A universal equation for computing the beam broadening of incident electrons in thin films

A universal equation for computing the beam broadening of incident electrons in thin films is presented. This equation is based on the concepts of anomalous diffusion with the Hurst exponent H. When the thickness to elastic mean free path ratio, t/λ, is greater than 1, the Hurst exponent goes to 0.5 and this random walk behavior leads to the Goldstein et al. [1] beam broadening equation when non-relativistic screened Rutherford elastic cross-sections are used. When t/λ≪1, the lack of elastic collisions for the electron trajectories gives an H exponent of 1 and a different beam broadening equation is obtained. A general equation to compute the beam broadening that takes into account the variation of H with t/λ is presented and this equation was fitted and validated with Monte Carlo simulations of electron trajectories in thin films.