Mechanisms of induced conductivity in polyvinylidene fluoride irradiated by X-rays

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Mechanisms of induced conductivity in polyvinylidene fluoride irradiated by X-rays

R. Faria

To cite this version:

R. Faria. Mechanisms of induced conductivity in polyvinylidene fluoride irradiated by X-rays. Journal

de Physique I, EDP Sciences, 1992, 2 (10), pp.1965-1977. �10.1051/jp1:1992259�. �jpa-00246676�

Classification Physics Abstracts

72.20J

Mechanisms of induced conductivity in polyvinyJidene fluoride irradiated by X-rays

R. M. Faria

Instituto de Fisica e

Quimica

de Sfio Carlos~UsP, CP 369, 13560 Sfio Carlos, Brazil

(Received 26 November J99J, revised J8 March J992,

accepted

J2 June J992)

Rksumk. Nous _avons mesurd _sous vide la conductivit6 induite due h la radiation des rayons X

sur des 6chantillons de

poly(fluorure

de

vinylidbne), pendant

et

aprbs

irradiation (composante retard£e). Pendantl'irradiation la conductivitd induite _est forrnde de deux diffdrentes

parties

:I'une est la conductivitd instantande, et l'autre est une fonction croissante _avec Ie temps. Grice h la

mdthode du courant 8timuId par la tempdrature, ex6cutde _8ur de8 6chantiIIon8

vierges

d'une part, et irrad16s d'autre part, nous avons conclu h l'existence de niveaux de

pidges profonds

dans Ie matdriau. Nou8 _avon8 par la 8uite

ddveIopp6

un moddle de

cin6tique

de8 porteur8

qui explique

I'dvolution _avec Ie temp8 ^{de la} conductivit6 induite. Le8 dIectron8 chaud8 crdd8 par la radiation ont 6t6 consid6r6s _comme

re8ponsabIe8

de la conductivit6 induite in8tantan6e. Nous montron8 au88i que Ies 6Iectrodes sont

non~bIoqu6es

pendant Ies _mesures de courant

dlectrique

_sous irradiation,

alors que le

champ

61ectrique

appliqu6 rejette

les porteurs ^{hors de} l'6chantillon.

Abstract.

Prompt

and delayed components ^of

conductivity

of

polyvinylidene

fluoride (PVDF)

samples

induced

by

continuous irradiation of X-rays _were measured under vacuum. The prompt component was

composed

of two distinct parts, ^classified as instantaneous radiation-induced

conductivity

(RIC) and

time-dependent

evolution of the RIC. With the

help

of

thermally

stimulated

current measurements carried out with both

virgin

and irradiated

samples,

which indicated the

existence of

deep-trap

levels in the material, we

developed

_a model of kinetics of the carriers to

explain

the time-evolution of the RIC. Hot electrons

generated

by irradiation _were considered _as

responsible

for the instantaneous part ^{of the RIC. We} also showed that the electrodes had _{a non-}

blocking

behaviour

during

the electrical _current measurements under irradiation, while the extemal electric field caused the

generated

carriers to drift out of the

sample.

1. Introduction,

Dielectric

materials,

in

particular synthetic polymers,

which under normal conditions _are very

good insulating materials,

have their electrical

conductivity

increased

significantly

when

exposed

to

ionizing

radiation such _as

photon (

_y-rays,

X-rays,

and

uv)

_or electronic beams. This increase in

conductivity,

which is similar to the

photoconductivity

of semiconductors and of

some

insulating inorganic materials,

is in

general

called _« radiation-induced

conductivity

(RIC)

_». Even after the radiation is switched

off,

the induced

conductivity

still

persists

for _a

long

time albeit

decreasing gradually.

This component ^is

usually

called

«

delayed

radiation- induced

conductivity (DRIC)

_».

Polymer

films have found

widespread technological applications, mainly

because of their

unique

combination of mechanical and electrical

properties. They

_present, in

general,

a strong

capacity

of storage ^{of electric carriers for} a very

long

time. Radiometer

devices,

communi- cation satellite

exposed surfaces,

and

measuring equipment

which

operates

^{in radiation} environments _are

already

_some of the

applications

of

polymers

^which _are resistant to

high

radiation doses. The RIC

technique

is

employed

to

study

in _some detail the mechanisms involved in the

generation

of carriers

by irradiation,

in the

trapping-detrapping

of

carriers,

and in the recombination of carriers

[1-7].

