Analytical long-term NBTI recovery model with slowing diffusivity and locking effect of hydrogen considered

The NBTI degradation caused by hole trapping in gate insulator process-related preexisting traps (∆ VHT) and in generated bulk insulator traps (∆ VOT) can recover in several seconds (< 10 s), whereas the long-term recovery is dominated by interface trap generation (∆ VIT). In this paper, various explanations of NBTI recovery have been reviewed and a compact analytical long-term NBTI recovery model in which the slowing down diffusivity and locking effect of H2 are involved has been derived. The triangular diffusion profile of H2 is approximated and the fitting coefficient ξ of slowing down diffusivity is related to the stress and recovery time. Our proposed model has been validated by the previous theories and numerical calculation. Moreover, the investigation of NBTI recovery on a 40-nm CMOS process has been experimentally carried out and the results show that our compact NBTI recovery model can describe the long-term recovery well.