IEEE TRANSACTIONS
ON
ELECTROh- DEVICES
VOL.
ED-13, YO. 12
FEBRUARY,
1966
An Investigation of Instability and Charge Motion
in Metal-Silicon Oxide -SiliconStructures
Abstract-The results of a detailed study of the charge motion
and instability in thermally grown, undoped
silicon dioxide films
at highelectricfields
and elevated temperaturesarepresented.
The transient behavior of the chargemotion in theoxide is analyzed
and a model proposed to explain the observations. It is shown that
the instability consists of the motion of positively charged ions and
that interface trapping effects play a significant role in determining
the transient behavior. Detailed consideration is given to the nature
of these trapping effects, and it is concluded that caution must be
exercised in ascribing the activation energy measuredforthe
instability to that for the true mobility of these ions in a “bulk”
oxide. The effects of various ambient treatments on the instability
are discussed, and conclusions are drawn concerning the physical
and chemical nature of the observed instability.
charge. Typically, oxide charge which has been generated
by an applied field 3 x 10’‘ V/cm for several hours a t
200°C may relax or recover within a fraction of a second
a t this temperature after bias is removed. This type of
“asymmetric” instability has also been reported by Logan
and Kerr [4] in their investigation of instability in MOS
capacitors and appears tobe due toa different mechanism
than that observed by Snow et al. [2].
It has been proposed’ that the asymmetry of the instability is related t o ionic trapping at the metal-oxide
interface andthatthe
“fast” recovery, ratherthan
the slower initial (forward) drift, is more closely related
to the true nature of the ionic species causing this instability.
This species possesses substantially higher moI. INTRODUCTION
bility than thatobserved for sodium in silica and has been
NE OF THE MORE formidable obstacles block- tentatively identified as ahydrogen ion (or proton) reing the development of practical MOS tran- leased by hydrolysis of adsorbedwater
atthe oxidesistors was migration of charge within the gate metal interface. A similar high mobility ion has also been
insulator under conditions of high electric field and tem- observed by Hetherington, Jack, and Ramsey [5] in their
perature. An empirical technique, the use of phosphorus experiments with ionic motion in quartz. They, too, relate
doped oxide 111, provided a solution to this problem of this ion to the hydrolysis of water adsorbed at thesurface
instabilityand allowed fabrication of practical devices, of the silica.
butthe mechanisms causing the instability were still
This paper will present the results of a n investigation
not clearly understood.
intothe behavior of thisasymmetrictypeinstability.
Recently Snow, Grove,Deal,
andSah [2] have re- The experimental results are presented in detail, and a
ported on the motion of sodium ions in the oxide of a n model for an asymmet,ric instability is proposed and comMQS capacitor. The ions were introducedbydipping
paredwithexperiment.Finally,
conclusions aredrawn
the test oxide (before metallization) into a rinse of dilute concerning the physical and chemical nature of the insodium chloride solution. Their contaminated oxide was stability and the interrelationshipbetween the symmetric
found to have a significmtly increased instability com- (e.g., alkali ion) instabilityandtheasymmetric
(e.g.,
pared to their control unit, which had the metal electrode water-based )instability.
applied immediately following oxidation. The activation
energy for the initialdrift was found to agree closely
with that for sodiummigration in silica (e.g., 1.4 eV).
11. EXPERIMENT
The recovery or relaxation time constant of the injected
charge was also foundto be of the same order as the time A . Discussion of Measurement Methods
The instabilityor drift of charge in theoxide a t elevated
constant for the initial drift, indicating a relatively symbe measured by
metric type of behavior [3].Based on these results, Snow temperaturesandappliedbiasmay
et al. [2] concluded that the instability observed in MOS several methods:
transistors may well be due to this typeof contamination.
1) shifts in the C vs. V curve of a n MOS capacitor
The present work involves experimental and theoretical
UI, PI,
consideration of the charge migration in a metal-silicon
2) shifts in the surface conductivity vs. applied gate
dioxide-silicon structure. It has been found that in the
bias curve of an MOS transistor,
type of oxides under investigation the time required for
3) timeintegration of thecurrent injected intoan
the apparent relaxation of charges in the oxide upon reMOS capacitor t o obtain the total effective charge
moval of bias may be orders of magnitude shorter than
injected into the oxide [4].
the timerequired
forthe generation of this injected
,
1 Part of this work was presented at the 1965 Solid State Device
Research Conference, Princeton, N. J.
Manuscript received October 12, 1965; revjsed November 9,1965.
The author is with RCA Laboratorles, Prmceton, N. J.
222
1966
HOFSTEIK:
AND
INSTABILITY
223
CHARGE MOTION
Figure 1 illustrates thetypicalresults
observed by
Methods 1 and 2. WhenusingMethod
1 a t elevated
temperatures, the injected charge tends to relax during
1 he measurement of the C vs. V curve, particularly during
: h e period when negative voltage is applied to the gate.
.:.tis therefore usually necessaryto cool the sample before
?.hemeasurement, so as to "freeze-in" the injected charge.
, i n advantage of Method 2 is that thesurface conductivity
nay be monitored continuously without
the need to relnove the drift bias or change the sample temperature.
'!?he disadvantage of Method 2 is that it necessitates the
use of the more complex MOS transistor rather than the
: impler MOS capacitor structure.
I n order to continuously measure the oxide charge in1. Instability in MOS structures as reflected in the shift of
~fucedvoltage shift during the heating-bias cycle, a simple Fig.
the capacitance vs. voltage curve of an MOS capacitor, and the
shift in thesurface conductivity vs. gate voltage curve'of an MOS
I :lectronic sampling technique for monitoring surface contransistor.
liuctivity shifts has been developed. This technique gives
; I direct indication of the voltage shift by measurements
,:.equiring only several microseconds removal of the drift
'5ias. Thetestcircuitandgate
voltagewaveform are
GATE VOLTAG'E WAVEFORM
h o w n in Fig. 2. The "on" voltage, V,,,, is adjusted
nanually and is usually fixed during a test. Thesampling
:)ulses are approximately fiveps long and havea repetition
:,ate of approximately 20 c/s.Thegate
voltageduring
SERVO
. b e samplingperiod, defined as V O Tis
, adjustedautoAMPLIFIER GATE OUTPUT
TEST
TRANSISTOR
.naticallyby a feedbackamplifier tomaintaina
fixed
tmtput pulse height and hence a fixed channel current.
'Shifts in V,, are,therefore,identical
tothe voltage
:,hiftsobserved in the capacitance vs.voltagecurve
as
].hedevice drifts with time. The value
of V,, is monitored Fig. 2. Block diagram of sampling system used to detect shifts in
gate thresholdvoltage. GOTis adjusted to maintain fixed drain
14nd recordedcontinuously
on a strip-chartrecorder.
voltage pulse height during sampling period.
'!?he response time of the amplifier to changes in V o T
i s limited by the sampling repetition rate andthe response
rime of the peak reading voltmeter. For the circuits used,
I his response time was of the order of 0.1 second. Careful
Ineasurements, withthe samplingpulsesrunning
conlinuouslyandwiththe
samplingpulsesappliedonly
periodically (e.g., every five minutes), have shown that
1he sampling does not affect the drift behavior.
I
./I. Xample Preparations
The MOS transistorstructure used for thetests is
illustrated in Fig. 3. The fabrication is as follows:
An oxide, heavilydopedwithphosphorus,isdeposited on the surface of the silicon to a thickness of
one micron.
The oxide ismaskedwithphotoresist
and etched
away, leaving blocks where the source-drain regions
are to be formed.
The surface of the silicon is etched lightlyto remove
any traces of excess phosphorus.
The baresilicon overthe channel region is reoxidized
in dry 0, a t 1100°C foronehourresulting
in an
oxide film of 0.1 p thickness (w,,~= 1000 A). After
the oxidation, the samples are immediately annealed
in dry nitrogen for an additional hour a t t h e same
temperature. An R. F. furnace, with a water-cooled
quartz tube, is used for the oxidation so as to mini-
I/
Fig. 3. Schematic cross section of the transistor used for the tests.
