Swelling as a stabilizing mechanism in irradiated thin films: II. Effect of swelling rate

It has long been observed experimentally that energetic ion-beam irradiation of semiconductor surfaces may lead to spontaneous nanopattern formation. For most ion/target/energy combinations, the patterns appear when the angle of incidence exceeds a critical angle, and the models commonly employed to understand this phenomenon exhibit the same behavioral transition. However, under certain conditions, patterns do not appear for any angle of incidence, suggesting an important mismatch between experiment and theory. Previous work by our group (Swenson and Norris 2018J. Phys.: Condens. Matter30304003) proposed a model incorporating radiation-induced swelling, which is known to occur experimentally, and found that in the analytically-tractable limit of small swelling rates, this effect is stabilizing at all angles of incidence, which may explain the observed suppression of ripples. However, at that time, it was not clear how the proposed model would scale with increased swelling rate. In the present work, we generalize that analysis to the case of arbitrary swelling rates. Using a numerical approach, we find that the stabilization effect persists for arbitrarily large swelling rates, and maintains a stability profile largely similar to that of the small swelling case. Our findings strongly support the inclusion of a swelling mechanism in models of pattern formation under ion beam irradiation, and suggest that the simpler small-swelling limit is an adequate approximation for the full mechanism. They also highlight the need for more-and more detailed-experimental measurements of material stresses during pattern formation.