Mean-Time-To-Failure Equations for Electromigration, Thermomigration, and Stress Migration

King-Ning Tu*, A. N. Gusak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The equation of mean-time-to-failure (MTTF) for electromigration has been reevaluated from the viewpoint that in irreversible processes, entropy production is the controlling factor. We have justified that the power factor on current density is n = 2, as given in Black's equation. Furthermore, on the basis of entropy production, we provide a unified model of the equations of MTTF for thermomigration and stress migration. The effect of thermal conduction on the physical link between entropy production and the failure of void formation is discussed.

Original languageEnglish
Pages (from-to)1427-1431
Number of pages5
JournalIEEE Transactions on Components, Packaging and Manufacturing Technology
Issue number9
StatePublished - Sep 2020


  • Entropy
  • Production
  • Electromigration
  • Heating systems
  • Integrated circuit interconnections
  • Mathematical model
  • Thermodynamics
  • entropy production
  • mean-time-to-failure (MTTF)
  • reliability
  • stress migration
  • thermomigration

Cite this