New techniques for modeling focused ion beams

Abstract

Monte Carlo computer simulations of e‐beam systems have proven quite successful in determining the contribution of mutual particle repulsion to critical beam parameters such as spot size and energy spread. For similar simulations on ion beams, the small charge‐to‐mass ratio of ions results in significant numerical problems which do not occur in the simulation of electron beams. New techniques are introduced which extend the application of this Monte Carlo technique to higher perveance beams. These techniques include the use of a periodic boundary condition on the simulation charge packet, a dynamic sphere of influence which reduces the number of interactions to be evaluated, and a dynamic time step which accounts for varying ion densities and random ion collisions. The resulting program is used to simulate a focused 50 kV Ga+ beam, with a source divergence angle of 2 mrad and currents of up to 1 μA. Significant beam broadening was observed at currents in excess of 10 nA and the broadening was observed to increase with the application of a retarding field. Finally, arrival time distributions at the target plane were analyzed and no reduction in the statistical noise was observed as a result of space charge smoothing.