Linear stability and instability patterns in ion-sputtered silicon

Abstract

We study the patterns formed on Ar+ ion-sputtered Si surfaces at room temperature as a function of the control parameters ion energy and incidence angle. We observe the sensitivity of pattern formation to artifacts such as surface contamination and report the procedures we developed to control them. We identify regions in control parameter space where holes, parallel mode ripples and perpendicular mode ripples form, and identify a region where the flat surface is stable. In the vicinity of the boundaries between the stable and pattern-forming regions, called bifurcations, we follow the time dependence from exponential amplification to saturation and examine the amplification rate and the wavelength in the exponential amplification regime. The resulting power laws are consistent with the theory of nonequilibrium pattern formation for a type I (constant wavelength) bifurcation at low angles and for a type II (diverging wavelength) bifurcation at high angles. We discuss the failure of all sputter rippling models to adequately describe these aspects of the simplest experimental system studied, consisting of an elemental, isotropic amorphous surface in the simplest evolution regime of linear stability.

Molecular dynamics of single-particle impacts predicts phase diagrams for large scale pattern formation

“…Despite these limitations of our approach, when one considers the lack of any free parameters in the theory, the agreement with experiment is remarkably good. The agreement remains good even when the erosive coefficients are omitted, and the similar shapes of the redistributive moments at 100 and 250 eV is consistent with the reported 23 energy insensitivity of the stability/instability phase boundary.…”

“…To corroborate this finding, we calculate in Figure 2 the coefficients (5) of the linearized equation (4) for the 250 eV moments, and compare the pattern wavelengths they predict to experimental observations in the same environmental conditions 23 . (Note: Clean linear experimental data at 100 eV are not currently available.…”

“…Also, the ripples originally reported in ref. 23 at 250 eV for angles below 20° have been omitted because those authors have recently shown them to be an experimental artefact.) The agreement is excellent, with two minor exceptions.…”

Surface instability and pattern formation by ion-induced erosion and mass redistribution

“…It is, therefore, suited to compare my calculations using Monte Carlo simulations with the carter function analysis based on MD simulations. Experimentally, parallel ripple patterns with wavelength decreasing from about 50-20 nm were observed in the angular regime 50°-75° [46]. Perpendicular mode ripples with short wavelength around 25 nm were observed at an ion incidence angle of 85°.…”

“…This ion-target combination was studied experimentally by [46] and also investigated using MD simulations and crater function analyses [22]. It is, therefore, suited to compare my calculations using Monte Carlo simulations with the carter function analysis based on MD simulations.…”