Numerous inelastic scattering processes are involved in electron scattering. The mean-free-path length of inelastic scattering is about 50–300 nm for most materials, thus more than 50% of the electrons will be inelastically scattered if the specimen thickness is close to the mean-free-path length. Inelastic scattering not only affects the quality of REM images and RHEED patterns but also makes data quantification much more complex and inaccurate. In this chapter, we first outline the inelastic scattering processes in electron diffraction. Then phonon (or thermal diffuse) scattering will be discussed in detail. The other inelastic scattering processes will be described in Chapters 10 and 11.

Inelastic excitations in crystals

The interaction between an incident electron and the crystal atoms results in various elastic and inelastic scattering processes. The transition of crystal state is excited by the electron due to its energy and momentum transfers. Figure 9.1 indicates the main inelastic processes that may be excited in high-energy electron scattering. First, plasmon (or valence) excitation, which characterizes the transitions of electrons from the valence band to the conduction band, involves an energy loss in the range 1–50 eV and an angular spreading of less than 0.2 mrad for high-energy electrons. The decay of plasmons results in the emission of ultraviolet light. The cathode-luminescence (CL) technique is based on detection of the visible light emitted when an electron in a higher energy state (usually at an impurity) fills a hole in a lower state that has been created by the fast electron.

In 1986, E. Ruska was awarded the Nobel Physics Prize for his pioneering work of building the world's first transmission electron microscope (TEM) in the late 1920s. The mechanism of TEM was originally based on the physical principle that a charged particle could be focused by magnetic lenses, so that a ‘magnifier’ similar to an optic microscope could be built. The discovery of wave properties of electrons really revolutionized people's understanding about the potential applications of a TEM. In the last 60 years TEM has experienced a revolutionary development both in theory and in electron optics, and has become one of the key research tools for materials characterization (Hirsch et al., 1977; Buseck et al., 1989). The point-to-point image resolution currently available in TEM is better than 0.2 nm, which is comparable to the interatomic distances in solids.

High-resolution TEM is one of the key techniques for real-space imaging of defect structures in crystalline materials. Quantitative structure determination is becoming feasible, particularly with the following technical advances. The installation of an energy-filtering system on a TEM has made it possible to form images and diffraction patterns using electrons with different energy losses. Accurate structure analysis is possible using purely elastically scattered electrons, scattering of which can be exactly simulated using the available theories. The traditional method of recording images on film is being replaced by digital imaging with the use of a charge-coupled device (CCD) camera, which has a large dynamical range with single-electron detection sensitivity.

Introduction

Ion implantation is a process by which virtually any element can be injected into the near-surface region of any solid by causing a beam of high-velocity ions, usually 10 to 400 keV in energy, to strike a target mounted in a vacuum chamber. The resulting depth concentration profile of implanted dopant atoms can be calculated using the theoretical considerations discussed in Chapter 6. At low ion doses, ø (i.e., the number of ions per unit area), the depth concentration profiles are well characterized by a Gaussian distribution centered about an average projected range, Rp. At high fluences, ≥ 1017/cm2, where the concentration of implanted atoms approaches tens of atomic per cent, other effects, such as sputtering and ion beam induced migration of atoms, can significantly alter or limit the ultimate concentrations attainable.

This chapter deals with the erosion of the sample by energetic particle bombardment. In this process, called sputtering, surface atoms are removed by collisions between the incoming particles and the atoms in the near-surface layers of a solid. Sputtering sets the limit of the maximum concentration of atoms that can be implanted and retained in a target material. The yield of sputtered atoms, the number of sputtered atoms per incident ion, typically lies in the range 0.5–20 depending upon ion species, ion energy, and target material. For direct ion implantation into a target material, the maximum concentration of implanted species is inversely proportional to the sputter yield.