RIC has also shown _a

complex dependence

_on both dose rate and the total absorbed dose

[1, 8-10],

_as well _{as a} strong

dependence

on the environments in which the measurements are carried out

[I I].

In this paper we present ^RIC measurements of

polyvinylidene

fluoride thin films with different

experimental conditions,

and _a model

involving recombination, trapping-detrapping,

and field-extraction of the

generated

carriers _was

developed

in accordance with the

experimental

results.

2.

Experimental procedures.

The

experimental

setup ^for radiation-induced currents is illustrated in

figure

I. A

sample (a-

PVDF

Kureha)

inserted into the

apparatus

^had a free surface _to receive the incident radiation, which

passed through

a thin PET window.

Samples

used in these

experiments

_were circular films 8 _cm in diameter and 25 _~Lm thick. The

samples

were cleaned with

methyl

alcohol before

having

both surfaces metallized with

evaporated

aluminium _or

gold

electrodes of 50-100 _nm thickness. The electrodes of 4 _cm in diameter _were also circular and concentric with the

sample.

The _rear electrode

(measuring electrode)

_was

protected by

a

guard-ring

with _an inner diameter of 5 _cm and _an outer diameter of 6 _cm. The

samples

were also sandwiched in between

a « front _» and _{a « rear »} PVDF foil _as thick _as the

sample.

Such _a structure is necessary ^to reduce the

photo-Compton (or

electron

emission)

current observed with

unprotected samples,

caused

by

^the directional and uniform beam of

X-rays.

The

secondary photoelectrons

generated by

the

X-rays

_are scattered

mainly

in the forward direction and

consequently

constitute _an electronic conduction _current.

Figure

2 shows the linear

dependence

of the short- circuited

photocurrent

_{as a} function of the absorbed rate, as was

predicted by

Gross

[12].

The front electrode of the

sample

could be

grounded

_or

energized by

a

voltage

source, while the _rear electrode _was connected to an electrometer. The RC time of the

measuring

circuit _was less than 0.3 _s. Directional radiation _was

produced by

_an

X-ray generator

with _a

tube-voltage

of 75 kV and _a tube-current of 3 _to 10 mA. The absorbed rate was

mapped

at the

place

of the

sample by

_a

CaF~

thermoluminescence dosimeter and the exposure rate with _an ionization

chamber,

and _a

quite

uniform value _was found

(2.5 Gy/s

for lo mA of tube

current). During

the

irradiation,

the chamber _was evacuated to a pressure of 10-4 _tom. In

general,

irradiation

was started

only

after the dark _current became constant. Since the dark _{current was a}

significant

fraction of the radiation-induced current, it _was

always

subtracted from the measured _current under irradiation. With each

sample

it _was

possible

to

perform

at least four well

reproducible experiments.

The absorbed dose in _one measurement of three hours _was

about 27

kGy.

So _we conclude that PVDF is resistent _to radiation

damage

_up to 100

kGy.

The carrier

generation

rate g is the ratio between the dose _rate absorbed

by

^{the material and} the energy W necessary for the creation of _a hole-electron

pair.

The absorbed dose _rate is

empirically given by

6.2 _x 10~

pR,

where _p is the _mass

density

of the material

(approximately

1.8

g/cm3),

and R is the dose rate defined in

Gy/s.

^One

Gy

is

equivalent

to 6.2 _x 10~~

eV/g.

Thermally

stimulated

conductivity

measurements were carried _out

by heating

both

virgin

CHAMBER ^X-RAYS OFVACUUM

MYLAR

~~

FRONT ELECTRODE

ELECTROMETER

AMPLE~

ELECTRODE

, '

,

' "

' '

' ' '

'

' '

' '

, ' '

, ' ' '

'

',

Fig. I. Schematic setup ^for radiation-induced

conductivity

(RIC) measurements. The window where the X-ray pass through ^{is made} by _a thin foil of PET which is resistent to _a pressure of _one

atmosphere.

5. o

Si 5.o

1

Fig.

and

pre-irradiated samples

with _a

relatively

low

voltage applied

to their electrodes,

resulting

in

an electric field of about

104 V/cm.

The

temperature

_was increased _at the _{constant rate} of I.I

°C/min.

3.

Experimental

results and discussions.

