Charge Trapping and Variability in CMOS Technologiesat Cryogenic Temperatures

3.3 4-State Nonradiative Multiphonon Model

The 2-state NMP theory is very efficient for describing BTI on large-area devices, where large ensembles of defects are simultaneously active. However, when looking at the single defect level (RTN, TDDS), there are certain
phenomena which can not be explained with 2 states. A prime example for failing of the 2-state model is the observation of anomalous RTN (aRTN), in which the RTN signal is interrupted for longer periods of time [118].
This behavior can only be explained by introducing an additional third state [194]. As can be seen in Fig. 3.14, a defect captures
and emits a charge with a high frequency transitioning between state 1 and 2. After a certain time, a transition between state 2 and happens and the defect stays for a comparably long period in state .

This observation combined with the knowledge from DFT simulations (see Section 2) motivates the introduction of the 4-state NMP
model. Additionally to the two stable states 1 and 2 which occur in 2-state NMP theory, two additional meta-stable states and are introduced. A direct transition from one stable state to the other stable state is only possible via one of the two meta stable states or , see Fig. 3.15. Analogously to the stable states, one-meta stable state is neutral while the second meta-stable
state is charged. The transition between a neutral and a charged state, which would be the transitions and in Fig. 3.15 are modeled using NMP transition rates, while transitions between a state and the meta-stable state with
the same charge and are thermal transitions which are described within classical transition state theory leading to transition rates of the form where is a constant, i.e. gate voltage independent barrier.

Using the more complex potential energy surfaces shown in Fig. 3.15 allows to express the four NMP and the four thermal
transition rates as shown in [174]. This rates allow obtaining the overall capture and emission time from one stable state to the other. Using Markov theory, the probability of a defect to be in state can be derived enabling reliability simulations.