of the th level in element of atomic number Z and are the energies of the same levels in the next element up in the periodic table. While useful in practice, a more rigorous model accounting for effects such as screening and relaxation probabilities between energy levels gives the Auger energy as: where is the energy of interaction between the B and C level holes in a final atomic state x and the R'''s represent intra- and extra-atomic transition energies accounting for electronic screening. Auger electron energies can be calculated based on measured values of the various and compared to peaks in the secondary electron spectrum in order to identify chemical species. This technique has been used to compile several reference databases used for analysis in current AES setups. Experimental setup and quantification Instrumentation Surface sensitivity in AES arises from the fact that emitted electrons usually have energies ranging from 50 eV to 3 keV and at these values, electrons have a short mean free path in a solid. The escape depth of electrons is therefore localized to within a few nanometers of the target surface, giving AES an extreme sensitivity to surface species. Because of the low energy of Auger electrons, most AES setups are run under ultra-high vacuum (UHV) conditions. Such measures prevent electron scattering off of residual gas atoms as well as the formation of a thin "gas (adsorbate) layer" on the surface of the specimen, which degrades analytical performance. A typical AES setup is shown schematically in figure 2. In this configuration, focused electrons are incident on a sample and emitted electrons are deflected into a cylindrical mirror analyzer (CMA). In the detection unit, Auger electrons are multiplied and the signal sent to data processing electronics. Collected Auger electrons are plotted as a function of energy against the broad secondary electron background spectrum. The detection unit and data processing electronics are collectively referred to as the electron energy analyzer. Since the intensity of the Auger peaks may be small compared to the noise level of the background, AES is often run in a derivative mode that serves to highlight the peaks by modulating the electron collection current via a small applied AC voltage. Since this , the collection current becomes . Taylor expanding gives: Using the setup in figure 2, detecting the signal at frequency ω will give a value for or . Plotting in derivative