Simulation Study of Beam Temperature Effects of Carbon Nanotubes Field Emission Source

Abstract

Summary form only given. Carbon nanotubes (CNTs) are promising electron sources for field emission displays (FEDs) due to their excellent characteristics. But the temperature effects upon the spreading of the emitting electrons and upon the field emission characteristics have seldom been discussed. In this study, the particle-in-cell finite-difference time-domain (PIC-FDTD) method is used to study the temperature effects of the electron beams. A field emission model based on the Fowler-Nordheim equation using the local electric field at the nanotube top is established. The transverse and longitudinal temperature effects are introduced through adding energy of the emitted electrons with the Botzlmann distribution. For considering the junction effects of the carbon nanotubes grown on doped silicon substrate, the phenomena of the reversed saturated currents are also included in our emission model. Moreover, due to the essence of the PIC-FDTD method, the space-charge effects are considered in the simulation automatically. The simulation geometry is shown in figure 1. The two-dimensional cylindrical coordinate (z-r-thetas) with thetas symmetry is adopted. Figure 2(a) and 2(b) plot the energy distributions of the emitted electrons for the anode voltage of 10000 V, with and without the junction effects, respectively. As shown in Fig. 2, due to the emission current limited by the junction effect, the emitted electrons present the Botzlmann distribution but with less noise. Figure 3 plots the beam radius as a function of the anode voltage for different beam temperatures and without the junction effect. Figure 3 presents that the beam radius increases with the anode voltage. And the beam temperature has more apparent effects on the beam radius on larger anode voltage only. Figure 4 shows the F-N plots for different beam temperatures, with and without the junction effects. As shown in Fig. 4, the beam temperature has little notable effect on the F-N plot. But the emission current is limited by the junction effect much earlier than by the space-charge effect