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Published online by Cambridge University Press: 21 February 2011
One of the generic scenarios in molecular beam epitaxy is the growth of large scale pyramid-like three-dimensional structures. These structures are a consequence of non-equilibrium surface diffusion currents that result from a transport of adatoms in the uphill direction in regions of the surfaces that are tilted away from a high symmetry orientation. The microscopic origin of these currents are, e.g., diffusion barriers at step edges that suppress the diffusion of adatoms to lower terraces. The temporal evolution of the resulting instabilities can be described by simple continuum equations that display slope-selection, pyramid-like structures, and coarsening. We show that similar scenarios can be found in microscopic models investigated by Monte-Carlo simulations. However, crossover phenomena can complicate the comparison of the asymptotic theory with computer simulations or experiments. We therefore discuss criteria that allow to distinguish experimentally between kinetic roughening with exponents ζ ≃ 1 and unstable pyramid-like growth.