Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision

In the literature about field emission, finite elements and finite differences techniques are being increasingly employed to understand the local field enhancement factor (FEF) via numerical simulations. In theoretical analyses, it is usual to consider the emitter as isolated, i.e, a single tip field emitter infinitely far from any physical boundary, except the substrate. However, simulation domains must be finite and the simulation boundaries influences the electrostatic potential distribution. In either finite elements or finite differences techniques, there is a systematic error ($\epsilon$) in the FEF caused by the finite size of the simulation domain. It is attempting to oversize the domain to avoid any influence from the boundaries, however, the computation might become memory and time consuming, especially in full three dimensional analyses. In this work, we provide the minimum width and height of the simulation domain necessary to evaluate the FEF with $\epsilon$ at the desired tolerance. The minimum width ($A$) and height ($B$) are given relative to the height of the emitter ($h$), that is, $(A/h)_{min} \times (B/h)_{min}$ necessary to simulate isolated emitters on a substrate. We also provide the $(B/h)_{min}$ to simulate arrays and the $(A/h)_{min}$ to simulate an emitter between an anode-cathode planar capacitor. At last, we present the formulae to obtain the minimal domain size to simulate clusters of emitters with precision $\epsilon_{tol}$. Our formulae account for ellipsoidal emitters and hemisphere on cylindrical posts. In the latter case, where an analytical solution is not known at present, our results are expected to produce an unprecedented numerical accuracy in the corresponding local FEF

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Recent analyses of the field enhancement factor (FEF) from multiple emitters have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest $0<c/h\lesssim5$ ($c$ being the separation and $h$ is the height of the emitters) and $c\rightarrow\infty$, has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this letter, we use first principles to derive a simple two-parameter formula for fractional reduction that can be of interest for experimentalists to modeling and interpret the FEF from small clusters of emitters or arrays in small and large separations. For the structures tested, the agreement between numerical and analytical data is $\sim1\%$

Zero-energy states in graphene quantum dots and rings

We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.Comment: 8 pages, 3 figures, references added, typos corrected, discussion section expande

Method to obtain nonuniformity information from field emission behavior

Copyright © 2010 American Vacuum Society / American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Vacuum Science and Technology Part B: Microelectronics and Nanometer Structures, 28(3), Article number 441 and may be found at http://scitation.aip.org/content/avs/journal/jvstb/28/3/10.1116/1.3327928.This article describes the characterization of field emission from a planar cathode to a spherical anode with the approach curve method (ACM). In such a diode configuration the electric field strength at the cathode surface is nonuniform. This nonuniformity gives an extra degree of freedom and it allows the interpretation of the current-voltage and voltage-distance (V×d) curves in terms of nonuniformity. The authors apply the ACM to Cu emitters to explain the nonlinearity of the V×d curve in ACM measurements. This analysis provides a good insight into field emission phenomena, supporting a method for nonuniformity characterization based on field emission behavior

Diversidade e filogenia de estirpes de Rhizobium pela metodologia de MLSA.

O nitrogênio (N) é um dos elementos mais requisitados pelas culturas, sendo um fator determinante na produtividade agrícola. Sabe-se que o grupo de bactérias conhecidas como rizóbios pode fixar o N2 atmosférico, suprindo total ou parcialmente a carência do mesmo no solo. Dessa forma, a caracterização molecular e filogenética de rizóbios nativos de solos brasileiros é importante para futuros estudos. O objetivo deste trabalho foi caracterizar a diversidade filogenética de cinco estirpes de Rhizobium, que apresentam fortes indicações de representarem novas espécies por estudos filogenéticos anteriores. Todas as estirpes foram crescidas em meio de cultura específico e submetidas à análise por MLSA (Multi-Locus Sequence Analysis) e BOX-PCR. Os resultados de ambas análises agruparam as estirpes em clusters separados das demais espécies do gênero, reforçando a hipótese de que tais bactérias podem representar uma nova espécie dentro do gênero Rhizobium.Fertbio

Produtividade de linhagens de Dactylis glomerata na região da campanha gaúcha.

Resumo.Fernando Flores Cardoso, Daniel Portella Montardo, José Carlos Ferrugem Moraes, Marcos Flávio Silva Borba, Sandro da Silva Camargo, editores técnicos