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Origin of the enhanced space-charge-limited current in poly(p-phenylene vinylene)

C. Tanase,1 P. W. M. Blom,1 and D. M. de Leeuw21Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

2Philips Research Laboratories, 5656 AA Eindhoven, The Netherlands

(Received 25 June 2004; published 5 November 2004)

It is demonstrated that the enhancement of the space-charge-limited (SCL) hole current of poly(p-phenylenevinylene) (PPV) derivatives at high bias at room temperature is due to the carrier density dependence of the

hole mobility. Contrary to numerous reports the dependence of the mobility on the electric field is only

observed at low temperatures. Analysis of the hole transport without taking into account the charge carrier

density dependence of the mobility leads to an incorrect charge carrier and electric field distributions in organic

light-emitting diodes.

DOI: 10.1103/PhysRevB.70.193202 PACS number(s): 73.61.Ph, 72.80.Le

Since the discovery of electroluminescence in poly(p-phenylene vinylene) (PPV), light-emitting diodes (LEDs)made from -conjugated polymers have been studiedextensively.1 It has been recognized that the charge transport

properties are of great importance for the operation and theefficiency of polymer based LEDs. The current throughpolymer LEDs based on poly[2-methoxy-5-(3, 7-dimethyloctyloxy)-p-phenylene vinylene] OC1C10-PPV isspace-charge limited (SCL) and governed by a constant holemobility h of 510

11 m2 /V s at low bias voltages at

room temperature.2 At high bias voltages the field and tem-perature dependence of the SCL current have been describedwith an empirical law for the hole mobility:3

hE,T = h0,TexpTE , 1

with h0 , T the hole mobility at zero field and T the

field activation factor, which reflects the lowering of the hop-ping barriers in the direction of the applied electric field.Introduced to explain the charge transport in OC1C10-PPV,

3

the concept of a SCL current and a field- and temperature-dependent mobility has been extensively applied to transportmeasurements on organic semiconductors. For instance, ithas been used to analyze the charge carrier mobility of vari-ous PPV derivatives,4,5 the current and transient transport invarious PPV and polyfluorene derivatives,6,7 as well as theelectron transport in diodes based on small molecules oftris(8-hydroxyquinolato)aluminum.8 Furthermore, the field-dependent mobility [Eq. (1)] has also been incorporated innumerical simulations to model the current-voltage charac-teristics and the transients of PPV-based LEDs.911

In a recent study the dependence of the hole mobility hon the carrier density in OC1C10-PPV has been investigatedby a combined study on polymeric diodes and field-effecttransistors.12 It has been demonstrated that the hole mobilityof OC1C10-PPV is constant for charge carrier densities typi-cally1022 m3 and increases with a power law with densityfor carrier densities 1022 m3. In the analysis of chargetransport properties of polymeric SCL devices such depen-dence has not yet been taken into account. In a space-charge-limited device an increase of the applied bias gives rise to asimultaneous increase of the electric field and charge carrier

density. Consequently, the contributions of the charge carrierdensity and the electric field to the mobility cannot be disen-tangled from a SCL current. For the understanding of thecharge transport in polymeric devices it is of fundamental

importance to know whether the current is governed by thefield and/or the carrier density dependence of the mobility. Inthis work we demonstrate that the enhancement of the cur-rent density in SCL diodes is dominated by the carrier den-sity dependence of the hole mobility at room temperatureand, in contrast to what has been assumed so far, 311 not byits field dependence. Analysis of the transport data withouttaking the density dependence ofh into account leads to anincorrect charge carrier and field distribution in organic SCLdiodes.

The devices used in this study consist of OC1C10-PPV asthe active semiconductor in a hole-only diode and in a field-effect transistor (FET). The field-effect structure has been

described previously.12

In the hole-only diode OC1C10-PPVis sandwiched between an indium tin oxide (ITO) anode anda gold (Au) cathode. In Fig. 1 the current density-voltageJ V measurements for hole-only diodes are shown forvarious temperatures. At room temperature the SCL currentincreases quadratically with the applied field up to an appliedbias of 1 V. In this bias range the hole mobility is indepen-

FIG. 1. Temperature-dependent current density vs voltage char-

acteristics of OC1C10-PPV hole-only diode. The solid lines repre-

sent the prediction from the SCL model including the density-

dependent mobility [Eq. (2)].

