arXiv subjects

Thiago A. de Assis

Publications and source records attributed to Thiago A. de Assis.

At least 19 recordsLinked to original sources

arXiv2026

Physics-based logarithmic description of electrostatic field enhancement in hemisphere-on-cylindrical-post structures for high-field applications

Electrostatic (ES) field enhancement at sharp conducting structures plays a central role in lightning protection, corona discharge, electrical breakdown in vacuum (for example in particle accelerators), and more generally in technological applications of field electron emitters. A canonical geometry for studying this ES effect is the hemisphere-on-cylindrical-post (HCP) model, in the regime where the structure stands on a planar conductor of large lateral extent, and a large gap exists between the structure and the counter-electrode. A parameter of major interest is the apex field enhancement factor (AFEF) (apex-ES-field/background-ES-field). For this (and other) structures, a formula for the AFEF can be written in the form AFEF = ASC x ASR, where the apex sharpness ratio (ASR) is given by the ratio (post-height/apex-radius-of-curvature), and the apex sharpness coefficient (ASC) depends on the post shape. For the HCP model, no exact analytical formulas for the ASC or the AFEF are currently known. (Quite possibly none exist.) This paper develops a compact analytical approximation for the ASC and hence for the AFEF. This compact formula has a logarithmic-style structure, rather than the power-style structure used in previous approximations. When compared with precise finite-element analyses of the HCP model, over the computationally accessible range 1 to 1000 for the ASR, this logarithmic-style formula has a maximum error-magnitude of 0.15 percent, which is significantly better than older approximations.

cond-mat.other↗

arXiv2025

Universal scaling relation for growth phenomena

The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational means, show that the Family-Vicsek relation can be generalized to a new scaling independent of the size, substrate dimension $d$, and scaling exponents. We use properties of lattice growth models in the Kardar-Parisi-Zhang and Villain-Lai-Das Sarma universality classes for $1 \leq d \leq 3$ to support our claims.

cond-mat.stat-mech↗

arXiv2025

Universal scaling of electrostatic effects of a curved counter-electrode on the emitter field enhancement

Experiments on field electron emission from single-tip nanoemitters have typically been carried out using a counter-electrode with a finite curvature radius $R$, positioned at a distance $d_{\rm{gap}}$ from the emitter's apex. The effects of the counter-electrode's curvature on the apex field enhancement factor ($γ_{\rm{Ca}}$) of the emitter are still not understood. In this Letter, we theoretically explore how the apex field enhancement factor of an emitter, represented by a hemisphere on a cylindrical post (HCP) with apex radius $r_{\rm{a}} = 50$nm, is influenced by the curvature of a spherical-shaped counter-electrode. Importantly, our results show that for HCPs with sharpness aspect ratios typically between $10^2$ and $10^3$, there is a universal scaling such that $γ_{\rm{Ca}} = γ_{\rm{Pa}} Ψ\left({R}/{d_{\rm{gap}}} \right)$, where $γ_{\rm{Pa}}$ represents the apex field enhancement factor for the emitter assuming a planar counter-electrode, and $Ψ\left({R}/{d_{\rm{gap}}} \right)$ is a universal scaling function such that $Ψ\sim 1$ for ${R}/{d_{\rm{gap}}} \gg 1$ and $Ψ\sim \left({R}/{d_{\rm{gap}}} \right)^α$, with $α$ close to unity, for $ {R}/{d_{\rm{gap}}} \ll 1$. These findings help partially explain discrepancies observed in orhtodox field electron emission experiments, who reported that the effective $γ_{\rm{Ca}}$ values extracted from the current-voltage characteristics of single-tip carbon nanotubes typically underestimate the theoretical $γ_{\rm{Pa}}$ values when $R \sim d_{\rm{gap}} \gg r_{\rm{a}}$, a trend that is predicted by our results.

cond-mat.mes-hall↗

arXiv2024

Bifractality in one-dimensional Wolf-Villain model

We introduce a multifractal optimal detrended fluctuation analysis to study the scaling properties of the one-dimensional Wolf-Villain (WV) model for surface growth. This model produces mounded surface morphologies for long time scales (up to $10^9$ monolayers) and its universality class remains controversial. Our results for the multifractal exponent $τ(q)$ reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edward-Wilkinson (EW) universality class for negative and positive $q$-values, respectively. Therefore, although the results corroborate that long-wavelength fluctuations belong to the EW class in the hydrodynamic limit, as conjectured in the recent literature, a bifractal signature of the WV model with an MBE regime at short wavelengths was observed.

cond-mat.stat-mech↗

arXiv2023

Field emitter electrostatics: efficient improved simulation technique for highly precise calculation of field enhancement factors

When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulae have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a "tolerance" $ε_{\rm{tol}}$. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD Extrapolation Technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane (HEP) and hemisphere-on-cylindrical-post (HCP) emitter shape models.

