Dynamics of crosshatch patterns in heteroepitaxy

Regular surface undulations, called cross-hatch patterns, appearing at the free surface of lattice-mismatched heteroepitaxial films are a key signature of plastic relaxation. Here we show that the dynamics of cross-hatch formation is accurately described by a continuum model based on strain-mediated surface diffusion, provided that a realistic distribution of dislocations is considered. We demonstrate quantitative agreement between our time-dependent simulations and dedicated atomic force microscopy experiments on ${\mathrm{Si}}_{0.92}{\mathrm{Ge}}_{0.08}$ films grown on Si(001) at various thicknesses, finally shedding light on the origin and on the dynamical behavior of a widely investigated pattern, first observed more than half a century ago.