Compilation and Comparison of Electron Penetration Ranges as a Function of Effective Number of Valence Electrons

Teancum Quist

Abstract

The continuous-slow-down approximation (CSDA) is used to create a simple composite analytical formula to estimate the range or maximum penetration depth of bombarding electrons into traditional materials including conductors, semiconductors, and insulators. This formula generates an approximation to the range using a single fitting parameter, N_v, described as the effective number of valence electrons. This applicability of the formulation extends to electrons with energies from <10 eV to>10MeV. These calculations are of great value for studies of high electron bombardment, such as electron spectroscopy or the vacuum of space. A list comprised of 187 materials has been collected that greatly extends the applicability of this model. Several key material constants were compiled for each material, including the atomic number, atomic weight, density, and band gap. To determine the single fitting parameter, N_v, the model was then fit to existing data from the ESTAR and IMFP databases (2, 3) compiled by NIST. Comparison of Nv with the materials constants from this large database of materials was made, which could possibly lead to the prediction of N_v for materials which have no supporting data.