Hybrid Models of Step Bunching

TL;DR

This paper introduces hybrid models of step bunching on crystal surfaces, combining features of two primary models, and analyzes their complex behaviors and scaling properties in step dynamics.

Contribution

The paper develops and analyzes two novel hybrid models of step bunching, revealing unique surface slope distributions and scaling behaviors not seen in the primary models.

Findings

LW2MM model preserves minimal step-step distance feature

LW2MM exhibits a time-scaling exponent of ~1/3 for N

MM2LW shows step bunch growth and decay dynamics

Abstract

We introduce two hybrid models of step bunching on vicinal crystal surfaces. The model equations for step velocity are constructed by the two possible exchanges of terms between the equations of two primary models MM2 and LW2 [arXiv:1011.1863], both showing the specific type of bunching with minimal step-step distance lmin in the bunch independent of the number of steps N in it. This feature is preserved only in the hybrid model LW2MM (the first term in the model equation comes from LW2 and the second one - from MM2) but in a rather complex fashion -- the surface slope is largest in the both ends of the bunch and after a sharp decrease jumps again to become constant in the inner part. We restrict our considerations to the simplest case of p = 0, p being the exponent in the destabilizing term in the velocity equations. The time-scaling exponent of N in LW2MM is ~1/3 and is independent of n, the exponent in the stabilizing term of the velocity equations. The other model, MM2LW, shows an interesting type of step bunching -- some bunches grow to a certain size and then decay emitting steps towards the two adjacent bunches. The bunch compression with the increase of N is pronounced.