Unstable Growth and Coarsening in Molecular-Beam Epitaxy

The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich-Schwoebel step-edge barrier for adatom diffusion. Two mechanisms of coarsening are identified: (i) surface diffusion driven by an uneven distribution of bonding energies, and (ii) mound coalescence driven by random deposition. Semiquantitative estimates of the coarsening time are given in each case. When the surface slope saturates, an asymptotic dynamical exponent $z=4$ is obtained.