The present volume is a graduate-level introduction to the physics of solid surfaces. It is designed for students of physics, physical chemistry and materials science who are comfortable with modern condensed matter science at the level of, say, Solid State Physics by Ashcroft & Mermin (1976) or Principles of the Theory of Solids by Ziman (1972). In the latter, Ziman points out that scientific knowledge passes from the laboratory to the classroom by a sequence of literary vehicles: original research papers, review articles, monographs and finally textbooks. I believe this book fits well into none of these categories. It is not a textbook – at least not in the traditional sense. The field of surface physics is simply not mature enough to support such an enterprise; too many results are untidy and too many loose ends remain. On the other hand, it is not a review or monograph either. My purpose is neither to set down an established wisdom nor to establish priority among claimants. Indeed, I steadfastly ignore who did what when – except when it is a matter of historical interest.

Physical phenomena explicitly associated with condensed matter surfaces have been studied since antiquity. Perhaps the oldest written record of experience in this area appears in Babylonian cuneiform dating from the time of Hammurabi (Tabor, 1980). A form of divination, known today as lecanomancy, involved an examination of the properties of oil poured into a bowl of water. The detailed behavior of the spreading oil film led the diviner, or baru, to prophesy the outcome of military campaigns and the course of illness.

In later years, many observers commented on the fact that choppy waves can be calmed by pouring oil into the sea. In particular, Pliny's account was known to Benjamin Franklin when he began his controlled experiments during one of his frequent visits to England. Franklin's apparatus consisted of a bamboo cane with a hollow upper joint for storage of the oil.

Introduction

The study of phase transitions plays a central role in modern condensed matter physics. Changes of phase often are very dramatic events and certainly one wants a good understanding of such transformations. However, the stature of this field derives mostly from the recognition that the fundamental concepts, language and methodology developed to attack the phase transition problem have far-reaching utility in other areas of physics. In this chapter, we take advantage of the successes in this branch of statistical physics as a part of a two-pronged program. On the one hand, we apply the phenomenological methods of the modern theory (which focus on notions such as symmetry and order) to highlight those aspects of surface phase transitions that do not depend on the details of the system. On the other hand, a few specific examples are examined in more depth to illustrate that an appreciation of these details can significantly deepen our understanding of surface processes. We begin with a brief review.

Phase transitions occur because all systems in thermodynamic equilibrium seek to minimize their free energy, F = U − TS. One phase will supplant another at a given temperature because different states (e.g., liquid/vapor, magnetic/non-magnetic, cubic/tetragonal) partition their free energy between the internal energy U(T) and the entropy S(T) in different ways. It is useful to characterize competing phases in terms of a so-called order parameter.

Introduction

Our account of adsorption to this point has been restricted largely to one particular, albeit important, special case: the situation where adsorbate–substrate interactions dominate adsorbate–adsorbate interactions. This is sufficient for discussion of the vast majority of interesting chemical processes that occur at surfaces. Important inter-adsorbate forces surely come into play – there would be no surface reactions otherwise – but what counts the most is just the fact that the species do in fact find themselves on a surface. This is what we mean by heterogeneous catalysis.

The rules of the game change somewhat when we consider the other major driving force for research into our subject: the microelectronics industry. Here, surface physics per se is not so crucial as the closely related field of interface physics. The interfaces in question typically involve the junction of two micron-sized wafers of metal, semiconductor, ceramic, etc. Since these junctions break translational invariance, it is unsurprising that certain ideas (such as interface localized electronic and vibrational states) reappear almost unchanged. But a great many new features enter which would carry us far outside the intended scope of this book. Luckily, there is one aspect of the problem which does fall within our purview: the concept of epitaxy and epitaxial growth.

Introduction

This chapter begins our exploration of the physics of dynamical processes at solid surfaces – adsorption, diffusion, reaction and desorption. To do so, we must leave the ground state problem and concentrate on the excited states of adsorbed atoms and molecules. One way to proceed focuses on the excitation spectrum. As we know, this spectrum comes in two parts: single particle excitations and collective excitations. Our earlier discussion for clean surfaces (Chapter 5) dwelt primarily with the latter and it is possible to duplicate that effort here. For example, Fig. 13.1 illustrates the calculated and measured (by EELS) dispersion of two types of collective excitations for two vastly different adsorbate/substrate combinations. The left panel pertains to vibrations localized in an oxygen adlayer on Ni(100), i.e. overlayer phonons. Theory and experiment are in good accord for this system. Both exhibit three dispersive branches. The low frequency acoustic excitation is the (oxygen-modified) Rayleigh mode of the nickel substrate.

