Deep Multistream Diffusion in Ion Implantation

Very deep penetration of ions injected into crystals has been reported in several recent experiments. These "supertails," which extend deeper into the crystals than the normal stopping range or channeling range, have the form $n_s\sim {(x-x_0)}^{-\eta }$, where $n_s$ is the number of incident ions per ${\mathrm{cm}}^3$, $x$ is the distance from the surface of the crystal, $\eta$ is typically ∼2-8, and $x_0$ is ∼1 μ or less. Multistream steady-state-diffusion models are developed to explain these supertails. The results agree well with published experimental data. Multistream diffusion may also be involved in other experiments, such as radiation-enhanced diffusion experiments and implantation experiments in which channeling is suppressed, but the measured concentration profiles are within the maximum channeling range.