Measurements of radiation-induced currents in a-PVDF

samples

under _{vacuum were} carried out _as follows _:

a)

_a

voltage

was

applied

to the

sample,

and time _was allowed for the dark

transient

conductivity

_to become

negligible b)

the irradiation _was switched _on, and the RIC

was recorded _{as a} function of the irradiation-time

c)

the irradiation _was switched

off,

and then the DRIC

decay

was observed for _a

prolonged

time.

Figure

3 shows the

typical

behaviour of RIC and DRIC of _our

samples.

When

voltage

_was

applied

to a non-irradiated

sample,

_a fast-

decaying

transient

dark-current, usually

called

absorption

current, was observed. Short-

circuiting

of the

sample

was followed

by

_a transient

discharge

_current,

obeying perfectly

the Linear

Superposition Principle [13]. Prompt

RIC

component

^{consisted of} an instantaneous

conductivity

_«~,

directly responsible

for the

lo

_current, and another contribution

deriving

from

a current which varies with time.

I~

increases from _zero up to a finite value

immediately

after

the irradiation is switched _on.

During

the first half _an

hour,

the RIC increased

linearly,

and thereafter

sublinearly, tending probably asymptotically

to a constant value for

prolonged

irradiation. After termination of

irradiation,

the RIC of the

sample

did not

disappear instantaneously,

but rather the DRIC

initially

diminished

rapidly

followed

by

a slow and

gradual decay.

^{It carries}

charge

which amounts

only

to about 10 fb of the

charge

recorded

during

the

previous

RIC measurement. Thus

significant trapping

has occurred, since the

delayed

current is due _to the

gradual detrapping

of

previously trapped

carriers.

Thermally

stimulated current measurements, which will be

presented below,

have confirmed the role of the carrier

trapping during

irradiation. Similar results with

polymeric

materials _were observed

in many measurements for the first time

by

Fowler

[ii.

Jo-o

~i 5.0

~

- ijo)

5

~

=25Gy/s ~fi

E=4 _Ox10~

V/cm

Fig.

3.

_-

3.I ABSENCE OF POLARIZATION. The

time-dependent

electric _current evolution in

insulating

materials

during step-voltage

measurements is, in

general, strongly

affected

by

the electrodes.

Blocking

electrodes may cause

polarization effects,

in

particular

due to the formation of _a

Shottky layer [14, 15].

We carried _out RIC measurements where the

sample

_was

periodically

poled

for short

periods

of about 30 _{s, a}

period

of time sufficient for

having

_a

negligible

value of the

superimposed

dark current. In between

poling periods

the

sample

_was

kept

in short-circuit.

The

good

agreement ^between a standard RIC measurement and _a measurement

using

an

intermittently applied voltage

_on the

sample,

shown in

figure 4, definitely

eliminates the

hypothesis

of electrode effects _on the RIC of a-PVDF. When the

polarity

of the

applied voltage

was inverted

during irradiation,

the direction of the RIC _was also

inverted,

while its

amplitude

remained the _same. These results show strong ^{evidence that the evolution of the RIC} on time is

exclusively

due _{to an} interaction process between the radiation and the

material,

and that the electrodes _are

completely

neutral

during

the process.

lo-o

o

8.0

-

~

z-o

(o)

2.O

t(io~s)

Fig.

carried out

a

sample under _a applied field

;

the _circles give a curve

sample

irradiated in

and

poled for short period _f time (30

s).

3.2

INSTANTANEOUS OF THE

RIC.-

Since two distinct _components on the

prompt RIC _of

a-PVDF samples were observed, one can consider that there

conduction _mechanisms nvolved: one responsible for

the

instantaneous component

«~, and the other

for

the me-dependent component. We

distinct

kinds of X-ray enerated

carriers

are

_available for moving _under an

extemal

_electric

field, namely, t-electrons

and thermalized

^carriers. RIC measurements on

polymer

films _and

on

_amorphous materials _carried out under igh-intensity and very

short

pulsed

irradiation,

already

been

explained by a simple

model

in which only

hot-electrons

were

_available

photoconduction [16].

The

nstantaneous

irradiation and

is

^as shown

in figures

5 and 6. When the

radiation is itched

off

_this component

decays

to

zero

exhibiting a reversible

behaviour.

