This book is intended to introduce plasma processing and technology, so that the reader can readily understand the issues involved in processing and can immediately access the state-of-the-art literature. The reader is not assumed to have any knowledge of plasmas, but only some undergraduate background in basic electromagnetism. In fact, wherever possible the treatment even avoids quoting results from one part of the book for use in another part. In many cases it develops new ideas more than once, each time they are needed, to make the discussion easier to follow.

Plasma reactors and the physical and chemical processes that take place in them are discussed in considerable detail, the main emphasis being on capacitive, inductive, and electron cyclotron resonance (ECR) reactors. However, this is an area in which there are few simple (or perhaps even right) answers. It is not usually possible to give a complete description of a plasma reactor, so we are largely concerned, here, with showing how one should go about thinking about what is happening in the reactor.

The chapters of the book are organized in the order in which we need to consider material to understand the reactor. This can sometimes mean that we do not treat a single topic in one chapter separately from other topics. Instead, subject matter will often be introduced where it is needed as we build up the picture of how systems work.

Plasma Chemistry

The chemical processes that can take place in a plasma are exceptionally complicated and little understood. A treatment of all the possible chemistries of interest for semiconductor fabrication would be an enormous undertaking. Here we establish some guidelines for thinking about plasma chemistry, rather than attempting to describe all the possibilities. A number of texts on plasma chemistry are available, although the emphasis in many is more on plasma polymerization than on silicon processing [83–91].

The term plasma chemistry is usually not appropriate to describe the important effects. The hot electrons from the plasma are responsible for driving unusual chemistry – mostly neutral chemistry. (The main exception to the electrons driving the chemistry is activation of surfaces by ions.) Perhaps only the first step in a chain of reactions even involves the electrons, however. The energy an electron needs to ionize a neutral is much higher than the energy needed to dissociate most neutrals. There are usually vastly more electrons with enough energy to dissociate neutrals than there are electrons that have enough energy to ionize neutrals.

The terrestrial magnetosphere comprises the region of space where the properties of naturally occurring ionized gases are controlled by the presence of Earth's magnetic field. This very broad definition means that the terrestrial magnetosphere extends from the bottom of the ionosphere to more than ten Earth radii (Re) in the sunward direction and to several hundred Re in the antisunward direction.

The magnetosphere is formed as a result of the interaction of the supersonic, superalfvénic, magnetized solar wind with the intrinsic magnetic field of the Earth. To understand this interaction, we first briefly discuss the main characteristics of the intrinsic terrestrial magnetic field and then turn our attention to the interaction between this intrinsic field and the solar wind.

The Intrinsic Magnetic Field

A couple of hundred years ago Gauss showed that the magnetic field at the surface of the Earth can be described as the gradient of a scalar potential. In general the near Earth magnetic field can be expressed as

where Φint and Φext represent scalar potentials due to intrinsic and external sources, and Φtot is the sum of these two potentials (describing the total geomagnetic field). In general, planetary magnetic potentials are expressed as an infinite series using associated Legendre polynomials:

where θ and ϕ are geographic colatitude and east longitude, respectively.

This book provides a comprehensive introduction to the physics of the space environment for graduate students and interested researchers. The text is based on graduate level courses I taught in the Department of Aerospace Engineering and in the Department of Atmospheric, Oceanic, and Space Sciences of the University of Michigan College of Engineering. These courses were intended to provide a broad introduction to the physics of solar—planetary relations (or space weather, as we have started to call this discipline more recently).

The courses on the upper atmosphere and on the solar wind and magnetosphere have been taught for a long period of time by many of my friends and colleagues here at Michigan before I was fortunate enough to teach them. I greatly benefited from discussions with Drs. Thomas M. Donahue, Lennard A. Fisk, and Andrew F. Nagy here at the University of Michigan and Drs. Thomas E. Cravens (University of Kansas), Jack T. Gosling (Los Alamos National Laboratory), and József Kóta (University of Arizona). I am grateful for their advise, criticism, and physical insight.

