A simple micro field emitter is shown below. Note that one unit on this plot is 1 micro-meter and the cathode is a parabola. There is a very fine mesh over the cathode region to simulate the very small emitter. Almost all of the current is emitted in a forward direction because of the parabolic shape of the cathode.

Micro field emitter with parabolic cathode and 95 volts on the extraction electrode.



Current density distribution from the field emitter.

The current from the field emitter falls off rapidly and very little goes to the extractor. The distribution of current at the exit plane is seen in the figure below.  The angular spread of the electrons is relatively large but the diameter of the beam is only a few microns.  The final plot is of the fine mesh equipotentials.

Current density distribution at the field emitter target plane.



Equipotentials on the field emitter fine matrix.