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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]

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]

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]

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]