I would also like to acknowledge the constructive criticism of Konstantin Kabin, my graduate student here at the University of Michigan. His mathematical rigor and helpful suggestions greatly helped me in producing the final version of the manuscript.

It has been observed under certain conditions that most mediums in the space environment can experience abrupt changes of macroscopic parameters. In a broad sense shocks and discontinuities are defined as transition layers where the state of the fluid changes from one that is near an equilibrium state to a different one. Examples involve detonation waves in the atmosphere, shocks, and transition layers in the magnetosphere, the interplanetary medium, and in the Sun. In all these cases the transition layer is very narrow compared to the characteristic scale of the problem.

In this chapter we consider the fundamental theory of shocks and discontinuities in neutral gases and quasineutral plasmas.

Normal Shock Waves in Perfect Gases

In the perfect gas approximation shock waves are discontinuity surfaces separating two distinct gas states. In higher order approximations (such as the Navier—Stokes equations) the shock wave comprises a region where physical quantities change smoothly but rapidly. In this case the shock has a finite thickness, generally of the order of the mean free path.

Because the shock wave is a more or less instantaneous compression of the gas, it cannot be a reversible process. The energy for compressing the gas flowing through the shock wave is derived from the kinetic energy of the bulk flow upstream of the shock wave.

Most space plasmas are quasi-neutral statistical systems containing mobile charged particles. On the average, the potential energy of a mobile particle due to its nearest neighbor is much smaller than its kinetic energy. This definition excludes high density plasmas (such as solid states or stellar interiors), but the description of these forms of matter goes far beyond the scope of this book.

Owing to the long-range nature of electromagnetic forces, each charged particle in the plasma interacts simultaneously with a large number of other charged particles. This process results in collective behavior of the plasma particles: In some respect even a low density space plasma behaves as a continuous medium.

In gaseous, nonrelativistic plasmas the motion of individual particles is governed by electromagnetic fields, which are a combination of internally generated (due to the presence and motion of charged particles) and externally imposed fields. The motion and interaction of plasma particles can be described by nonrelativistic classical mechanics and by electrodynamics, quantum mechanical effects are usually neglected.

The interaction of charged particles with electromagnetic fields is described by the force (Eq. 1.16), whereas the electromagnetic field itself obeys Maxwell's equations (Eqs. 1.1, 1.2, 1.3, and 1.4). It should be noted that one must include the contributions of plasma particles to the charge and electric current densities.

Sidney Chapman introduced the nomenclature used to describe the various regions of the upper atmosphere. The classification is primarily based on the variation of temperature with altitude. In this system the regions are called “spheres” and the boundaries between the regions are called “pauses.”

The troposphere (in Greek it means “turning sphere”) is the lowest atmospheric region. It begins at the surface (which provides the major heat source for the atmosphere) and extends to about 10–12 km. This region is mainly characterized by a negative temperature gradient (≈ -10 K/km). The troposphere is bounded by the tropopause, which separates the troposphere from the stratosphere (Greek word for “layered sphere”). The temperature at the tropopause is about 200 K. Originally the stratosphere was thought to be isothermal, but in fact, in this region the temperature increases about 2 K/km due to the absorption of solar UV radiation by stratospheric ozone. Stratospheric ozone is particularly important because it absorbs UV radiation harmful to life.

The maximum temperature (≈270 K) is reached at the stratopause, which is located at around 50 km altitude. Above the stratosphere lies the mesosphere (middle atmosphere), where the temperature again decreases with altitude. The temperature reaches its minimum (≈180 K) at the mesopause, located at an altitude of about 85 km.

There are ions and electrons at all altitudes of the terrestrial atmosphere. Below about 60 km thermal charged particles (which have comparable energies to the neutral gas constituents) do not play any significant role in determining the chemical or physical properties of the atmosphere. Above ≈60 km, however, the presence of electrons and ions becomes increasingly important. This region of the upper atmosphere is called the ionosphere. Note that the ionosphere overlaps with the upper mesosphere, the thermosphere, and the geocorona.

