The influence of the localized interface states and fixed oxide charge on
changes in the charge-pumping characteristics after stress will be discussed in
this section. Typical characteristics, namely the charge-pumping current
versus gate bottom level 
is considered. The changes in
can provide a good quantitative estimate of the amount of the
generated interface traps. However, only restricted information on the trap
location and nature, as well on parameters of the damaged region consisting of
oxide trapped charge is accessible [492][380][196][194][187][77][38]. Although the authors are clearly aware of these
limitations [196][194], a quantitative study is still missing in
literature.
In the first example we consider an 
-gate/-channel conventional MOSFET
stressed at maximum substrate current: 
, 
. After analyzing
the spatial distributions of the field, Figure 3.23, and the
current injected into the oxide [172] by using MINIMOS, we
assume that the peak of the damaged region is located at 
. The damage
consists only of acceptor-like interface states (stress at maximum 
) which
are gaussian distributed along the interface. The chosen standard deviation of
is somewhat smaller compared to a realistic two to three times
larger value. In fact, we consider a narrow distribution to emphasize an
influence of the exact position of the damage. Before the stress, the traps are
uniformly distributed along the whole interface in an amount of
. These virgin and stressed devices are those
introduced in Appendix D. No fixed charge is present in the
devices. Figure 3.21 shows the curve
calculated numerically for both, the virgin and the stressed device.
Apparently, a large shift to the left occurs for the stressed device with
respect to the virgin device, in spite of a large amount of acceptor-like traps
which should increase the local threshold voltage. To explain this unexpected
result we analyzed the spatial distribution of the charge-pumping threshold
and flat-band voltage 
near and within the drain
junction, Figure 3.22. A large difference of 
between
in the middle of the channel and at the location of
the damage 
causes the localized traps to be scanned at a lower gate
top level than the traps in the channel, resulting in the shift to the left and
not to the right, as expected. Even in the channel region close to the
metallurgical junction, is remarkably lower than in the middle
of the channel; at the metallurgical junction 
this difference
becomes 
, which corresponds to a density
of 
uniformly
distributed trapped charge in our example. An unexpectedly large lowering of
in the channel region near the junction (excluding them) is
produced by 1) decreasing channel doping and 2) the two-dimensional
effects due to the proximity of the junction - charge sharing.
A second observation is that the increase of the local charge-pumping threshold
voltage due to the interface charge is only 
at the location of the
trap peak density, in spite of a large amount of traps. Three facts deserve
attention here:
. Because
can be much lower than 
(equivalently,
much higher than 
), particularly at low
frequency, the Fermi level can lie away from the band edges; many
interface states remain empty close to the band edges. Consequently,
being uncharged they do not contribute to the potential shift.
. The shift of the gate bias is,
however, nearly directly dependent on 
. With further decreasing
gate length and oxide thickness, the local potential change will become
even smaller, thereby inducing difficulties in interpreting the
curve for the next generations of MOS devices.
should produce a gate-bias change of 
, where we
accounted for the Fermi-level position. However, the potential increase
calculated by the two-dimensional numerical approach is only , as
shown in Figure 3.22. This finding deserves more
attention.
Henceforward, we focus on the latter effect. In order to estimate the amount of
the localized interface charge, the local potential shift is a quantity usually
subjected to measurements. Typical examples represent the displacement on the
voltage axis of the GIDL characteristics [455][278][111][4],
the voltage shift in the charge pumping [492][480][196][194][74][39][30] and capacitance measurements [288], as well as
different voltage changes connected with terminal
currents [490][481]. For a uniformly distributed charge at the
oxide/bulk interface, it yields a density of 
from the measured voltage shift 
. As a rule this expression is also
used for a localized charge, in such a way that the measured voltage shift
associated with some position at the interface 
is converted in
the local interface charge density at this position by simply setting
. This approach is incorrect and can lead
to a large underestimation in the density-peak. A very detailed analytical and
numerical study of this problem is presented in Appendix F. Hence,
an example is adduced and some conclusions from Appendix F are
noted. Let us consider the interface charge with a constant density of 
in the interval 
.
