Statistical mechanics based model for negative bias temperature instability induced degradation

Abstract

A physics based model for negative bias temperature instability (NBTI) induced degradation is proposed. Like previous models, this model attributes NBTI to depassivation of Si–H bonds at the SiO2∕Si interface. The two distinguishing features of the proposed model are: (i) statistical mechanics is applied to calculate the decrease in interfacial Si–H density as a function of stressing conditions, and (ii) hydrogen diffusion in the oxide is assumed to be dispersive and the diffusing species is identified with the positively charged hydrogen ion (Hi+). The model assumes that as Hi+ diffuses away from the interface into the oxide, interfacial and bulk traps are created. Based on these model assumptions, an equation for the threshold voltage shift (ΔVt) is derived as a function of stressing time, oxide field, temperature, oxide thickness, and initial Si–H density at the interface. The model predicts that ΔVt would increase with a power law dependence at earlier stressing times and would saturate at longer times. The power law increase at earlier stress times is attributed to dispersive hydrogen diffusion and ΔVt saturation at longer stress times is ascribed to occur when all bonded hydrogen (Si–H) has been removed from the interface. These and other model predictions are verified using published NBTI data from various research groups for p-channel field effect transistors (pFETs). In addition, the model is shown to be compatible with NBTI data for HfO2 pFETs.