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We derive the reflection and refraction laws for an electron spin incident from a quasi-two-dimensional semiconductor region (with no spin–orbit interaction) on the metallic surface of a topological insulator (TI) when the two media are in contact edge to edge. For a given incident angle, there can generally be two different refraction angles for refraction into the two spin eigenstates in the TI surface, resulting in two different ‘spin refractive indices’ (birefringence) and the possibility of two different critical angles for total internal reflection. We derive expressions for the spin refractive indices and the critical angles, which depend on the incident electron’s energy for given effective masses in the two regions and a given potential discontinuity at the TI/semiconductor interface. For some incident electron energies, there is only one critical angle, in which case 100% spin polarized injection can occur into the TI surface from the semiconductor if the angle of incidence exceeds that critical angle. The amplitudes of reflection of the incident spin with and without spin flip at the interface, as well as the refraction (transmission) amplitudes into the two spin eigenstates in the TI, are derived as functions of the angle of incidence.

The carbon nanotube (CNT) is celebrated for its electrothermal property, which indicates the capability of a material to transform electrical energy into heat due to the Joule effect. The CNT nanostructure itself, as a one-dimensional material, limits the electron conduction path, thereby creating a unique heating phenomenon. In this work, we explore the possible correlation between CNT alignment in sheets and heating performance. The alignment of carbon nanotubes is induced by immersion and stretching in chlorosulfonic acid (CSA) solution. The developed CSA-stretched CNT sheet demonstrated excellent heating performance with a fast response rate of 6.5 °C/s and reached 180 °C in less than 30 s under a low voltage of 2.5 V. The heating profile of the stretched CNT sheet remained stable after bending and twisting movements, making it a suitable heating material for wearable devices, heatable smart windows, and in de-icing or defogging applications. The specific strength and specific conductance of the CSA-stretched CNT sheet also increased five- and two-fold, respectively, in comparison to the pristine CNT sheet.

Many ice basin tests have been performed on ships to assess the ice resistance of the hull in an ice floe field. During these tests, many parameters are studied, the most important of them being the transit speed, the thickness and the concentration of ice. Given the cost and the time required to carry out these basin test campaigns, it is imperative to keep the number of tests to the strict minimum, whilst still making it possible to draw conclusions about the sizing of the vessel. Hence, the influence of ice floe shape and their distribution in the field are generally not considered. A way to achieve sensitivity studies regarding these parameters is to use numerical simulations in addition to a basin test. There are few advanced numerical design tools available in the market, especially those able to cope with any kind of structure geometry and a large variety of ice interaction & failure mechanisms. In 2012 TechnipFMC, Cervval and Bureau Veritas initiated a common development program to offer a new tool for the design of offshore structures interacting with ice combining a variety of models and approaches such as analytical, numerical and empirical. This numerical tool called Ice-MAS (www.ice-mas.com) uses a multi-agent technology and has the possibility to combine, in a common framework, multiple phenomena from various natures and heterogeneous scales (i.e. drag, friction, ice-sheet bending failure, local crushing and rubble stack up). The study presented in this paper compares the simulation results for different ice floe fields not only in terms of concentration, maximum size of floe and their distribution but also in the way to generate the ice floe and its shape.

Recently, we introduced an accurate algorithm to calculate the spatial dependence of the temperature distribution along a carbon nanotube (CNT) during field emission (FE). The algorithm considers the effects of Joule heating in the CNT, radiative losses from the CNT sidewall and tip, as well as the rate of heat exchange per unit area at the CNT tip due to either Henderson-cooling or Nottingham-heating effects. The previous work assumed that the temperature at the base of the CNT was the same as the temperature of the chuck to which it is attached and that the latter acts as a perfect heat sink. In this work, we consider the effects of contact resistance between the base of the CNT and the chuck and investigate its influence on the CNT FE properties. All other parameters being equal, our simulations show that the temperature profile along a CNT and its emission current are actually found to be larger those determined assuming a constant temperature T 0 = 300 K at the CNT/chuck contact [1].

