1 / 19

On-Off Intermittency and Criticality in Early Stage Electromigration

On-Off Intermittency and Criticality in Early Stage Electromigration. Wouter Arts Peter Koelman. Index. General introduction Introduction to intermittency Theoretical statistical behavior Numerical simulations Real life situation Comparison Conclusion. General introduction.

lethia
Télécharger la présentation

On-Off Intermittency and Criticality in Early Stage Electromigration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On-Off Intermittency and Criticality in Early Stage Electromigration Wouter Arts Peter Koelman

  2. Index • General introduction • Introduction to intermittency • Theoretical statistical behavior • Numerical simulations • Real life situation • Comparison • Conclusion Chaos - 3T220

  3. General introduction • Article: On-Off Intermittency and Criticality in Early Stage Electromigration • By: Eric Dalton, Ian Clancy, David Corcoran, ArousianArshak and George Gooberman • Main focus on on-off intermittency Chaos - 3T220

  4. Introduction to intermittency • Logistic map: • Three times iterated • Characterized by laminar/turbulent region Chaos - 3T220

  5. Chaos - 3T220

  6. Noise driven logistic map • Use of multiplicative noise: • Additive noise • Used in article Chaos - 3T220

  7. Statistical behavior • Three characteristic statistical properties: • Theoretically derived: • Critical value of stability is e • PDF of return time to turbulent phase is a power law of: • Simulated: • PDF of return time • Fractional resistance change has a power law of: Chaos - 3T220

  8. Criticality • Noise-driven logistic map: • Taking the natural logarithm, this can be written as: • Critical value if • Substituted • Thus Chaos - 3T220

  9. Power law • PDF of the length of the laminar phase • Laminar phase: Chaos - 3T220

  10. Power law • This set can be rewritten using the following notation: • The set of the laminar phase becomes: • Shifting the origin: • The chance of finding a certain length: Chaos - 3T220

  11. Power law • Around criticality the noise is logarithmic additive: • This leads to the simplification of: • Direct substitution: • This function is solved in an article by Heagy et al. The solution is proportional to: Chaos - 3T220

  12. Numerical simulations • PDF of return time • Theory reasonably well of Chaos - 3T220

  13. Numerical simulations • Probability density of change (Δx) • Close to theoretical prediction of Chaos - 3T220

  14. Real life situation • Article: Early stage electromigration • Short bursts of fractional resistance change • Signal is intermittent • Statistics experimentally derived • Statistics compared to simulations and theory Chaos - 3T220

  15. Comparison Article Our simulation Chaos - 3T220

  16. Comparison Article Our simulation Chaos - 3T220

  17. Conclusion • Numerical simulations made of intermitted signal • Theoretical derivation made of return time • Statistics derived with simulations • Numerical simulation closely match theoretical predictions and experimental data • No theoretical prediction could be made of probability density of change (Δx) Chaos - 3T220

  18. Reference List • C. Toniolo, A. Provenzale, and E.A. Spiegel, Phys. Rev. E 66, 066209 (2002). • J.F. Heagy, N. Platt, and S.M. Hammel, Phys. Rev. E 49, 1140 (1994) Chaos - 3T220

  19. The End • Questions? Chaos - 3T220

More Related