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. 5.3 (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 ofITH=−60µA. Therefore the measurement data is first fit in the linear regime. Afterwards the extracted parametersβ andθ are reinserted into (2.7) and reformulated as
VG= VD
2 + ID,lin
βVD−θID,lin +Vθ, (5.1)
withID,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. 5.4, where the standard FPM scheme is examined. The pulse slope used for theVTH-extraction is highlighted with circles for the three modes of operation: the initial, the stress, and the relaxation phase.
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 ID(VG)-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.
In the following all meaningful pulse edge combinations for both NBTI and PBTI are schemat-ically compared in Tab. 5.1. The extracted values of VTH are displayed in Fig. 5.5 (left) for a 1 ms-pulsed NBTI-FPM. Depending on which edges are used, the degradation is either overesti-mated (rising or first pulse edge) or underestioveresti-mated (falling or second pulse edge). The first case is due to the fact that the device obviously still relaxes whileVTH is determined, while the latter already suffers from too long delay times, i.e. the time of one pulse edge (1 ms) is already missed.
Chapter 5. Pulsed BTI Measurements 39
VG
init stress relax
NBTI
log(t)
VG
log(t)
PBTI
stress relax
init
Figure 5.4: 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.
NBTI init stress relax PBTI init stress relax
Rising pulses Rising pulses≡ Second
Falling pulses Falling pulses≡First
First Permutation #1
Second Permutation #2
Both averaged Both averaged
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.
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
It is a challenge to determine the range of measurement data within the FPM pulse, which is further used to extract VTH. This is because on the one hand side the noisy subthreshold region should be avoided, but at the same time a preferably large range of data points is required for the fitting algorithm. This balancing act is illustrated in Fig. 5.5 (right). A good compromise is found by using all data points betweenVG=−0.32 V, where the signal-to-noise ratio is still reasonable high, and the stress level of NBTI at VG =−3.0 V. This range provides the best possible agreement of the manual fitting and the two proposed extraction schemes, avg and avg +ITH.
5.2.2 Impact of the Pulse Amplitude
Unfortunately, the different FPM-setups for NBTI and PBTI featuring different pulse amplitudes do not give comparable qualitative results for degradation and relaxation (cf. Fig. 5.4). During an FPM-pulse, always the same number of data points per 1 V is recorded to guarantee a constant resolution of pulse amplitude per time, i.e. a constant slope. However, VTH-extraction using (5.1) strongly depends on the data range of the gate pulse. The usable range was already determined to
1 10 100 1000
Figure 5.5: Changes of the threshold voltage of the SPICE level 1 model fit to FPM after [24, 51]. Left: The results of the manual extraction routine, which is applied according to [24,25,51] (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 ∆VTH-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.
Right: TheVG-range used to extractVTHproperly is restricted by the noise in the subthreshold regime on the one hand and by the maximally accessible inversion regime on the other hand. The optimum VG-range goes from−0.32 V to−3.0 V.
be less than 3 V wide for NBTI stress, but is unavoidably even more limited for PBTI stress. That is because it is important to avoid any NBTI stress during a PBTI-FPM, since the interplay between NBTI and PBTI is not yet understood and therefore not distinguishable at the present day. In fact, the readout pulse during PBTI mainly covers the accumulation regime and just records the onset of inversion; it is not allowed further towards more negative bias. This yields a very limited range of−0.32 V down to−1.0 V for theVTH-extraction during PBTI.
Unfortunately, the noisy measurement data in combination with the avg fitting algorithm results in an oscillating stress curve, depicted clearly in Fig. 5.6 (left). Applying the avg +ITH-extraction heavily reduces this oscillation as the current criterion in the linear regime (ID = 60µA) is less sensitive to a change of the slope of the ID(VG)-characteristics. For NBTI, the strongly differing degradation values after 1 s as well as the differing slopes of the degradation curves for the manual fitting, the avg-, and the avg+ITH-extraction can be explained by the different mobility degradation of the correspondingVTH. As the extraction scheme of VTH is at least comparable for the manual and the avg +ITH-extraction, because both are extracted in the linear drain current regime, the corresponding degradation and relaxation is also similar.
5.2.3 Varying Pulse Rise/Fall Times
An important point has not yet been discussed so far. When investigating short pulsed BTI mea-surements such as FPM, the time-resolution of the measurement equipment is of utmost importance.
Chapter 5. Pulsed BTI Measurements 41
Figure 5.6: Fast pulsedID(VG)-measurements after [24, 51]. Left: In order to prevent any effects caused by NBTI stress, the possible pulse amplitude during PBTI stress is limited. Hence fitting these pulses yields very noisy output in contrast to NBTI, whose pulses are not strictly constrained. These different limits of the usable pulse amplitude make the FPM routine less applicable to PBTI stress compared to NBTI stress. Right: The comparison between longer and shorter pulse times reveals no surprise, as the longer 1 ms-NBTI-pulse gives the best match to the manually extracted one.
To determine the limits of the used setup, a short 1 ms- and a very short 1µs-pulse mode2 are com-pared for NBTI in Fig. 5.6 (right). Not surprising, the extracted values using the 1 ms-pulses are smoother than those using the 1µs-pulses. This is due to the best signal-to-noise ratio of all four performed FPM (NBTI/PBTI using 1µs/1 ms), previously depicted in Fig. 5.3.
5.2.4 Consequences
The two described extraction schemes of the FPM-method, namely the avg- and the avg +ITH -extraction, have shown that fully automated handling of a dataset helps to consistently compare experimental results. However, the performed measurements also underlined the fact that even with proper fitting/smoothing methods to avoid noise as much as possible, the practicability of the measurement routine has to be checked first, especially when dealing with different pulse polarities for NBTI and PBTI.
In the case of PBTI a detailed characterization via FPM is simply not possible because the pulse settings are not suitable for both PBTI stress and recovery characterization in a single mea-surement. The settings are usually a compromise between maximizing the data range for the ID(VG)-characteristics on the one hand and preventing the device from undesired NBTI stress on the other hand. The latter case occurs when the device is driven too far into inversion. Despite these drawbacks the trend of the degradation can be determined, cf. Fig. 5.3. It features a negative shift of the threshold voltage, comparable to NBTI but smaller. So far this refutes the existence of electron tunneling as stated in [24], but unfortunately the actual type of defects contributing to BTI still remains unclear. Therefore the measurement technique proposed at the beginning of
2The pulse time here corresponds to the added rise and fall time of the pulse.
this chapter using charge pumping will be investigated next. Special emphasis is again put on the measurement method itself.