Nanoscale materials hold tremendous promise for the miniaturization of devices and components in applications ranging from biomedicine to nanoelectronics. As silicon-based nanodevices reach their natural size limitations, carbon-based materials such as nanotubes and graphene have emerged as exciting alternatives. Because graphene consists of a single 2D planar layer of carbon atoms, and possesses unique physical properties, graphene is thought to be better suited for large-scale circuit design than nanotubes, which typically exhibit large intrinsic resistance in contacts that limits their effectiveness. To realize their promise, large and defect-free graphene sheets must be grown or placed on non-metallic substrates. It is therefore important to understand the mechanisms that govern the growth and morphology of graphene. Indeed, controlling the graphene morphology has proven to be a major challenge, and the kinetics of graphene growth remain poorly understood. The investigators will address these issues here. The main objective of this proposal is to investigate the nonlinear dynamics of the mechanisms that govern the growth and morphology of graphene and develop strategies to control its growth by (1) developing and applying state-of-the-art adaptive numerical methods to large-scale computation and (2) performing analytical, numerical and modelling studies of important constituent processes. More specifically, the investigators will perform fundamental studies of the growth of graphene films from a thermal treatment of a silicon carbide substrate. This process is unique among epitaxial growth mechanisms because there is no deposition flux of carbon. Rather, silicon desorbs from the surface freeing carbon atoms to diffuse on the surface and nucleate first to form a precursor layer and then a graphene layer. A significant challenge is that the structure and morphology of graphene layers is determined both by atomic-scale phenomena and by the elastic interaction of surface features over length scales of hundreds of nanometers. Consequently, no single model is able to describe all the processes involved in the formation of graphene sheets on silicon carbide. The investigators will therefore adopt a multiple-scale approach that includes atomic scale simulations, genetic algorithms for determination of surface structure, and continuum models for shape evolution and patterning. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study.
Nanocrystalline materials have physical properties that make them ideally suited for a wide range of potential applications including areas of Federal strategic interests such as nanotechnology, information technology (via advanced optoelectronic and magnetic storage units), biotechnology, (via biological or chemical sensors), and energy technology (via photovoltaic devices). Because of their unique structural and electronic properties, carbon-based devices, such as defect-free graphene layers, can extend miniaturization beyond the natural limits of their silicon-based counterparts. Recent advances in experimental techniques indicate that the key obstacle in achieving large and uniform graphene layers necessary for device applications is the roughness of the surface on which it grows. However, a quantitative understanding of the interaction among the surface properties and graphene growth processes remains elusive. The investigators will develop new mathematical theory and advance the state-of-the-art in numerical simulation to perform fundamental studies of graphene growth. These studies will provide guidance in the quantitative interpretation of experimental measurements on the dynamics of graphene layer formation and will suggest mechanisms to control graphene growth. The theory and methods developed here will also be useful in the study of other nanoscale materials arrays of semiconductor quantum dots. Two Ph.D. students will receive interdisciplinary training while performing the proposed work. The investigators will develop and teach a course on crystal and epitaxial growth for gifted high school students as part of the Calif. State Summer School for Mathematics and Science (COSMOS) at UC Irvine.
