Statistical Distribution of Defect Parameters

The statistics of bias temperature instability (BTI) is derived within the “defect-centric” paradigm of device degradation. This paradigm is first briefly reviewed, drawing on similarities between BTI and random telegraph noise (RTN). The impact of a single trap on FET threshold voltage V th is then shown to follow an exponential distribution with the expectation value η. The properties of η, such as its area and gate oxide thickness dependences, are discussed. The statistics of multiple defects is then developed, assuming (1) the single-trap exponential distribution and (2) a Poisson distribution of the number of traps in each device. The properties of the resulting time-dependent total ΔV th statistics and its moments are then treated. Finally, the combined time-dependent and time-zero statistics of the total threshold voltage V th is discussed, together with its properties and a brief example of its implications for circuit performance metrics.

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