Figure 3.24 shows the
spatial distribution of the local threshold voltage 
in the area
around the localized charge, where 
, with the normalized
charge width 
being a parameter. The MOS structure consists of
-type bulk which is uniformly doped in moderate concentration
. The threshold voltage at a particular position 
is
defined in a standard way, as 
necessary to induce the surface electron
concentration of 
at this position. The variation of the threshold
voltage associated with the middle of the trap region 
lies far
behind its extreme value which is connected with the spatially uniform charge
, even when the width of the trap region is larger than the oxide
thickness (
). As opposed to the uniform charge which results in
a simple translation on the voltage axis, is not constant, but
is affected by several parameters: gate-bulk bias , oxide thickness
, charge density , charge width 
and bulk doping 
in
the general case. An exact calculation can be carried out exclusively by a
two-dimensional numerical model, although a fairly accurate theoretical model
can be derived assuming the total depletion approximation, as is done in
Appendix F. To explain the physical mechanism lying behind small
surface potential changes for a localized charge, remember the mechanism
taking place when a uniform charge is inserted at the interface; a problem
which can be considered in one dimension. Hence we fixed the gate-bulk bias. A
negative interface charge reduces the surface field 
in semiconductor,
thereby reducing the total charge in the semiconductor per unit area 
which corresponds to . The surface potential 
decreases to a value
determined by . Decreasing causes the oxide field 
to
increase, consequently increases, as well. The latter effect partially
cancels the initial lowering of . For the localized interface charge the
initial decrease in induces a smaller decrease in than that for
the uniform charge, because the space-charge region residing remotely from the
interface is influenced strongly by the oxide field from the interface region
surrounding the localized charge due to the two-dimensional effect. The
phenomenon is particularly pronounced when the width of the localized traps is
much shorter than the depletion region width; a condition typically fulfilled
in total depletion and inversion. When the trap region is supposed to be
sufficiently wide to gain control over the whole space-charge region under
itself, this two-dimensional effect vanishes and the local surface potential
becomes close to that corresponding to the uniform interface charge.
When carefully exploring the effect of a spatially inhomogeneous interface
charge 
, two problems can be extracted:
occuring due
to . The gate and other terminal biases are assumed constant.
necessary to
establish the same conditions in the point 
at the interface with
presence of the charge in device, as those conditions holding
at with absence of charge. In this problem 
,
and 
are fixed.
. The localized
charge becomes ineffective in both, perturbing the surface potential
and shifting the gate bias ;
Figures 3.24 and F.5. If the bulk is only
shallowly depleted, increases, easily approaching the limiting
value of 
. As opposite, attenuates, although
increases with respect to its extreme value influenced by the
depletion-region width; expression F.22 and
Figure F.3. This condition corresponds to e.g. flat-band
calculation, presented in Figure F.4.
From the preceding analysis two practical consequences arise: 1) a very
localized interface charge can be quite ineffective in perturbing the local
potential and 2) if some kind of the distribution which is
connected with the damaged region is available from measurements, it is not a
trivial task to reconstruct the exact interface charge distribution which
produces , even though the doping profile is known in this
region. In particular, from the measured an average interface
charge density cannot be calculated by 
, but the width
of the damaged region and the width of the bulk depletion region must be
accounted for in the calculation, as well. A useful engineering approach has
not been developed yet, but the study in Appendix F has laid a
solid base to accomplish this task.
Generally we may conclude that an artificial shift, due to doping profile, vicinity of the junction and other two-dimensional effects, is absolutely dominant over the local voltage shift due to charge in the damaged region itself, including the damage located in the channel near the junction. However, in nonuniform hot-carrier stress the damage is never generated in the channel areas remote from the junctions.
We continue the discussion on the charge-pumping characteristics. Evidently,
changes in the potential depend on the charge density. To examine the influence
of the trap density on in a quantitative manner, we vary both,
the location and the peak density of the gaussian distributed traps for the
same devices as in the first example. The numerically calculated differential
charge-pumping curves 
are shown in
Figure 3.25, where the curves for the density of
are multiplied by 
. The family of the
characteristics for the density of 
is less displaced to
the left with respect to the virgin device, than the family for
, as results from a higher local potential
increase induced by the trapped charge. The differences in the voltage shift
between the two families are much less than the changes in the shift when
varying the location of the peak by 
only. Note that a distance of
nearly represents the resolution of the charge-pumping methods for the
extraction of the lateral trap profile. Moreover, in spite of the traps
located at 
also residing in the channel, the displacement of the
post-stress curve is only influenced by the density of the induced traps
slightly.
