GROWTH ROUGHNESS AND INSTABILITIES DUE TO THE SCHWOEBEL EFFECT - A ONE-DIMENSIONAL MODEL

A very simple, one-dimensional model (<< Zeno model >>) of crystal gro wth by molecular beam epitaxy is studied numerically. The essentiel fe ature 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 diffusing atoms stick preferably to the upper ledge. In contrast with other, more microscopic descriptions, the Zeno model takes the di ffusion of adatoms into account through a deterministic diffusion equa tion, so that the computing time is greatly reduced and a systematic i nvestigation of the effect of the different parameters is possible. De ep 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 cert ain cases. the roughness increases proportionally to time, in agreemen t with experiments on silicon and with other calculations. In the abse nce of Schwoebel effect, surface defects are healed during growth.