Interfacial phase-change and geometry modify nanoscale pattern formation in irradiated thin films

When a Group IV semiconductor wafer is irradiated, it may amorphize. Beyond a certain angle of irradiation, the so-called critical angle, spontaneous pattern formation on the amorphized surface is often observed, but differences in the formed patterns, their angle-dependence (especially critical angle for pattern formation), and other behavior across various ion, target and energy combinations currently lacks a comprehensive explanation. To address this, we consider the hydrodynamic stability of ion-irradiated thin films, modeled as a modified Stokes flow, where the typically-used no-penetration boundary condition has been relaxed to a phase-change or mass conservation boundary condition. Then, we determine simple closed-form expressions for the geometry of the amorphous–crystalline interface entirely in terms of the free interface and the statistics of the implantation-induced collision cascade, an improvement on frequently-used ad hoc approximations. We find that phase-change at the amorphous–crystalline boundary, and the geometry of that boundary, impart a surprisingly strong ion-, target-, and energy- dependence. For validation of our theoretical work, we consider argon-irradiated silicon, where the presence of phase-change at the amorphous–crystalline interface appears to correctly predict the experimentally observed, strong suppression of pattern formation near 1.5 keV for that system.