Organic Light-Emitting Diodes: Principles, Characteristics & Processes

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OrganicLight-Emitting

DiodesPrinciples, Characteristics, and Processes

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DK1217_title 10/13/04 11:39 AM Page 1

OrganicLight-Emitting

DiodesPrinciples, Characteristics, and Processes

JanKalinowski

Technical University of GdanskGdansk, Poland

MARCEL DEKKER NEW YORK

M A R C E L

D E K K E R


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Preface

The remote discovery by Bernanose and coworkers [1] thatorganic films subjected to an external electric field can emitlight, resounded nowadays in high-brightness, thin filmorganic light-emitting diodes (LEDs) converting electricalcurrent to light, without recourse of any intermediate energyforms, such as heat. The effect, called electroluminescence(EL), underlies various classes of organic light-emittingdevices, some of which being now adequate for many applica-tions (for a comprehensive review on organic EL and possibleEL devices, the reader is referred to Ref. 2; a recent overviewof materials underlying organic LEDs can be found in Ref. 3).In order to tailor the function and performance of suchdevices, one has to understand three fundamental processes:(i) electrical energy supply, (ii) excitation mode of emittingstates, and (iii) light generation mechanism itself. These pro-cesses are interrelated; for instance, the energy supply modecan determine possible mechanisms of excitation of the radia-tive system. The excitation mode, in turn, determines thetypes of excited states and their relaxation pathways. Variousexcitation modes are illustrated in Fig. 1 (See Sec. 1.1).

iii

5647-8 Kalinowski Preface R2 090804


Supplying electrical energy with insulating or non-injectingelectrodes using voltage waves or pulses imposes field-induced creation of excited states (high-field EL as shown inFig. 1a) or the generation of charge carriers inside the ELmaterial, leading to charge carrier-mediated impact EL(Fig. 1b). Direct current (dc)—and alternating current (ac)—type EL can be observed as a result of electron–hole recombi-nation processes, the carriers being injected either at a semi-conductor p–n junction (Fig. 1c) or from metallic contacts to aluminescent material (Fig. 1d).

Although high-field and impact EL mechanism havebeen utilized in pioneer works on organic EL to explain emis-sion properties of films and powders [1,4–7] as well as crystals[8–11] and fluorescent liquid solutions [12,13], only a scantattention has been given to them after more exact examina-tion of EL in organic single crystals [14] and recent successfulfabrication of EL devices comprised of multi-layers of evapo-rated low-molecular-weight organic materials [15,16] andpolymeric systems prepared via precursor polymerization[17,18] or casting from solution without subsequent proces-sing or heat treatment [19,20]. Their EL properties are nowcommonly ascribed to the formation of emissive states viathe recombination of charge carriers injected from the electro-des (Fig. 1d). In general, only a part of the injected carriersundergoes recombination in emitter bulk, the remainder isdischarged at the counter electrical contacts, forming theleakage currents. Obviously, the proportion between therecombination and leakage currents determines the light out-put from EL devices. Studying the kinetics of injected freecarriers, this proportion can be translated into the recombina-tion probability PR¼ (1þ trec=tt)

�1, where trec is the carrierrecombination time and tt is the time required for a carrierto traverse the inter electrode distance d. Two limiting casesof the recombination EL have been distinguished based on thevalue of the recombination-to-transit time ratio: (i) volume-controlled EL (VCEL) for trec < tt that is PR > 0.5, and (ii)injection-controlled EL (ICEL) for trec > tt that is PR < 0.5(Ref. 21, see also Sec. 5.4). The recombination probabilityPR¼ 0.5 stands for a demarcation value when the rate of

iv Preface


monomolecular decay (leakage current) and the rate ofbimolecular decay (recombination current) of the carriersare equal to each other. High recombination EL efficiencyrequires the trec-to-tt ratio to be kept at a minimum, thenPR!1. To exploit this principle for LED optimizing, oneneeds to understand the processes that control this ratio:(i) the injection of charge carriers, (ii) their transport, and(iii) recombination. Furthermore, the overall quantum ELefficiency as well as spectral features of the emitted lightdepend on the type and decay pathways of the excited states.

It is the purpose of this book to give an outline of theproblems underlying the function of organic LEDs utilizingbimolecular charge recombination as a generation process ofemitting states.

ACKNOWLEDGEMENTS

This book, reflecting the skills and interests of its author,is underlain by a remote but still inspiring experience ofscientific and personal contacts of the author with ProfessorMartin Pope (New York University), which played animportant role in the author’s understanding of electronicphenomena in organic solids.

The author acknowledges the invaluable contribution ofhis past and present coworkers of the Gdansk and BolognaLED groups. In the first instance, the author’s thanks aredue to Dr. Piergiulio Di Marco who invited him to work formore than five years with Molecular Electronics Group atCNR Center in Bologna, where the main body of the author’swork on thin film organic LEDs has been developed.

Fully as important as the scientific contribution of mycoworkers in completing the book have been the patienceand sacrifice of my wife Krystyna who made the work muchmore efficient. Her and the author’s son Sebastian assistancein technical preparing the manuscript are recognized withdeep appreciation.

Preface v


Contents

Preface . . . . iii

1. Generation of Excited States by ChargeRecombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1. Introduction . . . . 11.2. Initial and Volume-Controlled Recombination . . . . 31.3. Langevin and Thomson Recombination . . . . 51.4. Multiplicity of Excited States in theRecombination Process . . . . 8

2. Types and Decay Pathwaysof Excited States . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1. Introduction . . . . 132.2. Optical Spectroscopy . . . . 152.3. Monomolecular and Bimolecular ExcitedStates . . . . 222.4. Energy Transfer By Excited States . . . . 612.5. Excitonic Interactions . . . . 802.6. Electric Field-Assisted Dissociation ofExcited States . . . . 135

vii


3. Spatial Distribution of Excited States . . . . . . . 1473.1. Introduction . . . . 1473.2. Photoexcitation . . . . 1503.3. Recombination Radiation. RecombinationZone . . . . 156

4. Electrical Characteristics ofOrganic LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

4.1. Introduction . . . . 1714.2. Current–Voltage Characteristics . . . . 1714.3. Space-Charge- and Injection-ControlledCurrents . . . . 1774.4 Diffusion-Controlled Currents (DCC) . . . . 2274.5. Double Injection . . . . 2294.6. Charge Carrier Mobility . . . . 236

5. Optical Characteristics of Organic LEDs . . . . . 2735.1. Introduction . . . . 2735.2. Emission Spectra . . . . 2755.3. Light Output . . . . 3445.4. Quantum EL Efficiency . . . . 376

6. Summary and Final Remarks . . . . . . . . . . . . . . 423

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

viii Contents


1

Generation of Excited States byCharge Recombination

1.1. INTRODUCTION

The charge recombination process can be defined as a fusionof a positive (e.g. hole) and a negative (e.g. electron) chargecarrier into an electrically neutral entity though the positiveand negative charge centers on it do not necessarily coincide.The radiative decay of such an entity or following its evolutionsuccessive excited states produces light called recombinationradiation. This underlies directly recombination EL, the ELtype depicted in Fig. 1c,d to be compared with other types ofEL phenomena (Figs. 1a, b) in which the recombinationradiation still can participate as mentioned in Preface. Theinitial (or geminate) recombination and volume-controlledrecombination can be distinguished on the basis of chargecarrier origin.

1

5647-8 Kalinowski Ch01 R2 090704


Figure 1 The schematic representation of various electronic exci-tation mechanisms due to ac or dc external electric fields: (a) thetuneling electrons from the valence band (VB) to the conductionband (CB) and ionization of an acceptor state (-�-) (Zener effect) fol-lowed by electron–hole recombination, indicated by horizontal andvertical arrows, respectively; (b) excitation or ionization by electronimpact; (c) recombination of electrons (�) and (�) holes at a semicon-ductor p–n junction; and (d) bulk recombination of electrons andholes injected from electrodes. Adapted from Ref. 2

2 Organic Light Emitting Diodes



1.2. INITIAL AND VOLUME-CONTROLLEDRECOMBINATION

The initial or geminate recombination (IR or GR) isthe recombination process following the initial carrierseparation from an unstable locally excited state, forming anearest-neighbor charge-transfer (CT) state. It typicallyoccurs as a part of intrinsic photoconduction phenomena inorganic solids due to generation of charge from light-excitedmolecular states (see Fig. 2). The probability of the GRcan be expressed by the primary (electric field independent)quantum yield in carrier pairs for the absorbed photon, Z0,and the (e �� h) pair dissociation probability, O:

PIR ¼ PGR ¼ 1� Z0O ð1Þ

Since the probability of the initial recombination can beexpressed by the separation step rates, the natural way ofits determination is to measure the bulk-generated photocur-rent. However, one should keep in mind that the measuredphotocurrent contains carrier mobilities in addition to theeffective separation probability (Z0O). The carrier mobilities

Figure 2 Initial recombination (IR) of a geminate (e��h) pairformed by absorption of light (hnexc). Adapted from Ref. 21a.

Chapter 1. Generation of Excited States 3



and their possible field dependence must be, therefore,determined independently. Moreover, other mechanisms ofcharge generation such as injection or photoinjectionfrom the electrodes may lead to grave errors in evaluationof Z0O .

Another possibility to determine PGR , which is free ofthese drawbacks, is electric-field modulation (EFM) of photo-luminescence (PL). Electric-field effect on the effective chargeseparation efficiency ( Z0O ) shows up in the varying populationof CT states, and consequently, in the varying concentrationof the emitting states. It is expected that the field-inducedincrease in the charge separation efficiency would translateinto PL quenching. The ratio ( d) of the PL efficiency in thepresence ( jPL (F )) and in the absence (j PL(0)) of an externalelectric field (F ) would give directly PGR

d ¼ jPL ð FÞ=j PL ð0 Þ ¼ 1 � Z0 O ð2 Þ

A more detailed discussion of the GR and experimental exam-ples of its manifestation are presented in Sec. 2.6.

If the oppositely charged carriers are generated indepen-dently far away of each other (e.g. injected from electrodes)volume-controlled recombination (VR) takes place, the car-riers are statistically independent of each other, the recombi-nation process is kinetically bimolecular. It naturallyproceeds through a Coulombically correlated electron–holepair (e �� h) leading to various emitting states in the ultimaterecombination step (mutual carrier capture) (Fig. 3; for moredetails, see Figs. 11 and 27 in Sec. 2.3). As a result, the overallrecombination probability becomes a product of the probabil-ity of the pair formation, PR

(1)¼ (1þ tm=tt)�1, and the capture

probability, PR(2)¼ (1þ tc=td)

�1,

PR ¼ Pð1ÞR P

ð2ÞR ¼ ð1þ tm=ttÞ�1ð1þ tc=tdÞ�1; ð3Þ

where td is the dissociation time for the pair. There are twolimiting cases of the VR: (i) the Langevin-like, and (ii) theThomson-like recombination.




