Scattering from Surfaces

Abstract

As in many branches of modern physics, scattering experiments are an important source of information in surface research. The scattering process on a surface is therefore a central topic among the various interactions of a solid. Like in bulk solid-state physics, elastic scattering can tell us something about the symmetry and the geometric arrangement of atoms near the surface, whereas inelastic scattering processes, where energy quanta are transferred to or from the topmost atomic layers of a solid, yield information about possible excitations of a surface or interface, both electronic and vibronic ones. In principle, all kinds of particles, X rays, electrons, atoms, molecules, ions, neutrons, etc. can be used as probes. The only prerequisite in surface and interface physics is the required surface sensitivity. The geometry and possible excitations of about 10¹⁵ surface atoms per cm² must be studied against the background of about 10²³ atoms present in a bulk volume of one cm³. In surface and interface physics the appropriate geometry for a scattering experiment is thus the reflection geometry. Furthermore, only particles that do not penetrate too deeply into the solid can be used. Neutron scattering, although it is applied in some studies, is not a very convenient technique because of the “weak” interaction with solid material. The same is true to some extent for X-ray scattering. X rays generally penetrate the whole crystal and the information carried by them about surface atoms is negligible. If used in surface analysis, X-ray scattering requires a special geometry and experimental arrangement. In this sense ideal probes for the surface are atoms, ions, molecules and low energy electrons [4.1]. Atoms and molecules with low energy interact only with the outermost atoms of a solid, and low-energy electrons generally penetrate only a few Ångstroms into the material. The mean-free path in the solid is, of course, dependent on the energy of the electrons, as may be inferred from Fig.4.1. In particular, for low-energy electrons, the “strong” interaction with matter — i.e. with the valence electrons of the solid — leads to considerable problems in the theoretical description; in contrast to X-ray and neutron scattering multiple-scattering events must be taken into account, and thus the simple analogy to an optical diffraction experiment breaks down. In quantum mechanical language, the Born approximation is not sufficient. The detailed treatment using the so-called dynamic theory (Sect.4.4) takes into account all these effects by considering the boundary problem of matching all possible electron waves outside and inside the solid in the correct way.