temperature dependence of the field‐effect conductance in thin polycrystalline cds films c. a....

8/18/2019 Temperature Dependence of the Field‐Effect Conductance in Thin Polycrystalline CdS Films C. A. Neugebauer

1/11

Temperature Dependence of the Field‐Effect Conductance in Thin Polycrystalline

CdS Films

C. A. Neugebauer

Citation: Journal of Applied Physics 39, 3177 (1968); doi: 10.1063/1.1656753

View online: http://dx.doi.org/10.1063/1.1656753

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/39/7?ver=pdfcov

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2/11

EFFECT

OF W A L L S

ON THE

D IOCOTRON INSTAB IL ITY 3177

Figures 5 and 6 do show

that

instability can occur

just off the y=O axis that is when an inner surface just

appears. Figures 4 and 5 also show how the instability

region in the

X ,

y

space narrows down in the

X+

direction and disappears

at

the

y=O

axis. The value

of

X+ at which this takes place can be calculated from

Eq. 30) by setting

F=O. t

is given

by

X = [ _ :m X_-1)J/[2X_-1-tm X _-1)].

39)

Figures 5 and 6 show a plot of this point for various

values

of

m and for

X_=

-1, i.e., no inner wall. For

JOURNAL OF APPL IED

PHYSICS

this case

we

have

X =

- m-l)/ m-3).

40)

For X_=O, which corresponds to an inner conducting

wall, we have

X =

-m/2)/ m/2

-1 .

41

For m greater than

2,

there are no positive values of

X+

which satisfy Eq. 39) for any value

of

X_

There

fore, thick charge layers are always stable with positive

X , and by Fig. 2 this means

that

any Xw greater or

equal to zero which includes the configuration of no

walls) is stabilizing.

VOLUME

39 NUMBER 7

JUNE 1968

Temperature Dependence of the Field Effect Conductance in Thin

Polycrystalline

CdS Films

C. A. NEUGEBAUER

General Electric Research and Development Center, Schenectady, New York

Received

23

October 1967; in final form 15 January 1968)

The field-effect conductance and the capacitance-voltage characteristics of thin-film, polycrystalline

CdS-SiCh-AI field-effect structures were measured as a function of temperature in the range from 100° to

-50°C,

and mechanical stress because of differential thermal expansion.

It

was concluded

that

1) the

channel mobility varies exponentially with temperature with an activation energy of the order of 0.06 eV,

which corresponds to the height of the intercrystaIIine barriers

at

the grain boundaries, 2) the channel

mobility increases with the induced charge-carrier density, 3) the flat-band voltage varies linearly with

temperature

at

a rate of the order of 0.01 V/deg, which corresponds to an interface state density of the

order of

10

13

cm-

eV-l

in

the bandgap in the vicinity of the conduction band, 4) the flat-bond voltage

increases with compressive stress at a rate as high as several hundred volts per percent strain and 5)

contact barriers between the source and drain electrodes and the surface channel become significant at

temperatures below -25°C.

INTRODUCTION

The field-effect conductance in semiconductors differs

from ordinary bulk conductance in

that it

refers to the

conductance of a thin channel of accumulated charge

at

the surface.

In

order to accumulate this charge,

an

electric field is applied perpendicular to the surface.

This

is

most commonly done by making the semi

conductor

part of

a metal-oxide-semiconductor MOS)

structure. A potential is applied across a thin oxide

film between the metal field plate and the semicon

ductor leading to the accumulation or depletion of

charge

at

the semiconductor-oxide interface. Since the

induced charge is in close proximity of the interface,

where surface states deplete the free carrier density

and surface scattering decreases the mobility, the tem

perature dependence

of

the field-effect conductance is,

in general, quite different from

that of

the bulk con

ductance even in single crystals.

In single-crystal semiconductors, the temperature

d ~ p e n d e n c e

of the field-effect conductance is determined

only by the temperature dependence of the channel

mobility and the channel charge density. In single

crystal silicon, for instance,H the channel mobility

depends on lattice scattering on the one hand, which

has a negative temperature coefficient, and surface

scattering, which has a positive temperature coefficient.

