ABSTRACT
The Schottky emitter is used in systems that make either a probe or a more or less collimated beam to illuminate samples for different purposes. Only a small part of the facet emission is used for this. The column of systems consists of several lenses that make a few intermediate images of the “virtual” source before making the final (de)magnified image onto the specimen (in the case of a probe system) or the final collimated beam (for parallel illumination). The virtual source is not the physical emitting surface but the virtual crossover formed by the field near the emitting tip. The position and size of the virtual source are of importance to the design of the lens system: they determine the parameters for the optics in between the virtual source and the specimen, such as the lens strength and aperture sizes. The virtual source is addressed in Section 4.1. A good source for probe formation allows one to squeeze a large current in a small focus spot, while for transmission electron microscopy (TEM) purposes it is associated with a large current in a fully coherent beam. The parameter that determines this ability is the practical brightness. Practical brightness is introduced in Section 4.2. Diffraction and aberrations make the spot of a focused beam larger than the source image and decrease the spatial (spherical aberration) and temporal (chromatic aberration) coherence of a parallel beam. These different contributions have different
dependencies on the opening angle of the beam, which leads to an optimum angle for which the spot size is smallest for a given probe current. The optimum probe current-probe size relation for a given set of source properties will be addressed in Section 4.3. The chromatic aberration contribution depends on another relevant source parameter: the spread in energies of the electrons in the beam. The practical brightness and energy spread of the beam can be affected by interactions between electrons in the beam. This is the topic of Section 4.4. Finally, in Section 4.5 the findings of the preceding paragraphs are used to quantify beam properties that are relevant to applications, as a function of the conditions at the emitting surface. 4.1 Imaged by the Electron-Optical System: The
Virtual SourceThe size and position of the virtual source depend on the source geometry, extraction voltage, temperature, and on which part of the total emitted current is selected for the final probe. The latter depends on the application; for example, for high-resolution imaging the beam current is in the order of picoamperes, but for microanalysis the probe current needs to be much higher. For multibeam applications with off-axis beamlets an additional parameter is introduced: the amount of current is relevant to not only the size and position of the virtual source but also the position of the selecting aperture. For simplicity we will place the beam-defining aperture (the aperture that selects the probe electrons) right behind the extractor in the field-free zone. In most commercial systems currently available the beam-defining aperture is further away. The position of the virtual source can be found by tracing the probe electrons back from the field-free zone to the point where they cross the optical axis. Figure 3.4 has already shown that not all trajectories necessarily cross the optical axis in the same point. The position of the plane perpendicular to the axis that contains the smallest full width containing 50% (FW50) diameter of the extrapolated trajectories of the probe electrons is the position of the virtual source. Most electrons emitted by an operating Schottky emitter have zero tangential energy. Let us first consider an imaginary cold field
emitter, which only emits electrons with zero tangential energy, thus perpendicular to the emitting surface. Later we will add the effect of the thermal energy of the electrons. We will investigate a single-emitter geometry that, in Fig. 3.1, is the standard gun geometry with a suppressor-extractor distance of 0.75 mm and a protrusion of 242 mm, a suppressor voltage of –0.3 kV, and an extraction voltage of 5.5 kV with respect to the emitter, unless stated otherwise. 4.1.1 Imaginary Cold Schottky Source Basically, cold electrons determine the position of the virtual source. When the beam-defining aperture has a small acceptance angle, it can be assumed that the electrons originate from a small surface patch for which the field can be assumed to be constant and for which the lens between the emission site and the extractor is aberration free. As a consequence, the electrons appear to be originating from a single point, which for an on-axis aperture is on the axis (traced back from the aperture) and off the axis for an off-axis aperture, as illustrated in Fig. 4.1. The crossover is the position of the virtual source, and its size is infinitely small.
