A critical analysis of sampling-based reconstruction methodology for dielectric breakdown systems (BEOL/MOL/FEOL)

Abstract

We investigate the validity of the sampling-based reconstruction methodology for its general applications to dielectric breakdown with variability or non-uniformity. For the first time, a sampling-number dependence of reconstructed Weibull slope is reported. Through both experimental studies and Monte Carlo simulation, we confirm the original concept of the reconstructed distribution to represent a distribution as if no thickness/spacing variation as advanced by Roussel et al. [1], by using gate oxides with very tight thickness control. Despite this success, it is unclear whether this methodology can be generally applied to complicated systems such as BEOL and MOL dielectrics with large variation. By comparing two different cases of slightly and highly non-uniform dielectrics, we show that the use of small sampling number can give a false impression of the validity of this reconstruction methodology. Using detailed in-die TBD distributions across entire wafers with extraordinary statistics, we reveal the underlying in-die distributions being bimodal and non-Weibull, and following non-Poisson area scaling, which can be completely masked if not using very large sampling numbers. We demonstrate that reconstruction methodology and time-dependent clustering model yield comparable results when the assumptions of reconstruction methodology can be satisfied. In comparison, time-dependent clustering model is shown to be advantageous due to its simplicity in its implementation and its predictability using small statistics.