.1

Under the assumption that there is one major site of field emission and its emitting area denoted by Ae and with E = b(V/d) accounting for enhancement where V is the applied voltage, the total pre-breakdown current I as I = JAe in logarithmic form is given by I = (AeB1b2V2/(fd2)) exp (–dB2f3/2/(bV)) (9.2) The complete Fowler-Nordheim result is given by log (I/V2) = log ((1.54 ¥ 10-6Aeb2104.52f ^–0.5)/(fd2)) – ((2.84 ¥ 109df1.5)/β) (1/V) (9.3) The Fowler-Nordheim equation states that the emission current (I) increases exponentially with increasing voltage (V). According to the above equations, the emission current is strongly dependent on the following three factors: (a) the work function of the emitter surface, (b) the radius of curvature of the emitter apex and (c) the emission area. For a metal with a flat surface, however, the threshold field is impractically high and is typically around 104 V/μm. All the electron field emitters rely on field enhancement factor b at the sharp tips/protrusions. One way to fabricate sharp field emitters is a lithography process [18]. It is immediately apparent that a field emitter could be more power-efficient than a thermionic emitter, which requires heating. Field emission sources also offer several attractive characteristics such as instantaneous response to electric field variation, resistance to temperature fluctuation, and a high degree of focus ability in electron optics due to their sharp (0.2-0.3 eV) energy spread. Furthermore, the field emitted electrons are confined to a narrow cone angle along the electrical field direction, where thermal electrons are randomly distributed. However, due to the high electric field experienced at the tips of the materials during field emission, the metal atoms often diffuse or electromigrate, causing failure and thermal runaway. As a result, the conventional field emitters of Spindt tips have not been used in practical devices since they in general suffer from high turn-on field, low emission current, high cost and poor stability with limited lifetime. CNT is a unique form of carbon filament/fiber in which the graphene walls roll up to form tubes, with diameters typically 1-50 nm and lengths of a few microns. It has high electrical and thermal conductivity, very high tensile strength, and a high aspect ratio. This makes it a very good material for field emitters. Figure 9.2a illustrates how a CNT emits electrons under the influence of a large electric field.