The channel charge density has a positive temperature

coefficient. These temperature dependencies largely

cancel each other,

so that

the net temperature de

pendence of the channel conductance is quite small

over a temperature range

of

several hundred degrees.

In sharp contrast to this is the very strong temper

ature dependence of the channel conductance observed

in field-effect structures utilizing polycrystalline thin

films. Studies

4

•

5

on polycrystalline films of CdS, CdSe,

IF.

P. Heiman and H. S. Miller, IEEE Trans. ED-12,

142

1965) .

• R. S. C.

Cobbold, Electron. Let ters 2,

190

1966).

3 H.

C.

DeGraaff and J. A. V. Nielen, Electron. Letters 3,

195 1967).

• A. Waxman, V. E. Henrich, F. V. Shallcross, H. Borkan, and

P. K. Weimer, J. AppJ. Phys. 36, 168 1965).

•

C.

Juhasz and J. C. Anderson, Proceedings

of

the Joint

I ERE-lEE Conference on Applications of Thin Films in Electronic

Engineering, London 1966.


Mar 2016 01:51:37


3/11

3178

C.

A. N E U G E B U E R

and InSb indicate a strong positive temperature

coeffi

cient of the channel conductance. Measurements on the

temperature dependence

of

field-effect structures using

single-crystal

CdS,6

on the other hand, show very little

temperature dependence. This strongly suggests that

the grain boundaries in polycrystalline material are

responsible for the temperature dependence observed.

Previous work bearing on this problem can be

summarized briefly as follows:

(1) The bulk conductivity (as distinguished from

the field-effect conductance)

of

polycrystalline CdS

displays a positive temperature coefficient,7,8 Plots of

the logarithm of the Hall mobility vs reciprocal temper

ature are linear over a large temperature interval,

indicating the presence

of

barriers, probably located

at

grain boundaries. (By contrast, the Hall mobility

of

single-crystal CdS has a negative temperature coeffi

cient above 100

o

K.)

(2) Measurement

of

the channel mobility

by

Hall

measurements by Waxman

et al

4

indicate a dependence

of the mobility not only on temperature,

but

also on

the voltage applied to the field plate, the mobility

increasing with applied voltage.

The field-effect conductance, however, is not only

determined by the mobility, but also the field-induced

charge density.

f

it were not for the presence of inter

face acceptor states at the semiconductor-oxide inter

face, which must be filled below the Fermi level, the

induced charge would simply be given by Qind=CV

where C

is

the MOS capacitance and

V

the applied

voltage. In general, however, interface states are pres

ent. In this case, the fraction

of

the induced charge

which is tied up in these states and its temperature

dependence must be known. This requires measurement

of the MOS capacitance-voltage characteristics as a

function of

temperature.

In this study, therefore, both the field-effect con

ductance and the capacitance-voltage characteristics

of polycrystalline CdS-Si0

2

-Al field-effect structures

were measured as a function

of

temperature. In ad

dition, the effect of mechanical stress (important be

cause of differential thermal expansion between sub

strate and film) on the field-effect conductance was

investigated.

SAMPLE PREPARATION

Thin films of CdS, Si0

2

,

Au, and Al were vacuum

deposited on glass substrates in the so-called "staggered"

thin-film transistor structure, using techniques similar

to those published

by

Weimer

9

and co-workers. Gold

6]. Conragen

and R. S.

Muller, Solid

State

Electron. 9,

182

(1966) .

7

F.

A.

Kroger, H. J. Vink,

and].

Volger, Phil. Res. Rept. 10,

39 (1955).

8 H. Berger, Phys. Status Solidi 1 739 (1961).

9 For

a review, see P. K. Weimer in Physics o Thin Films

(Academic Press Inc., New York, 1964) Vol. II p. 147; Field

Effect Transistors p. 216, (Prentice-Hall, Inc ., New York, 1966).

films are first deposited on the substrate as source and

drain contacts. On these, CdS is deposited

at

a 200°C

substrate temperature to a thickness of several microns.

