Mobility variations of photoinjected charge carriers in liquid sulfur

Journal of Electrostatics, 7 (1979) 283--291 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

V A R I A T I O N S OF P H O T O I N J E C T E D

MOBILITY

CHARGE

CARRIERS

283

IN

LIQUID SULFUR*

Donald H. Baird GTE Laboratories,

Inc., Waltham, MA 02154 U.S.A.

ABSTRACT Drift m o b i l i t y m e a s u r e m e n t s on electrons p h o t o g e n e r a t e d in liquid sulfur in the low v i s c o s i t y state have been extended to high electric field strengths and to large c o n c e n t r a t i o n s of injected carriers.

M o b i l i t i e s c a l c u l a t e d in the usual way from the

results at m o d e r a t e injection levels are in agreement w i t h the values r e p o r t e d by Ghosh and Spear

(ref. i).

They are found to be

i n d e p e n d e n t of field s t r e n g t h to at least 75 kV/cm.

The data at

low i n j e c t i o n levels also provide e v i d e n c e of the o c c u r r e n c e of e l e c t r o n trapping and release processes, used.

At high injection levels,

even in the p u r e s t sulfur

current amplitudes were o b s e r v e d

during the carrier drift time which were too large to be c o m p a t i b l e with the carrier v e l o c i t i e s o b s e r v e d at lower injection levels. This suggests that the i n t r o d u c t i o n of large excess carrier conc e n t r a t i o n s into liquid sulfur can increase the e f f e c t i v e mobility.

INTRODUCTION Studies by Ghosh and Spear

(ref. i) of carrier transport in

liquid sulfur at m o d e r a t e electric field strengths have indicated that the t r a n s p o r t process

is p r i m a r i l y e l e c t r o n i c and involves an

i n t e r m o l e c u l a r h o p p i n g mechanism.

Recently,

Proud and A u b o r n

(ref. 2) have i n v e s t i g a t e d the e l e c t r i c a l c o n d u c t i v i t y at high fields where they o b s e r v e d c h a r a c t e r i s t i c n o n l i n e a r i t i e s p r e S r e a k d o w n range. ities,

in the

To assist in u n d e r s t a n d i n g these n o n l i n e a r -

it appeared of interest to extend the drift m o b i l i t y

measurements

into the high field range.

This paper p r e s e n t s

*Work s u p p o r t e d in part by Office of Naval Research under C o n t r a c t No. N00014-74-0215.

284 the results

of this e x t e n s i o n

the d r i f t b e h a v i o r

together

in the p r e s e n c e

with

observations

of large

made

concentrations

of

of injected

carriers.

EXPERIMENTAL

METHODS

The m e a s u r e m e n t flight

of c a r r i e r s

electrodes. trode

technique

photoinjected

The cell used

through w h i c h

semitransparent pulsed

xenon

entirely

absorbed

imity of the p h o t o e x c i t e d Emphasis

was p r i m a r i l y

electrons. was

Therefore,

the cathode

excitation A reentrant eration

steel.

fur was m a i n t a i n e d a small

vertical

was m o n i t o r e d at the level

high

fields.

an argon

range of 120 ° to 150°C,

i.e.,

~

ELECT~~

TRANSPAREN'I"kL~:L ~

i.

Photoconductivity

followed

the cell.

and p e r m i t t e d

electrode,

The

was

liquid

The cell was h e a t e d

employed

in the low v i s c o s i t y

region

op-

which

separation,

to the o u t s i d e

cell - schematic.

of

electrode

the optical

across

of Pyrex.

The t e m p e r a t u r e s

LFUR

prox-

ensured.

tube and the sulfur

LIGHT PULSE Fig.

Ultraviolet

suitable

behavior

breakdown

HIGH < VOLTAGE

almost

was

The o p p o s i n g

fastened

of a thin

conduction

of e l e c t r o n s

sulfur.

STAINLESS STEEL ~

lamp output.

in the e l e c t r o d e

glass

The elec-

source was a

the t r a n s p a r e n t

atmosphere.

a thermocouple

of the electrode.

light

and thus

pulse which

surface

variation

nichrome°wrapped

with

of t h e

The body of the cell was under

The

of the sulfur

the d r i f t

i.

consisted

of the sulfur was

experiments,

eliminated

to p r o v i d e

in Fig.

to the e l e c t r o d e

the current

to m o n i t o r

at the d e s i r e d

of stainless

carriers

in m o s t

cell d e s i g n

could be m o v e d

portion

in liquid

on m e a s u r e m e n t

so that

served

schematically

The p h o t o r e s p o n s e

to the u l t r a v i o l e t

of the time-of-

light p u l s e p a s s e d

film on fused quartz.