The empirical _relations for the

initial

_ma

= 4.8

x 10~

rate of

2.5

R, and ma =

1.7

_{x lo} ~~ _k for ^an_lectric field of 4.0

from those xperimentalurves.

3.3 IME-DEPENDENT

EvoLuTioN

OF

function of _the

logarithm of the

time

_for different _values of the

extemal

E, at an

absorbed

rate of 2.5 Gy/s. With the onset of

irradiation,

the

induced

current

nitial

value Io, and _duringthe first minutes it

increases linearly with

time,

as shown _in the

inset. The ength of

the

linear region decreases ^ith increasing

values

of

E.

_The current-

z I. z

o.iJ o.9

fl

^°.fi

~

O.6

~

~

i-J. :1

~ ~

U-o

'? j I ^O-O

50 loo 150 250

Ill(ii

/,

~ ~~~~ _~

Fig.

5.

Fig.

6.

Fig. 5. lnstantaneous component ^{of the induced} current _as a function of the absorbed _rate.

Fig. 6. Instantaneous component ^{of the induced} current as a function of the

applied

electric field.

80

((

? fi 30

zo

~ ,o

60

~

o loo 300

,j~j IO~ V/Cm

$

40

)

20

io~ io~ io~

Log i (s)

Fig. 7. Radiation-induced currents as function of log irradiation time for differents values of the

applied

field. k _2.5 Gy/s. Inset Initial section of the _curve for E

= loo kV/cm.

voltage relation,

extracted from

figure

7,

obeys

an

empirical

_power law1

= 3.5 _x 10~ ^~° V°.~

for

applied voltages

of up to 000 V. The measurements were carried _out under _an exposure rate of 2.5 R and in the irradiation time of

10~

_{s. The induced current also}

depends

on the

absorbed rate

according

to the relation I _oc R°.~~.

According

_to the model

developed by

Fowler

II,

this last relation indicates that the distribution of traps, ^{in the} bulk of the

material,

is rather uniform in energy.

If the

sample

^{is irradiated for} a

long

^{time in} short-circuit, and then

poled,

the recorded RIC

initially

_{presents a great excess} of current, as shown in

figure

8. This current decreases very

quickly

as soon as the electric field is

applied,

and after few minutes it describes the _same evolution in time observed in _a standard RIC measurement.

So,

_we conclude that the great amount of carriers

generated

in short-circuited

samples

_were drawn _out of the

sample by

the field

applied subsequently.

60

50

0'J ioov ^0V

-

40

~f

~ 5

-

~~

Jo o

_5

1-o

Ii

Fig. 8. -

_{Induced current}

as

and^led fterward.

sample

_;

II)

measurement of the _same

sample

24 hours after

having

been irradiated

during

I hour with _a dose rate of 280 R/s _;

III)

measurement

repeated

with the _same

sample

24 hours after the termination of measurement II. The TSC _curve obtained in measurement I exhibited _a broad

peak

around 353 K, ^while a

sharper peak

around the _same

temperature

was recorded in measurement II. Curve III shows that the

trapped charge

_was

completely

eliminated after _a TSC measurement. So _we conclude that the

peak

of _curve I is due to

trapped charges already existing

in

virgin samples,

and those

existing

in irradiated

samples (curve II)

_were

captured

among the

radiation-generated

carriers. The

charge

obtained from the direct

integration

of the

peak

of _curve II

(irradiated samples),

_was about 0.5

mC,

in _contrast with the total amount of

the

radiation-generated charge

which _was

approximately

0.I C. So the

majority

of the

generated

carriers _were

gradually

eliminated

by

other mechanisms. Values of the average activation energy and escape

frequency

of the

trap levels,

_were calculated

by

^{initial rise time}

[17]

and Chen

[18]

methods both derived from the first-order kinetic. 0.94 eV _was the average

value found for the activation energy and 3.0 _x lo ^~~ _{s~ was} the average value obtained for the escape

frequency.

3.5 ORIGIN _{OF CARRIES AND TRAPS.} The

polarity

of dominant carriers in unirradiated PVDF which contribute to the dark _current is still _a

subject

of controversy.

Bamji

and Perlman

associated the

pyroelectric

_response of PVDF films with

negative

ions which _move into the bulk and get

trapped [19]. However,

other articles have considered

injected

holes

[20]

and

positive

dissociated ions

[21]

as

responsible

for

step-voltage

transient currents. Ieda and collaborators established _a correlation between the

changes

of the

polarity

of the carriers in

synthetic polymers,

which contributes to the dark current, and the

degree

of the fluorine substitution in the _monomer

[22].

