3.1.1 Stress Phase

As long as the bond-breaking dominates the rate equation, the reverse rate is negligible because there is simply not enough free hydrogen. Thus the degradation within this initial stress phase is only proportional to the stress time tstr   .

Once the interface reaction reaches equilibrium, the previously released hydrogen species diffuse towards the oxide. Under the assumption of a well passivated interface with only a few initial dangling bonds Nit,0   and atomic hydrogen H0   as diffusion species the diffusion-limited stress regime can be approximated by a power-law of the form 1∕4
tstr   . The mathematics behind this diffusion-limited process can be found in Appendix C.

However, not all measurement results are consistent with the predictions of the reaction-diffusion theory using atomic hydrogen. Quite to the contrary, the extracted exponents were found to depend on the measurement delay time; the exponents of 1∕4  were obtained for measurement data with large delay time only [759]. Shorter delay times on the other hand yielded exponents of around 1∕6  . Chakravarthi et al. now interpreted this weaker time dependence by introducing instant dimerization of the released atomic hydrogen at the interface via  0
H   +   0
H   ⇌ H2   and subsequent diffusion of the created H2   [60]. This theoretical assumption yields a smaller exponent of approximately 1∕6  because of the larger kinetic exponent (a = 2  for H2   instead of a = 1  for H0   , cf. Appendix C). When performing even faster measurements with delay times around a micro-second, e.g. OTF-measurements done by Reisinger et al., exponents of 0.12  were obtained [12] which does not correspond to the stress behavior predicted by the reaction-diffusion theory.