Grain sizes in the film are about 2000 X and the basal

plane of CdS is oriented parallel to the substrate.

Si0

2

is

now deposited by rf sputtering

of

quartz to a thickness

of

500-2000

X

in an argon-oxygen atmosphere

at

3X 10--

3

Torr, using techniques similar to those pub

lished by Davidse and Maissel.

lO

An aluminum-gate

electrode is now deposited over the source-drain chan

nel. The channel is 8

JL

long and 2 mm wide. The gate

width is of the order of 50

JL

A second Al electrode is

deposited over the source region away from the channel

to give a simple varactor structure. This is illustrated

in Fig. 1.

The CdS films were doped by excess cadmium whose

concentration was controlled by the substrate temper

ature during deposition and post deposition annealing.

The donor ionization energy is low,

E

D

- 0.03

eV, and

it

is assumed throughout this study

that

the temper

ature dependence

of

the ionized carrier concentration

is negligible compared to that of the mobility and the

trapped surface charge. All measurements were made

in the dark.

TEMPERATURE DEPENDENCE OF

CAPACITANCE-VOLTAGE CHARACTERISTICS

The MOS capacitance as a function

of

applied bias

voltage was measured with a capacitance bridge using

a Princeton applied research model No. HR-8 lock-in

amplifier. The bias voltage

V

g

was applied between

the aluminum field plate (or gate) and the gold film

(kept at ground potential). The frequency of the

measuring signal was 100 kHz.

At sufficiently high measuring frequencies, the ca

pacitance-voltage behavior can be described

by

(1

where C is the total MOS capacitance,

Co

is the ca

pacitance

of

the oxide film,

Csc

is the space-charge

capacitance of the CdS film. For the purpose of this

study, the space-charge capacitance is adequately given

by the relationship

E8/

A

n)

e

v

12

when electrons are accumulated at the semiconductor-

. Transistor Varactor

gate field plate

drain CdS oxide source

I I

channel

substrate

FIG. 1.

Experimental MOS configurations.

10

P. D. Davidse

and

L. I Maissel,]. App . Phys. 37, 574 (1966).


Mar 2016 01:51:37


4/11

F I E L D E F F E C T IN

P O L Y C R Y S T L L I N E CdS

F I L M S

3179

oxide interface, and by

t

fs/An)

v

s

1 2

when electrons are depleted

at

the interface. Here

fs = dielectric constant

of

CdS, An is a Debye length

defined

by

f.kT/2

q

2

n

1/2, q=electronic charge, n=free

electron density,

Vs=

is the normalized surface-barrier

height=qV./kT. The surface-barrier

V.

describes the

degree of band bending at the semiconductor-oxide

interface. For V.>O, electrons are accumulated, and

for V.


5/11

3180

C . A. NEUGEBAUER

o

u

0.2

0

-2 I

0

4

v

9

•volts

(al

1.0

0.8

0.6

u

0.4

0.2

0

-3 -2 -I

· 0

4

g • volls

(b)

FIG.

3. (a) Capacitance-voltage curves for

151B-l

v


6/11

FIELD Err-ECT

IX POLYCRYSTALLI)JE

CelS

FILMS

31Rt

FIG.

4.

Variation of flat-band voltage

with temperature for 151B-l and 3, giving

dVFB/dT=

-0.0071 V deg.

0.5

o 151B-1

o -40 -30 -20 -10

o

10

20 30 40

50 60 70

80

The channel mobility corresponding to the maximum

value of the slope of the sd vs

Vg

curves in Fig. 5 (b)

was plotted against reciprocal temperature for device

151B-3 in Fig.

6. The

straight line demonstrates the

validity

of

the relation

JI =Jl o exp( -qrj>/kT

(6)

for sufficiently high gate voltages in the temperature

range investigated. An activation barrier

rj>=

0.065 v and

a value f:>r Jl o= 200 cm

2

V· sec can be obtained from it.

This

is

approximately the Hall mobility of single-crystal

CdS in this temperature range.

The dotted

lines in Fig.

