de Gennes Narrowing-like Phenomenon and Nano-ripple Velocity Measurement in Self-Organized Ion-Beam Nanopatterning*

Real-time coherent Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) was utilized to investigate the kinetics and the fluctuation dynamics during ion beam nano-patterning. Initially flat silicon samples at room temperature were bombarded by a broad collimated beam of 1keV Ar⁺ or Kr⁺ ions at 65° polar angle, leading to the amorphization of the ion-irradiated surfaces and the spontaneous formation of nanoscale ripples. The temporal evolution of the average X-ray scattering intensity in GISAXS data shows the evolution of kinetics, whereas X-ray Photon Correlation Spectroscopy (XPCS) calculations help explain the fluctuation dynamics. The surface behavior at early times can be explained within a linear theory framework, but the behavior becomes highly non-linear since the intensity correlation function evolves into a compressed exponential decay on length scales corresponding to the peak ripple wavelength and a stretched exponential decay on other length scales. The correlation times for silicon nano-patterning are maximum at the ripple wavelengths while they are smaller at other wavelengths: a phenomenon that is reminiscent of the phenomenon of de Gennes narrowing observed in a wide range of soft materials. Overall, such dynamic behavior is found to be consistent with the simulations based on a nonlinear growth model. Following the formation of self-organized nano-ripples, they move across the surface. While homodyne XPCS is not sensitive to such nano-scale movements, because of the gradient of ion flux across the sample, we were able to measure the ripple velocity gradients by cross-correlating X-ray speckles and tracking their movements.