Modern technology depends on materials with precisely controlled properties. Ion beams are a favored method – and in integrated circuit technology, the prime method – to achieve controlled modification of surface and near-surface regions. In every integrated circuit production line, for example, there are ion implantation systems. In addition to integrated circuit technology, ion beams are used to modify the mechanical, tribological, and chemical properties of metal, intermetallic, and ceramic materials without altering their bulk properties. Ion–solid interactions are the foundation that underlies the broad application of ion beams to the modification of materials. This textbook is designed to cover the fundamentals and applications of ion–solid interactions.

When we planned to offer an ‘ion implantation’ course at Arizona State University, we were unable to find a suitable textbook. Instead, we developed our own lecture notes, which form the basis of this book. Although intended as a textbook, we believe, on the basis of our own working experience in the field, that it will be a useful reference to professionals who have an interest in ion–solid interactions.

This text is aimed at undergraduate seniors and graduate students interested in electronic devices, surface engineering, reactor and nuclear engineering, and material science issues associated with metastable phase synthesis. The original course was offered by the Department of Materials Engineering. Approximately half of the students came from electrical engineering or disciplines other than materials engineering. Their backgrounds and training varied.

Introduction

It has been known for many years that bombardment of a crystal with energetic (kilo-electron-volts to mega-electron-volts) heavy ions produces regions of lattice disorder. The disorder can be directly observed by techniques sensitive to lattice structure, such as electron-transmission microscopy, MeV-particle channeling, and electron diffraction. The use of these and other techniques, along with the theoretical treatment of ion interactions in solids, has provided a basis for evaluation of implantation processes.

As an ion slows down and comes to rest in a crystal, it makes a number of collisions with the lattice atoms. In these collisions, sufficient energy may be transferred from the ion to displace an atom from its lattice site. Lattice atoms which are displaced by incident ions are called primary knock-on atoms or PKAs. The PKAs can in turn displace other atoms, secondary knock-on atoms, tertiary knock-ons, etc. – thus creating a cascade of atomic collisions. This leads to a distribution of vacancies, interstitial atoms, and other types of lattice disorder in the region around the ion track. As the number of ions incident on the crystal increases, the individual disordered regions begin to overlap. At some point, a heavily damaged layer is formed. The total amount of disorder and the distribution in depth depend on ion species, temperature, energy, total dose, and channeling effects.

Radiation damage and displacement energy

Radiation damage theories are based on the assumption that a lattice atom struck by an energetic ion or recoiling target atom must receive a minimum amount of energy in the collision to be displaced from its lattice site.

Introduction

In Chapters 2 and 3 we developed concepts essential to our understanding of ion–solid interactions. In Chapter 3 we derived equations describing the kinematics of binary elastic collisions. These equations enable us to calculate the amount of energy transferred to a target atom in a collision when the scattering angle of the projectile or the target atom is known. Conversely, we could calculate the scattering angles if the amount of energy loss in the collision were known. At the end of Chapter 3 we developed an expression for the center-of-mass scattering angle, θc, which is a function of the ion energy, the impact parameter b, and the interatomic potential energy V(r). The details of the interatomic potential energy were discussed in Chapter 2.

In Chapter 4 we will examine the probability of ion–solid scattering events. During ion irradiation and ion implantation experiments, many ions or energetic particles interact with many target nuclei. Due to the large number of interactions, the questions of how much energy will be transferred in a collision or what the scattering angle will be must be answered using statistics and probability. The differential cross-section is the fundamental parameter that we will develop. It gives a measure of either the probability of transferring energy T in the range between T and T + dT to a target atom or of the probability of scattering a projectile into some angle between θc and θc + dθc.

Introduction

Ion irradiation of crystalline metallic alloys causes structural changes. Crystalline phase can become amorphous or can change to a different crystalline structure. The transformation can be to metastable or equilibrium phases. The driving force for an irradiation induced transformation is provided by the energy to the lattice during the penetration and subsequent stopping of an energetic ion (see Chapter 7).

