Inverse photoemission spectroscopy

Typical IPE system with counter tube detector

The inverse photoemission spectroscopy (IPES), and inverse photoelectron spectroscopy or inverse photoemission (IPE), is one of the most important methods for experimental characterization of unoccupied electronic states of solids and surfaces . It is based on the time reversal of the external photo effect . While photoelectrons are released from a solid by electromagnetic radiation in the external photo effect, in inverse photoemission spectroscopy the solid is bombarded with electrons , which give off their kinetic energy in the form of photons when they interact with the solid . The spectra of the inverse photoemission allow conclusions to be drawn about the unoccupied electronic states in the solid, while “normal” photoemission spectroscopy essentially provides information about the occupied states.

The spectra are recorded in the simplest method, bremsstrahlung isochromate spectroscopy (BIS), by varying the electron energy and registering the emitted photons at fixed energy. If you subtract the photon energy from the starting energy of the electrons, you know the energy of the end states, i.e. H. the previously unoccupied states in the sample that the electrons take up. By varying the starting energy of the electrons, one can, so to speak, sample the final states on the energy axis, so that the number of registered photons provides information about how many final states are available at which energy. With suitable IPE systems it is also possible to obtain information about the wave vector and spin of these states.

As an alternative to the isochromatic method, a fixed electron energy can be used and the energy of the detected photons can be varied (spectrometer operation).

history

The principle of inverse photoemission was first used in 1915 by Duane and Hunt to determine the quotient of Planck's constant and elementary charge (h / e) using an X-ray tube . In the 1940s it was discovered that the bremsstrahlung isochromats in the vicinity of the threshold energy show structures which, as was later shown by Nijboer, are due to the unoccupied electronic states of the anode.

IPE publications 1980-2008

It was not until 1952 that Kurt Ulmer exploited this fact to systematically examine the conduction bands of the sample used as an anode in the experiment. Since the electrons only penetrate a few atomic layers deep into the sample, very clean surfaces are required, which was achieved at the time by permanently heating the sample. When ultra-high vacuum technology became available almost 30 years later , it was possible to examine samples after suitable cleaning at room temperature.

After first investigating the density of states of the unoccupied electronic states with inverse photoemission, a method was developed in the late 1970s and early 1980s with k resolved inverse photoemission (KRIPES) that allows to measure the wavenumber vector resolved band structure of the unoccupied states. The number of publications on inverse photoemission then rose sharply.

Before the development of photoemission spectroscopy and inverse photoemission spectroscopy, the electronic band structure was not directly accessible to experimental investigation. One could either check band structure calculations with the help of optical measurements via the detour of the dielectric function or determine properties of the Fermi surface with methods such as cyclotron resonance . With the two photoemission methods, the band structure has become measurable in principle.

Evaluation of the spectra

introduction

With inverse photoemission, unoccupied electronic states of solids and surfaces can be characterized with regard to their energy and, under suitable circumstances, also according to wave vector ( ) and spin. A major advantage of inverse photoemission is that it can also be used to investigate the vacant states between the Fermi level and the vacuum level , which are important for many properties and which are not accessible to photoemission spectroscopy. ${\displaystyle {\vec {k}}}$

Analogous to the photo emission, the inverse photo emission can be interpreted approximately in a three-stage model. The first stage is the entry of the electron from the vacuum into the sample (passage through the surface). The transport of the electron from the surface into the volume of the sample is the second stage, followed by the transfer of the electron with the emission of a photon as the third stage. The separation into three levels is a useful approximation for analyzing the spectrum, but it contradicts the uncertainty relation ; a correct description must describe the entire process quantum mechanically in one step.

When passing through the electron energy in isochromatic mode, the photon emission begins when the electrons have enough energy to generate photons by transition to the lowest unoccupied state of the sample, the energy of which is equal to that of the monochromator. The lowest final state energy corresponds to the Fermi level for metals and to the lower edge of the conduction band for semiconductors. After the threshold energy is exceeded, the spectrum scans the unoccupied states in the direction of higher energy.

