We introduce an algorithm for treating growth on surfaces which combines
important features of continuum methods 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. 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.
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