Inner-Shell Ionization Cross Sections

Values of cross sections for ionization of inner-shell electrons by electron impact are required for electron probe microanalysis, Auger-electron spectroscopy, and electron energy-loss spectroscopy. The present author has reviewed measurements and calculations of inner-shell ionization cross sections. This paper is an update and summary of these previous reviews.It is convenient to start with the Bethe equation for inner-shell ionization cross sections which is frequently used (and misused) in x-ray microanalysis:(1)where σnℓ is the cross section for ionization of the nℓ shell with binding energy Enℓ by incident electrons of energy E. The terms bnℓ and cnℓ are the Bethe parameters discussed further below. It has been assumed in the derivation of Eq. (1) that E ≫ Enℓ ; this requirement will also be discussed. Finally, it has been assumed here that E is low enough (≲50 keV) so that a relativistic correction is unnecessary.The extent to which a given set of measured or calculated cross-section data is consistent with Eq. (1) can be determined from a Fano plot in which σnℓE is plotted versus ℓnE; if such a plot is linear, Eq. (1) is consistent with the data and values of the Bethe parameters can be easily derived.