The typical vertical structure of the ionosphere is shown in Figure 10.1 (Hargreaves 1992). Inspection of Figure 10.1 reveals that the ionosphere exhibits a strong diurnal variation and it also varies with the solar cycle. The identification of the atmospheric layers is usually related to inflection points in the vertical density profile: The main regions are local minimums. The primary ionospheric regions are the following:

• D region (≈60–90 km, peaks around 90 km);

• E region (≈90–140 km, peaks around 110 km);

• F1 region (≈140–200 km, peaks around 200 km);

• F2 region (≈200–500 km, peaks around 300 km);

• Topside ionosphere (above the F2 region).

It can be seen that the D and F1 regions disappear at night, while the E and F2 regions become much weaker.

The Sun is an ordinary star of spectral type G2V with magnitude of 4.8. However, it is the only star we have in our immediate vicinity and it is the source of most of the energy that controls physical phenomena in our space environment. The Sun is also a living, dynamic star with varying activity as demonstrated in Figure 11.1. Changes in solar activity result in many important phenomena in the space environment, ranging from flares, to coronal mass ejections, to geomagnetic storms. The fundamental physical properties of the Sun are given in Table 11.1.

The Sun consists primarily of hydrogen (90%) and helium (10%). Elements such as C, N, and O constitute about 0.1% of its mass. The interior can be divided into four zones (see Figure 11.2):

1. The core. This is the high density, high temperature region at the center of the Sun, where thermonuclear energy production takes place. The core extends from the center to about R⊙/4 (1/64-th of the Sun's volume), but it contains about half of the solar mass. Practically all of the Sun's energy production takes place in this region.

2. The radiative zone. The energy produced in the core is transported through the core and the radiative zone by gamma ray diffusion. The gamma rays are scattered, absorbed, and reemitted many times before they reach the outer edge of the radiative zone.

3. […]

In its most general form the Boltzmann equation is a seven-dimensional nonlinear integro-differential equation. The solutions of the Boltzmann equation provide a full description of the phase-space distribution function at all times. In most cases, however, it is next to impossible to solve the full Boltzmann equation and one has to resort to various approximate methods to describe the spatial and temporal evolution of macroscopic quantities characterizing the gas.

Transport equations for macroscopic molecular averages are obtained by taking velocity moments of the Boltzmann equation. This seemingly straightforward technique runs into considerable difficulties because the governing equations for the components of the n-th velocity moment also depend on components of the (n + 1)-th moment. In order to get a closed transport equation system, one has to use closing relations (expressing a higher-order velocity moment of the distribution function in terms of the components of lower moments) and thus make implicit assumptions about the distribution function.

Moment Equations

Velocity Moments

We start by examining the physical interpretation of the various velocity moments of the phase-space distribution function.

Macroscopic variables, such as number density, average flow velocity, kinetic pressure, and so on, can be considered as average values of molecular properties.

Humanity has always been fascinated by atmospheric sources of light. The first records of auroras date back thousands of years to biblical, Greek, and Chinese documents. The name aurora borealis (latin for northern dawn) was coined by the French mathematician and astronomer, P. Gassendi, who described a spectacular event observed in southern France on September 12, 1621. Airglow was discovered in 1901 by Newcomb who explained it as light from stars too faint to be seen individually. It was not before the 1930s that scientists realized that the source of the faint “light of the night sky” must be zodiacal light and atmospheric luminescence. Figure 9.1 shows a photograph of a spectacular aurora.

Both aurora and airglow are caused by excitation of atmospheric species followed by subsequent radiation of photons. They are, however, quite different in terms of excitation mechanisms, temporal and spatial characteristics, intensity, and dominant emissions.

Airglow is the amorphous, faint optical radiation continuously emitted in wavelengths from the far UV to near infrared (but excluding thermal emissions in the long wavelength infrared). The Earth's airglow mainly originates from discrete atomic and molecular transitions (an exception is a weak continuum in the green). Airglow is mainly caused by three fundamental processes: direct scattering of sunlight, emissions associated with ionization and recombination, and radiation associated with neutral photochemistry.