IPE spectra have a background that increases with the energy. After the electrons have penetrated the sample, inelastic processes can initially take place before the optical transition, in which the electrons release part of their energy without radiation. The dominant process is the formation of electron-hole pairs. These processes lead to an energy-dependent, but structureless background in the spectra, which becomes so intense with increasing energy that ultimately no structures are visible any more.

Inverse photoemission in the direct transition model

If low energies below 20  eV are used - the energy of the emitted photons is then in the VUV range - the structures in the IPE spectrum are dominated by direct transitions that only take place at discrete points in the band structure, namely where two bands meet same value energetically differ by the photon energy used. The method then allows the unoccupied part of the band structure ( function) to be checked experimentally. ${\displaystyle {\vec {k}}}$ ${\displaystyle E({\vec {k}})}$

Inverse photoemission in the density of states model

At energies in the range of a few kiloelectron volts (soft X-ray radiation ), indirect transitions accompanied by phonons can take place, so that practically states in the range of the entire Brillouin zone are involved in the creation of the photon emission . This leads to an averaging effect in the space and the spectrum approximately reflects the density of states of the conduction bands. ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$

The intensity of the photon emission is mainly determined by the matrix element of the causative electronic transition (see Fermi's Golden Rule ) and the density of the final states involved. In contrast to photoemission, only the density of the end states is decisive, not the combined density of states from initial and end states ( Joint Density of States , JDOS). The reason for this is the fact that when displaying the IPE spectra, the photon count rate is divided by the sample flow in order to calculate the energy-dependent emission of the electron source. At the same time, the influence of the density of the initial states is eliminated.

Due to the nature of the IPE experiment - one particle is fed into the system - it is to be expected that band structure calculations in models of an effective potential (single-particle model) are only suitable to a limited extent for comparison with IPE spectra. A particle is fed into the system that cannot be expected to behave in an uncorrelated manner to the other electrons. More suitable are Quasiteilchenbandstrukturen to measured to compare functions with calculations. If you want to include not only the position of the structures, but also their width and the exact intensity curve of the spectra in the evaluation, it is best to use IPE spectra calculated in the one-step model. ${\displaystyle E({\vec {k}})}$

If a spin-polarized electron source is used for the inverse photoemission, the majority and minority states in ferromagnetic samples can be analyzed separately. This method is particularly suitable for researching the technologically important surface magnetism (application for magnetic data storage).

Because no electronic trunk levels are involved in inverse photoemission, in contrast to photoelectron spectroscopy of trunk levels ( ESCA ) it does not provide any information about the chemical elements in the sample.

Band mapping of volume and surface states

requirements

If you want to investigate the resolved band structure experimentally, you have to consider a number of influencing factors in order to keep the blurring in the IPE spectrum low. The blur must be significantly smaller than the extent of the Brillouin zone. The procedure is then called k resolved inverse photoemission (KRIPES). The most important requirements for resolved measurement are: ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$

