The growth of thin solid semiconductor films is at the heart of the development of modern electronic and optical devices. A key element in strategies for nanoscale fabrication is the exploitation of growth and kinetic instabilities to form surface nanostructures and patterns with desirable functionality.

Epitaxy is a term that is commonly used for the growth of a thin solid layer on top of a substrate. Homoepitaxy denotes the growth of crystals of a material on a crystal face of the same material, while the term heteroepitaxy is used if the materials of the substrate and the growing film are different. Molecular beam epitaxy (MBE) is a common experimental technique that is used to grow such solid films. A film that grows without defects is called a coherently grown film. In such a film the constituent atoms arrange themselves on top of the substrate as its natural extension. The film has the same crystal structure as the substrate.

In the epitaxial growth of a crystal film on another crystal, elasticity plays a dominant role and leads to long-range effective interactions between the adatoms on the surface. These interactions are repulsive and compete with the stronger shortrange chemical interactions. The repulsive nature of the long-range interactions can be qualitatively understood as follows. Consider a planar solid surface of a semiinfinite crystal. When an adatom is placed on this surface, its interaction with the atoms in the top layer creates a stress which changes the distance between its nearest neighbors in the top atomic layer of the surface.