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3.6 Random Telegraph Noise (RTN) Analysis

Due to the intensive down-scaling of MOSFETs, the gate area has reached dimensions in the nanometer regime where single capture and emission events of oxide defects are measurable. In this context, the observation of the so-called RTN became more likely. This phenomenon (shown in Subfigure 2.12b) has been known and modeled since the 1980s [16, 48, 62] and describes the discrete changes in the conductance of electronic devices generated by capture and emission of charge carriers by individual oxide defects. The capture and emission events can be measured as a change of $\Delta V_{\mathrm {th}}$ with either the setup for the cv $\Delta V_{\mathrm {th}}$ extraction shown in Figure 3.13 or the setup for the cc $\Delta V_{\mathrm {th}}$ extraction shown in Figure 3.15.

RTN analysis includes the characterization of the mean values of the characteristic $\tau _{\mathrm {e}}$ and $\tau _{\mathrm {c}}$ at different bias and temperature. Therefore, a $\Delta V_{\mathrm {th}}$ trace is recorded using linear time steps. For a proper analysis, the trace has to contain at least ten capture and emission events to calculate a mean value of the characteristic times

$(3.9–3.10) \{begin}{align} \label {eq:meantaucrtn} \tau _\mathrm {c}&=\dfrac {1}{N} \sum _{i=1}^N \tau _{\mathrm {c},i}\\ \label {eq:meantauertn} \tau _\mathrm {e}&=\dfrac {1}{N} \sum _{i=1}^N \tau _{\mathrm {e},i} \{end}{align}$

with

Using a step detection algorithm like the Canny algorithm [118] or a Hidden Markov Model, the discrete steps are located in time and $\tau _{\mathrm {e},i}$ as well as $\tau _{\mathrm {c},i}$ are extracted for each pair of emission and capture events $i$ . As a result, the mean values $\tau _{\mathrm {e}}$ $($ $V_\mathrm {G}$ $,$ $T$ $)$ and $\tau _{\mathrm {c}}$ $($ $V_\mathrm {G}$ $,$ $T$ $)$ provide important information about the behavior of the defect which has caused the steps in $\Delta V_{\mathrm {th}}$ .

The characterization of defects using the RTN analysis is only feasible for defects with rather similar capture and emission times, where $\tau _{\mathrm {e}}$ $\approx$ $\tau _{\mathrm {c}}$ is fulfilled. This limits the range of bias conditions drastically because of the properties of material defects in experiments as discussed in Subsection 2.1.3. Both, $\tau _{\mathrm {e}}$ and $\tau _{\mathrm {c}}$ change opposite to $V_\mathrm {G}$ . As a result, RTN analysis can be applied only within a narrow window around the gate bias of the intersection point of $\tau _{\mathrm {e}}$ $($ $V_\mathrm {G}$ $)$ and $\tau _{\mathrm {c}}$ $($ $V_\mathrm {G}$ $)$ . For a full characterization using the NMP model as required for an extraction of the important parameters which describe the nature of the defect, the characteristic capture and emission times have to be measured over a broad $V_\mathrm {G}$ range.

As soon as $V_\mathrm {G}$ is not within the narrow window around the intersection point of $\tau _{\mathrm {e}}$ $($ $V_\mathrm {G}$ $)$ and $\tau _{\mathrm {c}}$ $($ $V_\mathrm {G}$ $)$ , two cases can be distinguished, either $\tau _{\mathrm {e}}$ $\ll$ $\tau _{\mathrm {c}}$ or $\tau _{\mathrm {e}}$ $\gg$ $\tau _{\mathrm {c}}$ . The first corresponds typically to the defect properties at recovery conditions, where $V_\mathrm {G}$ is near $V_{\mathrm {th}}$ and the second corresponds typically to the defect properties at stress conditions, both discussed in Subsection 2.1.3. This means that $\tau _{\mathrm {c}}$ $\in [$ $t_\mathrm {str,min}$ , $t_\mathrm {str,max}$ $]$ and $\tau _{\mathrm {e}}$ $\in [$ $t_\mathrm {rec,min}$ , $t_\mathrm {rec,max}$ $]$ can be obtained by a kind of eMSM method, which has been developed particularly for the extraction of defect characteristics in experiments, the TDDS framework.

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$\tau _\mathrm {c}$ / $\tau _\mathrm {e}$	mean capture/emission time
$N$	number of capture or emission events
$\tau _{\mathrm {c},i}$ / $\tau _{\mathrm {e},i}$	individual capture/emission time of one event.