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 $\sim1\%$

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

Valor nutritivo de pastagens de capim-elefante manejadas sob sistema convencional e agroecológico.

O capim-elefante é utilizado, na sua grande maioria, em sistemas convencionais de produção animal. O objetivo deste trabalho foi comparar o valor nutritivo do capimelefante em sistemas de manejo agroecológico e convencional, quanto a proteína bruta (PB), fibra em detergente neutro (FDN) e digestibilidade in vitro da matéria seca (DIVMS). Foram usados quatro piquetes, com 0,12ha cada um. No sistema convencional, o capim-elefante foi estabelecido singularmente. No sistema agroecológico, o plantio foi feito em linhas afastadas de 3m. Nas entrelinhas, estabeleceu-se a aveia e o azevém no período hibernal, enquanto que no período estival permitiu-se o desenvolvimento de espécies espontâneas. A adubação foi feita com fertilizantes orgânicos (150kg ha-1 de N). No sistema agroecológico, foram conduzidos sete pastejos, de 24/04/2004 a 05/05/2005. Na pastagem convencional, usouse a mesma quantidade de N (uréia), sendo conduzidos quatro ciclos de pastejo, de 06/10/2004 a 05/05/2005. Para ambos os sistemas foram utilizadas vacas da raça Holandês, recebendo complementação alimentar de 3,5kg dia-1 de concentrado com 20% de proteína bruta, constituindo-se nos animais experimentais. Nas avaliações, considerou-se a massa de forragem inicial com base na matéria seca (MS), os componentes botânicos da pastagem e estruturais do capimelefante. As análises de qualidade foram feitas em amostras de pastejo simulado. O delineamento experimental foi o inteiramente casualizado com dois tratamentos, convencional e agroecológico, duas repetições (piquetes) e em parcelas incompletas subdivididas no tempo (pastejos). Houve interação (P<0,05) entre tratamentos e pastejos em todas as variáveis. Na pastagem agroecológica, o modelo que melhor se ajustou foi o cúbico para todas as variáveis, em função do tempo de pastejo. Na pastagem convencional, a PB e a DIVMS ajustaram-se melhor ao modelo linear, com taxa positiva de crescimento, sendo observado comportamento inverso para FDN, com o decorrer dos pastejos. Tanto na pastagem convencional quanto na agroecológica encontraram-se associações negativas entre lâmina foliar do capim-elefante com PB e DIVMS e positiva com FDN. Ambos os sistemas apresentaram teores qualitativos elevados das pastagens, considerando-se a adubação, o manejo e o tempo de utilização