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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.