Growth roughness and instabilities due to the Schwoebel effect : a one-dimensional model

A very simple, one-dimensional model ("Zeno model") of crystal growth by molecular beam epitaxy is studied numerically. The essentiel feature of the Zeno model is that it takes into account the asymetry of the sticking coefficient of adatoms to steps (Schwoebel effect), i.e., the diffusiog atoms stick preferably to the upper ledge. In contrast with other, more microscopie descriptions, the Zeno model takes the diffusion of adatoms into account through a deterministic diffusion equation, so that the computing time is greatly reduced and a systematic investigation of the effect of the different parameters is possible. Deep cracks form even for a weak Schwoebel effect, but they form after a time which is very long if the Schwoebel effect is very weak. In certain cases, the roughness increases proportionally to time, in agreement with experiments on silicon and with other calculations. In the absence of Schwoebel effect, surface defects are healed during growth.