Film delamination due to residual stress

As already noted, the state of stress in the film is essentially homogeneous biaxial tension or compression at distances far ahead and far behind the delamination front compared to hf. On the other hand, for material points close to the edge of the delamination zone, the state of stress is expected to be very non-uniform and to be highly concentrated. While the details of this stress distribution play little role in the conceptual development of this section, a few observations made on the basis of elementary arguments reveal the full nature of this stress distribution. 

The elastic strain energy density associated with a biaxial state of 

If the delamination front is straight and the film edge is free then the energy release rate is given in terms of system parameters by (4.34) with = 0. According to the Griffith condition, the delamination front will advance or 

For a given material system, the film thickness at which it is first possible to drive a delamination spontaneously is the critical thickness 

The result has several noteworthy features. At this level of modeling, the critical thickness for delamination depends on substrate properties only through their influence on the values of both the mismatch strain Cm and the separation energy F. The general form of (4.36) could have been anticipated on the basis of dimensional arguments alone the analysis provides the numerical factor 2. 

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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. 

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