Evidence for a linear low-voltage space-charge-limited current in organic thin films. Film thickness and temperature dependence in alpha-conjugated sexithienyl

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Submitted on 1 Jan 1990

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Evidence for a linear low-voltage space-charge-limited

current in organic thin films. Film thickness and

temperature dependence in alpha-conjugated sexithienyl

Gilles Horowitz, Denis Fichou, Xuezhou Peng, Philippe Delannoy

To cite this version:

Gilles Horowitz

_(1),

Denis Fichou

_(1),

Xuezhou

Peng

(1)

and

_{Philippe Delannoy}

₍₂₎

(1)

Laboratoire des Matériaux Moléculaires, CNRS, 2 rue

_Henry

Dunant, 94320 _Thiais, France

(2)

Groupe

de

_Physique

des Solides, Université Paris 7, 2

_place

_Jussieu, 75251 Paris Cedex 05,

France

Résumé. 2014 Les

caractéristiques

courant-tension

(I-V)

de structures

_{Au/03B1-sexithiényle/Au}

ont été mesurées. Les courbes I-V

_présentent

deux

régimes :

à tensions _élevées, on observe la loi en

V2 correspondant

au courant limité par la

charge d’espace (CLCE) ;

la variation linéaire à faible tension est

_{généralement}

attribuée au courant

_ohmique

dû aux _porteurs libres en volume. Une

étude du courant linéaire en fonction de

_{l’épaisseur}

de l’échantillon montre deux comportements.

Le modèle standard

_s’applique

aux films

_épais,

dont la conductivité calculée à

partir

de la _pente

des courbes I-V est

_{indépendante}

de

l’épaisseur.

Dans les films minces

_(moins

de 2

_03BCm),

on

obtient une conductivité

_dépendante

de

_{l’épaisseur.}

Ceci

s’explique

dans le cadre du modèle

développé

par Bonham et coll., dans

_lequel

on tient _compte de la diffusion des _porteurs

injectés

thermiquement.

La densité en volume de ces _porteurs

_injectés

croit

_{quand l’épaisseur}

est _réduite, et _peut devenir

plus grande

que celle des porteurs libres

déjà présents

dans le film. Les résultats

expérimentaux

sont en bon accord avec les

_prédictions

du modèle. On a _pu calculer la mobilité

effective du

03B1-sexithiényle (03B1-6T)

à

_partir

du

régime

quadratique

des courbes I-V. On a

également

effectué des mesures en fonction de la

_{température.}

On trouve une mobilité

thermiquement

activée, ce _que l’on

_interprète

_par l’existence d’un

_piège

peu

profond

situé à

0,3 eV au-dessus du sommet de la bande de valence. Abstract. 2014

The

current-voltage (I-V)

characteristics of

Au/03B1-sexithienyl/Au

sandwich structures

have been measured. The I-V curves _present two

_{regimes :}

at

_{high voltages,}

the square law

corresponding

to the

_{space-charge-limited}

current

_(SCLC)

is _{observed ;} the linear variation

occurring

at low

voltages

is

_generally

attributed to the ohmic current due to bulk free-carriers. A

study

of the linear current as a function of the

_sample

thickness shows that two behaviors are

encountered. The standard model is followed on thick _films, where the

conductivity

calculated from the

_slope

of the I-V curve does not

_depend

on the thickness. In thin films

(less

than 2

03BCm),

a

thickness

_{dependent conductivity}

is obtained. This is

_explained

within the frame of the model

developed by

Bonham and _co-workers, in which the diffusion of carriers

_{thermally injected}

is taken into account. The bulk

density

of these

injected

carriers increases when the thickness is

reduced,

and may become

higher

than that of bulk free-carriers

_already

_present in the film.

Experimental

results are in

_good

_agreement with the

predictions

of the model. The effective

mobility

of

_{03B1-sexithienyl (03B1-6T)}

could be calculated from the

_{quadratic regime}

of the I- V curves.

Measurements as a function of _temperature were also carried out. The

mobility

is found to be

thermally

stimulated, which is

interpreted

as due to a shallow _trap located 0.3 eV above valence band

_edge.

Introduction.

