Revealing the size dependence on point field emitter emission beam through continuous work function and atomic precise electric field

Nowadays, the nano/atomic-scale field emitters have shown convergent single electron beam, demonstrating an ultra-high brightness beneficial for high signal-to-noise ratio and high throughput for applications of electron microscopes and electron beam lithography. However, based on the existing field emission models, divergent electron beams are obtained on curved point cathodes regardless of the curvature radius, which is inconsistent with existing experimental phenomena. Herewith, a theoretical method for analyzing point field emission electron sources was established by introducing the continuous work function obtained by the linear interpolation and the precise electric field distribution obtained by atomic-scale edge arrangement. When the tip is large (R > 200 nm), the emission beam is mainly affected by the difference in the work function of varied crystal planes and results in a divergent beam. When the tip is small (R < 50 nm), the isotropic work function caused by the amorphous surface layer and the concentrated electric field caused by the atomic structure at the tip are considered, which cause the beam to be mainly affected by the electric field and generate a convergent single beam. Those results provided a method for understanding the nanoscale point electron sources and are beneficial for the next atomic-scale field emission electron beam technology.