Electron guns are not only necessary for obvious applications as particle accelerators or vacuum tubes. Electron guns are also used in many applications in the area of electronics - for example, in electron microscopes, electron beam lithography or printed electronics. In the latter, the electron beam is used for sintering the printed circuit on temperature-sensitive, flexible substrates.
The electron gun in these applications typically has to provide a high brightness beam with round cross section. Thus, engineers are interested in any deterioration of the beam path due to field disturbances. In addition, secondary electrons can be produced when the beam hits an object, and these are also of interest.
The electron gun used to illustrate the simulation in this article is derived from  and shown in figure 1....
The particle emission will happen from the tip of the field emitter (see figure 2, left). The emission settings could be either space charge limited or field dependent emission. In order to extract and accelerate the particles, electrostatic potentials are applied (figure 2, right). The potential of the suppressor is slightly more negative than the potential of the field emitter tip, such that the beam is focused.
The particle tracking solver of CST PARTICLE STUDIO® (CST PS) directly calculates the resulting potential and particle beam trajectory as shown in figure 3.
As we can see from the beam trajectory (figure 3, right), the beam would widen up with the configuration as described so far. This is certainly not wanted when dealing with high brightness. In order to improve the situation, an external B-field can be applied. For simplicity reasons a constant field was used here, but also complex 3D fields could be applied. These 3D fields could be loaded from an additional CST EM STUDIO<sup>&right;</sup> (CST EMS) simulation or from measurement data provided in a text file. After adding a constant field, the beam trajectory looks much sharper than before (see figure 4, right).
There is one thing very important for such a simulation: The mesh in the vicinity of the emission has to be fine enough to provide a good field distribution and thus correct particle emission. That means, no matter if hexahedral or tetrahedral mesh is used, the mesh has to be inspected before. Typical meshes are shown in figure 5.
The brightness, which is defined as current density per solid angle, can be evaluated from the particle current density plot in combination with the template based post processing. The template based post processing will give a 1D curve of the particle current density, which gives the radius of the spot and the average current density (see also figure 6). For this specific electron gun this yields 3.67 107 A/m2/sr considering a spot radius of 0.0835 mm at a distance of 8.365 mm. The average current density is 12000 A/m2.
A beam which collides with a substrate surface may release secondary electrons. The resulting secondary electrons will be recorded in the detector of the scanning electron microscope. Or, they might limit the resolution of e-beam lithography. Thus, the behavior of the secondary electrons is of interest and can be examined in a second step. In order to illustrate the principle of such a simulation a simplified example is used (see figure 7)
The release of secondaries depends on the material and the beam energy. The material properties are characterized by the secondary emission yield (SEY) in CST PS. The electron gun is replaced by a simplified electron beam emission with fixed current and beam velocity. This beam is shot onto the substrate's surface. The released secondary electrons are shown in the trajectory (see figure 8) and are recorded by the collision info of CST PS for each of the collector objects.
This article shows the principle of an electron gun simulation for electron beam lithography or electron microscopes. The simulation can be entirely performed with the tracking solver of CST PS, which gives the particle trajectory. Derived values as brightness or secondary emitted current can be evaluated in the post processing templates or by using appropriate material properties. Simulation is an easy way to gain some insights into the behavior, which becomes especially valuable for non-symmetric electron guns.
 Shin Fujita, "A new practical approach to evaluation of electron gun properties", Proceedings of the 3rd Symposium on Charged Particle Optics 18-19th September, 2003