1.3. LANGEVIN AND THOMSONRECOMBINATION

The classic treatment of carrier recombination can be relatedto the notion of the recombination time. The recombinationtime represents a combination of the carrier motion time(tm), i.e. the time to get the carriers within capture radius(it is often assumed to be the Coulombic radiusrC¼ e2=4pe0ekT), and the elementary capture time (tc) forthe ultimate recombination event (actual annihilation ofcharge carriers), trec

�1¼ tm�1þ tc

�1 (cf. Fig. 3). Following thetraditional description of recombination processes in ionizedgases, a Langevin-like [22] and Thomson-like [23] recombina-tion can be defined if tc� tm and tc� tm, respectively. Insolid-states physics, these two cases have been distinguished

Figure 3 Recombination of oppositely charged, statistically inde-pendent carriers (e, h) can lead to the creation of an emitting excitedstate through a Coulombically correlated charge pair (e��h). Thecharge pair formation time (diffusion motion time) and its capturetime are indicated in the figure as tm and tc, respectively. Theexcited states decay radiatively (hn) with the rate constant kf andnon-radiatively with an overall rate constant kn. After Ref. 21a.




from each other by a comparison of the mean free pathfor optical phonon emission, l, with the averagedistance (4rC=3) across a sphere of critical radius rC [24,25].One has Thomson recombination if l� rC and Langevinrecombination if l� rC. Two subcases should be consideredwhen l¼ (Dt0)

1=2, and l¼ vtht0. In the former, the momentum(p) exchange cross-section is larger than the energy(E)-loss cross-section. In the latter, the reverse is true.Here, D is the diffusion coefficient of a carrier, t0 is the life-time of p and E charge carrier states, respectively, and vthis the thermal velocity of the carriers. Due to the low car-rier mobility (m) in organic solids, one would expect to dealwith the first subcase with m¼ 1 cm2=Vs (D¼ mkT=e) andmean free path for elastic scattering l¼ 10 A. This valueof l is clearly much lower than rCffi 150 A (e� 4), stronglysuggesting a Lengevin-like model to be appropriate todescribe the recombination process in organics. Itssignature is a field and temperature-independentratio [26]

geh=mm ¼ e=e0e ¼ const; ð4Þ

where geh is the bimolecular (second order) recombinationrate constant, mm the sum of the carrier mobilities, and eis the dielectric constant. The essence of Eq. (4), derivedfrom the Smoluchowski expression relating geh to the sumparticle diffusion coefficient, D, and their interaction radiusR via geh¼ 4pDR, if one identifies R with the Coulombiccapture radius RC and assumes the validity of Einstein’srelation, eD¼ mkT, is that in the long-time limit, chargerecombination is a process controlled by diffusion. For mole-cular solids with typically e¼ 4, geh=m¼ 4.5� 10�7 V cmwhich span ge–h between 4.5� 10�5 and 4.5� 10�17 cm3=s,the range corresponding to the limiting values of the car-riers mobility from about 102 cm2=Vs in the case of somearomatic crystals at low temperatures [27,28] down to about10�10 cm2=Vs in the case of polymeric films [29].

The kinetic description of bimolecular reactions incondensed media, based on the solution of Smoluchowski




equation, leads to the time(t)-dependent rate constant [30,31]

gðtÞ ¼ 4pDR½1þ R=ðpDtÞ1=2 ð5Þ

Equation (5), seemed to be consistent with experimentaldata on time evolution of many chemical reactions, in liquids,is not adequate to describe the reaction kinetics in disorderedsolids. In disordered solids, the carrier motion is only partiallydiffusion controlled, carrier hopping across a manifold of sta-tistically distributed in energy and space molecular sites mustbe defined and taken into account [32–34]. Assuming that thecarrier hopping sites are subject to an energy Gaussian distri-bution r(E)¼ (2ps2)�1=2 exp(�E2=2s2), and introducing theaverage length of hops d, yields the average hoppingfrequency [35,36]

nðtÞ ¼ n0 expð�2d=d0ÞZCðtÞ

0

exp½ðE=kTÞ � ðE2=2s2ÞdE

8><>:

9>=>;

�1

ð6Þ

where n0 is the effective preexponential factor, d0 the chargelocalization radius [37] at a hopping site, and C(t)¼kT ln[s2n0t=(kT)

2] being only a weakly varying function oftime (t).

By substituting Eq. (6) into expression for the diffusioncoefficient

D ¼ d2nðtÞ ð7Þ

one obtains

DðtÞ ¼ D0ðn0tÞ�1þb ð8Þ

with the dispersion parameter b bearing a weak functionaltime dependence of the expression for C(t) and possible foran approximation by the time-independent empirical relation-ship [36]

b�1 ¼ 1þ s2=4kT ð9Þ




As long as s2=4kT > 1, b < 1, and D(t) is a decreasingfunction of time. The Monte Carlo simulation study of disper-sive transport in organic solids [38,39] has shown that Eq. (9)is applicable for s=kT ranging from 1 up to 20. However,s=kT¼ 1–5 may be too small for getting accurate estimationsby means of Eqs. (8) and (9).

The long-time balance between recombination and driftof carriers as expressed by the g=m ratio has been analyzedusing a Monte Carlo simulation technique and shown to beindependent of disorder [40]. Consequently, the Langevinformalism would be expected to obey recombination in disor-dered molecular systems as well. However, the time evolutionof g is of crucial importance if the ultimate recombinationevent proceeds on the time scale comparable with that ofcarrier pair dissociation (tc=td� 1). The recombination rateconstant becomes then capture—rather than diffusion-con-trolled, so that Thomson-like model would be more adequatethan Langevin-type formalism for the description of the

1.4. MULTIPLICITY OF EXCITED STATES INTHE RECOMBINATION PROCESS

The multiplicity of an electronic state is defined by its spinquantum number (s) as 2sþ 1. The most often occurring sing-let, doublet and triplet states are defined by their spin quan-tum numbers 0, 1=2, and 1, respectively. When an electronand a hole, representing doublet species, recombine in anorganic solid, an excited state of either singlet or triplet char-acter is formed. If both carriers are free, three times more tri-plets than singlets are produced due to spin statistics. Thismeans that the creation probability of singlets PS¼ 1=4, andPT¼ 3=4 for triplets. This holds as long as the conductiongap (Eg) or the electron–hole energy gap, Eeh, is larger thanor comparable with excited singlet energy (ES). Since onlysinglets fluoresce, the singlet fraction is required to calculatethe efficiency limit for fluorescent organic EL materials.The statistical upper limit of the electrofluorescence (EF)




recombination process (cf. Sec. 5.4).

quantum efficiency (jEL) is obviously 25%, provided all excitedsinglets decay radiatively. Triplet states can contribute to therecombination radiation either by phosphorescence (PH) ordelayed fluorescence due to thermal activation of triplets to

The latter is expected to improve electrofluorescence jEL

up to 35%, on the basis of triplet spin statistics. However, thespin statistics of doublet species, here charge carriers, breaksdown if one of the two recombining carriers is trapped (Fig. 4).

Let, for illustration, the depth of a discrete electrontrap be Et, then the generation of singlets requires a thermalactivation energy DE¼Et� (Eg�ES) > 0, and

PSt ¼1

4exp �½Et � ðEg � ESÞ=kT

� �

¼ 1

4exp½�ðES � EehÞ=kT < PS ð10Þ

Figure 4 Triplet–triplet annihilation contribution to the emittingsinglet states in the absence (a) and in the presence (b, c) of carriertraps. A 100% radiative decay is assumed for excited singlets in theevaluation of jEL.




singlets and or triplet–triplet annihilation (cf. Sec. 2.5.1).

On the extreme, when the electron–hole energy is much lowerthan the excited singlet energy due for example to deep trap-ping of electrons only triplets are energetically feasible andpossible emission is purely phosphorescence or delayed fluor-escence. In the latter case, the recombination yield of singletproduction drops down to 12.5% (Fig. 4c). Phosphorescence,neglecting triplet–triplet annihilation, would give the emis-sion yield limited only by phosphorescence quantum yield;for all emitting triplets, it would be as much as 100%. There-fore, unexpectedly, to further improve the EL quantum yield,a highly phosphorescent material with deep one carrier trapsmust be applied as an emitter in organic LEDs.

The triplet–triplet interaction, postulated to explainincreased quantum yield of thin film organic LEDs, has beenwell known in EF of organic single crystals [2,21,41]. One ofthe most spectacular manifestation of this type excitonicinteractions is spatial distribution of EL emission (see Sec.3.3). Interestingly, the EL light output resulting from thefree-trapped carrier recombination ðFt

ELÞ with respect to thatunderlain by free carriers recombination (FEL) does notdepend on the trap depth [2]

FtEL=FEL ¼ ð1=2ÞðHte;h=Neff Þ exp½ðEg � ESÞ=kT ð11Þ

but is a function of trapped electron or hole concentrationHte,h, density of states (Neff) and the difference between theenergy gap and excited singlet energy (Eg�ES). From Eq.(11), it is seen that for a given Eg�ES, that is for a givenmaterial, the EL flux depends solely on the concentration oftrapped carriers. Its value

Hte;h ¼ 2Neff exp½�ðEg � ESÞ=kT ð12Þ

gives the lower limit above which FtEL exceeds FEL. The effect

of deep traps on the singlet-to-triplet ratio can be expected incomposite materials where intentionally introduced or uncon-trolled chromophores are electrically active, forming e.g.recombination centers. In fact, the EL spectra of epoxy resin,dominated by a long-wavelength emission band, absent in thePL spectrum, have been assigned to the trap-enhanced




production of triplets emitting phosphorescent light. [42]An attempt to detect the singlet-to-triplet branching ratiofrom the electrofluorescence to electrophosphorescenceratio of the archetype organic LED’s emitter aluminum(8-hydroxyqninoline) (Alq3) doped with a phosphorescentdye, 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine plati-num (II) (PtOEP) led to a singlet exciton fraction (22 � 3)%[43]. It is, within the experimental accuracy, in accordancewith the spin statistics ratio 25%. However, this result canbe questioned due to the neglection of the direct excitonformation by the electron recombination on PtOEP mole-cule-trapped holes and possible triplet quenching by charge

question whether or not the spin statistics predicted branch-ing ratio is firmly established.

Another reason for breaking the simple spin statistics forrecombining carriers is that the capture time in the formationof singlet states ðtSc Þ can be different from that in the forma-tion of three equivalent triplet exciton states ðtTc Þ (cf. Fig. 3).This is underlain by the fact that the volume recombinationprocess proceeds through an intermediate unstable encountercomplex (e �� h) being a quantum mechanical mixture of theoverall eigenstate c(0)¼ceþch of the initial reactant species(jcei, jchi) and the overall eigenstate cf¼ (cS=cT)þcG of thefinal products of the capture, with (cS=cT) being either a sing-let or triplet excited state of one participant, and jGi being theground state of the other participant. For a non-zero electron-correlation, valid particularly for p-conjugated polymers, thece and ch states are no longer single configurations [44],but represent superpositions of multiple configurations invol-ving low occupied or high unoccupied one-electron levels. Ithas been argued that the formation cross-section of singletexcited states, sS � ðtSc Þ

�1, is larger than that for tripletstates, sT � ðtTc Þ

�1 because the correlated singlet excitonshave a stronger ionic character than triplet excitons [45,46].The sS=sT ratio can be measured applying continuous wave(cw) photoinduced absorption (PA) and photoinduced absorp-tion detected magnetic resonance (PADMR) techniques [47].These techniques have been used to measure the ratio sS=sT




carriers (cf. Secs. 2.5.2 and 5.4). Therefore, it remains an open

for a series of p-conjugated polymers and oligomers, showingits strong (non-monotonic) dependence on the optical gap, ES.The sS=sT ratio decreases from 5 for ESffi 1.8 eV [poly(thieny-lene vinylene)] to a minimum value of 1.8 for ESffi 2.3 eV(a-hexathiophene), and increases again up to �4.0 forES¼ 3 eV (polyfluorene) [45]. The value of �2.2 found for thesS=sT in poly(phenylene-vinylene) (PPV) (Effi 2.4 eV) leads tojEL of 42% in agreement with the data for jEL measureddirectly from PPV LED operation [48,49]. Understandingand quantifying such experimental observations by derivingan analytical relationship between the ratio sS=sT and inter-related positions of various electronic levels, and its possibledependence on electric field is a challenge for future work,though the simple spin statistics has been recently appliedto interpret the excitonic singlet–triplet ratios for bothlow-molecular weight materials and conjugated polymers[50]. The singlet–triplet ratios for Alq3 and poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) were found to be (20 � 1)% and (20 � 4)%, respectively,using a technique based on reverse bias measurements ofphotoluminescent efficiency from organic LEDs.