Over the last few years, there has been increased interest in Vacuum Field Effect Transistors (VFETs) with nanoscale features [1]-[4]. Compared to traditional MOSFETs and FINFETs, VFETs offer advantages in terms of electron velocity, fast switching speed, extreme operating temperatures, and radiation robustness. We calculate the field emission (FE) characteristics of a back-gated nanomembrane VFET making use of the concept of negative capacitance. It is found that the proposed negative capacitance VFET (NC-VFET) has a minimum subthreshold swing (SS) of 34mV/decade, well below the thermionic limit of 60mV/dec at room temperature.

Recently, Dall’Agnol et al. [1] have studied the field electron emission (FE) characteristics of carbon nanotube (CNT)-based looped fibers and shown that these cathodes have very high effective field enhancement factors (FEFs). Based on SEM images taken after FE measurements from looped CNT fibers, they proposed a two-stage model for FE from these cathodes consisting of a looped fiber with CNT fibrils near its apex. The modeling of a combined two-stage structure (looped CNT fiber + fibrils) based on COMSOL simulations lead to apex FEF values in excellent agreement with an orthodoxy theory analysis [2]-[4] of FE experiments performed on these fibers. In this work, we perform extensive computational simulations of the temperature distribution through the fiber and in some of the fibrils near it apex, which are eventually responsible for their observed large FEFs. In order to determine the condictions for thermal runaway in these looped CNT two-stage emitters, we determined the temperature at the end of a fibril located at the apex of the fiber as a function of the fiber and fibril geometries, their electrical and thermal conductivities, and the distance between the apex of the fiber and the anode.

In this contribution, we perform electrostatic numerical simulations of conducting semicircular arched fibers and predict a scaling law of their characteristic field enhancement factor (FEF) while varying their geometrical parameters. Conditions for maximum FEF inferred from the isolated emitter allow us to analyze arrays of arched fibers, as a function of the lattice parameters.

A recent algorithm developed by Tripathi et al. [J. Appl. Phys. 128, 025017 (2020); Erratum, J. Appl. Phys. 131, 169901 (2022)] is modified to study the effects of thermal contact resistance on the field emission (FE) properties of a carbon nanotube (CNT). The model takes into account the temperature dependence of the CNT electrical and thermal conductivities. The boundary condition proposed by Huang et al. [Phys. Rev. Lett. 93, 7 (2004)] is used to include the effects of thermal contact resistance at a CNT/chuck interface located at [Formula: see text], i.e., [Formula: see text], where r is the CNT radius, [Formula: see text] is the heat conduction coefficient at [Formula: see text], and [Formula: see text] is the thermal resistivity of the CNT/chuck interface. The chuck is assumed to be a perfect heat sink at temperature [Formula: see text]. For a given set of CNT parameters and values of the applied external electric field, it is shown that current constriction at the CNT/chuck contact point leads to self-heating effects which increase with the value of the thermal contact resistance, leading to an increase in the temperature profile along the CNT (including the temperature at its tip) and the FE current above their values obtained assuming the CNT/chuck interface is at the heat sink temperature [Formula: see text]. The fractional change of the emission current versus applied external electric field is calculated for increasing values of the parameter [Formula: see text].

We demonstrate optically pumped nearly photonic lasing from highly Zn-doped GaAs nanowires (NWs) on Fe films at 77 K. High Zn-doping enhances the radiative recombination rate and the material gain to overcome the plasmonic losses of Fe.

We present a general empirical model of secondary electron yield (SEY), which successfully fits the experimentally measured SEY of a flat gold surface for both normal and oblique incidence of primary electrons. This empirical model is applied in a two-dimensional Monte Carlo (MC) simulation to estimate the effective SEY reduction of a microporous surface. The simulation results are in very good agreement with the experimental data.

Exploitation of the Arctic’s resources requires the mastery of the risks caused by extreme ice conditions. The design of offshore structures subjected to extreme ice conditions is a challenge for engineers since there are very few advanced numerical design tools available in the market. Especially those able to cope with any kind of structure geometry and a large variety of ice interaction & failure mechanisms. For developments in arctic shallow water between 50m to 200m water depth it is not possible to use conventional drilling rigs as it is either too deep for fixed or too shallow for floating operations. The other possibility is to have drilling equipment on the platform such as on Prirazlomnaya but then, with a drilling campaign of 5 to 7 years this represents a significant CAPEX compared to the remaining operations time and could imperil the economics of the project. A smart solution would be to use a MODU for full year operations in Arctic regions. Such a solution would not only place the rig into OPEX but also reduce the living quarters on the platform to the minimum strictly necessary for the operations of the platform, the drilling staff being housed on the MODU. Such a solution could reduce the weight of the platform by nearly 50%. This paper presents how it is possible to use an Arctic class MODU such as Arcticheskaya for full year operations in ice infested water.

