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.

Figure 1

Emission stability of electron source CNT 1. (a) The probe current $I_p$ was measured as a function of time for a total emitted current of $200\mathrm{nA}$, an extraction voltage of 270 V, and a temperature of 600 K. (b) The normalized spectral density as a function of the frequency $f$. The spectrum was corrected for the noise background of the measuring system. The dashed line is a fit with the function $y=a/x^{0.97}$.

Figure 2

(a) Energy spectrum of CNT 2 and fit with the FN theory (dashed line). (b) Tunneling parameter $d$ as a function of $I$ for two CNTs, compared with numerically calculated curves.

Figure 3

Reduced angular current density $I_r^{\prime }$ normalized on $I_r^{\prime }$ at $100\mathrm{nA}$ for 8 CNT electron sources and a linear fit (dashed line).

Figure 4

Reduced brightness $B_r$ as a function of the tunneling parameter $d$ measured for 5 CNTs and compared with the calculated curve using $B_r=0.04\times J(d,\varphi =5.0\mathrm{eV})$ (dashed line).

Figure 5

$B_r$ as a function of $\Delta E$ measured for several CNTs at currents of 10–500 nA and temperatures of 600–700 K. Calculated curve (dashed line). The data of the Schottky emitter and the CFEG are also included.