The oxide tested is the 0.1t., thick region under the gate
electrode.
mize contamination of the oxide. Immediately following the annealing, the wafer is allowed to cool
t o room temperature(at a rate of approximately
200"C/min)inside
thequartztubewiththe
N,
flowing, and is transferred to a vacuum evaporator
for gate metallization. Themetal usual1.y used is
nichrome.Details
of the metallization, andparticularly the effectsof various metals and premetallizationhigh-teniperaturebakingin
the vacuum
system, are covered in Sections 11-E and 11-G. The
effects of deliberatecontamination
of the oxide
224
FEBRUARY
IEEE TRAXSACTIONS ON ELECTRON DEVICES
surface prior to metallization are discussed in Sections 11-D and 111-C.
5 ) Holes are opened (usingphotoresist and etching)
in the blocks which have formed the diffused sourcedrain regions during theoxidation, and metalsourcedrain contacts are evaporated onto thesample.
OXIDETHICKNESS
:O.lp
C. E$ed of Surface States
The effect of surface states, or more specifically oxidesilicon interface states, is in general more complex than a
Vg = Vg on
REDRIFT
(e.g. + 2OV)
Vg = Vg on
simple voltage shift, since these states communicate with
the silicon and hence will possess varyingamounts of
trapped charge depending on the applied bias and their
PERIOD
AT 1 6 O O C )
(e.g. 1000:1 )
distribution in energy. The genera1 effect of these states
TIME
is t o change the shapes of the C vs. V curve and the transfer Fig. 4. Qualitative plot of AVgr vs. time for typical test sequence
characteristic curve.
illustratinginitialdrift,apparent
recovery, true recovery time
period, and completely recovered redrift.
I n thispaper,only
the motion of chargewithin the
oxide will be investigated. The shapeof the transfer charF O R W A R D DRIFT WAVEFORM
acteristichasbeenfound
to be unchangedindrifted
T = t l A V ; T2 0 . 5
units,demonstrating that the surface-statedistribution
WATER CONTAMINATEOOXIDES;
for the types of oxides tested is stableunderthestress
0 1 AVO,_ - - 4 0 - 5 0 V
d CONTROLOXIDEAVgTs
-5V
conditions used to induce oxide charge motion.
-
D. Quantitative Results
Figure 4 illustrates a typical test sequence on a unit.
1) Initial Drift
a) E f e c t of surface contamination. The control oxide
was prepared as described in Section 11-B. For negative
applied voltage, no measurable drift was observed up to
250°C (the maximum temperature tested). For a positive
applied drift bias of +20V, a total AVgFshift of 1 to 5 V
wasobservedwithatimeconstant
of lo+*to
seconds
at 220°C.
An investigation was then made of the effects of exposing the oxide surface t o various contaminating treatments just prior to the gatemetallization. These separate
treatments were
1) immersion in hot saturated sodium chloride solution
(90’) for 15 minutes,
2) immersion in hot distilled water (90OC) for 15 minutes,
3) exposurefor
one hour toan atmosphere of 60
percent relativeohumidity,
4) removal of 200 A of the oxide using an HF-H,Q etch.
The first three of these treatments generated a significant
asymmetric type instability. The most dramatic increase
wascausedby
boththeNaCl
rinse andthe distilled
water rinse. Most interestingly, no significant difference
was observed between units treated in the distilled water
and units treated in the NaClrinse.
The etched oxide, on the otherhand,(Treatment
4)
wasfound to be naore stable than the “control” oxide
(e.g., AV,,, < 1V)eventhough
the surfacehad been
exposed to a waterrinse foIIowing the HF-H,Q etch.
It appears, therefore, that the action of the water which
produces the instability inthe unetched oxide is dependent
I
0
1.0
I
I
2.0
30
I
I
4.0
50
t’ = t,TF
I
6.0
I
7.0
8.0
I
9.0
Fig. 5. Normalized plot of time dependence of thresholdvoltage
shift for forward drift, i.e., initial drift and completely recovered
redrift. Note variation in slope near origin. (See Figs. 10 and 11
for variation of T~ with temperature and field, respectively.)
on the presence of a “catalytic agent” which is apparently
removedwhen the oxide surface is etched.(Thispoint
is discussed further in Section 111-C.> It has also been
found that exposure of this etched oxide surface t o a concentratedsodiumchloriderinsereintroducesa“quasisymmetric” or slow-recovery instability. This instability
is currently under further investigation.
The remainder
of the paper will be concerned primarily with the analysis
of the highly asymmetric type instability
exhibited by the
water-contaminated, unetched oxides.
b) Transientbehavior of the initial drift. The waveform of the AV,T vs. time curve for the initial drift was
generallyfound to be somewhatvariable.Figure
5 illustrates several of thesetypicalwaveforms.Although
the general shapes of the curves are exponential-like, the
slope near the origin can be quite nonuniform. The probable cause and significance of this nonuniformity is discussed in Sections 111-B and 111-c.
The time constant for a particular curve may
be defined as the time required for AV,T to reach 0.5 of its
maximum value. This point has been found t o be relatively insensitive to variations in the initial slope of the
curve.
1966
INSTABILIT
HOFSTEIN:
225
'Y AKD CHARGE ,MOTION
RECOVERY WAVEFORM
T E M P E R A T U R ED E P E N D E N C E OF
FORWARD DRIFT TIME CONSTANT
VgR =
- I.0V
T = 32°C T - I l O s e c
T = 42"C:T;=
54sec
Q
T 2 8o'c,rR= 2 . 1sec
n ? = I2O0C,TR= 0 . 2 2 sec
c
P
a
-=}THEORETICALCURVES
t" t /TR
Fig. 8. Normalizedplot of time dependence of thresholdvoltage
for (apparent) recovery. See Figs. 9 and 10 for variation of TR
with temperature andfie1 , respectively.)
6
I
0.I
I
0.7
0.6
I
I
I
200 120
160
0.8
To / T
I
I
100
0.9
I
I
80
60
OC
.Kg. 6. Temperature dependence of forward drift time constant.
200°C) by over four ordersof magnitude comparedt o that
of the controlwafer, andhas reduced the activationenergy
from 1.4 t o 1.0 eV. The maximum voltage shift
AV,,,
also increased by approximately one order of magnitude.
2) Recovery. I n order t o measurethe recovery time
constant as a function of temperature, the unit was first
drifted until AVO, was 30V; then the gate voltage was
returned t o -1.0 V. I n strikingcontrast to theinitial
drift, the waveforms of AVQTvs. t for recovery showed
much better uniformityfrom unit t o unit. Referringt o Fig.
8, the theoretical curves are 1) an exponential and 2) a
modified "exponential",where
it is assumed thatthe
time constant increases as the charge is exhausted from
the well. If, for example,
where to a first approximation r R a l/Q,then
where
8' = t/r&!*
Although it is n.ot apparent from superficial examination
that 1/(1
t') behavessimilarly to an exponential,it
can be seen from Fig. 8 that the difference between the
Fig. 7. Dependence of forward drifttimeconstanton
applied two curves is not very great, and
that it is significant
voltage.
primarily in the slower fall of the 1/(1 4- t') curve for
t' > 1. I n no case was a ( t ) type waveformobserved
for the recovery.
Figures 6 and 7 show semi-log plots of the typical temAnalogous t o the case of initial drift, the recovery time
perature and voltage dependences of the forward drift'
constant rB is defined as the time required for AV,,, t o
time constant for both an oxide which was immersed in
fall t o one half its maximum value. A semi-log plot of
hot distilledwater(90°C)foronehourprior
togate
rR vs. 1/T for both the control unit and the
oxide exposed
metallization and for the control
oxide. From Fig. 6 it
to water are shown in Fig. 9. One of the most significant
can be seen that the exposure of the oxide t o the hot
results is that the recovery time constant is substantially
H,O has decreased the forward drift time constant (at
smaller than the initial drift time constant, particularly
when one considers the relativelylow negative gate voltage
* The term "forward drift" refers to both initial drift and com- appliedduringtherecovery.Thisasymmetricbehavior
pletely recovered redrift (see Section II-D, Apparent Recovery and
has also been reported by Logan and Kerr [4] (see Fig. 10)
T r u e Recovery).
+
226
IEEE TRANSACTIONS ON ELECTROX DEVICES
1000-
-
1
I
I
RECOVERY
TIME
CONSTANT
vs.