5 a)

for device

151B-l

are

calculated values

of

the source-drain current based on

Eq. (5), using the experimental values for the flat-band

voltage obtained from C-

V

measurements given in

Fig. 3 b),

and

a value for the mobility based on the

maximum slope

of

the

sd

vs

V

g

curve

at that

temper

ature. Values for Co L

and

Vd are known. t is

apparent

that

the slope of the actual source-drain current lags

behind that of the calculated current at low gate volt

ages, but approaches it

at

higher gate voltages. This

can be interpreted on the basis

of

a gate-voltage de

pendent mobility. The mobility

is

plotted as a function

of

gate voltage for each temperature in Fig. 7. Since

Eq. (5) is

not

strictly applicable for low values of

the

gate voltage, only the mobilities for values of V

g

>2 V

in Fig.

7

should be considered as correct. The mobilities

below 2 V are more uncertain.

2. Discussion

The above results can be summarized as follows:

(1) The channel mobility determined from con

ductance

and

capacitance measurements is a function

of gate voltage at low voltages.

(2) A maximum channel mobility is reached

at

suffi

ciently high gate voltages which is no longer a function

of

voltage.

T C

(3) This maximum channel mobility

is

temperature

dependent according to J l o exp( -qrj>/kT .

(4) At very high gate voltages, the mobility de

creases again, but this is not considered here.

An exponential temperature dependence

of

the Hall

mobility in polycrystalline CdS films is well docu

mented.

4

s The

basic model used to explain this temper

ature dependence has first been proposed by Volger

14

and consists of

an

inhomogeneous semiconductor con

taining highly conducting grains separated by thin

layers of lower conductivity. The regions of lower con

ductivity are generally associated with the intercrystal

line boundaries. Theories have been

put

forth which

postulate

that

the lowered conductivity (1) arises from

a variation in the carrier density in the film 16 (2) is due

to space-change regions in the crystallites,16 or (3) is

due to intercrystalline barriers

7

.

S

such as

an

oxide

film in the intercrystalline boundaries. For this last

case, Petritz

9

derived a mobility of

JI =Jl o

exp(

-qrj>/kT

where J l o is only weakly temperature dependent and rj>

is the potential height of the barriers referred to the

conduction band edge. This is just the functionality

observed for the temperature dependence of the field

effect mobility in the present experiments.

Waxman et

al.

4

first considered the effect on the

activation energy of the mobility

by

the induction

of

charge

into

the polycrystalline semiconductor by the

field effect. The semiconductor was assumed to consist

of regions of high carrier densi ty nl, separated by regions

14 J. Voiger, Phys. Rev. 79 727 (1950).

16

A. von Hippel and E. S. Rittner,

J.

Chern. Phys.

14

370

(1946) .

16 E.

S. Rittner, Science 111 685 (1950);

J.

C. Slater, Phys.

Rev. 103 1631 (1956).

17

A. F. Gibson, Proc. Phys. Soc. (London) A64 603 (1951).

18 F. B. Michiletti and P. Mark, Appl. Phys. Letters 10

136

(1967) .

19

R. L. Petritz, Phys. Rev.

104

1508 (1956).


Mar 2016 01:51:37


7/11

3182

C . A.

N E U G E B U E R

140

25 C

1518

-I

120

calculated

experimental

100

80

0

-

60

40

20

00

6

V

g

•

volts

a)

90

80

70

60

50

40

30

20

10

0

-I

0

2

3

g

• yolts

b)

FIG.

5.

a) Source-drain currents as function of gate voltage

for 151B-1. Dotted lines indicate calculated values based on

capacitance-voltage measurements and a constant mobility.

b) Source-drain currents as function of gat e voltage for 151B-3.

of

low carrier density n2. The activation energy was

then taken as

qc >= k

Innl/n2

The activation energy within the depth

of

the accumu

lation layer

at

the semiconductor-oxide interface de

creases as charge is induced into the semiconductor,

since the change in the Fermi level in region 1 for a

given change in carrier density will be smaller

than

the

change in Fermi level of region 2. The activation

energy

of

the mobility thus decreases with applied

gate voltage, in agreement with the experimental re

sults.

