Revisiting step instabilities on crystal surfaces. Part II: General theory

TL;DR

This paper develops a comprehensive stability analysis of crystal surface steps without relying on the quasistatic approximation, revealing a new dynamics effect that influences step stability and offers alternative explanations for experimental observations.

Contribution

It introduces a general stability framework accounting for convective and transient effects, challenging the classical quasistatic approximation in crystal surface growth analysis.

Findings

Identification of the 'dynamics effect' influencing step stability.

Validation that the dynamics effect remains significant in slow growth regimes.

Alternative explanation for step bunching phenomena on Si(111) and GaAs(001).

Abstract

The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on stability of different mechanisms and their interplay: elastic step-step interactions, the Schwoebel barrier, and the chemical coupling of the diffusion fields on adjacent terraces. In this second part, we present a stability analysis of the general problem without recourse to the quasistatic approximation. This analysis reveals the existence of a supplementary mechanism, which we label the "dynamics effect" as it follows from accounting for all the convective and transient terms in the governing equations. This effect can be stabilizing or destabilizing depending on the ratio of step attachment/detachment kinetics to terrace diffusion kinetics. Further, we find that this dynamics effect remains significant in the slow deposition/evaporation regime, thereby invalidating the classical postulate underlying the quasistatic approximation. Finally, revisiting experiments of crystal growth on Si(111)-7x7 and GaAs(001), our analysis provides an alternative explanation of the observed step bunching, one that does not require the mechanisms previously invoked in the literature.