lamp.

is h i g h l y

determination

at one of a pair of plane p a r a l l e l

is shown

the e x c i t i n g

platinum

flash

due

radiation

involved

sulin

temperature

of the cell were

in the

of liquid

285

The sulfur was K o c h - L i g h t material, respect to m e t a l l i c impurities. stantial amounts

specified as 99.999% pure w i t h

However,

of o r g a n i c contamination.

to d e t e r i o r a t e on being m a i n t a i n e d

it was found to contain subAs a result,

v a c u u m d i s t i l l a t i o n removed p a r t i c u l a t e contamination. w e r e an increase in conductivity, drift m o b i l i t y experiment, high fields.

samples tended

in the liquid state, even after a The symptoms

a p o o r l y defined transit time in the

and an increased tendency to break down at

These are thought to have been due to c a r b o n i z a t i o n of

the organic material, sulfur molecules.

p o s s i b l y w i t h i n c o r p o r a t i o n of carbon into the

To m i n i m i z e these effects,

of m u l t i p l e d i s t i l l a t i o n s ,

a p r o c e d u r e was adopted

the last with p a s s a g e of the sulfur vapor

through a furnace tube at 1000°C

(ref. 3).

M a t e r i a l so treated tended

to show i m p r o v e d stability of e l e c t r i c a l p r o p e r t i e s and better defined transit time data.

Some of this m a t e r i a l was m a i n t a i n e d

in the liquid

state for many days w i t h o u t showing deterioration.

RESULTS AT LOW INJECTION LEVELS At s u f f i c i e n t l y low light levels, the space charge due to the injected carriers

is too small to p e r t u r b the applied field.

Then,

ideally,

the injected carriers should c o n s t i t u t e a thin sheet d r i f t i n g at constant v e l o c i t y in a u n i f o r m field.

This will give rise to a c o n s t a n t

current in the e x t e r n a l circuit which will end a b r u p t l y w h e n they reach the o p p o s i n g electrode.

Thus in this idealized case,

r e c t a n g u l a r c u r r e n t pulse as illustrated by curve

the result is a

(a) in Fig.

the r e l a t i v e l y high v o l t a g e s of the p r e s e n t experiments,

2.

Under

one would ex-

pect the spreading effects of carrier d i f f u s i o n on the trailing edge of such a pulse to be very small.

io

(a)

t Z u,i cc r.J

t 0

TIME

Fig. 2. P h o t o c u r r e n t vs. time after optical pulse. (a) Idealized: n e g l i g i b l e space charge and no carrier trapping. (b) Typical e x p e r i m e n t a l result.

286

The o b s e r v e d

shapes

this r e c t a n g u l a r After

value.

circuitry,

trations current number

during

the pulse

is reached

anode.

The

time

undergone

case of the trappin g tive

occurs

liquid

to,

which

decay

carriers

through when

probably

trapping

a temporary

trapped

the light pulse

current

to c o n t r i b u t e

appreciably

in terms

and release.

The

arrive

free.

at the is

which

long current in traps. the process

to the formation

of

of

region.

and this b r e a k

time

one,

state

few electrons

transit.

of a p o s i t i v e

to, an

in

and the number

significant

corresponds

time,

3 contains

in the e f f e c t i v e

system with which we are dealing,

an e l e c t r o n

constant

can be given

the c o n s t a n t

their

of the

At the low concen-

the first electrons

spent

behavior.

is due to the trapping

until

of the r e l a t i v e l y

during have

ion or the n e u t r a l i z a t i o n

slow-moving

type.

from

that the v a r i a t i o n s

of e l e c t r o n

the number

between

time,

no t r a p p i n g

is due to electrons

Fig.

by v a r i a t i o n s

the initial

between

interval

to the transit

zero.

of this

the p r o c e s s e s

is m a i n t a i n e d

in the curve

to an e s s e n t i a l l y

a rather w e l l - d e f i n e d

it is p r o b a b l e

free p h o t o e x c i t e d

equilibrium

The break

pulse

the typical

type of i n t e r p r e t a t i o n

to this mechanism,

equilibrium

2 shows

toward

are caused

This

involving

the o r i g i n a l l y

have

charge,

are very d i f f e r e n t

by the time constants

a decay

until

to drop

trace of a current

of electrons.

According

limited

follows

begins

of injected

of a m e c h a n i s m

equal

there

pulses

(b) of Fig.

rise,

is m a i n t a i n e d

the current

oscilloscope

Curve

current

This value

at w h i c h

This

form.

the initial

detecting

of the current

tail

In the of

of a nega-

the ion being

too

to the current.