physics.comp-ph↗

arXiv2022

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

This review of quantitative field emitter electrostatics, covering analytical, numerical and fitted-formula approaches, is thought the first of its kind. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is polarity independent; thus the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors that exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. The review focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in situations where analytical comparisons exist). Brief outline discussions, and core references, are given for each of many "related considerations" that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

cond-mat.mes-hall↗

arXiv2020

Statistics of adatom diffusion in a model of thin film growth

We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number, $N$, are determined in films with average thicknesses close to $50$ and $100$ monolayers for a broad range of values of the diffusion-to-deposition ratio $R$ and of the probability $ε$ that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with $Rε\lesssim 1$, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as $\langle N\rangle \sim R^{0.38\pm 0.01}$, and the distribution of that number decays approximately as $\exp\left[-\left({N/\langle N\rangle}\right)^{0.80\pm 0.07}\right]$. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between $\langle N\rangle$ and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, $\langle N\rangle$ crosses over to another regime when $Rε^{3.0\pm 0.3}\sim 1$, which indicates high mobility of all adatoms at terrace borders. The distributions $P\left( N\right)$ change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and $\langle N\rangle \sim Rε^{1.85\pm 0.15}$, which is explained by an analogy with submonolayer growth.

cond-mat.stat-mech↗

arXiv2020

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/$μ$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.

cond-mat.mes-hall↗

arXiv2019

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.

cond-mat.mes-hall↗

arXiv2019

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.

cond-mat.mes-hall↗

arXiv2018

Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension

We report local roughness exponents, $α_{\text{loc}}$, 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 $α_{\text{loc}}\in[0.96,0.98]$ 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 $α_{\text{loc}}=1-ε$ of the one-loop renormalization group analysis of the VLDS equation.

cond-mat.stat-mech↗

arXiv2018

First-principles analysis of nanoelectromechanical systems using Loewner equation

The Loewner equation (LE) is used to obtain conformal mappings that lead to exact and analytical expressions for several electrostatic properties of realistic quasi-unidimensional nanoelectromechanical systems (NEMS). The LE approach also embraces curved geometries, impossible to be addressed by traditional methods such as the Schwarz-Christoffel transformation, often used in this scenario. Among the possible applications of the formalism, we show that it allows for an exact evaluation of the field enhancement factor (FEF) close to the apex of different emitters. Despite its key role in the demodulation process for radio-receiver nano-devices, actual FEF values have been mostly obtained via numerical and/or phenomenological approaches. This work extends the already huge universe of applications of the LE and provides an analytical method to evaluate the FEF, even for curved emitters. Furthermore, our results provide a signature of the varying emitted current's response due to the nanostructure oscillation, justifying its role in the demodulation process of radio-frequency.

cond-mat.mes-hall↗

arXiv2018

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 ($ε$) 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 $ε$ 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 $ε_{tol}$. 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.comp-ph↗

arXiv2018

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 $\sim1\%$.

cond-mat.mes-hall↗

arXiv2018

Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. Moreover, the electrostatic effects due to the proximity between emitters on a LAFE may compete with the morphological ones. The balance between these effects may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF). The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, with a profile limited by two mirror-reflected triangular protrusions on an infinite line, is considered. The FEF near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that a tradeoff between morphological and proximity effects on a LAFE may provide an explanation for the observed reduction of the local FEF and its variation at small distances between the emitter sites.

cond-mat.mes-hall↗

arXiv2018

Origin of the literature discrepancies in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, $L$, and the height, $H$, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, $\varepsilon$, in the calculation of the apex-FEF as a function of $H$ and $L$. Importantly, our results show that the effects of $H$ and $L$ on $\varepsilon$ are scale invariant, allowing one to predict $\varepsilon$ for ratios $L/h$ and $H/h$, where $h$ is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, $δ$, from a single emitter, $γ_1$, and a pair, $γ_2$. We show that small relative errors in $γ_1$ (i.e., $\varepsilon\approx0.5\%$), due to the finite domain size, are sufficient to alter the functional dependence $δ(c)$, where $c$ is the distance from the emitters in the pair. We show that $δ(c)$ obeys a recently proposed power law decay in the limit of infinite domain size ($\varepsilon=0$, say), in contrast to a long time established exponential decay. Thus, power law functional dependence, $-δ\sim c^{-n}$, with $n=3$, is suggested to be a universal signature of the charge-blunting effect, at sufficient large distances between similar emitters with any shape. These results explain the origin of the discrepancies in the literature and improves the scientific understanding of the field electron emission theory, for accurate characterization of emitters in small clusters or arrays.

cond-mat.mes-hall↗

arXiv2017

Unexpected validity of Schottky's conjecture for two-stage field emitters: a response via Schwarz-Christoffel transformation

The electric field in the vicinity of the top of an emitter with a profile consisting of a triangular protrusion on an infinite line is analytically obtained when this system is under an external uniform electric field. The same problem is also studied when the profile features a two-stage system, consisting of a triangular protrusion centered on the top of a rectangular one on a line. These problems are approached by using a Schwarz-Christoffel conformal mapping, and the validity of Schottky's conjecture (SC) is discussed. The authors provide an analytical proof of SC when the dimensions of the upper-stage structure are much smaller than those of the lower-stage structure, for large enough aspect ratios and considering that the field enhancement factor (FEF) of the rectangular structure is evaluated on the center of the top of the structure, while the FEF of the triangular stage is evaluated near the upper corner of the protrusion. The numerical solution of our exact equations shows that SC may remain valid even when both stages feature dimensions of the same order of magnitude, reinforcing the validity of SC for multistage field emitters.

cond-mat.mes-hall↗

arXiv2017

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

We present an optimal detrended fluctuation analysis (DFA) and applied it to evaluate the local roughness exponent in non-equilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curved that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvdensky (CV) model in $2+1$ dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear Molecular Beam Epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for nMBE class whereas using the other methods it does not. We also characterized the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling.

cond-mat.stat-mech↗