1. The sample must be monocrystalline.
   A polycrystal contains areas of different crystalline orientations, so the incident electrons scan many different lines in the Brillouin zone. That is why single-crystal samples are chosen for band mapping. It is important that the crystalline order on the sample surface is not disturbed by excessively brutal procedures during sample cleaning, e.g. by sputtering with excessively high ion energies.
2. The k-uncertainty of the electron beam must be small enough.
   The electron beam should run as parallel as possible. The angular unsharpness of the beam Δθ leads approximately to an unsharpness of . The tolerable angular divergence of the electron beam thus decreases with increasing energy. The energy uncertainty of the electron beam is also associated with an uncertainty. ${\displaystyle {\vec {k}}}$ ${\displaystyle \Delta K(\Delta \theta )=\Delta \theta {\sqrt {(}}2mE)/\hbar }$ ${\displaystyle E=(\hbar k)^{2}/2m}$ ${\displaystyle {\vec {k}}}$
3. The electron penetration depth must not be too small.
   The low penetration depth (mean free path) of the electrons limits the location of the IPE transition. According to the uncertainty relation, the greater the localization, the greater the uncertainty of . The energy dependence of the mean free path for electrons in solids shows roughly the same course for all solids. The uncertainty in the range below 20 eV is sufficiently small for KRIPES. ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$
4. Phonon-accompanied transitions must not contribute too much to the spectrum.
   If phonons are involved in the photon-generating transition, the transition is no longer sustaining because phonons can absorb a momentum difference. In the energy range below 20 eV, the proportion of indirect transitions is in the order of magnitude of 1%, while it can be over 50% in the keV range. Even if a sufficiently low photon energy is chosen , the conservation can be switched off if states localized on the surface take part in the transition as initial states, which couple to free electron states in a vacuum, but quickly decay in the direction of solid body volume ("evanescent states"). According to the uncertainty principle, their localization is accompanied by a correspondingly large amount of uncertainty in the component perpendicular to the surface ( ). In this case, transitions with all values ​​of the Brillouin zone contribute to the IPE spectrum . In an IPE experiment, in which the photon energy is registered with a fixed electron energy, the one-dimensional density of states is reflected in the spectrum if the primary energy is chosen so that the initial state is an “evanescent state”. In an isochromatic experiment, “evanescent states” can only be involved as initial states at discrete points in the spectrum. ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle k_{\perp }}$ ${\displaystyle k_{\perp }}$

Evaluation of KRIPE spectra

Localization of the IPE junctions in a zincblende lattice in the free electron approximation

The component of the wave vector parallel to the surface ( ) is retained except for the parallel component of a reciprocal lattice vector (surface forces only act perpendicular to the surface): ${\displaystyle {\vec {k}}_{\|}}$

${\displaystyle {\vec {k}}_{\|}={\vec {k}}_{\|vac}+{\vec {G}}_{\|}}$

If is not equal to zero, it is called a flip process. When recording an IPE spectrum, a line is scanned in the direction of the incident electron beam. The direction of this line in the Brillouin zone can be determined by selecting the electron angle of incidence θ. If the work function of the sample Φ _{P is known} , one can calculate: ${\displaystyle {\vec {G}}_{\|}}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle {\vec {k}}_{\|}}$

${\displaystyle {\vec {k}}_{\|}={\sqrt {{\frac {2m}{\hbar ^{2}}}(\hbar \omega +E_{f}-\Phi _{P})}}\cdot \sin {\theta }}$

KRIPES measurements of InP (100) Top right: IPE spectrum at normal incidence. The insert shows the unoccupied part of the band structure (green) and almost free electron parabolas as initial states (red). The parabolas are shifted to the left by 9.9 eV (photon energy) on the energy axis, so that the points of intersection with the conduction bands show possible direct transitions. Peaks B and C are assigned to direct transitions into bands of volume, while peak A is caused by transitions into a surface state. Peak D corresponds to a maximum of the density of states. Bottom right: The dispersion of the surface condition was determined with the help of IPE spectra recorded at different angles of incidence (left). The black dots show the projected volume band structure.

Since surface states do not have a sharp value according to the uncertainty relation, knowledge of is sufficient to measure their energy dispersion . For this purpose, isochromats are recorded at different electron angles of incidence. From the position of peaks that can be traced back to transitions in surface conditions, the dispersion can be calculated directly with the aid of the above formula. ${\displaystyle k_{\perp }}$ ${\displaystyle k_{\|}}$ ${\displaystyle E({\vec {k}}_{\|})}$ ${\displaystyle E({\vec {k}}_{\|})}$

To determine the dispersion of volume states, one must also know the component perpendicular to the surface. This can be calculated if one knows the function of the initial state of the electrons. The almost free electron approximation is often a good approximation for this. It is assumed that the function is approximated by the parabola of free electrons, energetically lowered by an " inner potential ". This gives the following relationship between the initial and final energy of the electrons ( E _i and E _f ), the photon energy and the internal potential : ${\displaystyle E({\vec {k}})}$ ${\displaystyle {\vec {k}}}$ ${\displaystyle E({\vec {k}})}$ ${\displaystyle E({\vec {k}})}$ ${\displaystyle \hbar \omega }$ ${\displaystyle V_{0}}$

