Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases

The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates

Exact location of dopants below the Si(001):H surface from scanning tunnelling microscopy and density functional theory

Control of dopants in silicon remains the most important approach to tailoring the properties of electronic materials for integrated circuits, with Group V impurities the most important n-type dopants. At the same time, silicon is finding new applications in coherent quantum devices, thanks to the magnetically quiet environment it provides for the impurity orbitals. The ionization energies and the shape of the dopant orbitals depend on the surfaces and interfaces with which they interact. The location of the dopant and local environment effects will therefore determine the functionality of both future quantum information processors and next-generation semiconductor devices. Here we match observed dopant wavefunctions from low-temperature scanning tunnelling microscopy (STM) to images simulated from first-principles density functional theory (DFT) calculations. By this combination of experiment and theory we precisely determine the substitutional sites of neutral As dopants between 5 and 15A below the Si(001):H surface. In the process we gain a full understanding of the interaction of the donor-electron state with the surface, and hence of the transition between the bulk dopant (with its delocalised hydrogenic orbital) and the previously studied dopants in the surface layer.Comment: 12 pages; accepted for publication in Phys. Rev.

An Association between Head Circumference and Alzheimer's Disease in a Population-Based Study of Aging and Dementia

We investigated the association between head circumference (HC) and Alzheimer's disease (AD) in a cross-sectional population-based study of aging in North Manhattan. Six hundred forty-nine subjects underwent neurologic, neuropsychological, and anthropometric evaluations; apolipoprotein E (apoE) genotype was available for a subsample of 300 individuals. Logistic regression analyses were performed with AD the outcome of interest to evaluate any association between HC and AD. In these analyses, HC evaluated as a continuous variable was associated with AD (OR 0.8, 95% CI 0.7-0.9) after adjusting for age, education, and ethnicity, gender, and height. Analyses suggested that increased risk resided mainly in those with smallest HC. Thus, women whose HC was within the lowest quintile of HC for women were 2.9 (95% CI 1.4-6.1) times more likely to have AD, after adjusting for age, education, and ethnicity; and men in the lowest quintile of HC (for men) were 2.3 times more likely to have AD (95% CI 0.6-9.8). There was no confounding by height, weight, or apoE genotype. The results are consistent with previous studies that suggest that premorbid brain size may influence the age-specific risk for AD. Future epidemiologic studies seeking environmental risk factors for AD may benefit by making HC measurements on all subjects to decrease the variance associated with other potential risk factors

Single-Atom Control of Arsenic Incorporation in Silicon for High-Yield Artificial Lattice Fabrication

Artificial lattices constructed from individual dopant atoms within a semiconductor crystal hold promise to provide novel materials with tailored electronic, magnetic, and optical properties. These custom engineered lattices are anticipated to enable new, fundamental discoveries in condensed matter physics and lead to the creation of new semiconductor technologies including analog quantum simulators and universal solid-state quantum computers. In this work, we report precise and repeatable, substitutional incorporation of single arsenic atoms into a silicon lattice. We employ a combination of scanning tunnelling microscopy hydrogen resist lithography and a detailed statistical exploration of the chemistry of arsine on the hydrogen terminated silicon (001) surface, to show that single arsenic dopants can be deterministically placed within four silicon lattice sites and incorporated with 97$\pm$2% yield. These findings bring us closer to the ultimate frontier in semiconductor technology: the deterministic assembly of atomically precise dopant and qubit arrays at arbitrarily large scales

Room Temperature Incorporation of Arsenic Atoms into the Germanium (001) Surface

Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focused on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH3) on the germanium (001) surface. We show that, unlike any previously studied dopant precursor on silicon or germanium, arsenic atoms fully incorporate into substitutional surface lattice sites at room temperature. Our results pave the way for the next generation of atomic-scale donor devices combining the superior electronic properties of germanium with the enhanced properties of arsine/germanium chemistry that promises scale-up to large numbers of deterministically placed qubits

Room Temperature Incorporation of Arsenic Atoms into the Germanium (001) Surface**

Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focused on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH3) on the germanium (001) surface. We show that, unlike any previously studied dopant precursor on silicon or germanium, arsenic atoms fully incorporate into substitutional surface lattice sites at room temperature. Our results pave the way for the next generation of atomic-scale donor devices combining the superior electronic properties of germanium with the enhanced properties of arsine/germanium chemistry that promises scale-up to large numbers of deterministically placed qubits

Adsorption and Thermal Decomposition of Triphenyl Bismuth on Silicon (001)

We investigate the adsorption and thermal decomposition of triphenyl bismuth (TPB) on the silicon (001) surface using atomic-resolution scanning tunneling microscopy, synchrotron-based X-ray photoelectron spectroscopy, and density functional theory calculations. Our results show that the adsorption of TPB at room temperature creates both bismuth–silicon and phenyl–silicon bonds. Annealing above room temperature leads to increased chemical interactions between the phenyl groups and the silicon surface, followed by phenyl detachment and bismuth subsurface migration. The thermal decomposition of the carbon fragments leads to the formation of silicon carbide at the surface. This chemical understanding of the process allows for controlled bismuth introduction into the near surface of silicon and opens pathways for ultra-shallow doping approaches

Atomic-Scale Patterning of Arsenic in Silicon by Scanning Tunneling Microscopy

Over the past two decades, prototype devices for future classical and quantum computing technologies have been fabricated by using scanning tunneling microscopy and hydrogen resist lithography to position phosphorus atoms in silicon with atomic-scale precision. Despite these successes, phosphine remains the only donor precursor molecule to have been demonstrated as compatible with the hydrogen resist lithography technique. The potential benefits of atomic-scale placement of alternative dopant species have, until now, remained unexplored. In this work, we demonstrate the successful fabrication of atomic-scale structures of arsenic-in-silicon. Using a scanning tunneling microscope tip, we pattern a monolayer hydrogen mask to selectively place arsenic atoms on the Si(001) surface using arsine as the precursor molecule. We fully elucidate the surface chemistry and reaction pathways of arsine on Si(001), revealing significant differences to phosphine. We explain how these differences result in enhanced surface immobilization and in-plane confinement of arsenic compared to phosphorus, and a dose-rate independent arsenic saturation density of 0.24 ± 0.04 monolayers. We demonstrate the successful encapsulation of arsenic delta-layers using silicon molecular beam epitaxy, and find electrical characteristics that are competitive with equivalent structures fabricated with phosphorus. Arsenic delta-layers are also found to offer confinement as good as similarly prepared phosphorus layers, while still retaining >80% carrier activation and sheet resistances of <2 kω/square. These excellent characteristics of arsenic represent opportunities to enhance existing capabilities of atomic-scale fabrication of dopant structures in silicon, and may be important for three-dimensional devices, where vertical control of the position of device components is critical. Copyright © 2020 American Chemical Society

Nondestructive imaging of atomically thin nanostructures buried in silicon

It is now possible to create atomically thin regions of dopant atoms in silicon patterned with lateral dimensions ranging from the atomic scale (angstroms) to micrometers. These structures are building blocks of quantum devices for physics research and they are likely also to serve as key components of devices for next-generation classical and quantum information processing. Until now, the characteristics of buried dopant nanostructures could only be inferred from destructive techniques and/or the performance of the final electronic device; this severely limits engineering and manufacture of real-world devices based on atomic-scale lithography. Here, we use scanning microwave microscopy (SMM) to image and electronically characterize three-dimensional phosphorus nanostructures fabricated via scanning tunneling microscope–based lithography. The SMM measurements, which are completely nondestructive and sensitive to as few as 1900 to 4200 densely packed P atoms 4 to 15 nm below a silicon surface, yield electrical and geometric properties in agreement with those obtained from electrical transport and secondary ion mass spectroscopy for unpatterned phosphorus δ layers containing ~1013 P atoms. The imaging resolution was 37 ± 1 nm in lateral and 4 ± 1 nm in vertical directions, both values depending on SMM tip size and depth of dopant layers. In addition, finite element modeling indicates that resolution can be substantially improved using further optimized tips and microwave gradient detection. Our results on three-dimensional dopant structures reveal reduced carrier mobility for shallow dopant layers and suggest that SMM could aid the development of fabrication processes for surface code quantum computers.ISSN:2375-254