Molecular dynamic study for concentration-dependent volume relaxation of vacancy

Zhen Cui, Xuejun Fan, Guoqi Zhang

Research output: Contribution to journalArticleScientificpeer-review


In this paper, large-scale molecular dynamic (MD) simulation is performed to investigate the concentration-dependent vacancy volume relaxation in Al, Cu, and Au, respectively. The vacancy volume relaxation factor is calculated and correlated to the microstructure change based on MD results. It is found that the vacancy volume relaxation factor is nearly a constant at low to mid-vacancy concentration level, i.e., from 10−6 to 10−3 of the lattice concentrations. However, the volume of vacancies will completely collapse at the high vacancy concentration, and the coalescence of vacancies will form massive dislocations. The simulation results are in good agreement with the existing data from both experiments and simulations in the literature. A uniform empirical equation is developed to obtain the vacancy volume relaxation factor as a function of vacancy concentration. Furthermore, the hydrostatic stress is also calculated based on MD simulations. This paper also discusses the relationship between the vacancy volume relaxation and the diffusion-induced strain, such as in the application of electromigration. For a constrained condition, the hydrostatic stresses obtained from MD-based vacancy volume relaxation and a commonly used stress-vacancy equation are compared. An insight on the critical vacancy concentration at which electromigration failure would occur is discussed in detail.
Original languageEnglish
Article number114127
Number of pages7
JournalMicroelectronics Reliability
Publication statusPublished - 2021


  • Diffusion strain
  • Electromigration
  • Molecular dynamics simulation
  • Vacancy concentration
  • Vacancy volume relaxation


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