A new formulation of breakdown model for high-к/SiO2 stack dielectrics

Unlike previously accepted notions, we present the experimental evidence that the first BD events (TBD) follows a single-Weibull distribution (2-parameters) for high-κ/SiO₂ stack dielectrics using large-sample size experiments and fast-time measurements. It is found that neglecting the initial failure mode can lead to a false bending at low percentiles. In contrast, a bimodality with strong bending in residual time (T_RES=T_FAIL-T_BD) distributions is commonly observed in all cases, suggesting a universal bimodal progressive BD (PBD) distribution which plays a fundamental role in circuit reliability. Using a general Monte Carlo simulator including the multiple-spot competing PBD mode with a 5-parameter model [1] for PBD distribution, we have obtained an excellent agreement by simultaneously fitting three distributions: T_BD, T_RES, and T_FAIL(I_FAIL), thus resolving a wide range of conflicting observations in recent publications in a coherent framework.