Coupled Double-Well Model

8.3 Coupled Double-Well Model

Up to now the appearance of oxide traps and interface states was explained by independent processes adding up as the two components which have been empirically introduced in Chapter 4, i.e. the recoverable and the more or less permanent part of the BTI degradation. Results by Grasser et al. indicate that their inducing processes are coupled since their effect cannot be separated by the application of different stress voltages and stress temperatures [134]. By using the basic well-structure of the triple-well model [77], which was already mentioned in Chapter 3.2.1 and is depicted in Fig. 8.3 (left), a new model was introduced consisting of two weakly coupled double-wells [134], cf. Fig. 8.3 (right). During stress holes near the interface can be first trapped to act as a precursor for the creation of an interface state. The corresponding reactions are shown in Fig. 8.3 (right) and are based on an oxygen vacancy and a $Si–H –Si$ bridge, respectively [135, 136]. Upon the existence of $Si–H$ precursors, the second process, i.e. the release of a hydrogen atom, is assumed to be considerably enhanced due to the weaker binding energy of $Si–H$ , compared to that of $Si–H –Si$ ². The resulting dangling bonds are poorly recoverable and so account for the demanded permanent component [134].

Figure 8.3: Top Left: In the triple-well model the second well $V2$ is energetically higher than the first and the third well and forms a transitional saddle point. Bottom Left: Upon the application of stress $V2$ and $V3$ are energetically favored and get filled. Since the barrier between $V2$ and $V3$ is higher than between $V1$ and $V2$ during relaxation (not shown but comparable to top left), transitions from the second well back to the first well are fast, while the third well represents the permanent component/lock-in. Right: In the first step (left double-well) holes are captured at a $Si–H –Si$ bridge or an oxygen vacancy ( $Si–Si$ ) via a thermally activated process. This captured hole then triggers the release of the hydrogen atom which creates a dangling bond (right double-well).

The major improvement of the coupled double-well lies in the thermally activated hole capture process featuring a dispersive process necessary to explain the wide time scales observed in measurements [11, 134]. Moreover, with this model it was possible to explain a huge amount of experimental stress and relaxation data covering various temperatures, stress voltages, and even device technologies. Unfortunately the physical nature of the coupling inbetween the double-wells remains unclear. This is because a model explaining this coupling requires the consideration of the microscopic behavior of defects.

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