In writing a preface, an author is faced with the question: what is this book of mine? Of course, in the end only the reader will decide what it really is. The scope of this preface, as of all prefaces, is to say what it was intended to be.

This book tries to offer a reasonably complete description of the physical phenomena which make solid materials grow in a certain way, homogeneous or not, rough or smooth. These phenomena belong to chemistry, quantum physics, mechanics, statistical mechanics. However, chemistry, mechanics and quantum physics are essentially the same during growth as they are at equilibrium. The statistical aspects are quite different. For this reason, the authors have insisted on statistical mechanics.

Another reason to emphasize the statistical mechanical concepts is that they will probably survive. The concepts developed many years ago by Frank, or more recently by Kardar, Parisi and Zhang are still valid while, for instance, quantum mechanical calculations of the relevant energy parameters will certainly evolve a lot in the next few years. We have not considered it useful to devote too many pages to them, but we have tried to present the frame in which the data can be inserted, as soon as they are known.

However, although emphasis is on statistical mechanics, other aspects are not ignored, even though they may have been treated somewhat superficially. The reader will find more detailed information in an extensive bibliography, where all titles are given in extenso, thus making its use much easier.

This book is mainly devoted to growth, and therefore to non-equilibrium processes.

As long as possible we have postponed a general study of elasticity and its partial differential equations. Here they are!

The elastic equilibrium of a solid is generally treated in the continuum approximation. The strain satisfies certain equations in the bulk, and other equations at the surface. This set of equations has an infinite number of solutions, and the correct one is that which minimizes a given thermodynamic potential or free energy. This minimization is not needed for a semi-infinite solid because the good solution in this case is the one which vanishes at infinity.

The power of continuous elasticity theory is limited. In particular it is not appropriate to investigate the surface relaxation, i.e. the change in the atomic distance near the surface. Nevertheless, the continuum approximation allows for spectacular predictions, for instance the Asaro-Tiller-Grinfeld instability, which is one of the major obstacles to layer-by-layer heteroepitaxial growth.

Memento of elasticity in a bulk solid

In this section, the theory of linear elasticity in a homogeneous solid away from the surface will be recalled.

In order to write the condition for mechanical equilibrium, one has to consider the forces acting on a volume δV of the solid (Fig. 16.1). There may be an external force δfext, and there is a force produced by the part of the solid outside δV.

While the first chapter of this book dwelt on the confirmation of the fundamental ideas of the philosophers of the fifth century BC, this last chapter will be devoted to the twentieth century and to the transformation of our materialistic everyday life brought about by electronics.

The early developments employed electronic tubes which owed nothing to surface physics and crystal growth. Then came the transistor and the realm of silicon, of which huge, dislocation-free crystals can be grown from the melt. In this end of the twentieth century, electromagnetic waves play an increasingly important part. Their production and detection require more and more complex semiconducting materials, often grown by molecular beam epitaxy.

Introduction

The modernity of surface science lies for a large part in the fact that new experimental techniques now make surfaces accessible to investigation. But the present interest in surface physics is also much motivated by the technological importance of crystals grown with a well-controlled composition and a high degree of perfection, and this depends very much on the state of the crystal surface during growth.

The purpose of this chapter is to outline the technological importance of materials with a controlled purity and morphology.

We shall mainly discuss semiconductors. It is not very easy to find simple articles or books explaining semiconductor electronics to the ignorant, but the book by Parker (1994) accomplishes this function.