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IEEERANSA CTIONS ON ELECTRONEVICES, VOL. ED-15, NO.
12,
DECEMBER 1968 1009
Low-Temperature Hysteresis Effects in Metal-Oxide-
Silicon Capacitors Caused by
Surface-State Trapping
Abslracf-At low temperatures , charge exchange in all surface
states except those close to the band edgesan occur only by capture
of free carriers because emission rates become very slow.
If
means
are provided to supply minority carrie rs either from an extendedn-
version layer or ina gate-controlled diode), pronounced charge-trap-
ping effects can be bserved.
A
ledge in the
C-V
haracteristic
is
identified as being dueo the
charging of almost all surface states within the forbidden gap at a
surface potential dependent on surface-state density, capture cross
section and voltage sweep rate. Capture cross sections at low tem-
peratures can be estimated from the onset
f
the ledge.
When the
C-V
curves are traced from accumulation
t o
inversion
the capacitancedrops below the equilibriumminimumvalue nto
depletion and ncreases rapidly when nversion is reached. This
hook is caused by a barrier against minority carrier flow at the
boundary
of
the
MQS
capacitor. The barrier disappears when
suffi
cient voltage is applied to charge the surface states in the boundary
region.
d
I.
INTRODUCTION
OW-TEMPERATUREmeas ureme nts of metal-
oxide-silicon capacitorsremportant for a
variety of reasons. The surfac e-state dis tribution
close to heban d edges anbe nvestigatedby the
method described in
[ l ]
The question as to whether a
M O S
characteristic s dominated by surface states or
surface charge can often only be answered by perform-
ing
a
measurement at low tempera ture. Minority car-
riergeneration atesbecomeexceedingly mallwhen
temperature is lowered, an effectwhich makes M O S
diodes very light sensitive 2 J [ 3 ] .During the courseof
suchmeasurements twas ound hatanumber of
hithertounexplained eaturesoccurn apacitance-
voltage characteristics. Because complete understand-
ing of all low- temp era ture M O S phenomena is necessary
beforefirmconclusionscanbedrawnfromsuch low-
temperatureharacteristics,nnvestigation of th e
anomalous characteristics was undertaken.
In
this paper
a
num ber of effects will be described
and explained which occur when here s
a
noticeable
density of surface tatescombinedwithanexternal
source of minority carr iers. Externa l sourcesf minority
carriers are either extended surface inversion or a p-n
Manuscript received Ma y 31, 1968; revised June 11, 1968.
Murray Hill, N.
J. He
is
now
with the Institut e for Electronic Ma-
A.
Goetzberger was with the Bell Telephone Laboratories,
Inc.,
terials Research, Fraunhofer Society, Freiburg, West Germany.
Hill, N.
J .
J. C .
Irvin is with the Bell Telephone Laboratories,
Inc.,
Murray
7
7
I6o0
i
\\ I C
\
DEPLETION
I
I
LL
u
a
-
400
3
2
1 1 1 1 1 1 1 1 1 1 1
- 9 8
-7
6
5
- 4 3
-2
- I I 2 3 4 5
d
v
Fig. 1. Capacitance-voltage characteristic of p-t:ype140scapacitor,
oxide thickness 1000 A, measured a t liquid
Nz
temperature with a
1-MHz signal. Note absence
of
saturation in inversion.
junctionwithin he
MOS
structure hatcansupply
minority carriers when properly biased. A structure in-
corporating the p-n junction feature and very suitable
for
h 4 0 S
capacitancemeasurements
is
thegate-con-
trolleddiode [ 4 ] , [SI The esults eportedhere will
beequallyapplicable o MOS capacitorson nverted
surface s and to the gate capacitanc e of gate-controlled
diodes. As
will
be explained in more detail below, most
of the observe d phenomena result from the fac t ha t
surface states are not
in
equilibrium with he applied
dcvoltagebecaus e emission timeconstantsare arge
compared to the sweep time.