${\displaystyle {\frac {\hbar ^{2}}{2m}}(k_{\perp }^{2}+k_{\|}^{2})=\hbar \omega +E_{f}+V_{0}}$

Instead of using the almost free electron approximation, the final state can also be determined experimentally with the energy coincidence or triangulation method. For this purpose, a transition is sought that can be observed in IPE spectra of two differently oriented surfaces. The intersection of the lines established in the two measurements then gives the -vector of the transition. ${\displaystyle k_{\perp }}$ ${\displaystyle k_{\perp }}$ ${\displaystyle {\vec {k}}}$

Band structures are usually calculated on the highly symmetrical lines of the Brillouin zone. A comparison with IPE spectra becomes particularly easy if the spectra are recorded in the spectrometer mode. If you align the electron beam in a highly symmetrical direction and record a series of spectra with different electron energies, you can observe how peaks shift from spectrum to spectrum, because the electron energy also changes. In this way, the states can be sampled on the selected highly symmetrical line. This method corresponds to the use of a variable photon energy in photoemission, for which synchrotron radiation is required there; an effort that is not required in the inverse photo emission. ${\displaystyle k_{\perp }}$

Determination of the density of states

requirements

If one wants to determine the density of states, one uses photon energies in the range 1 to 5 keV; then indirect transitions accompanied by phonons dominate the spectra. For practical reasons, the spectrum is usually recorded as isochromates. In contrast to the spectrometer operation, with the mostly used focusing monochromators the sometimes complex alignment of the sample as a photon source, the monochromater crystal and the detector on the Rowland circle can remain unchanged. Polycrystals or vapor-deposited layers are preferred as samples. The energy must be chosen so that no characteristic X-rays get into the detector.

Evaluation of BIS spectra

Qualitatively, the isochromats can be compared directly with the calculated density of states. A more precise evaluation must take into account the influence of other factors that influence the spectrum. This includes the resolution function of the spectrometer used or energy losses that the electrons in the sample can suffer before the X-ray transition and which can be measured with energy loss spectroscopy. In order to be able to calculate these effects from the spectra, deconvolution algorithms have been developed.

Construction of an IPE apparatus

Because of the high surface sensitivity of the method, the apparatus is operated in an ultra-high vacuum . In addition to the main components sample, electron source and photon detector with energy filter, suitable means are required to clean the sample surface. These typically include a heater for the sample and an ion source for cleaning by ion beam sputtering . Samples with a clean and well-ordered surface can also be prepared by splitting crystals in situ or by vapor deposition of thin layers on suitable substrates. If the order of the surface is not important (e.g. for density of states measurements), sanding the sample in situ can also be useful.

Auger electron spectroscopy is often used to test surface cleanliness . For KRIPES, the surface order of the monocrystalline samples must also be ensured. The diffraction of low-energy electrons ( Low Energy Electron Diffraction , LEED) has proven itself as a control. However, it has been shown that in some cases KRIPES reacts so sensitively to disturbances in the surface order that changes in the IPE spectrum can be seen that are not yet visible in the LEED image.

One challenge is the fact that, for physical reasons, the inverse photo emission has to make do with considerably lower count rates than the photo emission. The probability that one photon is generated per incident electron in the inverse photoemission is about 5 orders of magnitude smaller than the probability with which one electron per photon is excited in the photoemission. In order to achieve a sufficient count rate at all, one has to be satisfied with a poorer energy resolution than with photoemission.

For the resolved measurement of surface conditions, the specimen holder should be rotatable in two directions. Computer-controlled drives for the sample rotation have proven to be effective, so that spectra series with varied electron beam angles can be recorded automatically. ${\displaystyle {\vec {k}}}$

The earth's magnetic field is compensated in the area of ​​the experiment with the help of Helmholtz coils in order to avoid a deflection of the electrons. The UHV recipient and the components used must be made of non-magnetic materials (e.g. stainless steel with low permeability, tantalum, oxygen-free copper).

