Scaling and Universality in Models of Step Bunching: The 'C+-C-' Model

摘要

We study further the recently introduced [Ranguelov et al., Comptes Rendus del'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystalgrowth over wide range of model parameters. The basic assumption of the modelis that the reference ("equilibrium") densities used to compute thesupersaturation might be different on either side of a step. We obtain thecondition for linear stability of the whole step train in the form CL/CR>1 (L/Rstands for left/right in a descending from left to right step train). Furtherwe integrate numerically the equations of step motion to monitor the bunchingprocess in the long times limit. Thus we obtain the exact size- and time-scaling of the step bunches including the numerical prefactors. We show that ina broad range of parameters the morphology is characterized with appearance ofthe minimal interstep distance in the bunch in the beginning of the bunches (atthe trailing edge of the bunch) and may be described by a single universalityclass, different from those already generated by continuum theories [Krug etal., PRB 71, 045412].