An existing cell-based percolation model with parameter correlation can find its potential applications in assessing soft-breakdown (BD) statistics as long as the oxide thinning due to the localized physical damage near the SiO2/Si interface is accounted for. The resulting model is expressed explicitly with the critical trap number per cell nBD and the remaining oxide thickness t′OX both as parameters. Reproduction of time-to-bimodal (soft- and hard-) breakdown statistical data from 3.3-nm-thick gate-oxide samples yields nBD of 3 and 4 for soft and hard breakdown, respectively. The extracted t′OX of 1.0 nm for soft breakdown, plus the transition layer thickness of 0.5 nm in the model, is fairly comparable with literature values from current-voltage fitting. The dimension and area of the localized physically damaged region or percolation path (cell) are quantified as well. Based on the work, the origins of soft and hard breakdown are clarified in the following: (i) soft breakdown behaves intrinsically as hard breakdown, that is, they share the same defect (neutral trap) generation process and follow Poisson random statistics; (ii) both are independent events corresponding to different t′OX requirements; and (iii) hard breakdown takes place in a certain path located differently from that for the first soft breakdown.
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