Electron sources

Electron gun according to Erdmann and Zipf

Electron gun according to Erdmann and Zipf

Requirements for the electron source are: small energy width and small angular divergence with the highest possible current strength in the relevant energy range. If a monochromator is used, a small spot is also important. In the keV area, these requirements are z. B. met by a Pierce electron gun.

In the low-energy range (5 to 30 eV), the electron guns according to Erdmann and Zipf and according to Stoffel and Johnson have prevailed. Both have in common that the electrons are first accelerated to a higher energy and then decelerated again. Indirectly heated barium oxide cathodes, which are characterized by a low work function, are particularly suitable as cathodes. This allows the heating temperature to be kept low, which is advantageous in order to achieve a narrow thermal energy distribution of the electrons. An inexpensive and at the same time high-quality solution is the use of cathodes from television picture tubes. It is necessary not to operate the electron gun with a current that is not too high, since space charge effects become noticeable with increasing current, which deteriorate the energy and sharpness. ${\displaystyle {\vec {k}}}$

For spin-resolved inverse photoemission, electron sources are used that are based on the emission of spin-polarized photoelectrons, which can be triggered by means of circularly polarized light from the surfaces of suitably prepared gallium arsenide or gallium arsenide phosphide crystals. These electron sources, which are considerably more complex in terms of apparatus than electron guns, have, correctly constructed and operated, in addition to spin polarization, also have a very good energy resolution (down to 125 meV).

Photon detectors and energy filters

Focusing crystal monochromators are used for IPE in the keV range . As crystals come z. B. mica (energy window 622.5 eV in the first order of diffraction and 1245 eV in the second order) or molybdenide (MoS ₂ ) crystals (1008.1 eV in the first order) into consideration. Photocathodes (e.g. made of CsJ) with channeltrons are used as detectors .

A simpler solution is to combine the X-ray detector with a simple absorption film instead of a monochromator, which has the task of absorbing all photons above a suitable absorption edge . The spectrum is recorded using modulation technology with a lock-in amplifier so that the spectrum is recorded as the differential of the signal. Otherwise, the integral of the spectrum would be recorded with a detector that is only limited in the direction of high energies .

IPE detector for an energy of 9.9 eV It is an acetone-filled counter tube with a calcium fluoride window.

In the low-energy range (KRIPES), two types of detectors have become established: energy-selective counter tubes and grating monochromators with spatially resolving detectors. The latter can e.g. B. consist of a microchannel plate and a chevron anode . As a result, a whole spectrum of photons can be recorded at the same time, so that the counting rate, which is considerably worse than that of the counter tubes, can be at least partially compensated for. In practice, the monochromator arrangements have their strength when it comes to band mapping of volume states, since band mapping on lines is possible in spectrometer operation . ${\displaystyle k_{\perp }}$

Counting tubes are advantageous when surface conditions are to be investigated that are blurred but require the highest level of detection sensitivity in order to be able to record spectra quickly enough before the sensitive surface conditions disappear due to contamination of the surface. ${\displaystyle k_{\perp }}$

The counter tube detectors implement an energy filter (band pass) in that the counting gas used defines a lower energy limit through its ionization energy. The energy window is limited at the top by a photon entry window from a single-crystal alkaline earth halide disk. These have a relatively sharp transmission limit in the high-energy direction. Usual combinations are: iodine as counting gas with calcium fluoride window (E = 9.7 eV, ΔE = 0.8 eV  FWHM ) or acetone with calcium fluoride (E = 9.9 eV, ΔE = 0.4 eV FWHM).

The counter tube detectors have a diameter of about 20 mm and are brought very close to the sample so that they detect photons in a large solid angle . Therefore, they have a much better detection sensitivity than detectors that work with monochromators.

