Change in ΔVTH

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7.5.2 Change in $ΔVTH$

Another possibility to evaluate the kink in the recovery characteristics is to determine the slope $dΔVTH ∕d log(trel)$ of the relaxation curve at each point of $trel$ . This is achieved via linear regression using multiple points of $ΔVTH$ around $trel$ to obtain the change in its central point $ΔVTH (trel)$ . Due to the apparent noise, a multiple-point regression is indispensable; a number of 20, 40, and 80 data points is used for each $trel$ . Thereby even very small changes in $ΔVTH$ are able to be identified, as illustrated in Fig. 7.11, where the last relaxation curve of a noisy and a less noisy device is depicted. In this figure the linear regression performed with 40 data points around each $trel$ yields small steps where the slope of $ΔVTH$ suddenly jumps. This issue will be discussed under the aspect of emission times $τe$ of certain defects [111] in the next section, where changes of the recovery behavior with varying $Eox$ and $t str$ are due to a change in the emission time rates of the defects [112, 100, 113, 114, 115].

Figure 7.11: The derivative of $ΔVTH$ identifies even very small changes in $ΔVTH$ . To suppress the noise multiple points ( $20,40,80$ ) are used to determine the slope $dΔVTH ∕d log(trel)$ via linear regression. This is labeled by LR $20$ , LR $40$ , and LR $80$ above. Using linear regression with more points on the one side smoothes the derivative but on the other hand side removes information at the beginning and at the end of the $ΔV TH$ -curve. This drawback vanishes in the area of interest, around the kink-point. Left: For noisy data the slope (LR40) suddenly jumps around $trel =$ $1s$ , $12s$ , and $170s$ , which is marked by circles. Publications dealing with emission time constants of certain defects provide further information [100, 113, 111]. Right: For a thinner device the data is less noisy and the times where the slope changes step-like are more evident, cf. $trelax =$ $1s$ and $10s$ .

Note that using even more than 80 data points around each $trel$ for the linear regression would even better suppress the noise but on the other hand side would disturb important information at the beginning and at the end of the $ΔVTH$ -curve. Fortunately, the region of interest (around the kink point) lies in the center of a $ΔV TH$ -curve.

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