Monte Carlo simulation of the charge distribution induced by a high-energy electron beam in an insulating target

We have developed a simulation model of the implantation of a negative charge into an insulating target by a fixed and well-focused high-energy electron beam. We are particularly interested in the evolution of the distribution of the charges trapped during the bombardment. Our simulation is based on a Monte Carlo method permitting us to account for the various electron-insulator interactions. The charge carriers, unless they are emitted into vacuum, are followed until they have lost most of their kinetic energy. After that, they drift along the internal electric field lines before getting trapped. The field generated by these trapped charges is calculated self-consistently by solving the appropriate Poisson equation. When the trapping site density is sufficiently high, the dynamics of the charge is principally governed by the self-regulation of the total secondary emission yield. The total number of implanted charges is therefore limited and a quasi-stationary regime arises. The charge distribution builds up, forming a negative semi-ellipsoidal shell whose extent is directly related to the maximum penetration of the primary electrons. The internal region corresponds to a mixing zone with a weak positive mean charge. This characteristic distribution appears at all the primary beam energies considered. On the other hand, when the trapping site density is too low, the whole region under the beam is saturated and the mixing zone is completely occupied by electrons before the self-regulation of the total secondary yield acts.