The apex-field enhancement factor (aFEF) is regarded as a good parameter to characterize field electron emission (FE) devices. It quantifies how much the emitter sharp tip locally magnifies the applied external electrostatic field and enhances its FE properties. In a single tip form, the aFEF increases with the emitter's aspect ratio. However, when in a cluster or an array, the aFEF decreases due to depolarization fields from neighboring emitters. Hence, in large arrays, there is a tradeoff between the height and density to maximize its aFEF. There are experimental and theoretical works that analyze FE from carbon nanotube (CNT) arrays with fixed spacing $(c)$ , fixed radii $(r)$ , and varying height $(h)$ . Those works discuss the existence of an aspect-ratio $(h/r)$ for which a maximum FEF is achieved. Here, we found for an infinite square array of identical hemisphere-on-cylindrical-post emitters a universal behavior, in which $\gamma$ scales as $\gamma\sim\gamma s(h/c)^{0.84}$ , valid for aspect-ratios $h/r\gtrsim 50$ and $h\lesssim 0.7c$ . For $h \gtrsim 0.7c$ , the aFEF simply saturate at $\gamma s$ .

With its low work function and high mechanical strength, the LaB6/VB2 eutectic system is an interesting candidate for high performance thermionic emitters. For the development of device applications, it is important to understand the origin, value, and spatial distribution of the work function in this system. Here we combine thermal emission electron microscopy and low energy electron microscopy with Auger electron spectroscopy and physical vapor deposition of the constituent elements to explore physical and chemical conditions governing the work function of these surfaces. Our results include the observation that work function is lower (and emission intensity is higher) on VB2 inclusions than on the LaB6 matrix. We also observe that the deposition of atomic monolayer doses of vanadium results in surprisingly significant lowering of the work function with values as low as 1.1 eV.

We advocate the use of lookup tables in the development of extremely fast and accurate multiscale models based on the coupling of a quantum-mechanical wave impedance approach and finite-element simulations to determine the local emission current density (LECD) from a metallic emitter of arbitrary shape. The lookup tables are prepopulated with numerical solutions of LECD that can be adjusted to accommodate any form of higher order physics, which is critical for current state-of-the-art emitters. Results show that the use of lookup tables can speed up numerical simulations of the field emission current from metallic cathodes by a factor of about 1000 × while retaining high precision, with a maximum error of less than 1% when compared to direct numerical solutions. Implementation of nanoscale emitter physics into lookup tables is discussed and used to assess the validity of the Kemble approximation for nanoscale metallic cathodes. The use of lookup tables is illustrated through a calculation of the LECDs of a metallic field emitter with a rugged surface and from an array of ellipsoid-on-a-post emitters. Section V contains our conclusions and suggestions for future work.

Curved carbon-based fibers, in the form of looped fibers, have been investigated as promising field electron emitters with high mechanical stability. Recently, the growth of semicircular arched carbon nanofibers (structures when the arch is incomplete) has received increased attention due to their potential application in next-generation electronic devices. In this Letter, we theoretically investigate the field enhancement factor (FEF) during the growth of these structures. We found the conditions for the optimal FEF, γmax, as a function of the geometrical parameters. Our results show that the local characteristic FEF at the top of the arch obeys a scaling law, γC≈γmax×Ω[(ψ/ψ*)2], where Ω is a nearly quadratic function of (ψ/ψ*), where ψ is a normalized arch angle of the fiber and ψ* is the ψ-value when γC=γmax. Importantly, our results show a universal behavior for γmax, namely, γmax≈κ[(R/r)α−0.45]ρ (where r and R are the radii of the fiber and the arch, respectively), α≡Rrim/r (where Rrim is the radius of the rim at the fiber top), and κ and ρ are positive constants. We point out several advantages of the arched fiber over the fully looped fiber for field emission devices, particularly the mechanical stability of the two-stage arched structures. Finally, starting with the conditions for γmax inferred from an isolated arch, the effects of electrostatic depolarization in regular arrays of arched fibers are analyzed as a function of the lattice parameters.

