Slope Selection and Coarsening in Molecular Beam Epitaxy

Abstract

We propose a simple Langevin equation that describes the growth of pyramidlike structures on a surface under conditions typical of molecular beam epitaxy. The slope of these pyramids is selected by the crystalline symmetries of the growing film. By analogy with the problem of domain growth of systems with a conserved order parameter we show that the dynamic exponent that controls the growth of the pyramids is $z\simeq 4$. There is no mechanism that limits the size of the growing structures. This implies that the roughness exponent is $\alpha =1\mathrm{}$, in agreement with recent experiments.