Jun He and Guanghai Xu (Intel Corporation)

Zhigang Suo (Harvard University)

pp. 3-14 in Proceedings of the 7th International Workshop on Stress-Induced Phenomena in Metallization, Austin, Texas, 14-16 June 2004, edited by P.S. Ho, S.P. Baker, T. Nakamura, C.A. Volkert, American Institute of Physics, New York.

A crack extends in a brittle material by breaking atomic bonds along the crack front. The physics of crack growth may well have been understood, from electrons to atoms and to microstructures. This statement by itself, however, is of limited value; it offers little help to the engineer trying to prevent cracking in an integrated structure. Hypes of multi-scale computation aside, no reliable method exists today to predict cracking by computation alone. The pragmatic approach is to divide the labor between computation and measurement within the framework of fracture mechanics. Some quantities are easier to compute, and others easier to measure. A combination of computation and measurement solves problems economically.

Of course what is easy changes with circumstances. As new tools and applications emerge, it behooves us to renegotiate a more economical division of labor. The history of the fracture mechanics makes an excellent case study of such divisions and renegotiations. For the last few years, in the course of studying cracks in interconnect structures, we have found it necessary to make a new division of labor. This paper gives a preliminary account of our work.

For a crack in a structure, the crack driving force, G, is the reduction of the elastic energy in the structure associated with the crack extending per unit area, when the external mechanical load is rigidly held and does no work. An existing protocol is to calculate G by solving a boundary value problem. Such solutions are accumulating for thin film structures. To prevent a crack from growing, the engineer must ensure that G is below a threshold value. The latter is estimated from experimental measurements.

The calculation of G is prohibitively difficult for three-dimensional structures that integrate diverse materials. This is particularly so when the stress-strain relations of the constitute materials, as well as the residual stress fields in the structures, are poorly characterized. On the other hand, compared to large structures such as airplanes and ships, small structures such as on-chip interconnects are inexpensive. It costs little to make many replicates of an integrated small structure, so that massive full-structure testing is practical. An integrated structure is an analog computer, and massive testing a form of parallel computing. Indeed, massive testing has been a key to the spectacular success of the microelectronic industry.

These considerations have motivated us to develop a method to measure the crack driving force experimentally. Our method relies on a familiar phenomenon: moisture-assisted crack growth. Water (and some other molecules) in the environment may participate in the process of breaking atomic bonds along the crack front. For the environmental molecules to reach the crack front and to break atomic bonds there, the crack extends at a velocity much below the sound speed in the material. The crack velocity V is an increasing function of the crack driving force G. In recent years, such V-G functions have been measured for various dielectric films.

The V-G function is specific to a given material and its environment.  Once determined, the same function applies when this material is integrated in a structure with other materials, provided environmental molecules reach the crack front.  In the integrated structure, an observed crack velocity, together with the known V-G function, provides a reading of the crack driving force.  The observed crack velocity can be used to measure deformation properties of ultrathin films.  We also describe a procedure to measure the crack driving force GR due to the residual stress field in the integrated structures, even when GR by itself is too low for the crack to extend at a measurable velocity.