Journal of Electronic Materials

, Volume 48, Issue 1, pp 182–193 | Cite as

Phase-Field Study of Electromigration-Induced Shape Evolution of a Transgranular Finger-Like Slit

  • Jay SantokiEmail author
  • Arnab Mukherjee
  • Daniel Schneider
  • Michael Selzer
  • Britta Nestler
TMS2018 Phase Stability in Electronic Materials
Part of the following topical collections:
  1. TMS2018 Phase Stability, Phase Transformations, and Reactive Phase Formation in Electronic Materials XVII


Electromigration damage due to void propagation in thin films has garnered much attention due to its implications for efficient design of interconnects. Voids can drift along the line, preserving its shape, or evolve into various time-dependent configurations, which are governed by the interplay between the capillarity and electron wind force. We have employed the phase-field method to elucidate the transition of a circular void to a finger-like slit. Following an initial transient regime, the void attains an equilibrium shape with a narrow parallel slit-like body, which contains a circular rear end, and a parabolic tip. The subsequent drift of the void is characterized by shape invariance along with a steady-state slit width and velocity, which scale with the applied electric field as \(E^{-1/2}\) and \(E^{3/2}\), respectively. The results obtained from phase-field simulations are critically compared with the sharp-interface solution. Repercussions of the study, in terms of prediction of void migration in flip-chip Sn-Ag-Cu solder bumps and fabrication of channels with desired micro/nanodimensions, are discussed.


Electromigration finger-like slit void propagation phase-field model solder joints 


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The authors are grateful for financial support from the cooperative graduate school ‘‘Gefuegestrukturanalyse und Prozessbewertung’’ of the Ministry of the State of Baden-Wuerttemberg and the ‘‘Mittelbau’’ Initiative. The authors gratefully acknowledge editorial support from Leon Geisen.


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Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Institute of Digital Materials Science (IDM)Karlsruhe University of Applied SciencesKarlsruheGermany
  2. 2.Institute of Applied Materials-Computational Materials Science (IAM-CMS)Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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