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

Abstract

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 T63) and area scaling characteristics of reconstructed Weibull distributions along with T63 variation (σT63) 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 σT63, 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 T63 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 VBD results can provide misleading conclusions due to the different scaling property of variance in Vbd and Tbd in use of reconstruction methodology.