I
/
TEMPERATURE
I
0.7
/
I
0.8
1
200
120
160
100
I.o
09
TOIT
-1
FEBRUARY
80
I
I
60
27
OC
Fig. 9. Apparent recovery time constant as a function of
temperature.
Fig. 11. Apparent recovery tiple constant as a function of applied
voltage during recovery. Semi-log plot.
100
-
IO
v)
z
u
-r-p
0
v)
I
I-
-z
2
CONTROL
,
-0
I
5
,
,
I
,
I
,
10
(sech
rn
,
,
~
15
I
1
/
1
1
20
Fig. 10. Plot
of.representative
injected
charge
vs.
curve
for forward drift and recovery in a thermally grown oxide, as
reported by Logan and Kerr [a]. Note the asymmetry and lack
of a clear P 2 behavior (courtesy of J. Logan and D. Kerr).
and is strikingly different from the more symmetric type
of drift-recovery reported by Snow et al. [a],131.
It is also interest’ing to note that although the forward
drift time constants for the two types of units differ by
orders of magnitude (see Fig. S), the recovery time constants show “factor of two” type agreement. The field
dependence of this “fast” recovery was measured for the
water-contaminated oxide by varying thenegative voltage
applied to the gate during
recovery. The results are plotted
in Fig. 11 on a semi-log scale and in Fig. 12 on a log-log
scale. These curves show that the field dependence of the
recovery differs substantially from the field dependence
of the forward drifts (Fig.
7 ) . The significance of these
results anda discussion of their probableorigin is presented
in Sect’ion111-B.
O’’
0.60.6
1.0
2
4
6 810,0
VgR
20
40 60
- Vgh
Fig. 12. Apparent recovery time constant as a function of applied
voltageduring
recovery. Log-log plot.Holdingvoltage
(Vgh)
measured as 1.0 & 0.1 V.
3) Apparent Recovery and True Recovery.
If, following
initial drift, the gate voltage is reduced to zero or some
negative value, the oxide voltage shift AVpT will recover
to zero. If, immediately following recovery, the positive
gate voltage is reapplied, the oxide voltage shift AVoT is
observed to rise to its prerecovery value a t a much faster
rate than that for the initial drift (see Fig. 4), Hence,
although V O Thasapparently recovered toits original
value, the oxide has obviously not been restored to its
original condition.Thisrecovery may be defined as an
Lt
apparent recovery”. If thegate is now maintained a t
zero or a negative bias for a period of time of the order
of severalinitialdrifttimeconstants,
then upon reap-
1966
227
HOFSTEIN: INSTABILITY A K D CHARGE MOTION
plication of apositive gate bias, the redrift is almost
identical to the initial drift. This is referred to as a “recovered redrift”. It is apparent, therefore, that some sort
of relaxation process, not reflected in changes in Vvr,
is
taking place in theoxide during this additional“relaxation
period”. This type of recovery may be referred to as a
true recovery (since the oxide appears to have been restored to its original predrifted state) and the required
relaxation period may be defined as the “true recovery
time period”.
Quantitatively, it has been found that if following apparent recovery the positive drift bias is applied to the
gate within a time period short compared with the apparentrecoverytimeconstant,
then the redrift occurs
-with a time constant essentiallyequal to the apparent
recovery time constant. I n other words, a “symmetrical”
type of instabilitywith a timeconstantmuchshorter
than that of the initial drift now takes place.
It will be shown that the apparent recovery vs. true
recovery, as well as the asymmetry in initial drift and
recovery time constants, is consistent with a trapping or
dissociation phenomenon taking place at the metal-oxide
interface region. This model and its evaluation in light
2f the experimental results is considered in Section 111-B.
E. Generation of a SymmetricInstability
in a WaterConta.minated Oxide
Since it appeared that exposure of the oxide surface
Go water vapor prior to gate metallization increased the
mtability, a heater was installed in the vacuum evaporator. With this arrangement, the wafer could be heated
in vacuum just prior to the gate
metallization. It was
hoped that this would remove the water adsorbed on the
SiO, surface [6].Indeed, it was found that a vacuum bake
: h t approximately 400°C to 500°C for several minutes restored thestabilitytothat
of the control wafer. The
Lotal voltage shift which could then be induced in a unit
of this type was AVO,. = 1 to 5 V, and the initial drift
time
constant
was
to
seconds a t 230°C. The
I’ecovery time constant, however, was still equal to that
of the distilled water-treated oxides and hence, was still
orders of magnitudesmaller thanthat for the initial
drift. In an attempt remove
to
what was believed to be the
lsemainder of the water adsorbed on the film, the vacuum
‘bake temperature was raised to 700°C. It wasfound
that the initialdrifts of oxides treated in this manner
were no different fromthose for the oxides baked a t
500°C. However, the recovery m7as now observed t o consist
of twocomponents; the original fast component and a
lnuch slower component with a timeconstant
much
(:loser to that of the initialdrift.This
is illustrated in
Fig. 13.
Experimentally, it is found that up toa certain voltage
shift AVL,, the recovery consists solely of the fast component. For AVgT > AVL,, the slow component of magIdtude AVg, - AVL, appearsinthe recovery. No sigIdicant change inthe waveform of the initialdrift is
observed a t AV,, = AV;,. This slow component is
I
V9,,’+2OV
vgR= -
I.0V
~
aI
SLOW RECOVERY
TIME
Fig. 13. Alternating forward driftand recovery cycles qualitatively illustratingappearance of slow component in recovery.
This behavior is typical of oxides preheated to 700°C in vacuum
to remove adsorbed surface water prior to gate metallization.
probably related to the “symmetric” type of instability
reported by Snow et al. [2], and may well be due to the
motion of alkali ions. This point is discussed further in
Section 111-C.
F. Efects of Hydrogen Annealing
The surface-statedensities of the control and watertreated oxide have been investigated using boththe
C vs. V measurement [7] and the shift in
threshold voltage
( V O r vs.
) temperature measurement [SI. The C vs. V
methodisparticularly
useful in determining the oxide
charge density and the density of fast surface states (or
more specifically, interface states) which lie in energy a t
least 6 k T away from the edge of the minority carrier
band (the conduction band, in thiscase, since we are using
p-type bulk silicon). The V O Tvs. temperature technique
complements the C vs. V technique in thatit can evaluate
surface-state densities lying within 6 k T of the conduction band edge.
The control oxide possessses a relatively low positive
oxide charge density (e.g., 3 X 10+11/cm2when reflected
tothe oxide-silicon interface)characteristic
of, “dry”
grown thermal oxides. However, an extremely high density
of fast acceptor typeinterface states (e.g., 5 X 10+12/cmz),
located within 10 k T of the conduction band edge, has
also been observed. The appearance of these fast states
seems to be due to the extremely dry oxide growth conditions, as the addition of slight traces of water vapor to
the oxygen ambient during growth reduces their density
to less than 5 X 10+11/cm2.
We have also examined the surface-state densities and
stability of finished devices which were annealed in hydrogen before metallization. The following observations
were made.
Exposure of the control oxides to hydrogen a t 700°C
forseveralminutes
a) reduced thefast surfacestate density
from
5 X
to less than 1 X
10+1z/cm2, andb) did not measurably increase the
positive oxide charge above its original value of 3 X
10+11/cm2.
Stability of the oxides exposed to hydrogen as described in the previous observation was the same as
that described for the unexposed control oxides.
228
IEEE TRANSACTIONS ON ELECTRON DEVICES
It may be inferred from this that the hydrogen which
reacts at the oxide-silicon interface t o remove the fast
surface states is chemically bound in a relatively stable
fashion. No definiteconclusion is drawn a t thispoint
regarding thestability of a hydrogen-inducedpositive
oxide charge under applied
field and elevated temperature.
G. Efects of Gate Metallization
To determinewhat effects, if any, thetype of gate
metal has on the instability, units were fabricated with
gates of gold, nichrome, chrome, nickel, and aluminum.
