Spiral Cracking Around a Strained Cylindrical Inclusion in a Brittle Material and Implications for Vias in Integrated Circuits

Abstract

The practice of forming electrical conduction paths in an insulating material by filling cylindrical holes with molten metal can result in high residual stresses when the metal cools. Residual stress is greatest near the metal-insulator interface, and stress relaxation by means of de-adhesion is possible. Another failure mode that poses greater practical difficulties is the growth of cracks along paths which spiral away from the interface into the brittle material. Such cracks may occur singly or in pairs, and their lengths can be sufficiently great to provide links with adjacent conduction paths. Such cracks are considered from the fracture mechanics point of view. The residual stress field is relaxed by the growth of spiral cracks which are modeled as continuous distributions of dislocations. It is assumed that these cracks grow so that the stress state on the prospective fracture plane just ahead of the crack tip is purely tensile. The paths are determined by means of an incremental numerical procedure.