I.s[F 1.0

- -

- -

- -

--7

l

i/i o

0.5

L

io

= 57 n A

I

to

= 5 . 5 ms

E

= 34 kV/cm

~ " k

~

0.056

0

L 0

0.5

I 1.0

1.5

2.0

t/t o

Fig. 3. P h o t o c u r r e n t pulse for low injection level (qo = 3.1 × 10-10C). Dashed curve: c a l c u l a t e d pulse including space charge effects (ref. 4).

287

If this m e c h a n i s m it follows

that the time c o n s t a n t s

release

processes

If they

are longer

and the current very

short,

course

is r e s p o n s i b l e

than

transit

not be evident.

samples

which

The

this,

p u l s e will

t o will

trapping

w here

electrons

approximate will

in such

with

will

This break

current

not be t r a p p e d one.

trapping

in fact,

suggesting

and

of the transit

poorly

time.

at all

If they are events

and the c h a r a c t e r i s t i c is,

waveforms,

the t r a p p i n g

the i d e a l i z e d

undergo many

are not well p u r i f i e d

in the

break

defined

an increased

at

in

rate of

samples.

type of current

pulse One

observed is given

here may be c o n s i d e r e d in the usual w a y

to define

in terms of t o by: (1)

o L is the e l e c t r o n

In terms

of the m o d e l

untrapped

electrons.

i ° = qo/to cuit

most

of the cell,

two types of mobility. L P - Et

associated

m u s t be of the order of m a g n i t u d e

then all c a r r i e r s

of their

for the o b s e r v e d

separation

discussed Where

and E the e l e c t r i c

above,

is the current w h i c h w o u l d have

mobility,

which

represents

takes

flowed

of

charge,

in the e x t e r n a l

had occurred.

into a c c o u n t

strength.

the m o b i l i t y

qo is the total p h o t o i n j e c t e d

for the time t o if no t r a p p i n g

an average

this

field

cir-

We m a y also d e f i n e

the time spent

in traps,

as:

= P(ic/i o) where

(2)

i c is the c o n s t a n t

part of the c u r r e n t

pulse.

of t o were m e a s u r a b l e , 0.7 with

rather

shapes were

field

strengths

1.33

sample,

of t

values

observed

obtained

and values

in conductivity.

vs.

samples

for w h i c h

up to 75 kV/cm,

x 10 -2 cm and the cell

rocal

In pure

found

latter

in the range

for a given

field

of transit

sample

values 0.3 to

indepen-

temperature

strength

given

120°C.

in Fig.

the results

line,

x 10 -4 cm2V-is -I,

found by Ghosh

and Spear

current

field

These

for

spacing was

The p l o t of the recip-

4 shows no e v i d e n c e

correspond

i).

0.4,

to show s u b s t a n t i a l

strength.

As

of

indi-

to a free e l e c t r o n

in s a t i s f a c t o r y

(ref.

about

time d e t e r m i n e d

high

The i n t e r e l e c t r o d e

up to the highest

values

the

in w h i c h w e l l - d e f i n e d

sufficiently

cated by the solid of 1.13

during

this ratio was

o appreciable nonlinearity

mobility

flowing

strength.

On a p a r t i c u l a r pulse

of current

the ratio ~/~ has been

consistent

dent of the field

nonlinearities

value

agreement

results

with

indicate

the that

288

the nonlinearities originate

in conduction

in variations

in liquid sulfur at high fields do not

in carrier mobility.

m

80

o

60--

o

E

(kV/cm) 40

20-

iy

0

P = 1.13 X 10 - 4 cm2/V-s

1

I

200

400 1/t ° ($-1)

I

600

Fig. 4. Reciprocal of electron transit time vs. field strength. Electrode separation: 1.33 × 10 -2 cm. Temperature: 120°C. RESULTS AT HIGH INJECTION LEVELS When the intensity of the optical pulse is increased quantity

of injected charge,

the electric

and with it the

effects due to space charge p e r t u r b a t i o n

field are to be expected.

The total injected charge,

is given by the time integral of the current pulse.

It determines

of

qo' the

"self-field"

Eq = qo/eA where area.

(3)

e is the dielectric

constant of liquid sulfur and A the electrode

The extent of the space charge p e r t u r b a t i o n

ratio Eq/E.

E is the average electric

is governed by the

field strength,

= Va/L

(4)

where V a is the applied voltage.

The theory of space charge effects on

the present type of experiment has been developed by Papadakis The results

in the preceding

where E q / E << 1 so that space charge effects are negligible. loscope trace in Fig.

(ref. 4).

section were obtained under conditions The oscil-

3 shows a pulse recorded under such conditions.

