3.5 Extended Measure-Stress-Measure (eMSM)

The eMSM method consists of single point measurements of either (corresponds to the constant voltage (cv) method in this thesis) or (corresponds to the constant current (cc) method in this thesis) at a point near during the recovery phase and a subsequent extraction. The basic measure-stress-measure sequence of this method is quite similar to the sequences discussed in the previous section. The main differences are that the measure phase refers to a recovery phase where or is measured and that neither stress nor recovery is interrupted. Both measurement methods are discussed and compared in the following.

The cv method and and the cc method have been introduced in the literature as the fast- method and the fast- method, respectively [31, 39, 40, 116]. The extraction of for both methods is shown in Figure 3.12.

• • The cv method: is measured by recording at a constant voltage, typically near and subsequently converting to using the initial - [31, 116].

• • The cc method: is monitored by recording , which is controlled by a feedback loop of an operational amplifier to achieve a constant drain current, typically near the threshold current [39].

The eMSM technique allows for a more extensive analysis of compared to other techniques. First, eMSM allows for short-term measurements (  1 s after the recovery phase is triggered) because the recovery is measured without any distortions of the degradation or recovery state which is in contrast to the MSM method (discussed in the previous section and in Subsection 2.1.2). Furthermore, due to the fact that no bias modulation is applied during the stress phase which is the case if the OTF technique is used, no systematic error is introduced by periodic changes of the gate bias. Moreover, considering a statistical error of 1 mV in , the relative accuracy in the measured needs to be in the eMSM technique, which is achievable with reasonable integration times. Furthermore, this technique is insensitive to mobility changes induced by stress in contrast to the OTF technique [108]. Finally, the information about the recovery evolution of the MOSFET in eMSM measurements allows for the observation of both, the recoverable and the permanent component of the degradation [71]. In the context of measurements, these facts make the eMSM technique advantegeous.

Both extraction methods, the cv and the cc method, have been developed mainly for BTI measurements and provided equivalent results for NBTI stress. However, recent recovery measurements recorded after mixed NBTI/HC stress have shown that extracted from the cv method and from the cc method can differ significantly. These deviations might lead to inconsistent model parameters and lifetime predictions. Therefore, in this section, the difference between both measurement methods is thoroughly analyzed and discussed considering the shifts of MOSFET parameters like , , and .

3.5.1 Constant Voltage (cv) Method

The basic experimental setup which has been introduced for TDDS measurements in 2010 [16, 33, 40] is shown in Figure 3.13. The voltages applied to the gate and drain contacts are provided by constant voltage sources while is measured simultaneously by a transimpedance amplifier. The feedback resistor of the transimpedance amplifier defines the measurement range for . The evolution of , and over time for all three phases is shown in the measurement procedure in Figure 3.14.

The extraction for the cv method is illustrated in the left bottom panel of Figure 3.12. During the first measure phase an initial - characteristics within a narrow gate bias window around the is measured at (typically −0.1 V in the measurements performed for this thesis) in order to characterize the unstressed device. The corresponding drain current is labeled with in the left bottom panel of Figure 3.12:

Thereafter, the device is subjected to a stress bias ( and ) for the time and immediately afterwards to recovery bias ( and ) for the time . As a result of the degradation of during stress, directly after stress release the - characteristics are shifted and the drain current is reduced to :

While subjecting the device to recovery conditions, recovers from its reduced value towards its initial value and is monitored simultaneously. In a postprocessing step, each measured value of is transformed to a voltage , which corresponds to the gate voltage at on the initial - characteristics ( , , ...). Finally, the threshold voltage shift can be calculated as

3.5.2 Constant Current (cc) Method

Obtaining from the cc method requires a measurement setup as shown in Figure 3.15 [39]. Similar to the cv method, the gate and drain voltages during the stress phase as well as the drain voltage during the recovery phase are provided by constant voltage sources. In contrast to the cv method, in the cc method the drain current during the recovery phase is controlled by a feedback loop of an operational amplifier in order to achieve a constant value, typically near the threshold current. The evolution of , and over time for this case is shown in the measurement procedure in Figure 3.16.

obtained using the cc method does not require a transformation since can be calculated directly as shown in the right bottom panel of Figure 3.12. First, the gate voltage labeled with which corresponds to the measurement current is obtained by recording for a short duration at recovery conditions (drain current is held at at ):