A metallized adsorbate layer can support collective excitations of its charge density in addition to the more familiar phonon modes. The right panel of Fig. 13.1 compares theory and experiment for the dispersion of two-dimensional plasmons in an ordered potassium overlayer adsorbed on a dimerized Si(100)2 × 1 surface.

Introduction

The phenomenon of condensation is one of the most familiar properties of bulk matter and so has attracted the attention of physicists for decades. The basic questions are straightforward to pose but remarkably difficult to answer. In fact, a conceptual revolution was required before truly rapid progress was achieved (Wilson, 1979). As we have indicated earlier (Chapter 5), dimensionality plays a crucial role in this modern theory of phase transitions (Ma, 1976). It then is natural to ask how much (if any) of our common three-dimensional experience and intuition carry over to the two-dimensional problem. Typical questions might be: What is the nature of the adsorbate phase diagram? How does a surface species pass from an ordered crystallographic state to a disordered state? What microscopic mechanisms are involved? How does an overlayer freeze and/or melt? Are any properties unique to two dimensions?

From the thermodynamic point of view, we have learned that clean surface critical phenomena and melting do indeed both differ from their three-dimensional bulk counterparts. We further quantify this notion here and examine the universality hypothesis, which states that only symmetry considerations and (in some cases) the range of adsorbate interactions determine the intrinsic nature of overlayer phase changes on a Langmuir checkerboard. Both static and dynamic issues will receive attention.

Introduction

The interaction of light with the first few atomic layers of a solid is relevant to (at least) two rather different aspects of surface physics. First, the strength of the experimental signal for many of the spectroscopic tools at our disposal such as photoemission, electron scattering, Raman scattering, etc., depends crucially on the intensity of the electric and magnetic fields near the surface. One typically calculates these field amplitudes by use of the classical Fresnel formulae. It is important to inquire whether this approach is sufficient if one is interested in phenomena within an Ångström or two of the crystal surface. These considerations alone suggest that a thorough understanding of the nature of near-surface electromagnetic fields is of both practical and fundamental interest. A rather different motivation to study these fields comes from the realization that very long wavelength elementary excitations of the surface will couple directly to the ambient field. To account for this, we must generalize the results of the previous chapter beyond the static limit to include the finite propagation velocity of light. These excitations, known as surface polaritons, are coupled modes of the surface + electromagnetic field system. It is convenient to use the language of optics to discuss surface polaritons, although, in principle, no external driving field is needed to excite them.

Fundamentals

The weakest form of adsorption to a solid surface is called physical adsorption, or physisorption. It is characterized by the lack of a true chemical bond between adsorbate and substrate. If this is true, some other attractive force must exist that binds a gas phase species to a solid. One possibility that suggests itself is the ubiquitous van der Waals interaction. To see its origin, consider a closed shell atom that sits a distance, z, above a solid surface. We restrict our attention to distances z ≪ c/ωp (~ 1000 Å) so that the finite propagation velocity of light can be ignored. Even at these distances, a mutual attraction between the atom and the surface exists that arises from the interaction of the polarizable solid with dipolar quantum mechanical fluctuations of the atomic charge distribution. Put another way, the atomic electrons are attracted to their images in the solid.

A one-dimensional harmonic oscillator model of the hydrogen atom is sufficient to capture the essential physics of the van der Waals, or dispersion, force between an atom and a solid. Let the oscillator coordinate, r, represent the projection of the electron's orbital motion along the normal to the surface. Consider first the image system appropriate to a perfectly conducting substrate (Fig. 8.1).

Introduction

In this chapter we investigate the electronic properties of clean solid surfaces. Certainly this is a prerequisite to any fundamental understanding of the electrical behavior of surfaces and interfaces. However, it also is essential to a coherent view of other surface phenomena, viz., oxidation, heterogeneous catalysis, crystal growth, brittle fracture, etc. There is no question that applications such as these provide most of the impetus behind surface science research. Nevertheless, we restrict ourselves here to only the most basic physics questions. What is the charge density in the neighborhood of the vacuum interface? Are the electron states near the surface different from those in the bulk? How do chemical bonding states in the first few atomic planes rearrange themselves after cleavage? What is the electrostatic potential felt by surface atoms?

The principal experimental probe of these issues is photoelectron spectroscopy and we will have much to say about this technique below. It turns out that the relevant measurements are relatively easy to perform but that the interpretation of the data is not entirely straightforward. It is helpful to have some idea of what to expect. Therefore, we defer our account of the experimental situation and proceed with some rather general theoretical considerations.

The methods of surface electronic structure are the same as those used to analyze the corresponding bulk problem.