Skip to main content

Advertisement

SpringerLink
Log in

Effect of Electric Current on Trijunction Equilibrium and Grain Rotation of Lossy Dielectrics

  • Published:
Journal of Electronic Materials Aims and scope Submit manuscript

Abstract

To understand the structural stability of lossy dielectrics under the action of an electric current, the effect of an electric current on the stress evolution, the change of chemical potential, and the electric energy stored in a grain boundary is examined. Analytical forms of the stress, chemical potential, and electric energy are obtained, which depend on the current density. The concept of an apparent grain boundary energy, which is a linear function of the square of the current density, is introduced. One needs to use the apparent grain boundary energy in analyzing the equilibrium state of a trijunction. An expression for the rate of grain rotation is proposed, which includes the contributions of the change of chemical potential and the electric energy in grain boundaries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. D’Haen, P. Cosemans, J.V. Manca, G. Lekens, T. Martens, W. De Ceuninck, M. D’Olieslaeger, L. De Schepper, and K. Maex, Microelectron. Reliab. 39, 1617 (1999).

    Article  Google Scholar 

  2. J. Bohm, C.A. Volkert, R. Monig, T.J. Balk, and E. Arzt, J. Electron. Mater. 31, 45 (2002).

    Article  Google Scholar 

  3. Y. Jung and J. Yu, J. Appl. Phys. 115, 083708 (2014).

    Article  Google Scholar 

  4. S. Kumar, J. Smetana, D. Love, J. Watkowski, R. Parker, and C.A. Handwerker, J. Electron. Mater. 40, 2415 (2011).

    Article  Google Scholar 

  5. C.A. Pico and T.D. Bonifield, J. Mater. Res. 6, 1817 (1991).

    Article  Google Scholar 

  6. S.M. Kuo and K.L. Lin, J. Electron. Mater. 36, 1378 (2007).

    Article  Google Scholar 

  7. G.C. Xu, H.W. He, and F. Guo, J. Electron. Mater. 38, 273 (2009).

    Article  Google Scholar 

  8. A.T. Wu, A.M. Gusak, K.N. Tu, and C.R. Kao, Appl. Phys. Lett. 86, 241902 (2005).

    Article  Google Scholar 

  9. G.F. Zhao, M. Liu, Z.N. An, Y. Ren, P.K. Liaw, and F.Q. Yang, J. Appl. Phys. 113, 183521 (2013).

    Article  Google Scholar 

  10. A.T. Wu, K.N. Tu, J.R. Lloyd, N. Tamura, B.C. Valek, and C.R. Kao, Appl. Phys. Lett. 85, 2490 (2004).

    Article  Google Scholar 

  11. B.C. Valek, J.C. Bravman, N. Tamura, A.A. MacDowell, R.S. Celestre, H.A. Padmore, R. Spolenak, W.L. Brown, B.W. Batterman, and J.R. Patel, Appl. Phys. Lett. 81, 4168 (2002).

    Article  Google Scholar 

  12. A.S. Budiman, W.D. Nix, N. Tamura, B.C. Valek, K. Gadre, J. Maiz, R. Spolenak, and J.R. Patel, Appl. Phys. Lett. 88, 233515 (2006).

    Article  Google Scholar 

  13. K. Chen, N. Tamura, B.C. Valek, and K.N. Tu, J. Appl. Phys. 104, 013513 (2008).

    Article  Google Scholar 

  14. S. Kumar, M.T. Alam, Z. Connell, and M.A. Haque, Scripta Mater. 65, 277 (2011).

    Article  Google Scholar 

  15. J.C.M. Li, J. Appl. Phys. 33, 2958 (1962).

    Article  Google Scholar 

  16. G. Herrmann, H. Gleiter, and G. Baro, Acta Metall. Mater. 24, 353 (1976).

    Article  Google Scholar 

  17. D. Moldovan, V. Yamakov, D. Wolf, and S.R. Phillpot, Phys. Rev. Lett. 89, 20601 (2002).

    Article  Google Scholar 

  18. J.F. Nye, Physical Properties of Crystals (New York: Oxford University Press, 1985).

    Google Scholar 

  19. D.C. Dube and A.K. Saraswat, J. Appl. Phys. 53, 7095 (1982).

    Article  Google Scholar 

  20. F.Q. Yang and J.C.M. Li, J. Appl. Phys. 74, 4382 (1993).

    Article  Google Scholar 

  21. J.D. Verhoeven, Fundamentals of Physical Metallurgy (New York: Wiley, 1975).

    Google Scholar 

  22. P.G. Shewmon, in Recrystallization, Grain Growth and Textures (Metals Park, OH: Am. Soc. for Metals, 1966), pp. 165.

Download references

Author information

Authors and Affiliations

  1. Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY, 40506, USA

    Fuqian Yang

Authors
  1. Fuqian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fuqian Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, F. Effect of Electric Current on Trijunction Equilibrium and Grain Rotation of Lossy Dielectrics. J. Electron. Mater. 43, 4497–4501 (2014). https://doi.org/10.1007/s11664-014-3445-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11664-014-3445-2

Keywords

Search

Navigation