Then, the device is subjected to a stress bias ( and ) for the time and subsequently to the recovery bias while the drain current is held at for the time . The consequence of the - characteristics shift due to the device degradation during stress is a reduced gate voltage directly after stress release:

During recovery, the gate voltage recovers towards its initial value and is monitored simultaneously. Finally, the threshold voltage shift can be calculated for all :

3.5.3 Comparison of Extraction Methods

The cv method and the cc method can be considered equivalent only if the following requirements are met. The - characteristics shifts along the -axis during stress and recovery and the shape (slope and curvature) of the curve section between and in the left bottom panel of Figure 3.12 equals the shape of the curve section between and in the right bottom panel. In other words, neither nor change significantly during the experiment and the device-to-device variability is considered properly by setting each measurement point according to  0 s. In fact, all MOSFET parameters drift during stress and recovery differently, strongly depending on the stress conditions. As a result, the shapes of the unstressed and stressed - curves differ from each other, which leads to as it will be discussed in the next subsection.

For a comparison of the different threshold voltage extraction methods 21 large-area devices were measured. The measurements were performed at   130 °C (controlled by a thermo chuck) using fabricated silicon wafers. Initially, - characteristics for the linear (  −0.1 V) and saturation (  ) regime were taken. Considering the - in the linear regime, was extracted as the gate bias where the extrapolation of the - slope at its maximum transconductance intercepts the x-axis (extrapolation in the linear region method in [2]). This results in   mV. During the subsequent stress/recovery measurements, each of the 21 devices was subjected to one combination of gate and drain stress voltage ( is −1.5 V, −2 V and −2.5 V, is 0 V, −0.5 V, −1 V, −1.5 V, −2 V, −2.5 V and −2.8 V) for a stress time   1.1 ks and subsequently is measured for a recovery time   3 ks. Immediately afterwards, - characteristics for the linear region and in the saturation regime are measured in order to compare the characteristics of the tested and the virgin devices. Doing so, the maximum transconductance shift (), , the saturation drain current shift () and the sub-threshold swing shift () are extracted for each device. Furthermore, and was extracted from the - characteristics of the degraded devices and the unstressed devices in two different regions near of the initial curve: the subthreshold region, abbreviated with sub in the following, and a region above the threshold voltage. Two cases are distinguished, both illustrated in Figure 3.17: with and without device variability.

In the first case, the recovery conditions are chosen in equidistant intervals to for each device (top panel in Figure 3.17). This means that or has to be set individually, depending on . In the shown measurements, recovery conditions were defined as  mV or  mV for the subthreshold region and  mV or  mV for the region above , both at . This ensures that the measurement current in the cc method corresponds always to the measurement voltage in the cv method. In the second case, the recovery conditions are set to fixed values, independent from , which is  −0.43 V or  −13 µA in the subthreshold region and  −0.6 V or  −60 µA in the region above in the measurements performed for this thesis. On average, the requirement is met but this does not hold true for every particular device as shown in Figure 3.17 bottom. If it holds true, strongly depends on the deviation of the individual - characteristics from the average.

At a first glance, it seems that the second case is easier to implement. The reason is that it requires only one analysis per device architecture and device dimensions prior to all experiments in order to determine an average - characteristics and define the recovery conditions. By contrast, the first case needs an - analysis per device prior to each experiment, which means much more effort for the experimentalist. However, the second case means that the recovery conditions differ for the cv and the cc method depending on the deviation of the individual - characteristics from the average. From Figure 3.18 it can be seen that different recovery conditions lead to different recovery traces. This introduces a difference between and . The following results lead to a similar conclusion.

In Figure 3.19 the relative difference between extracted from the cv method and extrated from the cc method () is calculated as

and is plotted against the relative degradation of , , , and under consideration of the device variability. Each point in the scatter plot corresponds to the measurement of one particular device, which has been subjected to one particular combination. Additionally, in order to analyze if the difference between both measurement methods correlates with the degradation of MOSFET parameters, the Pearson correlation coefficient as a measure for a linear correlation between and , , , and is given for each region: for the subthreshold region and for the region above . As can be seen, correlates differently with the relative change of the MOSFET parameters:

• • increases with larger degradation of , , and ,

• • on average, is lower for the subthreshold region,

• • the maximum difference  6 %,

• • correlates strongly with in the subthreshold region but weaker in the region above and

• • correlates strongly with , , in the region above but weaker in the subthreshold region.

