X-Ray Data Booklet Section 3.2 LOW-ENERGY ELECTRON RANGES IN MATTER

The electron range is a measure of the straight-line penetration distance of electrons in a solid [1]. Electrons with energies in the kilo-electron volt range, traveling in a solid, are scattered inelastically in collisions with the electrons in the material. For low-Z materials, such as organic insulators, scattering from the valence electrons is the major loss mechanism for incident electron energies from 10 eV to 10 keV. The core levels contribute less than 10 % to the electron’s energy dissipation for energies between 1 keV and 10 keV [2]. A. CSDA RANGES For electron energies below 5 keV, the usual Bethe-Bloch formalism is inadequate for calculating the electron energy loss in a solid, and an approach using the dielectric response of the material is used [3]. The complex dielectric function ε(k,ω) describes the response of a medium to a given energy transfer hω and momentum transfer hk. The dielectric function contains contributions from both valence and core electrons. References 4 and 5 describe the steps for calculating ε(k,ω) for insulators and metals, respectively. For an electron of energy E, the probability of an energy loss w per unit distance is given by [2] τ(E, hω)