Organic

semiconductors have received a renewed attention since

_they

have been used as the active

component

in electronic

_devices,

_Schottky

diodes and more

recently

field-effect

transistors

_{(FET’s). Organic}

FET’s have been fabricated with

_{conjugated polymers,}

polyacetylene [1, 2]

and various

_{polythiophene}

derivatives

_[3,

_4],

_{metallophthalocyanines [5],}

and

_{a-sexithienyl (a-6T) [6],}

an

_{alpha-conjugated oligomer}

of

_thiophene

that is

_currently

studied in our

_laboratory

as a model molecule of its

_{homologue polymer.}

The

_improvement

of

these

_organic

devices

_requires

a better

understanding

of the

charge-carrier

_transport

mechanism in these materials.

Organic compounds [7] generally

present

very low electrical conductivities.

Raising

the

conductivity

to the

semiconducting

range can be obtained

_{by doping,}

i.e.

_introducing

small amounts of electron

_donating

or

_{accepting impurities. Unfortunately, impurities}

in

_organic

semiconductors act more often as

_traps

rather than

_dopants.

A

_probable

reason for this is the low electron

_affinity

of

_{organic compounds,}

as

_compared

to that of

_covalently

bound

inorganic crystals.

The

_question

arises of the

_origin

of the carriers in

non-intentionally

doped

materials. Most

_experimental

information comes from the

_{current-voltage (I P)}

characteristic

of films sandwiched between two metal

_electrodes,

which

_usually

_presents

at

_{high applied}

voltages

a

superlinear dependence

in

Vn, n >

2

_[8].

This is an evidence for a

space-charge-limited current

_{(SCLC) resulting}

from carriers

_{injected by}

the metallic electrodes. The linear variation at low biases is

_generally

attributed to an ohmic current due to bulk free

_carriers,

coming

from some

_doping

_{agent present}

in the material.

_However,

as has been shown in

theoretical papers

[9-12],

this linear current _may also

_arise,

in the case of thin

_films,

from

charges injected

from the contact electrodes.

Experimental

results on a-6T films of various thicknesses are

_presented

here to illustrate these

_previous

models. It is shown that the actual ohmic current is not observed but on

samples

thicker than several micrometers. The very low

density

of

_{doping impurities already}

found in

_{polythiophene [13]}

is confirmed here.

Experimental.

Alpha-conjugated sexithienyl

was

_synthetized

from

_{a-terthienyl (Aldrich) according}

to the method described earlier

_[14].

The

_{current-voltage}

measurements were carried out on sandwich structures. A 500 nm

_gold

layer

was first

_sputtered

on

_glass

slides. a-6T was then

_{evaporated by heating}

the

_powdered

material in a

_tungsten

crucible under a pressure of 5 x

10-3

Pa. The front contact was

realized

_{by evaporating gold}

dots

_{(area :}

0.00018

_cm2,

thickness : 25

_nm)

_through

a mask on

top

of the

_{organic layer.}

The current was measured in a metal box which

_provided

a

_capacitive

and inductive

_shielding.

_Tungsten

_microprobes

were used to contact the metal dots. The I- V

characteristics were obtained with a Hewlett-Packard 4140B

_{pAmeter/d.c. voltage}

source,

monitored with a HP 310 desk

_computer.

Low

_temperature

measurements were made under reduced _pressure

₍

10-1

1 Pa)

in a

Displex

DE 202

_{(Air-Product) close-cycle}

_cryostat.

The

_temperature

was

adjusted

within

± 0.1 K with a APD-E

_temperature

controller.

Results and discussion.

Fig. 1. - Log-log plot

of the

current-voltage

characteristics of

Au/a-sexithienyl/Au

structures for various thicknesses of the

_{organic layer.}

The

_straight

lines are

_{least-square adjustment}

to the

experimental points,

with a

_slope

of 1 at low _biases, and 2 at

_high

biases

_(SCLC).

are shown in

_figure

1. In all cases, the variation of the current

_density

is linear at low

_voltages

and

_quadratic

at

_{high voltages.}

The

_straight

lines drawn in

_figure

1

_correspond

to

_least-square

adjustments

to the

_{experimental points}

with

_slopes

of 1 and 2.