2

Types and Decay Pathwaysof Excited States

2.1. INTRODUCTION

The excited states of molecular solids are traceable to proper-ties of individual molecules. However, the energy of interac-tion between the molecules imposes a communal responseupon the molecular behavior in the condensed phase; the col-lective response is embodied in an entity called an exciton (seeSec. 2.4.1). A molecular (localized) exciton model is applicableto van der Waals force-bonded solids (e.g. polyacenes, raregases or polymers) [26,51]. In contrast to the Mott–Wannierexcitons in tightly bonded inorganic semiconductors, themolecular excitons are usually located much below the loweredge of the conduction band being, in essence, an ionized statestabilized by a polarization energy (cf. Fig. 1d). Its narrow-ness makes the carriers highly localized at room temperatureand the traditional one-electron band picture is inadequatefor a description of the conducting properties of the over-whelming majority of organic solids. It is for this reason that

13



the term ‘‘conduction level’’ is sometimes used instead of theusual ‘‘conduction band’’ designation. On the other hand, asin the case of inorganic semiconductors, the positive ion inmolecular solids is referred to as a ‘‘hole’’ since it is an electronvacancy. The band designation can be used for the higher-energy conducting states because of the greater delocalizationof charge carriers. Such a higher conduction band has beensuggested to exist in anthracene crystal in order to explainits EL properties as being due to electron impact excitation[8]. Superimposed on the conduction levels are the higherneutral excitonic levels. Their quantum-mechanical couplingprovides an additional (auto-ionization) channel for the decayof the neutral excited states. Due to the same reason, elec-tron–hole recombination leads to creation of neutral excitons.However, optical transitions occur mostly from the relaxedlowest excited singlet because of fast internal conversionwithin the singlet manifold relative to the rate of radiativedecay and auto-ionization from higher, excited singlet states.The energy of a localized (Frenkel type) exciton may be splitinto as many components (Davydov splitting) as there areindividual molecules per unit cell in an organic crystal. Thissplitting is in addition to the level splitting produced by theinteraction between two adjacent identical molecules. TheDavydov splitting (D¼ 2jL12(k¼ 0)j) depends upon the reso-nance interactions between molecules that are translationallyinequivalent, whereas the mean energy displacement down-ward (L11) depends on resonance interactions between trans-lationally equivalent molecules. The wave vector selectionrule kffi 0 imposes the direct transitions to occur only betweenthe bottom states of the exciton bands. The exciton banddispersion can be expressed as

EðkÞ ¼ Eg �D� L11ðkÞ � L12ðkÞ ð13Þ

where D is the gas (Eg)-to-crystal shift term arising from thenon-resonant interaction between an excited molecule and itssurrounding medium. The Davydov splitting, as small as10 cm�1 for triplet states due to the short range of exchange




interactions, can vary from a few hundred cm�1 to severalthousands cm�1 for highly excited singlet states. In additionto this spectral splitting, the Davydov components havedifferent polarization properties [52].

2.2. OPTICAL SPECTROSCOPY

Optical spectroscopy is a natural tool for investigatingphoto-excited states. While absorption spectroscopy providesinformation about the excited states as they are created, lumi-nescence spectroscopy reflects properties of relaxed excitedstates. In general, absorption and emission spectra of organicsolids are complex compositions of various electronic transi-tions and their analysis can be a complicated task. For example,the presence of Davydov components can be observed in theabsorption or emission spectrum of organic solids, althoughtheir identification is not necessarily straightforward becauseof an overlap with vibronic bands and disorder broadening ofthe bands. In Fig. 5, the Davydov splitting is apparent inthe absorption spectrum of a polycrystalline tetracene film,a-polarized component at ffi505 nm and b-polarized compo-nent at ffi520 nm; Dffi 600 cm�1

In the front recorded emission spectrum at room tempera-ture, the b-polarized transition appears at 535 nm implyinga large Stokes shift (ffi500 cm�1) between the 0–0 transitionabsorption and fluorescence. This shift reduces to typical260 cm�1 for the emission spectrum corrected for spatial dis-tribution of excitons (Fig. 5b), illustrating how the excitondynamics combined with the internal absorption and reflec-tance can influence the shape of the spectrum [56]. Sucheffects contribute to a variety of losses attenuating lightleaving EL cells. Thus, the external EL quantum efficiencydiffers from the internal quantum efficiency as discussed inSec. 5.4. The large Stokes shift can be due to conformationalchanges of molecules upon excitation. An excellent exampleis provided by the PL and EL spectra of Alq3 [the aluminum(III) 8-hydroxyquinoline complex] one of the most usedmaterials in organic EL diodes [16,57,58]. A large Stokes

Chapter 2. Types and Decay Pathways of Excited States 15



(see also Refs. 54 and 55).

shift (0.4–0.7 eV) between the broad emission and the firstabsorption transition in Alq3 has been ascribed to the struc-tural distortion of the molecule, leading to deep localizationof the first excited singlet [58,59].

Figur e 5 (a) Absorption ( a) and emission (PL) polarized spectra oftetracene: kb and ?b Davydov splitting components of a tetracenesingle crystal seen in the absorption spectrum of a polycrystallinetetracene layer (upper full curve) as double features at ffi505 andffi520 nm; the PL spectrum (1) as measured, the PL spectrum (2)corrected for the spatial distribution of excitons in the crystal asshown in part (b). (b) The spatial distribution of singlet excitons[ f(x)] in a 4.7 mm-thick tetracene single crystal, obtained accordingto the procedure described elsewhere [53] (see also Sec. 3.1).




Another reason for optical spectra to differ from thosedetermined by well-defined molecular energy levels is thestructural disorder in organic solids [38]. Depending onthe degree of disorder, one can distinguish two limitingcases: completely random systems (strong disorder) charac-teristic of high-molecular weight organic solids (mostly poly-mers) and systems exhibiting long-range order, typical forperfect single organic crystals. It is, however, easily concei-vable and experimentally confirmed that a large group oforganic solids displays an intermediate degree of disorder,characterized by the presence of aggregates whose structureis similar to the crystal structure. Static and=or dynamicstatistical fluctuations of the molecular coordinates, thedegree of which depends on the formation conditions ofthe solid, cause a splitting of the exciton bands into a dis-tribution of localized states and the spectral profiles mapthe energy distribution of the absorbing or emitting sites.Davydov splitting, which must vanish in a completely ran-dom system because the average over the intermolecularenergies is 0, appears in solids composed of highly asym-metric molecules where the intermolecular potential is suchas to favor certain molecular configurations. Some of thesecan lead to the formation of incipient dimers responsiblefor excimer emission [60–63].

A general feature of the disorder-affected spectra is theirlarge width and extended long-wavelength tail due to a highdensity of defects resulting from structural inhomogeneities.All of these features are exemplified in Figs. 6 and 7 by absorp-tion (A) and emission (PL) spectra of some materials usedextensively in organic EL devices.

The structural disorder formalism has been mostly uti-lized to discuss electronic transport in organic solids [29,38]

interpret optical spectra [62,67], and, recently, quantum effi-ciency of organic LEDs [68]. The absorption spectrum of anorganic material with impurities disorder, local electric fields,or strong exciton–phonon coupling exhibits an exponentialtail, commonly referred to as the Urbach tail [69,70]. Such aspectrum can often be decomposed into broad bands featuring




(cf. Sec. 4.6), and only a few works show its applicability to

Figur e 7 Absorption ( A) and photoluminescence (PL) room-temperature spectra of (a) thin films of polyvinylcarbazole (PVK),[64] (b) a-sexithiophene (a-6T) [65], and (c) poly-( p-phenylenevinylene) (PPV) [66].

"

Figur e 6 Absorption ( A) and photoluminescence (PL) room-temperature spectra of SL and DL thin film structures based onmaterials described in the upper part of the figure. The small greenluminescence contribution of Alq3 (emission maximum at ffi520 nm)to the blue luminescence of TPD (emission maxima at ffi400 andffi420 nm) for the DL film structure TPD =Alq3 excited through theTPD layer reflects the filtering action of the TPD layer for theexciting light lexc




¼ 355 nm. For more details, see Ref. 57.




Gaussian profiles (Fig. 8). Gaussian profiles are ascribed tothe Gaussian distribution of energies (e) of the emittingstates:

gðeÞ ¼ ð2ps2Þ�1=2 expð�e2=2s2Þ ð14Þ

The distribution parameter s reflects the root-mean squarestandard deviation of the non-resonance interaction energyD [cf. Eq. (13)] corresponding to the polarization energy of a

tribution to D is the difference of the van der Waals energiesbetween an unexcited and excited molecule embedded in amedium of polarizability a.

Figure 8 The absorption spectrum and its decomposition intoGaussian profiles for a pentacene film deposited at 80 K, and thespectrum recorded at 240 K. The main S0!S1 transition hn0

(1) isaccompanied by the upper Davydov component hn0

(2), in the crystalspectrum, its first vibronic band, hn0

vibr, and a defect band hn0D.

Adapted from Ref. 67.




charge carrier in a medium (cf. Sec. 2.3.1). The essential con-

For a dipole-allowed singlet transition (i) characterizedby an oscillator strength fi, it can be expressed as

Di � fi aXi6¼k

r�6ik ð15Þ

Variation of the intermolecular distances by h D r= ri causes anaverage relative fluctuation of the D-term by

s =D ¼ 6hD r= ri ð16Þ

For Dffi 0.3 eV, the level splitting s exceeds the exciton band-width, �0.01 eV [52] if h Dr =ri > 0.6%. This in the case exem-plified by disordered tetracene and pentacene films for whichthe width of the Gaussian to fit the S0! S1 0–0 transition var-ies between 0.037 eV (ffi300 cm�1) and 0.08 eV (ffi650 cm�1)depending on film formation conditions [67] (cf. Fig. 8).

All disordered organic solids investigated so far showbroad fluorescence spectra red-shifted with respect to theabsorption spectra (cf. Fig. 7). They reveal the radiative decayof single molecule based excited states [71–74] but arestrongly characteristic of excimers (double-molecule-basedexcited states) [62,72,74,75]. A typical example is shown inFig. 9, where Gauss-analysis of the emission spectrum of atetracene layer evaporated on a cold glass substrate is pre-sented. Two dominating Gaussian bands (III, IV), ascribedto excimeric emission, are accompanied by a weaker band IIunderlain by the monomer (defect) emission, and a weak bandV reflecting emission of an additional (low-populated) exci-mer. Such an assignment is confirmed by different decay timeconstants, t1ffi 7 ns for monomeric component, and t2ffi 21 nsfor excimeric emission centered near 610 nm.

The appearance of both, monomer and excimer emissionbands in emission spectra of organic films, demonstrates thatlacking long-range order (crystal) structure they containshort-range order imposing local molecular pair configurationsimilar to that in the corresponding crystal. The dominatingexcimer emission suggests important role of two molecules-underlain excited states (bimolecular excited states) (seeSec. 2.3). Furthermore, since the originally excited singlet




state does not fluoresce (the lacking band I in Fig. 9), rapidenergy transfer to both monomeric defects and incipientdimers (closely spaced parallel molecular pairs) capable toexcimer formation must exist (see Secs. 2.3.1 and 2.4).

2.3. MONOMOLECULAR AND BIMOLECULAREXCITED STATES

The excitons in the weak coupling limit are practically loca-lized on one molecule, forming monomolecular (monomeric)

Figure 9 The emission spectrum of a tetracene film evaporatedonto a glass substrate kept at 89 K and the emission monitored at180 K (full circles). Its decomposition into Gauss profiles (II, III,IV, V) is shown by solid lines. The dashed curve is the sum of thegaussians. The lacking band I (ffi540 nm) is characteristic of themonomer emission from crystalline films formed at T > 140 K.Adapted from Ref. 72.




excited states. If, for some reasons, as for example energy orcharge exchange, a nearest-neighbor molecule becomesinvolved to form the excited state, a bimolecular excited stateis created. Its properties are different from those of mono-meric states and depend on electronic structure of interactingmolecules.

2.3.1. Single Component Emitters

In addition to the localized (monomeric) excited states (M�)

jM�Miloc, charge-transfer excimer jMþM�iCT, and electromer(Mþ–M�) states can be created by light or electron–holerecombination in single component organic solids (Figs. 10and 11).

The term single component solids means that except forunavoidable chemical impurities, only one sort of molecules ispresent. The electronic structure of an excimer can beapproximated by a linear combination of locally excited,jM�Miloc, and charge-transfer (CT), jM�MiCT, configurationsof complexing species [76]:

jM�Mi ¼ ajM�Miloc þ bjMþM�iCT ð17Þ

The coefficients, a and b, determine the extent of mixingbetween local and CT configurations. Their binding energiesdiffer because the binding energy of the local configurationis due to excitation resonance (M�M$MM�) and that of theCT configuration to charge resonance (MþM�$M�Mþ)effects. The relative contribution of the two configurations(a=b), depends on the intermolecular separation, with thecharge resonance contribution increasing with decreasing dis-tance of separation [77–79]. This is illustrated in Fig. 12. Thelarge bandwidth of the excimer luminescence is caused byradiative transitions to a steep-rising, repulsive, ground-statepotential curve. The spectral region of the emission band(f(l)) is correlated with the amount of charge resonance char-acter on the one hand, and the vertical transition energy, on




(cf. Sec. 2.4.1), the locally excited pair states of excimer

the other. The relatively low quantum yield of emission(jPLffi 0.3) suggests that the triplet state of the molecularsandwich pair is formed with high efficiency or internalconversion to the ground state is a dominant photophysical

Figure 10 Light-generated excited states in single componentorganic solids.




process (for a more detailed discussion, see Ref. 80).

