Grain Boundary Curvature in Polycrystalline Metallic Thin Films
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Grain Boundary Curvature in Polycrystalline Metallic Thin Films Alexander H. King1, Rakesh Mangat2 and Kwame Owusu-Boahen3 1 School of Materials Engineering Purdue University, West Lafayette IN 47907-1289. 2 Massachusetts Institute of Technology Cambridge, MA, 02139. 3 Department of Materials Science & Engineering State University of New York, Stony Brook NY 11794-2275. ABSTRACT Well-annealed thin films are typically observed to exhibit mean grain diameters that are approximately equal to the film thickness. The standard explanation of this “sheet thickness effect” is that it results from a balance of grain boundary curvature in two different directions which, in turn, results from pinning at grain boundary grooves. TEM experiments have been performed to assess this model, and it is found that the predicted curvature about axes in the film plane is absent. Alternate explanations of the sheet thickness effect are considered.
INTRODUCTION Provided that the films are flat, uniform and pore-free, structural impacts on most polycrystalline thin film properties are dominated by the grain size and texture. Our ability to control these aspects of the microstructure is rather limited. The texture can be affected by the substrate preparation [1] or stress in the film [2]. Grain size is, in principle, the simplest microstructural parameter to control, through the temperature of the substrate and the film deposition rate [3]. This control, however, is limited to a regime that is typically bounded by a saturated columnar grain size, with a mean equivalent grain diameter approximately equal to the film thickness. This “specimen thickness effect” was first identified in much thicker sheets than are addressed in this symposium [4], but it appears to operate in the nano meter scale, just as it does in the millimeter scale, and is largely accepted as a fact of life. The standard explanation for the specimen thickness effect was developed by Mullins [5] and it depends upon pinning of grain boundaries by their surface grooves. As a grain boundary migrates toward its center of curvature, the surface pinning causes the part of the boundary in the center of the specimen to advance ahead of the parts closer to the surface, so the boundary develops a catenoid form, embodying antic lastic curvature: the center of curvature about an axis parallel to the film normal lies on the opposite side of the boundary to the center of curvature about an axis that is parallel to the tangent to the boundary intersection with the film surface, as indicated in Figure 1. When the curvatures about the two orthogonal axes are equal, the net driving force for boundary migration is zero. Mullins shows that this may be expected to occur when the mean equivalent grain diameter is approximately equal to the film thickness. Our purpose in this paper is to examine the nature of the film thickness effect in the regime of film G7.8.1
thickness appropriate to current electronic and magnetic state -of-the-art technologies, and to determine whether the Mullins mechanism
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