Entire Relaxation

7.5.1 Entire Relaxation

Interestingly, when the ratio $b ∕b 2 1$ of each relaxation curve is plotted over the stress time, the resulting curves are ranked according to their electric field during the stress. In Fig. 7.9 equal $Eox$ conditions at various $tstr$ values are connected for better visibility and are separated by dotted lines for different electric fields. Different $Eox$ values ranging from NBTI with $− 8MV ∕cm$ up to PBTI with $+ 8MV ∕cm$ result in gradually increasing $b2∕b1$ , despite some minor deviations for different device thicknesses. Samples stressed with NBTI feature a $b2∕b1$ smaller or equal to $1$ due to only a small kink or no kink at all, while on the other hand PBTI stress, shows ratios from $1$ up to $20$ .

Figure 7.9: The ratio $b2∕b1$ increases with increasing $tstr$ and $Eox$ ranging from NBTI with $− 8MV ∕cm$ up to PBTI with $+ 8MV ∕cm$ . NBTI-stressed samples with a negative kink feature a ratio smaller or equal to $1$ , whereas PBTI-stressed ones possess values from $1$ up to $20$ . Higher ratios are restricted by the maximum allowed electric field $Eox$ before the oxide breaks down.

Hence, the ratio $b2∕b1$ gives a measure of the symmetricity of the relaxation curve. The ratio indicates which section of the relaxation transient the original experiment recorded. If $b2∕b1 < 1$ , the experiment probed the second half of the S-shape, i.e. the long-term relaxation, which is usually the case after NBTI. For $b ∕b ≈ 1 2 1$ , the “main” part of the relaxation was monitored and both the initial as well as the late relaxation phase contribute to the total recovery to about the same degree.

Modeling the recovery with a single slope, which would then be approximately equal to the geometric mean of $b1$ and $b2$ , clearly obscures the fact that the oxide electric field has an impact not only on the slope, but on the shape of the recovery as well. As depicted in Fig. 7.10, with a mean recovery it is thus only possible to distinguish between the $tstr$ . Moreover, the geometric mean requires symmetricity of the recovery trace, which is only given under moderate stress conditions.

Figure 7.10: Using only a single slope for the recovery characterization obviously eliminates the visible effect of $Eox$ . Hence, the geometric mean of $b1$ and $b2$ is nearly constant for all analyzed devices despite its weak $tstr$ -dependence. This implies that the evaluation of a single slope is not valid for heavier stress conditions because of the asymmetric and limited observation period.

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