Aging statistics based on trapping/detrapping: Silicon evidence, modeling and long-term prediction

The aging process due to Negative Bias Temperature Instability (NBTI) exhibits a significant amount of variability and thus poses a dramatic challenge for long-term reliability prediction from short-term stress measurement. To develop a robust prediction method in this circumstance, this work first collects statistical device data from a 65nm test chip with a resolution of 0.2mV in threshold voltage (Vth) measurement. By comparing model prediction from short-term stress data (<;20k second) with direct long-term measurement (up to 200k second), we conclude that (1) the degradation follows a logarithmic dependence on time, as opposed to the conventional power law; (2) the Reaction-Diffusion (R-D) based tn model significantly overestimates the aging rate and exaggerates its variance; (3) the log(t) model, derived from the trapping/de-trapping (T-D) mechanism, correctly captures the aging variability due to the randomness in number of available traps, and accurately predicts the mean and the variance of Vth shift. These results guide the development of a new aging model for robust long-term lifetime prediction.