The linear

_regime

can be characterized

_by

a low

_{voltage conductivity :}

Here, j

is the current

_density

and L the thickness of the film. The variation of 6 as a function of L is shown in table 1 and

_figure

2. If the linear current was due to the bulk free

carriers,

one

should not

_expect

it to _vary when

_changing

the film thickness.

_Obviously,

this behavior is not followed for thicknesses lower than about 2 _ktm.

The standard

_{space-charge-limited}

current

_density

for shallow

_{trapping jsc}

_obeys

Here e is the dielectric _constant

_(e

_{= e, Eo, with} a relative dielectric constant _6, = 2 for

a-6T),

and IL the

mobility. 0

is the fraction of the total

_charges

free to move, which

_depends

on

the

_trap

_density

and

_temperature,

and will been

_explicited

further. In the

_trap-free

case

0 =

1,

but

usually

the

majority

of the

injected charges

is immobilized in

_traps

and

Table 1. - Parameters

_of

the current

_voltage

characteristics

_{of Au/a-6T/Au}

sandwich

structures with various thicknesses

of

the

_organic

_layer.

The low

voltage

conductivity 0,

is

deduced from

the

_{slope of}

the linear

_{region, j sc}

and the

_{effective mobility}

_8ft

_from

the

_quadratic

regime

of

the characteristics. A relative dielectric constant

_{of 2}

was taken.

_Vi

is the

_intercept

bias between the linear and

_quadratic

regimes.

Fig.

2. -

Variation of the low

voltage

conductivity o,

as a function of thickness, deduced from a

least-square

adjustment

of the I h curves in

_figure

1 at low

_voltages.

equating equations (1)

and

₍₂₎

where o- is the low

_{voltage conductivity.}

A

_{log-log plot}

of the variation of

_Vi

as a function of the thickness is shown in

_figure

3.

_Again,

the standard behavior

_{predicted by}

_equation

₍₃₎

is not observed at thicknesses lower than 2 um.

Because there is no

_analytical

solution to the

_{general single-carrier}

conduction

_problem,

the

standard SCLC

_theory

has been derived

_{by neglecting}

the carrier diffusion. More

_complete

analytical

or numerical resolutions

_{already reported [9-12]}

have shown that at low

_voltages,

a

linear current also arises from carriers

_injected

from the contacts. As stated in a

_previously

Fig.

3. - Variation of the

_intercept

bias between linear and

quadratic regime

of the I- V curves, as a

function of

sample

thickness.

_{Vi-sc correspond}

to the theoretical value for thin films.

given,

in the case of two

_{perfectly injecting}

contacts,

by

where q

is the

_charge

of the carriers.

_{Equation (4)}

shows that there exists a concentration of

charge

thermally injected by

the contacts without any

applied voltage,

the minimum value of

which is _nmin = 2

’TT 2 EV TI qL 2

(here,

the thermal

voltage

VT

=

kT/q,

which controls the

injected

space

charge,

appears

explicitely

in the

formula).

This

voltage independent charge

density gives

rise to a

_linearly

_varying

current at low

_{applied voltages. Importantly,}

this concentration increases when the thickness L

_decreases,

and _may become

_higher

than the

density

of the free carriers

_already

_present

in the bulk. The linear current will then

_correspond

to a

_{conductivity ui}

_resulting

from

_injected

carriers :

which can be

_compared

to the ohmic

_conductivity

_an

_{generated by}

ionised bulk

_acceptor

impurities :

where nn is the

density of non-injected

bulk free carriers. The variation of the

conductivity

of

a-6T as a function of

thickness,

given

in

figure

2,

is now well described

by equations (5)

and

(6) :

it decreases as

L - 2

_{(slope -}

2 in a

_{log-log plot)}

for thicknesses lower than ca. 2 _um, and is thickness

_{independent beyond}

this value. The actual ohmic

_{conductivity corresponds}

to the thickness

_independent

_value,

_namely

1.3 x

10-7

S

cm-l.

For shallow

_trapping

the

_{parameter 0}

is

_{given by [8] :}

for a dominant

_trapping

level at _energy

_Et

and

_{density Nt.}

_Nv

is the

_density

of state on

_top

of

the valence band at

_{Ev, g}

the

_degeneracy

factor

_(generally

taken as

_2).

