Split singularities: Applications and implications

In the microelectronic system, many materials are integrated together in complex structures, from the level of transistors to the level of motherboard. These materials are of different thermomechanical properties, and usually meet together to form the sharp features, such as trenches, wedges, corners or junctions. These sharp features can concentrate stresses, which in turn fail the devices in the ways of cracking, debonding, or injecting dislocations, etc. The singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers. In the latter case, a stronger and a weaker singularity coexist, known as split singularities. The weaker singularity can readily affect the outcome of failures. A dimensionless parameter, called the mode mixity, is defined to characterize the proportion of the two modes at the length scale where the processes of fracture occur. If the mode mixity is nearly zero, then the singular stress field can be simplified to a single mode, and be characterized by one stress intensity factor, on which the criteria of avoiding the failure initiated from the sharp features can be established. Otherwise, both modes need to be considered. We apply this theory to crack penetration or debond, and dislocation injection into strained silicon.