The contribution _to the dark _current

changes

from

negative

to

positive

carriers as the

degree

^of fluorine in fluorinated

polymers

increases.

Electronegative

fluorine atoms _were considered _to

provide

electron traps ^and _suppress ^the current due to

negative

carriers. This conclusion is in agreement ^{with evidence} that

negative

and

positive

carriers _are considered dominant carriers in unirradiated

samples

of

polyethylene [23]

and

fluorethylenepropylene, respectively [24].

The

binding energies

of atoms of PVDF obtained from Electron

Spectroscopy

for Chemical

Analysis techniques,

_were 689.6 eV for

Fi~,

an 290.8 and 286.3 eV for

Ci~ corresponding, respectively,

_to the

-CF2

and

-CH2

carbons

[25].

So either free carriers _or traps

(carbon-

cation _on the backbone of the

polymer,

for

example)

_can be

produced

in the bulk of the

sample

as the result of the ionisation of those

bindings by secondary

electrons.

Moreover,

_traps and carriers _can have their

origin

_on the ionisation of

impurities

and additives

deriving

from the

processing

of the

plastics,

_or absorbed from the environment. It _was observed that the moisture absorbed from the air contributed to increase the RIC for

PVDF,

and to decrease it for

polyethylene terephthalate (PET)

and

polyimide (PI) [ill. Probably

the radiation generates

more carriers than traps ⁱⁿ

PVDF,

while for PET and PI the

opposite

takes

place.

4. Theoretical model and

comparison

with

experimental

results.

The

density

of the

generated

hot-electrons n~ is calculated from the

product

^between the lifetime _r of these

carriers,

and the absorbed energy of the

X-ray

beam

by

the

sample,

per unit volume per unit

time,

divided

by

the energy

Eo

necessary for the creation of _a

single

hot- electron. For an absorbed rate of 2.5

Gy/s,

the

density

_{energy per} unit time transferred to a

PVDF

sample by

the

X-ray

beam is about 3

x10~~eV/cm~s;

_so the carrier

density

n~

is,

~°

~ _~

~~~

^{~ ~~ ~ ~~~}

On the other

hand,

the electrical

conductivity given by

the hot electrons «o is no e~ r/m, where

e is the electronic

charge

and _m is the _mass of the electron. So the radiation-induced instantaneous

conductivity

is

given by,

~ _~ ~16 ~2 ²

"°

E~

m

~

~~'~~

~~~

We _assume

here,

for the PVDF, a model of band structure of

amorphous-disordered

materials

[261,

similar _to that defined for

glassy

insulators

[27],

and that the energy gap

E~

^is

typically

between 2 and 6 eV. In addition that the hot-electrons _are assumed to lie within _an energy

range of

E~

^{above the conduction band}

^(to

^avoid

being captured by

both shallow and

deep

traps),

so

Eo

is

approximately equal

to

2E~. Using equation (2),

the value of 4.8 _x 10~ ^~~

(n.cm

)~ ^{extracted from}

figure 6,

and also the

assumption

established above, P,e

estimate that the lifetime of the hot-electrons is of the order of 10-14 _s. The _mean free

path

^I of the hot-electrons _can also be estimated from the

equation

_r

=

flu,

where _v is their _mean

velocity.

For _v of the order of

106m/s,

the _mean free

path ^I

^{will be about 10-8m.} The

mobility

of the hot-electrons _v =er/m, ^{in these}

conditions,

will be

approximately

20cm2 V-I

s-I,

_so for _an

applied

field of

100kV/cm

the instantaneous

component

^{of the} RIC will be established in nanoseconds for _our

samples.

On the other

hand,

the induced

conductivity resulting

from the thermallized electrons is

strongly

affected

by geminate

recombination and

by trapping

effects. The

parallel plate capacitor

structure of _our

samples

irradiated

by

the directional

X-ray

beam reduces the RIC model _{to a one} dimensional

problem.

In

general,

for

polymers,

the

trap-modulated

^mobilities

of the

positive

and

negative

carriers _are very

different,

_so that it is reasonable to _assume the one-carrier electric

transport approach.

Like in other

highly insulating materials,

the diffusion

component

^{of the total electric} current is

negligible compared

_even ^{with the dark} current.

