Surfaces and Interfaces of Solid Materials

A solid interface is defined as a small number of atomic layers that separate two solids in intimate contact with one another, where the properties differ significantly from those of the bulk material it separates. A metal film de­posited on a semiconductor crystal, for example, is thus separated by the semiconductor-metal interface from the bulk of the semiconductor.

As is generally true in physics, in the field of surface and interface studies one wants to investigate model systems which are simple in the sense that they can be characterized mathematically by a few definite parameters that are determined from experiments. Only for such systems can one hope to find a theoretical description which allows one to predict new properties. The understanding of such simple model systems is a condition for a deeper insight into more complex and more realistic ones.

To begin with, it will be useful to give a brief definition of the terms morphology and structure. The term morphology is associated with a macroscopic property of solids. The word originates from the Greek μορφή, which means form or shape, and here it will be used to refer to the macroscopic form or shape of a surface or interface. Structure, on the other hand, is associated more with a microscopic, atomistic picture and will be used to denote the detailed geometrical arrangement of atoms and their relative positions in space.

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.

Classical bulk solid-state physics can, broadly speaking, be divided into two parts, one that relates mainly to the electronic properties and another in which the dynamics of the atoms as a whole or of the cores (nuclei and tightly bound core electrons) is treated. This distinction between lattice dynamics and electronic properties, which is followed by nearly every textbook on solid-state physics, is based on the vastly different masses of electrons and atomic nuclei. Displacements of atoms in a solid occur much more slowly than the movements of the electrons. When atoms are displaced from their equilibrium position, a new electron distribution with higher total energy results; but the electron system remains in its ground state, such that after the initial atomic geometry has been reestablished, the whole energy amount is transferred back to the lattice of the nuclei or cores. The electron system is not left in an excited state. The total electronic energy can therefore be considered as a potential for the movement of the nuclei. On the other hand, since the electronic movement is much faster than that of the nuclei, a first approximation for the dynamics of the electrons is based on the assumption of a static lattice with fixed nuclear positions determining the potential for the electrons. This approximation of separate, non-interacting electron dynamics and lattice (nuclear/core) dynamics is called the adiabatic approximation. It was introduced into solid-state and molecular physics by Born and Oppenheimer [5.1]. It is clear, however, that certain phenomena, such as the scattering of conduction electrons on lattice vibrations, are beyond this approximation.

Since the surface is the termination of a bulk crystal, surface atoms have fewer neighbors than bulk atoms; part of the chemical bonds which constitute the bulk-crystal structure are broken at the surface. These bonds have to be broken to create the surface and thus the formation of a surface costs energy (surface tension) (Sect.3.1). In comparison with the bulk properties, therefore, the electronic structure near to the surface is markedly different. Even an ideal surface with its atoms at bulk-like positions (called truncated bulk) displays new electronic levels and modified many-body effects due to the change in chemical bonding. Many macroscopic effects and phenomena on surfaces are related to this change in electronic structure, for example, the surface energy (tension), the adhesion forces, and the specific chemical reactivity of particular surfaces. A central topic in modern surface physics is therefore the development of a detailed understanding of the surface electronic structure. On the theoretical side, the general approach is similar to that for the bulk crystal: In essence the one-electron approximation is used and one tries to solve the Schrödinger equation for an electron near the surface. A variety of approximation methods may then be used to take into account many-body effects.

If one puts a positive point charge into a locally neutral electron plasma (electrons on the background of fixed positive cores), the electrons in the neighborhood will rearrange to compensate that additional charge; they will screen it, such that far away from the charge the electric field vanishes. The higher the electron density, the shorter the range over which electrons have to rearrange in order to establish an effective shielding. In metals with free-electron concentrations of about 10²² cm⁻³ the screening length is short, on the order of atomic distances. On the other hand, in semiconductors the free-carrier concentrations are usually much lower, on the order of 10¹⁷ cm⁻³ may be, and we thus expect much larger screening lengths, of the order of hundreds of Ångstroms. These spatial regions of redistributed screening charges are called space charge regions.

In comparison to the solid-vacuum interface, i.e. the clean, well-defined surface of a solid, other solid interfaces are of much more practical importance. The solid-liquid interface, for example, plays a major role in electrochemistry and biophysics. Studies of that particular interface have a long tradition in physical chemistry. A detailed treatment of solid-liquid interfaces is far beyond the scope of this text although certain general concepts, e.g. that of space-charge layers, are similar to those of the solid-vacuum and solid-solid interface.

In previous chapters we have considered two types of interfaces, the solid/vacuum and the solid/solid interfaces. This last chapter is devoted to problems of the solid/gas interface. Some of the questions related to this interface have already been touched on in connection with film growth and the deposition of atoms and molecules to yield a second solid phase and thus a new solid/solid interface. In the present chapter we consider the interaction between a solid surface and foreign atoms in a more fundamental way.