: Field Emission and Vacuum Devices
Vacuum or field emission devices where electrons are extracted from metals or semiconductors are a minority in the world of devices. However, we will begin our discussion of devices with field emission ones because of their simplicity: they involve only two electrodes, usually called anode and cathode, between which conduction by tunnelling through vacuum occurs. Transistors, on the other hand, which are made of semiconducting materials, are three terminal devices in which the third electrode, called gate, modifies the conductance between the other two. The above statement is incorrect from a historical point of view. The vacuum valve was the predecessor of the modern transistor and was the first tool to produce electronic amplifiers, oscillators, etc. Actually, the vacuum valve in solid state form—a transistor with vacuum as its channel—seems to have been revived lately but our choice of starting from vacuum devices, mainly diodes, stems from the simplicity of not only their configuration but also of applying our quantum formalism: the current is only from the cathode to the anode and there is no current in the opposite direction as there is in all semiconductor devices. A further simplification is that collisions during emission do not play a significant role and are usually omitted. We have emphasized many times that due to the nanometric size of present day devices, only a quantum approach to conduction can yield accurate results, such as the Landauer theory of conduction which relates the conductive properties to the transmissive properties of a medium. In the previous chapter, we have shown how to calculate the transmission coefficient of mathematically simple barriers with no collisions. Unfortunately, such simple barriers rarely occur in modern diodes and transistors. An exception is the RTD discussed in the previous chapter where the vast majority of the current is a tunnelling current. In MOSFETs and other forms of transistors, the conduction is 3-dimensional and over the barrier, not through the barrier. Therefore, a proper knowledge of the wavefunctions themselves is mandatory, not just of the transmission coefficient, as will become evident in the next chapter. A method capable of doing this for arbitrary but slowly varying potentials without resort to numerical calculations is the WKB method which we initially touched upon in chapter 1. We now discuss it at some depth as it will be useful in many cases of device analysis.