30

20

10

u

9

8

7

N

E

6

u

-

\

\

4

\

,

\

\

0

\

\

4 5

6 7

lIT x

3

•

OK I

FIG. 6. Channel mobility, based on maximum slopes in Fig.

5 b), versus reciprocal temperature for 151B-3. Activation

energy=O.065 eV, Po=200 cm

2

/V·sec

However, to accommodate the experimental obser

vation

that

the mobility is voltage independent in the

high gate-voltage range, it is postulated here that the

total activation energy is the sum of a voltage-inde

pendent barrier c/> and a voltage-dependent barrier VB

This would be consistent with the third model of an

inhomogeneous semiconductor discussed above in which

the crystallites behave like single crystals, with an

intercrystalline barrier

c >

between them. In addition,

however, it is postulated that interface states exist at

grain boundaries, and that the bands of the semi

conductor will therefore be bent up

at

the boundary

by an amount VB This is shown in Fig. 8 a). Here,

c > is essentially voltage independent, but V will vary

with induced charge, as shown in Fig. 8 b). This


Mar 2016 01:51:37


8/11

F I E L D E F F E C T IN

P O L Y C R Y S T L L I N E CdS

FIL MS

3183

variation

of

V8 with induced charge will now be esti

mated.

The height

of

barrier V8 is given by

Q8= CdV

s

where

Q8

is the charge trapped

at

the grain boundary and

Cd

the depletion layer capacitance. f it is assumed that

the Fermi level is not strongly pinned

at

states at the

grain boundary, then the introduction

of

field-induced

charge will increase the carrier density in the boundary

region, within the depth

of

the accumulation layer,

thereby neutralizing some

of

the positive space charge

due to the ionized donors. The depletion-layer capaci

tance

at

the grain boundary can be given by

7)

12

1

8

;.

6

N

E

oi

4

2

1518-1

3 4

5

~ g , v o l t s

FIG.

7. Channel mobility as function of gate voltage

of

device

151B-l for three temperatures.

where f8 is the dielectric constant

of

CdS,

An

is a Debye

length= f8kT/2q2n) 11

2

,

v.=qVs/kT,

and n

is now the total carrier density

Here ni is the initial carrier density in the grain far

away from the grain boundaries and before the intro

duction

of

field-induced charge. Solving for

V

in terms

of

the charge trapped

at

the grain boundary gives

8)

which shows

that

V.

decreases as charge is induced.

This relationship is approximately valid even in the

presence of a heavy accumulation layer, since

V.

cannot

take on large positive values, thus V.' '-'O

at

high gate

voltages. The mobility can now be described from

/ '

, d ' ~

T

depletion

layer ¢

Vs

V.B.

0)

b)

no induced charge

with induced charge

FIG.

8. Model for an intercrystalline barrier in

the

surface

space charge region

of

a polycrystallil;te semiconductor.

The

grain

boundary is perpendicular to the semiconductor-oxide interface.

6) and 8):

J I =

J l o

exp

-q


9/11

3184

C. A.

N E U G E B U E R

1.0

-44 C

-65

0.8

-88

-109

0.6

o

-133

0.4

-154

0.2

o

-2

I

o

Vg.volis

FIG.

10. C a p a c i t ~ n c ~ v l t a g e characteristics at low temperatures

for 151B-3, mdlcatmg the presence of contact barriers.

particular energy, thus preventing further reduction of

V

with induced charge.

In

addition, at high gate

voltages, diffuse scattering of electrons in the channel

of the insulator-semiconductor interface becomes im

portant, tending to lower the mobility and causing it to

peak out.

t should also be pointed out here that the channel

mobility considered here is defined by Eq. (5), and is

therefore not necessarily the same as the Hall mobility

which was measured by Waxman t al.

4

on similar

field-effect structures.

