Relaxation Behavior

6.5 Relaxation Behavior

For relaxation, based on the assumption of full recovery after each stress/relaxation cycle, $I = I (t ) D0,rel D P$ is chosen with $t P$ being the pulse period, and implying $ΔID (tP) = 0$ . Therefore $ID0,rel$ is independent of $ϵ$ , whereas $ID0,str = ID(t0,ref)$ depends on the $ϵ$ used. Note that due to record length constraints of the DSO, not the entire relaxation characteristic up to $tP$ is recorded, but only the initial relaxation up to around three to four times $tstr$ . The point $t = tP$ nevertheless is available in the pre-trigger data of the DSO.

Data extraction turns out to be extremely sensitive to the choice of $ϵ$ , indicating that the settling time of $V G$ plays a crucial role in OTF experiments. To demonstrate this fact, Fig. 6.18 shows relaxation after $tstr = 1ms$ for different values of $ϵ$ . If the criterion is too conservative, i.e. $ϵ$ is chosen small, thereby cutting off the initial relaxation phase, the shape of the relaxation characteristics is significantly altered. On the other hand, too large values of $ϵ$ , i.e. too liberal limits for gate voltage settling, may produce spurious relaxation transients. In other words, with different $ϵrel$ values more or less points are considered for the relaxation curves leading to different initial slopes. The ‘real’ initial data, as seen in Fig. 6.18, then becomes artificially dispersed when too many data points are cut off (small $ϵ$ ).

Figure 6.18: Comparison of the fast- $VTH$ measurement and the fast pulsed $ID(VG )$ -method both developed by Reisinger [12]. Depending on the relative epsilon criterion $ϵrel$ , more or less points are considered for the relaxation curves leading to different initial slopes. While $ϵrel = 0.003$ results in an artificial plateau, as the data points are stretched out towards shorter times, $ϵ = 0.025 rel$ shows good agreement with the data obtained from the fast- $VTH$ measurement, which do not have a plateau.

Assuming the relaxation follows $log(trel∕t0)$ as indicated by the red curve in Fig. 6.18, and setting the starting point of the extracted relaxation to later times (through smaller $ϵ$ ) gives a dependence of $log((trel + Δt)∕t0)$ , which produces the artificial plateaus seen with the blue curves in the figure. This may lead to the wrong conclusion that the time constants are smaller than they actually are. Possibly the saturation towards smaller relaxation times found in [42, 102, 107] could be explained that way, i.e. the plateaus observed are not a feature of NBTI relaxation but an artifact due to finite settling times and synchronization inaccuracies, in turn invalidating the assertion that a measurement delay in the micro-second regime is sufficient to correctly capture the relaxation characteristics of NBTI. Besides, though an $ϵrel$ of 0.025 seems to be quite large, the resulting $VG$ only lies within $7.5mV$ of the settled $V G,rel$ . Therefore these values well account for the relaxation region.

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