The cumulative distribution of the failure time, which includes the time to first breakdown (BD) and the progressive current growth time, is the function of interest for reliability of ultrathin gate oxides. Depending on oxide area and stress conditions, oxide failure is determined by a single BD spot or by multiple competing spots. In this letter, we present an analytical compact model for the final failure distribution which is valid for any failure percentile and which is applicable to both the single and the multiple BD spot limits. This model is intended to be the core of a reliability assessment methodology either for the SiO 2 -based or high-k gate insulators of interest for the hp45 technology node and beyond.
The breakdown of high-K (HK) stack gate dielectrics is shown to be analogous to the failure of ultrathin SiO2-based oxides showing progressive breakdown. The breakdown of a HK stack is shown to occur in two phases. First, one or several percolation paths are formed in the SiO2-based interfacial layer. Then, these partial breakdowns propagate into the HK through defect generation in this layer. This propagation phase is equivalent to the progressive breakdown local degradation phenomenon. As a consequence of this analogy, the reliability assessment tools developed for ultrathin single-layer oxides can also be used without significant changes to assess the reliability of HK stacks. This analogy is so strong that the experimental distinction between HK propagation and conventional progressive breakdown appears to be rather difficult. However, the residual time distribution from first breakdown to final oxide failure is shown to be significantly different for both processes at low failure percentiles. This has allowed us to obtain experimental evidence of HK propagation (as opposed to conventional progressive breakdown effects) in relatively thick Hf-based gate stacks where the detection of first BD appears to be feasible.
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