Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.Comment: A slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes using the Induced Electron Density

In many field electron emission experiments on single-walled carbon nanotubes (SWCNTs), the SWCNT stands on one of two well-separated parallel plane plates, with a macroscopic field FM applied between them. For any given location "L" on the SWCNT surface, a field enhancement factor (FEF) is defined as $F_{\rm{L}}$/$F_{\rm{M}}$, where $F_{\rm{L}}$ is a local field defined at "L". The best emission measurements from small-radii capped SWCNTs exhibit characteristic FEFs that are constant (i.e., independent of $F_{\rm{M}}$). This paper discusses how to retrieve this result in quantum-mechanical (as opposed to classical electrostatic) calculations. Density functional theory (DFT) is used to analyze the properties of two short, floating SWCNTS, capped at both ends, namely a (6,6) and a (10,0) structure. Both have effectively the same height ($\sim 5.46$ nm) and radius ($\sim 0.42$ nm). It is found that apex values of local induced FEF are similar for the two SWCNTs, are independent of $F_{\rm{M}}$, and are similar to FEF-values found from classical conductor models. It is suggested that these induced-FEF values relate to the SWCNT longitudinal system polarizabilities, which are presumed similar. The DFT calculations also generate "real", as opposed to ``induced", potential-energy (PE) barriers for the two SWCNTs, for FM-values from 3 V/$\mu$m to 2 V/nm. PE profiles along the SWCNT axis and along a parallel ``observation line" through one of the topmost atoms are similar. At low macroscopic fields the details of barrier shape differ for the two SWCNT types. Even for $F_{\rm{M}}=0$, there are distinct PE structures present at the emitter apex (different for the two SWCNTs); this suggests the presence of structure-specific chemically induced charge transfers and related patch-field distributions

On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor

Measurements of current-voltage characteristics from ideal carbon nanotube (CNT) field electron emitters of small apex radius have shown that these emitters can exhibit a linear Fowler-Nordheim (FN) plot [e.g., Dean and Chalamala, Appl. Phys. Lett., 76, 375, 2000]. From such a plot, a constant (voltage-independent) characteristic field enhancement factor (FEF) can be deduced. Over fifteen years later, this experimental result has not yet been convincingly retrieved from first-principles electronic structure calculations, or more generally from quantum mechanics (QM). On the contrary, several QM calculations have deduced that the characteristic FEF should be a function of the macroscopic field applied to the CNT. This apparent contradiction between experiment and QM theory has been an unexplained feature of CNT emission science, and has raised doubts about the ability of existing QM models to satisfactorily describe experimental CNT emission behavior. In this work we demonstrate, by means of a density functional theory analysis of single-walled CNTs "floating" in an applied macroscopic field, the following significant result. This is that agreement between experiment, classical-conductor CNT models and QM calculations can be achieved if the latter are used to calculate (from the "real" total-charge-density distributions initially obtained) the distributions of $\textit{induced}$ charge-density, induced local fields and induced local FEFs. The present work confirms, more reliably and in significantly greater detail than in earlier work on a different system, that this finding applies to the common "post-on-a-conducing plane" situation of CNT field electron emission. This finding also brings out various further theoretical questions that need to be explored

Catálogo Taxonômico da Fauna do Brasil: setting the baseline knowledge on the animal diversity in Brazil

The limited temporal completeness and taxonomic accuracy of species lists, made available in a traditional manner in scientific publications, has always represented a problem. These lists are invariably limited to a few taxonomic groups and do not represent up-to-date knowledge of all species and classifications. In this context, the Brazilian megadiverse fauna is no exception, and the Catálogo Taxonômico da Fauna do Brasil (CTFB) (http://fauna.jbrj.gov.br/), made public in 2015, represents a database on biodiversity anchored on a list of valid and expertly recognized scientific names of animals in Brazil. The CTFB is updated in near real time by a team of more than 800 specialists. By January 1, 2024, the CTFB compiled 133,691 nominal species, with 125,138 that were considered valid. Most of the valid species were arthropods (82.3%, with more than 102,000 species) and chordates (7.69%, with over 11,000 species). These taxa were followed by a cluster composed of Mollusca (3,567 species), Platyhelminthes (2,292 species), Annelida (1,833 species), and Nematoda (1,447 species). All remaining groups had less than 1,000 species reported in Brazil, with Cnidaria (831 species), Porifera (628 species), Rotifera (606 species), and Bryozoa (520 species) representing those with more than 500 species. Analysis of the CTFB database can facilitate and direct efforts towards the discovery of new species in Brazil, but it is also fundamental in providing the best available list of valid nominal species to users, including those in science, health, conservation efforts, and any initiative involving animals. The importance of the CTFB is evidenced by the elevated number of citations in the scientific literature in diverse areas of biology, law, anthropology, education, forensic science, and veterinary science, among others

Journal of Applied Physics

p. 114512-(1-7)The effect of geometrical irregularities in the work function and emitting properties of metallic surfaces at low potentials is studied. For this purpose, we propose a simplified model consisting of rectangular fractures and a classical formalism for the work function determination. The dependence of the work function with the fractures size is determined by using the electrostatic image potential method. The emission current density properties when an external electric field is applied are also analyzed