Extreme-Value Statistics and Poisson Area Scaling With a Fatal-Area Ratio for Low- k Dielectric TDDB Modeling

During the study of time-dependent dielectric breakdown (TDDB) of back-end-of-line low- k dielectrics, accurate statistical and area-scaling models are important for the final reliability lifetime projection. The extrapolated product lifetime from high percentiles to low percentiles has strong depen...

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Bibliographic Details
Published in:IEEE transactions on electron devices 2011-09, Vol.58 (9), p.3089-3098
Main Authors: Fen Chen, Shinosky, M. A., Aitken, J. M.
Format: Article
Language:English
Subjects:
Back-end-of-line (BEOL) process integration
Capacitance
Capacitors
Chips
Cu-interconnect reliability
Electric breakdown
Extrapolation
fatal-area ratio
Law
Life cycle assessment
low- k reliability
low- k TDDB Weibull distribution
low- k time-dependent dielectric breakdown (TDDB)
Mathematical models
metal-area scaling
Poisson area scaling
Product life cycle
Projection
Reliability
Shape
shift and compare (S&C)
Statistical analysis
Weibull distribution
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Summary:During the study of time-dependent dielectric breakdown (TDDB) of back-end-of-line low- k dielectrics, accurate statistical and area-scaling models are important for the final reliability lifetime projection. The extrapolated product lifetime from high percentiles to low percentiles has strong dependence on the choice of a statistical model. Meanwhile, the lifetime of a product chip is obtained typically by extrapolating TDDB data from small test structures to large chip areas by an area-scaling law. In this paper, a thorough investigation of low- k TDDB statistical distribution with large sample size and various metal areas was conducted to validate a physically relevant statistical model for low- k TDDB modeling. In addition, we explored the various TDDB dependence on metal area and introduced a new fatal-area-ratio concept for low- k TDDB area-scaling model in the event that the conventional Poisson area-scaling law failed based on the as-designed area ratio. A graphic shift-and-compare method was then developed to determine, experimentally, the fatal-metal-area ratio. The determination of the fatal-metal-area ratio should be critical for an accurate low- k TDDB lifetime projection and process assessment.
ISSN:0018-9383
1557-9646
DOI:10.1109/TED.2011.2159120