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8.2 Frequency Dependence of the Transition Times

To study the frequency dependence of the transition time, the DC stress signal of the conventional TDDS is replaced by an AC stress signal, see Figure 8.16.

(image)

Figure 8.16:  (top) During AC BTI stress the gate bias switches between (math image) and (math image) with the signal frequency \( f \). (bottom) From the two-state perspective, the occupancy of the defect on depends effective stress time \( \tStressEff \) which is the product between the duty cycle and total stress time. In the underlying case, the defect has a similar capture and emission time which are larger than \( 1/\fs \). Otherwise the defect will be either be permanently charged or discharged during the AC stress cycle.

The capture probability of the defect, that is the defects occupancy during the stress cycle, increases during the high cycles and decreases during the low cycles of the AC signal. From the two-state perspective, the capture probability only depends on the effective stress time \( \tStressEff =\alpha \tStress \), which is primarily determined by the duty cycle \( \alpha \) of the AC stress signal and the overall stress time \( \tStress \). Thus the two-state model does not implicate any frequency dependency of the charge capture and emission times. However, by performing AC stress experiments defects have been found which show frequency dependent capture times, see Figure 8.17.

(-tikz- diagram)

Figure 8.17:  (a) The conventional DC TDDS is used to identify four defects, namely A1 to A4. (b-d) By increasing the frequency of the AC stress signal it is observed that the clusters of defects A3 and A4 become fainter. Thus these defects show a visible dependence on the frequency of the AC stress signal which can be explained by an increase of the capture time at higher frequencies. Such a behavior cannot be explained using a two-state model [MWC25].

The defects A1 and A2 visible in the spectral maps do not show any frequency dependence because they have a capture time below \( \tauc <\SI {10}{\micro \second } \), which is shorter than the AC stress pulse width. In contrast, the clusters for the defects A3 and A4 become fainter with increasing frequency. This can be explained with increased capture times at higher frequencies which leads to a reduced capture probability at the end of the AC stress cycle. Quite remarkably, the frequency dependence of the capture times can be nicely reproduced by the four-state NMP model, shown for defect A3 in Figure 8.18.

(image)

Figure 8.18:  With an increase of the AC stress frequency, the charge capture time of defect A3 increases. The lines are calculated with the four-state NMP model which very well reproduces the frequency dependent capture times [MWC25].

In general, experiments using high frequency AC signals exceeding \( \SI {1}{\mega \hertz } \) have to be thoroughly designed as capacitive and inductive couplings may affect the measurements. Reference measurements have to be performed to guarantee the signal integrity of the configuration. Nonetheless, AC measurements using frequencies from several MHz up to GHz require special test structures. Recently, an on-chip oscilloscope has been proposed to study the frequency dependence of NBTI and PBTI of high-k transistors [158]. Although PBTI was found to be frequency independent for \( f>\SI {75}{\kilo \hertz } \), NBTI appears to be frequency dependent up to at least \( f=\SI {30}{\mega \hertz } \). The former is in agreement with the frequency dependent capture time of defect A3, see Figure 8.18, as this investigations were performed on a pMOSFET as well.

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