Abstract
The Poisson distribution of event-to--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.
Highlights
Individual interacting impurity atoms can be important for donor qubit gates, such as that proposed by Stoneham et al [1], while an important class of theoretical physics problems is produced by the Hubbard model, which relies on hopping and magnetic interactions between neighbours in chains [2]
Contemporary work in this area [8] has focused on analytically understanding the interactions between donors, the dependence these interactions have on donor spacing and using the results of homogeneous Poisson point process statistics, optimising for these interactions
We show that in the case of a Gaussian distribution of events an analytic solution for the nonhomogeneous nearest neighbour distribution exists
Summary
The Poisson distribution of event-to-ith-nearest-event radial distances is well known for homo-. Any further distribution of geneous processes that do not depend on location or time. We investigate the case of a nonthis work must maintain attribution to the homogeneous point process where the event probability (and the neighbour configuration) author(s) and the title of the work, journal citation depends on location within the event space. The particular non-homogeneous scenario of interest to and DOI. 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
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