Carriers

_originating

and the ohmic

_conductivity

can be written as :

The value of the

_product

01£

deduced in table 1 from the

_quadratic

SCLC

_{regime gives}

a

density of acceptors

Na

= 3.2 x

1013

cm-

3,

which is

_extremely

low. One tentative

_explanation

would be that the

_density

of

doping

centers is much lower than the total concentration of

impurities,

most of which behave as

_trapping

centers

_[13].

A most

_interesting

outcome _{of the space}

_charge

model

_including

diffusion is the

_prediction

that the

_{intercept voltage Vi-sc}

between the

_{space-charge-limited}

linear

_{(Eq. (5))}

and

quadratic (Eq. (2)) regimes, given by [12] :

is

_independent

of the

_transport

_{properties (i.e. mobility 11),}

the thickness of the

_sample,

the nature of the material

_(i.e.

its dielectric

_constant),

and its

_trapping

parameters

(i.e.

0 (Nt, Et )).

It is

_{only proportional}

to the

_temperature.

This comes from that in both

_regimes,

the

_{charge density}

involved is the

_injected

space

charge.

For the linear

dependence,

the

thermally injected

effective free

density

is

_(in

the case of shallow

_{trapping) :}

In the standard

_{space-charge regime,}

the

_{field injected}

effective free

_density

is :

By

equating

the two

_charge

_densities,

_{equation (10)}

is obtained. At room

_temperature

(300 K) Vi-sc

= 0.91 V. These _two

important

_tests,

namely

the thickness

_independence

of the

intercept voltage,

and its absolute value close to 1

_V,

are both verified in

_figure

3 for thin films

(L

less than 2

_um).

_Conversely,

when the

_low-voltage

linear

_regime

is due to

_non-injected

free carriers

_{of density}

_{n n,} the

_{intercept voltage}

is

_{given by equating}

this

_density

with the field

injected density

nSc

(Eq. (12))

to

give :

which is

_dependent

on the

_thickness,

the nature of the

_material,

and the amount of

_dopant.

Again,

the variation of the

_{intercept voltage}

of a -6T films

_{(Fig. 3)}

is in

_good

_agreement

with

this model.

More accurate numerical

_computations

made

_by

Bonham and Jarvis

[11]

have

shown

_that,

in

_fact,

neither the linear nor the

_quadratic

laws are

_good

_{approximations}

around the

_intercept

bias. Their calculated curve

_greatly

resembles the

_experimental

I- V

_plots

of

_figure

1. For a

trap-free

material

(or

a material with

_only

shallow

_traps)

the standard SCLC square law is

only

verified at

_{voltages higher}

_{than about 5 V. A consequence of this} wide intermediate

regime

is a _{poor accuracy in the} determination of the

_intercept

bias. This could

_explain

the

scattering

of the values obtained on thin

_films,

as can be noticed in

_figure

3.

At

_{higher voltages,}

the current

_{predicted by}

the

_{complete theory}

_{merges with the} standard

quadratic

SCLC. It can be seen in

_figure

4 that the variation of the

_{space-charge-limited}

current on our

_samples

follows a

L - 3

law all over the whole thickness _range.

_Similarly,

the

effective

_mobility

deduced from

_{equation (2)}

is

_{roughly independent}

of the

thickness,

as shown in table I. A decrease of the

_mobility

as the thickness is lowered has

_already

been

Fig.

4. -

Log-log plot

of the

_{space-charge-limited}

current vs.

_sample

thickness. A

_slope

of - 3

corresponds

to the standard SCLC

theory.

transistors

_[4,

_6].

Such a decrease could account for the deviation from the

_straight

line in

figure

4 at low values of L.

VARIATION WITH TEMPERATURE. - The variation of the 1- V characteristics as a function of

temperature

is

_given

in

_figure

5 and table II. The thickness is 1.8 um

(sample # 1).

It must be noted that the measurements at low

temperatures

were carried out under reduced pressure. We have

previously reported

that,

in this case, an

_undoping

of a-6T occurs

_[6],

which

_explains

the

_lowering

of the low

_{voltage conductivity.}

_However,

a mere

_undoping

cannot account for the concomitant

_lowering

of the

_SCLC,

which does not

_depend

on the

dopant

induced bulk carrier

_density.

