42
IEEE TRANS.!I@TIONS ON ELECTRON DEVICES, VOL. ED-31, NO.
1,
JANUARY
1984
REFERENCES
[3]
Y.
Amemiya,
T.
Sugeta, and
Y.
Mizushima, “Novel low-loss and
high-speed diode utilizing an ideal ohmic contact,”
IEEE
Truns.
rectifier and the Schottky rectifier,” in
Proc,
IEEE/IAS
An,lual
[4]
D.
J.
Page, “Theoretical performance of theSchottkybarrierpower
Meet.,
pp. 60-68, 1976. rectifier,”
Solid-state Electron.
voL 15, pp. 505-515, 1912.
[2]
J.
R.
Hauser and
P.
M.
Dunbar, “Minority carrier reflecting prop-
[SI
A.
Nakagawa and
M.
Kurata, “Computer-aided design considera-
erties of semiconductor high-low junctions,”
Solid-state i’lec-
tion
on
low-loss p-i-n diode,”
IEEE
Trans.
Electron Devices,
voL
tron.
voL 18, pp. 715-716, 1975.
ED-28, pp. 231-237, 1981.
[
11
R.
A. Smith and
J.
M.
Zias, “Comparison of the p-n fast switc ling
Electron Devices,
voL ED-29, pp. 236-243, 1982.
A
Reliable Approa’ch to Charge-Pumping
Measurements
in
MOS
Transistors
GUIDO
GROESENEKEN,
HERMAN
E.
MAES,
NICOLAS
BELTRAN,
AND
ROGER
F.
DE
KEERSMAECKER
Abstract-A
new and accurate approach to charge-pumping measure-
ments for the determination of the Si-Si02 interface state densit). di-
rectly on
MOS
transistors
is
presented. By a careful analysis
of
the
different processes
of
emission
of
electrons towards the conduction
band and
of
holes towards the valence band, depending on the charge
state
of
the interface, all the previously ill-understood phenomena can
be explained and the deviations from the simple charge-pumping thl!ory
can be accounted
for.
The presence
of
a geometric component in s3me
transistor configurations is illustrated and the influence
of
trapping
time constants is discussed. Furthermore, based on this insight, a new
technique is developed for the determination of the energy distribution
of
interface states in small-area transistors, without requiring the kn2wl-
edge
of
the surface potential dependence on gate voltage.
I.
INTRODUCTION
S
INCE THE existence of surface states at the silicon/silicon
dioxide interface was demonstrated, several technic,ues
have been proposed for the determination of the density of
these states and of their energy distribution in the forbidden
energy gap of silicon.
Most of these techniques are based on measurements on
MOS
capacitors
[
11
-
[4]
and have been studied in great detail.
Consequently they have become sufficiently reliable
tc
be
used routinely in most laboratories. For the determination
of
the surface-state densities directly on MOS transistors
olrtly
a
few techniques are available; they are not commonly used,
however, partly because of a poor quantitative reliability and
partly because they are not very practical to use. Therehe
none
of
these techniques can be qualified
as
generally accepted
for MOS transistors.
A first method developed for
MOS
transistors extracts in-
formation on the surface states from the transistor behavior
in the weak inversion region. Although satisfactory rewlts
were obtained using this technique it is only applicable for
Manuscript received April 6, 1983; revised August
2,
1983.
The authors are with the ESAT Laboratory, Katholieke Univer giteit
Leuven, Kardinaal Mercierlaan 94, B-3030 Heverlee, Belgium.
long-channel devices
(>
20
pm) and at low drain voltages
[6]
.
The deep-level transient-spectroscopy technique (DLTS)
which was developed for capacitors can also be performed on
transistors [7], This technique yields information on surface-
state densities and captures cross sections from the measure-
ment of capacitance transients resulting from electron and
hole emission from the states to the conduction and the
valence band. However, this set-up requires a high-quality
averager to detect the small capacitance transients, and the
analysis
is
rather complex.
The reported relation between
l/f
noise and surface-state
density
[SI,
[9] has been used in some cases to determine this
surface state density. However, in view
of
the lack of agree-
ment among the different theories on llfnoise such a determi-
nation
is
only qualitative.
And finally, we want to discuss the charge-pumping tech-
nique which was introduced by Brugler and Jespers
[
101
.
This
technique is based on a recombination process at the Si/Si02
interface involving the surface states. This induces a substrate
current which can be directly related to the surface-state den-
sity. In spite of its capability for measurements
on
small-area
MOST devices, it never became a standard technique because
of some ill-understood phenomena which made the method
qualitative rather than quantitative. Despite some separate
attempts to explain these phenomena [lo]
-[
151
,
a
general
model for the charge-pumping mechanism was not available
until now.
