Scripta METALLURGICA Vol. 26, pp. 1325-1330, 1992 Pergamon Press Ltd. et MATERIALIA Printed in the U.S.A. All rights reserved ON THE PINNING OF GRAIN BOUNDARY MOTION BY SURFACE GROOVES J.E. Sanchez, Jr., and E. Arzt Max-Planck-Institut f'tir Metallforschung, Institut f'tir Werkstoffwissenschaft, D-7000 Stuttgart, Germany Received February 24, 1992) Introduction The microstructural evolution m vapor deposited thin films is of significant technological interest. For example, the reliability and performance of interconnects in VLSI integrated circuits patterned from deposited A1 alloy thin films are critically determined by their microstructure (1). Interconnect grain size and grain size distribution (1,2) are known to affect electromigrafion lifetimes such that significant improvements in reliability may be achieved with larger, more uniformly sized grain populations. However, because of the "specimen thickness effect" (3), the in-plane median grain diameter (D) of typical metallization films is limited during normal grain grow.th to approximately the film thickness. Understanding this effect is therefore important for the design of more reliable interconnect material systems. Mullins (4) has previously described the specimen thickness effect as due to the pinning effect of surface grooves on the migration of grain boundary segments whose motion is driven by their in-plane curvature. Surface grooves (5) form at grain boundary-surface intersections due to the equilibration of the surface and boundary tensions. In Mullins' model (4) the pinning is determined in part by the catenoidal through-thickness curvature which may develop in the boundary segments. Consideration of both the geometry of the surface groove and the angle which the boundary makes with the groove leads to a critical angle for pinning of the boundary segment. This critical condition in turn leads to a relation between the pinned in-plane boundary curvature (r) and the specimen thickness (a), for both "static" and "dynamic" conditions of the groove, that is, for stationary and mobile grooves, respectively. For typical values of material surface and boundary tensions, these relations predict stagnant grain populations with average in-plane diameter D = a. Central to this model is the calculation of the critical boundary-groove angle which determines the pinning of boundary segment motion. The Mullins' model will be discussed in more detail below. We present a simpler alternative analysis for the pinning effect of surface grooves on the migration of cylindrically curved boundary segments in thin films. We consider only the change in the boundary segment area during its motion along the groove geometry as a function of boundary in-plane curvature, groove geometry and film thickness, independent of the groove depth and through-thickness catenoidal curvature. This leads to a relation between critical in-plane curvature of (pinned) boundary segments and film thickness that is essentially identical to the Mullins' static and dynamic solutions. We suggest that this analysis applies also to catenoidally curved boundary segments as treated by Mullins. The Model Consider a segment of cylindrically curved boundary segment in a supported thin film, Figure 1, such as in a vapor deposited A1 film on a Si substrate. The surface groove is assumed to form in order to equilibrate the surface and boundary tensions at their point of intersection as shown in Figure 2. Physically, such grooves form during moderate to high temperature deposition techniques, during post-deposition annealing treatments or during the high temperature deposition of overlayer passivation films. We assume that the surface and boundary tensions (and energies) are isotropic, and that, similar to the "static" case considered by Mullins, new 1325 0036-9748/92 $5.00 + .00 Copyright (c) 1992 Pergamon Press Ltd.