Fundamental statistical properties of reconstruction methodology for TDDB with variability in BEOL/MOL/FEOL applications

In this work, we investigate the validity of the so-called big-data deconvolution approach with its use of sampling-based reconstruction methodology for general applications to BEOL and MOL dielectrics with substantial non-uniformity and multiple variability sources. Unlike conventional statistical sampling, we have found that all parameters (β and T
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) and area scaling characteristics of reconstructed Weibull distributions along with T
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variation (σT
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) across the sampling units (chips or dies) show a strong dependence on sampling number per unit (chip). We developed the statistical theory to correctly characterize the sampling number dependence of reconstructed Weibull slope and σT
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, including a criterion for the general applicability of the sampling-based reconstruction methodology. We have examined why the big-data deconvolution approach cannot be used for BEOL/MOL dielectrics with multiple variability sources. The sampling-number dependence of reconstructed T
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fundamentally nullifies the feasibility of this approach while sampling-number dependence of area scaling should be always demonstrated prior to the use this methodology. Finally, we show that V
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results can provide misleading conclusions due to the different scaling property of variance in Vbd and Tbd in use of reconstruction methodology.