- Stress Accumulation During Ion Irradiation
- Steep Feature Evolution
- Crater Functions
- Relevant publications
Many distinct morphologies self-organize on surfaces under uniform energetic ion irradiation (Fig. 1), including ripples, pits, hillocks, and ultrasmooth surfaces. The length scales of these structures can range from hundreds of nanometers down to 7 nm (Wei et al., Chem. Phys. Lett. 452, 124 (2008)), depending on the material and system parameters.
Fig. 1. Nanopatterns self-organized under ion irradiation. A range of materials, pattern types, length scales, and degree of ordering can be seen. Image courtesy of Dr. Bashkim Ziberi.
Due to the high degree of ordering in some of these patterns, and because there is in principle no limit to the size of a uniform ion beam, ion bombardment holds promise in the high-throughput fabrication of simple devices. Metamaterial devices, which generally feature an array of repeating, simple structures, could be particularly well-suited to this technique. Examples of metamaterial devices include optical antenna arrays (Fig. 2), and the split ring resonators used in negative refractive index materials and optical cloaking (Fig. 3).
Fig. 2. An optical antenna array, a metamaterial that could be quickly self-organized, given enough understanding and control over the processes involved in ion bombardment. The length scale and simplicity of the patterns makes this structure a good candidate for the technique. Image from E. Smythe et al., Optics Express 15, 12 (2007).
Fig. 3. An array of split-ring resonators, a metamaterial used for negative index of refraction cloaking devices. With enough understanding of ion irradiation-induced nanopatterning, such a metamaterial could be quickly manufactured over an arbitrarily large area. Image from Enkrich et al., PRL 95, 203901 (2005).
Our research focuses on understanding the fundamental mechanisms involved in nanoscale morphology evolution under ion irradiation in order to ultimately control it as a processing tool.
In collaboration with Professor Karl Ludwig (Boston University), we have conducted grazing-incidence small-angle x-ray spectroscopy (GISAXS) in order to study realtime, in-situ morphology evolution. A schematic of the experimental setup is shown in Figure 4. The resulting data have allowed comparison between various models and experiment, allowing us to prove the importance of mass redistribution as a driving effect for pattern formation [Ref. mja202].
Ongoing work in this area investigates GISAXS of different target/ion combinations, and the morphology evolution of late-time, high amplitude structures (the nonlinear regime).
Fig. 4. Schematic of the GISAXS experimental setup. Ions irradiate a target from above, the x-ray beam impinges on the sample from the right, and the diffraction pattern is captured by a detector on the right. As nanoscale patterns emerge or disappear, their evolution is measured by the detector. Image reproduced from H. Zhou et al., PRB 78, 16 (2008).
We are nearing completion of a custom multi-beam optical stress sensor (MOSS) system. This system will measure the time-resolved stress accumulation in targets undergoing ion irradiation at a full range of angles, from normal to grazing incidence. Sample data are shown in Figure 5.
Fig. 5. The average in-plane stress of a Si sample before, during, and after normal-incidence 250 eV Ar+ bombardment, measured using a multi-beam optical stress sensor (MOSS) system. The MOSS system currently nearing completion will allow the collection of stress data at all incidence angles.
Under uniform ion irradiation, steep features propagate along surfaces in a manner mathematically similar to a shock front. They further evolve to a specific slope that is determined by the choice of ion energy, ion species, and target species (Fig. 6) [Ref. mja165].
Fig. 6. SEM image of a pit in a Si target, before and after ion irradiation of 1.5x1019 ions/cm2. The pit wall propagates along the target, and the pit expands from 3 µm (A) to 5.3 µm (B). Image from Chen et al.
Work in preparation shows that these complex, three-dimensional structures can be effectively modeled as two-dimensional shapes. These simpler models are easier to simulate than the full dynamics, and can be used to solve the "inverse problem" of predicting a shape that will evolve into a desired final structure under ion irradiation.
Atom probe samples are steep, conical tips that are frequently sharpened via ion irradiation (Fig. 7). Reliable models and simulations of steep feature evolution under ion bombardment could be of great use for the atom probe community.
We have also collaborated with Professor Scott Norris (Southern Methodist University) and Professor Kai Nordlund's group (University of Helsinki) to develop and test a crater function theory, which uses the results of parameter-free molecular dynamics simulations to predict surface stability/instability to pattern formation, predict wavelength coarsening of the resulting patterns, and probe the underlying mechanisms driving the process [Refs. mja192, mja200].
mja202. C.S. Madi, E. Anzenberg, K.F. Ludwig, Jr., M.J. Aziz, "Mass Redistribution Causes the Structural Richness of Ion-Irradiated Surfaces", PRL 106 (2011) 066101. In this paper, we show that the erosion-based mechanism of pattern formation that the community accepted for a quarter century doesn't explain the phase diagram for the Ar+/Si system, but mass redistribution explains it well instead. Click here to see the paper.
mja193. C.S. Madi, H.B. George, M.J. Aziz, "Linear stability and instability patterns in ion-sputtered silicon", J. Phys.: Condens. Matter 21 (2009) 224010. This paper presents an energy/angle phase diagram of Ar+/Si at energies below 1.1 keV. However, a later paper  showed that the pattern formation in the low-energy, low-angle corner was actually formed by multiple scattering. Click here to see the paper.
mja214. C.S. Madi, M.J. Aziz, "Multiple Scattering Causes the Low Energy-Low Angle Constant Wavelength Topographical Instability of Argon Ion Bombarded Silicon Surfaces", Appl. Surf. Sci. 258 (2012) 4112. In this paper, we show that the pattern formation in the low-energy, low-angle corner of the Ar+/Si phase diagram reported in  is actually formed by multiple scattering, thus demonstrating that artifacts can form even in systems free of chemical impurities. Click here to see the paper.
mja192. S.A. Norris, M.P. Brenner, M.J. Aziz, "From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation", J. Phys. Condens. Matter 21 (2009) 224017. Click here to see the paper.
mja200. S.A. Norris, J. Samela, L. Bukonte, M. Backman, F. Djurabekova, K. Nordlund, C.S. Madi, M.P. Brenner, M.J. Aziz, "Molecular dynamics of single-particle impacts predicts phase diagrams for large scale pattern formation", Nature Comm. 2 (2011) 276. Click here to see the paper.
mja228. J.C. Perkinson, C.S. Madi, M.J. Aziz, "Nanoscale topographic pattern formation on Kr+-bombarded germanium surfaces", 31 (2013) 021405. Click here to see the paper.
mja229. E.A. Anzenberg, J.C. Perkinson, C.S. Madi, M.J. Aziz, K.F. Ludwig, Jr., "Nanoscale surface pattern formation kinetics on germanium irradiated by Kr+ ions", PRB 86 (2012) 245412. Click here to see the paper.