In
this paper we will present
a
model which describes
and explains all of the poorly understood phenomena taking
into account the emission of holes and electrons to the valence
band or the conduction band, respectively, depending on the
state of Si-Si02 interface. This model is completely con-
firmed by the experiments. By applying the technique in an
adapted way it even becomes possible to obtain the energy
distribution of the interface states from
a
very simple measure-
ment, without knowing the dependence of the surface poten-
tial on the applied gate voltage
[SI.
0018-9383/84/011:rQ-0042$01.00
0
1984
IEEE
GROESENEKEN et
al.:
CHARGE-PUMPING
MEASUREMENTS
IN
MOS
TRANSISTORS
43
The new insight in the underlying mechanisms of charge
pumping makes this technique into a powerful and reliable
quantitative method for determining interface-state densities,
even on small-area
MOS
transistors. The simple standard
equipment which is required for this technique makes it
readily accessible for each investigator and moreover, because
of the very short measuring times, it is extremely well suited
for process evaluation, for example with wafer mapping.
First, in Section I1 the basic principles of the charge-pumping
technique will be reviewed and the different proposed measur-
ing procedures will be compared. Next, the problem areas and
the poorly understood effects inherent to the charge-pumping
technique will be indicated in Section 111. In Section IV a re-
liable model for the charge pumping process will be presented.
The experimental results will be described in Section
V
and
compared with the model predictions. Finally,
in
Section VI
a new technique based on the new insight into the charge-
pumping process will be presented which allows the determina-
tion of the energy distribution
of
the interface states even on
small-area
MOS
transistors.
11. THE CHARGE-PUMPING TECHNIQUE-BASIC PRINCIPLE
The basic experimental set-up, as introduced by Brugler and
Jespers
[lo]
,
is
illustrated in Fig. 1 in the case of an n-channel
transistor. The source and drain of the transistor are con-
nected together and held at a certain reverse bias voltage with
respect to the substrate. When the transistor is pulsed into in-
version, the surface becomes deeply depleted and electrons
will flow from the source and drain regions into the channel,
where some of them will be captured by the surface states.
When the gate pulse is driving the surface back into accumula-
tion, the mobile charge drifts back to the source and drain
under the influence of the reverse bias, but the charges trapped
in the surface states will recombine with the majority carriers
from the substrate and give rise to a net flow of negative
charge into the substrate. This is the so-called charge-pumping
effect. The charge Q,, which will recombine is given by
QSS
"AG
'
Yktt(E)
dE.
(1)
It can also be expressed as
Qss=A~
'4'
*Dit.
AQs (2)
where
AG is the channel area of the transistor (cm'),
Dit@)
is the surface-state density at energy level
E
(cm-'
.
-
ev-l),
Di,
is the mean surface-state density, averaged over the
energy levels swept through by the Fermi level
(cm-'
.
eV-l
>,
A+,
is the total sweep of the surface potential, and
4
is the electron charge
(C).
When applying repetitive pulses to the gate with frequency
f,
this charge Q,, will give rise to a current in the substrate given
by
ICp=f*Q,,=f*AG
*q2
.Z.A$,.
(3)
Vr
4
-1
MOST
I----T--
L
I
Fig.
1.
Basic experimental
set-up
for
charge-pumping measurements.
By measuring this substrate current, an estimate of the mean
value of the interface-state density over the energy range swept
by the gate pulse can be obtained,
Charge-pumping measurements have been performed in dif-
ferent ways:
method
A:
by keeping the pulse base level in accumulation
and pulsing the surface into inversion with in-
creasing amplitudes
[
101
;
method
E:
by varying the pulse base level from inversion to
accumulation while keeping the amplitude of
the pulse constant
[
111
;
and
method
C:
by keeping the pulse base level in inversion and
pulsing the surface into accumulation with in-
creasing amplitude
[
121
.
In method
A
a saturation level for the charge-pumping cur-
rent is expected when the top of the gate pulse exceeds the
threshold voltage of the
MOS
transistor. This saturation level
corresponds to the value
of
the charge pumping current, given
by
(3)
for a maximum value of
A$,
and yields the number of
interface states over this range, assuming all other parameters to
be known. The work of [lo] has been extended by one
of
the
authors of the method [13]
.
A
second increase in the charge-
pumping current was shown to be a contribution from the
field region under the bonding area of the gate, and the loga-
rithmic dependence of the current saturation level on the
length of the gate pulse was suggested to be the result of the
capture of carriers by oxide traps close to the interface due to
a tunneling mechanism.
