Langevin Charge Injection and Recombination at the Metal–Organic

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6 January 1999

.Chemical Physics Letters 299 1999 115119

Charge injection and recombination at the metalorganicinterface

J. Campbell Scott ), George G. Malliaras( )IBM Research Diision, Almaden Research Center and Center on Polymer Interfaces and Macromolecular Assemblies CPIMA , 650 Harry

Road, San Jose, CA 95120, USA

Received 11 September 1998; in final form 28 October 1998

Abstract

We consider the mechanism of charge injection from metals into amorphous organic semiconductors. By first treating

charge recombination at the interface as a hopping process in the image potential, we obtain an expression for the surface

recombination rate. The principle of detailed balance is then used to determine the injection current. This simple approach

yields the effective Richardson constant for injection from metal to organic, and provides a means to derive the electric field

dependence of thermionic injection. The result for the net current, injected minus recombination, is in agreement with a

more exact treatment of the driftdiffusion equation. q1999 Elsevier Science B.V. All rights reserved.

The process of charge transfer at the contact .between a metal and an organic or polymeric semi-

conductor plays an important role in many areas of

technology. For example, in organic light emittingw xdiodes 1 , which are being developed for use in flat

panel displays, metal electrodes inject electrons and

holes into opposite sides of the emissive organic . w xlayer s . In the organic photoconductors 2 used in

laser printers and photocopiers, photogenerated

charge must be extracted from the bottom of thew xpolymer film. Organic semiconductors 3 are being

considered for use in the logic circuitry of inexpen-

sive smart cards. Yet some of the fundamental

aspects of the charge injection process are not under-

stood in any real detail. It is the purpose of this

Letter to propose a simple approach to the basic

)

Corresponding author. E-mail: [email protected]

science of metalorganic injection that can be re-lated to bulk properties of the materials involved and

therefore makes predictions that are amenable to

experimental test.

The history of the study of charge injection from

a metal to an insulator can be traced back to the w x.RichardsonDushman equation see, e.g., Ref. 4

which was first applied to thermionic emission from

a metal cathode into vacuum and later modified byw xBethe, Schottky and others 5 for charge injection at

.the interface between a crystalline, inorganic semi-

conductor and a metal. The calculation is predicated

on the assumption that electrons in the semiconduc-

tor are freely propagating in the conduction band of

the semiconductor with a thermal distribution of

kinetic energies. There are two contributions to the

current, flowing from the semiconductor to the metal

and vice versa. At zero voltage they are equal andw xopposite; the net current is zero. Later work 6

extended the early formalism to include diffusive

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. .P I I : S 0 0 0 9 - 2 6 1 4 9 8 0 1 2 7 7 - 9


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( )J.C. Scott, G.G. Malliarasr Chemical Physics Letters 299 1999 115119116

contributions to the current, but still within the

framework of electron velocities and mean-free-

paths.

The difficulty in extending the calculational pro-

cedures from crystalline to highly amorphous semi-

conductors arises because charge transport in the

latter is no longer free propagation in extended states,

but rather hopping between localized states. Thisw xproblem was treated by Emtage and ODwyer 7

who solved the driftdiffusion equation in a poten-

tial which included the attraction of each charge to

its image in the electrode. Their result, which gives a

current proportional to carrier mobility, involves the

determination of an integral which can only be ap-

proximated analytically at high and low electric field.

In recent simulations of injection from metal tow xpolymer, Abkowitz et al. 8 and Gartstein and Con-

w xwell 9 used a transfer rate that depends on the

distance of the target site from the interface. Thisrate was taken to be similar to that for site-to-site

hopping, as previously used in the bulk transportw xsimulations of Bassler et al. 10 . It can therefore be

obtained, in principle, by comparison with experi-

mental mobility data or by quantum-mechanical cal-

culations of molecule-to-molecule charge transferw xmatrix elements. Davids et al. 11 have modeled the

injection from metal into conjugated polymers using

a phenomenological surface recombination velocity,

which by detailed balance is proportional to the

Richardson constant, but they take no account ofhow the electronic structure of the polymer might

modify the injection rate.