Building on recent efforts to characterize carbon nanotube fibers (CNFs) as efficient electron emission sources suitable for compact, high power, high frequency vacuum electronic devices, this chapter proposes an exhaustive approach towards optimizing CNF field emission (FE) properties. It outlines how a platform of scientific enquiry geared towards a meaningful comparison between different CNF-based emitters can be developed. The platform envisages an iterative procedure involving (a) the growth, processing, and functionalization of CNFs, (b) full investigation of the CNF material properties before and after FE diagnosis, and (c) multi-scale modeling of FE properties, including self-heating, shielding effects and beam characteristics in the CNFs and in the emitting carbon nanotubes (CNTs) at the fiber apexes. The modeling would be applicable to a wide variety of CNFs and wire-like sources, and would provide essential feedback to the growth, processing, and functionalization of CNFs, in order to optimize their FE properties, especially long-term stability, low noise, maximum emission current, current density, emittance, and brightness.

We observe hybrid plasmonic lasing from highly Zn-doped GaAs nanowires on a gold substrate and from nanowires coated with a 10 nm thick gold layer at temperatures ranging from 5 K up to room temperature.

In the previous chapter, building on recent efforts to characterize carbon nanotube fibers (CNFs) as efficient electron emission sources suitable for compact, high power, high frequency vacuum electronic devices, an exhaustive approach towards optimizing CNF field electron emission (FE) properties was proposed. It consists of a platform of scientific enquiry geared towards a meaningful comparison between different CNF-based emitters. The platform envisages an iterative procedure involving (a) the growth, processing, and functionalization of CNFs, (b) full investigation of the CNF material properties before and after FE diagnosis, and (c) multi-scale modeling of FE properties, including self-heating, shielding effects and beam characteristics for both CNFs and the emitting carbon nanotubes (CNTs) at the fiber apexes. The modeling would be applicable to a wide variety of CNFs and wire-like sources, and would provide essential feedback to the growth, processing, and functionalization of CNFs, in order to optimize their FE properties, especially long-term stability, low noise and maximum emission current, current density, emittance and brightness. In this chapter, we first report simulations of the influence of self-heating effects on the field emission (FE) properties of CNFs and their dependence on the product of the electrical and thermal conductivities of the fibers. We study the sensitivity of the FE of CNFs as the dimensions and numbers of CNTs at the apex of the fiber are varied. The influence of the field enhancement factors of both the shank of the fiber and the CNTs at its apex on the FE properties of CNFs is also analyzed. We conclude the chapter with a study of the influence of the electrostatic shielding on the FE characteristics of two CNFs as a function of the distance between the axes of the two fibers.

Carbon nanotube (CNT) technology is improving around the world to the point where new types of devices can be made. Spinning millimeter-length CNT into yarn and drawing ribbon and twisting into yarn have been demonstrated, and the yarn is being used as electric and thermal conductors. It is also becoming feasible to use carbon nanotube hybrid conductive tapes and yarn to make tiny electromechanical components such as wires, coils, transformers, and electric motors. These components further enable the manufacturing of precision medical devices, such as biomedical wires, sensors, actuators, manipulators, and millirobots for minimally invasive in vivo diagnosis and treatment. Precision biomedical microdevices promise to improve disease diagnosis and treatment, improve health-care delivery, and spur novel medical system development. Treatments for heart disease, cancer, neural repair, drug delivery, probing, reconstruction, and healing might be advanced using miniature precision devices. The concept of CNT-based precision medical devices is a new area of research, and the state of the art in their development and potential applications are discussed in this chapter.

The field electron emission properties of carbon nanotube (CNT) films composed of densely packed and highly aligned CNTs were investigated. The CNT films were produced by a continuous film casting process and are spooled into long lengths with the CNTs aligned lengthwise in the film. The anisotropic nature of the CNT film morphology was confirmed by performing specific conductivity measurements in directions both parallel and perpendicular to the aligned CNT microstructure. Field emission experiments were performed on 5 and 10 mm wide films that were mechanically cut into small samples and then vertically mounted so that the emission occurred from the film edge. The films were mounted with the aligned CNT microstructure oriented either parallel or perpendicular to the direction of the applied electric field. The highest emission currents were produced by films mounted in the parallel alignment configuration. Additional experiments were performed on films that were folded, which eliminated surface irregularities at the film edge due to the cutting process. SEM imaging performed at the ridge of the folded film before and after field emission (FE) experiments showed that films mounted in the parallel alignment configuration had minimal surface damage after FE, while films mounted in the perpendicular alignment configuration showed substantial damage. The effective emission area and field enhancement factor were extracted from the FE data using the orthodox Fowler–Nordheim theory. Folded CNT film cathodes mounted in the parallel alignment configuration produced the highest emission currents, while demonstrating a larger emission area and lower field enhancement factor.

