So far in this book on radio-frequency plasmas the properties of plasmas have been investigated in the absence of periodic time-dependent parameters or boundary conditions, therefore effectively in a DC steady state. In this chapter the restriction to DC conditions will be relaxed to prepare the ground for the discussion of plasmas that are sustained by radio-frequency (RF) power supplies. Although quantities such as electric fields and potentials then become a combination of steady and periodic values, there are many useful situations that appear to be (RF) steady states when viewed over many cycles – all relevant quantities exhibit coherent oscillations and identical conditions are reproduced within each cycle. When the plasma is sustained by a combination of volume ionization and surface loss, and the response of ions is restricted by their inertia, as is the case in many RF plasmas, the density structure of the plasma shows barely any temporal modulation. The ion space charge in sheath regions is similarly robust. That is, the density profile of the plasma and that of the ions in the sheath remain steady. However, because the electrons are much more mobile, they are able to respond virtually instantaneously, thereby changing the spatial extent of sheaths and quasi-neutral plasmas. The potential profile is related to the spatial distribution of charges through Gauss's law, and this will change in line with applied potentials and consequent rapid redistribution of electrons.

In the previous chapter fundamental equations were established that govern the properties of low-pressure plasmas. Elementary processes such as collisions and reactions were described, and fundamental electrodynamic quantities such as the plasma conductivity and the plasma permittivity were derived. These concepts were mostly considered in the context of an infinite plasma or else were viewed as part of a global system without reference to the internal structure of the plasma volume.

Laboratory plasmas are confined. The consequence of the presence of boundaries on the structure of an electrical discharge through an electropositive gas will be discussed in this chapter. The basic idea to keep in mind in the discussion is that in this case charged particles are predominantly produced in the plasma volume and lost at the reactor walls. This was the basis of the global balances in the previous chapter. Conditions in the central volume may differ to some extent from those near the edge. Close to the walls a boundary layer spontaneously forms to match the ionized gaseous plasma to the solid walls; whether insulators or conductors, the walls have a major influence.

Figure 3.1 is a picture of a discharge generated between two parallel electrodes by a 13.56 MHz power supply. The discharge appears to be stratified, with regions of different properties. Light is emitted from the central region, with evidence of internal structure particularly away from the main vertical axis.

Plasmas

A plasma is an ionized gas containing freely and randomly moving electrons and ions. It is usually very nearly electrically neutral, i.e., the negatively charged particle density equals the positively charged particle density to within a fraction of a per cent. The freedom of the electric charges to move in response to electric fields couples the charged particles so that they respond collectively to external fields; at low frequencies a plasma acts as a conductor but at sufficiently high frequencies its response is more characteristic of a dielectric medium. When only weakly ionized (the most common situation for industrial applications) a plasma also contains neutral species such as atoms, molecules and free radicals. Most of this book is about weakly ionized plasmas that have been generated at low pressure using radio-frequency (RF) power sources.

Plasma is by far the most common condition of visible matter in the universe, both by mass and by volume. The stars are made of plasma and much of the space between the stars is occupied by plasma. There are big differences between these plasmas: the cores of stars are very hot and very dense whereas plasmas in the interstellar medium are cold and tenuous. Similar contrasts also apply to artificially produced plasmas on Earth: there are hot dense plasmas and colder less dense plasmas.

In the previous chapter it was shown that single-frequency capacitive discharges do not allow ion flux and ion energy to be varied independently. To overcome this limitation, inductive discharges may be used, in which the plasma is produced by an RF current in an external coil while the wafer-holder is biased by an independent power supply. These discharges are studied in the next chapter.

It should also be possible to achieve a reasonable level of control of the ion flux independently of the ion energy, by using dual-frequency CCP. Figure 6.1 shows the inspiration for this assertion: the ion energy is plotted as a function of the ion flux at the grounded electrode of a symmetrical CCP for three different single-frequency discharges. The symbols are measurements from a planar probe and from a retarding field analyser inserted in the grounded electrode (see Chapter 10 for background on these measurements). The lines in the figure are from a global model similar to that developed in the previous chapter. It appears as expected that the trajectory in flux–energy space is a single line for each driving frequency. At 13.56 MHz, there is a clear trend towards high ion energies and small ion fluxes, while at 81.36 MHz the opposite arises. Etching often requires ions to have energy in excess of 100 eV to enhance chemical reactions, but less than about 500 eV to avoid physical damage to the surface being etched, or to the photoresist mask.

Capacitively coupled plasma reactors have some natural limitations. Although very high-frequency CCPs achieve high plasma density (typically ne ≈ 1017 m−3), this is accompanied by major uniformity problems. Moreover, the ion flux and the ion energy cannot be varied totally independently, even when multiple-frequency excitation is employed. Inductively coupled discharges overcome these limitations to some extent. They are used in plasma processing and for plasma light sources.

Inductive discharges have been known since the end of the nineteenth century. The principle is to induce an RF current in a plasma by driving an RF current in an adjacent coil. From an electromagnetic point of view, the changing magnetic field associated with the coil current induces an electromagnetic field similar to the H-mode studied in the previous chapter. However, the coil is much more efficient than a pair of parallel plates in exciting an H-mode. Interestingly, the coil also couples to the plasma electrostatically, which means that an inductive discharge may also operate in an E-mode and therefore it can experience transitions between E and H-modes. These transitions are usually sharper than in VHF capacitive discharges, with strong hysteresis effects and instabilities when electronegative gases are used.

Adding a static magnetic field to an RF-excited plasma has two major consequences. Firstly, the plasma transport is reduced in the direction perpendicular to the magnetic field lines; this will be discussed in the next chapter. It will be shown that the magnetic field reduces the transverse plasma flux and may therefore be used to increase the plasma density at given power. More generally, the addition of a static magnetic field can be used to adjust the uniformity of the plasma flux, and to modify the electron temperature or the electron energy distribution function. This is achieved by changing the magnetic field topology. Some of these properties are used in magnetically enhanced reactive ion etching (MERIE) reactors, which are capacitively coupled reactors with a magnetic field parallel to the electrodes. In some instances, this magnetic field is designed to rotate at low speed in order to average out modest asymmetries of the plasma parameters.

Secondly, a static magnetic field enables the propagation of electromagnetic waves at low frequencies, that is at ω « ωpe; a class of such waves, known as ‘helicons’, are of particular importance in plasma processing and in space plasma propulsion. Helicons are part of a bigger group of waves called ‘whistlers’. The first report of whistlers, that is whistling tones descending in frequency from kilohertz to hundreds of hertz in a few seconds, was in the early twentieth century.