CONT CT B RRIERS

The MOS capacitance at sufficiently high gate volt

ages of the devices in Fig. 5 is not a function of temper

ature at temperatures above about - 25°C, Moreover,

the value of the oxide thickness calculated in this

region by setting the measured capacitance at high

gate voltages equal to the oxide capacitance, C= Co

agrees well with the measured oxide thickness. This

indicates that at temperatures above - 25°C, there

is

no additional barrier layer of appreciable thickness in

the MOS structure. However, as the temperature

is

lowered below - 25°C,

it

appears

that

a depletion

layer of increasing thickness

is

inserted in series into

the MOS structure, and acts to decrease the capaci

tance, even in the accumulation region at high gate

voltages. This is illustrated in Fig. 10.

This barrier can be rationalized in terms

of

a contact

barrier of perhaps a few tenths eV between the semi

conductor and the source and drain electrodes, having

associated with

it

a certain capacitance and resistance.

However, at temperatures above - 25°C, the therm

ionic current over this barrier is so high, and therefore,

the contact resistance so

low

that the measuring signal

of the capacitance bridge is effectively short circuited

across the contact-barrier capacitance. Only at temper

atures below

-25°C

does the contact resistance be

comes appreciable, and therefore also the contribution

of

the contact capacitance to the total capacitance.

An alternate explanation would be a thickening of

depletion layers at intercrystalline barriers in the semi

conductor film parallel to the

film

plane with decreasing

temperature, due to a greater density of occupied inter

crystalline boundary states.

In the presence of contact resistance, the interpre

tation

of

the source-drain current is no longer simple

and Eq. (5) should therefore, strictly speaking, only

be applied at temperatures above - 25°C.

DEPENDENCE

O

THE FIELD EFFECT

CONDUCT NCE ON MECH NIC L STRESS

ND DIFFERENTI L THERM L EXP NSION

Since the expansion coefficient of the substrate and

the thin-film MOS structure on it will, in general, not

be the same, changes in mechanical stress will occur

when the temperature is changed. If, therefore, the

field-effect conductance of thin, polycrystalline CdS

films

is

stress dependent, there will be a temperature

dependence as well due to this source.

All

thin-film

field-effect devices tested in this laboratory were indeed

found to be stress sensitive to some degree. Tension

increases the field-effect conductance, compression de

creases it. Although no systematic study of the de

pendence of the stress dependence on processing con

ditions was made, it appears

that

MOS structures

with the thicker oxide films are more stress sensitive.

MECH NIC L STRESS TESTS

Mechanical stress was introduced by bending the

glass substrate in a bending beam experiment. The

strain introduced in a thin

film

on the surface can be

taken to be that

at

the surface of the substrate itself.

In

this way, a maximum strain of approximately 0.03

cou1d

be applied to the thin-film structure in compres

sion or tension. The change in the field-effect conduc

tance in one of the more stress-sensitive film transistors

is

shown in Fig. 11 where the I d

is

plotted against gate

voltage in the region of drain-current saturation. t

appears that the conductance curve of this transistor

is shifted with applied stress at the rate of approxi

mately 400 V strain. The effect is entirely reversible

indicating

that

the elastic limit was not reached. It

should be noted

that

only very small changes in con-

Io.sma

°

v

2428-6

FIG. 11.

Effect of mechanical stress on the conductance-voltage

characteristics of 242B-6.


Mar 2016 01:51:37


10/11

F I E LD

E F FECT

IN

POLYCRYSTALL I NE

CdS F I LMS

3185

FIG. 12. (a ) Effec t of mechanical stress on

the capacitance-voltage characteristics of

242B-9. Bias sweep=3 Hz. (b) Effect of

mechanical stress on the conductance-voltage

curves of 242B-9. Bias

sweep=3

Hz.

-2 o

2

30

2428- 9

4

Vg volts

V

g

,

,oils

0)

ductivity

are observed in

the

CdS film alone under

stress, without the oxide and gate film.

In order

to

ascertain the origin ' of the stress de

pendence, field effect conductance measurements as a

function of gate voltage were carried out simultaneously

with the measurement of the capacitance-voltage curves

under

compression

and

tension,

and the

result

is

given

in Fig. 12 for device 242B-9. The voltage shift in the

conductance curves corresponds to

the

shift in

the

C-

curve, within experimental error.

