Using non-homogeneous point process statistics to find multi-species event clusters in an implanted semiconductor

Abstract

The Poisson distribution of event-to-ith-nearest-event radial distances is well known for homogeneous processes that do not depend on location or time. Here we investigate the case of a nonhomogeneous point process where the event probability (and hence the neighbour configuration) depends on location within the event space. The particular non-homogeneous scenario of interest to us is ion implantation into a semiconductor for the purposes of studying interactions between the implanted impurities. We calculate the probability of a simple cluster based on nearest neighbour distances, and specialise to a particular two-species cluster of interest for qubit gates. We show that if the two species are implanted at different depths there is a maximum in the cluster probability and an optimum density profile.

Photoassisted ionization spectroscopy of few implanted bismuth orbitals in a silicon-on-insulator device

“…12 From the spreading resistance profile, the distribution of nearest neighbor separations was computed using non-homogeneous Poisson point process statistics. 13 As shown an inset in Fig. 1, a definite 2D integral of this surface is the probability of a bismuth atom existing in a range of depth with a first nearest bismuth atom existing within a certain radial distance range.…”