Statistical Characterization and Modeling of the Temporal Evolutions of $\Delta V_{\rm t}$ Distribution in NBTI Recovery in Nanometer MOSFETs

NBTI trapped charge characteristics and recovery mechanisms are examined by a statistical study of individual trapped charge emissions in nanoscale HfSiON/metal gate pMOSFETs. We measure individual trapped charge emission times in NBTI recovery in a large number of devices. The characteristic time distributions of the first three emitted holes are obtained. The distributions can be well modeled by using a thermally-assisted tunnel (ThAT) detrapping model. NBTI trapped charge energy and spatial distributions and its activation energy distribution in the ThAT model are discussed and extracted. Based on the ThAT model and measured result of single-charge induced V_t shifts, we develop a statistical NBTI recovery ΔV_t evolution model. Our model can well reproduce the temporal evolutions of a ΔV_t distribution in a number of NBTI stressed nanometer MOSFETs in relaxation.