Collaborative Research: Modeling and simulation of graphene growth

纳米材料在从生物医学到纳米电子学的应用中为器件和组件的小型化提供了巨大的希望。随着硅基纳米器件达到其自然尺寸限制，碳基材料如纳米管和石墨烯已成为令人兴奋的替代品。由于石墨烯由碳原子的单个2D平面层组成，并且具有独特的物理特性，因此石墨烯被认为比纳米管更适合于大规模电路设计，纳米管通常在接触中表现出较大的固有电阻，这限制了它们的有效性。为了实现它们的承诺，必须在非金属基底上生长或放置大型无缺陷的石墨烯片。因此，重要的是要了解控制石墨烯的生长和形态的机制。事实上，控制石墨烯形态已被证明是一个重大挑战，石墨烯生长的动力学仍然知之甚少。调查人员将在这里解决这些问题。该提案的主要目标是研究控制石墨烯生长和形态的机制的非线性动力学，并制定控制其生长的策略，方法是：（1）开发和应用最先进的自适应数值方法进行大规模计算;（2）对重要的组成过程进行分析、数值和建模研究。更具体地说，研究人员将对碳化硅衬底的热处理生长石墨烯薄膜进行基础研究。这一过程在外延生长机制中是独特的，因为没有碳的沉积通量。相反，硅从表面解吸，释放碳原子以在表面上扩散并首先成核以形成前体层，然后形成石墨烯层。一个重大的挑战是，石墨烯层的结构和形态是由原子尺度的现象和表面特征在数百纳米的长度尺度上的弹性相互作用决定的。因此，没有一个单一的模型能够描述在碳化硅上形成石墨烯片所涉及的所有过程。因此，研究人员将采用多尺度方法，包括原子尺度模拟，用于确定表面结构的遗传算法，以及用于形状演变和图案化的连续模型。这些问题的高度非线性性质使得快速、准确和鲁棒的数值方法对它们的研究至关重要。纳米晶体材料具有的物理特性使它们非常适合于广泛的潜在应用，包括联邦战略利益领域，如纳米技术、信息技术（通过先进的光电和磁存储单元）、生物技术（通过生物或化学传感器）和能源技术（通过光伏器件）。由于其独特的结构和电子特性，碳基器件（如无缺陷石墨烯层）可以将微型化扩展到硅基器件的自然极限之外。实验技术的最新进展表明，实现器件应用所需的大而均匀的石墨烯层的关键障碍是其生长表面的粗糙度。然而，表面性质和石墨烯生长过程之间的相互作用的定量理解仍然难以捉摸。研究人员将开发新的数学理论，并推进最先进的数值模拟，以进行石墨烯生长的基础研究。这些研究将为石墨烯层形成动力学实验测量的定量解释提供指导，并将提出控制石墨烯生长的机制。本文的理论和方法对其他纳米材料半导体量子点阵列的研究也有一定的借鉴意义。两个博士学生将在执行拟议工作的同时接受跨学科培训。研究人员将开发和教授晶体和外延生长课程的天才高中学生作为加州的一部分。加州大学欧文分校数学与科学暑期学校（COSMOS）

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.