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

The 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.