The energy of an excited pair state of identical molecules(M) can be expressed as (see e.g. [81])

1 ;3EðMMÞ� ¼ 1 ;3EM� �m2

r3cos a� 3 cos2 y� ��

� EMþM�

� �

ð18Þ

where 1,3 EM� are zero-point singlet or triplet (1 or 3 super-script, respectively) excitation energies of individual mole-cules. The interaction between an excited (M�) andunexcited (M) molecule leads to exciton resonance splittingdependent on their intermolecular distance, r, and the rela-tive orientation. The intermolecular orientation in (18) isrepresented by the angle a between the dipole M!M� transi-tion moments, m, and the angle y between the transitionmoments and the line of centers of the two interacting mole-cules. Configuration interaction of each exciton-resonancestate (the two terms in the square brackets) with thecorresponding charge-resonance state of energy

1 ;3EMþM� ¼ I � A� EcðrÞ ð19Þ

Figur e 11 Excited states created by bimolecular electron–holerecombination in single component organic solids. In contrast tophoto-excitation (Fig. 10), recombination of oppositely charged,statistically independent carriers (e, h) leads to molecular andbimolecular excited states through unavoidable Coulombicallycorrelated electron–hole pairs (e��h).




yields two additional energy sublevels of mixed singlet ortriplet bimolecular excited states. In the absence of orbitaloverlap between the two molecules, the four charge-resonancestates (18) are degenerate with a common energy of anelectron–hole pair (19), where I is the molecular ionizationpotential, A is the electron affinity, and Ec(r)¼ e2=4pe0er isthe isotropic Coulombic interaction potential with e being the

Figure 12 Potential energy diagram correlating the spectralregion of the emission band, f(l) with the amount of charge reso-nance character (b) of the wave function in Eq. (17) with interplanarseparation, r, of the molecules forming excimer. Adapted fromRef. 80.




dielectric constant of the material (or solvent) and e standingfor the electronic charge. The states with a negative charge-transfer-resonance component have the lowest energies.

The equilibrium separation of the molecules in a typicalaromatic excimer is ffi0.33 nm. In anthracene and its deriva-tives, the strong 1La–1A transition dipole is polarized alongthe line joining the 9- and 10-carbon positions in the firstexcited singlet state, S1 (

1La in the Platt notation), so that mis directed along the short molecular axis and lies in the mole-cular plane. The two anthracene molecules in a parallel over-lapping arrangement with the meso-positions adjacent toeach other (a¼ 0, y¼ 0) are prepared to form the photodi-mer-dianthracene (M2) with the �0.16 nm long 9 to 90 and10 to 100 C–C bonds (Ref. 76 and references therein). The for-mation of the exact sandwich dimer, named otherwise incipi-ent dimer [82,82a], shows up in a long-lived (ffi200 ns) redexcimer emission with a maximum at lmaxffi 575 nm. It occursin rigid environments where the sandwich pair cannot evolveto a more energetically favored configuration with the mole-cules ‘‘slided’’ over each other. Such a red excimer emissionhas been observed in the crystal of dianthracene in whichregular close packing of dianthracene molecules does notallow the photochemically produced sandwich pair to moveto configurations of lower repulsion energy [83,84]. Its broadspectrum is shown in Fig. 13 (curve 4). For anthracene mole-cules incorporated in rigid low-temperature glasses, theexcimer emission has two components, one red and the othergreen [84]. The proportions of these components vary some-what from sample to sample because their microscopic struc-tures vary from amorphous-like to crystalline-like dependingon preparation conditions, and the green emission disappearsat higher temperatures than the red emission. Blue and greenemission components have been distinguished in the fluores-cence of non-crystalline anthracene films [75]. The differencebetween the red, the green and the blue emission has beenascribed to different excimer conformations. Possible anthra-cene excimer conformations and their spectral consequencesare presented in Fig. 13. It is commonly accepted that therigidity and size of the environmental cage play a major role




Figur e 13 Possible anthracene excimer conformations (a), andtheir spectral features (b). (a) (i) Exact parallel overlappingarrangement (incipient dimer) with the angles a¼ 0 and y¼ p =2[cf. Eq. (18)]; (ii) parallel molecules ‘‘slided’’ slightly over each other( a¼ 0, y 6¼ p=2); (iii) parallel molecules with one benzene ring displa-cement along the long molecular axis (a¼ 0, y 6¼ p=2); (iv) parallel

an angle about 60 ( a 6¼ 0, y 6¼ p=2). (b) 1 represents the long wave-length tail of the fluorescence spectrum, F( l), of a 34 nm-thick sub-limation grown anthracene single crystal excited at 366 nm; 2 and 3are the time-resolved fluorescence spectra of non-crystalline anth-

4 is the fluorescence spectrum of the anthracene excimer emissionproduced by the photocleavage of dianthracene (A2) crystal with

difference DF=F0 in the fluorescence of the single anthracene crys-tal as in 1, taken in the absence (F0) and in the presence (F) of thepositive charge injected from an electrode into its emitting zone(limited by the penetration depth ffi 0.2 mm) of the exciting light366 nm [85]. The spectra 2, 3, 4 are normalized to the 4 band maxi-mum. The spectral slit in measurements of the charge modulatedfluorescence (5) increases towards long wavelength region up toffi20 nm. For explanations, see text.




racene films sublimed onto a 89 K glass substrate (see Ref. 75);

254 nm light at 10 K (see Ref. 84); 5 represents the relative

overlapping arrangement with the short molecular axes forming

in determining the type of excimer. The appearance of thegreen emission in a solid methylcyclohexane solution, andthe green and blue emission in non-crystalline anthracenefilms (curves 2 and 3 in Fig. 13) indicates that the relaxationof the environmental cage allows the molecules to move overeach other yielding more stable excimer conformations. Exci-mer conformations (ii)–(iv) have been suggested to be respon-sible for the blue and green emissions in non-crystallineanthracene films [75]. The large width of the green emissionband, 3, has been ascribed to a statistical fluctuation in con-formational parameters, including incipient dimers. Since,however, no low-temperature absorption, due to photodimers,was observed, the density of the fully eclipsed pair structure(i) with D2h-symmetry [86] must be low, thus, insufficient toform a separate red emission band observed from anthraceneexcimers generated by photo cleavage of dianthracene crystal(curve 4 in Fig. 13). Band 2 and a more blue-shifted bandpeaking at 457 nm (not shown in Fig. 13) have been assignedto well-defined (more stable) structures (iii) and (iv), respec-tively, by an analogy to anti-[2,2](1,4)anthracenophane form-ing an excimer with lmax¼ 450 nm [87]. Another configurationof anthracene dimer has been proposed on the basis of absorp-tion and fluorescence spectra of methylcyclohexane rigidglasses containing dianthracene irradiated with 254 nm light[88]. This is so called ‘‘55 dimer’’ in which the short molecularaxes make an angle of (55 � 5) with each other while thelong axes are parallel (Fig. 14a). Its 0–0 emission peak(ffi420 nm) falls within 0–1 vibronic component of anthracenecrystal, thus lies far beyond long-wavelength excimer emis-sions [60]. Two anthracene molecules linked chemically canstill form excimer-like pairs though their formation compe-tes with the formation of zero-overlap excited anthraceneunits. An example is 1,1-di(9-anthryl)alkane, which, in addi-tion to the short-wavelength structured excitonic emissionof the compound, reveals unstructured red-shifted compo-nents characteristic of charge-transfer type (Fig. 14b) andexcimer-type (Fig. 14c) anthracene unit pairs [89].

It has been pointed out that the molecular arrangementsin the solid solution of anthracene are similar to those of two




Figur e 14 Schematic representation of anthracene dimers withno parallel molecular planes: (a) ‘‘55

overlap twisted intramolecular charge-transfer type pair; and(c) large overlap excimer-type conformation of anthracene units




dimer’’ (see Ref. 88); (b) zero

in 1,1-di(9-anthryl)alkane (see Ref. 89).

molecules in the unit cell of the crystal [60,88]. They can bematched by a structural imperfection of the crystal, leadingto an effective trap for the excitation energy and emissionfeatures characteristic of either the excimer configurations(Fig. 13a) and the stable dimers like ‘‘55 dimer’’ (Fig. 14a).Such features, observed naturally in full defect microcrystal-line films [60,88,90], can be found even in sublimation growngood quality single anthracene crystals. A strong maximum atffi465 nm, and weak shoulders at ffi500 nm and ffi575 nm, ofthe long-wavelength tail of the emission spectrum of such acrystal (Fig. 13b, curve 1), suggest emission from various exci-mer conformations, including that of the exact overlappingarrangement of the ‘‘incipient dimer’’ (Fig. 13a). Also, thecrystal sites, at which the configuration of adjacent moleculesdiffers from the regular lattice structure, form charge carriertraps. If charge concentration is sufficiently high, the exciton( S) and charge ( q) trapping processes are in direct competition(see the scheme in Fig. 15). The concentration of the excitedstates in traps (St) and, consequently, their contribution tothe crystal emission, are controlled by the filling factor givenby the ratio of trapped charge of concentration nt to the totalconcentration of defects Sot. The fractional change dt in thetrap fluorescence due to the presence of trapped charge isthus given by dtffint=Sot. The observed fluorescence variationdue to the positive charge (holes) photoinjected from aqueouselectrodes into anthracene crystals confirms this supposition[85]. An example is shown in Fig. 13b (curve 5). The relativeincrease in the fluorescence intensity in the absence of charge(F0) to that in its presence (F) shows maxima within the spec-tral ranges corresponding to the emission of different excimerconformations, the effect over �5% observed for the emissionby incipient dimers. This indicates that the concentration ofcrystal sites enabling formation of the exact parallel arrange-ment molecular pairs is lower than that for defects leading tothe formation of weaker overlapping molecular pairs (seeFig. 13a). The average trapped charge concentration withinthe emission region (<0.3mm from the illuminated water elec-trode) can be evaluated from the intensity (I0) of the excitedlight and the Mott–Gurney function describing the charge




distribution injected at the water=crystal contact [85,91]. ForI0¼ 4 1015 quanta=cm2 s (lex¼ 366 nm), ntffi 2 1014 cm�3

which with dt¼ 5% gives Sotffi 4 1016 cm�3. This means thata fraction Sot =S0¼ 4 1016=4 1021¼ 0.001% of crystal sitesforms defects enabling formation of the incipient dimers(S0ffi 4 1021 cm�3 is the concentration of molecules inanthracene crystal). The defects leading to formation of par-tial overlap excimer configurations [(ii)–(iv) in Fig. 13a] arepopulated by approximately one order of magnitude more(dt� 1%). One should keep in mind that there exists a groupof aromatic crystals in which adjacent parallel molecules havea large overlap and are relatively closely spaced, as in pyrene[92]. Their emission spectra are structureless, reveal a largeStokes shift, and are characteristic of the excimer [93].

Figure 15 The kinetic scheme illustrating the interplay betweenexciton (S) and charge carrier (q) trapping by crystal defects (Sot).The PL spectrum of the crystal contains the excitonic emission(kr, hnM) and the trap center emission (kt

r, hnt), the latter being con-trolled by the number of the defect sites available for excitation. Theexciton capture process (gst) competes directly with charge carriertrapping (gqt). The defects filled with charge reduce the emissionresulting from radiative relaxation of the excited states producedat defect sites. For further explanations, see text.




