A detailed study of the extraction of the spatial distribution of interface traps in MOSFETs by means of charge pumping is presented. Both problems, MOSFET before and after a nonuniform stress are considered. The analysis is based on the rigorous two-dimensional transient model of the charge-pumping experiment, which has been introduced in the preceding section. The accuracy of the extraction procedures is analyzed. A systematic error is found in some charge-pumping methods, which occurs due to the variation of trap emission times during the course of experiments. The present techniques are improved to account for this effect. A charge-pumping method is discussed, which does not suffer from this error.
Hot-carriers in devices produce interface (and bulk) traps, trapped charge in the oxide and additional oxide traps, which could change the device characteristics. How the characteristics of an MOSFET is degraded depends on the amount, location and the nature of the damage. It is quite difficult to extract the parameters of the damaged region from the device static characteristics like the threshold voltage, the transconductance and the drain current, although these quantities are often used as a monitor for the degradation. In fact, the inverse approach is the only way to extract some information from these quantities: for assumed distributions of interface states and fixed surface charge the changes in device static characteristics are modeled by simulation. Comparisons of the simulation results with experimental data provide information on the ``quality'' of the assumed spatial distributions, nature of traps and amount of charge (see references cited in Section 3.5).
Experimental methods for the extraction of the amount and the spatial distribution of interface traps and fixed oxide charge which are generated in nonuniform hot-carrier stress are based on:
), since these
traps give the dominant contribution to the leakage current. Moreover, the
amount of the extracted traps depends directly on the corresponding capture
cross-sections 
and 
, because of
.
The capture cross-sections are, however, not known accurately, particularly
for the spatially localized mid-gap traps generated under nonuniform stress.
Unlike the gated-diode leakage methods, in the large-signal charge-pumping
techniques the extracted trap density is only weakly dependent on the error in
determining the capture cross-sections due to a logarithmic dependence of the
active energy interval in the band gap on and .
Charge-pumping techniques have been extensively used to extract the spatial
distribution of interface traps
[423][398][374][288][287][272][78][34][9] and
fixed oxide charge 
[480][288][78][75][74] along the
oxide/semiconductor interface in MOS devices before and after electrical
stress. The procedures used to calculate the charge distributions from
the experimental data are based on analytical expressions which, however, rely
on some approximations:
and in the
channel and within the junctions is still unknown, because there is no method
to measure these distributions directly.
In this study, a rigorous two-dimensional transient model of the
charge-pumping experiment is used to evaluate the validity of the extraction
procedures. Our approach is described in Figure 3.29.
For assumed distributions of interface traps and fixed oxide charge the result
of some charge-pumping measurement (e.g. 
versus source and drain
junction reverse bias 
) is calculated numerically. The calculated
is further used instead of the experimental data. Comparing
the obtained trap and charge distributions with the assumed distributions, we
are able to evaluate and improve the present experimental techniques. Here we
benefit from the ability of the numerical model to provide an exact solution
to the problem for an assumed physical model of interface traps, physical
parameters and dopant distribution in the device. This model accounts for all
parasitic transient effects in the charge-pumping experiment, as well as for
all restrictions in the analytical approaches noted above.
Before discussing the extraction methods, remember the definitions for the
charge-pumping threshold and flat-band voltage; those referred to the total
filling of traps. The charge-pumping flat-band potential 
is
defined as the gate-bulk bias at which the surface hole concentration 
equals to some critical concentration 
sufficient to refill all
interface traps during the gate-pulse bottom level 
. By introducing
, where 
is the hole capture time constant
, one obtains
It is expected that 
, which results in the total filling of almost
all traps with holes during . Analogously, the charge-pumping threshold
voltage 
is defined as the gate-bulk bias at which the surface
electron concentration equals to some critical value 
sufficient
to refill all traps during the gate-pulse top level 
. It follows that
and depend on the characteristic time intervals
and . A comparison between and
and the conventional device threshold 
and flat-band 
voltages
is given in Section 3.3, where one-dimensional analytical
model of the MOS structure is employed. Both, and
can differ from and significantly. Therefore, and
should not be applied for the extraction of spatial trap distributions.
We focus only on the interface states and neglect fixed oxide charge in the
following. The mostly applied charge-pumping technique to measure
consists of applying gate-bulk trapezoidal pulses with all parameters
, 
, 
, 
, and fixed, while the
drain/source-bulk reverse bias is varied in the experiment. The technique
is known as method II from [374]. This technique will be analyzed
henceforward. With the reverse bias the current changes due to
two effects (in 
-channel devices):
at the source side 
and the drain
side 
move with the reverse bias . This is the desired
effect used to scan the interface. The edges 
and 
are defined by the local .
and the
charge-pumping flat-band potential (in the junctions)
vary with the reverse bias; Figure 3.30. The
threshold voltage 
and the flat-band potential
which determine the emission times, vary with
as well. Consequently, the emission times for electrons 
and holes 
and therefore, the electron and hole emission
levels 
and 
change with at
each position at the interface. This effect has been neglected
previously in literature. However, due to the 
effect, the charge-pumping current changes with
not only due to 
and 
, but also because of the
contribution of the whole channel to changes with . In
order to describe the effect rigorously, care must be taken of the
fact that the emission times are an explicit function of both, the
spatial coordinate and the reverse bias: 
.
The relations and may be obtained
numerically [423][398][374][9] as also done in this study,
assuming that the doping profile is known. An analytical model for the
width of the depletion region in the lateral direction has been employed
too [272][271]. This approach is too rough to be applied in practice,
because of the strong two-dimensional distributions in the doping, potential and
carrier concentration around the drain/bulk junction close to the interface.
In our study, we analyze the accuracy of the extracted trap distributions with
respect to variations in . The latter concentration is not known
accurately in measurements, since it depends on the capture cross-sections of
the stress-induced traps.