The

principal

effect of mechanical stress, therefore,

is to shift the

fiat-band voltage, V

FB

•

The sensitivity of the turn-on voltage to mechanical

stress in

CdS field-effect transistors

has

been reported

previously by Muller and Conragen

20

21 and was ex

plained by them on the basis of the piezoelectric prop

erties of CdS.

Under

stress, a charge density equal to

the normal component of the electric displacement in

duced by the stress will appear

at

the surface of the

material. Since here a channel region is formed in the

surface of the CdS as part of the field-effect s tructure,

the presence of the stress induced charge is detectable

through changes in the source-drain conductance and

Vg V

sd

CONSTANT

1440 8

ON

SOD LIME

GLASS

T

0

...

o_-cJ ---

TeC

2748 -I

ON

FUSED

SILICA

FIG. 13. Temperature dependence of the field-effect conduct

ance for thin-film transistors on two substrates with different

expanison coefticients, demonstrating the contribution maoe to

(he

tempature

dependence by mechanical stress.

20 R. S. Muller

and]

Conragen, App . Phys. Letters 6,

83

(1965) .

21 R. S. Muller and]. Conragen,

IEEE

Trans. Electron Devices

ED12, 590 (1965).

a)

shifts in the capacitance-voltage curves.

The

direction

of these shifts is consistent with

the

c axis of the CdS

film being perpendicular to the substrate.

A relationship between stress and interface charge

distribution in thermally oxidized silicon has been sug

gested by Abowitz et

al.,22

although this effect appears

to be small.

23

DIFFERENTI L THERM L EXP NSION

Taking the linear thermal expansion coefficient of the

glass

substrates

and

the

CdS films as 9.0X

10-

6

and

5.

7X

10-

6

deg-t, respectively,

it

is

apparent

that

the

film will be under greater tensile stress as the temper

ature is increased. According to the results above, this

would give rise to a shift of the capacitance-voltage

characteristics and the transistor conductance curves

toward more negative values of the gate voltage with

increasing temperature. This stress dependence is,

therefore, at least

partly

responsible for

the total

ob

served temperature dependence as reported above.

To

estimate this contribution, the total temperature de

pendence of V

FB

was obtained from the capacitance

voltage characteristics measured at various temper

atures for sample 242B-9, for which the mechanical

stress measurements have been reported above.

The

total temperature coefficient of the fiat-band voltage is


11/11

3186

C . A.

NEUGEBAUER

effect conductance will change with the substrate ma

terial.

In

particular, by choosing a substrate with a

linear thermal expansion coefficient less

than

that of

CdS, the thermal expansion effect should at least

partially cancel the true temperature coefficient. This is

indeed observed and is illustrated in Fig.

13,

where the

source-drain current

at

constant gate and drain voltage

in the region of current saturation is plotted against

temperature for two transistors, one on a stlda lime

glass substrate, the other on fused silica. The temper

ature dependence of the latter is considerably less.

SUMMARY

The temperature dependence

of

the field-effect con

ductance in thin, polycrystalline CdS films in the tem

perature range of 100°C to

-50°

can be summarized

as follows:

1) The channel mobility varies exponentially with

the reciprocal temperature, with an activation energy

of

the order

of

0.06

eV.

2) The channel mobility increases with the induced

charge carrier density at low carrier densities, but

becomes independent

of it at

high densities. This can

JOURNAL OF APPL IED

PHYSICS

be interpreted as due to a depletion layer

at

the grain

boundary.

3)

The flat-band voltage

of

the CdS-Si0

2

-AI

var

actor increases linearily with temperature at a rate of

the order

of

0.01 V;CC. This can be interpreted in

terms of a semiconductor-oxide interface state density

of the order of 10

13

cm-

2

eV-1 in the bandgap in the

vicinity of the conduction band.

4) The flat-band voltage increases with compressive

stress

at

a rate as high as several hundred volts per

percent elastic strain. This causes a faster. increase in

flat-band voltage with temperature if the expansion

coefficient

of

the substrates is larger than that of the

CdS film, and a slower increase with temperature if

the reverse is true.

