Near-neighbor configuration and impurity-cluster size distribution in a Poisson ensemble of monovalent impurity atoms in semiconductors

Edgal, U. F.; Wiley, J. D.

doi:10.1103/physrevb.27.4997

Cited by 11 publications

(8 citation statements)

References 14 publications

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“…Previously, clusters of impurities with homogeneous density have been discussed in terms of the distribution of neighbour-neighbour distance [15]. In order to put our discussion into this context we give the nonhomogeneous case, which follows immediately from equation (2).…”

Section: Non-homogeneous Poisson Point Processmentioning

confidence: 99%

“…The ability to model a distribution of points in an event space and be able to quantify irregularities such as clustering of points helps provide an insight into correlations between events and the consequences resulting from such a distribution. Using the well understood construct that is the Poisson point process [12,13], the nearest neighbour distribution of an impurity species has been used to model optical properties of donors in silicon [14] due to nearest neighbour interactions and also to calculate the probability of finding large clusters of donors [15] in homogeneously doped bulk semiconductors.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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Section: Non-homogeneous Poisson Point Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…There has been an increased interest in nearest-neighbor distributions (and neighbor distributions in general) in the statistical mechanics of fluids and related systems. − Interest has also been focused on the functions that comprise the neighbor distributions. In this paper, dealing with hard particle systems, we make use of these functions to develop Ornstein−Zernike-like equations and to derive relations that are valid on the stable branches of hard particle pressure−density isotherms and that are not necessarily valid on metastable branches.…”

Section: Introductionmentioning

confidence: 99%

“…There has been an increased interest in nearest-neighbor distributions (and neighbor distributions in general) in the statistical mechanics of fluids and related systems. [1][2][3][4][5][6][7] Interest has also been focused on the functions that comprise the neighbor distributions. In this paper, dealing with hard particle systems, we make use of these functions to develop Ornstein-Zernike-like equations and to derive relations that are valid on the stable branches of hard particle pressure-density isotherms and that are not necessarily valid on metastable branches.…”

Section: Introductionmentioning

confidence: 99%

Ornstein−Zernike-like Equations in Statistical Geometry: Stable and Metastable Systems

1996

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Statistical geometric methods based on nearest-neighbor distributions are used, in connection with hardparticle systems, to develop Ornstein-Zernlike-like equations that have already been of considerable value in the statistical thermodynamic analysis of such systems and that promise to have even greater value. In this paper, we use these equations to (1) develop a relation that is valid for a hard particle system in unconstrained equilibrium and that shows that the insertion probability cannot vanish (short of closepacking) in such a system, (2) study the still incompletely settled issue concerning the equality of the hard-particle densities on the peripheries of cavities which are and are not occupied by hard particles and, in so doing, arrive at a relation that holds in a system in stable equilibrium but fails in a metastable system, (3) provide insight into the geometric mechanism of hard-particle phase transitions and allow simple estimates of the freezing densities, and (4) suggest a new physical interpretation for the direct correlation function.

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“…where r 0j is the distance from the central atom to its jthnearest neighbor and ρ is the Rydberg atom density [37,38]. Beyond-nearest-neighbor atoms may be closer to each other than to the central atom.…”

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confidence: 99%

Time Dependence of Few-Body Förster Interactions among Ultracold Rydberg Atoms

et al. 2020

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Rubidium Rydberg atoms in either jm j j sublevel of the 36p 3=2 state can exchange energy via Stark-tuned Förster resonances, including two-, three-, and four-body dipole-dipole interactions. Three-body interactions of this type were first reported and categorized by Faoro et al. [Nat. Commun. 6, 8173 (2015)] and their Borromean nature was confirmed by Tretyakov et al. [Phys. Rev. Lett. 119, 173402 (2017)]. We report the time dependence of the N-body Förster resonance N × 36p 3=2;jm j j¼1=2 → 36s 1=2 þ 37s 1=2 þ ðN − 2Þ × 36p 3=2;jm j j¼3=2 , for N ¼ 2, 3, and 4, by measuring the fraction of initially excited atoms that end up in the 37s 1=2 state as a function of time. The essential features of these interactions are captured in an analytical model that includes only the many-body matrix elements and neighboring atom distribution. A more sophisticated simulation reveals the importance of beyond-nearest-neighbor interactions and of always-resonant interactions.

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Near-neighbor configuration and impurity-cluster size distribution in a Poisson ensemble of monovalent impurity atoms in semiconductors

Cited by 11 publications

References 14 publications

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

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

Ornstein−Zernike-like Equations in Statistical Geometry: Stable and Metastable Systems

Time Dependence of Few-Body Förster Interactions among Ultracold Rydberg Atoms

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