To study the electron structure of solids, ARPES makes use of the photoelectric effect, as detected by Hertz in 1887.  The photoelectric effect is demonstrated when a beam of light (with a high-enough frequency) shines on a clean surface.  The light will cause electrons to leave that surface.  In our ARPES experiments, a helium-discharging lamp emits high-frequency light waves onto a sample.  An ARPES sensor gathers the ejected electrons.  Click here to see the ARPES sensor and equipment in our lab. 

Though the procedures and apparatus may seem sophisticated, the basic principles behind ARPES are simple. ARPES utilizes the phenomenon of the photoelectric effect. First, a lamp emits photons on a small, thin substance. the photons bombard electrons out of the substance, and a sensor collects these electrons. The sensor measures the number of electrons, their momentum (measured by the angles) and kinetic energy.

 The data collected by the ARPES sensor provides information about electrons' energy after the photons bombard them from the sample.  Making use of the Law of Conservation of Energy, this data is used to describe the electrons' energy before the collision.  Thus, data gathered in the ARPES sensor provides information about the electrons' energy when they are still in the sample.  The total energy is conserved before and after the photoelectric effect.  The main equation depicting this is:

This means the energy (before the collision) of the incoming photon (h w) equals the kinetic energy of the electrons (E_kin), plus the work function (f), plus the binding energy (E _B) of the electrons in the sample.  In other words, the energy put into the system, the photons, h w, equals the energy out of the system, E_kin plus the energy required for the electrons to leave the metal,  f, and E _B, the binding energy of the electron.   f is a property of the target material called its work function.  To escape from the target, an electron must pick up a certain minimum energy from the photon h w = f.  

The Law of Conservation of Momentum also applies to the electrons during the photoemission process.  We measure the momentum of the electrons only in the direction parallel to the surface of the sample.  This is because the momentum of the electrons in a direction parallel to the surface of the sample is conserved, whereas the discontinuity of the surface of the sample breaks the conservation of momentum of the electrons in the direction normal to the surface.  Also, the momentum of the incoming photon is negligible compared to the momentum of the electrons.  This is why the parallel component of the momentum of the ejected electrons approximately equals the momentum of the electrons in the solid.  Thus, with the momentum data collected by the ARPES sensor, we are able to discern the momentum of the electrons inside the solid, in a plane parallel to the surface of the solid.  The following equation represents momentum as a function of energy, mass, and the angle of the ARPES sensor.   

See the figure above for a visual representation of the momentum.  It is the projection of the actual three-dimensional momentum on a plane tangential to the surface of the sample. 

The photoemission spectrum displays the distribution of the electrons' intensity, N(E), as a function of kinetic energy.   

As shown above, the ARPES sensor, displayed as "Spectrum" in blue, displays the intensity of detected electrons, N(E), that have various kinetic energies, E.  These values obtained by the ARPES sensor correspond to the actual values of the "Sample", displayed red.  In a solid material, the electrons are distributed to an energy level below E_Fermi, the Fermi Level.  The ARPES spectrum reveals peaks with an identical energy distribution as the one in the solid.  However, the peaks are slightly wider, due to electron scattering during the process.  

Note on the top graph, as the horizontal peak of these electron energies at various angles is noted.  These are then recorded onto another graph, which represents energy at various angles,