The study of degradation mechanisms prevalent in transistors includes a thorough experimental characterization of time-dependent variation and time dependent drifts of MOSFET parameters.
Therefore, different measurement methods and sequences have been developed. In this chapter, an overview is given and the purposes, advantages and challenges of commonly used techniques are introduced. Then, challenges which
had to be faced during the measurements for this thesis, are discussed. In this context, the fact that most of the measurement techniques have been developed for the characterization of either NBTI or
HCD degradation plays an important role. For the discussion of such challenges, the focus lies on the extraction methods applied using
MSM techniques as this method is most relevant for the understanding of the results presented in Chapter 5.
Figure 3.1: Range of stress conditions: Schematic illustration of the different stress conditions NBTI, HCD and mixed
NBTI/HC. The area of stress conditions defines the boundaries of the 2-dimensional parameter space applied in this thesis. Different colors separate the
voltage combinations which trigger different degradation mechanisms, while the color intensity indicates the increasing impact of the stress on the parameter shifts.
As an introduction to this chapter, Figure 3.1 illustrates the stress conditions for triggering both degradation mechanisms, NBTI and HCD, including the so-called mixed NBTI/HC stress conditions applied for the characterization of the unavoidable interplay of both. The
region of stress conditions in this figure shows the 2-dimensional parameter space applied in this thesis. The measurements discussed
in the current and the following chapters were conducted on 2.2 nm
pMOSFETs of a 130 nm commercial
technology (
−1.5 V and
465 mV). One has to distinguish between large-area devices and
nano-scale devices. The first have the dimensions
10 µm and
120 nm or
130 nm, and the second
160 nm and
120 nm or
130 nm.
Using the OTF measurement method, MOSFET parameter shifts are probed directly during operation without interruption of the applied voltages. It was
introduced in 2004 for the purpose of measuring the device degradation during stress conditions
[106], which typically refer to much higher biases than used at nominal operating conditions. This technique aims for the direct characterization of the
evolution.
The basic measurement procedure is shown in Figure 3.2 for BTI measurements. It consists of a periodic modulation of with the modulation amplitude (
) at a certain
drain measurement voltage (
) while
is determined at three measurement
points for each modulation period
. The modulation of
induces a
, which changes over the
modulation periods due to the degradation-induced
during stress. From the
modulation amplitude and the corresponding
the transconductance can be
obtained according to
with
gate stress voltage | |
drain voltage applied during measurement | |
drain current | |
stress time | |
threshold voltage. |
A step-by-step integration of /
gives the threshold voltage shift during
stress:
with
sequential number of measurement | |
number of |
One challenge arises due to the fact that a parameter which is typically measured at a level near the threshold regime, namely , is extracted from a measurement at
stress level where the applied voltages are considerably higher than the threshold voltage. A proper separation of the impact of mobility fluctuations at stress level and
drifts at a level near the threshold
regime on the measurement is, therefore, an issue [107]. The reason is that shifts of the transfer characteristics along the
-axis (
drifts) and “tilts" of the transfer
characteristics (see Figure 3.3) are indistinguishable at the stress level. Such “tilts" are caused by defects located near or at the oxide/substrate interface which contribute to surface
scattering and lower the carrier mobility. Based on a simple SPICE level 1 model, the following three parameter equation meets this challenge and separates the mobility and the
effect from each other:
with
drain-source conductance | |
global mobility (parameter) | |
gate voltage | |
threshold voltage (parameter) | |
leads to an asymptotic approach to a maximum value |
|
the mobility decrease due to surface roughness for high gate fields (parameter). |
The SPICE model has an empirical background and describes above
in the linear
regime rather well, as shown in
Figure 3.3. However, it does not explain the threshold voltage shifts near the regime typically defined as the threshold regime in other measurement methods.
The extraction of depends on the modulation
around
. Therefore, two
measurement points on the transfer characteristics, namely
(
-
/2) and
(
+
/2) or
and
,
respectively, are inserted into Equation 3.3. Assuming that
is known from an initial characterization of the device the two-equation system
containing only two unknowns,
and
, can be solved and as a result the
threshold voltage can be calculated using
with
corresponds to |
|
gate stress voltage | |
amplitude of gate stress voltage modulation | |
drain-source conductance at |
|
asymptotic approach to a maximum value |
|
the mobility decrease due to surface roughness for high gate fields. |
Unfortunately, the extraction of from a measurement at stress level
and not from a measurement in the threshold regime introduces errors. In general, due to the modulation of the gate bias, the stress level changes, leading to a different degradation state than the state obtained after constant stress
over the whole
. For example, it has been shown that
is underestimated with the
OTF method [43]. This systematic error could be minimized by a small modulation amplitude
. However, the
error in
in Equation 3.1 is inversely proportional to
and thus the
smaller the amplitude is, the more error is introduced to
. Since the error in
determines the error of the
extraction in Equation 3.4, the choice of the modulation amplitude affects the statistical error in
[107].
Moreover, the modulation time plays a major role in the obtained degradation state. In order to minimize the change of the degradation state due to the modulation, the time within which the modulation is performed must be as
short as possible. As a consequence, the integration time of the measurement has to be as short as possible. However, a decrease of the integration time in measurements leads to an increase of the statistical error of the measured
. Integration times in the order of
µs or ms lead to a relative accuracy in the measured
of
or less. This corresponds to a statistical error of
of
12 mV, which is too high. In order to
achieve a statistical error of, e.g.,
1 mV in
,
has to be measured with a relative
accuracy of
. With standard equipment, the
integration time required to achieve such a relative accuracy would be more than 20 ms which enlarges the measurement time enormously. Unfortunately, 20 ms is way too long if the prevention of recovery during
the measurement is required. [107]
The OTF method is quite sensitive to mobility changes induced by stress [108] while it is quite insensitive to changes because the
-
curve flattens out at the stress level
[107]. Since
is the parameter of interest, an
insensitivity to the changes of the threshold voltage shift is a considerable disadvantage. Together with the introduced systematic error due to the voltage modulation, this disadvantage makes the OTF
method unfavorable for this thesis.