From cascades to patterns: A Monte Carlo approach

This chapter dscribes a top-down Monte Carlo modeling approach to self-organized pattern formation by ion beam erosion. After a discussion of the general topic and its present status, we briefly introduce two of the more microscopic theories - the binary collision approximation (BCA) molecular dynamics and kinetic transport theory - to highlight some results, which should be taken into account when constructing Monte Carlo models. Then we describe a basic simulation model in detail and very briefly discuss its range of applications. The basic model ignores several of the results from the more detailed theories. We show that it is very easy to include the disregarded findings and exemplify the impact of the refinements and extensions on ion-induced pattern formation.