Method B was introduced by Elliot
[
111, in order to also de-
termine an energy distribution
of
interface 'traps. This mea-
surement yields three regions, depending
on
the position of
the pulse base level
VGL.
Only the second region (with
V,
-
AVG
<
V,,
<
VFB
where
V,,
Ab',
,
and
V~B
represent
the threshold voltage, the pulse amplitude, and the flatband
voltage, respectively) gives the charge-pumping current as de-
termined by (3). Elliot derives the energy distribution from
the rising edge of the current-voltage curve, when the pulse
base level is going from inversion to accumu.lation, while the
pulse top level is still in inversion. In this paper however, we
will show that the variation of the charge-pumping current in
this region cannot be used to determine the energy distribu-
44
IEEE TRANSACTIONS ON ELECTRON DEVICES,
VOL.
ED-31,
NO.
1,
JANUARY
1984
Fig.
2.
Influence of pulse shape on the charge-pumping current
wlm
using method
B
(Icp
as a function of gate pulse base-level
VGL).
tion
of
the interface states essentially for the same reason :.or
which the rising edge in method
A
[IO] could not be used !‘or
this purpose.
In method
C,
finally, [12] the pulse base level is kept ccm-
stant in inversion in order to avoid the so-called geometric
component of the current,
or
at least to keep it consta.lt.
However, this goal is not reached because of several otller
mechanisms which are occurring and which will be described
in Section
IV.
The geometric component refers to an ad ji-
tional substrate current when some fraction of the mobi1.e
channel charge does not drift back to source and drain
[
101
.
111.
POORLY
UNDERSTOOD
PHENOMENA
The charge-pumping technique, as described in the previclus
section, has been used to determine the interface-state density
in the silicon forbidden energy gap from a single substrzte
current measurement in an
MOS
transistor.
As
stated in the
introduction, however, it never became a standard techniqle
in spite of its attractiveness for measurements on small-area
transistors because of some phenomena which were never w :11
explained. In this section we will list some of these prob1e:tns
and mention the efforts which were undertaken by differe:n.t
investigators in order to explain these phenomena separately.
A.
Dependence on the Pulse Shape
From the very first experiments on charge pumping, a stro lg
dependence of the charge-pumping current on the shape of t.le
applied gate pulses was observed [lo], [14]. In Fig.
2
tilis
effect is illustrated when using method
B
on one of our
(:e-
vices. The first curve on this figure is obtained when usi:Ig
square pulses, the second when using sawtooth pulses. T.le
transistor under test was a p-channel device with a chanrel
length of
6
pm
and a channel width of
30
pm. The pulse
frequency was
20
kHz and the reverse voltage was equal
to
1
V,
which should be sufficient
to
eliminate any geometlic
component in the current. It is obvious that, even in t1.is
short-channel transistor, a strong influence of the pulse shal~e
on
I,,
is observed.
n
-chamel
Vr
=OV
f
=loOKHz
VGLZ
-
LV
Fig.
3.
Current increase as a function of the top level of the gate pulse
for different measurement conditions, using method
A.
This phenomenon has been explained in the past by a
geometric component [lo], consisting of free minority
carriers which do not have enough time to flow back to source
and drain and are recombining with majority carriers and
therefore also contribute to the charge-pumping current.
It was believed that by using sawtooth pulses this component
could be eliminated because of the longer time available for
the mobile carriers to reach source and drain when driving the
surface back towards accumulation. This was, however, not
confirmed experimentally, as the charge-pumping current is a
continuously decreasing function of the pulse fall and rise
times, whereas a saturation would be expected for any fall and
rise time larger than a few microseconds.
B.
Current Increase with Increasing Gate Voltage
When using method
A
one expects a saturation of the cur-
rent for sufficiently large gate amplitudes because the surface
potential is pinned at
24p
once the channel is in inversion.
However, one always observes a small but consistent current
increase for increasing gate voltage amplitude [lo] (Fig.
3).
This phenomenon was initially again explained by the geo-
metric component. If some fraction
a
of
the mobile charge
does not drift back to source and drain, this part of the mobile
carriers which can be expressed as
Qmob=a’Cox(VG-
VT)
(4)
is recombining with majority carriers. The total substrate cur-
rent is then given by
1cpzf.A~.
[q2
.~A$,+aC,,(V~
-
VT)].
(5)
It was believed that this geometric component could be elim-
inated by using sawtooth pulses as mentioned before, by using
a reverse voltage at drain and source or by using method
C
mentioned in Section
11.
