Stress concentration near a film edge

Near the free edge of the film, some traction is exerted on the film by the substrate across the common interface. Far from the edge, the film stress 

This edge problem can be studied at several scales of observation. It is instructive to consider states of stress for two extreme sites, namely, for points that are very close to the edge compared to film thickness and for points that are very far from the edge compared to film thickness. For points close to the interface edge for which + /if, the problem of 

While both of these as5rmptotic extremes provide useful information about film edge effects, they do not address the important question of load transfer posed above. Specifically, what is the character of the transition in response between these two hmiting cases, and over what size scale does this transition occur This issue is taken up next, beginning with the simplest system that reveals the nature of this transition more realistic systems are discussed subsequently. 

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The discussion of stress concentration near a film edge in the next section is followed by a brief review of linear elastic fracture mechanics concepts, a prelude to a discussion of delamination and cracking due to film residual stress. A survey of these topics set in the context of fracture mechanics has been presented by Hutchinson and Suo (1992). The chapter also includes descriptions of various experimental techniques for evaluating the fracture resistance of interfaces between films and substrates. In addition, representative experimental results on the interface fracture resistance, as a function of interface chemistry and environment, are presented for a variety of thin film and multilayer systems of scientific and technological interest. 

A related issue has to do with the initial wafer-level uniformity (wafer thickness, wafer warp and bow, thicknesses of thin films across the wafer surface, uniformity of stress in such thin films across the wafer) and the subsequent impact on wafer-level polish performance. Some examination has been made of the impact of wafer warp and bow on the polish performance [68], where it was found that the initial warpage can have significant impact (with the implication that reclaimed wafers may not be appropriate monitors of wafer-level polish performance). Other work has considered inherent variation due to Von Mises stress concentrations at the edge of the wafer (conceptually, a downward pressure on the wafer causes lateral stress buildup near the edge of the wafer) [64]. 

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