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.

This text concerns the basic elementary physics of plasmas, which are a special class of gases made up of a large number of electrons and ionized atoms and molecules, in addition to neutral atoms and molecules as are present in a normal (non-ionized) gas. The most important distinction between a plasma and a normal gas is the fact that mutual Coulomb interactions between charged particles are important in the dynamics of a plasma and cannot be disregarded. When a neutral gas is raised to a sufficiently high temperature, or when it is subjected to electric fields of sufficient intensity, the atoms and molecules of the gas may become ionized, electrons being stripped off by collisions as a result of the heightened thermal agitation of the particles. Ionization in gases can also be produced as a result of illumination with ultraviolet light or X-rays, by bombarding the substance with energetic electrons and ions, or in other ways. When a gas is ionized, even to a rather small degree, its dynamical behavior is typically dominated by the electromagnetic forces acting on the free ions and electrons, and it begins to conduct electricity. The charged particles in such an ionized gas interact with electromagnetic fields, and the organized motions of these charge carriers (e.g., electric currents, fluctuations in charge density) can in turn produce electromagnetic fields.

This book is intended to provide a general introduction to plasma phenomena at a level appropriate for advanced undergraduate students or beginning graduate students. The reader is expected to have had exposure to basic electromagnetic principles including Maxwell's equations and the propagation of plane waves in free space. Despite its importance in both science and engineering the body of literature on plasma physics is often not easily accessible to the non-specialist, let alone the beginner. The diversity of topics and applications in plasma physics has created a field that is fragmented by topic-specific assumptions and rarely presented in a unified manner with clarity. In this book we strive to provide a foundation for understanding a wide range of plasma phenomena and applications. The text organization is a successive progression through interconnected physical models, allowing diverse topics to be presented in the context of unifying principles. The presentation of material is intended to be compact yet thorough, giving the reader the necessary tools for further specialized study. We have sought a balance between mathematical rigor championed by theorists and practical considerations important to experimenters and engineers. Considerable effort has been made to provide explanations that yield physical insight and illustrations of concepts through relevent examples from science and technology.

The material presented in this book was initially put together as class notes for the EE356 Elementary Plasma Physics course, newly introduced and taught by one of us (USI) at Stanford University in the spring quarter of 1998.