The electron yield is determined by two factors, the electron-impact cross-section and fluorescence yield. While the latter does not depend on the incident beam, the first one does:
https://www.fxsolver.com/browse/formulas/Auger+electron+spectroscopy+-+electron+impact+cross-section
A simple answer is that the primary beam energy should be 3-5x larger than the emitted Auger electron.
Sensitivity of AES is not too high: the detection limit if around 1 atomic %. The sensitivity in AES depends on ionization efficiency of electron in core shell, and secondary electron flux which defines background. To get maximum ionization efficiency, the primary electron energy should be around 3-5 of the ionization potential of electron in analyzed core shell (K, L, M....), as mentioned Dr. Kolibal above. The secondary electron emission depends strongly on material, there is no analytical solution for the secondary electron emission yet. One more important remark is about alternative mechanism of vacancy occupation formed in core shell by a primary electron impact, as Dr. Weippert mentioned (fluorescence). For light elements (Z20) emission of photons (X-Ray) prevails.
As for electron beam energy, taking into account all above, the typical beam energy of 3-5 keV is used in AES systems.
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