Due to the thinning of the insulating layers and the increase of the electric field inside the devices used in modern CMOS technology, understanding reliability issues such as Negative Bias Temperature Instability (NBTI) and Hot-Carrier Injection (HCI) has gained considerable importance. Many investigations have identified the omnipresent hydrogen as one of the major proponents in these phenomena. Although the exact nature of the involvement of hydrogen has not been unequivocally identified, it appears that the ability of hydrogen to passivate and depassivate silicon dangling bonds is of utmost importance. Once the hydrogen is released from the dangling bond, it diffuses away, and many publications show that this diffusion is non-classical. This is due to the ability of hydrogen to form various bonding configurations associated with a broad distribution of bonding energies, which slows down the effective diffusivity. This kind of transport is also referred to as dispersive transport in literature.
Some recent publications have included this dispersive behavior into NBTI models, thereby modifying our understanding of the time evolution of the degradation compared to the classic reaction-diffusion model. Interestingly, although based on apparently similar assumptions, like depassivation of interface states and dispersive diffusion of protons, these models suggest completely different and contradictory influences of the dispersive diffusion on the overall model behavior. In order to clarify these discrepancies, the coupling of the dispersive transport equations to the possible bonding configurations at the interface has been studied in detail. Furthermore, the different initial conditions assumed for the passivation and depassivation kinetics of the dangling bonds and the different interpretations of how these bonds are active in electrical measurements contribute significantly to the different model predictions. A generalized model has been developed which contains the previously published models as special cases.