No significant difference in instabilitywas observed. These
results are in substantial agreement with those obtained
by Yamin [9] concerning the effect of various metallizationson the chargestoragein
SiO, films. Yamin has
reported thatthe noblemetals
(e.g., gold,platinum)
produced charging curves which differed in some respects
from those produced by “active” metals (e.g., aluminum,
chrome).However,these
differences were slight compared with, for example, the effect of phosphorus.
It has been found in the presentinvestigation, however,
that at elevatedtemperatures (e.g., 4OO0C), reactions
between the various metal electrodes and the oxide can
occur which will modify the behavior of the instability
and,inparticular,
the forwarddrift activation energy.
This is notably so for the case of aluminum. It should
thereforebeemphasized
thatthe results discussed in
this paper were obtained for and apply only to the case
of inert or “unreacted”gateelectrodes.
The possible
effect of metal ions on the initial drift activation energy
is discussed further in Section III-C.
111. DISCUSSION
A . Qualitative Aspects of the Model for Instability
From the general shape (or behavior) of the AV,, vs.
time curves,severaldeductionscan
be maderegarding
the natureof the instability.
1) Asymmetry of Initial Drift with Respect
to Polarity
of Applied Bias. The application of negative voltage to
the metal gate has been found to produce no drift in the
type of oxides under investigation. It may be concluded
from this observation that the mobile charge responsible
for the instability is not initially distributed throughout
the oxide. If it were, application of both polarities of
voltage would result in charge motion and drift in the
thresholdvoltage.(Thissymmetricaltype
of behavior
has beenobserved in MOS capacitorsusing a layer of
glass as the insulator, indicating that the glass as fabricateddoes,
in fact,containmobilecharge.)Hence,
the chargeresponsiblefor
thedriftmust
beeither 1)
positive charge at themetal-oxide interface or 2) negative
charge at the oxide-semiconductor interface.
The lack of initialband-bending(asdeterminedby
C vs. V measurements) characteristic of negative charge
in the oxide, however, indicates that the source of the
instability is positive charge which moves into the oxide
from the oxide-metal interface region.
FEBRUARY
Whether this charge is injected by the metal contact
or whether it is already present at a point slightly inside
the oxide cannot be determined from the voltage polarity
asymmetry experiment alone. The injecting or blocking
nature of the metal-oxide contact can, however, be determined from the following behavior.
2 ) Saturation of Drift Voltage. It has been found that
after a sufficient period of time, the oxide voltage shift
saturates a t some value AVn,,. If the metal-oxide contact
is a blocking or noninjecting contact, this saturation can
be explained as a supply limitation effect, where all the
available positive charge near
the metal-oxide interface
has been moved across the oxide to the silicon interface.
If the metal-oxidecontact is injecting,a saturation of
A V O ,could be explained as a steady-state situation, where
the injection of positive ions into the oxide by the metal
is balancedby the neutralization of this charge a t t h e
oxide silicon interface via trapping of electrons from the
silicon. Direct measurement of the current flow into the
metal gate of the samples tested, however, hasshown that
aftersaturation is reached, current flow is reduced to
essentially zero. I n addition, once AV,T saturates a t
AV,T,, increases in bias or temperature cause no further
change in AVO*, alsoindicating thatthesaturation
is
not a steady-statebalancing out of two opposing processes.
A second possibility with an injecting contact is that the
injected ions polarize the oxide, so that the field at the
metal-oxideinterface is suppressed to zero and the injection ceases. However, since increases in bias or temperature produce no further drift in V O T
once saturation
is reached, this model is also ruled out.
It may therefore be concluded that the initialdrift
is due to the transport of a fixed number of positive ions
from the metaI-oxide interface region to the oxide-semiconductor interface region.
3) QualitativeAspects of the Apparent Recovery. The
recovery or relaxation of the positive charge in the oxide
may be due to twomechanisms:
1) the positive charge is transported back to the oxidemetal interface region;
2) the positivechargeremains
atthe oxide-silicon
interface, but isneutralized
bythe trapping of
electrons.
I n order to evaluate the possibility that the positive
ions act aselectronic trapping levels deepin theforbidden
gap of the oxide, the effects of excitation of electrons from
the silicon into theconduction band of the oxide by means
of ultravioletlight were investigated. R. Williams [lo]
has reported on the injection of electrons into thermally
grown SiO, of MOS capacitors by means of ultra violet
excitation.Hismeasurements
on drifted oxides have
shown the presence of astrong(e.g.,10+13/cm2)layer
of positive transported charge inthe drifted unit, but have
not indicated an increase in the number of active electron
traps [ll].These traps remained at the undrifted initial
value of 10+10/cm2.I n experiments involving the direct
effect of theultravioletirradiationontheinstability,
1966
HOFSTEIN
: ISSTABILITY AND
the author has observed no effects on either the initial
drift, recovery, or redrift. Based o n these results, it may
beconcluded thatthe positivelychargedions
inthis
case do not act as electron traps. Since the drifted positive
charges are not neutralized by
electron trapping, it can
further be surmised that the recovery of a drifted oxide
is due to the motionof these positive charges back to the
oxide-metal interface region.
The next two sections will consider, respectively, a) the
quantitative electronic and physical characterization and
bj the chemical nature of the model for the instability.
B . ElectronicandPhysicalCharacterization
for the Instability
of the Mode2
It has beenproposed that the asymmetry of the instability is related to an ionic trapping effect at themetaloxide interface. I n this model, it isassumed thatthe
positivelycharged mobile ionsinitiallyresideintraps
locatednear the metal-oxideinterface. The initialdrift
consists of “emission” or dissociation of the ions from
these traps under the influence of the appliedelectric
field, followed by a rapid drift of the ions across the film
t o the oxide-silicon interface region.The activationenergy
and ‘ trap half-width”, i.e., distance from center to edge
of potential well, calculatedfrom the initialdrifttemperature and field dependences are, therefore, related
to
thetrap potential well depthandwidth,
respectively.
(Thus, this model differs from that of Snow et al. [a]in
which trapping effects are neglected and in which it is
therefore assumed that the initial drift activation energy
is directly related to thediffusion coefficient for ionmotion
in a ‘.bulk” oxide.) The asymmetrical rapid apparent recovery is then due to thelack of a similar strong trapping
effect at the oxide-silicon interface. Whether or not
the
lower activation energy for recovery represents the true
mobility of the ions in the bulk of the oxide or whether it
is due to a weaker trapping at the oxide-silicon interface
is discussed in this section under Quantitative Aspects.
There, it is concluded that, trapping may still play a role.
Following apparent recovery and the returnof the ions t o
the oxide-metal interface, the true recovery time period
ensues, corresponding to the slow “retrapping” of these
ions until the oxide is once againrestored to its initial
state.
The nature of this trapping at themetal-oxide interface
and the mechanismsgoverning the behavior of the apparent recovery will now be considered in detail.
1 j Nature of thetrappingat
the Metal-oxideinterface.
The excellent exponentialvariation of the initialdrift
time constantwithtemperatureand
field yield clearly
defined values for the trap potential well depth and well
‘half-width”. Referring to Figs. 6 and 7 for the materweated samples, the trap depth is approximately 1.0 t,o
1.1 eV, and the half-widthis of the order of 7.5 h to 8.0 A .
For theuncontaminatedcontrolunits,initialdrift
ativation energies of the order of 1.4 eV are observed.
This larger activation energy is also quantitatively con-
C H A R G E LIOTION
229
sistent with the observed greater initial drift time
constant, e.g., for E l = 1.0 eV and G2 = 1.4 eV, one predicts
and for T
=
200°C
Referring to Fig. 6, it can be seen that this predicted ratio
is in good agreement with the observed value.
It may also be concluded from these results that the
potential well depth of the traps (or dissociation energy
for the mobile ion) at the oxide-metal interface is somewhatvariableand
will dependon
thetreatmentthe
oxide surface received prior to metallization. This in is
strong contrast to the close agreement in time constants
and uniform activation energy observed for the apparent,
recovery of both the control and distilled water-treated
units (see Fig. 9).