The purpose of this Letter is to derive expressions .for the injection metal to organic and recombina-

.tion organic to metal currents which involve exper-

imentally determined properties of the organic mate-

rial. Our approach is based on the premise that

surface recombination is a field-enhanced diffusion

process, entirely analogous to Langevin bimolecularw xrecombination in amorphous semiconductors 12,13 .

We then use detailed balance to find the injection

current, and obtain the effective Richardson constant

for the metalorganic interface. We emphasize that

this approach is quite general and independent of the

microscopic details of the injection process.

In the Langevin theory, applicable in the case

where random, diffusive motion of charges is domi-

nant and drift can be viewed as a small bias in the

time-averaged displacement for a review, see Ref.w x.14 , the average electronhole pair that approach

each other within a distance such that their Coulom-

bic binding energy exceeds kT will ultimately re-

combine. The demarcation distance should of course

be understood in a statistical sense. It is known as

the Coulomb radius

r s e2r4p kT. 1 .C 0

The Langevin mechanism is justified in the present

case by considering the attractive image potential .acting on a charge carrier electron in the organic

material as it approaches the metal surface see inset. w xof Fig. 1 5

f x sf y eEx y e2r16p x, 2 . .B 0

where f is the Schottky barrier height the differ-Bence between the workfunction of the metal and the

.electron affinity of the semiconductor , E is theapplied electric field assumed to be constant over

.the distance range of interest and is the permit-0tivity of the organic material. First consider the

Fig. 1. Net injected current density as a function of electric field at

the interface. Solid line shows the results of the analysis presented ..here Eq. 12 . The current is normalized by the factor J s0

. . .N mkTr r exp yf r kT ; the field according to Eq. 8 . The0 C Bdashed and dotted lines show the asymptotic results of Emtage

w xand ODwyer 7 for low and high field, respectively. Inset electron potential energy vs. position near the interface of a metal . .left and semiconductor right . f is the Schottky barrier height.B

.Dashed line a shows the image potential in the absence of an

applied electric field. The energy is lower by an amount kT at a .distance x from the interface. Curve b is the potential due to aC

uniform applied field. When both image and applied field are

included one obtains the potential given by the full solid line

which illustrates the reduction in barrier height.


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( )J.C. Scott, G.G. Malliarasr Chemical Physics Letters 299 1999 115119 117

zero-field case; the electronimage binding energy is

equal to kTat a distance x s r r4. At room tem-C Cperature and for typical values of the dielectric con-

.stant s 3.5 , x f 4.0 nm, which is ;10 timesClarger than an intermolecular distance. Therefore, the

assumption of diffusive transport holds, namely thatthe mean-free-path of the carrier in this case, the

.mean hopping distance is shorter than the Coulomb

capture distance. We therefore proceed in the same

spirit; the average charge that approaches the inter-

face within x inevitably recombines. Thus the re-Ccombination current is that at the plane x sx ,C

2 2J s n emE x s 16p kT n mre , 3 . . .rec 0 C 0 0

where n is the charge density at the interface0 .strictly at x and m is the the electron mobility.CThe recombination process at a semiconductor inter-

face is frequently parameterized in terms of a surfacerecombination velocity, SsJ rn e. Thus, the zerorec 0field value is

2 3S 0 s 16p kT mre . 4 . . .0

In order to determine the injection current from.metal to polymer we invoke detailed balance. With-

out an applied electric field, the thermionically in-

jected current, is equal to, but opposite in direction

to the surface recombination current. Write J sinj .Cexp yf rkT where Cis a constant to be deter-B

mined. The density n is given by a Boltzmann0factor, then

J yJ s C exp yf rkT y n rN s 0 , 5 . .inj rec B 0 0

where N is the density of chargeable sites in the0polymer. Hence

Cs 16p k2N mT2re 2 sA)T2 . 6 .0 0

A) is the effective Richardson constant, in analogy

with the metalvacuum and metalsemiconductor

cases. . ..Note that the expressions Eqs. 4 and 6 for S

and A) contain only properties of the organic mate-

rial, namely the dielectric constant, the site density

and the mobility. Unlike the case of crystalline semi-

conductors, the effective mass and Plancks constant .related to the density of states do not enter here.

Nevertheless, the injection current has the same tem-

2perature dependence T in the pre-exponential fac-.tor as the ballistic electron case, but contains the

mobility and density of states in the form reminis-w xcent of Schottky diffusion 5 . The proportionality to

mobility justifies the assumption by Gartstein andw xConwell 8 discussed above concerning the metal-

to-organic hopping rate.

