Scaling and universality in models of step bunching: the “C+–C-” model

Abstract

We recently introduced a novel model of step flow crystal growth -the so-called "" model [B. Ranguelov et al., CR Acad. Bul. Sci. 60, 389 (2007)]. In this paper we aim to develop a complete picture of the model's behaviour in the framework of the notion of universality classes. The basic assumption of the model is that the reference ("equilibrium") densities used to compute the supersaturation might be different on either side of a step, so R L C C / region where the above scaling exists cannot be assigned to a specific universality class and thus should be considered non-universal. I. IntroductionMonatomic steps on crystal surfaces appear when the crystal is cut along a plane that is not parallel to the atomic planes. These steps are the subject of longstanding interest both from a technological and a fundamental point of view. So-called step flow growth, in which the crystal grows via attachment of atoms to the existing network of steps and not through nucleation of islands on the terraces between the steps -is the growth mode of technological importance. This is also the reason for intensive theoretical work involving playing with steps and their movement. One independent direction is the study of unstable step flow growth leading to two general instabilities -step bunching, when the initial equidistant step spacing is lost and steps group to form bunches, and step meandering, when the initially straight steps bend to form meanders similar to those formed by rivers in nature. The interest in introducing novel models of surface instabilities has recently been stimulated further by experiments on step flow growth of Cu-[1,2] and Si-vicinals [3] in which simultaneous step bunching and step meandering was observed. This phenomenon is quite unexpected and contradicts the contemporary paradigm of surface instabilities. The reason is that according to the present concepts, the normal Schwoebel effect in growth, i.e. adatoms attach to the steps preferentially from the lower terrace, results in step meandering, while the inverse Schwoebel effect, in which adatoms attach to the steps preferentially from the higher terraces, results in step bunching. In principal, besides the destabilization from various sources, all of the models of step bunching instability contain also a stabilizing factor due to the step-step repulsion. Typically the destabilizing factors are the electromigration force acting on adatoms or the Ehrlich-Schwoebel effect. Step-step repulsions of different nature stabilize and promote the equidistant step distribution. In the models, the stepstep repulsion affects the equilibrium concentrations used to compute the supersaturation/undersaturation and thus, the step velocity in growth/sublimation. Here we present a new model in which a difference of the "equilibrium" adatom concentrations on both sides of the step is assumed. In this manner the destabilization and stabilization are "intrinsic" and a consequence of the same source -the step-step repulsion. In the new model the shape of the bunches formed as...

Step bunching and macrostep formation in 1D atomistic scale model of unstable vicinal crystal growth

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Experimental quantitative study into the effects of electromigration field moderation on step bunching instability development on Si(111)

“…Mean values of maximum slope y m were determined for 1 nm intervals of h (similar to the monitoring scheme MS-II in Ref. 30) 30 and y m (h) was plotted as shown in Fig. 3.…”

Simulation of the Growth Kinetics in Group IV Compound Semiconductors

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