Efficient two-dimensional Monte Carlo simulation of ion implantation

We have developed a Monte Carlo code for 2D-simulations of ion implantation which allows fairly arbitrary geometries. To alleviate the problem of large computer times, we apply two methods. First, in the case of complex geometries, most of the time is spent to detect, whether the ions cross boundaries. This extra time-as compared with implantations in infinite targets-may be almost eliminated by putting a grid over each region of the simulation area, and giving each grid element the information whether an ion located inside this element may cross a boundary during the next free flight path. Secondly, we use a precomputed table to evaluate scattering angles 0. Tabulating cot 0/2 instead of 0, allows moderate table dimensions and small interpolation errors. In a typical example presented in this paper, the execution time could be reduced by a factor of 4 using these methods.