To estimate the surface recombination velocity in

materials of interest, take a mobility, at room tem-

perature, of 10y5 cm2 Vy1 sy1 ; then one obtains . y1S0 s 0.6 cm s . As expected this is considerably

smaller than that for crystalline semiconductors of4 y1 w x.order G 10 cm s 5 or for crystalline an-

y1 w xthracene at 100 cm s 15 . However, it is of the

same order as the few available values for glassyy1 w xorganic dyes at ;0.1 cm s 16 . We know of no

cases where the recombination velocity and mobility

have been measured in the same material, so this

prediction of the theory cannot yet be tested. Thecorresponding Richardson constant, assuming a value

of the site density of 10 22 cmy3, is A)s 10y2 A

cmy2 Ky2 compared to the free-electron value of

120 A cmy2 Ky2 .

Admittedly there are several approximations made

in the derivation of these equations. Most notable isw xthe neglect of the disorder-induced broadening 2,9

in the energy density of states in the organic, typi-

cally 0.1 eV. Thus the simple relations probably will

only hold for barrier heights somewhat larger than

this. Nevertheless the equations should describe manycases of practical interest. Space charge effects have

also been neglected. This is not a severe limitation

however, since the carrier density at which interac-

tions between electrons becomes comparable to the

electronimage attraction is xy3 f 1.6=1019 cmy3 ,Chigh compared to most cases of experimental inter-

est. In real material combinations there is the possi-

bility of an additional interfacial barrier layer, for

example a native oxide. If such a layer is thinnerthan the Coulomb capture distance taking into ac-

.count its dielectric constant then it should not signif-

icantly affect the recombination process. Charges

will still be attracted to and bound by their own

images, and although there may be slower final

recombination across the barrier, the dipolar field

produced by the recombining pair will have a rela-

tively small effect on the motion of other charges.

Surface states are known to modify the recombina-


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( )J.C. Scott, G.G. Malliarasr Chemical Physics Letters 299 1999 115119118

tion process at inorganic semiconductor interfaces. It

is generally believed, and has recently been shownw x17 in some prototypical organic systems, that an

insignificant number of interface states are formed

when an organic material is deposited on a metal

surface. The converse, metal on organic, may not be

so ideal. We have considered only electrons in the

above discussion; clearly the same analysis will ap-

ply to hole injection at the anode, with appropriate

identification of the density of states and mobility.

Lastly we consider the electric field dependence

of the injection and recombination currents, which is,

after all, the experimentally relevant behavior. The

primary effect of the field is to lower the energy

barrier by an amount proportional to the square rootof the applied field the Schottky effect see Fig. 1,

.inset . The resulting exponential increase in the in-

jection current dominates the voltage dependence.

The surface recombination velocity is also field de-pendent. Now taking the Coulomb capture distance

as that at which the energy is kTbelow the field-de-

pendent maximum, one finds

S E s S 0 1rc2 yf r4 , 7 . . . .

where the reduced electric field is

fs eEr rkT 8 .C

and

1r2y1 y1r2 y1 1r2

c f sf qf yf 1 q 2f . 9 . . .The field dependence of S is considerably weaker

than that due to barrier height reduction. Since the

effective Richardson constant is not expected to de-

pend explicitly on field, the net current is

JsA)T2 exp yf rkT exp f1r2 y n e S E . . .B 010 .

In many organic materials the carrier mobility m isw xelectric field dependent 2,9 , in which case it may

be more accurate to use, in the expressions for A)

. .and S E , the mobility at field E x . By equatingC .the net surface current, Eq. 10 , to the bulk current

leaving the interface, Js n emE, we obtain an ex-0pression for the field dependence of the surface

charge density

n s 4c2N exp yf rkT exp f1r2 11 . .0 0 B

which, rather surprisingly, is independent of the

mobility. The net current is then

Js 4c2N emEexp yf rkT exp f1r2 . 12 . .0 B

This result, plotted in Fig. 1, is in exact agreementw xwith the asymptotic result of EO 7 at low electric

.fields f

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Langevin Charge Injection and Recombination at the Metal–Organic