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 parameters 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 stabilty.