The control oxide initial drift waveform has also been
found to vary somewhat between units, particularly with
respect to the slope of the curve at the origin. This could
well be due to nonuniformity in the distribution of remnant adsorbedwateron
the surface of the oxide. It is
interesting to notethat,incontrast,themater-treated
oxides show excellent reproducibility and uniformity of
the exponential-like init’ialdrift waveform. Snow et al. [2]
have reported that although their curves were generally
of exponentialshape, theyappeared
to possess a t”’
dependence for t < rR. This type of dependence is characterized primarily by a steeply rising curve and infinite
slope at the origin. Logan and Kerr [3] havereported
that their initial drift curves failed to show a similar t”’
dependence (see Fig. 10). In the presentinvestigation,
insufficient evidence has been found to support a fit to
a t’” type behavior for the initial drift or recovery of the
asymmetric type i n ~ t a b i l i t yIn
. ~ general, a spread of only
a few k T in the activation energy of the interface traps
can modify the shape of the exponential sufficiently to
account for the observed results.
The exponential-likeshape of the AVgT vs. t initial
drift curve is also consistent with the model of emission
of ions from traps. Quantitatively,
(a)
where Q T ( 0 ) = total charge unitarea initially trapped
at the oxide-metal interface, and r F = ( v * Z ~ ).~ ” ~ ~
For € T
1.0 eV, k T = 0.031 eTT (T = lOO”C), and
assuming v*
1 0 + l z / ~ e ~ ~[13],
n d the predictedt’ime
constant for initial drift is of the order
-
r, =
(10+12*e-32j-1
w IO+’ seconds.
(6)
3 The theoreticalprediction
of a t 1 / 2 dependence derived by
Snow et al. arises from an artifice used in setting up their model.
This is discussed in Appendix I.
230
IEEE TRANSACTIONS ON ELECTROX DEVICES
This is in quite good agreement with the experimentally
measuredvalue a t thistemperature,particularly
considering the simplifying assumptions employed.
Some additional boundary conditions on
the possible
nature of the traps may be determined by evaluating the
behavior of the forward redrift before completion of the
true recovery period. It has been assumed that the apparent recovery consists of the motion of the mobile ions
back to the oxide-metal interface and that the true recovery is then due to the subsequent slow retrapping of
these ions as they wander about thermally in the oxidemetal interface region. Based on this model, it would be
expected that a forward redrift before the completion of
true recovery would consist of two components. The
first would be a“fast”component,due
to the drift of
the still untrapped ions back to the oxide-silicon interface.
The second would be a slower component, similar t o the
initial drift, duet o the emission of the trapped ions.
This “two-component” type of behavior, corresponding
to twodistinctactivation
energies, although observed
for the recovery of some units (see Fig. 13) hasnever
been observed for the forward redrift. Rather, it appears
as if there is a single activationenergyfortheredrift
which increases continuouslyduring thetrue recovery
time period from an initial value (immediately following
theapparent recovery) close t o that for theapparent
recovery, to a final valueequal to that for the initial
drift.Thus,itmay
be concluded that during the true
recovery period, the trapping mechanism must act in a
relatively uniform fashion on all the ions if the two component type redrift is not to be observed.
It should be emphasized thattheapparent need to
assume uniform action on the ions by the traps does not
mean that thetrapping at theinterface cannot be localized
defect trapping. Rather, it simply means that the time
constant for this trapping must
be quite small with respect to the true recovery time period and that a second
mechanism other than this trapping time must be found
to explain the subsequent true recovery time period.
It is of interest a t this point to numerically evaluate
this trapping time constant for theoxides currently under
discussion and t o compare it t o the observed true recovery time period. This calculation is done in Appendix
11 using the experimentally measured parameters. There
it is shown that the trapping time constant is of the order
of
seconds (T = 140°C). The observed true recovery
time period at this temperature is of the order of loc2
seconds. Hence, it maybe concluded that all of the mobile
ions are essentially reassociated with a trapping site almost
immediately after the apparent recovery. The word “reassociated” rather than re-trapped has been specifically
chosen to indicate that there is now an additional internal
relaxation process which takes place within each ion-trap
pair. Specifically, it appears as if the ion-trap pair slowly
changes its internal structure during the true recovery time
period so thatthebindingenergy
or potentialwelldepth
FERRTSAPY
forthe ionincreasesfromsomeinitiallysmallvalue
to a
jinalvalueequal
to theoriginalinitialdriftactivation
energy.
2) QuantitativeAspects of the Apparent Recovery. Fo1.lowing saturation of the initial drift, the mobile ions are
crowded close to theoxide-silicon interface [see Fig. 14(b)].
The averagespatialdistribution
of these ions may be
found by solving Poisson’s equation in conjunction with
Boltzmannstatistics. For the simple case of a “senliinfinite” bulk of intrinsic material with an applied surface
field E , and with a sufficient number of carriers so that
all the surface field may be terminated on these carriers,
i.e., E ( a ) = 0, the field, voltage, and chargedensity
profile may be shown t o be [12], [14]
n
jqx’) =
b
1 + X ’ -
p(x’) =
x,
=
E,
=
- electric field a t point
8
Qx =
p,
(1
(71
2’
+ x’) 2 = charge density a t point x’
[?I”’
=
DebyeLength4
SurfaceField
Lm
p(x) dx
=
M
= Q,/e
=
=
VT/E,
(8)
(10)
E(0)
2qpp,X,
T’olume density of ions a t surface
=
p(0)
=
P(O)/XS.
Fig. 14. Qualitativeillustration of the motion of chargein the
oxide. Trapping sites arenot indicated. (a) initial condition,
positive charge located close to the metal-oxide interface. Essentially,none of the oxide changeiscompensated in the silicon.
(b) After initial drift, oxide charge is located close to the oxidesilicon interface. Essentially, all of the oxide charge is compensated in the silicon. (e) Holding voltage applied, further reduction
in the applied voltage will result in recovery. (d) Apparent recovery, charge has returned to oxide-metal interface.
4 Note that this Debye length is not an intrinsic property of the
insulator, but rather depends on the surface field and excess charge
density.
1966
HOFSTEIN: INSTABILITY AND CHARGE MOTION
Since, however, there is usually a fixed amount of ion
charge Qx availableperunitarea,theapplied
surface
field may be such that
E , 2 Q d e = Ex.
The exact analytic solution to Poisson’s equation for this
case, which would give E(x) and V ( x )explicity, is quite
complex and is not readily suited for purposesof physical
interpretation. I n order to understandthe
significant
aspects of the physical behavior, however, the approximation may be made that the mobile charge layer extends
from the surface into the insulator
to a point a t which
the voltage is several 8,.This is equivalent to saying
that most of the chargeresides within a few Debye lengths
from the surface, where the Debye length is computed
on the basis of the charge density at the surface p , [14];
[see (lo)].
The oxide maytherefore beconsidered to consist of
two regions: a potential well region extending from x = 0
t o x = X, = VT/E, whichcontainsthe mobile charge;
andacharge-free region X, < x < W,, where the field
is essentially const’ant a t
E,
=
( E , - EA).
(11)
231
Ths use of the geometric capacitance C, is justified since
the charge Qx lies very close to the interface as compared
to the oxide thickness.
3. Transient Behavior of Recovery. As long as the field
E , in the “bulk” or charge-free region of the oxide remainsevenslightly
positive, the positive ions will remain close to the oxide-semiconductor interface.
As E , is made slightly negative, the ion charge in the
potent,ial wellwill begin to be “enzitted” over the edge
of the well and mill be transported to the metal-oxide
interface region. For the simplified case of no ion trapping,
we may consider thetransient behavior following the
application of a “step” recovery voltage VnR<< AV,,.
For timessmallcompared
with the ion transit time
across the oxide, the charge injected by the
well is localized
near the well and its magnitude is given by C0VGE.
In
one transit time this injected
space charge spreadsthrough
the bulk of the film giving a distributed charge for which
thecapacitance is approximatelydoubled.The
leading
edge of the charge arrives at the opposing interface in a
time slightly shorter than the uniform field transit time
T T = Wox2/pV,
since it sees a higher average field during
its transit due to the increased capacitance effect of the
distributed charge. After the leading edge of the charge
arrives at thecathode the current in the
film will be higher
than its steady-state value since the space charge in the
film is slightly higher than its steady-state value. Within
a n additional transit time, the space charge in the film
drops to its steady-state value and a quasi-steady-state
current is observed untilthe wellis exhausted of its
charge. When the volume density of charge in the well
drops to that in the bulk adjacent to the well, a trailing
edge of the charge appears, similar to the leading edge
generated at the start of current flow. This trailing edge
moves across the film in a time of the order of a transit
time, the current dropping sharply as it reaches the opposing interface. This transient behavior has been analyzed
quantitativelybyMany
[15], Markand Helfrich [16];
their results are illustrated in Fig. 15.
