Breakdown of step-flow growth in unstable homoepitaxy

– Two mechanisms for the breakdown of step flow growth, in the sense of the appearance of steps of opposite sign to the original vicinality, are studied by kinetic Monte Carlo simulations and scaling arguments. The first mechanism is the nucleation of islands on the terraces, which leads to mound formation if interlayer transport is sufficiently inhibited. The second mechanism is the formation of vacancy islands due to the self-crossing of strongly meandering steps. The competing roles of the growth of the meander amplitude and the synchronization of the meander phase are emphasized. The distance between vacancy islands along the step direction appears to be proportional to the square of the meander wavelength. Introduction. – Growing surfaces are commonly divided into two classes, vicinal or singular [1–3]. On vicinal surfaces the density of atomic steps, originating from the miscut of the sample, is high, so that most of the atoms arriving on the surface attach to these steps and the nucleation of adatom islands on the terraces may be neglected. The crystal then grows in the step-flow mode, simply by propagation of the steps. As no new steps appear, all the steps have the same sign, and the surface profile remains monotonic in the direction of vicinality. Even if the step morphology is unstable against step meandering, the growth may be considered as a two-dimensional problem. It has been observed however in experiments [4,5] as well as in computer simulations [4,6,7] that the step-flow mode is only metastable. Eventually steps having a sign opposite to the original vicinality appear on the surface. This destroys the two dimensional character of the growth and leads to the formation of genuinely three-dimensional structures. Steps of opposite sign may originate from two different mechanisms: either from the nucleation of adatom islands on the terraces, or through the formation of vacancy islands. Island nucleation on the terraces is severely suppressed by the steps as they collect the deposited adatoms, keeping the adatom concentration low. Due to fluctuations, however, some nucleation events do occur. Nucleation of islands on the terraces alone is not enough to destabilize (∗) Present and permanent address.