Emission from the End Facet

Of all electrons emitted by a Schottky source, the emission from the end facet is the most important because it delivers electrons that are used for probes and beams in commercial applications. Up till recently focus has been on the emission properties of the center of the facet. This is because most commercial systems use only a very small percentage of the total current emitted by the facet (typical beam currents of the order of picoamperes to nanoamperes compared to typical facet currents of tens of microamperes). With the recent efforts to develop multibeam systems (Zhang & Kruit, 2007; Young et al., 2009) the interest in the emission properties of all of the facet has increased and also its stability in terms of its shape. The effect of the operating conditions on the uniformity of the emission properties across the facet, and on the stability of the shape of the facet, can be investigated by looking at the facet emission pattern. The emission pattern is a strong function of the conditions. It can look quite different for a single emitter, even for a constant geometrical shape of the emitter. This was already shown in Fig. 2.5. For correct interpretation of the emission pattern we need to know the translation between the current density distribution on the facet and the current density distribution in the emission pattern. This will be the focus of this chapter. In Chapter 5 the emission pattern will be used to monitor changes in the physical shape of the emitter. The emission pattern is a current density distribution that is measured in a plane just behind the extractor. The current density distribution across the facet can be calculated with the electron

emission theory of Chapter 1 for a given temperature and work function if the field distribution across the facet is known. The latter can be found with the charge density method. But how does the current density distribution on the facet translate into an emission pattern? We will first investigate the lens effect between the facet and the extractor. On the basis of this investigation we will make the approximation that all facet emission can be traced back to a single “point source” on the optical axis. In that case the emission pattern can also be considered an angular intensity distribution, a distribution in the angular current density, or current per solid angle, emitted by a point source. In this chapter we will assume that all electrons have zero energy upon emission. In practice this is not the case (see Chapter 1), but the effect of this on the shape of the emission pattern is only small. We will discuss the effect of the energy distribution of the electrons in more detail in Chapter 4. With the results from the lens effect analysis, the current density on the facet can be converted into an angular intensity distribution, which can be compared with experimental emission patterns. In Section 3.1 we investigate the conversion of a current density distribution to an emission pattern for one specific case. In Section 3.2 we will discuss the effect of the voltage settings (in more detail than we did in the previous chapter) and in Section 3.3 the effect of the emitter geometry. Section 3.4 is addressed to “Schottky plots,” an experimental method that can yield the conversion factor between the voltage applied and the field at the emitting surface. In Section 3.5 the effect of the emitter temperature is discussed. 3.1 The Facet Extractor Lens

To find the emission from the end facet it is first of all required to know the field distribution across the facet. This can be done with the charge density method, which has already been introduced in the previous chapters. For the following example (Figs. 3.2-3.5) we take the emitter geometry as given in Fig. 3.1, and the gun geometry from Fig. 1.2, with a protrusion of 242 nm and a distance between the suppressor and the extractor of 0.75 mm. The field distribution across the facet is given in Fig. 3.2.