Referring to Fig. 14(c), it can be seen that the application of a positive voltage of a few volts to the metal gate
should maintain E , positive and AVO, at its maximum
drifted or saturated value. This is true even if the voltage
drop of order V , = k T / q across the potential wellcontaining the ions and the typicalwork function differential
between the metal gate and the
semiconductor are included.
Experimentally, it has been found that values of AVnTs
as high as several tensof volts have been maintained with
appliedgate voltages as low as + l to +2 volts (e.g.,
Fig. 11) confirming the conclusion that the positive ions
are crowded close to the oxide-semiconductorinterface.
I n typical devices, the interface field generated by the
ionic charge may rise into the 1 to 5 X 10‘ V/cm range.
The correspoonding calculated Debye lengths [see [lo)] are
‘t6
1 to 5 A for T = 200°C. I n silicon, a Debye length
xor electrons or holes this smallwouldimmediately inIs c
rlicate that the carrier density must be degenerate (e.g.,
I
>2 X
cm3) and hence thatthe use of Boltzmann
scss
statistics is invalid. For the case of a massive localized
particle such as a n ion and the densities under consideration,Fermistatisticsarenot
applicable, andthe ions
may be treated asa Boltzmann gas.
It is interesting to note thatfor oxide fields high enough
so that the calculated X, is less than the oxide lattice
044
EXHAUSTION^\
wacing,theions
will be essentially containedwithin
O F CHARGE
FROM RESERVOIR \\
the first lattice plane at the interface.
\
The threshold or “flat band”voltageshiftgenerated
by the ionic charge transportedto theoxide-semiconductor
TIME
iliterface is
Fig. 15. Startingtransient
of space-charge-limited current flow
(as analyzed by A. Many and by P. Mark and W. Helfrich).
AVO,= C o Q h .
(12)
232
1EE.E TRANSACTIONS ON ELECTRON DEVICES
For anapplied voltage V,, >> AVOTO,the well willinject
all of its charge into the film immediately following the
application of the voltage, and a “supply-limited”current of the order
I---=-&x
TT
COAV,T,
TT
(13)
will be observed for a time rT.
Returning tothe
“space-charge limited” case, i.e.,
V q R<< AV,,,, thetimeconstant
for the recovery is
simply the timerequiredfor
the space-charge current
to exhaust the charge reservoir, whence
where I,, = average transient space-charge current flow
during recovery. Since for V n R<< ABoTo,
T, >> r Tand the
space charge current flow is essentiallyconstant a t its
“steady-state” value
during the major portion of the apparent recovery, the
approximation of (14) is quite good, i.e., I,, M I,,,,. The
time dependence of QA and AV,, should t’lzereforebe
FEBRUARY
waveform of AVoT vs. t for AVOTO= - 1OV was identical
to the -lOV < AVO, < OV portion of the waveform
obtainedfor AV,To = -3OV. Thisbehavior was particularly striking for some curves which possessed a slight
“fine structure” (e.g., slight “bump” in the curve a t a
particularvalue of AV,,) where it was found that the
fine structure always appeared atthe samevalue
of
AV,T regardless of the value of AT’,,..
These results, and in particular the dependence of waveform on only the instantaneous values of AVO, (and hence
the instantaneous value of ions remaining in the well a t
the interface) strongly indicate that the behavior during
recovery is controlled by a “supply-limited” emission
from the well of ionic charge rather than by some form
of space-charge dominated transient behavior in the bulk
region of the oxide with the well acting as a virtual anode.
The trapping mechanism cont’rolling the emission from
this well, however, seems substantially different from that
controlling emission at the oxide-metal interfacefor a t
least two reasons.
1) S o long relaxation time analogous to the true recovery time period isfound following initial drift.For
example, the recovery waveform andactivationenergy
are independent of the length of time that AV,, is maintained in saturation following initial drift, and for that
matter, whether or not AB,, is even allowed to reach
saturation before recovery is induced,i.e.,
\AVQToI<
lAV*T81.
This indicates that the oxide-silicon interface traps do
not possess the unusual internal relaxation process of the
where
oxide-metal interface traps discussed in the first part
of Section 111-B.
2) The field dependence of the recovery time constant
(see Fig. 11) in the high-field regime, Le., VgR < -lOTi,
I n other words, for the trap free case under consideradoes not show the same well-defined exponential behavior
tion AVQT should decrease linearlywithtime
untilit
observed for the initial drift time constant.
returns to zero.5
The exponential field dependence, predicted foremission
Experimentally, it is found (see Section 111-B, Quanfrom a trap, stems from the simplifying assumption of a
titative Aspects) that the A V e T vs. t waveform is very
fixed potential barrier width and hence a linear variation
close to an exponential. I n addition, it is also found that
of the trap’s barrier height wit’h applied field. If the apas V,, is increased to values comparable with A V Q T ono
plied field is of the same order as the internal field of the
transition from a space-charge limited case t o a ‘Lsupplytrap, however, this perturbation technique is no longer
limited” case is observed. I n fact, it is found that with
validand the variation of thetrap’spotential
barrier
appropriate normalization of the time scale, the recovery
width with applied field must also be evaluated.
waveform is independent of V,, forvalues of V,, exFor example, an ion which lies close to the oxide-silicon
tending from a fraction of,a volt t o the maximum vaiue
interface will experience a trapping force due to its OTW
before oxide breakdwon (e.g., V,, = 5OV, W,, = 1000 A).
image chargesimilar t o that observed for an electron
I n anotherexperiment, the recovery waveform was exemitted from a metal. This image charge createsa poaminedfora
fixed value of V B R(e.g., -1.0 TrOlt) and
tential well which extends out from the interface with a
several different values of AV,,,. It was found that the
field and potential profile
transientbehavior
of ABo, during- apparent
recovery
-was
independent
of the value of AVQTO.
For
example, the
E ( x ) = ___q
(18)
16r E X 2
6 This behavior is in contrast t o that for the model proposed by
Snow et al. [ 2 ] , where it is assumed that emission from the well of
ions is the limiting factor even in the absence of traps. In Appendix I,
it is shown that
this
last
assumption is inconsistent’with
the physical
model.
and
V ( s ) = -Q
16r
E
x
HOFSTEIN : IKSTABILITY AND CHARGE MOTION
1966
Modulation of thispotential well profile by the application of a n electric field normal to the surface of the
metal is simply the well-known Schottky “barrier lowering” effect. This leads to acurrentand
recoverytime
constant of
233
This is a very large diffusion Coefficient for ionic motion.
For example, Owen andDouglas [17] havereporteda
diffusion coefficient for Kain SiO, a t 140°C of about
4 X 10-4pZ/hour,which is about 1 X
cm2/s.From
(23), the diffusion coefficient a t 140°C is
D 2 5 X lo-’’ cm2/s at
a t least four orders of magnitude larger than that for Na.
Summarizing, it appears as if the apparent recovery is
dominated by trapping effects at the oxide-silicon interface. The exact origin of these traps is not known (e.g.,
image force trapping, defect trapping,etc.)otherthan
the fact that they differ in several aspects from the traps
at the oxide-metal interface. Using the recovery data,
a lower limitfor the diffusion coefficient of the mobile
ion has been computed.Thetrue
value may be substantiallylarger if trapping at the oxide-semiconductor
interface is, in fact, the cont,rolling mechanism.
where
B
=
constant,
or
In
TR
CY
-In I ,
7
-
CY
VBE,
=
YdE
where
y =
14OoC,
constant.
Referring t o Fig. 11, it can be seen that theIn T , vs. V o R
curve does possess a “roll-off” qualitatively similar to a
In rBa behavior.Quantitatively, however, it
is found that the “roll-off” is faster than a
dependence, with T , tending to saturate at some minimum
value (e.g., 0.2 seconds for Fig. 11). This indicates that
the applied field rapidly reduces the effective barrier
width to such a small value that further increa,ses in this
field result in only slight decreases in the barrier height.
