Irradiation of semiconductor surfaces often leads to the spontaneous formation of rippled structures at certain irradiation angles. However, at high enough energies, these structures are observed to vanish for all angles, despite the absence of any identified, universally-stabilizing physical mechanisms in operation. Here, we examine the effect on pattern formation of radiation-induced swelling, which has been excluded from prior treatments of stress in irradiated films. After developing a suitable continuum model, we perform a linear stability analysis to determine its effect on stability. Under appropriate simplifying assumptions, we find swelling indeed to be stabilizing at wavenumbers typical of experimental observations. We relax simplifications and perform a numerical linear stability analysis on the nonlinear model, where stability regimes result from our parameter sweeps. Therefore, this mechanism may account for the vanishing ripples observed at high energies.

Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is an experimental technique that can be used during ion bombardment to study nanostructures. However, in the nonlinear regime, the GISAXS profile no longer equals the structure factor and therefore cannot be directly compared to mathematical calculations. Here, we compare nonlinear regime experiments to nonlinear simulations and simulated GISAXS. After numerically simulating an appropriate PDE, we simulate GISAXS scattering across the simulated surfaces. We discover that the sawtooth and chevron structures found in experiments also appear in our simulated surfaces. Additionally, asymmetry and harmonic peaks observed in experimental GISAXS profiles are also visible in our simulated GISAXS. Therefore, this framework may establish a useful way of interpreting late-stage GISAXS data.

Degree Date

Spring 2018

Document Type


Degree Name





Scott A. Norris

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License