However, the more common aromatic crystals show spectralproperties resembling those of anthracene. Substitution inthe 9- and=or 10-positions in anthracene introduces sterichindrance to the approach of the two molecules and therebymodifies the photodimerization and excimer fluorescencebehavior. The steric hindrance to the close approach of thepair molecules reduces or prevents photodimerization butnot excimer formation. The fluorescence spectra of such sub-stituted anthracenes are broad, structureless bands, similarto the excimer, with maxima at ffi489 nm for 9-methylanthra-cene, at ffi494 nm for 9-chloroanthracene at ffi495 nm for9-bromoanthracene [88]. Even anthracene-substituted largemolecules reveal the excimer-like PL spectra of anthracene(Fig. 16). ANTPEP in dilute solution exhibits a structured vio-let fluorescence emission band, with a 0–0 transition atlM� ffi 398 nm, characteristic of the excited molecule A�. Theconcentration quenching of the molecular fluorescence isaccompanied by the appearance of an increasing broad struc-tureless blue fluorescence, with the peak intensity atffi470 nm being red-shifted by about 0.5 eV as compared tothe A� transition. This structureless emission band is due tothe fluorescence of excimers produced by the interactionbetween excited and unexcited units of A in the A-basedsupramolecules of ANTPEP. It corresponds well to theemission band at ffi465 nm observed from non-crystallinefilms and perturbed regions of anthracene crystals, whichhas been assigned to the excimer conformation presented inFig. 13a as (iv).

The autoionization of optically excited states (M�s, M��s in

Fig. 10) or bimolecular charge recombination (Fig. 11)processes lead to direct formation of nearest-neighbor elec-tron–hole pairs (Mþ–M�) which can realize a cross-radiativetransition, producing light within the long-wavelength tailof the emission spectrum. They must not be confused withthe CT excimer, jMþM�iCT, which requires short intermolecu-lar distances (<0.4 nm) and a large overlap intermolecularconformation in the A�–A interaction process. A new namefor such a pair, ‘‘electromer’’ (EM) , has been, therefore, pro-posed [74]. It is understood that the electromer emission will




appear preferably in the recombination radiation when, dueto structural defects, the carriers are not available for inter-molecular transfer until a delay time of a carrier pair has

Figure 16 The PL spectra of anthracene (A) 10-substituted with along molecular thread (ANTPEP:10-[3,5-di(terbutyl)phenoxy]decyl-2-(f2-[(9-anthrylcarbonyl)amino]gacetate)) in a bisphenol A polycar-bonate (PC) matrix at different concentrations shown in the figure.The PL spectrum in the dilute solution of dichloromethane (DCM) isdisplayed for comparison (curve 4). Molecular structures of thechemical compounds are shown in the upper part of the figure.Adapted from Ref. 94.




elapsed. In fact, the electromer emission, absent in the PLspectra, appears in the recombination EL spectra of poly-carbonate (PC) dispersion of anthracene (Fig. 17). It isrepresented by the EM band (ffi540 nm) emerging on the long-wavelength tail of the broad band emanated from a series ofanthracene intermolecular excimers (EXs) emitting at 457,465 and 510 nm dependent on the degree of the p orbital over-lap within molecular pairs (see Fig. 13). Yet, the strongestradiative transitions in molecular excitons are apparent onthe structureless band of the excimer emission (cf. the PLspectrum in Fig. 13). A most striking example of the electro-mer emission has been reported in the EL emission of thinfilms of 1,1-bis(di-4-tolyloamino=phenyl) cyclohexane (TAPC)[74]. The EL and PL spectra of TAPC appear to be completelydifferent (Fig. 18). Whereas the broad PL spectra reveal major

Figure 17 PL and EL spectra of a 20% anthracene-doped PC film.The PL spectrum obtained at excitation with lex¼ 330 nm, and theEL spectra recorded at two different voltages applied to the film, asgiven in the figure. The absorption spectrum (OD) of the film isshown for comparison. Adapted from Ref. 94.




maxima at ffi370 and 450 nm, a strong regular band at 580 nmis characteristic of the EL spectra. In contrast to PL, which iscomposed of molecular exciton (monomer) (370 nm) and exci-mer (450 nm) emission, EL is underlain by emission of electro-mers formed by electrons and holes trapped on tritolylaminesubunits of different TAPC molecules. However, intramolecu-lar excimer formation cannot be excluded due to the moleculefolding imposed by opposite charges located on tritolylaminesubunits at one TAPC molecule. Intramolecular formation of

Figure 18 Comparison of PL and EL spectra of a 200 nm-thickTAPC film. The dashed curve is the PL spectrum of TAPC in solu-tion. After Ref. 74. Copyright 2000 American Institute of Physics.




excited complexes is known in bichromophoric compounds[89] and random copolymers [95], treated as single componentmaterials (cf. Fig. 14). Since, however, in the latter case,the excited-state complexes are formed between electrondonor and electron acceptor moieties constituting pendantgroups to the polymer chain, they should be considered ashetero-complexes (eloctroplexes) rather than electromers(see Sec. 2.3.2).

Triplet excimer formation is assumed to occur in crystals[96] and concentrated solutions of some compounds in rigidglasses at 77 K [97,98]. The compounds exhibit normal mole-cular (3M�) phosphorescence but there appears broad emis-sion band peaking below the 0–0 band of the molecularphosphorescence spectrum, ascribed to triplet excimers. Theemission decays non-exponentially with a half-lifetime of<1 ms, its excitation spectrum corresponds to the absorptionspectrum of molecular species and can be detected whenexcited directly into their lowest triplet state T1 [98]. Excimerphosphorescence from crystals of three halobenzenes is facili-tated by their crystal structure enabling excimer formation.Translationally equivalent molecules in the crystal latticeare spaced closely along the c-axis in such a manner as tomaximize the hydrogen–hydrogen and p– p intermolecularoverlap implying intermolecular charge–resonance interac-tions within the crystal to dominate in the stabilization ofthe triplet excimers [96]. Formation of triplet excimers, anddimers, has been recently observed in organic neat filmsof the phosphorescent molecule: platinum (II) (2-(40,60-difluor-ophenyl)pyridinato-N,C2)acetyl acetate [99]. Its square pla-nar structure allows it to facially pack in a crystal with anintermolecular separation of only 0.34 � 0.01 nm, therebyfacilitating excimer formation between adjacent molecules.While triplet excimers could be excited efficiently at eitheroptical or electrical excitation, the emitting triplet dimerstates were detected only under electrical pumping in alight-emitting device based on this organic phosphor (seeSec. 5.2.2). Interestingly, the dimer emission spectrum showsno structure, which, as compared with the vibronic progres-sion clearly resolved in the monomer spectrum, provides




evidence that the ground state of this aggregate is onlyweakly bound. The dimer state is not apparent in the opticalpumping experiments because of a low efficiency of themonomer triplet exciton transfer to low populated molecularpairs with configurations where the Pt–Pt contact promotesits formation.

The conformation of the excimer and electromer formingmolecular pairs is reflected in the temporal behavior of theemission. Their luminescence response function for high con-centration systems can be expressed by the luminescence rate

FðtÞ ffi e�t=t � e�t= tf

t� tfð20Þ

where tf is the formation time of the pair excited state and

t / h n�3in3jmtrj2

ð21Þ

is the luminescence lifetime. The value of t is determined bythe mean value h n�3i of n�3 over the luminescence spectrumgiven by the quantal flux F(n)[s�1] as a function of light fre-quency (n), the mean refractive index (n) of the solvent(matrix) over the luminescence band, and the mean electronictransition moments for excimer

mtr ¼ hM�MjmmEXjMMi ð22Þ

or electromer

mtr ¼ hMþ � M�jmmEMjMMi; ð23Þ

where mEX and mEM are excimer and electromer dipolemoment operators, respectively.

Some examples of the time evolution of PL for excimer-emitting organic films are presented in Fig. 19. A very shortformation time, falling within the rise time of the excitingflash, is observed for ANTPEP films (Fig. 19a) while it isapparently larger for the layers of TAPC (Fig. 19b) revealingthe excimer emission at ffi450 nm (see Fig. 18). It is likely that




(cf. Ref. 76) as

Figur e 19 Time-dependent PL intensity of ANTPEP (a) (seeFig. 16) and TAPC (b) (see Fig. 18) solid films. (a) The PL excitedat lex¼ 350 nm and detected at 500 nm, the curves approximatedby two exponentials for short- and long-time behavior with thedecay times t1 and t2, respectively (dashed and dotted lines). Singleexponential decay with tffi 3.2 ns is observed in a dilute (10�5 M inDCM) ANTPEP solution (solid line). (b) The PL excited at lex¼337 nm and detected in various emission spectral regions (cf. absor-ption and PL spectra in Fig. 18): (1) 370 nm (t < 1 ns); (2) 450 (t¼2.3 ns); (3) 525 nm (4.8 ns) and (4) 580 nm (t¼ 6.4 ns) (after Ref. 74).




the long-time parts of the PL response curves belong to exci-mers in both cases, but their lifetimes in ANTPEP (t2¼ 40 ns)and TAPC (tffi 6.4 ns) are largely different. The energy (thusn) shift in the emission maximum from 470 to 450 nm, respec-tively (cf. Figs. 16 and 18), is insufficient to explain such a bigdifference according to Eq. (21). A twofold larger electronictransition dipole moment (22) for TAPC would, thus, beexpected to yield the observed difference in the decay rateconstants. The large values of mtr (23) for electromers couldstrongly influence their lifetime. But, on the other hand, theelectromer lifetime has its upper limit due to the excimer for-mation process. Activated diffusion implies that carriers willnot be available for intermolecular transfer until a delay timeafter formation of a carrier pair has elapsed. For the electricfield-assisted thermal activation, the electron hopping timeis given by

thop ¼ t0 exp½ð D E� erFÞ= kT� ð24Þ

where t0¼ n0�1 ( n0—frequency factor), r is the intermolecular

(inter-ion) distance, and DE is the height of the barrier due tothe localization energy of the electron. The situation is sche-matically depicted in Fig. 20. The electron transport(LUMO!LUMO electron transition) dominates in unper-turbed environment resulting in dominating monomer andexcimer emission of the e–h pair. The electron localizationon a defect site impedes electron transport and increasesthe probability for the excess electron to recombine directlywith a HOMO-located hole on the other molecule of the ionpair. If such a cross-transition occurs radiatively, a long-wavelength EM emission can be observed. Its time constanttEC has an upper limit determined by the electron hoppingtime (24). Furthermore, the steric hindrance to the closeapproach of the ion pair can drastically impede formation ofexcimer, the emission will be dominated by electromer pairs.Such a situation has been reported for macromolecules of themethyl-exopyridyne-anthracene rotaxane (EPAR-Me), whereanthracene molecule plays a chromophore role as pendantgroup located close to a large macrocycle of a more complex




supramolecular structure (Fig. 21). In contrast to ANTPEP,both PL and EL spectra of EPAR-Me practically coincide sug-gesting a common emission species [94]. The PL lifetime(ffi20 ns) is by a factor ffi0.5 shorter than that for the long-wavelength (500 nm) of ANTPEP (see Fig. 19a). The explana-tion was based on the kinetic scheme presented in Fig. 22.The electromer pair (Mþ–M�) can be formed by approaching

Figure 20 Energy level scheme of molecular ionic states andselected electronic transitions in unperturbed (a) and defect-con-trolled (b) local environments. Dominating intermolecular electronLUMO!LUMO transition in case (a) meets a competing processof intermolecular electron LUMO!HOMO transition (cross-transi-tion) due to an energy barrier (DE) for electron transport in case (b).




