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Analysis of multistate models for electromigration failure

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1 Author(s)
Dwyer, V.M. ; Department of Electronic and Electrical Engineering, Loughborough University, Loughborough LE11 3TU, United Kingdom

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The application of a multistate Markov chain is considered as a model of electromigration interconnect degradation and eventual failure. Such a model has already been used [Tan etal, J. Appl. Phys. 102, 103703 (2007)], maintaining that, in general, it leads to a failure distribution described by a gamma mixture, and that as a result, this type of distribution (rather than a lognormal) should be used as a prior in any Bayesian mode fitting and subsequent reliability budgeting. Although it appears that the model is able to produce reasonably realistic resistance curves R(t), we are unable to find any evidence that the failure distribution is a simple gamma mixture except under contrived conditions. The distributions generated are largely sums of exponentials (phase-type distributions), convolutions of gamma distributions with different scales, or roughly normal. We note also some inconsistencies in the derivation of the gamma mixture in the work cited above and conclude that, as it stands, the Markov chain model is probably unsuitable for electromigration modeling and a change from lognormal to gamma mixture distribution generally cannot be justified in this way. A hidden Markov model, which describes the interconnect behavior at time t rather than its resistance, in terms of generally observed physical processes such as void nucleating, slitlike growth (where the growth is slow and steady), transverse growth, current shunting (where the resistance jumps in value), etc., seems a more likely prospect, but treating failure in such a manner would still require significant justification.

Published in:

Journal of Applied Physics  (Volume:107 ,  Issue: 3 )