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].
Figure 3.12: Two different methods to extract the threshold voltage shift during recovery: The cv and cc methods.
Top: Characteristics of an unstressed device (blue) and of a device after degradation (red). During the measure phase the parameters and thus the shape of the -
characteristics drift towards their initial
values. Bottom:
is monitored using either the
cv method (orange) by recording
at a constant voltage
near
and mapping to
using the initial
-
or the cc
method (green) by recording
at a constant current
near the threshold current.
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
.
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.
Figure 3.14: Measurement procedure for the cv method: After the initial characterization of the unstressed device, and
are applied. During
degrades. Afterwards, the measurement
voltages gate voltage at recovery conditions using the cv method (
) and
are applied and
recovers. During the last phase,
is recorded in order to ex-
tract
.
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
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.
Figure 3.16: Measurement procedure for the cc method: After the initial characterization of the unstressed device, and
are applied. During
degrades. Afterwards, the measurement
voltage
is applied while
is held at the constant value drain
current at recovery conditions using the cc method (
). During the last phase,
recovers and is recorded in
order to extract
.
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 :
Figure 3.17: Difference between considered device variability and not considered device variability: Top: Variability is considered as the recovery conditions are chosen in
equidistant intervalls to for each device individually. This
ensures that the measurement current for the cc method corresponds always to the measurement voltage in the cv method indicated by the black markers. Bottom:
Variability is not considered as the recovery conditions are fixed for every device so that in average
.
For devices which deviate from the average characteristics the recovery conditions set in the cv method (indicated by the orange markers) differ from recovery conditions set in the cc
method (indicated by the green markers), which leads to a significant difference of the extracted
.
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.
Figure 3.19: Correlation of with the degradation of MOSFET parameters: Each point in the scatter plots
corresponds to the degradation after subjecting the MOSFET to a particular
-
combination. The relative difference
increases with larger degradation and it is in average lower for the subthreshold
region.
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].
Figure 3.21: Unstable stress voltages in the cc method: The applied voltages are not stable during stress as soon as
0 V. As soon as the device de-
grades its
reduces and the ratio between the drain-
to-source voltage and the voltage over the serial resistance
changes. Both, the voltage between
the drain and the source contact (
) and the voltage between the gate and
the source contact (
) drift slightly, which results in voltage
differences
and
compared to the unstressed de-
vice.
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.