Correlation functions in the theory of atomic collision cascades: Ion location and the distribution in depth and size of damage clusters

Abstract

Simple depth distribution functions of ion bombardment damage predict the spatial extension of the cumulative damage caused by a beam of ions. Correlation functions need to be considered when more detailed information is desirable, such as the average size or depth of individual damage clusters, the average location of an ion within its damage cluster, and the fluctuations of these quantities. In this paper we establish an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy. This pair correlation function determines the damage caused by all those ions that come to rest at a specific penetration depth. Solutions of the integral equation are found by standard methods. Explicit results are presented for elastic scattering governed by power cross sections. The depth distribution of damage clusters turns out to be significantly narrower than the gross damage distribution at all mass ratios except for M ₁ ≪ M ₂, and the size distribution appears insensitive to depth when measured perpendicular to the ion beam, but varying with depth when measured parallel. Predictions on ion location suffer from a surprizingly sensitive dependence on the scattering cross section. A note on the fluctuation of the sputtering yield by individual ions concludes the paper.