3.2.1 Dispersive-Reaction-Rate Models

Due to the amorphous structure of the interface, the binding energy of the Si–H  -bonds at the interface is not constant but varies from site to site. Electron-spin-resonance (ESR) studies revealed the binding energies as distributed Gaussian with a variance of 0.02 − 0.08eV  [70], i.e. weaker bonds break first, while stronger bonds remain passivated. Longer stress times or a larger applied electric field are required to break those stronger bonds [71].

Charge pumping (CP) as the measurement of choice for the assessment of the amount of interface states (cf. Chapter 2.4) revealed some interesting facts. The observed amount of recovering interface states accessed via CP after NBTI stress was too small to be able to explain the overall recovery of ΔVTH   . Therefore a part of the community [62727374] considered the generated interface states as permanent once created. This assumption will be discussed in Chapter 8.

Quite in contrast, Mahapatra et al. stated that CP measurements in the range of seconds are too slow to detect the recovery of interface states because of inherent delay of the measurement setup. Another possibility to explain the missing recovery involves the CP technique itself, as it pulses into accumulation which in turn causes unwanted additional relaxation [75].

In order to clarify the issue of how interface states contribute to recovery, Li et al. developed the on-the-fly fast interface trap CP method (OFIT) [5125], described in Chapter 2.5. Based on the results of this OFIT method [512476], which showed recovery faster than a second, but also revealed long-term recovery, Grasser et al. derived a BTI-model based on interface states only in [77]. Therein they describe two distinct components of the recovery as two facets of a single degradation mechanism proceeding as a series of steps. By assuming dissociation of Si–H  bonds (dispersive bond breaking) the so-called double-well (and subsequently refined triple-well) model is able to describe quite complex stress-relaxation-patterns. Though the mathematics in this model describe the NBTI phenomenon correctly, its microscopic assumptions are likely unjustified [78], an issue that will be examined in detail in Chapter 5.