Predictive Formula for Electron Penetration Depth of Diverse Materials over Large Energy Ranges

Anne C. Starley, Utah State University
Gregory Wilson, Utah State University
Lisa Phillipps, Utah State University
JR Dennison, Utah State Univesity


An empirical model that predicts the approximate electron penetration depthβ€”or rangeβ€”of some common materials has been extended to predict the range for a broad assortment of other materials. The electron range of a material is the maximum distance electrons can travel through a material, before losing all of their incident kinetic energy. The original model used the Continuous Slow Down Approximation (CSDA) for energy deposition in a material to develop a composite analytical formula which estimated the range from10 MeV with an uncertainty of200 materials which have tabulated range and inelastic mean free path data in the NIST ESTAR and IMFP databases. Correlations of 𝑁𝑁𝑉𝑉𝑒𝑒𝑒𝑒𝑒𝑒 with key material constants (e.g., density, atomic number, atomic weight, and band gap) were established for this large set of materials. Somewhat different correlations were found for different sub-classes of materials (e.g., solids/liquids/gases, conductors/semi-conductors/insulators, elements/compounds/polymers/ composites). A predictive formula was developed to accurately determine 𝑁𝑁𝑉𝑉𝑒𝑒𝑒𝑒𝑒𝑒 for arbitrary materials.