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dent on both electric field and charge carrier density andamounts to 51011 m2/V s. However, at high bias the cur-rent density increases more than quadratically with the ap-plied bias. This enhancement is the more pronounced thelower the temperature.

Recently, the dependence of the mobility on the chargecarrier density has been obtained from the transfer character-istics of OC1C10-PPV based field-effect transistors (FETs).

12

The experimental field-effect mobility FET is directly calcu-lated by differentiating the channel current Id with respect tothe gate voltage Vg. The field-effect mobility increases super-linearly with the charge carrier density. The dependence hasbeen quantitatively interpreted using a hopping percolationmodel in an exponential density of states (DOS),13 which is agood approximation of the tail states of the Gaussian DOS. 12

Unification of the diode and field-effect measurements showsthat the dependence of the hole mobility on charge carrierdensity is given by

hp,T = h0,T +0

e

T0

T4 sin T

T0

23Bc

T0/T

pT0/T1 ,

2

where h0 , T is the hole mobility at low densities obtainedfrom the quadratic SCL current, 0 is a prefactor for theconductivity, 1 is the effective overlap parameter betweenlocalized states, T0 is a measure of the width of the exponen-tial density of states, and Bc is the critical number for theonset of percolation. The parameters 0,

1, and T0 areobtained from the temperature dependence of the transfercharacteristics of the FET. These transfer characteristics areconsistently described by a single set of values, namely, T0=540 K, 0 =3.110

7 S/m, 1 =0.14 nm, and Bc =2.8.12 It

should be noted that this unification is only possible forhighly disordered polymers as OC1C10-PPV, in which thecharge transport is isotropic.12 For more ordered PPV deriva-tives with higher field-effect mobilities the transport is aniso-tropic and unification is not possible.14 In Fig. 2(a) the ex-perimental mobility (symbols) and the dependence of themobility on charge carrier density calculated using Eq. (2)(solid lines) are presented for various temperatures and car-rier densities in the range of 31020 to 31025 m3 forOC1C10-PPV. A good agreement between experimental andcalculated mobilities is obtained. This experimentally deter-mined mobility dependence on carrier density now enablesus to disentangle the contributions of the electric field andthe carrier density to the enhancement of the SCL current athigh bias.

As a first step the SCL current is calculated using only thedensity-dependent mobility as given by Eq. (2). In these cal-culations any field dependence of the mobility is disregarded.It should be noted that the density dependence of the mobil-ity as given by Eq. (2) does not contain a fit parameter; themobility at low density directly follows from the quadraticpart of the J V characteristics, whereas the power-law de-pendence at high carrier densities is independently measuredin the FET. The SCL current is now calculated by combiningEq. (2) with

J= pxehpxEx, 3

0r

e

dEx

dx = px, 4

with px the density of holes at position x. By numericallysolving Eqs. (2)(4) the J V characteristics are obtained, asshown in Fig. 1 by the solid lines. Figure 1 shows that atT=275 K and T=293 K the calculated SCL current densityfor OC1C10-PPV at high fields using Eqs. (2)(4) is in goodagreement with the experimental current densities. Surpris-ingly, a possible field dependence ofh, which has been usedas an explanation for the SCL current enhancement at highbias so far,311 is not required to describe the experimentalJ V characteristics. Therefore, the field enhancement of themobility at room temperature is only a minor effect. As anupper limit we estimated that T at room temperature is atleast more than an order of magnitude lower than previouslyreported values.3 Furthermore, from Fig. 1 it appears that attemperatures lower than T=275 K the carrier density depen-dence of the mobility alone does not explain the observedincrease of the SCLC. Apparently, at low temperatures thefield dependence of the mobility becomes important. Atpresent, there is no theoretical model available describing thefield activation at both low and high carrier densities. Con-sequently, at low temperatures where both field and densitydependence play a role the J V characteristics cannot yet be

FIG. 2. (a), (b) Temperature-dependent mobility hp , T vshole density for OC1C10-PPV. The solid lines are the calculated

hp , T using Eq. (2) with the parameters mentioned in the text.

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