Similar result come out when analyzing the impact of the nature of the traps
on the post-stress . Figure 3.26 presents the
result carried out by numerical calculation for the same device, assuming either
a donor or acceptor nature of the induced traps. Acceptor-like traps induce a
shift to the right, mostly at the rising edge, while donor-like traps induce a
shift to the left, mostly at the falling edge of the differential
characteristics. As follows from the calculation, a
drastic change in the nature of the traps has just the same impact on the
characteristics as minor changes in the position of the damage by .
The conclusion that the exact location of the damaged region is more important
than the density and nature of the traps induced by stress is consistent with
the observations in the literature [196]. It has not been expected,
however, that the effect be so strong. It is worth to adduce that, although the
shift of the post-stress curves cannot provide reliable
information of the nature and density of the induced traps, the derivation
of these curves at the upper plateau from the maximum to the abrupt
part of the falling edge directly yields the spatial trap
distribution (cf. Section 3.5.2).
It has been proposed that the back-shift of the edges of the stressed
curve after a subsequent hot-electron injection may be used to
estimate the amount of fixed positive charge which is trapped in the oxide in
the primary stress [380][196][194][30]. Considering -channel
devices, after hot-electron-hole stress (EH-stress) and hot-hole stress
(H-stress) at a medium and a low gate bias with respect to the drain bias
(
) both, interface trap generation and trapping of holes in
the oxide occur. During short subsequent channel-hot-electron injection
(E-stress) at a high gate bias (
), electrons are
efficiently trapped
characteristics after the E-stress is
directly proportional to the positive charge trapped in the oxide, we carried
out additional model-experiments including fixed charge 
in our
device. Figure 3.27 shows the calculated
characteristics for different locations of the positive
charge: 1 - at the same position as interface traps 
, 2 - left from
the interface traps, in the channel and 3 - right from the traps, in the
junction. Both, 
and have a gaussian distribution with
. Interface traps reside partially in the channel, but mostly
in the junction. The dashed curve is 
for absence of any fixed
charge. It can model the characteristics after neutralization of all trapped
holes by E-stress if no electron trapping on neutral sites occurs. Calculations
show that the back-shift 
is affected by the position of the
peak of the oxide charge 
with respect to interface states .
However, this fact may be exploited to estimate the relative positions of both
damages with respect to each other. Small changes in the deep-tail region (low
) suggest that is generated mostly left from in
the region towards the channel. Large differences in the deep-tail region
clearly show that is produced right of in the area towards
the drain. According to simulation, a fairly parallel shift of the rising edge
occurs when the locations of and coincide.
In this example, we calculate 
from the shift of 
. This value is
smaller than the value 
assumed in the calculations, as a
consequence of the local effect studied in Appendix F.
If electrons are trapped on the neutral sites which are generated in the
initial stress, fixed oxide charge will be negative after the E-stress.
The charge-pumping characteristics for this case are shown in
Figure 3.28. From the upper figure we conclude that it seems
to be impossible to judge in practice whether the curve
is shifted to the pure- curve (dashed line) or to the
curve (dotted lines) after the E-stress. Examining the
characteristics on the lin-log scale qualitative differences between dashed and
dotted lines may be observed in the deep-tail region. If the negative charge
resides near the interface states, the differential characteristics with the
negative charge (dotted curve 1) and without the negative charge (dashed curve)
behave similarly. If the negative charge is displaced from the localized
interface states in the region towards the drain, the negative charge is
able to lower the local threshold voltage so that the negative
differential charge-pumping current occurs. The change in the sign of
is a typical indication of the presence of a negative
trapped charge in the oxide. This effect can be used to prove the existence of
the trapped electrons in a device, but only the presence not the absence
can be checked. In the stress at low and very low gate bias the traps are
produced in small amount and the hole injection
dominates (-channel devices). In these conditions the change in the sign
of may be well observed [492], indicating that a large
amount of neutral electron traps are generated in the oxide while injecting
holes [103]. For the stress at 
, the situation
is much more complicated. This stressing conditions are known to result in a
maximal generation of interface states. After the subsequent E-stress the change
in sign of may or may not appear, which is dependent
on the relative position of the generated interface states and oxide trapped
electrons to each other. Both curves, 1 and 2 in Figure 3.28,
are calculated assuming a large amount of negative oxide charge, but only the
latter exhibits a sign change. Additional experimental work, connected with
numerical modeling, is necessary to explore the potentials of this effect to
study the degradation at maximum stress.
