Nucleation and growth of islands in epitaxy is simulated using a continuum phase-field model. In addition to local density of adatoms, a local phase-field variable, varying in the real space, is introduced to describe the epitaxial islands. Evolution of this phase field is determined by a time-dependent Ginzburg-Landau-like equation coupled to a diffusive transport equation of adatoms. When applied to nucleation and growth of islands in the submonolayer regime, this model reproduces both the scaling laws of island density and experimental size and spatial distributions of islands. For island growth in the multilayer regime, this phase-field model reproduces mound structures consistent with experimental images concerned. Accurate coarsening and roughening exponents of the mounds are obtained in this model. Compared with atomic models and mean-field models, this model can provide a fine visualized morphology of islands at large space and time scales of practical engineering interests.
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