### 7.2 States of a Bistable Defect

In the eNMP model, the defects are described by the form of their adiabatic
potentials. Motivated by TDDS and EPR experiments [53, 185, 42], they are
assumed to feature one stable and one metastable configuration. This bistability is
reflected in the double well form of their adiabatic potentials (see Fig. 7.2). Note
that it is the key aspect of the eNMP model since it can give an explanation for
a plenty of challenging experimental observations, addressed later in this
chapter.

The configuration coordinate diagram of such a bistable defect is depicted in
Fig. 7.2. The numbers and denote the positive and neutral charge
state of the defect, respectively, and the metastable states are marked
by additional primes. In the configuration coordinate diagram, there
exist two crossing points, where each of them is related to one of the two
charge transfer reactions and . Their corresponding NMP
barriers
and are derived by evaluating equation (7.17) for the energy
differences

respectively (see Fig. 7.2). The resulting expressions for the NMP barriers read
Inserting them into the equations (7.30) and (7.31) delivers the transition rates
with In order to reduce the number of fitting parameters in the numerical simulations, the
cross sections are expected to be within the same order of magnitude for all
charge transfer reactions and are thus set equal. The field dependence of the charge
transfer reactions and is governed by the relative position of the
‘neutral’ and the ‘positive’ adiabatic potential. When a negative bias is applied to the
gate of a pMOSFET (see Fig. 7.2), the ‘neutral’ potential is raised. As a result, the
barriers and are reduced, which facilitates the charge transfer reactions
and , respectively. Conversely, the transitions and are
slowed down since the corresponding barrier heights and have become
larger. The transitions and are thermally activated and do not vary
with the applied gate bias. According to transition state theory, they can be
expressed as where the barriers are defined as in Fig. 7.2 and stands for the attempt
frequency, which is typically of the order . Using
and , the rates and can be rewritten as
The defect in the eNMP model has a state diagram as shown in Fig. 7.3. With the
rates (7.36)-(7.47), the defect kinetics are described by