Instability, Intermittency and Multiscaling in Discrete Growth Models of Kinetic Roughening

TL;DR

This paper investigates the instability phenomena in discretized nonlinear growth models like KPZ and Lai-Das Sarma, showing how controlling these instabilities leads to intermittent multiscaling behavior similar to turbulent epitaxial growth.

Contribution

It reveals the presence of a generic instability in discretized growth models and demonstrates how to control it to observe multiscaling and intermittent phenomena.

Findings

Discretized models exhibit a generic instability leading to pillar or groove growth.

Controlling instability results in intermittent multiscaling behavior.

Simulated behavior resembles turbulence in epitaxial growth models.

Abstract

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such ``controlled instability'' models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the ``turbulent'' behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth. [pacs{61.50.Cj, 68.55.Bd, 05.70.Ln, 64.60.Ht}]