Model of the negative-bias temperature instability of $p$-MOS transistors

A new quantitative model of the negative-bias temperature instability (NBTI) of $p$-MOS (metal-oxide-semiconductor) transistors is developed. The model is based on the reaction of the depassivation of surface states at the Si–SiO$_2$ interphase boundary (IPB) and hydrogen-containing hole traps near the Si–SiO$_2$ IPB by positively charged hydrogen ions H$^+$, accumulated in the $p^+$-type inversion layer of the silicon substrate. The dependences of the surface and space charges in $p$-MOS transistors on the NBTI time are controlled by the kinetics of H$^+$-ion diffusion and drift from the silicon substrate to the Si–SiO$_2$ IPB. The effect of the gate voltage on the NBTI is explained by the effect of the electric-field strength on the H$^+$ ion segregation coefficient at the Si–SiO$_2$ IPB. The relaxation of positive space charge introduced into the gate dielectric during NBTI is described by the tunnel discharge of oxide traps by silicon-substrate electrons.