At oom emperature,devices of thekind nvesti-
gated here exhibit high capacitance in both accumula-
tion anddepletionwith a minimum in between.The
inversion response occurs by means
of
charge
flow
into
and from egions external to the
M O S
capacitor
[ 6 ] ,
7 ]
If there is no external source f charge, the low-tempera-
ture curves are very similar o he room-temperature
pulse [S I ,
[9]
biascurves. In both cases theminority
carrierconcentration is una ble o follow theapplied
voltage. Theref ore the width of the depletion ayer is
not imited o he equilibrium value but can ncrease
until a nontherm al process like avalanche
or
tunneling
[ 9 ] suppliesminoritycarriers.Anexample of sucha
curve which is dominated by majority carriers
only
is
shown in Fig. 1,
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45 r I
I I . RESULTS ND INTERPRETATION
A .
Relat ive m por t anc e of Capture ndnvers ion liy
Surjace States
35L
Inorder o explain theobserved ow-temperature
characteristics it is necessary to show that charge
ex
change by surface states
s
much more likely by capture
ratecan bechanged bychange of surfacepotential
whileemission rat e can not . It can beshown th at all
V
surfacetatesorehan
a
temperature-dependent
30 thany emissionrocesses. This
is
so because capture
1
25 I
, 2 I I
I
-15
-10
- 5
0 5 IO
15 20
4 0
r
30
10
40
30
-
20
10
0
4 5
-10
- 5 0 5 IO - 15
V
c >
Fig.
2. MOS
characteristics
of
different capacitors measured a t
liquid N t temperature and
1
MHz. All samples are p-type and
have inverted surfaces. a) Substrate doping 4.8X10 l7 cm-a in-
sulator 880 of Si8X4. b) Substrate doping 3X1014, 1000 A of
SiOz.
thermal SOz. c) Substra te doping 3 X 1014, 940 A of thermal
If minority carriers are available, curves ike hose
shown in Fig. 2 a), b), and c) are observed. Although
they are from different samples, they display a number
of common eat ures, he origins of which will be ex-
plored in this pape r. The hyst eres is effect abeled 3 in
Fig. 2 a) on th e inversion side of the curves was found
to be caused by theell-known surface-charge migration
phenomenonwhichhaspreviouslybeen dentified a t
room temperature
[ 6 ] ,
[7] . This hysteresis was found to
depend on surface treatment and preceding biasing con-
diti ons. It will not be considered further in this paper
because
i t
does not seem to be related to the semicon-
ductor-insulator interface.
energy
Elirn
away from either band edge can be charged
anddischargedbycapture of freecarriersonly.The
analysis is carriedout for ingle-level statesbut he
pertinent results apply also o he more realistic case
of a surface-state continuum.
Using recombination-generation statistics [lo], [ l l
it can be shown tha t the tim e con sta nt for captur e of
electrons by surface statess
1
r c
=
1)
w s
and the emission time constant is
1
e - E ~ i k T )
r e = = 2)
e , C&i
where
C, =
capture constant cmz.
s-l, n =
free electron
d en si ty at th e s ur fa ce ~ m - ~ ,
,
=emission constant per
second,
ni =
intrinsic carrier density, and
T
=energy of
surface-state level. Comparisonbetween 1) an d 2)
shows that th e capture r ate can be changed by change
of surface potent ial because
r c
depends on n,) while r e
cannot. Therefor e the mission rate determi nes wh ether
a
surface state
at
level ET can stay in equilibrium with
a given ra te of change of surface potenti al. Themission
ra te of electrons from surface states can be expressed
G, = fATssc,KT ) exp
[
k : e 3 )
where f= Fermi factor,N , , = surface-state density cmW2,
and K T )
= 3 97 X
1016T3/2 m - ~ . T h ectivation energy
of
3) is
the energy b etween the tr ap level and th e con -
duction band. An equivalent expression holds for emis-
sion of holes.
A qualitative description of surface-state behavior a t
low temperature is as follows. In an n-type sampl e all
the surface states are charged with electronsn accumu-
lation.
On
changing the bias towards depletion, capture
timecons tant s of allsurfacestatesdecreasebecause
carrier densities decrease. States very close t o the con-
duction band edge are able to emit electrons and thus
follow the changing bias, but most surface states stay
charged negatively until strong inversion with high hole
density p , is reached. Then capture
f
holes which have
to
be
supplied from outside the T\/IOScapacitor) occurs,
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GOETZBERGERNDRVIN:YSTERESISFFECTSNETAL-OXIDE-SILICONAPACITORS
1011
chargingsurfacestatespositively.Thussurface-state
charging and discharging takes place only inrelatively
narrow range of surface potential close t o the cond uc-
tion or valence band.
