Numerical calculations of field enhancement and field amplification factors for a vertical carbon nanotube in parallel-plate geometry

Three types of models, with various emitter shapes in planar electrodes, have been employed to investigate field electron emission characteristics by finite element method. With the model of “hemisphere on a post”, two definitions of field enhancement and field amplification factors and their relation have been discussed systemically at different anode locations. The field distribution in the gap, between emitter apex and anode, is quantified by a field saturation factor. Simulation indicates that field distribution is an important aspect for explaining the nonlinear variation of field amplification factor at different anode locations. Furthermore, the field saturation factor can reflect the saturation degree of field amplification factor. The findings can be used not only in the model of “hemisphere on a post” but also approximately in the models of “two-stage hemisphere on a post” and “hemi-ellipsoid on plane”. Therefore, the fact can be approximately applied to every protruding shape of emitter that is supposed. Comparisons with previously reported experimental and theoretical results are also given.