In the latter case, the geometric com-
ponent was expected to be nonzero but constant because the
inversion level
of
the pulse
VGH
is constant. However from
Fig.
3
it is obvious that the substrate current still increases
even when a reverse bias voltage or sawtooth pulses are used.
Fig, 4 shows a comparison of the charge pumping currents for
Method
C
I
Method
P
i
Fig.
4.
Current increase with top level (method
A)
and base level
(Method C) of the gate pulse, respectively.
3
-
*SIVI
r
2-
-
t
1-
Vr
=2V
Vr =1V
Vr =OV
n-channel
-1
-5
0
5
IO
vg
(VI
Fig.
5.
Calculated dependence of surface potential
on
gate voltage for
different reverse voltages at source and drain.
method
A
and method
C.
It is clear that in neither case a satu-
ration is obtained.
Another explanation for the current increase could be sought
in the dependence of the surface potential on gate voltage.
This surface potential is indeed not exactly pinned at
2@F
when increasing the gate voltage, as is usually assumed, but is
slightly dependent on the gate voltage in inversion. Fig.
5
shows this dependence for different reverse voltages
V,.
One
can see that once in inversion the surface potential still slightly
increases. This means that for increasing gate voltage ampli-
tudes the energy range over which the interface states are con-
tributing to the substrate current slowly increases and
so
would also the substrate current in view of the previous inter-
pretation of the charge-pumping mechanism.
However, as will become clear in Section IV, the surface po-
tential does not play an important role in the actual value of
the charge-pumping current, and therefore this explanation is
irrelevant.
C.
Nonlinear Frequency Dependence for Triangular Pulses
According to
(3)
a linear dependence of the charge-pumping
current on the frequency
f
is expected. This is indeed ob-
served when using square pulses
[lo],
but when sawtooth
or
triangular pulses are used, a nonlinear frequency dependence
n-channel
f
=
1
OOKHz
vGL'-Lv
W-80pm
L=7prn
1
\
ob"'~"'~"'~"~2'
Y
v,
ivi
Fig.
6.
Charge-pumping current as a function of
top
level of the gate
pulse (upper scale) and of reverse voltage at source and drain (lower
scale).
is observed. Different explanations
for
this phenomenon were
proposed. Brugler and Jespers [lo] tried to explain it by the
maximum trapping time constant, but did not succeed in giv-
ing a quantitative description. Backensto and Viswanathan
[15] claimed that this nonlinear relationship could be ex-
plained by a trap distribution with decreasing concentration
into the oxide. However, their argumentation starts from an
expression which is only valid for small signal responses and
if thermal equilibrium occupancy functions hold. In the case
of charge pumping, however, one does not deal with small
signals and certainly not with thermal equilibrium. Moreover,
the traps which are located deeper into the oxide will interact
as long as they can be filled by inversion carriers. Therefore,
the time that the surface is inverted should be larger than the
trapping time constant of these traps. When this condition is
no longer fulfilled, they will not contribute to the current
anymore. This phenomenon has already been described by
Declercq and Jespers [13]
.
Furthermore, the nonlinear rela-
tionship obviously is not observed when applying rectangular
pulses, while the explanation based on oxide traps does not
take the pulse shape into account.
D.
Current Decrease
with
Increasing Reverse Voltage
By applying a reverse voltage at source and drain, the charge-
pumping current is observed to decrease
[
101
,
[
111
,
[
131
.
On
Fig.
6
the charge-pumping current is plotted as a function of
the reverse voltage at source and drain, while the gate pulse is
kept at a constant amplitude and base level. In the same figure
the normal charge-pumping characteristic is also shown for in-
creasing gate pulse amplitudes, and a constant reverse voltage
at source and drain. The two curves differ mainly in two ways.
First the current step towards saturation is occurring for a
different
(VG~
-
V,)
value. For the curve with variable re-
verse voltage, this step occurs at about
12
V
-
7
V
=
5
v,
while
for the one with variable gate amplitude
it
occurs at
5
V
-
2
V
=
3
V. This difference can be simply explained by the
body effect on the threshold voltage. For the curve with con-
stant reverse voltage, this influence is constant, while for the
other one, the body-effect changes with the applied reverse
voltage.
46 IEEE TRANILACTIONS ON ELECTRON DEVICES, VOL. ED-31, NO. 1, JANUARY 1984
The second difference between the two curves is the leTd at
which the current saturates. For the variable gate amp1 tude
curve, it saturates at a higher level, but the subsequent increase
is less than for the variable reverse voltage curve, This beh.wior
can be explained by the modulation of the effective area under
the gate where the recombination process occurs as a rest It of
the widening of the surface space-charge layers around swrce
and drain with increasing reverse voltage during the accurmla-
tion period. However, when one tries to predict this mo hla-
tion with a simple one-dimensional model, one obtains
a
surface doping concentration which is about
50
percent Iower
than the one obtained with other methods for the deterrjlina-
tion of the surface doping concentration.
