Positron stopping in multilayer materials

Positron annihilation spectroscopy provides a sensitive toolset for defect characterization. In beam based studies of single-layer targets, the form of implantation profiles is well established, depending on the kinetic energy and angle of incident positrons relative to the target surface and the density and average atomic number of the target. For multilayer systems, the difference in density and across the layers makes derivation of an analytical form difficult. To date, the determination of positron stopping profiles in multilayer targets has primarily involved Monte Carlo simulations. We present here an alternative approach that estimates the energy distributiondN/dEof those positrons transmitted past each layer boundary, by fitting the remaining tail of the stopping profile after each layer with a basis set comprised of calculated stopping profiles in the same material they are transmitted through. The stopping profile in the next layer is then found by summing a series of stopping profiles in the new medium in proportion to the determined distributiondN/dE. The results of our model are compared with simulation results in a system of alternating layers of Al and Au and find reasonable agreement in the predicted profile and excellent agreement in the predicted mean implantation depth. Lastly, we derived a simple formula-based approach for the calculation of the mean implantation depth in two-layer systems that provides results in excellent agreement with the full model.