Calculation of electron-beam induced displacement in thin films by using parameter-reduced formulas

Based on the Mott cross sections of relativistic electron collisions with atoms, we calculate displacement creation by electron beams of arbitrary energies (up to 100 MeV) in thin films of arbitrary atomic numbers (up to Z = 90). In a comparison with Mont Carlo full damage cascade simulations, we find that total number of displacements in a film can be accurately estimated as the product of average displacements created per collision and average collision numbers in the film. To calculate average displacements per electron-atom collision, energy transfer from Mott cross section is combined with NRT model. To calculate collision numbers, mean deflection angles and multi-scattering theory are combined to extract collision number dependence on film thickness. For each key parameter, parameter-reduced formulas are obtained from data fitting. The fitting formulas provide a quick and accurate method to estimate radiation damage caused by electron beams.