Stability analysis of a viscoelastic model for ion-irradiated silicon

TL;DR

This paper models the stress in ion-irradiated silicon as a viscoelastic response, finds it stabilizes the surface at normal incidence, and suggests elasticity can be neglected in future analyses of surface evolution.

Contribution

It introduces a viscoelastic model for ion-induced stress in silicon and demonstrates its stabilizing effect, challenging previous assumptions about stress-driven pattern formation.

Findings

Steady compressive stress matches experimental data.

Stress at normal incidence is unconditionally stabilizing.

Elastic moduli are negligible in primary stress effects.

Abstract

To study the effect of stress within the thin amorphous film generated atop Si irradiated by Ar+, we model the film as a viscoelastic medium into which the ion beam continually injects biaxial compressive stress. We find that at normal incidence, the model predicts a steady compressive stress of a magnitude comparable to experiment. However, linear stability analysis at normal incidence reveals that this mechanism of stress generation is unconditionally stabilizing due to a purely kinematic material flow, depending on none of the material parameters. Thus, despite plausible conjectures in the literature as to its potential role in pattern formation, we conclude that beam stress at normal incidence is unlikely to be a source of instability at any energy, supporting recent theories attributing hexagonal ordered dots to the effects of composition. In addition, we find that the elastic moduli appear in neither the steady film stress nor the leading order smoothening, suggesting that the primary effects of stress can be captured even if elasticity is neglected. This should greatly simplify future analytical studies of highly nonplanar surface evolution, in which the beam-injected stress is considered to be an important effect.