Probe current, probe size, and the practical brightness for probe forming systems

Abstract

Probe size, shape, and current are important parameters for the performance of all probe forming systems such as the scanning (transmission) electron microscope, the focused ion beam microscope, and the Gaussian electron beam lithography system. Currently, however, the relation between probe current and probe size is ill defined. The key lies in a lacking definition of “size.” This problem is solved with the introduction of the “practical brightness.” In literature, many different definitions of “brightness” can be found, but for systems in which the whole of the virtual source is imaged onto the target, it is the practical brightness of a source that determines how much current is in the probe. This means that only with the practical brightness the performance of a probe forming system can be calculated quantitatively. The beauty of the practical brightness is that this source property is unaffected by the quality of the column: without interactions between electrons in the beam, the practical brightness is conserved down to the target. This makes it the only relevant brightness for probe forming systems to be used to compare different sources. The practical brightness can be measured, but can also be calculated when the source intensity profile is known. The Gaussian source intensity profile of thermionic, Schottky, and cold field emitters yields a practical brightness of 1.44ej∕π⟨ε⟩, where j is the current density on the emitting surface and ⟨ε⟩ is the average tangential electron energy.