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Vicinal surface growth: bunching and meandering instabilities

The morphology of a growing crystal surface is studied in the case of an unstable two-dimensional step flow. Competition between bunching and meandering of steps leads to a variety of patterns characterized by their respective instability growth rates. The roughness exponent is shown to go from 1/2 to 1, between the pure bunching to the meandering regimes. Using numerical simulations, we observe that generically, a transition between the two regimes occurs. We find surface shapes and roughness time evolution in quantitative agreement with experiments.