Evolution of Semiconductor Substrates due to Ion Irradiation
In the process of ion irradiation, a semi-conductor target is bombarded with ionized noble gases. Upon impact with the substrate, these ions transfer kinetic energy, via a collision cascade, to target atoms, leading eventually to atom ejection, or “sputtering.” This ejection, in turn, causes surface erosion, which can lead to at least two interesting phenomena. Historically applied as a method of surface polishing, it has more recently been observed under certain experimental regimes to cause the spontaneous formation of patterns such as ripples and especially dots. If this process could be harnessed to generate long-range order, it could be used as the basis of “bottom-up” fabrication processes. In addition, more recent experiments on high-slope targets reveals the the steady propagation of shock-like surface features, which could potentially be harnessed to shrink pre-etched structures into smaller electronic components. However, despite the practical interest, and the application of more than 40 years of research, this process is still not understood to the point where the outcome of most experiments can be predicted ahead of time by theory.
The classical theoretical approach to this problem consists of first (a) establishing the effect on the target of a single ion impact, and then (b) integrating nearby impacts in space in time to obtain a continuum integro-differential equation on the interface evolution, which can be further simplified through asymptotic expansion if certain scale disparities are present. However, there is increasing evidence that the macroscopic system behavior obtained from step (b) may depend sensitively on the nature of the single-impact response obtained from step (a). Importantly, this “crater function” contains the effects of both erosion and redistribution, and while the former has been well-studied, the latter has received much less attention until recently. Thus, attention has increasingly turned to MD simulation of the single-ion impact, and a fundamental problem is then to directly link the results of MD simulation to a parameter-free continuum PDE for the interface. We have recently derived an analytical framework establishing this link, and are in collaboration with colleagues gathering molecular dynamics data for Silicon irradiated by Ar+ at 250eV. With the resulting data set, we will construct a PDE directly informed by MD, and the phase diagram it predicts will be compared with experimentally measured phase diagrams obtained under identical environmental conditions.
Evolution of Fully-Faceted Interfaces
In many crystal-growing procedures of interest, a micro-scale faceted surface appears and proceeds to evolve, often exhibiting coarsening and even dynamic scaling, whereby statistics describing surface geometry remain constant even as the characteristic lengthscale increases through the vanishing of small facets. For many evolving faceted surfaces, a facet velocity law can be observed, assumed, or derived, which specifies the normal velocity of each facet, often in configurational form which depends on the geometry of the facet. Coupled with an appropriate geometric simulation tool, such surfaces can be simulated with overall computational complexity equivalent to that of a system of ODE’s. The large-scale numerical simulations enabled by this approach allow the statistical investigation of coarsening and dynamic scaling, and the subsequent development of a mean-field theory describing the dynamically scaling state.
Nanowire Formation
This is a project I am just beginning. When several monolayers of Au are deposited onto a Si substrate and then heated in an atmosphere of Silane (SiH_4), the Au coalesces into droplets which act as catalysts, extracting Si from the Silane and depositing it on the substrate. As this process continues, Si wires are self-assembled, with the catalyst droplet riding on top. Projects associated with this problem include determining (a) the equilibrium droplet/wire shapes, (b) the speed of wire growth in terms of environmental parameters, and (c) the eventual fate of the Au droplets, which can decrease in size due to incorporation into the wire or diffusion along the wire surface. The aim is to understand the mechanisms by which uniform wires can be reproducibly grown for use in novel electronic applications.