To understand irradiation induced phase transformations on a thermodynamic level, let us consider an A–B binary phase diagram and the associated free energy of three of the components (Fig. 12.1). We choose A and B to be fcc metals, AB3 to be a line compound with many atoms per unit cell, AB to be a simple CsCl structure with an extended phase field (the CsCl structure has two atoms per unit cell) that exists over a 10 to 20% range in composition, and the region α to be an fcc solid solution. A free energy curve with small curvature (wide phase field) indicates that the irradiation induced deviations from equilibrium do not result in large increases in the compound's free energy. Large curvature (narrow phase field) indicates just the opposite; small increases in the equilibrium defect concentration or changes in composition produce large increases in the free energy. As a result, compounds with large phase fields can tolerate a higher degree of irradiation damage and should be more irradiation stable relative to compounds with narrow phase fields (Brimhall et al., 1983; Hung et al., 1983).

Introduction

Ion beam processing of materials results from the introduction of atoms into the surface layer of a solid substrate by bombardment of the solid with ions in the electron-volt to mega-electron-volt energy range. The solid-state aspects are particularly broad because of the range of physical properties that are sensitive to the presence of a trace amount of foreign atoms. Mechanical, electrical, optical, magnetic, and super-conducting properties are all affected and, indeed, may even be dominated by the presence of such foreign atoms. The use of energeticions affords the possibility of introducing a wide range of atomic species, independent of thermodynamic factors, thus making it possible to obtain impurity concentrations and distributions of particular interest; in many cases, these distributions would not be otherwise attainable.

Recent interest in ion beam processing has focused on the studies of ion implantation, ion beam mixing, ion induced phase transformations, and ion beam deposition. These interests have been stimulated by the possibilities of synthesizing novel materials with potential applications in the semiconductor, tribological, corrosion, and optical fields.

Ion beam processing provides an alternative and non-equilibrium method of introducing dopant atoms into the lattice. In typical applications, a beam of dopant ions is accelerated through a potential of 10–100 kV. The implantation system shown in Fig. 1.1 illustrates the basic elements required in this technique: ion source, acceleration column, mass separator, and target chamber.

Introduction

The ion beam systems currently employed for surface modification studies involving either direct ion beam implantation or ion beam assisted deposition have evolved from distinctly different predecessors, including isotope separators and exploratory space propulsion devices, respectively. The features of directed beam ion implanters will be discussed first, followed by features of plasma source ion implantation (PSII), and finally the lower-energy broad-beam ion sources commonly used for IBAD studies.

The earliest ion implanters evolved from the isotope separators of the 1940s and later. Ion implanters are frequently classed according to their ion current capabilities, ranging from low currents (i.e., microampères) to high currents (one to several milliampères). The specific design criteria have been mainly driven by the particular fluence (dose) and depth profile requirements for semiconductor device fabrication. The history of ion implanter evolution and development is in itself an interesting study of technology transfer. It is covered comprehensively in a series of Conference Proceedings (see the Suggested reading section) that parallel the developments in Si device technology that has demonstrated such explosive growth since the early 1970s (Rose, 1985). Although this area of accelerator application is not the focus of this book, many ion implanters in research and development usage today, for general materials science studies, are either converted semiconductor ion implanters or are based on their design. Therefore, the basic design and system features of these systems will be briefly treated.

Introduction

The previous chapters have used analytical approaches to ion–solid interactions: ion ranges and radiation damage. Here, we discuss the use of computer simulations to describe the slowing down and scattering of energetic ions in solids. Two different types of computer simulations will be examined: Monte Carlo (MC) and molecular dynamics (MD). The Monte Carlo method relies on a binary collision model, and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. Eckstein (1991) provides a review of computer simulation of ion–solid interactions.

The defects generated in ion–solid interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10−11 s), the remaining vacancy–interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach. Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom, and local kinetic processes can be described on the basis of a liquid-like diffusion formalism.

Monte Carlo simulations

The Monte Carlo methods, applied to ion–solid interactions, have a number of distinct advantages over analytical calculations based on transport theory. The MC approach allows for a more rigorous treatment of elastic scattering and of the determination of angular and energy distributions. As the name MC suggests, the results require averaging over many simulated particle trajectories.