Search

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Plot of the spatial dependence of the temperature along a 3 m CNT for a value of the external electric field of E e x t =464.658 V/cm and for three different values of the CNT diameter, d =2, 2.1, and 2.2 nm. Plot of the temperature profile along a 2.1 nm diameter and a 3 m long CNT for an external electric field of E e x t =465.956 V/cm assuming that the temperature dependence of the electrical resistivity (T) is given by Eq. (32) where 0 is selected to be either 0(1)=3.26×10-5 m, 0(2)=2 0(1), or 0(3)=3 0(1). 2 for different values of the applied external electric field E e x t. From bottom to top, E e x t is equal to 440, 450, 455, 460, 463, and 464.658 V/cm, the latter being 0.001 kV/cm less than the value of the critical electric field E c at which thermal runaway occurs. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

A vacuum field effect transistor (VacFET) is proposed that consists of a modification of a conventional AlGaN/GaN high electron mobility transistor to include a nanogap near the gate on either the source (cathode) or drain (anode) side of the device. The current flowing through the two-dimensional electron gas (2DEG) under the gate is obtained using a charge-control model, which is forced to be equal to the tunneling current across the nanogap. The latter is modeled using a modified version of Simmons tunneling theory of a metal–insulator–metal junction to include the effect of barrier lowering across the nanogap. When compared to other recently fabricated VacFETs, the proposed device has potential for much higher emission current densities and transconductance levels, of the order of several hundreds of mA/mm and tens of mS/mm, respectively. For similar material parameters and physical dimensions, the proposed VacFET has a turn-on voltage that depends on the location of the nanogap on either the source or drain side of the gate. It is shown that the current–voltage characteristics of VacFETs with a nanogap either on the drain or source side of the gate are highly sensitive to their physical parameters and biasing conditions, making them a very strong candidate for chemical or gas sensing applications. This is due to the sensitivity of the tunneling current to the effective barrier height and field enhancement factor of the nanogap. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Wet spun carbon nanotube fibers were characterized using both field emission and electron energy distribution measurements. Fowler-Nordheim analysis of the field emission results showed that the carbon fibers demonstrated a large effective emission area, 2 x 10-12 m2, which resulted in a reduced brightness of 1.84 x 1010 A/m2/sr/V. By considering the emission and number of carbon nanotube emitters it can be shown that the brightness is consistent with previous reports for single nanotube emitters. Additionally, using the effective emission area determined from the Fowler-Nordheim analysis an emittance value around 0.70 μm was found. These characteristics are useful metrics in determining the applicability of using wet spun carbon nanotube fibers for field emission devices. [ABSTRACT FROM AUTHOR]

Reducing the emission of secondary electrons from materials is critical to improved efficiency and increased performance in high power vacuum electronics. A new mathematical expression for the secondary emission yield (SEY) as a function of the impact voltage up to a maximum of 5 kilovolts is proposed which is an extension of a formula first suggested by Vaughan. The new analytical fit and Vaughan’s fit are compared with SEY experimental data reported by others and measured by our group. The new analytical expression gives good fits to SEY experimental data in all cases, even when the SEY maximum is either slightly larger or below unity, two situations for which Vaughan’s fit is either inadequate or inapplicable. [ABSTRACT FROM AUTHOR]