In the case of Fig. 6 one needs a surface doping of less than
1
X
10l6 cm-3 in order to explain the difference betweer1 the
two saturation levels. However, the surface doping concel~tra-
tion obtained by conventional measurement techniques (e.g.,
body effect) was found to be 2
X
10l6
~111~~.
This mean:; that
the charge-pumping current shows a more rapid decrease ,with
increasing reverse voltage than could be expected from the
one-dimensional model. Declercq and Jespers [13] triej to
explain this phenomenon by assuming an increase in the
interface state density in the vicinity of the junctions due to
the presence of impurities or dislocations associated with1 the
diffusion mechanism of source and drain.
IV.
A
RELIABLE
MODEL
FOR
CHARGE
PUMPING
In order to understand all the phenomena mentioned in the
previous section, one has to consider in more detail the di.ffer-
ent mechanisms which are occurring when applying pulsels at
the gate. In this derivation we assume that no geometric c1)rn-
ponent is present during the experiment which will be
on-
firmed later on. Brugler and Jespers [lo] already showed (hat
this condition is normally fulfilled if the geometry of the Yan-
sistor is such that
W/L
>>
1.
When the transistor is switched from accumulation
10-
wards inversion and vice versa, the state of the channel
of
the
MOSFET goes through three different modes, each of wkich
can be characterized by a different time constant and es:en-
tially corresponds to one of the conventional operating regims
of
an
MOS
structure (i.e., accumulation, depletion, and .in-
version). Let us consider a p-type material (n-channel tlan-
sistor).
A
waveform as shown in Fig.
7
is applied to the gate
of the transistor. It has a rise time
t,
and a fall time
tf:
an
amplitude
AVG
=
VG,
-
VG,,
and a period
Tp.
Fig.
8
shows
a schematic representation of the different processes which
are operating during one cycle. When the surface is in ac-
cumulation
(V,
negative), all of the surface states below the
quasi-Fermi level of the minority carriers are filled with e ec-
trons, while those above it are empty, The states are thu in
equilibrium with the energy bands.
1)
When the gate voltage increases, the surface potential is
changing at a certain rate. Therefore, holes that have to) be
emitted from the states towards the valence band (whick in
fact are electrons from the valence band emitted to the stales)
in order to maintain equilibrium, will flow back to the
sib-
strate. Initially, the rate of emission of trapped charge is able
1
TP
Fig.
7.
Waveform applied at the gate when performing charge pumping.
The different parameters
are
indicated
on
the figure.
to meet the one which is required to keep the trap occupation
in dynamic equilibrium with the voltage sweep. The channel
is in steady-state condition as long as
[
161
where
dQt/dt
Its
is the rate of change
of
trapped charge density,
required to maintain steady-state condition, and is given by
and
dQt/dtlem
is the real rate
of
change
of
trapped charge den-
sity as imposed by the emission of holes to the valence band,
and is given by
d
dt
with
nt(t)
=
carrier density
(=
holes) in the traps (cm-').
2)
As
soon as this rate of change of trapped charge imposed
by the emission process becomes smaller than the one re-
quired by the voltage sweep at the gate (7), the channel'is in
the nonsteady-state regime and the emptying of the traps is
controlled completely by the emission process, as described in
detail by Simmons and Wei
[
161 and Kaden and Reimer
[
171
-
E211
.
In this case the occupancy function of holes is shown to
be similar in shape to the Fermi-Dirac distribution function,
but is dependent on time. The transition from the steady state
to the nonsteady state occurs at a certain gate voltage which
can be calculated from (7) and
(8).
Because of the shape of
the
Gs
versus
V,
curve (Fig.
5)
and the relatively high fre-
quencies which are needed in order to measure a significant
substrate current, this transition point between steady state
and nonsteady state will always be very close to the flat-band
voltage
VFB
[22].
Indeed, from the flat-band voltage on the
surface potential sweeps very fast from flat-band position to
strong inversion through the depletion region, even if a reverse
voltage is applied
so
that the quasi-Fermi level of minority
carriers is dependent on time. In this depletion region, the
concentration of frek carriers (holes or electrons) is very small.
Therefore, the time constant is only controlled by the time
constant of the hole emission. Because of this high rate of
change for the surface potential, the steady-state condition will