Carbon fibers passing current are subject to resistive heating. When failure occurs, this is related to their local temperature. The failure temperature and its location are estimated. The temperature variation is calculated using analytical models for electrical and thermal conductivities based on the temperature dependent electron–phonon relaxation time. In the absence of radiative heat loss, an analytic expression of temperature along the fiber is given from which a maximum possible emission current is derived and is governed by a single introduced parameter ω o. A method of treating the radiative heat loss is developed and is governed by a second parameter γ, which allows a rapid numerical means to calculate the correction to the analytic form. Heat variation along a thick carbon fiber is contrasted to that along a multi-walled carbon nanotube (MWNT): it is shown that the relative magnitude of ω o compared to γ determines that the analytical formula is a good approximation for MWNTs but requires numerical correction for fibers. Furthermore, it is shown that the analytical form of ω o specified a maximum current beyond which the carbon emitter fails due to thermal runaway. The theoretical models are used to interpret observed behavior of field emission from carbon fibers and the resulting damage they endure when the extracted field-emission current is high. Results from implementing the developed temperature variation model into the MICHELLE beam optics simulation code are presented, with an example application predicting the conditions for stable equilibrium operation as well as for the onset of fiber failure.

Structures with a sharp apex amplify an applied macroscopic field, FM, substantially and generate significant field electron emission (FE). The apex barrier field, Fa, is related to FM by the apex field enhancement factor (aFEF), γ a ≡ F a / F M. In this Letter, we provide a theoretical explanation for extremely high-effective FEFs ( 10 4 ≲ γ eff ≲ 10 5) recently extracted from an orthodoxy theory analysis of the emission current–voltage characteristics of looped carbon nanotube (CNT) fibers, making them promising candidates for FE applications. In this work, we found a dependence of γa on the geometrical parameters for an isolated conductive looped CNT fiber, modeled via the finite element technique. The aFEF of looped CNT fibers is found to scale as γ a = 2 + [ h f / r fiber ] [ ln ( 2 h / r fiber ) ] − 1, where f ≡ 1 + θ [ r fiber / b ] α [ ln ( 2 h / r fiber ) − 1 ], in which h is the height of a looped fiber standing on an emitter plate, b is its base length, rfiber is the radius of the fiber, and θ and α are fitting parameters that have a nonlinear dependence on the scaling parameter h/b. Our results show that the scaling law predicts that 10 ≲ γ a ≲ 100 for looped CNT fibers with parameters: 10 μm ≤ r fiber ≤ 100 μm, 0.4 ≤ h / b ≤ 2, and d / h ≥ 1, where d is the distance between the apex of the looped fiber and the anode. However, scanning electron microscopy images reveal the presence of microfibrils protruding from the looped CNT fiber surface close to its apex. We show that the modeling of a combined two-stage structure (looped CNT fiber + fibrils) leads to aFEF values in excellent agreement with an orthodoxy theory analysis of FE experiments performed on these fibers.

We report exhaustive measurements of the secondary electron yield (SEY) from a gold film containing an array of micropores as a function of the angle of incidence of the primary electrons. The SEY measurements are in good agreement with Monte-Carlo (MC) simulations. A highly accurate empirical fit to the SEY data as a function of the incident electron impact angle is also proposed. In this study, the micropores have aspect ratios (ratio of pore height over pore diameter) ranging from about 1.5 to 3.5. The effect of the pore array density (porosity) and pore aspect ratio is analyzed in greater detail. It is found that increasing the pore aspect ratio and porosity leads to a sharp reduction in the total SEY in agreement with MC simulations.