Because the

sample

is very

thin,

the absorbed radiation is

independent

^{of the}

penetration length (x-coordinate),

_so the

continuity equation

for the conduction carriers is

usually

~~-g-T+D-r

(3)

where _g

= 6.2 _x lo

pk/W

_{is the carrier}

_generation

_{rate, T is the carrier}

_trapping

_{rate, D is the}

carrier

detrapping

rate, and _r is the carrier recombination _rate. The last _term represents ^the recombination between the conduction carriers and the

trapped opposite-signal

carriers.

Assuming

the

approximation

that the recombination term is

mainly dependent

on the free carriers _{n, we can} establish the

approximate

relation _r

=

n/r~,

where _r~ is the recombination time. T is also

proportional

to n, and

similarly

written _as

n/r~,

ⁱⁿ our case r~ is the

trapping

time of _a trap ^{level which takes the}

place

of _a compact distribution of trap ^{levels. D is}

equal

to

n~/r~,

where _n~ is the

density

of the

trapped

carriers and _r~ is the

detrapping

time.

The

continuity equation (3)

has terms that are

apparently independent

of the extemal field.

But the measurement exhibited in

figure

8 indicates that the variation of n with time

depends

on the electric

field,

in the _sense that it draws free carriers _out of the

sample.

So _{a more}

complete equation

must take into account the field

dependent

term

vEn/d,

where _v is the trap-

modulated

mobility,

E the extemal electric

field,

and d the

sample

thickness. To

accomplish

our model _we added _to the

continuity equation,

a

detrapping

kinetic

equation

and _an ohmic behaviour for the

RIC,

dn~ _n n~

$

r~ r~

~~~

J

=

nevE (6)

J is the

density

of the radiation-induced current.

The initial conditions established for the

equations (4)

and

(5)

are

n(0)

=

0,

_n~

=

0,

[dn/dt]o

₌ g and

[dn~/dt]o

₌ ^{0. The}

analytical

solution of the linear

equation (4) is,

n

(t

= g r'

jA

_exp

(at )

₊ B exp

(bt )

₊ I

(7 )

where r'~

=

(r~

+

vE/d)~

Similar

equations

_are established for the

delayed component

^{of the induced}

conductivity (DRIC), obviously considering

that the carrier

generation

is

instantaneously stopped just

after the radiation is switched

off,

~~'

=

~~

~'- ~'- ^~~~'

(8)

dt _r~ r~ r~ d

~ ~ j

~~~

Now the initial conditions _are

n'(0)= n(t,)=N,

where

t~ is the

irradiation-time,

and

[dn'/dt

_Jo should be

equal

to

[dn/dt ], [dn/dt Jo),

_{or more}

specifically ( [dn/dt ],

g

).

In _a

good approximation

the _term

[dn/dt],

_can be

neglected

for _a very

prolonged

irradiation. The

general

solution of these

equations is,

n'(t)

= ~

i (Nb

_g

),

_exp

(at (Na

_g

),

_exp

(bt

)1

(10)

The

amplitudes

A and B, ^and the

exponential

factors _a and

b,

that

appeared

in solutions

(7)

and

(lo)

_are functions of the time _constants r~, r~, and

r',

A

=

(b

₊ r'~

)/(a b),

and B

=

(a

₊ r'~

)/(a

b

,

a =

(X/2 ), (1 Y)

,

and b

=

(X/2 ). (I

+

Y),

j X

=

I/r~

₊

I/r~

+

I/r~

and Y

= [1

4/(r'r~ X~)]~

Figures

lo and it present

comparisons

between

experimental

RIC and DRIC _curves and the theoretical results obtained from the

equations (7)

and

lo), respectively.

The

detrapping

time r~ has _a

negligible

influence _on the RIC _{curves even} after many hours of measurements. It

indicates that the value of r~ is ^at least close to

104

_{s. The value} of the

parameters

used in the

theoretical-experimental fitting

are

presented

in table I. It _was found that the

trapping

time r~ for the induced

conductivity during

the irradiation

(RIC)

is

larger

than that obtained for the

DRIC _curve.

Probably during

the irradiation _some

deep trap

^{levels became shallow} traps,

modifying

both

deep

and shallow trap

distributions,

and

consequently changing

the

trapping

time of the

deep

traps. ^{The carrier}

generation

rate g can be estimated from the value of the energy ^W necessary for the creation of _an electron-hole

pair.