The

_{global lowering}

of the current could be due to an

increase of the

_trap

_density.

One

_{possible explanation}

for this behavior _{is that oxygen} acts as a

trap-killer.

Its _presence in films

_exposed

to ambient

_atmosphere

would then result in a

decrease of the

_{trapping efficiency. Conversely,}

the decrease of the oxygen content when the

films are

_put

in vacuum would result in an increase of the

_density

of

_traps.

Due to this increased

_trapping,

the linear

_regime

of the I V curve is now

_space-charge

limited

_{(Eq. (7)),}

as

indicated

_by

the value of the

_{intercept bias,}

which is close to the theoretical value

_(0.91

V at 300

K).

As was stated

above,

_Vi-sc

is

independent

of the thickness and the nature of the

material,

but it is

_{linearly dependent}

on the

temperature.

A

_{plot of Vi}

vs.

_temperature

is shown in

_figure

6. The

_straight

line

_corresponds

to the theoretical value

_{(Eq. (10)).}

A fair

agreement

is found for

_temperatures

_higher

than 240

K ;

the

_slight

difference can be ascribed to _{poor accuracy in}

_{determining Vi,}

as noted above. At lower

_{temperatures,}

a

_strong

departure

from the calculated curve is observed.

_Up

to now we have assumed that the SCLC

was characterized

by

a

_quadratic

variation with the

_{applied voltage.}

Such a variation is valid

for a

_trap-free

_material,

and can be extended to materials with shallow

_trap

levels. When

_deep

traps

are _present, their

_{gradual filling}

as the

_voltage

increases results in a variation of the

Fig.

5. -

Log-log plot

of the I- V characteristic of

sample #

1

_(1.8

_um) under reduced pressure

(

10-1 Pa)

at different _{temperatures.} The

_{experimental points}

are

_adjusted

to

_straight

lines with a

slope

of 1 at low

_voltages,

and 2 at

_higher

biases

(full lines).

The dashed lines

correspond

to

adjustements

with

_slopes

_greater than 2.

Table II.

_{- Variation of}

the _parameters deduced

_from

current

_voltage

characteristics as a

function of

the _temperature.

_{Sample #}

_1,

_Au/a-6T/Au,

thickness : 1.8 J.Lm. See table

1 for

the

Fig.

6. -

Variation of the

intercept

bias between linear and

quadratic regimes

for

_{sample #}

1 v.s.

temperature. The variation

_{predicted by}

our model is indicated

by

the full line.

Fig.

7. -

Arrhenius

_plot

of the effective

mobility,

calculated from SCLC on

_{sample #}

_1, and

the SCLC increases

_slightly

when the

_temperature

_decreases,

_indicating

that the shallow

traps

are

_filling

as the Fermi level

_approaches

the valence band

_{edge. Consequently,}

an

_intercept

bias calculated from

straight

lines with a

_slope

of 2 is no

_longer

valid when the

_temperature

decreases below 240 K.

The presence of

traps

can be shown

_by

an Arrhenius

plot

of the effective

_mobility

0»

where 0 is

_{given by equation (7) (Fig. 7).}

Also drawn in

_figure

7 is the variation of the

conductivity.

Since the bulk

_conductivity

cannot be deduced from the linear

_regime

of the I- V curves, it was measured on a film with two

_gold

contacts on the same

_side,

_{separated by}

90 um. With this

configuration,

the I- V curves were linear _up to ± 100 V. The Arrhenius

_plot

of 6 is

_parallel

to that of the effective

_mobility,

and

_gives

an almost

_equal

activation _energy,

roughly

0.3 eV. This shows that the same dominant

_trapping

level at 0.3 eV controls the free carrier

_density

in both cases, in

agreement

with

_{equation (8).}

A similar feature has been

reported

on metal-free

_{phthalocyanine single crystals [ 15],}

and was attributed to a donor level

located at the same distance from the conduction band

_edge

as the shallow

_trap

level

_(in

this

particular

case, metal-free

_{phthalocyanine}

was found to behave as

_{a n-type}

semiconductor).

