Ordering At Surfaces From Elastic And Electrostatic Interactions

Elastic and electrostatic interactions can sometimes have a profound influence on surface morphology. Here, we review the conditions under which surface stress or surface dipole variations can give rise to spontaneous domain formation at surfaces, and focus especially on the case of the Si(100) surface. In principle, the anisotropy of the surface stress should cause the spontaneous formation of a striped domain structure on Si(100). In practice, the length scale for this domain structure turns out to be so large as to prevent its direct observation, although the influence of the elastic interactions has been observed indirectly in a variety of related experiments. It is now evident that by introducing Ge or B atoms, the conditions can be tuned in such a way that the spontaneous domain formation is strikingly observed. Because surface electrostatic dipolar interactions scale in the same way as elastic ones, it follows that similar effects can arise from these sources. We consider a simple model two-phase surface system with1/r3dipolar interactions, and find that the model exhibits spontaneous formation of two kinds of periodic domain structure. A striped domain structure is stable near half-filling, but as the area fraction is changed, a transition to a hexagonal lattice of almost-circular droplets occurs. The relation of this model to experimental surface systems, especially that of Langmuir layers at the water–air interface, will be discussed.