Part of the reason for this discrepancy may lie in the use
of a “bulk” dielectric constant for t’he field and potential
profile, whereas inreality, localized field distlortions in
the oxide over the atomic dimensions involved may sub.$tantially modify this concept.
C. Chemical N a t w e of the Instability
I n Section 11-D, brief consideration was given to the
dc
effects o n the initial drift resultingfromcontamination
of the surface of the oxide prior t o gatemetallization.
It has been found that the presence of water a.dsorbed on
a n unetched oxide surface severely increases the subsequent asymmetric type instabilityand that a light etching of the oxide surface greatly reduces this sensitivity
towater. Based on theseresults, itmaybe
surmised
that theasymmetric instability is relat,ed to aninteraction
of adsorbed surface water with a “catalytic impurity”that
is located near the surface of the oxide. The highly mobile
ion produced may well be a hydrogen ion, as this species
is well-known for its high mobility in silica. For example,
4) Difusion Coeficient. ReferringtjoFig.
12, itcan
Hetherington et al. [5] have reported observing a highly
he seen that in the lowfield regime, i.e., s i g R > -lOV,
mobile ion in silica postulated t o be hydrogen and produced
:I log-log plot of rR T ~ S . VllRshows an excellent empirical
in
their samples by the hydrolysis of surface water under
:it to
the anode. From their measurements,theyhavedeter1
mined that the rate of the hydrolysis is determined by
i-8 CY -*
entry of the hydrogen at theanode, andt’llatthe resist’ivity
V:,
of this anode region is given by log,, p = 5.4 -t 54OO/T.
This behavior may be used to establish minimum values This last relation corresponds t o an activation energy of
Sor the diffusion coefficient and mobility of the ions in 1.1 eV. Hence, it may be surmised tha,t the hydrolysis
t.he oxide. To do this, we make the “a priori” assumption and injection of hydrogen into silica observed by Hetherthat the square-law behavior of r R vs. V,, in Fig. 12 is, ington et al. [S]corresponds t o the mechamism responsible
in fact, due to the
dominance of space-charge currents for the water-based instability and specifically, the initial
n
i the bulk of the oxide; for, if this were not actually
drift discussed in this paper.
the case (as is likely) it merelymeans thatthe ionic
It is also interesting to note that the diffusion coeffinlobility in the bulk is higher than that calculated under cient for hydrogen in silica reported by Lee [MI, i.e.,
that assumption.
-0.45
Using the data of Fig. 12 with (17) yields
D H 1
0 .56 x 10-3 exp
cm*/8
(24)
dc
(xT-)
p
2 0.8 exp (-0.68/kT) cm2/V-s
(22)
and
D 2 2 X lo-’ exp (0.68/kT) cm2/s.
(23)
issubstantiallylarger
(over thetemperature range of
interest,i.e., <300”C) than the minimumvalue necessary t o explain the recovery (23). For example, a t 140”c,
from (23), D 2 5 x loW1’cm2/s; and from (24), R H , =
234
IEEE TRANSACTIONS ON ELECTRON DEVICES
1X
cm2/s which is consistentwith the conclusion
that the recovery is interface rather than bulk controlled.
The initialdriftactivation
energy inthis model is
simply the chemical dissociation energy required to free
the hydrogen ion from the adsorbedwater. It is quite
possible, therefore, thatthe
action of the “catalytic
impurity” is to react with the adsorbed water to form a
complex in which the hydrogen ion is more easily dissociated and that without this impurity the dissociation
energy for the hydrogen ion is too high t o result in any
significant instability. Variations in the structure of these
complexes could also explain the observed variation in
the initial drift activation energy.
Hetherington et al.
[5]have also reportedthat hydrolysis
of water at the surface of their silica samples appeared
to modify the oxide structure so that alkali ions could
no longer be injectedfromdeliberatelycontaminated
electrodes. In thepresent work it has been. found that the
presence orlack of sodium ions inthewater
used to
contaminate the unetched oxide surface does not appear
to modify the form of the subsequent instability. This
also tends t o support the supposition that the electrolysis
of the adosrbed water blocks the oxide against the subsequent injection of the alkali ions. Extrapolating furt’her,
the appearance of a slow recovery component (see Section
11-E) in oxides baked (prior to metallization) to remove
adsorbed water could then be explained by the presence
of soldium or similar ions injected into the oxide as the
density of electrolysed water sites becomes insufficient to
block this injection.
Atthispointinthe
investigation, however, further
speculation on the complex chemical inter-relationships
associated with the instability would be too heavily based
on guesswork without sufficient direct experimental support. Hopefully, additional work in this area will resolve
these difficulties.
PCERT-CARV
drift ‘behavior andmay be classified as genenzting 21,
“symmetric”instability.A
second type, discussed i n
this paper, possesses asimilarforward
drift,, but a n
asymmetrically fast recovery, and is characterized ‘by a
diffusion coefficient severalorders of magnitude greater
than that for sodium. This species has been tentatively
identified as hydrogen ions released from adsorbed water
that ishydrolyzed at the metal-oxide interface. It has
also been found thatthe appearance of this“waterbased” instability is probably dependent on the presence
of a third, as yet unidentified catalytic impurity which
is removed when the oxide surface is etched.
Since, in general, the transient behavior of the oxide
charge motion can be dominated by interface controlled
phenomena, it will be necessary to usemeasurement,
techniques which are preferentially sensitive to ion mot’ion
inthe bulk of the oxide (e.g., high-frequency ac loss
measurements) in order to determine the true mobility
of the ions. These measurements, coupled with the transientbehaviormeasurements,
will yield information on
the true mobility as well as the trapping effects at the
interfaces. Additional study is also needed t o determine:
1) The nature of the relaxationphenomena observed
for thetrapsatthe
oxide-metal interface which
results in the true recovery time period.
2 ) The chemical inter-relationships of theinstability
(e.g., the catalystnecessary to “activate” the waterbased instability).
3) The effect of using different types of oxide preparation techniques. The present investigation has dealt
exclusively with oxides thermally grown on the
silicon in a dry oxygen ambient. Preliminary results
indicate, however, that there is asubstantial difference in thebehavior of oxides grown in steam and
pyrolytically deposited oxides.
It appears, therefore, that there remain a wide variety
of phenomena associated with charge motion in thin inThere are many
mechanisms which can cause instability sulating films which presentinteresting andimportant
in an insulator under conditions of high-electric field and challenges for future investigations.
elevated temperature. For the case of thermally grown,
undoped silicon oxides, the dominant mechanism is the
APPENDIXI
motion of positively charged ions initially located in the
oxide near the oxide-metal interface. Trapping of these
APPLICABILITY
OF “BOUNDARY LAYER MODEL”
ions at the metal-oxide interface can dominate the tranal.
[a]
have
considered the special case for which
Snow
et
sientbehavior of this motionforpositiveapplied
gate
the
applied
field
E,
=
V,/W,, is just sufficient to cancel
voltage (forward drift) and will generally tend to obscure
the
electric
field
and
drift
component of current in the
the differences between the various ions which cause the
well.
This
corresponds
t
o
Qo
= CoV, = Qk.They make
instability. The recovery or motion of these ions back to
the
following
approximations:
the oxide-metal interface is found to be much more closely
related t o the true behavior of the ions in the oxide due
1) the film maybebroken up into two regions: the
to a significantly weakertrapping at the oxide-silicon
well region, extending from x = 0 t o x = X , (X, = X,
interface.
in Snow et al.’s notation)where X , is the initial
At least two types of ions have been observed to cause
well width, and a drift region X , < x < I T o x .
a n instability. One type, represented by sodium [ 2 ] ,
possesses a recovery behaviorsimilar
tothe forward It is further assumed that
IV. CONCLUSIONS
1966
IKSTABILITY
HOFSTEIN:
2) current flow in the well is by diffusion only,
3) the transit time across the drift region of the film
is much less than the relaxation time of the well,
so that the charge density for x > X , is essentially
zero,
4) the well width remains constant
a t X, during the
relaxation of charge,
L
1.0
X‘
Based on these assumptions, a relaxation time for
the
well charge is derived as r , FZ X ; / D . As shown in Section
111-B, QuantitativeAspects,the
well width is related
to the charge in the well by
whence
The transit time across the drift region is
235
AND CHARGE MOTION
I
2 .o
,t‘= I
(b)
Fig.16.Comparison
of (a) actual equilibriumcharge distribution
with (b) the charge distribution assumed for the Boundary Layer
model. The dotted lines indicate the distribution in the Boundary
Layer model for t’ << 1, t’
I, t‘ >> 1.
