Editing Photoelectric effect (section)

=== Photoemission from atoms, molecules and solids ===
Electrons that are bound in atoms, molecules and solids each occupy distinct states of well-defined [[Binding energy|binding energies]]. When light quanta deliver more than this amount of energy to an individual electron, the electron may be emitted into free space with excess (kinetic) energy that is <math>h\nu</math> higher than the electron's binding energy. The distribution of kinetic energies thus reflects the distribution of the binding energies of the electrons in the atomic, molecular or crystalline system: an electron emitted from the state at binding energy <math>E_B</math> is found at kinetic energy <math>E_k=h\nu-E_B</math>. This distribution is one of the main characteristics of the quantum system, and can be used for further studies in quantum chemistry and quantum physics.{{citation needed|date=November 2023}}

====Models of photoemission from solids====
The electronic properties of ordered, crystalline solids are determined by the distribution of the electronic states with respect to energy and momentum—the electronic band structure of the solid. Theoretical models of photoemission from solids show that this distribution is, for the most part, preserved in the photoelectric effect. The phenomenological ''three-step model''<ref>{{Cite journal|last1=Berglund|first1=C. N.|last2=Spicer|first2=W. E.|date=1964-11-16|title=Photoemission Studies of Copper and Silver: Theory|journal=Physical Review|volume=136|issue=4A|pages=A1030–A1044|doi=10.1103/PhysRev.136.A1030|bibcode=1964PhRv..136.1030B}}</ref> for ultraviolet and soft X-ray excitation decomposes the effect into these steps:<ref name="Stefan2003">{{cite book|last=Hüfner|first=S.|title=Photoelectron Spectroscopy: Principles and Applications|publisher=[[Springer (publisher)|Springer]]|year=2003|isbn=3-540-41802-4}}</ref><ref>{{Cite journal|last1=Damascelli|first1=Andrea|last2=Shen|first2=Zhi-Xun|last3=Hussain|first3=Zahid|date=2003-04-17|title=Angle-resolved photoemission spectroscopy of the cuprate superconductors|arxiv=cond-mat/0208504|journal=Reviews of Modern Physics|volume=75|issue=2|pages=473–541|doi=10.1103/RevModPhys.75.473|s2cid=118433150|issn=0034-6861}}</ref><ref name=":0">{{cite journal|last1=Sobota|first1=Jonathan A.|last2=He|first2=Yu|last3=Shen|first3=Zhi-Xun|title=Angle-resolved photoemission studies of quantum materials|journal=Reviews of Modern Physics|year=2021|volume=93|issue=2|page=025006|doi=10.1103/RevModPhys.93.025006|arxiv=2008.02378|bibcode=2021RvMP...93b5006S|s2cid=221006368}}</ref>

# Inner photoelectric effect in the bulk of the material that is a direct optical transition between an occupied and an unoccupied electronic state. This effect is subject to quantum-mechanical [[selection rule]]s for dipole transitions. The hole left behind the electron can give rise to secondary electron emission, or the so-called [[Auger effect]], which may be visible even when the primary photoelectron does not leave the material. In molecular solids [[phonon]]s are excited in this step and may be visible as satellite lines in the final electron energy.
# Electron propagation to the surface in which some electrons may be scattered because of interactions with other constituents of the solid. Electrons that originate deeper in the solid are much more likely to suffer collisions and emerge with altered energy and momentum. Their mean-free path is a [[Inelastic mean free path|universal curve]] dependent on electron's energy.
# Electron escape through the surface barrier into free-electron-like states of the vacuum. In this step the electron loses energy in the amount of the ''work function of the surface'', and suffers from the momentum loss in the direction perpendicular to the surface. Because the binding energy of electrons in solids is conveniently expressed with respect to the highest occupied state at the Fermi energy <math>E_F</math>, and the difference to the free-space (vacuum) energy is the work function of the surface, the kinetic energy of the electrons emitted from solids is usually written as <math>E_k = h\nu -W - E_B</math>.

There are cases where the three-step model fails to explain peculiarities of the photoelectron intensity distributions. The more elaborate ''one-step model''<ref>{{Cite journal|last=Mahan|first=G. D.|date=1970-12-01|title=Theory of Photoemission in Simple Metals|journal=Physical Review B|volume=2|issue=11|pages=4334–4350|doi=10.1103/PhysRevB.2.4334|bibcode=1970PhRvB...2.4334M}}</ref> treats the effect as a coherent process of photoexcitation into the final state of a finite crystal for which the wave function is free-electron-like outside of the crystal, but has a decaying envelope inside.<ref name=":0" />