Fractal geometry of collision cascades

Abstract

The fractal nature of self-ion collision cascades is first described using an inverse power potential and then by the more realistic potential of Biersack–Ziegler. Based on the model of Cheng et al. and TRIM Monte Carlo simulations, the average cascade fractal dimension is a function of both atomic mass and initial energy. The instantaneous fractal dimension increases as the cascade evolves. A critical energy Ec for producing a dense subcascade is derived and it is shown that Ec agrees well with the onset energy for constant damage efficiency.