Resistive switching (RS)-based random access memory has been envisaged as a viable alternative to existing memory technology due to its nonvolatility, high switching speed, high endurance/retention, and considerably low operating voltage. Herein, a new uniform, repetitive, and stable RS phenomenon is demonstrated based on very low-cost two-terminal metal�insulator�metal stack fabricated using a highly redox-active vanadium-based polyoxometalate (POM) molecular clusters, V10O286��belonging to polyoxovanadate (POV) family. The RS is observed to be unipolar and nonvolatile in nature, and occur at a fairly low operating bias voltage (less than 2 V), making it suitable for low-power operations. The switching event is attributed to the cycling between formation and rupture of tiny conductive nanofilaments formed due to trapping and detrapping of positively charged ionized oxygen vacancy sites present in the active switching layer of V10O286�. POMs, in their rich abundance, are highly stable early transition-metal oxide nanosized clusters, capable of storing as well as releasing a large number of electrons. In addition, they can undergo fast and reversible redox reactions (both in solid and liquid electrolyte media) in �stepwise� manner�a property that makes them a promising candidate for ultrafast and multi-level nonvolatile molecular memory for high-density data storage. Preliminary investigations on the POV-based memory cells result in device resistance ratio �25, endurance for more than 200 cycles, and stable retention time around 2200 s, in fully open air condition.

An efficient algorithm is described to calculate the spatial dependence of the temperature distribution along a carbon nanotube (CNT) during field emission (FE). The algorithm considers the effects of Joule heating in the CNT and radiative losses from the CNT sidewall and tip. The CNT emission current density and the rate of heat exchange per unit area at the CNT tip due to either Henderson-cooling or Nottingham-heating effects are calculated using recent analytical expressions derived by Jensen [J. Appl. Phys. 126, 065302 (2019)]. The latter are valid in the thermionic and field emission regimes and in the transition region between these two extremes. The temperature dependence of the electrical resistivity ρ ( T ) and the thermal conductivity κ ( T ) of the CNT is also included in the model. It is shown that replacing ρ ( T ) and κ ( T ) by their spatial averages over the length of the CNT can lead to an overestimate of the value of the external electric field threshold at which thermal runaway of the CNT occurs. These results should be considered when calculating the field emission characteristics of CNT arrays such as from a carbon nanotube fiber whose FE properties are primarily determined by the FE properties of the array of CNTs at the tip of the fiber. Using the new algorithm, the simulation times to calculate the CNT FE characteristics and the spatial temperature distribution are found to be nearly two orders of magnitude faster compared to those required when both the current and energy exchange at the CNT tip are calculated numerically.

The apex-field enhancement factor (aFEF) is regarded as a meaningful parameter to characterize field electron emission (FE) devices. If experimentally extracted from orthodox current–voltage characteristics, this parameter reliably quantifies how much the emitter's sharp tip locally magnifies the applied external electrostatic field. Many experimental works have reported FE from arrays of carbon nanotubes with fixed spacing (c) between nearest-neighbor emitters, fixed apex-radii (r), and various height (h) and claimed the existence of an aspect ratio (h/r) at which a local maximum effective aFEF is achieved. Hereafter, it is shown that those results are not consistent with simulations using basic electrostatics for both finite or infinite regular square arrays of emitters. Quite interestingly, our results show that the aFEF (γa), for an emitter in an infinity regular array, simply saturates at γs for h ≳ 0.7 c. Additionally, we found a universal behavior in which γa scales as γ a ∼ γ s ( h / c ) 0.84, when h ≲ 0.7 c, for h / r ≳ 50. These results provide a practical rule for the design of large arrays of field emitters, which can be used to build FE nanoelectromechanical resonators with both mechanical strength and reduced Joule losses.

