Nanoscale pattern formation on ion-sputtered surfaces

Abstract

Self-organized, nano-scale structures appear on solid surfaces under ion beam irradiation with ion energies in the keV range. Within the last decade, surface engineering by ion beam sputtering (IBS) has become a very promising candidate for bottom-up production techniques of nano-devices. Morphologies like ripples, and regular arrays of dots, pyramids and pits as well as ultra-smooth surfaces have been obtained on a wide variety of substrates, including important semiconductor materials like Si, Ge, GaAs and InP.In spite of many substantial improvements of experimental surface structuring by IBS, the physical mechanisms underlying the pattern formation are still poorly understood. In this work we use Kinetic Monte Carlo (KMC) simulations and continuum theory to study the effects of the following mechanisms in detail: (i) the interplay of surface erosion with different surface diffusion mechanisms (Wolf-Villain, Hamiltonian, thermally activated hopping via transition states, including barriers depending on both initial and final configuration in a hop) and the crossover from erosion-driven to diffusion driven patterns, (ii) random orientational fluctuations of ion trajectories within the beam, leading to ion beam divergence, (iii) co-deposited, steady-state, (sub)-mono-layer coverages of the substrate with a second atomic species (``surfactant sputtering"") and (iv) multi-beam and rotated-beam (or rotated sample) setups.We find that all the four mechanisms under study may have a profound _ and sometimes unexpected _ impact on the pattern formation. Different diffusion mechanisms, which all give rise to the same leading order terms in a continuum description lead to rather different long-time behavior of patterns in KMC simulations. Orientational fluctuations change the bifurcation scenarios of pattern formation and surfactant sputtering may give rise to qualitatively new effects like mesoscopic or even macroscopic patterns on top of nano-scale patterns, and the ordering of the surfactant on top of the structured surface. This ordering leads to a feedback mechanism due to the modulation in sputtering yield caused by the surfactant. On the other hand, many of the promising proposals concerning the usage of multi-beam and rotated beam setups could not be confirmed (in accordance with recent experiments), but we can outline some physical reasons for this failure, which could guide an improved usage of these techniques.