Effect of the electric field on the form stability of a Schottky electron emitter: A step model

Abstract

The stability of the physical shape of an electron emitter (co)determines the stability of the performance of electron-beam equipment. A typical short-term instability of the Schottky electron source is the instability of the (100) facet at the tip end known as “collapsing rings.” This instability causes probe instabilities, but it is known from experiments that this can be prevented by applying high enough extraction voltages. The phenomenon of collapsing rings can be explained with a step-flow model, which is based on variations in equilibrium concentrations of adatoms on the surface. The effect of the extraction voltage can be incorporated by acknowledging the redistribution of the surface charge associated with adatom formation. For operation at constant extraction voltages the adatom formation energy becomes a function of the local charge density. The charge-density distribution on the emitter surface as a function of the applied extraction voltage can be calculated with boundary-element methods. It is shown that, provided the relevant material properties are known, it can be predicted if, for a given tip shape, a collapse is to be expected.