This work investigates secondary electron yield (SEY) mitigation from a metal surface with a microporous array fabricated using the laser drilling technique. We propose a general empirical model to fit the experimentally measured SEY of a flat gold surface for normal and oblique incidences of primary electrons. Using this empirical model, we develop a two-dimensional Monte Carlo (MC) simulation scheme to determine the effective SEY of a microporous array. It is found that the SEY from a porous surface is significantly reduced compared to that of the flat surface. By taking into account all the generations of secondary electrons inside a well, our MC results are found to be in very good agreement with the experimental data. The dependence of the SEY on the aspect ratio of the micropores and porosity of the surface is examined. A simple empirical formula has been proposed to evaluate the effective SEY of the gold microporous array for pores of arbitrary aspect ratios.This work investigates secondary electron yield (SEY) mitigation from a metal surface with a microporous array fabricated using the laser drilling technique. We propose a general empirical model to fit the experimentally measured SEY of a flat gold surface for normal and oblique incidences of primary electrons. Using this empirical model, we develop a two-dimensional Monte Carlo (MC) simulation scheme to determine the effective SEY of a microporous array. It is found that the SEY from a porous surface is significantly reduced compared to that of the flat surface. By taking into account all the generations of secondary electrons inside a well, our MC results are found to be in very good agreement with the experimental data. The dependence of the SEY on the aspect ratio of the micropores and porosity of the surface is examined. A simple empirical formula has been proposed to evaluate the effective SEY of the ...

A methodology for implementing the recently developed reformulated general thermal-field equation describing simultaneous thermal and field emission contributions to electron emission is developed, with modifications directed to enhancing speed and accuracy of computation as demanded by emitter characterization and electron beam simulations. An accurate factor to correct both thermal-field ( T F) and high field (Fowler-Nordheim or FN) predictions based on a rapid Lorentzian fit model is given. The analytic protrusion model is constructed from modifications to a point dipole model that allow surface elements and field enhancement factors to be rapidly evaluated. The model is applied to an analytical model of a protrusion on a bump in a diode configuration to characterize how current-voltage I ( V ) relations are affected by T F emission conditions. In addition, it is also shown (i) how aggressively Schottky’s conjecture is undermined as the protrusion dimensions become larger; (ii) how the total current in the T F regime can be substantially larger than predicted by canonical [FN and Richardson-Laue-Dushman (RLD)] formulations; (iii) how an optimal protrusion size may exist; and (iv) how the inference of field enhancement, notional emission area, and work function are poorly predicted using conventional methods relying on the canonical FN and RLD equations even outside the thermal-field regime, even though data can be linear on FN and RLD plots.

A thorough approach to quantum mechanics should rely on an algebraic operation of multiplication based on proper algebraic structures, i.e., division algebras. Quaternions, with their commutation rules isomorphic to SU(2), effort such a framework. In this work, a quaternion approach derived from the finite groups is used to solve the spatially invariant time-dependent Pauli-Schrӧdinger equation and derive the Rabi formula and the principle of nuclear magnetic resonance and its generalization. The spatial and time-dependent Pauli-Schrӧdinger equation is then written using left-chirality quaternions, i.e., by expressing the Pauli spinor, its time derivative, and the Hamiltonian as elements of the same division algebra. The quaternion formalism is used to derive the dispersion relation of a free electron and of an electron in a constant magnetic field. Finally, the formalism is applied to calculate the transmission probabilities through a one-dimensional delta-scatterer and through a resonant tunneling structure composed of two one-dimensional quaternionic delta-scatterers in series. The results are compared to the transmission probabilities calculated using traditional (complex) quantum mechanics.

The manner by which photo-assisted field-emitted electrons are generated, the impact of delays associated with transport to the surface, emission through and over emission barriers, and the time scales associated with accompanying tunneling / fly-over processes is complicated by conditions associated with emission from realistic surfaces. Recently studies treating transport to and emission past non-linear and resonant/reflectionless potentials motivate consideration of analytic models to be used to assess and compare characteristic time scales associated with transport to the surface, emission over and through surface wells and barriers (heterostructures), and tunneling. The formulation allows for an investigation of time-dependent effects for a class of analytically solvable models. The methods are intended to be useful for the investigation of tunneling and transmission associated with field and photoemission at short time scales.

A multiscale model of field emission (FE) from carbon nanotube fibers (CNFs) is developed which includes a detailed treatment of the heat exchange mechanisms in the array of carbon nanotubes (CNTs) located at the tip of the fiber. The model takes into account Joule heating within the fiber, radiative cooling at the fiber apex, and the transition from Nottingham heating to Henderson cooling in the CNTs in the array at the apex of the fiber as the external electric field is increased. The model uses numerical calculations of the current emitted from each CNT and the energy exchange at their tips. The model predicts the fraction of CNTs being destroyed as a function of the applied external electric field. For the surviving CNTs, the model also predicts the fraction of CNTs either undergoing Henderson cooling or Nottingham heating for both the up and down sweeps of the applied external electrical field. This investigation sheds new light on the FE properties on CNFs.

