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 [112100113114115].


PICPIC


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 LR20  , LR40  , and LR80  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 [100113111]. 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.