New mechanism for impurity-induced step bunching

– Codeposition of impurities during the growth of a vicinal surface leads to an impurity concentration gradient on the terraces, which induces corresponding gradients in the mobility and the chemical potential of the adatoms. Here it is shown that the two types of gradients have opposing effects on the stability of the surface: Step bunching can be caused by impurities which either lower the adatom mobility, or increase the adatom chemical potential. In particular, impurities acting as random barriers (without affecting the adatom binding) cause step bunching, while for impurities acting as random traps the combination of the two effects reduces to a modification of the attachment boundary conditions at the steps. In this case attachment to descending steps, and thus step bunching, is favored if the impurities bind adatoms more weakly than the substrate. Introduction. Step bunching is a morphological instability of a vicinal crystal surface, in which a regular train of equally spaced steps separates into regions of high step density – the step bunches – and large flat terraces. The process can be driven energetically by an attractive step-step interaction, or by a variety of kinetic mechanisms, which all share the common feature of breaking the symmetry between the ascending (upper) and descending (lower) step bordering the vicinal terrace [1]. In growth or sublimation, the symmetry breaking is provided by the different kinetic rates for the attachment and detachment of adatoms [2] (or some other species required for growth [3]) at the upper and the lower step; step bunching occurs under growth if atoms attach preferentially to the descending step. For electromigration-induced step bunching, the asymmetry is introduced by the electric field, and the step train is unstable if the adatom motion is biased in the down-step direction [4]. It has been appreciated for a long time that in many cases step bunching must be attributed to the presence of impurities [5]. The traditional view is that impurities pin the steps [6]. Once a step is slowed down relative to its neighbors, more impurities accumulate in front of it and delay it even further, leading to a feedback mechanism which drives the instability [7]. A different kind of impurity-mediated step bunching was suggested in recent work on Si1−yCy layers grown on Si(100) by molecular beam epitaxy, in which C plays the role of a codeposited impurity [8]. The key observation is that different parts of the vicinal terrace have been exposed to the impurity flux for different durations. Therefore the impurity concentration is smallest on the freshly created part near the descending step, and largest near the ascending