First-principle dynamical electronic characteristics of Al electromigration in the bulk, surface, and grain boundary

Abstract

Formulas for the driving force of electromigration have been presented using concepts of the tension density, the external force density, and the effective charge tensor density. The ``dynamic'' wind charge tensor density $Z{\ensuremath{\downdownarrows}}_{a\mathrm{dynamic}\mathrm{}\mathrm{wind}}(\mathbf{r})$ has been revealed over and above the conventional ``static'' wind charge tensor density $Z{\ensuremath{\downdownarrows}}_{a\mathrm{static}\mathrm{}\mathrm{wind}}(\mathbf{r}).$ We have demonstrated the application of the concepts to electromigration reliability problems of ultralarge-scale integration devices where extremely high current densities should be maintained through ultrathin film interconnects. Quantum mechanical wave-packet propagation of an Al atom has been examined in some models of thin Al lines which contain atomic defects, using the first-principle electronic structure calculations under the periodic boundary condition. The dynamical electronic properties by our simulation have demonstrated the characteristic features of the $Z{\ensuremath{\downdownarrows}}_{a\mathrm{dynamic}\mathrm{}\mathrm{wind}}(\mathbf{r})$ in the course of the Al electromigration in the bulk, surface, and grain boundary.