A model calculation of the tip field distribution for a single carbon nanotube

Abstract

In order to study the tip field of the carbon nanotube (CNT) or CNT array standing upright on a cathode plane, we proposed a model in which the long CNT is replaced by a floating top segment at the cathode potential. Using the fictitious charge and image method, a simple approximate formula for the field enhancement factor of a single CNT linear with the height-to-radius ratio has been deduced. This result is evidently improved compared to that from the floating sphere model. The normalized field strength distribution on the top hemisphere is also calculated and plotted, with the result depending slightly on the height-to-radius ratio. An estimation shows that the field emission intensity on the cylindrical surface of CNT is negligible compared to that on the top hemisphere.

Effect of plasma parameters on growth and field emission of electrons from cylindrical metallic carbon nanotube surfaces

“…The theoretical observation can be used to validate the fact that the field enhancement factor b for spherical CNT tip will be larger as comparison to the cylindrical CNT surfaces as b / r À 1 2 that has also been experimentally observed. The emission from the CNT tip is dominant that has also been reported by Shang et al 34 Our theoretical results are in accordance with the experimental observations of Lee et a1. 18 and Srivastava et al 19 The present work is motivated by important experimental investigations carried out by Lee et al 18 and Srivastava et al 19 According to Srivastava et al, 19 upon an increase in the microwave power, more ionization of the gas occurs, which increases the density of plasma species of relatively higher energy.…”

High power impulse magnetron sputtering and its applications

“…Anders et al [19] recorded a series of current waveforms taken at a fixed voltage with varying target materials. As figure 4 shows the current waveform typically exhibits an initial peak followed by a second one.…”

“…After investigating the discharge characteristics of HiPIMS in the Cr target (Φ50 mm), Wu et al [20] divided the target current into two stages as shown in figure 5: in the first stage, the peak current appearing at the beginning of the pulse was called the pulse peak current; in the second stage, the stable current was called the pulse holding current. At a constant voltage mode the initial current peak was attributed to argon ions and secondary electrons, and the second peak was associated with the sustained self-sputtering [19].…”

Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle

“…Calculation difficulties in these numerical methods arise due to the large nanotube aspect ratio and very long distance between cathode and anode in comparison with emitter height. Usually, these numerical results were generalized and simple fitting formulas of field enhancement factor for individual nanotube [21,22,25,26], for nanotube in space between parallel cathode and anode planes [27][28][29][30], and for a nanotube surrounded by neighboring nanotubes with a screening effect [31][32][33][34][35] were suggested.…”