The iodine counter tube is the first to record isochromates in this energy range and it has been used successfully in many laboratories. The acetone counter tube was developed later and, in addition to better energy resolution, has a negligible dead time (no correction required) and, unlike the iodine counter tube, does not need to be temperature stabilized. In addition, it is more durable because it does not use chemically aggressive iodine. Other window / counting gas combinations have also been used, e.g. B. strontium fluoride / iodine (E = 9.5 eV, ΔE = 0.5 eV FWHM) or calcium fluoride / carbon disulfide (E = 10.2 eV, ΔE = 0.07 eV FWHM). It has been observed that the energy resolution of the bandpass can sometimes be significantly worse than calculations based on the window transmission and the ionization probability of the counting gas suggest.

Another bandpass variant uses solid-state photocathodes instead of a counter tube gas, usually in combination with a secondary electron multiplier (discrete secondary electron multiplier or channeltron , or microchannel plate ).

literature

Review article KRIPES

• PT Andrews, IR Collins, JE Inglesfield: Inverse Photoemission and How it is Used, in: Topics in Applied Physis, Vol 69: Unoccupied Surface States (1993), pp. 244-275
• R. Schneider, V. Dose: Further Topics in Low-Energy Inverse Photoemission, Topics in Applied Physis 1993, 278-305
• FJ Himpsel : Inverse photoemission from semiconductors . In: Surface Science Reports . tape 12 , no. 1 , 1990, p. 3-48 , doi : 10.1016 / 0167-5729 (90) 90005-X .
• PD Johnson, SL Hulbert: Inverse photoemission . In: Review of Scientific Instruments . tape 61 , 1990, pp. 2277 , doi : 10.1063 / 1.1141352 .
• Can V .: Momentum-resolved inverse photoemission . In: Surface Science Reports . tape 5 , no. 8 , 1985, pp. 337-378 , doi : 10.1016 / 0167-5729 (85) 90006-8 .
• NV Smith, DP Woodruff: Inverse photoemission from metal surfaces . In: Progress in Surface Science . tape 21 , no. 4 , 1986, pp. 295-370 , doi : 10.1016 / 0079-6816 (86) 90004-3 .
• B. Reihl: Unoccupied surface states on metal surfaces as revealed by inverse photoemission . In: Surface Science . tape 162 , no. 1-3 , 1985, pp. 1-10 , doi : 10.1016 / 0039-6028 (85) 90867-2 .

Review article spin-resolved inverse photoemission

• M. Donath: Polarization effects in inversephotoemission spectra . In: Progress in Surface Science . tape 35 , no. 1-4 , 1990, pp. 47-50 , doi : 10.1016 / 0079-6816 (90) 90019-G .

Review article BIS

• JC Fuggle: bremsstrahlung isochromatic spectroscopy (BIS or High-Energy Inverse Photoemission) . In: Applied Physis, Vol 69: Unoccupied Surface States . Springer, 1992, ISBN 0-387-54162-4 , pp. 307-337 , doi : 10.1007 / 3540541624_20 .
• H. Scheidt: Recent developments in the field of bremsstrahlung isochromate spectroscopy . In: Progress of Physics / Progress of Physics . tape 31 , no. 7 , 1983, pp. 357-401 , doi : 10.1002 / prop.2190310702 .
• K. Ulmer in: Band Structure Spectroscopy of Metals and Alloys, DJ Fabian, LM Watson (Ed.), London 1973
• H. Merz, Silicates Industriels 4 (1976), 285

theory

• G. Borstel, G. Thörner: Inverse photoemission from solids: Theoretical aspects and applications . In: Surface Science Reports . tape 8 , no. 1 , 1988, p. 1-41 , doi : 10.1016 / 0167-5729 (88) 90006-4 .

Books

• David P. Woodruff, TA Delchar: Modern techniques of surface science . 2nd Edition. Cambridge Univ. Press, Cambridge 1994, ISBN 0-521-42498-4 .

