Charge Trapping and Variability in CMOS Technologiesat Cryogenic Temperatures

8.3 TDDS Measurements at Cryogenic Temperatures

The time-dependent defect spectroscopy (TDDS), next to RTN, is the second electrical characterization method presented in this work, to characterize single defects. TDDS measurements have the advantage that the charging of a trap can be enforced by applying a high gate bias compared to RTN characterization, and has been used for characterizing a device of Tech. C with drawn dimensions \( W\times L=70\times \SI {70}{\nano \meter ^2} \). After applying a stress bias of \( \vg [,s]=\SI {16}{\volt } \) for \( \ts =\SI {100}{\second } \), a recovery trace at \( \vg [,r]=\SI {8}{\volt } \) has been recorded. This has been repeated 25 times at \( T=20, 40, 60, 80 \) and \( \SI {100}{\kelvin } \). From the set of recovery traces recorded at one temperature, e.g. Fig. 8.11 (left) for \( T=\SI {20}{\kelvin } \), it is possible to extract a heatmap of the step heights and the emission times as it can be seen in Fig. 8.11 (center). The heatmap shows that the emission times are exponentially distributed with a mean of \( \overline {\taue }=\SI {8.5}{s} \) and a mean step height of \( \overline {\Delta I}=\SI {3.7}{\nano \ampere /\micro \meter } \). Note that often multiple steps with significantly different mean step heights and time constants can be found in a single recovery trace. These defects are then located in clearly separated clusters in the heatmap.

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Figure 8.11: A set of recovery traces (left) measured at \( \vg [,r]=\SI {8}{\volt } \) and \( T=\SI {20}{\kelvin } \) shows a charge emission event after a stress of \( \vg [,s]=\SI {16}{\volt } \) for \( \ts =\SI {100}{\second } \). From the set of recovery traces the mean emission time \( \overline {\taue } \) and the mean step height \( \overline {\Delta I}/W \) can be extracted and the distribution of parameters can be presented in a heatmap (center). \( \overline {\taue } \) for a set of temperatures shows that the emission time behaves not Arrhenius-like but gets dominated by nuclear tunneling towards cryogenic temperatures (right). The Figures taken from [MJC6, 241].

The extracted mean emission times for each measured temperature can be plotted in an Arrhenius plot in Fig. 8.11 (right). As can be seen, the mean emission times do not exhibit an Arrhenius-like temperature activation towards 20 K. As discussed in the previous chapters, this can be explained by the full quantum mechanical version of the NMP theory. At cryogenic temperatures the vibrational groundstates of the initial and final state of a charge transition are still occupied and overlapping, which allows nuclear tunneling between the atomistic configurations. Therefore, the transition rates become constant towards cryogenic temperatures allowing charge transitions even at low temperatures.

To summarize this chapter, BTI measurements on large area devices and TDDS measurements on down-scaled devices show that the freeze out behavior of the degradation shows a strong technology dependence. While BTI on SiON devices freezes out completely, there is still PBTI degradation on nMOS HKMG devices. This can be modeled with the reliability simulator Comphy by using the 2-state NMP charge transition model. The TDDS measurements on Tech. C confirm single defect emission events in the limit of cryogenic temperatures also for devices made from 2D materials.