Open AccessUsing non-homogeneous point process statistics to find multi-species event clusters in an implanted semiconductor
Author(s) -
Kristian Stockbridge,
Steven Chick,
Eleanor Crane,
A. J. Fisher,
B. N. Murdin
Publication year - 2020
Publication title -
journal of physics communications
Language(s) - English
Resource type - Journals
ISSN - 2399-6528
DOI - 10.1088/2399-6528/ab6049
Subject(s) - point process , event (particle physics) , cluster (spacecraft) , poisson distribution , homogeneous , statistical physics , point (geometry) , mathematics , computer science , algorithm , statistics , physics , geometry , quantum mechanics , programming language
The Poisson distribution of event-to- i th -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 non-homogeneous 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.