At every temperatur e there is limiting surface-state
energy Elirn Fig.
3 )
beyond which surf ace sta tes will be
unable
to
follow the dc bias because theiremission ra te
is too slow. This level which depends on temperature,
voltage sweep rate and surface-state density will now
be estimated.
The conditionused
as
anapproximatecriterion is
tha t, for surface states to follow
a
given ra te of vo ltage
change
= d V / d t ,
the emission current
G,
has obe
equalorgreater han hecurrentcharging heoxide
capacitance. For electron emission this means
where the equal ign applies to the limiting en ergy level.
Replacing
G,
from ( 3 ) and usinghe efinition of
Elirn= E,/2) -ET
as given in Fig.
3 ,
qNsscnK T)e- Eli ,kT) =
CoxV.
( 5 )
Equation ( 5 ) has been derivedunder heassumption
that nitially all raps are fu l l , i.e., f= 1. Taking the
logarithm of
5 ) ,
Elirn
is thereforeapproximately a linear unct ion of
temp erat ure. An nalogous xpressionholds orhe
limiting energy level for hole emission:
The ow-temperaturephenomenondescribedherecan
only be observed when he wo critical energy ranges
are not overlapping or
When condition 8) is fulfilled, charge trappedn surface
states n henonoverlapping ange sdischargedby
ca pt ur e, no t by mission. This conclusion is not limited
to silicon at low temperature. I t appliesalso owide
bandgap semiconductors a t room emperature.
B. Ex pe r i m e n t a l Re su l t s on Gate-Controlled Diodes
Measurementsongate-controlleddiodes eveal he
effects just discussed very clearly. Fig. 4 showstypical
gate capacitance versus substrate bias curve at liquid
nitrog en temperature. The device shown here has been
X-rayrradiated14]oncreaseheurface-state
clusions. We wan t t o than k them forpreprint of their work.
Brown and Gray [13] have independently come to similar con-
E,
E STATES
IN
EQUIL IBRIUM
E l i m ,
SURFACE STATES
E l
-
- - -
NOTN QUIL IBRIUM
WITH D C VOLTAGE
Ellrn, p
IN
EQUILIBRIUM
EV
Fig. 3. Schematic band diagram showing three different regions of
surface-state response.
E,
= conduction band edge,
E y =
valence
band edge. Surface states above Eli can :stay in equilibrium
by electron emission, those below E I ~ ~ , ~y hole emission. Those
in between can only change charge by capture.
Fig. 4. Gate capacitanceversus substr ate bias curve
of
gate-con-
trolled diode. Substrate resistivity was
1
hl.cm. This diode was
irrad iated to crea te high surface-state density. Dashed line gives
location of points to which capacitance drift s within one minute
if
bias is kept constant.
density.2 The
p+
region is shorted during the measure-
ment to the n-substrate. This curve was obtained
at 1
MHz with a swee p r ate of
0.05
Hz/s. In some portions
of the characteristic there are pronounced drift effects.
The dashed curve gives the location
of
points to which
the capacitance drifts during one minute
at
constant
bias.
Thecurvedoesnotexhibit hehyst eres is effect in
inversion labeled
3
in Fig. 2 a). This is another indica-
tion that this effect s caused by surface migration of
charges. In
a
gate-controlled diode the injecting junc-
tion is under the metal contact and can therefore not be
influenced by surface-charge motion.
The remaining hysteresis effect results from charge
trap pin g in surface states. Referring to the resultsf the
preceding ections he oppar t of thecharacteristic
A-+B+C+D+E)
can now be understood in the fol-
lowing. Point A is n nversion,allsurfacestatesare
child Semiconductor for this device.
a We are indebted to A. S. Grove and D. Fitzgerald from Fair-
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1012 IEEE TRAKSACTIONS Oh- ELECTRO?: DEVICES,ECEMBER
1968
filled with holes. I n going towards depletion, point
B
is
reachedwhere heelectricalconnectionwith he
p
region is pinched
off.
