Model of Development of Knock-On Atom Cascades in Solids

Abstract

The nonstationary distribution function characterizing the energy distribution of a cascade of moving atoms (with their multiplication factored in) is determined by solving the kinetic Boltzmann equation. The development of such cascades in materials consisting of identical atoms is examined without regard to the lattice-site binding energy. It is assumed that the interaction cross section is inversely proportional to velocity and the scattering of moving atoms is elastic and spherically symmetric in the center-of-mass system. These simplifying assumptions provide an opportunity to derive simple analytical formulas for the nonstationary distribution function of a cascade of decelerating atoms and analyze its features. The obtained results may also be used to estimate the accuracy of various approximate solutions.