N
where
h(x, t ) = po - p(x, 1).
and since &,
=
Qx by the original assumption,
than X , ,
However,since W,, is usuallymuchgreater
it can be seen that the “a priori” assumption
that the
transit time across the drift region of the film is short
compared to the relaxationtime of the well charge is
notvalid.Physically,thismeans
that the current flow
for a trap free model will be limited by space-chargeeffects
in the bulk of the film rather than by emission from the
well of ions. This case has been discussed in the section
on QuantitativeAspects.
Another significant result of the Boundary Layer Model
is the prediction of a A V C i , , o l ddependence for t << 7,.
Although it has just been shown that the approximation
rT << r, is inconsistent with the trap free model, we will
assume for the moment that this boundary condition is
valid, and then demonstrate that the resulting AV,,a&
dependence predicted for t << rpis simply a result of the
high artificial ‘‘step function” charge distribution assumed
for 2 < X , (see Fig. 16) and that it is not predicted if a
smoothdistributionapproximatingtheactualdistribution is used.
The diffusion of ions out of the well for t << r , can be
examined by alternatively considering the complementary
viewpoint of diffusion of “vacancies” or “holes”from
x > X , into the ion well. Theboundarycondition
of
p = 0 for x > X, may then be considered as a constant
density of vacancies
h(z, t) = po
x>
x,
4%
For
<< X , , the vacancy diffusion boundary will
have penetrated only slightly into the ion well. The well,
therefore, appears essentially as a semi-infinite bulk into
which vacancies are diffusing from a fixed “surface” concentration of h ( X l ) = p,. The distribution of vacancies
is then
t
h(x, t )
= po.erfc
X2
<< 2
D =
0 < x
rr
<x,.
The ion distribution is
and the total charge lost from the
well is
AQ(t) = 4 /x’
h(x, t ) dx NN qp,d?%,
t
<< T,..
This is theasymptoticresultobtainedby
Snow et al.
for t << 7,.
As t -+ r1 the diffusion boundary has moved across the
well and the effect of the blocking contact, a t IZ: = 0 must
be considered [see Fig. 16(b)].
For t > T , the ion current out of the well is approximately
Hence,
236
and since Q
-
IEEE TRANSACTIOKS OK ELECTROK DEVICES
qp,X1,
FEBRUARY
and (2.5) becomes
d P(t)
dt
The solution to this equation is
Q(t)
=
Q(0)e-"Tr
t
>
7,.
(P(t)yCraT
-
x,
This is similar to (1) and gives an exponential-like (see
Section 11-D, Recovery) P ( t ) / P ( O ) = ( t / T T R ) / ( l
t/TTR)
solution with a time constant
+
This is the asymptotic behavior obtained by Snow et al.
for t >> 7,.
If the ion distribution of Fig. 16(b) is compared to the
actual distribution illustrated in Fig. 16(a), it can be seen Typically,
that it is the distribution for t
T , which approximates
P(O) = N,(O) 2 10+12/cm2.
(28)
the initial distribution in the real model, and that it is,
therefore, only the predicted transient behavior for t > T~
2 ) T r a p Cross-Section ( u ) . Thetrapping cross-section
which will be observed in the real model. The square root (assuming coulomb attractive retrapping) is
time dependence fort << rr corresponds to thedispersion of
u
n(d/2)'
the sharp discontinuity in the
charge distribution assumed
for the BoundaryLayerModeland
is an extraneous
where d / 2 is the trap potential-well half-width computed
solution as far asphysical reality is concerned.
from the initialdrift field-dependence data. From Fig.
7, then,
APPENDIXI1
-
-
CALCULATION
OF TIMECOXSTANT
FOR TRAPPIXG
MOBILEIon-s AT THE METAL-OXIDE
INTERFACE
3 ) AveyageThermalSpeed
(aT). Theaveragethermal
The rate of trapping of the mobile ions at the oxidespeed
of
an
ion,
hopping
thermally
from well to well in
metal interface is
the lattice, is
OF
0, =
D
a
where
p(t)
=
P(t)
=
NT(t)=
X,
=
=
=
=
rTR
=
S
U
iiT
volumedensity of free ions in the interface
region
total sheet density/unit area of free ions in the
interface region
Sheet density of unoccupied t.raps
recombination
velocity
= NTdT
trapping cross-section fora single trap
averagethermalspeed of untrapped ion
width of layer of free ions a t metal-oxide
interface
trappingtimeconstant
= h,/s.
The trapping time constant is
Wemay now computea "worstcase",
i e . , maximum,
value for r T R and show that it is still small compared to
the observed true recovery time period.Typicalvalues
for the important parameters follow.
1) Tyap density ( N T ) .The minimum density of empty
traps corresponds to one empty trap per freed ion. Then
the number of unoccupied traps at any instant is simply
where D = diffusion coefficient, and a = inter-well
spacing. If we assume that the potential wells correspond
to the lattice interstices,
a FZ5 8
=
5 X IO-' em.
A lower limit on D,and hence c T , may be obtained from
the recovery time constant 7,. This calculation is done in
Section 111-B, Quantitat'ive Aspects, and yields a typical
value
D
2 3 X lo-" cm2/s
lr=1400C
whence
4 ) Ion Accumulation Layer or Well Width. To a good
approximation, the analysis of Section 111-B may be
applied t o yield a well width
X,
5 IOOK
=
em.
(32)
Using the numericalvalues of ( 3 2 ) , (31)) (29)) and (28)
in (26) yields
-
rTR
lo-' seconds.
(33)
237
HOFSTEIX: INSTABILITY AND CHARGE M O T I O S
GLOSSARY
OF SYMBOLS
Gate voltage applied during initial drift
Gate threshold voltage for
given channel conductance
Shift in gate threshold voltage
Maximumshiftingatethresholdvoltage
following initial drift
Shiftingatethreshold
voltageimmediately
preceding recovery
Gate voltage applied during apparent recovery
h: T / q
Holding voltage
Charge density/unit volume
Charge density/unit area
c
O
A
v
g
T
Charge/unit area in layer (well) of ions
Charge/unitarea
on silicon a t oxide-silicon
interface
Trapped charge/unit area
Unit electronic charge
Particle (ion) density/unit volume
Particle (ion) density/unit area
Particle (ion) density/unit volume a t surface
Trapped particle density/unit area
Trapped particle density/unit volume
Oxide thickness
Oxide capacitance = e/WOx
Debye length
Debye lengthbased on surface charge concentration
Position
Temperature
Time
Dielectric constant
Boltzmann’s constant
Electric field
Activation energy (general)
Activation energy for apparentrecovery
Activation energy for forward drift (initial drift
and completely recovered redrift)
Activation energy for traps
Atomic vibrational frequency
Diffusion coefficient
Mobility
Inter-well spacing
Insulator (oxide) lattice spacing
Surface recombination velocity
Average thermal speed
Capture cross section
Empty trap density/unit area
rR
rF
rT
rTR
I
I ,c
= Apparent recovery time
constant
Forwarddrift(initialdriftand
completely recovered redrift) time c0nstan.t
= Transit
time
= Trapping
timeconstant
= Current/unit
area
= Spacechargelimited
current/unitarea
=
v. ACKKOWLEDGMEN’T
Thanks are due t o W. J. Merz and F. P . Heiman for
many stimulating discussions,to A. Revesz for a critical
reading of this manuscript, to K. H. Zaininger for discussion and criticalreading, and to R.Persingforhis
contributions t o the experimental work. The authorwould
also like to acknowledge the helpful comments and suggestions made by members of the RCA-Somerville technical staff. The automatic servo amplifier used to obtain
the data was designed by A. K. Rapp.
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“8