ABSTRACT
E , (5.3)where A and B are constants with the value of 1.56 × 10-10 (AV-2 eV) and 6.83 × 103 (VeV-3/2 µm-1), respectively. The field enhancement factor b in FN equation reflects the degree of the FE enhancement of
any tip over a flat surface. It represents the true value of the electric field at the tip compared with its average macroscopic value. For a nanostructured emitter, the b value is related to the geometry, crystal structure, conductivity, work function, and nanostructure density. According to the FN equation, low electron barrier is beneficial to FE; therefore, the materials with low work function are suitable for cold electron emission. Doping is an effective approach to adjust the energy level structure for semiconductors. The relationship between electron concentration and the Fermi level can be written as 33 p= -2 3 2 F C2 2 /( * / ) exp[( ) / ]n m kT h E E kT , (5.4)where n is the electron concentration, m* is the electron effective mass, k is the Boltzmann constant, T is the absolute temperature, h is Planck’s constant, EF and EC are energies at the Fermi level and bottom of conduction band, respectively. This indicates that the FE performance can be improved through n-type doping because the Fermi level is lifted up and hence, the work function is reduced. In fact, researchers have obtained FE with low threshold and enhanced emission current from n-type doped ZnO.17, 22 Furthermore, negative electron affinity, which is very advantageous for electron emission, can be possibly generated through heavy doping under certain conditions.34 The energy level diagrams for different materials are shown in Fig. 5.1.
