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13.3 Permanent Component and the Hydrogen Release Model

So far the recoverable component of BTI has been successfully explained using the four-state NMP model. For simplicity, the DW model had been used to describe (math image). Although the latter explains the limited amount of experimental data available at that time, it does not rely on a correct physical mechanism. In order to provide a accurate description of the permanent threshold voltage shift the HR model has been introduced. The HR model relies on chemical reactions between H atoms with defects and hydrogen transport through the oxide. These mechanisms are supported by DFT calculations.

At the beginning (math image) is studied on a large-area pMOSFET subjected to zero volt at all four terminals of the transistor, \( \VD =\VG =\VS =\VB =\SI {0}{\volt } \). Subsequently, (math image) sweeps are recorded and (math image) extracted. Quite remarkably, a drift of (math image) was found over several days, see Figure 13.7.

(image)

Figure 13.7:  Even at zero volt applied at all terminals the permanent (math image) of the pMOSFET drifts slowly. At higher temperatures the accumulation of (math image) is accelerated. The lines are calculated based on normally distributed activation energies [188, MWC6].

At higher temperatures (math image) gets more pronounced, a consequence of newly created defects. Note, during fabrication a forming gas anneal process step with a duration of typical \( t\approx \SI {30}{\minute } \) at \( T\approx \SI {400}{\second } \) is performed. Compared to the time scale of defects determining P, several days up to months, see Figure 13.7, the annealing step is an order of magnitude smaller. Furthermore, earlier publications assumed that (math image) simply to be baked “away” at higher \( T \). This notion has to be carefully reconsidered, since also at zero bias a significant amount of (math image) is accumulated, albeit on a very large time scale.

Figure 13.8 shows the characteristics of (math image) extracted from our first long exploratory time experiment.

(image)

Figure 13.8:  During the long term experiment the stress voltage and the temperature is varied. To measure the (math image) sweeps and analyze (math image), the temperature was switched back to \( T=\SI {200}{\celsius } \). During stress phases with \( \VGStress =\SI {-1.5}{\volt } \) (B,D, and F) a lot of new defects are created and thus (math image) increases. In contrast, (math image) only changes slightly at cycles A,C, and E where \( \VGStress =\SI {0}{\volt } \). During phases G and I a considerable reduction of (math image) is visible. At the end of the cycles the latter shows a slightly higher (math image) due to additional defects with very long time constants created in phase H. First, the HR model is evaluated considering a fixed total number of reactive H atoms (blue dashed). As can be seen, phase F, where a large number new defects are created, is not covered by this model. Next, the HR model considers an H\( _2 \) reservoir located at the gate side. With this extension the HR model explains the behavior of (math image) in all phases well [MWC6].

A single large-area pMOSFET has been probed for sixty days. The stress bias was switched between \( \VGStress =\SI {0}{\volt } \) and \( \VGStress =\SI {-1.5}{\volt } \) while the device temperature was changed to \( \SI {250}{\celsius } \), \( \SI {300}{\celsius } \) and \( \SI {350}{\celsius } \). After each stress cycle the temperature is switched back to \( \SI {200}{\celsius } \) where the (math image) sweeps are recorded. From each voltage sweep cycle a new (math image) is obtained. Figure 13.8 clearly shows a large increase in (math image) during the stress phases with \( \VGStress =\SI {-1.5}{\volt } \). In contrast, when \( \VGStress =\SI {0}{\volt } \) is applied, (math image) changes only slightly. The characteristics of (math image) recorded over several month can be nicely explained by the HR model.

A second long-term experiment has been performed on a virgin pMOSFET with dimensions \( W=L=\SI {10}{\micro \meter } \). This time the stress bias of \( \VGStress =\SI {-1.5}{\volt } \) is applied during \( T=\SI {300}{\celsius } \) cycles. Again, (math image) is extracted from 20 (math image) sweeps performed at \( T=\SI {200}{\celsius } \). Figure 13.9 shows the characteristics of (math image) recorded from measurements during 90 days.

(image)

Figure 13.9:  The second long term experiment is performed with alternating \( \VGStress =\SI {-1.5}{\volt } \)/\( T=\SI {300}{\celsius } \) and \( \VGStress =\SI {0}{\volt } \)/\( T=\SI {350}{\celsius } \) cycles. During phase B a lot of (math image) is built up and saturates, however, during the subsequent phase C all these defects can get neutralized and (math image) is settled at the same level as in phase A. Next, during phase E and F a small number of new defects are created. Furthermore, a reversal of the degradation has been observed during E and F. During the stress cycle H performed at \( \VGStress =\SI {-1.5}{\volt } \)/\( T=\SI {300}{\celsius } \) many new defects are created. As can be seen, the HR without H\( _2 \) reservoir can not reproduce the experimental data, however, by considering the proposed H\( _2 \) reservoir the HR model covers the behavior of (math image) [MWC6].

Quite remarkably, although the device is heavily stressed during phase D, the permanent component decreases. This degradation reversal behavior is due to defects with an energy level close to the valence band edge which are annealed in phase B and can not be recharged again during phase D. Except for the degradation reversal, which requires closer inspection, the HR model again is able to explain the experimental data very well.

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