Hiroo Omi | Searcharxiv

arXiv2009

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

We study further the recently introduced [Ranguelov et al., Comptes Rendus de l'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystal growth over wide range of model parameters. 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. We obtain the condition for linear stability of the whole step train in the form CL/CR>1 (L/R stands for left/right in a descending from left to right step train). Further we integrate numerically the equations of step motion to monitor the bunching process 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 in a broad range of parameters the morphology is characterized with appearance of the minimal interstep distance in the bunch in the beginning of the bunches (at the trailing edge of the bunch) and may be described by a single universality class, different from those already generated by continuum theories [Krug et al., PRB 71, 045412].

cond-mat.stat-mech↗

arXiv2007

New universality class for step bunching in the "C+ - C-" model

We formulate a new (1+1)D step model of potentially unstable vicinal growth that we call "C+ - C-" model and study the step bunching process in it. The basic assumption is that the equilibrium adatom concentrations on both sides of the step are different and this may cause destabilization of the regular step train. We deduce equations of step motion and numerically integrate them to obtain the step positions on a discrete time set. New dynamic phenomena are observed during the bunching process: 1. parts of the crystal surface undergo temporary evaporation in the course of coalescence of two bunches, the larger being the one that "goes back", 2. the minimal interstep distance appears in the beginning rather than in the middle of the bunch. We speculate that the latter may serve as a diagnostic criterion for a new universality class constructed from the time- and size-scaling exponents describing the bunching process in the diffusion-limited regime.

physics.chem-ph↗