Figur e 21 Absorption ( A) photoluminescence (PL) and electrolu-minescence (EL) spectra of EPAR-Me-doped PC (75 wt%) (molecularstructures of EPAR-Me and PC are given in the upper part of thisfigure and Fig. 16, respectively). The ANTPEP unit in EPAR-Meis shown in bold. Adapted from Ref. 94.




ions of a geminate ion pair (Mþ��M�) preceded by the encoun-ter complex of molecular exciton (M�) and ground-state mole-cule (M) or from the encounter ion pair (Mþ��M�) produced inthe course of the volume recombination of statistically inde-pendent holes and electrons (e.g. injected from electrodes).Due to the steric hindrance by the macrocycle, the opticallyexcited singlet cannot approach close enough to form an exci-mer, the encounter complex (M��M) decays predominantly byelectron transfer from M� to M creating a separated electron–hole pair (Mþ��M�) which is likely to relax to the electromer,i.e. a pair of closer located ions (Mþ–M�). In the volume

Figure 22 The kinetic scheme used to describe the electromer(EC) emission (hnEM) excited with light (a) and resulting fromvolume recombination of statistically independent holes and elec-trons (b). The low-efficient processes are indicated by the crossesin bold.




recombination process, the EC state comes into existencenaturally by the diffusion approaching of independent chargecarriers. Its formation competes with the generation pro-cesses of M� and (MM�). The latter become very inefficientfor large inter-ion separations as for the system in Fig. 21,where the anthracene units are, in average, rffi 1.2 nm apart,that is the distance between them is much larger than that inanthracene crystal (rffi 0.6 nm) and even that in the solid PC:ANTPEP solution ( rffi 1 nm) [94]. Consequently, the non-radiative relaxation and formation of electromers kf

EM

� �are

dominating decay channels for encounter ion pairs. One ofthe important premises in understanding the notion of elec-tromer is that electromer species are formed at molecularseparations and relative orientations as to maximize the rateof the radiative cross-transitions. They are different thanthose resulting from statistical averages for molecular disper-sion, but yet undergo some statistical fluctuation which mustbe reflected in the shape and width of the electromer emissionband. The electromer spectra presented in Fig. 21 are largelydominated by the broad electromer band at lffi 540 nm, and aweak monomer emission around 400 nm. An apparentlystronger monomer emission in the PL spectrum than that inthe EL spectrum reflects the radiative decay of photo-excitedmolecular species (M�) to be a competitive process to the diffu-sion-controlled formation of the encounter complex (M��M).A very weak monomer component in the EL spectrum sup-ports an assumption that the formation rate of M� from theion pairs (Mþ��M�) is negligibly small (cf. Fig. 22). The largewidth (ffi0.6 eV) of the electromer band suggests that thisemission stems from electromers whose conformational para-meters are subject to a statistical distribution. The optimizedintermolecular distance for the EM emitting entities (rEM) canbe estimated from the general relationship between the ECtransition energy (h nEM equivalent to hnEC) and the firstmolecular excited state energy EA� ffi 3.3 eV [76],

hnEM ffi EA� � 2DE� Ec ð25Þ

where D E is the localization energy (see Fig. 20) andEc¼ e2=4pe0erEM is the isotropic Coulomb attraction energy




within the electromer. The localization energy can be esti-mated from the lifetime data using Eq. (24). For EPAR-Me:PC, tEMffi thopffi 20 ns, which with t0ffi 10�12 s (resultingfrom the commonly used value of the frequency factorn0¼ 1012 s�1), and T¼ 300 K yields D Effi 0.25 eV at F¼ 0(photoexcitation). A reduction in the hopping barrier in theelectric field applied to the EL emitting sample and suggestedto enhance slightly formation rate of the excimer componentin A:PC system (see Fig. 17) does not seem to be of importancefor the transition energy h nEM since the dominating featuresof the PL and EL spectra of the EPAR-Me:PC system arequasi-identical (see Fig. 21). Using this value of DE ande¼ 3, Eq. (25) yields Ecffi 0.5 eV and REM¼ 1.0 nm. The photonenergies at the half-width (0.6 eV) limits of the EC spectrumgive the distance range (0.7–2.4) nm corresponding well tothe optimum value of the rEM estimated from the lifetimedata. These values for rEC are too large to enable formationof an excimer.

A comment should be made regarding the interrelationbetween the electron–hole pair energy (19) and the transitionenergy (25). They are different because unrelaxed ion pairs,formed either optically or by approaching of uncorrelated car-riers, have different energy than that of relaxed emitting ECstates. Like charge-transfer (CT) excitons in aromatic crys-tals, the charge pair states are vibrationally excited states,the vibrational energy for CT pairs in anthracene, as inferredfrom electro-absorption measurements, is Evffi 0.3 eV [100].This makes the difference between the vertical (‘‘optical’’)band gap Eopt

g ¼ 4:4� 0:05 eV and adiabatic (‘‘electrical’’) bandgap Eel

g ¼ 4:1� 0:1 eV for anthracene crystal, and can accountfor the difference between EEC and hnEC in non-crystallinesolids and concentrated molecular solid solutions.�

� We note that the notions ‘‘optical’’ and ‘‘electrical’’ gap are here used in thecontext of the classical band theory of solids and can be confusing in appli-cation to molecular (van der Waals bonded) solids, where they have theopposite meaning: the ‘‘optical gap’’ reflects the energy of excitonic (loca-lized) states, while the ‘‘electrical gap’’ stands for the lowest energy betweenfree carrier states.




The solid-state values of the ionization potential (I) and theelectron affinity (A) in (19) are related to their values in thegas phase (Ig, Ag) through the polarization energies of positive(Pþ) and negative ( P�) carriers, thus Eq. (19) may be replacedby the relationship

EEM ¼ Ig � Ag � 2 P� EC � Ev ð26Þ

where Pþ¼ P�¼ P has been assumed. From (26), it followsthat Pffi 1.9 � 0.1 eV is required to identify EEM withh nEM¼ 2.3 eV for the A:PC (Fig. 17) and EPAR-Me:PC(Fig. 21) solid solutions. Ig¼ 7.5 eV, Ag¼ 0.6 eV [26], and theabove discussed values of Ev¼ 0.3 eV and Ec¼ 0.5 eV havebeen assumed in this evaluation. The value of P¼ 1.9 eV fallswithin the 1–3 eV range of the polarization energies deter-mined experimentally by ultraviolet photoelectron spectro-scopy for a broad spectrum of various organic compounds[26], and equal to P¼ 1.7 � 0.1 eV for solid anthracene, ascalculated from P¼ Ig� Ic with the ionization energy of thecrystalline anthracene Ic¼ 5.8 eV [101].

The quasi-one dimensional (quasi-1D) nature of somepolymeric semiconductors used in EL cells is the source of dif-ferences in description of excited states as compared withthose in conventional organic solids. In such polymers, ifthere is no empty level below the conduction band, the excesselectron will cause a chain deformation about 20 sites long

mation process, a level is pulled out of the valence band withits two electrons and a level is pulled out of the conductionband. Two levels in the gap are created, the lower one filledwith the two electrons brought up from the valence band,the upper containing the added electron. Although its energylevels are in the gap, the polaron can move freely on its ownchain, its lattice distortion moving with it. When in a conven-tional organic solid, an electron and a hole move freely, contri-buting to transport, until they recombine forming a stableexciton, in quasi-1D polymer the added electron and holecan in addition create a pair of polarons, one positivelycharged, the other negatively charged, in the manner




called a polaron (see e.g., Refs. 26, 102, and 103). In the defor-

described above. If these polarons meet, they recombine. Anexception to this behavior is trans-polycetylene, in which soli-tons, a different type of excitation from polarons, are formed.At high carrier concentrations, when the polarons come closetogether, the charge carriers donated to the chain are housedin bipolaron states. Summarizing, the formation of solitons,polarons, or bipolarons introduces states in the band gap ofthe quasi-1D polymers (Fig. 23). Charged excited states havebeen detected through the sub-gap (<Eg) optical transitionsand electron spin resonance technique. The question of inter-est here is whether, and if so, how these gap states show up inelectroluminescence. The injected carriers are transported assingly charged polarons or bipolarons. Their combination mayform singlet polaronic excitons (Fig. 23) which decay radia-tively producing electroluminescence with energy quantahn < Eg. Since singlet excitons in conventional organic solidsfall also below Eg, this fact cannot be taken as an experi-mental evidence for the existence of polaronic excitons. Atheoretical reasoning pointing a difference between elec-tron screening suggests different origin of the EL emission.

Figure 23 Energy levels of various types of elementary excita-tions in quasi-1D conjugated polymers. Adapted from Ref. 21.




The central issue relates to the strength of the electron–elec-tron interactions and the spatial extent of the excited statewave function. Strong electron–electron interactions (elec-tron–hole attraction) lead to the creation of highly localizedand strongly correlated electron–hole pairs (excitons); well-screened electrons and holes are more appropriatelydescribed using a band picture [104,105]. It seems, however,that this difference has a quantitative character rather thana fundamental significance for electronic processes in EL.For example, it is not quite clear what should be the exactrelation between electron–phonon coupling and electron–electron interaction in order to distinguish between bandpicture and molecular model of organic solids (cf. discussion

2.3.2. Two- and Multi-component Emitters

In an emitter consisting of two- or more component materials,specific interactions between them must be taken into accountin the formation process of excited states. Of particular inter-est are interactions between electron donor molecules (D) andelectron acceptor molecules (A) characterized by partial orcomplete electron transfer from D to A. The degree of electrontransfer depends on the ionization potential (ID) of the donorand the electron affinity (AA) of the acceptor.

A 1:1 DA complex is formed by the reversible process

Dþ A ! ðDAÞ ð27Þ

The molecular equilibrium constant Keq¼ [DA]=[D][A], wheresquare brackets indicate molar concentrations of donors, [D],acceptors, [A], and complex [DA].

The theory of donor–acceptor interaction has been devel-oped by Mulliken [106,107] and followed by many researchersin interpretation of results on optical spectra of D–A molecu-lar mixtures (a comprehensive overview of past works is givenby Birks [76]). The ground-state function of the DA complexmay be written as

jD;Ai ¼ ajDAi þ bjDþA�i ð28Þ




in Sec. 5.2.2).

where jDAi is the non-bond wave function of the DA struc-ture, and jDþA�i is the dative-bond wave function of theDþA� structure, in which an electron is transferred from Dto A. The corresponding wave function of the excited stateof the DA complex is

jD;Ai� ¼ a�jDþA�i � b�jDAi ð29Þ

The coefficients a, b, a� and b� determine the extent of mixingbetween different electronic configurations of donor andacceptor molecules. For a weak DA complex, a� ffia¼ 1 andb� ffi bffi 0. The jD,Ai! jD,Ai� transitions are thus appropri-ately described by a charge-transfer transition, since it corre-sponds approximately to a jDAi! jDþA�i transition. It is,however, incorrect to describe the ground-state DA complexas a charge-transfer (CT) complex. The ground-state electro-nic configuration is a result of the interaction between thep-orbitals of the components and can be considered as avan der Waals complex ‘‘prepared’’ for charge transfer beforeexcitation. The ratio

l ¼ b2

a2 þ b2ð30Þ

determines the fractional contribution of the DþA� to theground state and this fractional ionic character can vary froml¼ 0 for no charge transfer to l¼ 1 for complete electrontransfer.

The coefficients a, b, a� and b� for various DA com-plexes have been evaluated from their dipole moments. Ina complex of a nonpolar donor with a nonpolar acceptor,the non-bond structure DA has a negligible dipole momentm0ffi 0, but the dative bond structure DþA� has a finite dipolemoment m1ffi erDA, directed from D to A, where e is electro-nic charge, and rDA is the equilibrium separation of the twocomponents in the complex. The analysis of coefficientsdescribing configuration interaction mixing in the groundstate indicates a minor admixture of CT configuration(<0.005) that is a=b > 15. The energy of intermolecular




interactions in the ground-state configuration (DA) can beexpressed as

EðDAÞ ¼ EvdWðDAÞ þ EelðDAÞ ð31Þ

where Ev dW is the energy of van der Waals interactions andEel is the energy of electrostatic interactions between thenet charges on the two molecules.

The energy of the CT configuration (DþA�) is

EðDþA�Þ ¼ ID � AA � EC þ EvdWðDAÞ ð32Þ

where EC is the Coulomb interaction in the (DþA�) configura-tion which is formed upon electron transfer from the highestoccupied molecular orbital (HOMO) of the donor to the lowestunoccupied molecular orbital (LUMO) of the acceptor, and

EC ¼e2

4pe0erDAð33Þ

Coupling between the CT state and ground electronic state isexpressed by the matrix element of the Hamiltonian (H) of thesystem (A,D) and shown to be proportional to the overlap inte-gral (S):

hDþA�jHjDAi ¼ 21=2KS ð34Þ

where

S ¼ hDþA�jDAi ð35Þ

and the K is a constant dependent on chemical nature of theinteracting moities [108].

