| Electromigration is one of the failure mechanisms that occur in Very Large Scale Integration (VLSI) interconnections. The transport of atoms due to electromigration can cause an open circuit failure in an interconnecting wire. Methods currently used to characterize an interconnection's susceptibility to electromigration are costly, time consuming, destructive and complicated.;In this study we report an analytic investigation into one of the suspected causes of electromigration in thin film conductors; namely localized hot spots in the temperature profile. These arise because of voids in the interior of the conductor material. The reentrant corners on these voids create singularly high local current densities, and the enhanced ohmic heating produced by this current crowding disrupts the temperature profile.;By restricting the shape of the void to a simple polygon we are able to solve the electric potential and heat transfer equations using a Schwarz Christoffel transformation, while retaining the essential features of current crowding.;In our rigorously developed mathematical model interesting facts have been uncovered that give insight into the causes of other electromigration effects. In particular it is seen that the classical electrical and thermal models predict bounded peak temperatures and unbounded temperature gradients in the conductor. |
