Dispersive Transport and Negative Bias Temperature Instability: Boundary Conditions, Initial Conditions, and Transport Models

Negative bias temperature instability (NBTI) has evolved into one of the most serious reliability concerns for highly scaled pMOSFETs. It is most commonly interpreted by some form of reaction-diffusion model, which assumes that some hydrogen species is first released from previously passivated interface defects and then diffuses into the oxide. It has been argued, however, that hydrogen motion in the oxide is trap-controlled, resulting in dispersive transport behavior. This defect-controlled transport modifies the characteristic exponent in the power law that describes the threshold-voltage shift. So far, a number of NBTI models based on dispersive transport have been published. Interestingly, although seemingly based on similar physical assumptions, these models result in different predictions. Most notably, both an increase and a decrease in the power-law time exponent with increasing dispersion have been reported. Also, different functional dependences on the dispersion parameter have been given in addition to differences in the prefactors and the saturation behavior. We clarify these discrepancies by identifying the boundary and initial conditions which couple the transport equations to the electro-chemical reaction at the interface as the crucial component. We proceed by deriving a generalized reaction (dispersive) diffusion formalism and provide the missing link between the various published models by demonstrating how each of them can be derived from this generalized model.