In

_fact,

in

_{equation (9)}

the factor 0 can be

_{indifferently assigned}

either to

_{Na, giving}

in this

case a free carrier

_{density nf}

=

BNa moving

with a

_{microscopic mobility}

_J-L, or to the

_mobility,

in which case one assumes that all the

_acceptors

of

density

Na

are ionized and that the carriers

move with an effective

_mobility

J-L eff =

0 u.

The latter

approach

is the most often used in

papers

dealing

with the

SCLC,

simply

because the field

dependent

density

of

injected

carriers does not _appear

_explicitly

in

_equation

_{(2). However,}

it should be

_kept

in mind

_that,

_basically,

the

_concept

of effective

_mobility

mirrors the fact that an electric current is the result of two distinct

_{phenomena -}

carrier

_generation

and

recombination,

including trapping,

on the one

hand,

and

_charge

_transport

on the other hand - which cannot be

_separated

from I-V measurements alone. The determination of the

_{microscopic mobility,}

and its

_temperature

dependence, requires

other kinds of

_experiments,

e.g. Hall

effect,

time of

flight,

etc. Such an

independent

measurements would also be necessary for

calculating

the

density

of

traps.

Conclusion.

Although

its limitations have been noticed for more than a

_decade,

the standard SCLC model

is still

_commonly

used for

_interpreting

the I-V curves of

weakly conducting

materials. We

have

_presented

here a set of

_experimental

data obtained on

_{Au/ a-6T/Au}

sandwhich

structures, which substantiate the

_validity

of the model

developed by

Bonham and co-workers

[11]

]

where the effects of diffusion was calculated. The variation of the low

_voltage

conductivity

as a function of

_sample

thickness establishes the existence of two

_regimes.

For

thicknesses

_larger

than a few

micrometers,

the classical behavior is

followed,

and the

conductivity

is thickness

_independent.

When the thickness

_decreases,

becomes

_proportional

to _{the reversed square}

_thickness,

which is consistent with thermal _space

_{charge injection.}

The actual

_conductivity

could be

deduced,

and a

_density

of

_acceptors

of 3.2 x

1013 cm-3

at 300 K

was calculated.

Although

fondamental in nature,

voltage independent

thermal

_injection

is

_scarcely

taken into account in

_{interpreting experimental}

I h characteristics.

However,

analytical [12]

and numerical

_[11]

]

calculations,

together

with our

_experimental

results,

clearly

show that the contribution of thermal

_injection

may be dominant at low

_{applied voltages}

in thin films.

The variation of the I V curve as a function of

_temperature

shows that the effective

_mobility

is

_thermally

activated. This can be attributed to a shallow

_trap

level,

the distance of which

from the valence band

_{edge corresponds}

to _{the activation energy : 0.28 eV.}

[6] (a)

HOROWITZ G., FICHOU D., PENG X., XU Z. and GARNIER F., Solid-State Commun. 72

₍₁₉₈₉₎

381 ;

(b)

HOROWITZ G., PENG _X., FICHOU D. and GARNIER F., J.

_{Appl. Phys.}

67

₍₁₉₉₀₎

528.

[7]

For a detailed review of the

_physical

_properties

of

_{organic compounds}

see : POPE M. and

SWENBERG C. E., Electronic Process in

_{Organic Crystals (Oxford University}

Press,

Oxford)

1982.

[8]

LAMPERT M. A. and MARK P., Current

_Injection

in Solids

_(Academic

Press, New

_York),

1970.

[9]

DE LEVIE R., SEIDAH N. G. and MOREIRA H., J. Membr. Biol. 10

₍₁₉₇₂₎

171.

[10]

ORMANCEY G. and GODEFROY G., J.

_Phys.

France 35

₍₁₉₇₄₎

135.

[11]

BONHAM J. S. and JARVIS D. H., Aust. J. Chem. 30

₍₁₉₇₇₎

705.

[12]

DELANNOY _P., Mater. Sci. 7

₍₁₉₈₁₎

13.

[13]

NISHIKITANI Y., FICHOU D., HOROWITZ G. and GARNIER F.,

Synth.

Met. 31

₍₁₉₈₉₎

267.