Quasicontinuum Monte Carlo: A method for surface growth simulations

We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods ~such as the level-set method! and kinetic Monte Carlo ~KMC! simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the dielectric breakdown model. Our method allows us to give a realistic account of fluctuations in island shape, which is lacking in deterministic continuum treatments and which is an important physical effect. Our method should be most important for problems close to equilibrium where KMC becomes impractically slow.