Further Data Extraction Options

5.2 Further Data Extraction Options

By focusing on the fast pulses only, the measurement setup is simplified. The next step is to examine the postprocessing of the measurement signal, as done in [24]. Thereby a very important fact becomes visible. The experimental output of the fast pulsed method, depicted in Fig. 5.5 and Fig. 5.6 (third and forth subfigure), was fitted by hand for each stress and relaxation time step.

To avoid the manual fitting, two methods to process all measurement data consistently are proposed. The first fits the data by using the SPICE level 1 compact model (2.7) from [37] and returns the threshold voltage as already introduced in Chapter 2.3. A second method combines the SPICE level 1 compact model with the constant current criterion of $ITH = − 60μA$ . Therefore the measurement data is first fit in the linear regime. Afterwards the extracted parameters $β$ and $θ$ are reinserted into (2.7) and reformulated as

V I VG = --D + -----D,lin---- + Vθ, 2 βVD − θID,lin

(5.1)

with $ID,lin = ITH$ . These two extraction schemes will be refered to as “avg” and “ $avg + ITH$ ” in the following. Before addressing their differences further, another point needs to be discussed.

The pulse polarity differs for NBTI and PBTI during the stress phase. This becomes obvious in Fig. 5.7, where the standard FPM scheme is examined. The pulse slope used for the $VTH$ -extraction is highlighted with circles for the three modes of operation: the initial, the stress, and the relaxation phase.

Figure 5.7: FPM performed with triangular gate pulses. The circles mark the different pulse shapes during the initial phase, the stress phase, and the relaxation phase. Left: NBTI stress relaxation sequence. Right: PBTI stress relaxation sequence.

The transistor is usually driven from accumulation towards inversion and back, i.e. a falling pulse edge is followed by a rising pulse edge. Only during NBTI stress the polarity of this pulse is reversed. What at a first glance seems to be irrelevant, namely which edge is chosen for the extraction, actually turns out to be significant. The $I (V ) D G$ -curves extracted from the two pulse edges forming each pulse do not necessarily coincide as primarily assumed, rather they show a hysteresis. This hysteresis originates from slightly stressing or relaxing the device through the pulsed measurement itself. Consequently the pulse hysteresis influences the extracted values of the threshold voltage.

Table 5.1: Each pulse of the FPM can be split into two pulse edges, a rising and a falling part. When describing the three different phases of the initial reference, the stress, and the relaxation measurement, which are schematically depicted in the figure above, the highlighted permutations are feasible.

In the following all meaningful pulse edge combinations for both NBTI and PBTI are schematically compared in Tab. 5.1. The extracted values of $VTH$ are displayed in Fig. 5.8 for a $1ms$ -pulsed NBTI-FPM. Depending on which edges are used, the degradation is either overestimated (rising or first pulse edge) or underestimated (falling or second pulse edge). The first case is due to the fact that the device obviously still relaxes while $VTH$ is determined, while the latter already suffers from too long delay times, i.e. the time of one pulse edge ( $1ms$ ) is already missed.

Figure 5.8: Changes of the threshold voltage of the SPICE level 1 model fit to FPM after [24, 51]. The results of the manual extraction routine, which is applied according to [51, 24, 25] (filled symbols), are compared to the proposed “ $avg + ITH$ ” extraction scheme. By using various pulse edges of the measurement data as displayed in Tab. 5.1, more or less smooth $ΔV TH$ -curves are obtained. The extraction which uses both pulse edges (averaged pulse) yields the best possible results that can be obtained for FPM. Due to the hysteresis between the rising and falling edge all other pulse combinations give barely acceptable results.

During relaxation the same pulse form is used for both NBTI and PBTI. Therefore the hystersis does not affect the extracted results. As expected, smoother results are obtained by averaging the pulses.

  5.2.1 Determination of the Fitting Region
  5.2.2 Impact of the Pulse Amplitude
  5.2.3 Varying Pulse Rise/Fall Times
  5.2.4 Consequences

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