Nonlinear amplitude evolution during spontaneous patterning of ion-bombarded Si(001)

The time evolution of the amplitude of periodic nanoscale ripple patterns formed on Ar+ sputtered Si(001) surfaces was examined using a recently developed in situ spectroscopic technique. At sufficiently long times, we find that the amplitude does not continue to grow exponentially as predicted by the standard Bradley–Harper sputter rippling model. In accounting for this discrepancy, we rule out effects related to the concentration of mobile species, high surface curvature, surface energy anisotropy, and ion-surface interactions. We observe that for all wavelengths the amplitude ceases to grow when the width of the topmost terrace of the ripples is reduced to approximately 25 nm. This observation suggests that a short circuit relaxation mechanism limits amplitude growth. A strategy for influencing the ultimate ripple amplitude is discussed.