Nanocrystal formation on patterned substrates during heteroepitaxy is studied. Deposition on a substrate with a mesa induces a qualitatively new morphological instability that is driven solely by capillarity. If the film possesses a lattice parameter misfit with the substrate, this instability then propagates as a traveling wave along the substrate. This traveling wave yields large regions of highly ordered nanocrystals. Strongly anisotropic surface energy greatly increases the growth rate of the instability of a planar film and, thus, decreases the distance over which the traveling wave propagates. Even in this case, however, deposition on a substrate with a periodic arrangement of mesas can yield highly ordered arrays of nanocrystals.

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