Electromigration revisited: competition between Kirkendall shift and backstress in pure metals and two-phase alloys

Abstract

The simple phenomenological model and analytical approach of electromigration in the two-phase alloy (solder) under combined influence of the Kirkendall effect, backstress and sedimentation is presented. It is compared with electromigration in pure metal under condition of quasi-equilibrium vacancies (unlimited power of vacancy sinks-sources) and electromigration in pure metal with account of nonequilibrium vacancies.

Keywords:

• electromigration
• phase separation
• ultra-high gravity
• backstress
• Kirkendall effect

Acknowledgements

This paper is dedicated to the memory of Prof. Vitaliy Slezov, who passed away on October 30, 2013. His ideas and rigorous mathematical treatments of the diffusion-controlled first-order phase transformations kinetics (from nucleation to coarsening) are now classical. Discussions with him were very useful for better understanding the of stresses–vacancies–Kirkendall synergy. One of the authors (AG) is grateful to AGH University for hospitality, and also to the Ministry of Education and Science of Ukraine and to Ukrainian State Fund for Fundamental Research for partial support.

Notes

1. Authors are not aware about such experiments with aluminum or copper lines.

2. We emphasize this since in some experimental papers authors use both Equations (6(6) ) and (7(7) ), and that is wrong.

Additional information

Funding

This work is supported by a National Science Center (Poland) decision number DEC-2011/02/A/ST8/00280.