Reflection high-energy electron diffraction is a Bragg case, in which the beams to be detected are those reflected from the bulk crystal surface. Owing to the strong interaction between the incident electron and the crystal atoms, multiple (or dynamical) scattering is very strong. Although the positions of RHEED beams can generally be predicted by kinematical scattering theory, quantitative analysis of RHEED patterns relies on dynamical calculations. In this chapter, we will first illustrate the quantum mechanical approach for electron diffraction. Then we will outline a few commonly used dynamical theories accompanied by some calculated results.

Based on the first-principles approach, we will consider the fundamental equation that governs the scattering of high-energy electrons in crystals. Before we show the mathematical description, it is important to consider the nature of the events that we are studying. The average distance between successive electrons that strike the crystal in a transmission electron microscope is about 0.2 mm (for 100 keV electrons) if the electron flux is on the order of 1012 s−1 This distance is much larger than the thickness (typically less than 0.5 μm) of the specimen, thus the interaction between any successive incident electrons is extremely weak. Therefore, the interaction between the incident beam and the crystal can be treated one electron at a time. In other words, electron diffraction theory is basically a single-electron scattering theory.

Strictly speaking, scattering of high-energy electrons obeys the Dirac equation. The Dirac equation contains not only the relativistic effects but also electron spin.

Electron energy-loss spectroscopy (EELS) has proven to be a powerful method for studying the electronic structure and performing microanalyses of materials in a transmission electron microscope (see for example, Egerton (1986)). In conjunction with imaging of thin films by TEM and STEM, EELS has permitted chemical analysis of small specimen regions with high spatial resolution. The analysis of energy-loss edges for inner-shell excitation has allowed the determination of valence states of atoms from the energy-loss near-edge structure (ELNES) and determination of the local environments of atoms from the extended energy-loss fine structure (EXELFS). The use of EELS in the glancing incidence, surface-reflection mode for bulk samples is an attractive topic since the penetration of the electron beam into the surface, in general, is just a few atomic layers. This is the technique of high-energy reflection electron energy-loss spectroscopy (REELS). The analysis of the composition and structure of thin surface layers can form an important adjunct to high-resolution surface imaging by REM, or in combination with scanning REM (SREM), microdiffraction and secondary electron (SE) imaging, which are possible with STEM instruments.

In this chapter and Chapter 11 we describe high-energy REELS experiments performed in a TEM or STEM with high spatial resolution. The basic theory of valence excitation will be given and its applications to RHEED are described.

EELS spectra of bulk crystal surfaces

When an electron passes through a thin metal foil, the most noticeable energy loss is due to the plasmon oscillations in the sea of conduction electrons.

Reflection high-energy electron diffraction (RHEED) is a powerful technique for in situ observation of thin film growth in molecular beam epitaxy (MBE). The technique is particularly useful for providing in situ real-time structure evolution during thin film growth, and it is becoming an indispensable technique for characterizing phase transformation in synthesizing new materials of technological importance. In this chapter, we will apply the kinematical diffraction theory introduced in Chapter 1 to describe the fundamental characteristics of RHEED and its applications in determining surface structures. RHEED oscillation and its applications for monitoring film growth are systematically described. This remarkable phenomenon allows layer-by-layer monitoring of thin film growth.

The geometry of RHEED

RHEED was first used for oxide film studies by Miyake (1937), and it has been widely applied to monitor thin film growth during MBE deposition (Ino, 1987). A review of the RHEED geometry and the associated reciprocal space analyses has been given by Mahan et al. (1990) and Dobson (1987). A summary of surface structure determination using RHEED has been given by Ino (1987). Recent studies by Locquet and Machler (1994) have shown the sensitivity of the entire RHEED pattern to the layer-by-layer growth of DyBa2Cu3O7−x high-Tc superconductor thin films.

Figure 2.1 shows the scattering geometry of RHEED, in which the incident electron beam strikes the sample surface at a grazing angle of 1–3°. The electron energy can be as low as a few kilo-electron-volts and as high as 1000 keV (in TEM only).

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.