The steering of positively charged energetic particles between atomic rows or planes of a crystalline solid. The particles can be positive ions, protons, positrons, or muons. If the angle between the direction of the particle and a particular axis or plane in the crystal is within a small predictable limit (typically a few degrees or less), then the gradually changing electrostatic repulsion between the particle and each successive atomic nucleus of the crystal produces a smooth steering through the crystal lattice (Fig. 1). Thus, the trajectory of the channeled particle is restricted to the open spaces between atomic rows and planes of a crystal (Fig. 2). See also: Crystal structure
An obvious consequence of this steered motion is that it prevents violent collisions of the particles with atoms on the lattice sites. Hence, as compared with a randomly directed beam of particles, the channeled beam loses energy more slowly, penetrates more deeply, creates much less damage to the crystal along its track, and is prevented from participating in all close-encounter processes (nuclear reactions, Rutherford scattering, and so forth) with lattice atoms. See also: Nuclear reaction; Scattering experiments (nuclei)
A related channeling phenomenon is the channeling of energetic electrons or other negative particles. In this case, the particles are attracted to the positively charged atomic nuclei, so that the probability of violent collisions with atoms on lattice sites is enhanced rather than being prevented, and the particles are steered along the rows or planes of nuclei rather than between them.
A closely related phenomenon is called blocking. In this case, the energetic positive particles originate from atomic sites within the crystal lattice by means of fission, alpha-particle decay, or by wide-angle scattering of a nonchanneled external beam in a very close encounter with a lattice atom. Those particles emitted almost parallel to an atomic row or plane will be deflected away from the row by a steering process similar to that shown in Fig. 1. Consequently, no particles emerge from the crystal within a certain critical blocking angle of each major crystallographic direction. A piece of film placed some distance from the crystal provides a simple technique for recording blocking patterns (Fig. 3). Theoretical considerations show that the same principle is involved in blocking as in channeling; hence, both phenomena exhibit an identical dependence on particle energy, nuclear charge, lattice spacing, and so forth. See also: Nuclear fission; Radioactivity
Channeling effects were predicted by J. Stark in 1912. However, despite the evident simplicity of the channeling phenomenon, firm experimental evidence for its existence was not recognized until the early 1960s, when it was observed that energetic heavy ions sometimes penetrated to unexpectedly large depths in polycrystalline aluminum and tungsten. In 1962, it was shown by computer simulation that these deep penetrations were probably due to particles being channeled along the open directions in some correctly oriented microcrystals. Single-crystal experiments in several laboratories subsequently confirmed that such channeling was indeed an extremely general phenomenon, occurring for all charged nuclear particles (atomic nuclei, positrons, muons, and so forth) over an energy range from a few electronvolts up to hundreds of gigaelectronvolts. At about the same time, a comprehensive theoretical framework for predicting the behavior of channeled trajectories was developed, which led not only to an understanding of the channeling phenomenon but also to its widespread application in many other fields.
Applications of channeling include the location of foreign atoms in a crystal, the study of crystal surface structure, and the measurement of nuclear lifetimes.