Remarks

1. ↑ The number of publications was determined by querying the SCOPUS database for publications with "inverse photoemission" in the title, abstract or keywords.
2. ↑ Although the VUV photons of the inverse photoemission are bremsstrahlung, the term "bremsstrahlung isochromatic spectroscopy" (BIS) is only used for IPE in the X-ray range.

Individual evidence

1. ^ W. Duane, FL Hunt: On X-Ray Wave-Lengths . In: Physical Review . tape 6 , no. 2 , 1915, p. 166-172 , doi : 10.1103 / PhysRev.6.166 .
2. ^ P. Ohlin: Arkiv för matematik, astronomi och fysik . A29, no. 3 , 1942.
3. ^ BRA Nijboer: On the intensity distribution of the continuous x-ray spectrum near its short-wavelength limit . In: Physica . tape 12 , no. 7 , 1946, pp. 461-466 , doi : 10.1016 / S0031-8914 (46) 80060-0 .
4. ^ Kurt Ulmer: New Method for the Evaluation of h / e from the Quantum Limit of the Continuous X-Ray Spectrum . In: Physical Review Letters . tape 3 , no. 11 , 1959, pp. 514-516 , doi : 10.1103 / PhysRevLett.3.514 .
5. ↑ G. Denninger, V. Dose, HP Bonzel: Evidence for Direct Optical Interband Transitions in Isochromat Spectra from Pt Single-Crystal Surfaces . In: Physical Review Letters . tape 48 , no. 4 , 1982, pp. 279-282 , doi : 10.1103 / PhysRevLett.48.279 .
6. ^ V. Dose: VUV isochromatic spectroscopy . In: Applied Physics . tape 14 , 1977, pp. 117-118 , doi : 10.1007 / BF00882639 .
7. ↑ See e.g. B .:
   R. Courths, S. Hüfner: photoemission experiments on copper . In: Physics Reports . tape 112 , no. 2 , 1984, p. 53-171 , doi : 10.1016 / 0370-1573 (84) 90167-4 . G. Borstel, G. Thörner: Inverse photoemission from solids: Theoretical aspects and applications . In: Surface Science Reports . tape
    8 , no. 1 , 1988, p. 1-41 , doi : 10.1016 / 0167-5729 (88) 90006-4 .
8. ^ M. Donath: Polarization effects in inversephotoemission spectra . In: Progress in Surface Science . tape 35 , no. 1-4 , 1990, pp. 47-50 , doi : 10.1016 / 0079-6816 (90) 90019-G .
9. ↑ EO Kane: Implications of Crystal Momentum Conservation in Photoelectric Emission for Band-Structure Measurements . In: Physical Review Letters . tape 12 , no. 4 , 1964, pp. 97-98 , doi : 10.1103 / PhysRevLett.12.97 .
10. ↑ R. Stiller, H. Merz, W. Drewes, H.-G. Purwins: bremsstrahlung isochromatic spectroscopy of light rare earth compounds . In: Le Journal de Physique Colloques . tape 48 , C9, 1987, pp. 4 , doi : 10.1051 / jphyscol: 19879177 .
11. ↑ Volker Dose: Ultraviolet bremsstrahlung spectroscopy . In: Progress in Surface Science . tape 13 , no. 3 , 1983, p. 225-283 , doi : 10.1016 / 0079-6816 (83) 90005-9 .
12. ↑ JR Pierce: Rectilinear Electron Flow in Beams . In: Journal of Applied Physics . tape 11 , 1940, p. 548 , doi : 10.1063 / 1.1712815 .
13. ^ Peter W. Erdman, Edward C. Zipf: Low-voltage, high-current electron gun . In: Review of Scientific Instruments . tape 53 , 1982, pp. 225 , doi : 10.1063 / 1.1136932 .
14. ^ NG Stoffel, PD Johnson: A low-energy high-brightness electron gun for inverse photoemission . In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment . tape 234 , no. 2 , 1985, pp. 230-234 , doi : 10.1016 / 0168-9002 (85) 90910-6 .
15. ^ O. Klemperer, ME Barnett: Electron Optics . 1st edition. Cambridge University Press, 1971.
