Some Studies on Phase Segregation and the Influence of Microstructure on Multispecies Thin Solid Film Growth

题目：相偏析及微观结构对多组分薄膜生长影响的研究摘要：在许多多组分薄膜中都存在相偏析现象，二次相岛可能在薄膜表面成核生长，从而影响薄膜的性能。影响可能是有害的，也可能是有益的。例如，富含钡的镱钴薄膜可能会失去其超导特性，但另一方面，镱钴薄膜上的岛屿可能充当磁场的固定中心。相偏析和二次相岛形成的进一步应用发现于半导体中的量子点和线。因此，了解相偏析的机制和二次相岛的稳定性对薄膜的设计和可控性至关重要。本研究项目的一个目标是，在多组分薄膜沉积的背景下，提供一个数学上严格且热力学上一致的方程推导，该方程控制着薄膜、蒸汽和二次相相交的界面三重结的演化，远离平衡。这种连续体模型有助于进行稳定性分析，从而可能阐明地表沉淀形成和生长的条件。当薄膜表面相邻时，生长可以通过台阶流动发生——即原子高的台阶的横向运动，这些台阶将几个单位细胞宽的梯田分开。在多组分薄膜中，气相原子的沉积可能是竞争性的——也就是说，不同的物质在单个梯田上的吸附可能发生在同一位置。本提案的第二个目标是建立一个多组分薄膜的微观力学模型，该模型考虑了平台和壁架微观结构、吸附原子扩散和竞争性吸附-脱附动力学的综合影响。该项目的第三个目标是以本构关系的形式将薄膜生长的微观力学模型的均匀化所获得的平均信息整合到宏观模型中，从而将纳米尺度与微观尺度联系起来。薄膜是许多新技术的基本组成部分。例子包括微型和光电器件应用中的半导体，工业切削工具中的钻石，各种防腐和抗磨涂层，作为微机电系统（MEMS）执行器的形状记忆合金，以及无线通信设备中的超导体。在大多数工业应用中，多组分薄膜比单组分薄膜应用更广泛。这些薄膜的性质及其在非常严格的条件下的性能取决于它们的化学成分和薄膜表面的形态细节。为了在生长过程中更好地控制薄膜的化学和微观结构，对基本的物理和化学机制有严格的数学理解是必要的，特别是当原子对原子的材料制造不再是一个遥远的梦想时。应用数学家可以（并且已经这样做了）通过开发物理上合理的预测模型来为这种全球努力做出重大贡献，这些模型可以严格分析并用于数值模拟。现代连续介质物理学的概念，当与现代数学工具（例如，均匀化和非线性偏微分方程理论）相结合时，构成了一种强有力的方法，用于解决与多组分薄膜生长有关的许多具有挑战性的问题。

Proposal: 0204939PI: Michel JabbourInstitution: University of KentuckyTitle: Some studies on phase segregation and the influence of microstructure on multispecies thin film growthABSTRACTThe phenomenon of phase segregation is commonly observed in many multispecies thin films, where secondary-phase islands may nucleate and grow on the surface of a film and thus influence the properties of the film. The influence may be detrimental or beneficial. For example, barium-rich YBCO films may loose their superconducting properties but, on the other hand, islands on YBCO films may act as pinning centers for the magnetic field. Further applications of phase segregation and the formation of secondary-phase islands are found in quantum dots and wires in semiconductors. Understanding the mechanisms underlying phase segregation and the stability of secondary-phase islands is therefore crucial for the design and controllability of thin films. One objective of the present research project is to provide, in the context of deposition of multispecies thin films, a mathematically rigorous and thermodynamically consistent derivation of the equations governing the evolution, away from equilibrium, of interfacial triple junctions along which the film, vapor, and secondary phases intersect. Such a continuum model lends itself to a stability analysis and may thus shed light on the conditions under which surface precipitates can be expected to form and grow. When the film surface is a vicinal one, growth can occur via step flow---that is, lateral motion of atomic-high steps which separate several-unit-cell-wide terraces. In multicomponent films, the deposition of gas-phase atoms can be competitive---that is, adsorption of distinct species on individual terraces can occur on the same site. The second objective of this proposal is to develop a micromechanical model for multicomponent films that accounts for the combined effects of the terrace-and-ledge microstructure, adatom diffusion, and competitive adsorption-desorption kinetics. A third objective of this project is to link the nanoscale to the microscopic scale by incorporating averaged information obtained by homogenization of the micromechanical model of film growth discussed above into macroscopic models in the form of constitutive relations.Thin films constitute a fundamental component of numerous novel technologies. Examples include semiconductors in micro- and opto-electronic device applications, diamonds in industrial cutting tools, various anticorrosion and antiwear coats, shape-memory alloys as actuators in microelectromechanical systems (MEMS), and superconductors in wireless communication devices. In most industrial applications, multispecies films are more widely used than their single-component counterparts. The properties of these films and their performance under very stringent conditions depend on their chemical composition and the morphological details of the film surface. To better control the chemistry and microstructure of thin films during the growth process, a mathematically rigorous understanding of the fundamental physical and chemical mechanisms at play is necessary, especially as the atom-by-atom fabrication of materials is no longer a remote dream. Applied mathematicians can (and already do) make a significant contribution to such a global effort by developing physically sound predictive models which can be analyzed rigorously and implemented for numerical simulations. The concepts of modern continuum physics, when combined with the tools of modern mathematics (for example, homogenization and the theory of nonlinear partial differential equations), constitute a potent methodology with which to address many of the challenging issues related to the growth of multicomponent thin films.