5) Contact barriers between the gold source and

drain electrodes and the surface channel become sig

nificant

at

temperatures below approximately - 25°C.

ACKNOWLEDGMENT

Valuable discussions with

R.

Swank, B. Segall, D.

Marple,

P.

Gray, D. Brown, R. Joynson, R. Sigsbee,

and A. Chen are gratefully acknowledged. D. Miller

and

R.

Yelle prepared the specimens investigated.

VOLUME 39

NUMBER 7 JUNE

1968

Stress Relaxation in Nickel Single Crystals between 77°-350

o

K*

R . w ROHDEt

AND

C.

H.

PITT

Department

of

Metallurgy University

of

Utah Salt Lake City Utah

Received 26 July 1967; in final form 15 December 1967

Stress-relaxation tests were conducted in compression with nickel single crystals of various orientations

and purities.

The

experiments were performed at five temperatures, 77°, 153°, 198°, 298°, and 350

0

K.

The

data

are fit by the semilogarithmic equation, D.T= (kT/B) In A t+1), based on reaction rate theory.

Crystals oriented to produce glide on intersecting slip planes exhibited no relaxation at the three lower

test temperatures. This absence

of

relaxation is believed to be a result

of

the high activation enthalpy

necessary to produce dislocation motion across the intersecting glide dislocations which would markedly

reduce the rate of thermal activation. Crystals oriented to produce slip on a single set of planes

had

only

one relaxation curve at low temperatures; no subsequent relaxation after the initial one could be induced.

At

higher temperatures, after relaxation had ended, new relaxation was easily initiated by increasing the

stress slightly. The activated volumes obtained were almost independent of the crystalline purity and of

strain, and volumes varied between 6.5 X

10-

2

cm

3

at 350

0

K to 0.5 X

10-

20

cm

3

at 77°K. These volumes

were considerably larger and had a different temperature dependence than the ac tivated volumes previously

measured by etch-pitting methods which varied between l.OX

10-

20

cm

3

at 273°K to 0.2 X 10-20 cm

3

at 77°K.

The discrepancy is believed to result because the rate controlling mechanisms for dislocation motion in

etch-pitting and stress-relaxation experiments are different. t is shown

that

during stress-relaxation

dislocation-dislocation interactions are rate controlling. In the previous experiment where dislocation

velocities were directly measured, dislocation-dislocation interactions are believed to be of only secondary

importance. Thus, the stress relaxation test while providing a simple method for obtaining the activated

volumes associated willi macroscopic deformation does not seem applicable for the inference of the param

eters for dislocation motion in nickel measured

by

etch-pitting techniques.

INTRODUCTION

Direct measurements of dislocation motion in various

materials

1

-

s

have shown

that

the velocity of dislocations,

v

is a function of the applied, resolved shear stress,

T

The most widely utilized relationship

is

the empirical

equation:

. Work supported

by

a NASA Training Grant and in

part by

the United States Atomic Energy Commission.

t Present address: Sandia Laboratory, Albuquerque, N. M.

87115.

1

H. W. Schadler, Acta Met. 12, 861 1964).

2

w

G.

Johnston and

J.

J Gilman,

J.

Appl. Phys. 30, 129

1959) .

3

D.

F.

Stein and

J.

R. Low, Jr.

J.

Appl. Phys.

31 362

1960).

1)

4 J.

S. Erickson, J Appl. Phys. 33, 2499 1962).

5

A.

R.

Chaudhuri,

J. R.

Patel, and L G. Rubin,

J.

Appl. Phys.

33, 2736 1962). .

6 R. W. Rohde and C. H.

Pitt J.

Appl. Phys. 38, 876 1967).

1

W. F. Greenman, T. Vreeland, Jr., and D. S. Wood,

J.

Appl.

Phys. 38,

3595

1967).

8 D. P. Pope, T. Vreeland, Jr., and D. S. Wood, J. Appl. Phys.

38, 4011 1967).

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