Date of Award

Fall 2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Nuclear Engineering

First Advisor

Anter El-Azab

Committee Chair

Anter El- Azab

Committee Member 1

Jean Paul Allain

Committee Member 2

Gennady Miloshevsky

Committee Member 3

Vikas Tomar


Various self-organized patterns including ripples and quantum dots can be induced by ion beam sputtering (IBS). For the past decades, the understanding of such phenomenon has been mainly relied on the Bradley-Harper theory that attributes the formation of self-organized patterns to the interplay between roughening by curvature dependence of erosion and smoothening by surface diffusion. Recently, the development of the crater function theory has overturned this erosion-based paradigm to a redistribution-based paradigm. The theory has proved that erosion is irrelevant and negligible in the pattern formation at low and intermediate incidence angles. Despite the success, there are still some questions open to discuss. The role of erosion for the ripple formation at glancing angles is still unclear. Furthermore, the current application of the crater function theory is limited in the linear regime. The applicability in the nonlinear regime is unknown. In this work, a hybrid MD/kMC (Molecular Dynamics/kinetic Monte Carlo) multiscale atomistic model is developed to elucidate these unknown issues. This model uses the crater functions, which are obtained by MD simulations, to model the prompt mass redistribution due to single-ion impacts. Defect migration, which is missing in previous models using crater functions, is treated by a kMC Arrhenius model. Using this model, a systematic study was performed for silicon bombarded by Ar+ions of various energies (100 eV, 250 eV, 500 eV, 700 eV and 1000 eV) at incidence angles of 0° to 80° with fluence up to 1018 ions/cm2 to cover both the linear and nonlinear regimes. The simulation results are in very good agreement with the experimental findings and the moment-description continuum theory in many features of surface evolution, namely, the phase diagram, wavelength dependence of ion energy and incidence angle, and the nonlinear evolution of surface roughness. The simulations elucidate that erosion plays the dominant role in the pattern formation at glancing angles. In the nonlinear regimes, the ripples first undergo coarsening and then reach saturation state. The surface roughness obeys the scaling theory and yields the growth exponent β=0.358, which is very close to the experimental finding. Ion irradiation with simultaneous sample rotation is also simulated, resulting in the formation of arrays of squared ordered dots. The patterns with sample rotation are found to be strongly correlated to the rotation speed and the pattern types formed without sample rotation.