16. ↑ Joachim Kessler: Polarized electrons . 2nd Edition. Springer, 1985, ISBN 3-540-15736-0 .
17. ↑ An overview of the literature on sources of spin-polarized electrons up to 2000 can be found e.g. B. in W. Hilbert: Generation of a useful beam of spin-polarized electrons at the ELSA accelerator. Habilitation thesis, University of Bonn, 2000 ( PDF; 1.04 MB )
18. ↑ M. Budke, V. Renken, H. Liebl, G. Rangelov, M. Donath: Inverse photoemission with energy resolution better than 200 meV . In: Review of Scientific Instruments . tape 78 , 2007, p. 083903 , doi : 10.1063 / 1.2771096 .
19. ↑ M. Conrad, V. Dose, Th. Fauster, H. Scheidt: Isochromat spectroscopy using SXAPS equipment . In: Applied Physics . tape 20 , 1979, pp. 37-40 , doi : 10.1007 / BF00901784 .
20. ↑ Th. Fauster, FJ Himpsel, JJ Donelon, A. Marx: Spectrometer for momentum-resolved bremsstrahlung spectroscopy . In: Review of Scientific Instruments . tape 54 , 1983, pp. 68 , doi : 10.1063 / 1.1137218 .
21. ^ Th. Fauster, D. Straub, JJ Donelon, D. Grimm, A. Marx, FJ Himpsel: Normal-incidence grating spectrograph with large acceptance for inverse photoemission . In: Review of Scientific Instruments . tape 56 , 1985, pp. 1212 , doi : 10.1063 / 1.1137977 .
22. ^ V. Dose: VUV isochromatic spectroscopy . In: Applied Physics . tape 14 , 1977, pp. 117-118 , doi : 10.1007 / BF00882639 .
23. ↑ D Funnemann, H Merz: 10 eV photon detector for inverse photoemission . In: Journal of Physics E: Scientific Instruments . tape 19 , 1986, pp. 554-557 , doi : 10.1088 / 0022-3735 / 19/7/011 .
24. ^ W. Altmann, M. Donath, V. Dose, A. Goldmann: Dispersion of empty surface states on Ni (1 1 0) . In: Solid State Communications . tape 53 , no. 2 , 1985, pp. 209-211 , doi : 10.1016 / 0038-1098 (85) 90128-0 .
25. ^ PMG Allen, PJ Dobson, PR Webber: A new photon counter for inverse photoemission . In: Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films . tape 5 , 1987, pp. 3346-3350 , doi : 10.1116 / 1.574194 .
26. ↑ N. Babbe, W. Drube, I. Shepherd, M. Skibowski: A simple and compact system for combined angular resolved inverse photoemission and photo-emission in the vacuum ultraviolet . In: Journal of Physics E: Scientific Instruments . tape 18 , 1985, pp. 158-160 , doi : 10.1088 / 0022-3735 / 18/2/014 .
27. ↑ I. Shepherd, W. Drube, M. Schlüter, G. Plage, M. Skibowski: bandpass photon detector with high efficiency for inverse photoemission spectroscopy . In: Review of Scientific Instruments . tape 58 , 1987, pp. 710 , doi : 10.1063 / 1.1139244 .
28. ↑ Yoshifumi Ueda, Katsuhiro Nishihara, Kojiro Mimura, Yasuko Hari, Masaki Taniguchi, Masami Fujisawa: Performance of the inverse photoemission spectrometer with a new bandpass photon detector of narrow bandwidth and high sensitivity . In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment . tape 330 , no. 1-2 , 1993, pp. 140-143 , doi : 10.1016 / 0168-9002 (93) 91315-E .
29. ↑ F. Schedin, G. Thornton, RIG Uhrberg: Windows and photocathodes for a high resolution solid state bandpass ultraviolet photon detector for inverse photoemission . In: Review of Scientific Instruments . tape 68 , 1997, pp. 41 , doi : 10.1063 / 1.1147844 .