An effective 3-D finite element model was constructed for the field emission array to analyse the field emission current over a single tip. Considering the periodicity of field emission array and the axial symmetry of the single tip model

only 1/4 of the single tip model was analyzed. The electric field intensity distribution over the tip surface was established through calculation with appropriate voltage boundary condition applied

and it was found that the electric field intensity was the strongest at the apex of the tip

and the field emission current was also the strongest there. The field emission current density distribution over the tip surface was established using Fowler-Nordheim function

and the emission current over the single tip established by integrating the current density all over the single tip surface was 7 μA. Field emission currents were calculated for different apex radii at the gate voltage of 100V

and the results indicated that the field emission largely depends on the apex radius. Total field emission currents were calculated for 100 tips with an apex radius of 8 nm at different gate voltages

and the results indicated that both emission currents and opening voltages were in very good agreement with actual measurements.