Optical Performance of Carbon-Nanotube Electron Sources

The figure of merit for the electron optical performance of carbon-nanotube (CNT) electron sources is presented. This figure is given by the relation between the reduced brightness and the energy spread in the region of stable emission. It is shown experimentally that a CNT electron source exhibits a highly stable emission process that follows the Fowler-Nordheim theory for field emission, fixing the relationship among the energy spread, the current, and the radius. The performance of the CNT emitter under realistic operating conditions is compared with state-of-the-art electron point sources. It is demonstrated that the reduced brightness is a function of the tunneling parameter, a measure of the energy spread at low temperatures, only, independent of the geometry of the emitter. Individual carbon nanotubes (CNTs) can be used as point sources of electrons with extremely high brightness [1]. The energy spread of the emitted electron beam is typically on the order of 0.3 eV [2 – 4] for low currents and temperatures. Furthermore, when the emitting tip of the CNT is closed, the emission current can be highly stable [5,6]. The present status of the research on CNT electron sources was recently summarized [7]. But despite many reports, the figure of merit for the electron optical performance of CNT electron point sources has not yet been determined. This figure is the relation between the brightness and the energy spread for the current region of stable emission. The measurement of just one of these two parameters has a limited use as high brightness is usually obtained at the expense of an increased energy spread, adversely affecting the performance of the source in an electron optical system. In this Letter we present the figure of merit of the CNT electron source, derive a new model for this figure, and discuss its general applicability.