Penetration and energy-loss theory of electrons in solid targets

Starting from a simple atomic model giving the potential between electrons and atoms as V ( r ) = Ze 2 a s −1 / sr s with the empirical value s =fraction six-fifths, we combine the diffusion effect due to multiple collisions and the energy retardation in accordance with a modified Thomson-Whiddington law, with the scattering cross section in the Lenard absorption law. On this basis, consistent expressions are obtained for the fraction of transmitted electrons in amorphous solid targets, the backscattering fraction with depth, the fraction of electrons absorbed per unit mass-thickness and the depth-dose function, which are in good agreement with experiments over the energy range 10-1000 keV. A diffusion model represented by a sphere whose centre is located at the maximum energy dissipation depth, related to the diffusion depth and the range, is found to agree well with experiments.