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 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.
This study reports the effect of an increasing ion dose on both the electrical activation yield and the characteristic properties of implanted bismuth donors in silicon. A strong dependence of implant fluence is observed on both the yield of bismuth donors and the measured impurity diffusion. This is such that higher ion concentrations result in both a decrease in activation and an enhancement in donor migration through interactions with mobile silicon lattice vacancies and interstitials. Furthermore, the effect of implant fluence on the properties of the Si:Bi donor bound exciton, D0X, is also explored using photoluminescence (PL) measurements. In the highest density sample, centers corresponding to the PL of bismuth D0Xs within both the high density region and the lower concentration diffused tail of the implanted donor profile are identifiable.
Donor qubits in bulk doped silicon have many competitive advantages for quantum computation in the solid state: not only do they offer a fast way to scalability, but they also show some of the longest coherence times found in any quantum computation proposal. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction-mediated entangling gates. Second, using nearest neighbor Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. Third, using the moving-average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of the far-from-equilibrium magnetization dynamics of one species by the orbital excitation of another. We find agreement of our results with a Monte Carlo simulation that handles multiple donor structures and scales optimally with the number of dopants. The simulator can also extract donor structures not captured by our Poisson point process theory. The combined approaches to density optimization in random distributions presented here may be useful for other condensed matter systems as well as applications outside physics.
The electrically detected orbital spectrum of a mesoscopic silicon device containing a small number of donors has been investigated. The device was fabricated on silicon-on-insulator with an optically active channel containing 6 x 105 substitutional bismuth centers introduced by ion implantation. The 1s(A₁) → 2p± orbital transition at the energy associated with isolated bismuth donors was detected via a change in photocurrent when illuminated by THz light from a free electron laser. The spectral dependence on bias, temperature, and laser intensity is explored to determine optimum conditions for detecting orbital transitions in smaller devices with fewer donors. These results suggest that photo-induced impact ionization can offer a route for the spectroscopic detection of few impurities providing a useful tool for the development of solid-state quantum technologies.