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各种应用中，对器件和部件的小型化有着巨大的希望。随着硅基纳米器件达到其自然尺寸极限，碳基材料如纳米管和石墨烯已经成为令人兴奋的替代品。由于石墨烯由一个单一的二维平面碳原子层组成，并且具有独特的物理性质，因此石墨烯被认为比纳米管更适合大规模电路设计，而纳米管通常在接触中表现出较大的固有电阻，从而限制了它们的有效性。为了实现他们的承诺，必须在非金属衬底上生长或放置大而无缺陷的石墨烯片。因此，了解控制石墨烯生长和形态的机制是很重要的。事实上，控制石墨烯的形态已被证明是一个主要的挑战，石墨烯的生长动力学仍然知之甚少。调查人员将在这里解决这些问题。本提案的主要目标是研究控制石墨烯生长和形态机制的非线性动力学，并通过(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)对重要组成过程进行分析、数值和建模研究，来制定控制其生长的策略。更具体地说，研究人员将通过对碳化硅衬底进行热处理，对石墨烯薄膜的生长进行基础研究。该工艺在外延生长机制中是独一无二的，因为没有碳的沉积通量。相反，硅从表面解吸，释放碳原子在表面扩散，首先成核，形成前驱体层，然后形成石墨烯层。一个重要的挑战是石墨烯层的结构和形态是由原子尺度现象和表面特征在数百纳米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，确定表面结构的遗传算法，以及形状演变和图案的连续模型。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。纳米晶体材料的物理特性使其非常适合广泛的潜在应用，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（通过光伏设备）。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，可以扩展小型化，超越硅基器件的自然极限。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，对表面性质和石墨烯生长过程之间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。本文所建立的理论和方法也将有助于其他纳米级半导体量子点材料阵列的研究。两名博士生将接受跨学科培训，同时进行拟议的工作。作为加州大学欧文分校加州州立数学与科学暑期学校（COSMOS）的一部分，研究人员将为有天赋的高中生开发并教授一门关于晶体和外延生长的课程。

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.