Angle-resolved photoemission spectroscopy

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Condensed matter
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Neutron scattering
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An Experimental Setup of Angle-Resolved Photoemission Spectroscopy
Photoemission and metals

Angle-resolved photoemission spectroscopy (ARPES), is a direct experimental technique to observe the distribution of the electrons (more precisely, the density of single-particle electronic excitations) in the reciprocal space of solids. The technique is a refinement of ordinary photoemission spectroscopy, studying photoemission of electrons from a sample achieved usually by illumination with soft X-rays. ARPES is one of the most direct methods of studying the electronic structure of the surface of solids.

ARPES gives information on the direction, speed and scattering process of valence electrons in the sample being studied (usually a solid). This means that information can be gained on both the energy and momentum of an electron, resulting in detailed information on band dispersion and Fermi surface.

The technique is also known as ARUPS (angle-resolved ultraviolet photoemission spectroscopy) when using ultraviolet light (as opposed to X-rays) to generate photoemission.

Band mapping[edit]

In condensed matter physics, band mapping refers to the process of detection and measurement of the photoelectrons emitted from a surface at different emission angles. This process is employed in ARPES, which is then used to investigate the electronic structure of solids, solid surfaces and interfaces.

By employing the band mapping process, several fundamental physical properties of a solid can be determined. These include (but are not limited to) the following:

  • Kinetic energy of the electron(s);
  • Elasticity;
  • Electrical/Magnetic properties;
  • Optical properties.

The electronic states in the solid are described by energy bands, which have associated energy band dispersions E(k) — energy eigenvalues for delocalized electrons in a crystalline medium according to Bloch's theorem.

Band mapping has an advantage over optical spectroscopy. In the latter, only the energy-band separations at various optical critical points in k-space — energy between the initial and final states — are determined. ARPES, on the other hand, provides information about the absolute location of energy bands at different values of k relative to the Fermi level (EF).


From the energy conservation, for the photoemission process we have that


  • is the kinetic energy of the outgoing electron — measured
  • is the energy of the incoming photon — measured
  • is the binding energy of the electron
  • is the electron work function, i.e. the energy required to remove electron from sample to vacuum

The photon momentum is here neglected, because of its relatively small contribution compared with the electron momentum.

In the typical case, where the surface of the sample is smooth, translational symmetry requires that the component of electron momentum in the plane of the sample be conserved:


  • is the momentum component of the outgoing electron parallel to the surface — measured by angle
  • is the initial momentum component.

However, the normal component of electron momentum might not be conserved. The typical way of dealing with this is to assume that the final in-crystal states are free-electron-like, in which case one has

where denotes the band depth from vacuum, thus accounting also for the electron work function . The value of can be determined by examining only the electrons emitted perpendicular to the surface and measuring their kinetic energy as a function of incident photon energy.

The equations for energy and momentum can be solved to determine the dispersion relation between the binding energy, , and the wave vector, , of the electron.

See also[edit]


External links[edit]