145 research outputs found
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 () 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 at the
desired tolerance. The minimum width () and height () are given relative
to the height of the emitter (), that is,
necessary to simulate isolated emitters on a substrate. We also provide the
to simulate arrays and the 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
. 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 ( being the separation and is
the height of the emitters) and , 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
Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension
We report local roughness exponents, , for three
interface growth models in one dimension which are believed to belong the
non-linear molecular-beam-epitaxy (nMBE) universality class represented by the
Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum
detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801
(2017)] and compared the outcomes with standard detrending methods. We observe
in all investigated models that ODFA outperforms the standard methods providing
exponents in the narrow interval consistent
with renormalization group predictions for the VLDS equation. In particular,
these exponent values are calculated for the Clarke-Vvdensky and Das
Sarma-Tamborenea models characterized by very strong corrections to the
scaling, for which large deviations of these values had been reported. Our
results strongly support the absence of anomalous scaling in the nMBE
universality class and the existence of corrections in the form
of the one-loop renormalization group analysis
of the VLDS equation
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
. 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 . 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
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