The ReactionDiffusion (RD) model for the Negative Bias Temperature
Instability (NBTI) of MOS transistors is still popular amongst reliability
engineers for the interpretation of experimental data. This popularity comes
mainly from its intuitive concept and the straightforward prediction of the
observed powerlaw degradation. The model accounts the dominant part of the
longterm NBTI induced degradation to silicon dangling bonds at the
semiconductoroxide interface. These dangling bonds are formed during the
oxidation and are passivated by hydrogen in the manufacturing process. The RD
model assumes that the NBTI stress causes a depassivation of the silicon
dangling bonds while concurrently liberating hydrogen atoms at the
SiSiO2 interface. The liberated hydrogen atoms form H2 and diffuse into the
oxide. In order to explain the powerlaw degradation, one has to assume that
the diffusive flux of hydrogen molecules away from the interface determines
the macroscopically observed degradation.
In its standard formulation, the RD model is described macroscopically, using
a reaction rate equation and diffusion equations. We have developed an
atomistic version of the RD model based on the chemical master equation of
stochastic chemistry, which accounts for the granularity of the diffusing
hydrogen atoms and molecules. Initial comparisons of the microscopic and the
macroscopic RD model showed large differences between the predicted
degradation curves, with the microscopic RD model showing a delay in the onset
of the experimentally important powerlaw regime that is not obtained from the
macroscopic model. These differences could be traced back to the inappropriate
representation of the bimolecular reactions (repassivation and dimerization)
in the macroscopic RD model. As NBTI degradation usually resembles a
powerlaw over the whole measurement window, a delayed onset of this regime is
incompatible with the experimental data. The magnitude of the powerlaw delay
strongly depends on the parameters of the model and the microscopic topology
of the host material. Our initial calculations were based on a parameter set
that was designed to study the basic model behavior and was not related to
experimental data. In order to investigate the microscopic model in a more
realistic context, we have repeated this comparison based on a published
parameter set that has been calibrated to an NBTI degradation measurement.
The straightforward application of this parameter set in our microscopic RD
model results in a degradation that strongly deviates from the macroscopic prediction
over the whole simulation range (see figure). The powerlaw regime is shifted
far beyond the measurement window and is in stark contrast to the experimental data. Furthermore, it is not
possible to explain the experimental data using the microscopic RD model with
a physically reasonable parameter set. These findings support our previous
conclusions that the RD mechanism in its usually proposed
form is physically inconsistent and that the RD model for NBTI
is either incomplete or incorrect.
