Source brightness and useful beam current of carbon nanotubes and other very small emitters

Abstract

The potential application of carbon nanotubes as electron sources in electron microscopes is analyzed. The resolution and probe current that can be obtained from a carbon nanotube emitter in a low-voltage scanning electron microscope are calculated and compared to the state of the art using Schottky electron sources. Many analytical equations for probe-size versus probe-current relations in different parameter regimes are obtained. It is shown that for most carbon nanotube emitters, the gun lens aberrations are larger than the emitters' virtual source size and thus restrict the microscope's performance. The result is that the advantages of the higher brightness of nanotube emitters are limited unless the angular emission current is increased over present day values or the gun lens aberrations are decreased. For some nanotubes with a closed cap, it is known that the emitted electron beam is coherent over the full emission cone. We argue that for such emitters the parameter "brightness" becomes meaningless. The influence of phase variations in the electron wave front emitted from such a nanotube emitter on the focusing of the electron beam is analyzed.

Space charge effects in field emission: One dimensional theory

“…Applications that rely on field emission will benefit, and such applications include (but are not limited to): electron beam lithography [22,23] and transmission electron microscopes [24]; spacecraft propulsion [25,26]; mm-wave Vacuum Electronic amplifiers and THz devices [27,28]; and particle accelerators and Free Electron Lasers (FEL's) [29][30][31].…”

Probe current, probe size, and the practical brightness for probe forming systems

“…We did not include probe currents Ͼ20 nA because in this example, we have neglected the gun aberrations which become important at larger probe currents, when the acceptance angle at the gun has to become large. 35 As can be seen, the probe current for which the contributions from diffraction and source image have the same size B. This brightness current I AI separates the different regimes that can be distinguished in Fig.…”

Physics of Schottky Electron Sources

“…We did not include probe currents >20 nA because in this example we have neglected the gun aberrations which become important at larger probe currents, when the acceptance angle at the gun has to become large. [Kru06] As can be seen from In general, each section of the I p (d p )-curve has its own figure of merit for the source and for the column properties, which can be found from the equations. Increasing the right figure of merit will improve the system performance for the curve section of interest.…”