SCIENCE

UPDATE: An interdisciplinary team of researchers headed by Cornell Professor of Materials Science and Engineering Shefford Baker is using a unique combination of experiments, modeling, and simulations to study the behavior of defects in and mechanics of thin metal films. As part of this process, they are using the Windows high-performance computing systems at the Cornell Theory Center (CTC) to simulate the effects of dislocations, defects at the atomic level, on the behavior of the films. Thin metal films are a critical component of many high-tech devices. For example, they are used to form the microscopic conducting wires in integrated circuits; they act as optical reflecting or absorbing layers in cameras, photocopiers, and lasers; and they are used for both chemical protection (e.g. in ink-jet print heads) and chemical activation (e.g. in catalytic converters). In such applications, the film can develop enormously high stresses and the device will fail if the film cracks, peels off, or simply distorts the structure to which it is attached. Experiments have shown that the mechanical behavior of thin metal films can be quite different from the well-known response of the corresponding bulk metals. Designers rely on the fact that thin films are known to be able to sustain greater stresses than the corresponding bulk materials, however, this phenomenon is not well understood at the analytical level. Thus there is tremendous interest from both technological and fundamental perspectives, in understanding the unique mechanical characteristics of such thin films. Cornell University researchers are studying this question at the atomic level using dislocation dynamics simulations as part of an NSF-funded project entitled “Stresses, Deformation, and Dislocations in Thin Films: Combining Modeling and Simulations with Experiments.” Dislocations are line defects in a crystal that occur when the arrangement of atoms is disturbed in a certain way. When a force is applied, dislocations move resulting in permanent “plastic” deformation of the material. In bulk metals, dislocation motion is relatively easy, explaining why metallic objects can be easily deformed (e.g. dented or bent) without breaking. However, when dislocations are confined to the very thin slice of material that makes up a film, their behavior can change in unanticipated ways. “Thin films are often under high stress,” said researcher Prita Pant. Pant is a Cornell University graduate researcher in Baker’s group. “For example consider the copper wires that are made from thin films in integrated circuits in computers. These copper wires are affixed to silicon substrates. Copper and silicon expand and contract by different amounts when exposed to changes in temperatures. Since the copper is very thin relative to the substrate, this results in extremely high stresses in the wire. In fact these little wires can support much higher stresses than bulk copper, and we are trying to understand why this is so.” Since the strength of a metal depends to a large extent on the interaction of dislocations, understanding these interactions is essential for understanding why thin films are so much stronger than their bulk counterparts. The research group is using a simulation program called “PARANOID” (developed by Klaus Schwarz of the IBM T.J. Watson Research Center) to understand the mechanical behavior of small, constrained volumes of materials. With PARANOID, dislocations are placed in a 3-dimensional simulation space and allowed to move and to interact with each other in response to imposed boundary conditions. As a first step towards understanding dislocation behavior in thin films, the researchers have conducted a detailed study of interactions between pairs of dislocations. They ranked the strengths of the various interactions as a function of thickness and orientation, and studied the shapes adopted by dislocations as they move and interact in a film. This work has significantly improved understanding of these elementary processes and their contributions to stresses and mechanical hysteresis in films. A result from these simulations is shown in Fig. 1, where the yellow and the green lines represent dislocations in the film and the two have aligned to form a junction. “Dislocation interactions in thin FCC metal films,” the results of this work, was published in the June 2003 issue (volume 51, issue 11) of Acta Materialia, an international journal that advances the understanding of the structural and functional properties of materials: metals and alloys, ceramics, high polymers, and glasses. “Practically speaking, we hope that in the future, the knowledge that we generate will allow companies, for instance chip manufacturers, to produce more reliable components,” said Pant. “The data we are collecting may be able to be used to predict how the metals that form the components will behave. We hope that once we understand dislocation behavior in thin films, we will be able to predict what techniques and processes are more likely to cause failure, and how to increase reliability.” In ongoing work, the researchers will also be paying particular attention to the effects of film thickness and of the size of the individual small crystallites, called “grains” that make up a film. In a film, thickness and grain size are typically smaller than the characteristic length scale of dislocation structures in a bulk material, so dislocations are found predominantly at grain boundaries and interfaces. This investigation will result in simulations involving many dislocations and will discover whether dislocations are simply stopped at these boundaries, if they can dissipate into the boundary by some mechanism, or if they can initiate deformation in adjacent volumes. The research group is using a unique combination of modeling and experiments for achieving these tasks. On the modeling side, they have adopted a “mezzo-scale” approach that allows them to relate defect interactions on a local scale to global behavior of a small system. Previous research typically focused on either a limited number of dislocations (explaining local behavior but not how local dislocation interactions unite to determine strength and deformation behavior) or large simulations with as many dislocations as possible (explaining average behavior, but lacking specific information on controlling mechanisms). The second component of their approach integrates simulation and modeling efforts with experiments. The researchers perform stress and strain measurements in thin metal films as a function of temperature and grain orientation using substrate curvature and x-ray diffraction methods, and characterize the microstructure using Transmission Electron Microscopy (TEM), x-ray diffraction, and other techniques. “One of the key strengths of this effort is the integration of experiments, modeling, and simulations, all at a fairly high level,” said Professor Baker. “Previous attempts to understand deformation mechanisms have mostly been analytical, an approach which demands various simplifying assumptions that are not necessary using dislocation dynamics simulations. The unique combination of experimental and modeling efforts provides an unprecedented and detailed study of the mechanisms that control stresses and deformation in thin film metallizations during thermal cycling.” “The resources of the Cornell Theory Center are critical to this effort,” said Baker. “Calculating the force on a dislocation due to all the other dislocations is an order N2 calculation (N being the number of calculation points)—and this has to be done at every step of the simulation. So the total time for calculations increases rapidly as the number of dislocations in the simulation increases.” The high-performance computing resources at the Cornell Theory Center (CTC) allow the researchers to calculate and analyze the data in parallel. “Our recent simulations involve determining dislocation configurations, and stress distributions at four different applied strains during loading of a film,” said Pant. Each such simulation requires 100 processors running for about 30 days. Of course we want to run each simulation several times under different conditions. There is no way that this work could be done without first-class computational facilities such as those at CTC.” “A tightly integrated program of experiments and simulations will yield many new insights into the complex relationships between defect behavior and mechanical behavior in constrained volumes that would not be found in projects focused exclusively on experiments or simulations,” said Baker. “Although we are primarily an experimental group, the insights that we have gained by being able to run simulations have been invaluable. In the future, we plan to extend our simulations to include more detailed features of dislocation behavior, and to correlate our simulations directly with mechanical behavior and observations of dislocation structure. This is a truly interdisciplinary project that can only be accomplished by a team of disparate researchers—Klaus Schwarz at IBM and his excellent dislocation dynamics program, Eric Stach at the National Center for Electron Microscopy (NCEM) at the Lawrence Berkeley National Lab., and my team running experiments and dislocation simulations—with the support (both staff and hardware) of an exceptional facility like CTC."