Th e surface states lying closer to
the valence band than
Elim,p
n Fig. 3 are able to lose
holes by emission, but all other states are still in their
more positively charged state
at
point
B.
At this point,
which is a t a n applied voltage of a bou t 5 volts cor-
responding to the positive charge in surface states, the
capacitance increases toward flat-band capacitance. A t
point C, where the Fermi level is already close to the
conductionband, he urface lectron oncentration
becomeshighenough
so
thatsurfacestatescandis-
chargebyelectroncapture.Withina athernarrow
range of surfacepotentialbetween
C
and
D
most of
the surface states are discharged by electron capture.
Between D and
E
they are again in equilibrium with the
applied bias and a normal C-V curve is observed in the
accumulation range.
The shape of the ledge between C and D depends
on the sweep rate The downward drift
f
capacitance
at co ns ta nt bias in this region is a result of the limited
supply of electrons at con st ant bias. The tim e co nstant
of
electron capture depends on electron density accord-
ing to
1).
If bias
is
kept constant electrons are slowly
capturedby urface tates,which eads
to
electron
depletion and a concomitant change of surface poten-
tial. Thecapture processcomes toahaltwhen he
electron concentration n, has become sufficiently low.
Th e lower par t
of
the characteristic F+B in Fig.
4
is also a consequence of the presence of surface stat es.
I t will be interpret ed in Section 11-E.
C.Calculat ion of Capture romOnset
of
Sur face-S ta te
Charging
In he edge region he characteristic
is
determined
by the equilibrium between filling rat e of su rface st ates
andvoltagesweep ate.Theappliedvoltagedivides
between the oxide and the semiconductor space-charge
region :
v=+,+--+--
w Qs c
c o x cox
where
Q,,
is the charge in surface states and
QOe
s the
semiconductor space charge. The t ime der ivative of
9)
is
dV
.
a ,
1
dQS8
1 dQ S o
v
= -+-- __ +--.
10)
at
at
cox
at
cox at
In
the ledge region of Fig.
4
from
C
to
D
most of the
charge goes into surface states. Therefore,
Th e oxide capacity is charged by
a
current
I :
Thiscurrent sequated o he urface-statecapture
current
of 1)
a
at
CoxV = qR,
= q
lV,8fct)) =
qI~7ss~7L 1n,
13)
where Rn is the electron capture rate. Equation 13)
is
integrated with the condition that the charging starts
at
t = Q :
qN,,f =
c,,vt.
14)
Equation 14) is now inserted back into 13)
:
cox
v
n
=
15)
( q N , s Coxlit)
At the onset of charging,
t
=
0
point C in Fig.
4)
and
15) reduces to
cox
v
q N , s
Cn5z------.
16 )
N , ,
is the total number of surface states being illed and
is given by
qN = CozAV
where
A V
is the width of the
ledge. With his elation hecapture ate
c,
results
from the very simple expression
V
c n = - .
1
7 )
n,AV
If
N, ,
and
c,
depend
on
energy, then 17) gives an aver-
age of c, over all surface states between
El- limjp
nd
EZ Elirn n:
J y
E ) n E )
E
c, = 6,) =
18)
~ E E z A T s s E . ) d E
A
number
of
sampleswereevaluated in this manner.
The values for the capture cross sections
C , , ~ = C , , ~ / V ,
where
= 5 X
l o 6
cm/s average thermal velocity) were
foundoangeetweenndm2 at 100K
for p and n type.Theaccuracy of thesevalueswas
found to be limited by the precision with which surface
potential could be determined from theC-V curves.
D . Simultaneous Observat ion of Minor i t y Carr ier In jec-
t ion and Surface-State Charging
I t had been pointed out previously [3 ] that in sam-
ples not ontaining n xternal ource or ink) of
minority carriers, such carriers which were for instance
injected by light can be removed only if a forward bias
is developed across the surface space-charge layer. This
effect results in a ledge region very similar to t ha t ob-
servedwhilesurfacestatesarebeingcharged.Under
the appropriate conditions both effects can beseen in
the same characteristic.
