above chemical potential (above the Fermi energy). Analogous to ARUPS obtained in IPES in the UV range for the determination of the band structure, the K information from the direction of incidence of the exciting electrons.

In apparatus itself uses IPES spectrometer from a simple electron gun and a photon detector with band pass filter or monochromator together. Mostly used in the laboratory, the kinetic energy (primary energy ) of the electrons is varied and kept the photon energy in the detection constant. One speaks in this case of the isochromatic mode, which is also the name of BIS, Bremsstrahlungsisochromaten spectroscopy derives. Finding the most common use for energy in the UV range band-pass filter of the Geiger- Müller type, in which a Erdalkalifluoridfenster as a low pass (such as CaF2 or SrF2 ) and a suitable counting gas are combined as a high pass (eg I2 or CS2). Detection energy and bandpass width arising from the transmission threshold of the window material or from the molecular Photoionisationsschranke the counting gas ( about 9.5 eV). The bandpass width determines the spectrometer resolution substantially. Other types of detectors which combine with a suitable coating Erdalkalifluoridfenster channel electron multiplier (such as sodium chloride or potassium bromide ).

Because of the small cross section of the inverse photoemission process, the count rate is typically very small compared to the photo-electron spectroscopy. Therefore, can be in the IPES no comparable energy resolutions reached, because the signal of the bandpass width decreases linearly. Typical values ​​for the resolution will be a few hundred milli- electron volts, ie, two orders of magnitude worse than that of UPS. Detectors with grating monochromators principally achieve significantly better values ​​and are much more versatile 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 the laser pulse has decayed, the time is awaited. During this time, all the electrons move out with from the examination region. With the aid of an electric field are extracted and measured after a period of all of the remaining electrons.