For

polymers

^{W is considered} to lie between _a few hundred and _a few thousand

electron-volts,

but it

depends

_on the extemal

applied

field

according

to the influence of the field _on the

geminate

recombination

[281.

Table II shows the variation of g and W with the extemal

field,

thus

being

in agreement with the

Onsager

effect.

20 25

j6 20

12 15

f 5

~

8 * IO

o

4 5

O O

2000 6000 IOOOO ° 2°° 4°° 6°° 8°° '°°°

TIME _s TIME (s)

Fig.

10.

Fig.

ll.

Fig.

lo.

Fitting

of _a RIC curve. Continuous line _: calculated _curve. Dots

experimental

values.

Fig.

ll.

Fitting

of _a DRIC _curve. Continuous line calculated _curve. Dots _:

experimental

values.

Table I. List

ofparameters for

calculation

OfRIC

and DRIC components ^and obtained

from

TSC measurements.

Quantity

^Value

recombination time 7 700 _s

~,

trapping

time

(during

^{2 000} s

~,

trapping

time

(after irradiation)

300 s

~,

detrapping

time _~ 8 000 _s

~c,

trap-modulated mobility

x 10-~~ cm~ V-I

Table II.

Dependence ofthe

carrier

generated

rate

gand

the energy W

ofthe

electron-hole creation.

E g W

4.0 _x 104

V/cm

1.5 _x 1013

cm-3

s-I 730 eV

1.0 x 106 V/cm 3.5 _x I01~ cm-~ s-1 750 eV

1.5 _x

106 V/cm

6.4 _x

I01~ cm~3 s~l

420 eV

4.0 _x 106

V/cm

1.7 _x I014 cm-~ s-1 160 eV

The _excess of current observed in RIC measurements carried out in

samples previously

irradiated in short-circuit shown in

figure 8,

is also well

explained by

the model

developed

above. We calculated

n(t)

from

equation (4)

^{with E} ₌

0, during I04s,

and later with

E

= 4.0 _x

106

_{V/cm. The result is shown in}

curves I and III

presented

ⁱⁿ

figure

12, ^while curve

II shows the result obtained when the calculation _was made with E

= 4.0 _x

10~

_V/cm since

_

~'~

E=0 E=04MV/cm

~ ^,

,

''

~'~ ,'

~, _Ill

~U

' ^'

~

~ 0

/

~

~

_~

III

~

~

jj ^~ k=ZjGv/s

££

5

~

~~

o-o

^~

o 5 lo 16 zo

ljlo~s)

Fig.

12.

Density

of carriers available for the induced conduction _n(t ), calculated from equation (7) _: 1) n(t) ₌ 1.3 _x

10'~[-

0.839

exp(-1.82

_x 10~~ t)

0.161exp(-

7.12 _x 10~~ t) ₊ I II) n(t)

=

2.89 _x

10'~[-

_{0.508 exp(-} 5.17 _x 10~~ t) 0.492 exp(- ^1.14 x 10~~ t) + I] III) n(t)

=

2.89 _x

10'~[-

_{0.148 exp (- 5.17}

x 10~~ t) + 0.500 exp(- ^1.14 x 10~~ t) + I]. Inset

Experimental

results.

t

=

0. We observe that

n(t),

which _are the carriers available for the

conduction,

_are

larger

when the

sample

is short-circuited

(curve I),

but it tends towards _curve II _{as soon as} the field is

applied

to the

sample.

In the inset _we present an

experimental

result for

comparison

with the calculated values.

5. Conclusions.

In this

study

we have

provided

a

quantitative

theoretical fit to the

experimental

results of RIC and DRIC in

polyvinylidene fluoride, considering

two distincts kinds of

generated

carriers _:

hot-electrons and thermallized carriers. While hot-electrons _are

responsible

for _a very fast RIC component, ^{estimated of the order of} nanoseconds, thermallized carriers are under the influence of

trapping-detrapping

^and recombination kinetics which control the slow evolution of the RIC and the DRIC components. ^{Both the carrier}

generated

rate g and the amount of

charge

available for the conduction

n(t) depends

on the extemal electric

field,

while there is strong ^evidence that the irradiation also generates ^carrier traps ^{in the bulk of the material.}

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