Statistics of competing post-breakdown failure modes in ultrathin MOS devices

The statistical analysis of the time elapsed from first oxide breakdown to device failure (residual time) reveals that the distinction between hard breakdown (HBD) and soft breakdown (SBD) is meaningful for ultrathin oxides down to 1 nm. It also shows that the growth of the HBD current is progressive. Thus, the HBD prevalence ratio picture of post-breakdown reliability is generalized to include the HBD progressiveness. Moreover, it is shown that the statistics of residual time cannot be quantitatively understood unless the SBD mode is considered to be unstable and to finally cause the device failure. As a consequence, a worst case criterion is used to combine these two failure modes (unstable SBD and progressive HBD) into a global post-breakdown cumulative failure function. This combined approach is shown to be a valuable tool to interpret a broad range of apparently dissimilar experimental results in devices with gate oxides ranging from 2.7 to 1 nm. The existence of two post-breakdown failure modes highly complicates the complete characterization of the post-breakdown relevant magnitudes and introduces extra difficulties for the reliable extrapolation of reliability data to operation conditions and low failure percentiles. It is found that ultrathin oxides as thin as 1 nm show essentially the same post-breakdown phenomena as oxides above 2 nm. However, unstable SBD is found to have a more severe impact on the failure of these ultrathin oxides.