Self-diffusion of ion-implanted tracers

Tracer self-diffusion studies with ion-implanted stable isotopes require a high fluence of implanted ions (>1015 ions/cm2) due to the natural tracer background concentration present in a sample. Such a high fluence leads to considerable implantation damage, where a large part of the tracer is immobilized and does not take place in the diffusion process. As a consequence, diffusion profiles are observed which cannot be described with Fick's second law. In this study, a set of differential equations is presented, describing the diffusion of implanted isotopes as a trap-limited process with a sink and a source term, where the tracer atoms form immobile complexes with implantation damage-induced defects. These equations are solved numerically for the example of nitrogen diffusion in amorphous Si–B–C–N ceramics in order to illustrate diffusivity determination. The results are compared to the analytical solution of Fick's second law.