The formation of molecular complexes in the groundstate can be observed in the electronic absorption spectrum,in which one or more new, generally broad and structureless,absorption bands are found, which often occur at longer wave-length than those of the components. The longest wavelengthabsorption band of the complex (DA) corresponds to an elec-tronic transition, which, in the first approximation, can be




described as a CT transition jDAi! jDþA�i. An example isshown in Fig. 24.

The energy ECT of the maximum of the jDAi! jDþA�iCT absorption transition is given by a difference betweenthe energies of the DA complex in the excited (Eex) andground (Eg) states at the equilibrium separation ( rDA) of theground-state DA complex:

ECT ¼ Eex � Eg ð36Þ

Figure 25 shows diagramatically the potential energy curvesof a DA complex as a function of the intermolecular distance r.The curves EDA(r) and EDþA�(r) represent the energies of theDA and DþA� structures, respectively. ECT corresponds tothe vertical Franck-Condon Eg!Eex transition. The groundand excited state energies of the DA complex are given byMulliken [106,107]

Eg ¼ EDA �H01 � EDASð Þ2

EDþA� � EDAð Þ ð37Þ

Figure 24 The CT absorption band in solid anthracene–tri-nitrobenzene complex (1). Solid state absorption spectra of anthra-cene (2) and trinitrobenzene (3) are shown for comparison. AfterRef. 109.




and

Eex ¼ EDþA� þH01 � EDþA�Sð Þ2

EDþA� � EDAð Þ ð38Þ

where H01¼hDþA�jHjDAi.Equation (36) can thus be rewritten as

ECT ¼ EDþA� � EDA þH01 � EDþA� � Sð Þ2þ H01 � EDASð Þ2

EDþA� � EDAð Þð39Þ

Figure 25 Potential energy of DA complex vs. intermolecularseparation distance (r). Adapted from Ref. 76.




From the diagram

ECT ¼ Eex � Eg ¼ ID � AA � ðD Eex � D EgÞ ð40Þ

where DEex and D Eg are the energies of formation of the DAcomplex in the excited and ground states, respectively.

A molecular complex may be dissociated in the groundstate, and yet be associated in an excited electronic state.An excited molecular complex of defined stoichiometry, whichdissociates in the ground state, is known as an exciplex[110,111], the term being derived from ‘‘exci (ted comp) plex’’by analogy to ‘‘excimer’’ (¼‘‘exci (ted di) mer’’).

The excited-state function of a 1:1 exciplex formed from adonor molecule D and an acceptor molecule A has a generalform

jDAi� ¼ C1jDþA�i þ C2jD�Aþi þ C3jD�Ai þ C4jDA�ið41Þ

Exciplex formation in the excited singlet state manifests itselfin the fluorescence spectrum. An example is given in Fig. 26.The fluorescence of the TPD donor (D) is quenched by thePBD acceptor (A) (the latter is not practically excited by the360 nm exciting light) and a new broad and structurelessemission band appears at longer wavelength. This new emis-sion is ascribed to an exciplex, formed in the excited singletstate according to

1TPD� þ 1PBD ! 1ðPBD TPDÞ�

ð1D�Þ ð1AÞ 1ðADÞ� ð42Þ

As there is no corresponding change in the absorption spec-trum, the complex, evidently, is not formed in the groundstate.

Exciplexes formed between relatively strong donors andacceptors are preferably represented by 1(A�Dþ), expressingthe fact that the excited state is a singlet CT state [the coeffi-cients C2, C3 and C4 in (41) are negligibly small]; the emissionof the complex, therefore, corresponds to the CT transition,the reverse of the CT absorption, jDþA�i! jDAi. The energyof the pure CT state, jDþA�i, in the gas phase relative to




Figure 26 Emission spectra (PL, EL) in PC at room temperatureof 40 wt% TPD donor solution with a 40 wt% of PBD acceptor added.The photoluminescence (PL) spectrum excited at 360 nm, the elec-troluminescence (EL) spectra (I, II) originate from the recombina-tion radiation in a 60 nm thick film, taken at two differentvoltages. Absorption (Abs) and PL spectra (excitation at 360 nm)of (75 wt% TPD:25 wt% PC) and (75 wt% PBD:25 wt% PC) spin-castfilms are given for comparison. Molecular structures of the com-pounds used are given in the upper part of the figure: TPD [N,N0-diphenyl-N,N0-bis(3-methylphenyl)-1,10-biphenyl-4,40diamine; PBD[2-(4-biphenyl)-5-(4-tert.-butylphenyl)1,3,4-oxadiazole; PC[bisphe-nol-A-polycarbonate]. Adapted from Ref. 112.




the ground state, AþD, is given by Eq. (32). Therefore, in thefirst approximation, the energy of the CT emission band,h nmax

EX , should be linearly correlated with ID and AA, which,in turn, are related to the polarographic oxidation potentialof the donor, Eox

D , and to the polarographic reduction potentialof the acceptor, Ered

A , respectively. Such linear correlationsbetween h nmax

EX and EoxD � Ered

A

� �have been found for more

than 160 exciplexes in a non-polar solvent (hexane) (see

h nmaxEX ¼ Eox

D � EredA

with

D ¼ 0 :15� 0:1 eV

The applicability of this relation which holds within 0.1 eV(the combined error of frequency and potential measure-ments) is evidently due to the fact that the solvation energyin a polar matrix of the separate ions, Dþ and A�, is of thesame order and depends on the size of the ions in the sameway as the Coulomb term EC. Applying Eq. (43) to the(TPD:PBD:PC) film in Fig. 26, yields hnmax

EX ¼ 2.6 � 0.1 eV(476 � 15 nm) in excellent agreement with the experimen-tally observed location of the PL spectrum maximum usingEox (TPD)¼ 0.35 eV [114] and Ered(PBD)¼�2.4 eV [115]. Thisindicates the exciplex (42) to have a strong CT character.

The exciplexes with D values >0.2 eV and dipolemoments which are smaller than those of the CT exciplexesare formed as a result of interactions between the CT state1(A�Dþ) and non-polar (locally) excited complex states suchas 1(A�D) and 1(AD�) leading to stabilization of the CT stateand to lowering of the dipole moment [116]. The coefficientsC1 or C2, and C3 and C4 in the wave function (41) can be ofcomparable magnitude for such exciplexes. The value ofDffi 0.3 eV follows for the exciplex formed by the TPOB accep-tor [1,3,5-tris(4-fert-butylphenyl-1,3,4-oxadiazolyl)benzene]with the TCTA donor [4,40,400-tri(N-carbazolyl) triphenyla-mine] based on ED

ox¼ 0.69 eV and EAred¼�2.1 eV, and the




e.g., Ref. 113),

� D ð43Þ

position of its emission band, hnmaxEX ¼ 2.48 eV, observed from a

TPOB:TCTA equimolar mixture prepared in a form of spin-coated films [117]. This value of D implies a relatively smallenergy gap between CT singlet and locally excited singletstates, so that their mixing cannot be neglected forming anexcited complex termed the intermediate exciplex. Theseinteractions are even more important with typical excimers

Analogous to fluorescence from the singlet CT state,phosphorescence from the triplet CT state may be expectedif this state 3(A�Dþ) is energetically below the locally excitedtriplet states, 3(A�D) and 3(AD�). Under this condition, theenergy gap between CT singlet and locally excited singletstates is large, so that their mixing will be small or even neg-ligible. The singlet–triplet splitting, DST, for the CT state(A�Dþ) can be expressed as [108]

DST ¼ 1 E1ðA�DþÞ � 3 E1ðA�DþÞ ffi 102 S2ðeVÞ ð44Þ

where S represents the overlap between the HOMO of thedonor and the LUMO of the acceptor. For typically Sffi 0.01,DSTffi 0.01 eV is very small, and in fact, will be 0 for thezero-order CT state.

Exciplex phosphorescence can be studied with complexeswhich are present in the ground state [118]. Equation (43)and its corollaries with respect to variations in D are applic-able also to exciplex phosphorescence. For example, positivedeviations ( D > 0.18 eV) which have been found in the phos-phorescence of complexes with Eox

D � EredA

� �> 2.75 eV are

ascribed to the stabilizing interaction between the tripletCT state and energetically higher locally excited triplet states[108,119].

Contrary to the photodissociation, where electron–holepairs originate from photoexcited localized states, the chargepair states constitute primary species for final emittingstates in the bimolecular recombination process (see Fig. 27).The injected carriers (e, h), by diffusing together will forman encounter complex, i.e. a Coulombically correlated ionpair (A��Dþ). This ion pair comprises a large number of




where D > 0.6 eV and zero dipole moment (cf. Sec. 2.3.1).

configurations of A� relative to Dþ, which differ from thespecific configuration of A� and Dþ in the hetero-excimer[charge resonance component (A�Dþ)CT of the exciplex:(D�A)þ (A�Dþ)CT]. Like in excimer, in the exciplex, the mole-cular planes of A� and Dþ are parallel or nearly parallel toeach other with an interplanar separation of 0.3–0.4 nm,and with no matrix molecules in between (cf. Figs. 13 and14 in Sec. 2.3.1). As a consequence, only a fraction of the cor-related (A��Dþ) pairs leads to formation of exciplexes, thereminder should result in the formation of molecular excitedstates of either donors or acceptors. However, the formationprocess of the molecular excited state is inhibited by anenergy barrier for the excess electron located on the acceptormolecule to pass on the donor molecule. Possible electronpathways between molecules PBD and TPD are shown inFig. 28. The finite electron transit time in process 1 opens

Figure 27 Molecular (D�), exciplex [(D�A)þ (A�Dþ)CT], charge-transfer (A�–Dþ) excited species as generated by photo-excitationand electron–hole recombination processes in electron acceptor(A)–electron donor (D) molecular systems. hnD, hnEX, and hnEC

are corresponding transition energies to the ground state, to beobserved as different emission bands.




an additional relaxation pathway for the excessive electron onthe molecule A, which is the cross-transition to the holelocated on the HOMO of the donor (process 3). This resemblesthe cross-transition between energetically inequivalentmolecules in single component materials, considered as arelaxation of the specific excited state called electromer (seeFig. 20 and Sec. 2.3.1). The term ‘‘electroplex’’ (EC) becomesoften used to characterize a charge pair (A�–Dþ) with chargecarriers spaced by a distance rðA��DþÞ ¼ rEC > rðA�DþÞcr

butrEC < r(A��Dþ). It has been first introduced to explain thegreen emission band in the emission spectrum of the organic

Figure 28 The energy level scheme for some hole- (TPD) andelectron-transporting (PBD, Alq3) materials used in organic LEDs.Possible electron pathways between molecules of PBD and TPDare indicated by arrows 1 and 3. The relaxation channels for theexcited singlets of TPD are designated by 10 and 20. After Ref. 120.Copyright 2000 Institute of Physics (GB).




LED based on the PTOPT=PBD junction [121]. This bandlocated between the monomolecular red emission band froma conjugated polymer (PTOPT) and the molecular excitonviolet-blue emission from PBD, has been ascribed to a sortof ‘‘cross-reaction’’ between the LUMO of PBD and HOMOof PTOPT (Fig. 29). Its occurrence in this system showsthat the cross-transition does not necessarily require thehole transporting material (HTM) to have an electron affi-nity lower than that of the electron transporting material(ETM). This would suggest that the electron transition fromthe LUMO of ETM to the LUMO of HTM can be simplyconsidered as a hopping process across a disordered organicsolid with the high-field (F > 105 V cm�1) activation energyD(F)¼ D0(1� F= F0), where D0 is the Arrhenius zero-fieldactivation energy and F0 is a constant dependent on theintersite distance and disorder parameters. At F F0,D(F)� 0, the transport properties of the system are deter-mined by electron–phonon interactions. For a 0.1% triphe-nylamine (TPA) dispersion in polycarbonate (PC),D0ffi 0.58 eV and F0¼ 3.3 106 V cm�1 was found. Theseparameters change with concentration of the dopant [122].The Arrhenius-type behavior of carrier transport can beconsidered as an approximation of a non-Arrhenius-typetemperature dependence of carrier motion among transport-ing states which are subject to Gaussian distribution ofenergies (14), implying D0¼ (8=9)s2= kT and F0� D0= r (cf.

pattern of features for a broad class of disordered materialsindependent of their chemical composition and impurityeffects [39]. Consequently, the rate of electron transfer fromthe LUMO of an acceptor to the LUMO of a donor (route 1in Fig. 28) is determined by the disorder parameter, s, ofthe system rather than by the chemical nature of the inter-acting molecules.

