In heteroepitaxy, misfit stress leads to a well-known instability of planar films against “roughening.” In contrast, we find that growth of a strained-layer superlattice is dynamically stable under a range of growth conditions. Outside the stable range, the modulations of successive layers may be in phase, out of phase, or more complex, as summarized in a dynamical phase diagram. This remarkable behavior results from the collective influence of the buried interfaces, via their strain fields, on the evolution of the surface morphology.

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