Approximation of Range in Materials as a Function of Incident Electron Energy

A simple composite analytic expression has been developed to approximate the electron range in materials. The expression is applicable over more than six orders of magnitude in energy (<; 10 eV to >; MeV) and range ( 10^-9-10^-2 m), with an uncertainty of ≤ 20% for most conducting, semiconducting, and insulating materials. This is accomplished by fitting data from two standard NIST databases [ESTAR for the higher energy range and the electron inelastic mean free path (IMFP) for the lower energies]. In turn, these data have been fit with well-established semiempirical models for range and IMFP that are related to standard material properties (e.g., density, atomic number, atomic weight, stoichiometry, and bandgap energy). Simple relations between the IMFP and the range, based on the continuous-slow-down approximation, are used to merge results from the two databases into a composite range expression. A single free parameter, termed the effective number of valence electrons per atom N_v, is used to predict the range over the entire energy span.