Location of foreign atoms
The location of foreign (solute) atoms in a crystal is one of the simplest channeling applications. It is accomplished by measuring the yields of Rutherford back-scattered particles, characteristic x-rays, or nuclear reaction products produced by the interaction of channeled particles with the solute atoms. Such yields are enhanced for solute atoms that are displaced into channels of the crystal. Thus the solute atom sites can be identified by a triangulation technique, illustrated in Fig. 4 for a two-dimensional model of a cubic lattice. Numbers in angle brackets 〈 &x3009 x232A; identify the different kinds of crystal axes, whereas numbers in square brackets identify specific directions within a given kind. The shaded areas are shadowed by rows of host atoms (^) in the  and  channels. As shown by the table in Fig. 4, three possible sites for a foreign atom (•, x, and □) are readily distinguished by comparing the channeling behavior along the 〈10&x3009 x232A;- and 〈11&x3009 x232A;-type directions. Channeled ions do not have close-encounter interactions with solute atoms in substitutional positions (•), since these are completely shadowed by atomic rows in both 〈10&x3009 x232A;- and 〈11&x3009 x232A;-type channels. The x interstitial positions (halfway along the sides of the until cells) are 50% shadowed in both the  and  channels, but lie in the center of the  and [1 ] channels. The □ interstitial positions (in the center of the square unit cell) are completely shadowed in both 〈11&x3009 x232A;-type channels, but lie in the center of 〈10&x3009 x232A;-type channels. See also: Crystal defects
This method has been used to determine the lattice positions of solute atoms that have been introduced into crystals by a variety of means (for example, by melting, diffusion, or ion implantation). For example, channeling measurements show that furnace or laser heating of silicon that has been implanted with energetic boron, arsenic, or other electrically active atoms causes these atoms to move onto normal (substitutional) lattice sites, sometimes to concentrations far in excess of solubility limits. These measurements also are used to determine the amount of lattice damage (created by the ion implantation) which remains after the heating. These and similar applications have proved extremely useful in the development of semiconductor devices. See also: Ion implantation; Laser-solid interactions
When energetic particles strike a crystal, atoms can be ejected from normal lattice sites, leaving vacant lattice sites (vacancies). Solute atoms can trap these vacancies, creating unique geometric configurations, such as the tetravacancy–solute-atom complex (Fig. 5). In this complex, the solute atom (for example, a tin atom in aluminum) becomes displaced from a normal lattice site into the tetrahedral interstitial site, surrounded by four lattice vacancies at equal distance. Such a solute atom lies in the center of 〈100&x3009 x232A; channels, is halfway to the center of 〈110&x3009 x232A; channels, and is completely shadowed in 〈111&x3009 x232A; channels. Thus, its position is easily identified by channeling measurements along these three axial channels. These vacancy–solute-atom complexes are very stable thermally, and probably form nucleation centers for the creation of even larger vacancy clusters (voids) in irradiated materials. See also: Radiation damage to materials
Study of surface structure
In a similar way, channeling techniques are used to study the structure of crystal surfaces. Because of the asymmetric forces between atoms on the surface of a crystal, the surface plane of atoms is often reconstructed (that is, it has a different atomic structure from that of the bulk); also, it may be relaxed inward or outward. In Fig. 6, a method for measuring an outward relaxation of the surface plane of atoms by the channeling technique is shown. A beam of ions directed perpendicular to the (111) surface (〈111&x3009 x232A; incidence) “sees” only one atom per row of atoms. However, because of the outward displacement of the surface atoms, a beam of ions incident along a nonperpendicular (for example, 〈110&x3009 x232A;) axis “sees” two atoms per row at high ion energies (at which each surface atom casts a small shadow cone), and one atom per row at low ion energies (giving a large shadow cone). Information on surface relaxations (Δd) as small as 2 × 10−12 m and also on the vibrational amplitudes of the surface plane of atoms can be obtained by such studies. See also: Lattice vibrations; Surface physics
In addition, premelting at surfaces can be investigated. Channeling studies of the surface of lead near the melting point have shown that a thin surface layer becomes molten at a lower temperature than that of the bulk material. Such studies will contribute to an understanding of melting, which remains one of the more poorly understood physical phenomena.
Measurement of nuclear lifetimes
A different type of application is the measurement of extremely short nuclear lifetimes. Nevertheless, the same basic principles of atom location are involved; namely, the ability, by means of channeling or blocking, to pinpoint accurately the location of a nucleus (relative to the crystal lattice) at the instant that it is struck by or emits an energetic positive particle. Suppose that a lattice nucleus under external beam bombardment captures a beam particle to form a compound nucleus, recoiling with known velocity from its lattice site, and that this nucleus subsequently decays by emitting an energetic positive particle (proton, alpha particle, fission fragment, and so forth). From the resulting blocking pattern of these emitted particles, the recoil distance before emission and hence the nuclear lifetime can be accurately determined. In this way, lifetimes as short as 10−18 s are directly observable.