Despite regulations becoming more and more stringent, significant quantities of gas are still flared around the world every year. Indeed, for safety reasons, flaring remains a usual practice in oil and gas production in cases of process upset. For instance, emergency shutdown, when the unit must be depressurized in a short period of time, most of the gas inventories are flared to limit as much as possible the potential consequences of fire and explosion within the facility. With the increase of the global demand for energy and especially in Liquefied Natural Gas (LNG), the recent development of Floating Liquefied Natural Gas unit (FLNG) has raised new challenges concerning flare stack design. Since FLNG facilities handle large flammable gas quantities the flare stack needs to be designed considering much more stringent cases. It results in an increased length of flare stack, to reduce the radiation effects on personnel and equipment. The thermal response of the flare structure needs also to be accounted for in the design, in addition to other load cases such as piping and structural weight or vessel accelerations. To accomplish the structural design of the flare stack, the engineers will have to convert the radiative heat fluxes from the flame into the resulting temperature of the structure exposed. Indeed, temperature is the parameter that can be used as a thermal load case in any finite element analysis calculation code. Current temperature mapping methodologies applied on projects are not exhaustive and are often based on a simplified approach which is now challenged by operators and certification bodies who require more detailed verifications on flare structure heating during continuous or emergency flaring. Moreover, such simplified modelling approaches tends to overestimate thermal protection to mitigate the heat radiation impact. The proposed approach described in this paper will address these points through a multidisciplinary workflow to form a flexible, simple and robust technical methodology to be applied during project execution. The proposed approach will assess heat radiation and temperature calculations in a spatial-temporal reference including the dynamic response. This transient approach is more attractive as computed temperatures will be lower than steady-state approach results which are the usual engineering practice, especially for accidental loading cases, such as emergency depressurization, where the flare release can decrease quickly.

Summary Floating-liquefied-natural-gas (FLNG) units have been under development for decades. They are now becoming a reality, combining the design and installation of liquefied-natural-gas (LNG) units with a traditional floating production, storage, and offloading facility. Because FLNG facilities handle large flammable-gas quantities in a relatively small and congested environment compared with onshore LNG plants, the explosion risk is expected to be higher than that for some other offshore floating facilities. As a consequence, the intensity of the resulting blast loads on the unit can be more severe, even if the likelihood of explosion in the design is considered to be low through frequency analysis. Even if prevention and mitigation measures are implemented to reduce risk to as low as reasonably practicable, safety-critical elements (SCEs) such as main equipment and structures should be designed to withstand the blast event. Because the explosion events are very specific (high intensity and short duration), the common design rules and tools should be updated to take into account this accidental event. In addition, the associated performance criteria for SCEs should be modified. Finally, the entire design should comply with safety objectives (personnel protection, prevention of escalation). This paper focuses on the philosophy of design against a blast event on floating facilities in general, but with a particular focus on FLNG units. It will review the critical functions of the unit that must be maintained during emergency evacuation to protect people and identify the key parameters governing the explosion strength on floating facilities. It will show that the derivation of effective explosion loads on structures and equipment on the basis of computational-fluid-dynamics simulations is not straightforward and requires expertise in explosion modeling and explosion response. The paper will also show how all the engineering disciplines in Technip individually apply these blast loads in their designs through nonlinear-finite-element analysis. Finally, the paper will highlight the interface between the engineering disciplines and how a consistent demonstration through the design can be achieved to fulfill the safety goals, taking engineering further.

The transfer matrix formalism is used to show that the problem of finding the bound states of a quantum well with an arbitrary one-dimensional potential energy profile Ec(x) can be reformulated as a tunneling problem. The following theorem is proved: for an electron confined to a quantum well of size W with an arbitrary conduction band energy profile Ec(x) and maximum depth V0, the bound state energies (E1, E2, E3,…) can be found by adding a barrier of width d and height V0 on either side of the quantum well and calculating the energies at which the transmission through the resulting resonant tunneling structure reaches unity. More precisely, the energies at which the transmission coefficient reaches unity converge towards the bound state energy levels when the thickness d tends to infinity. Numerically, the bound state energies can be determined with enough accuracy by using barrier thicknesses of a few nm.