289

The solid curve in the graph gives the same data w i t h the time normalized to t o and the current to i o, w h i l e the d a s h e d curve is that calculated using Papadakis'

theory.

At this low i n j e c t i o n level,

a p p r o x i m a t e s closely a r e c t a n g u l a r pulse, space charge free case. 3.1 × 10-IOc. By c o m p a r i s o n Fig.

the idealized shape of the

The q u a n t i t y of injected charge here was

5 shows the result of i n c r e a s i n g the injected

charge to 3.6 x 10-9C with other c o n d i t i o n s the same. level,

this

At this injection

the effect of the space charge in the absence of t r a p p i n g should

be p r o n o u n c e d as shown by the dashed t h e o r e t i c a l curve.

The e x p e r i m e n -

tal and c a l c u l a t e d curves under these c o n d i t i o n s bear a q u a l i t a t i v e resemblance.

A s s u m i n g the d i f f e r e n c e b e t w e e n c a l c u l a t e d and o b s e r v e d

curves in Fig.

3 is due to trapping,

at the i n j e c t i o n level of Fig.

one is tempted to speculate that

5, the c o n c e n t r a t i o n of carriers

is suf-

f i c i e n t l y larger than the trap density that the role of trapping is minimized.

1.5~ 1.0

t-/

i/io

~~ //

\\

0.5

io

= 658 nA

to

= 5.5 ms

E" = 34kV/cm = 0.64

\ 0

0

I

0.5

I

1.0

\\

I

1.5

2.0

t/t o

Fig. 5. P h o t o c u r r e n t p u l s e for high i n j e c t i o n level (qo = 3.6 x I0-9C). Dashed curve: c a l c u l a t e d pulse including space charge effects (ref. 4).

W h i l e such trap s a t u r a t i o n may occur, the curves of Fig. that other factors are m o r e important.

6 indicate

In this case, the electrode

spacing and applied v o l t a g e were i n c r e a s e d in such a way as to give a s o m e w h a t larger e l e c t r i c field w i t h an increase in transit time to 9.3 ms.

The q u a n t i t y of injected charge was 3.7 x 10-9C.

The experi-

m e n t a l curve shows a peak w h i c h is far h i g h e r than any p o i n t on the

290 c a l c u l a t e d curve.

This indicates that the observed pulse currents are

too large to be e x p l a i n e d by space charge effects,

even in the absence

of trapping.

2.0[1.5 ¸

ill o

/~

I 1.0

. / /" j

.

\\

I

\

io

= 371 n A

to

= 9.3 ms

E

= 44 kV/cm

\\ Eq/E

\\

0.5 •

= 0.51

\ \

\

01

I

0

0.5

I t/to

1.0

1.5

Fig. 6. P h o t o c u r r e n t pulse for high injection level ( q o = 3.7 x i0-9C). Dashed curve: calculated pulse including space charge effects (ref. 4).

It appears,

therefore,

that such strongly peaked current pulses m u s t

be due to an increase during transit either of the number of carriers, as by a m u l t i p l i c a t i o n process due to impact ionization, m o b i l i t y of the injected carriers.

or of the

The o b s e r v a t i o n that the effect is

g o v e r n e d p r i m a r i l y by the number of carriers

injected rather than by

the field strength argues strongly against a carrier m u l t i p l i c a t i o n effect. change.

However,

this o b s e r v a t i o n may be c o m p a t i b l e with a m o b i l i t y

The effect is observed at c o n c e n t r a t i o n s of injected carriers

much larqer than the thermal e q u i l i b r i u m value and this large excess carrier density could lead to p e r t u r b a t i o n s

in the o c c u p a n c y of energy

levels a s s o c i a t e d with the hopping m e c h a n i s m of c o n d u c t i o n characteristic of liquid sulfur.

Further,

the shape of the e x p e r i m e n t a l curves is

c o m p a t i b l e w i t h the hypothesis of an increased m o b i l i t y in that the short time to the peak suggests transit by many carriers than the u n p e r t u r b e d transit time.

in a time less

291

ACKNOWLEDGMENTS The author w o u l d like to thank Dr. J.M. Proud for m a n y helpful discussions and Mr. R o b e r t Smith for a s s i s t a n c e in the e x p e r i m e n t a l work.

REFERENCES 1 2 3 4

P.K. J.M. T.N. A.C.

Ghosh and W.E. Spear, J. Phys. C, Ser. 2, i, 1968, 1347-1358. Proud and J.J. Auborn, Appl. Phys. Lett., 57, 1975, 265-267. G u l i e v and D.I. Zulfugarly, Zh. Prikl Khim. 47, 1974, 2643-2646 Papadakis, J. Phys. Chem. Solids, 28, 1967, 641-647.