**Kinetic Monte Carlo simulation of self-organized pattern formation
induced by ion beam sputtering using crater functions**

ZC Yang and MA Lively and JP Allain, PHYSICAL REVIEW B, 91, 075427 (2015).

DOI: 10.1103/PhysRevB.91.075427

The production of self-organized nanostructures by ion beam sputtering has been of keen interest to researchers for many decades. Despite numerous experimental and theoretical efforts to understand ion-induced nanostructures, there are still many basic questions open to discussion, such as the role of erosion or curvature-dependent sputtering. In this work, a hybrid MD/kMC (molecular dynamics/kinetic Monte Carlo) multiscale atomistic model is developed to investigate these knowledge gaps, and its predictive ability is validated across the experimental parameter space. This model uses crater functions, which were obtained from MD simulations, to model the prompt mass redistribution due to single-ion impacts. Defect migration, which is missing from previous models that use crater functions, is treated by a kMC Arrhenius method. 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 degrees to 80 degrees . The simulation results were compared with experimental findings, showing good agreement in many aspects of surface evolution, such as the phase diagram. The underestimation of the ripple wavelength by the simulations suggests that surface diffusion is not the main smoothening mechanism for ion- induced pattern formation. Furthermore, the simulated results were compared with moment-description continuum theory and found to give better results, as the simulation did not suffer from the same mathematical inconsistencies as the continuum model. The key finding was that redistributive effects are dominant in the formation of flat surfaces and parallel-mode ripples, but erosive effects are dominant at high angles when perpendicular-mode ripples are formed. Ion irradiation with simultaneous sample rotation was also simulated, resulting in arrays of square-ordered dots. The patterns obtained from sample rotation were strongly correlated to the rotation speed and to the pattern types formed without sample rotation, and a critical value of about 5 rpm was found between disordered ripples and square-ordered dots. Finally, simulations of dual-beam sputtering were performed, with the resulting patterns determined by the flux ratio of the two beams and the pattern types resulting from single-beam sputtering under the same conditions.

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