Compact modeling of statistical BTI under trapping/detrapping

The aging process due to negative bias temperature instability (NBTI) is a key limiting factor of circuit lifetimes in CMOS design. Recent NBTI data exhibits an excessive amount of randomness and fast recovery, which are difficult to be handled by conventional power-law model (tn). Such discrepancies further pose the challenge on long-term reliability prediction under statistical variations and dynamic voltage scaling (DVS) in real circuit operation. To overcome these barriers, this paper: 1) practically explains the aging statistics due to randomness in number of traps with the log(t) model, accurately predicting the mean and variance shift; 2) proposes cycle-to-cycle model (from the first principles of trapping) to handle aging under multiple supply voltages, predicting the nonmonotonic behavior under DVS; 3) presents a long-term model to estimate a tight upper bound of dynamic aging over multiple cycles; and 4) comprehensively validates the new set of aging models with 65-nm statistical silicon data. Compared with previous models, the new set of aging models capture the aging variability and the essential role of the recovery phase under DVS, reducing unnecessary guard banding during the design stage.