  The effects of a surfactant on two-dimensional pattern formation in epitaxial
growth are explored theoretically using a simple model, in which an adatom
becomes immobile only after overcoming a large energy barrier as it exchanges
positions with a surfactant atom, and subsequent growth from such a seed is
further shielded. Within this model, a fractal-to-compact island shape
transition can be induced by either decreasing the growth temperature or
increasing the deposition flux. This and other intriguing findings are in
excellent qualitative agreement with recent experiments.
