A numerical and experimental study of the electric field distribution within field emission systems

Abstract

The design of field electron and field ion sources which are useful in device fabrication systems, electron or ion microscopes requires an accurate and complete knowledge of the electric field distribution both within the gun and near the field emitter itself. Analysis has not been possible by conventional analytical methods due to the intractable nature of the equations. An analysis is presented in the present work which is obtained using the method of finite elements. The numerical approach allows the consideration of the geometric detail common to field ion and field electron microscopes. In these microscopes the ion or electron source serves as the actual specimen to be observed. It is shown that instrument features as far away as 105 tip diameters can substantially affect the electric field at the emitter. The dependence of the electric field at the apex is found to vary as k1 exp(−k2ϑ) where ϑ is the emitter shank angle. The constant k2 describes the strength of the shank angle dependence. These constants may be experimentally determined. Experiments are discussed, and ion images are shown, which demonstrate the marked effect of system geometry on ion trajectories. The ion images illustrate the large amount of trajectory bending which results from a change in the position of a microchannel plate detector. One case is shown in which a crystallographic analysis of the image confirmed that certain trajectories originate from regions on a bulb-shaped emitter which were not within the line of sight of the detector.