Angle-resolved photoemission spectroscopy (
ARPES), also known as
ARUPS (angle-resolved
ultravioletUltraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...
photoemission spectroscopyPhotoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
), 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. 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 surfaceIn condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
. This technique is a refinement of ordinary
photoemission spectroscopyPhotoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
.
Conservation of energy:
Photon momentum is neglected because of its smallness compared with electron momentum. Therefore, electron
momentum is conserved for parallel component
where
kinetic energy of the outgoing electron — measured.
incoming photon energy — measured.
electron work function (energy required to remove electron from sample to vacuum)
momentum of the outgoing electron, measured by angle
initial momentum of the electron
However,the normal component of electron momentum
can be expressed as,
in which
denotes the band depth from vacuum, including electron work function
that is the depth of Fermi surface from vacuum.
The equations for energy and momentum can be solved to find out dispersion relation between
(binding energy of the electron) and
(wave vector) .