Positron diffusion in solids and the reconstruction of inhomogeneous defect distributions from lifetime measurements

Abstract

The time dependent diffusion trapping equations for positrons implanted into inhomogeneous solids are analyzed. This problem is of central importance in the study of polycrystalline materials and for the application of pulsed positron beams to defect studies in materials research. The main problem in previous investigations was the necessity to solve the time-dependent diffusion equation. It prevented analytical treatment in all but the simplest applications. For the first time this difficulty is eliminated by invoking a new concept, the observable local annihilation characteristics for local implantation of positrons into the thermalized ensemble. It will be shown that the local annihilation characteristics are governed by field equations which reduce to the well known quantities of the standard trapping model in the case of homogeneous defect distributions. Furthermore, inhomogeneous defect distributions are uniquely determined from the field equations provided the local annihilation characteristics are known. Analytical solutions are derived and applied successfully to recent experimental results for a selection of simple, but realistic problems. The formal procedure includes internal drift fields and could be extended to cover also the epithermal period of positron thermalization, if necessary.