Photoelectron spectroscopy is a technique to know binding energy of electrons inside materials.
We irradiate a material with photons having a certain energy hν, and detect the electrons coming out from the material.
This process is well-known as the "photoelectric effect".
Through this process, the energy of the photon hν is given to an electron.
Suppose the photoexcited electron originally had an binding energy EB inside the material,
and the material has an work function of Φ.
In the case the photon energy hν is large enough, the electron can get out of the material by breaking the bound condition by paying the energy EB, and paying "tax energy to get out of the material" (work function) Φ and goes somewhere outside the material with a kinetic energy Ekin.
The energy conservation rule covering this process is expressed as follows.
hν = EB + Φ + Ekin
We count the number of the photoelectrons having kinetic energy Ekin, and obtain a spectrum I(Ekin).
Ekin can be converted to EB using the above relationship.
Thus, as a result, we obtain a spectrum which shows photoelecgtron intensity- binding energy relationship I(EB).
Existence of a photoelectron peak at EB indicates that there are many electrons having the binding energy EB inside materials.
That is, there is a high density of states at EB .
The most common purpose, I suppose, to use photoelectron spectroscopy is to see the chemical environment of atoms.
For example, by measuring the binding energy of 2p electrons of silicon inside silicon oxide,
we can find the valency of Si atom, Si0+, Si1+ Si2+, Si3+ or Si4+, and find the number of oxygen atoms binding to a silicon atom.
Electrons in core levels is most suitable to examine the chemical environment of atoms.
Because the binding energy of the core electron is large (typically 20eV - a few keV), photons for the photoelectron excitation should have large energy too. Such photon is called X-ray. Thus, this type of photoelectron spectroscopy is often called as X-ray photoelectron spectroscopy (XPS).
Another purpose to use photoelectron spectroscopy is to determine the valence band structure.
Electrons in the outer-most electron shell of the atoms inside crystals tends to interact with the outer-most electrons in neighboring atoms. Such electrons can move around inside crystal with some momentum. The behavior of the movement is often expressed through "energy-momentum relationship" called band structure.
Most of the electronic properties such as conductance, magnetism, superconductors, light emission, are related to this band diagram. Thus, it is very important to know the band structure of the crystals.
To obtain valence band structure, we need to get I(EB) at each photoelectron emission angle θ.
Because the momentum conservation rule is valid for the surface parallel component in the photoelectron emission process, we can specify the surface parallel component of the momentum of the photoelectron with kinetic energy Ekin and emission angle θ.