The correlation between and , , , and is dominated by the impact of the MOSFET parameter shift on the change of the slope and the curvature of the - characteristics. While characterizes essentially the slope and the curvature in the subthreshold region, , , and affect the slope and curvature at  mV. Thus, a change of during stress and recovery affects mainly in the subthreshold region. However, the analysis shows that does not exceed 4 % if the measurement point is chosen in the subthreshold region.

If the variability of the MOSFETs is not considered and the measurement points are chosen at fixed values near the mean value of , the main observations change. Subfigure 3.19b shows the correlation between and , , , and . Some observations are comparable to the observations in Subfigure 3.19a: increases with larger degradation and is lower for the subthreshold region on average. However, the maximum difference  10 %, which interestingly occurs at low degradation, is higher, and the correlation with all parameters is weaker than if variability is considered. Due to the fact that  0 s does not necessarily equal the two sections measured with the cc method and the cv method can differ in slope and curvature even if the degradation is low.

Recorded recovery during the measure phase confirms these results. For low degradation of the parameters (, , , and are less than 2 %), the cc method and the cv method show quite comparable results. By stark contrast, degradation caused by mixtures of BTI and HCD or pure HCD, where the parameter degradation exceeds 4 %, leads to completely different traces. Figure 3.20 shows two recovery traces where it can be seen that   −10 % at low but increases with , which indicates that the evolution of the slope and the curvature during the measure phase can differ significantly. For example, if does not recover but does recover, the shape of the - characteristics distorts during the measure phase. This is a realistic example since the transconductance is affected by scattering of channel carriers at charged interface states. The number of such interface states increases during stress and as a consequence, the transconductance reduces. As discussed in Chapter 2, interface state barely recover [22, 24, 93, 97, 117].

From this analysis, it cannot be concluded which of both techniques should be chosen for measurements. Nevertheless, the advantages and disadvantages of both measurement methods are discussed briefly. The constant voltage setup as used in [16, 40] measures the drain current with a transimpedance amplifier where the feedback resistor defines the measurement range for during stress as well as during the measure phase. Due to the fact that can vary between the stress and measure phase by a few orders of magnitude and in order to ensure a proper measurement resolution during the measurement, the feedback resistor has to be changed between stress and recovery. Thus, an additional delay on the order of ms is introduced and important information regarding the evolution of during the first ms after stress is lost. By contrast, the cc setup as proposed in [39] minimizes the delay between the stress and measure phase because no feedback resistor has to be changed between both phases. As a consequence, the cc method is advantageous in the case that the degradation of the device cannot be estimated prior to the MSM measurement, which is a requirement for the proper choice of the feedback resistor in the constant voltage setup. However, the requirement that the stress voltage applied to the gate contact has to be constant in order to avoid changes of the degradation state of the device makes the cv method easier to implement (as also discussed in [107]), e.g., using standard equipment. The reason is that the MSM cycles can be realized with one voltage source. This is not the case for the cc method where a voltage source is required during stress and a current source is required during recovery.

Further measurements using both methods showed that can be even higher, up to 100 %. One error has not been taken into account so far. By taking a look at the measurement setup for the cc method in Figure 3.15 it becomes clear that in the case that   0 V the stress conditions are not stable as shown in Figure 3.21. As soon as the device degrades, its reduces and the ratio between the drain-to-source voltage and the voltage over the serial resistance changes. The consequence is that the stress conditions of the device drift slightly during . It has already been discussed that changes of the stress conditions over lead to a different degradation state compared to the state after stable stress conditions.

As a comparison, Figure 3.22 illustrates that the setup for the cv method (see Figure 3.13) provides stable stress voltages. However, it has to be mentioned that the constant offset around 30 mV means that the set stress voltages do not correspond to the applied voltages. This offset introduces a systematic error for further modeling attempts. As shown in Figure 3.23 even slight deviations of the stress conditions, although stable, can make a difference for the recovery traces.

Both, the drift of the stress voltages using the cc method as well as the constant offset in the cv method, lead to a relative difference between and higher than obtained in Figure 3.19. Since a constant offset is easier to be considered for modeling attempts, the cv measurement method was applied for the results presented in the following chapters.