Fig. 5 depicts a characteristic obtained n he same
gate-controlled diode shown in Fig. 4 but with the
p
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1014 IEEERANSACTIONS O N ELECTRONEVICES,ECEMBER 1968
0
4
8
12 16
20
24
28
32 36
AV
Fig. 7. Plot of (Cml/Cm s. AV for
a
set of samples where only the
density by AV=qNeY , , /C , , . olid line is best fit to the data.
surface-state density s changed.
A V
is related to surface-state
N D
=bulk donor density, and8= dielectric permittivity
of the semiconduc tor.
Th e voltage
Vmz
at
which the curve reaches its mini-
mum Cm2 is given by Vmz= Vml+AV where V,I is the
voltage at which the surface-state free M O S capacitor
would have ts minimum
Cml,
and
AI
is the voltage
offset due to charge in surface states. Thus
z)21
+
Vm1 AV V F B
a2
20)
and
From 20) and 21) we have
From 22) we conclude hat
a
plot of
C,I/C,Z)~
is
linearly related to the surface-state density , ,
=
C O B
/ q .
Fig.
7
shows such
a
plot.
111. CONCLUSIONS
Low-temperature silicon M O S curves were shown to
differ in some important aspects from room-temperature
behavior. The presence of an externa l suppl y of minor-
itycarrierspermitsobservation of effec tscausedby
those carriers. The major results of this paper are as
follows.
1) Thema jo ri ty of deep-lying urface tatesget
charged and discharge d by capture of holes when the
Fermi level is close to th e valence band and by capture
of electrons when the Fermi level s close to the conduc-
tion band. This leads to pronounced hysteresis effects
dependent on the surface-state density and temperature
in
M O S
characteristics.
2 ) In going from inversion towards accumulation the
discharge of surface states is indicated by a ledge in the
charac teristic . From the onset of the charging the aver-
age capture cross sectionof surface states can be found.
3)
Going from accumulation to inversion the capaci-
tance drops below the equilibrium minimum value and
increases rapidly when nversion condition is reached.
This hook in the characteristic is caused by the neces-
sity of charging all the surface s tates in the e dgeegion
bordering the source
of
minority carriers until
a
stable
inversion ayer exists in this region. Only after this is
accomplished can minority carriers traverse this region
and char ge the res t of t he capa cito r. The magni tude of
the jump of capacitance depends on surface-state den-
sity.
REFERENCES
P
V. Gray a nd D. M. Brown,
App l .
Phys. Letters, vol. 8, p. 31,
J . Grosvalet and C. Jund, Influence of illumination on MIS
1966.
capacitances in the trong inversion region, IEEE Trans.
Electron Device, vol. ED-14, pp. 777-780, November 1967.
A.
Goetzberger, Behavior of MOS inversion layers a t low temp-
erature, IEEE Trans. ElectronDevices, vol. ED-14, pp. 787-
A. S. Grove and D. J. Fitzgerald, Solid-State Electron., vol. 9, p.
789, November 1967.
783,1966.
P.
P.
Castrucci and
J.
S.
Logan,
IBM
J.
ol.
8,
p. 394, 1964.
S. R. Hofstein an d G. Warfield, Solid-State Electron., vol. 7, p.
59,1964.
E.
H. Nicollian and A. Goetzberger, Lateral ac current flow
model
for
metal-insulator-semiconductor capacitors, IEEE
A. Goetzberger and E. H. Nicollian,
Appl .
Phys. Letters, vol. 9,
Trans. Electron Devices,
vol.
ED-12, pp. 108-117, March 1965.
p. 444, 1966.
W. Shockley and W.
T.
Read, Phys. Rev., vol. 87, p. 835, 1952.
F. P.
Heiman and F.Warfield, T he effect of oxide traps on the
MOS capacitance, IE EE Trans. ElectronDevices, vol. ED-12,
pp. 167-178, April 1965.
F.
J. Morin and
J.
P. Maita, Phys. Rev., vol. 94, p. 1525, 1954.
D.
M.
Brown and P. V. Gray, to
b
published.
D. J. Fitzgerald and
A. S.
Grove, Radiation-induced increase
in surface recombination velocity of thermally oxidized silicon
structures, Proc. IEEE Let ters), vol. 54, pp. 1601-1602,
November 1966.
J .
App l .
Phys., vol. 38, p. 4582, 1967.