2D reaction-diffusion computation of charge trapping evolution in dielectric materials submitted to an electron beam irradiation

In this work, we present a new two-dimensional mathematical modeling in a cylindrical coordinate system which computes the time evolution of trapped charges in Al₂O₃/SiO₂ material due to irradiation by primary electrons. A reaction-diffusion equation expressing the spatial distribution of free charges fluxes in the material is given. The contribution of the electric field induced by the charge distribution is also taken into account, coupled with the evolution of trapping sites. A new expression for Se(r, z), the electrons/holes pair created by the slowdown of primary electrons is given. The contribution of the diameter φ to Se(r, z) is computed numerically.