Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures
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Author(s)
Le, Jia-Liang
Bazant, Zdenek P.
Bazant, Martin Z.
Date Issued
November 2009
Journal
Journal of Applied Physics
Publisher
American Institute of Physics
Citation
Le, Jia-Liang, Zdeněk P. Bažant, and Martin Z. Bazant. “Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures.” Journal of Applied Physics 106.10 (2009) : 104119. © 2009 American Institute of Physics
Version
Final published version
Abstract
The two-parameter Weibull distribution has been widely adopted to model the lifetime statistics of dielectric breakdown under constant voltage, but recent lifetime testing for high-k gate dielectrics has revealed a systematic departure from Weibull statistics, evocative of lifetime statistics for small quasibrittle structures under constant stress. Here we identify a mathematical analogy between the dielectric breakdown in semiconductor electronic devices and the finite-size weakest-link model for mechanical strength of quasibrittle structures and adapt a recently developed probabilistic theory of structural failure to gate dielectrics. Although the theory is general and does not rely on any particular model of local breakdown events, we show how its key assumptions can be derived from the classical dielectric breakdown model, which predicts certain scaling exponents. The theory accurately fits the observed kinked shape of the histograms of lifetime plotted in Weibull scale, as well as the measured dependence of the median lifetime on the gate area (or size), including its deviation from a power law. The theory also predicts that the Weibull modulus for breakdown lifetime increases in proportion to the thickness of the oxide layer and suggests new ideas for more effective reliability testing.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1063/1.3256225