The field lowering of the intermolecular barrier for elec-tron transport implies a field-dependent branching ratiobetween formation of molecular excited states and electro-plexes, the competition to be extended to the formation ofexciplexes (cf. Fig. 27). A relatively weak, but well-discernable




Sec. 4.6). Thus, the transport properties reveal a recurrent

feature at lECffi 564 nm in the EL spectra of the(TPD:PBD:PC) film (Fig. 26), has been assigned to the electro-plex emission [112,120]. It can be separated as a Gaussianband which in a combination with other two Gaussian

Figure 29 Cross-reaction (a) underlying ‘‘electroplex’’ (green)emission band in the EL spectrum (b) of the LED based on thePTOPT=PBD junction. The PL spectra of PTOPT (right) and PBD(left) are shown for comparison in part (b). Adapted from Ref. 121.




bands, corresponding to the monomolecular emission of TPDand exciplex emission of 1(PBD TPD)�, reproduces well theexperimental EL spectrum (Fig. 30a). The contribution ofthese bands to the spectrum changes with applied voltageas shown in Fig. 30b. From these results, it is apparentthat the low-voltage EL spectrum is dominated by the exci-plex (�60%) and electroplex (�40%) emissions, the monomole-cular emission from TPD being practically negligible. Theelectroplex emission drops down at increasing voltages( <30% at 18 V) while both monomolecular and exciplex emi-ssions increase (�3% and �70%, respectively, at 18 V). Thecounterbalance between these changes suggests that theincreasing production of excited molecular donors (D�) andexciplex (A�Dþ)� occurs on the expense of the formationefficiency of electroplexes from their common precursor ofCoulombically correlated ion pair (A��Dþ) (cf. Fig. 27). Thisis consistent with the above premise predicting the enhancedformation of molecular excited states and exciplexes dueto the field-induced lowering of the LUMO! LUMO orHOMO HOMO intermolecular electron-transfer barrier(Fig. 28).

It is to be expected that the radiative rate constants forspontaneous emission of exciplexes and electroplexes willresemble those for excimer and electromers [see discussion

dent on the intermolecular configuration, the fluorescencelifetimes of exciplexes range between 10 and 200 ns, and thatthe emission lifetime of electroplexes is limited by the inter-molecular electron hopping time. Though there are no at pre-sent direct lifetime measurements on electroplexes, themeasurements on a series of donor–acceptor species in solid-state solutions of PC prove these predictions for exciplexes(Table 1).

2.4. ENERGY TRANSFER BY EXCITED STATES

The absorption of a photon or an electron–hole recombinationevent in an organic solid creates an electronic excitation,




of Eqs. (20) and (21) in Sec. 2.3.1)]. This implies that, depen-

Figur e 30 (a) The experimental EL spectrum of a (TPD:PBD:PC)film ( d¼ 60 nm) (solid line) deconvoluted into three Gaussian com-ponents (1, 2, 3), corresponding to its wavelength representation Iin Fig. 26. The dashed curve represents the best fit to the experi-mental spectrum. (b) The voltage evolution of the Gaussian compo-nents of the EL emission. A1, A2, A3 correspond to the contributionsof the EL components related by the area under the Gaussianprofiles peaking at hn1¼ 2.99 eV (l1¼ 415 nm; molecular excitonemission of TPD), hn2¼ 2.6 eV (l2¼ 477 nm; TPD–PBD exciplexemission), and hn3¼ 2.2 eV (l3¼ 564 nm; electroplex emission).After Ref. 120. Copyright 2000 Institute of Physics (GB).




which, dependent on the strength of the intermolecularinteractions (intermolecular coupling), has different degreeof delocalization. It is considered as a communal response ofa molecular aggregate, forming a quasi-particle called exci-ton. This quasi-particle was initially introduced by Frenkel[123] and was generalized by Peierls [124] and Wannier[125]. For strong intermolecular coupling, the phases of thewave functions of all excited molecules in the domain havea uniquely defined relationship to each other, the resulting

Tab le 1 Fluorescence Band Locations ( lmax) and Lifetimes (t) ofsome Electron Donor and Electron Acceptor Molecules-doped SolidPC films� (from Kalinowski, Cocchi, Virgili, Di Marco and Fattori, tobe published)

Films ( d¼ 60 nm)b lmax (nm) t (ns)

Single-dopant filmsTPD 75%:PC 25% 415 <1c

PBD 75%:PC 25% 390 <1c

m-MTDATA 75%:PC 25% 420 1.3d

TCTA 75%:PC 25% 390 1.1c

Exciplexes in films ofTPD 40%:PBD 40%:PC 20% 464 44e

m-MTDATA 75%:PBD 40%:PC 20% 535 145f

TCTA 40%:PBD 40%:PC 20% 445 37e

�Excitation wavelength: 300 nm monitored at c400 nm,d420 nm,e500 nm, and f600 nm.bMolecular structures of TPD, PBD and PC are given in Fig. 26; the molecular struc-tures of m-MTDATA [4,40,400-tris(3-methylphenyl-phenylamino)triphenylamine],and TCTA [4,40400-tri(N-carbazolyl) triphenylamine] are:




excitation moves in a wavelike manner and the exciton is saidto be free or coherent. Its mixture with exciting photons in the

quantum numbers characterizing the exciton do not change;for example, the wave vector ~kk is a good quantum numberand the direction of exciton propagation is fixed. Because ofinteractions with phonons and imperfections, transitions areinduced among the various states accessible to the excitonsand the coherence of the exciton is lost. The time for whichthe exciton remains coherent is called its coherence time, tcoh,and for organic materials tcoh at room temperature is gener-ally much less than 10�13 s because of the large exciton–phonon interaction energies characteristic of these solids [127].For times greater than tcoh, the exciton moves incoherentlyand generally is viewed as a localized excitation undergoinga random hopping like motion. The exciton wave vector ~kk isno longer a good quantum number, the large spread in ~kk,d ~kk, limits the exciton size which is inversely proportional tothe d ~kk [e.g., the extent along the x-axis d xffi ( dkx)

�1]. The aver-age value of d kx, evaluated from Boltzmann’s statisticsthrough the relationship �h2(dkx)

2=2meffi (3=2)kT, is on theorder of d kxffi 2 106 cm�1 for T¼ 300 K and me¼ rest massof the electron. Resulting dxffi 5 nm indicates the localizationof the exciton within a few neighboring molecules, we dealwith a small radius (Frenkel type) exciton. Its application toorganic crystalline solids was initially given by Davydov [128]

~kenergy dE(~kk)¼ �h~vvg(~kk)d~kk, where ~vvg¼ �h�1dE(~kk)=d~kk is the groupvelocity of the packet representing a localized exciton. Thismust not be confused with the width of the exciton band,DEb¼ 4jbj, which is determined by the energy of interactionbetween neighboring molecules b which can be either posi-tive or negative. For triplet excitons in 1,2,4,5-tetrachloroben-zene, b¼þ0.34 cm�1 [130], whereas, for triplet excitons in1,4-dibromonaphthalene, b¼�6.7 cm�1 [131].

In conventional solid-state physics, an exciton is consid-ered as an electron–hole pair separated by a medium witha well-defined dielectric constant, e. The time-independentSchrodinger equation with the inter-carrier Coulomb




medium is called polariton (see e.g., Ref. 126). In this case, the

(see also Ref. 129). The spread in k imposes a spread in

potential (�e2=4p e0e r) is solved leading to a series of discrete

Enð~kkÞ ¼ �mre

4

2�h2ð4pe0eÞ21

n2þ �h2k2

2ðm�e þm�hÞð45Þ

and corresponding electron–hole distances

an ¼4pe0�h

2

e2

emr

n2 ð46Þ

in which n is an integer (n¼ 1,2,3, . . . ), and mr¼m�em�h=ðm�eþ

m�h) is the reduced mass of the electron (m�e) and hole (m�h)effective masses. The binding energy of the exciton is givenby the difference between the energy gap and the energyvalues of (45), DEex¼Eg�En(~kk).

This type of exciton is envisaged by Wannier [125] andMott [132a], thus known commonly as a Wannier-Mott exci-ton. In this exciton, the electron and the hole revolve aroundeach other resembling the simple (Bohr) structure of thehydrogen atom. The energies (45) and inter-carrier distances(46) can, therefore, be readily related to the discrete energyspectrum ½EH

n ¼ mee4=2�h2ð4pe0Þ2n2� and radii of electron

orbits ðaHn ¼ a0n

2Þ in this atom. Neglecting kinetic energy,one arrives at

En ¼EH

n

e2

mr

me

� �ð47Þ

and

an ¼ a0me

mr

� �en2 ð48Þ

where a0¼ 0.053 nm is the atomic (Bohr) radius.The exciton binding energy is related directly to the ioni-

zation energy of the hydrogen atom, IH¼ 13.5 eV, according to

DEexðnÞ ¼13:5

e2n2

mr

me

� �eV½ � ð49Þ




hydrogen atom-like, energies (see e.g., Ref. 132)

The smaller the reduced mass of the exciton and higherdielectric constant of the material is, the larger is the excitonradius and weaker exciton binding. For example, the groundexcitonic state (n¼ 1) is characterized by a1 only about0.4 nm and D Eex (n¼ 1) as high as 0.4 eV for low-dielectric con-stant materials ( e¼ 4) and m�e¼ m�h¼ me ( mr¼ 0.5), whereasfor higher excitonic levels (say n¼ 5), and high-dielectric con-stant materials (say e¼ 12), the electron–hole distance aslarge as 32 nm but the carriers are loosely bounded withD Eex(n¼ 5)ffi 4 meV. In the first case, we deal with a small-radius (Frenkel) exciton typical for organics, in the latter withthe large-radius exciton characteristic of inorganic semicon-

have been discussed in Sec. 2.3.1 under the name of coulom-bically correlated electron–hole pairs or charge-transferstates.

The existence of the finite exciton bandwidth impliesthe kinetic energy of the exciton and exciton–phonon cou-pling to be accounted for in a more realistic description ofexcited states. For most materials, there is a dense systemof vibrational states that is strongly coupled to the electro-nic states. The exciton–phonon coupling strength, relativeto the intermolecular interactions, has been used as anothercriterion for localization of excitons. If the strength (J) ofthe interaction between an excited molecule (energy donor)and a ground-state molecule (energy acceptor) greatlyexceeds the vibrational bandwidth (DEv) of the acceptorelectronic state (jJj�DEv), we deal with the strong excitoncoupling limit. In this limit, the energy transfer is coherent,the exciton is said to be a free exciton. For dipole–dipoleinteractions, J� r�3, where r is the mean separationbetween donor (MD) and acceptor (MA) molecules, the timefor excitation energy to pass from MD to MA, t(MD!MA)� r3. It strongly depends on r and is shorter than thevibrational relaxation time of molecules [t(MD!MA) <DEv=�h]. This condition is, however, generally, not met inpractice. If jJj is much greater than the width of a singlevibronic level, the condition termed the medium interactioncase, the exciton is said to be an intermediate exciton. On




ductors (see e.g., Ref. 133). The intermediate size excitons

the other extreme, a localized exciton is defined by theweak-coupling condition jJj < DEv. The very weak-couplingcase is commonly distinguished jJj� DEv, the limit oftenencountered in practice and called long-range or Forsterenergy transfer [134,135]. There is a lack of consistencyin the terminology of energy transfer. In further consi-derations, the term of energy transfer will be used todescribe a process that involves one donor molecule andone acceptor molecule, whereas energy migration willrefer to the process of motion of the exciton. Typically,migration involves a series of transfers if no interveningtrap halts the process. The final step in the migrationprocess is then designated as trapping. If the trap is dueto a guest molecule allowing the excess energy to bereleased by a radiative decay, we deal with the quest- (ordopant-) sensitized luminescence. Two primary experimen-tally measured parameters are necessary to characterizethis phenomenon: (i) the motion time (1=M), i.e., the timeto get the exciton within the capture radius of a guestmolecule, and (ii) the elementary capture time (1= C). Thus,the host (H)–guest (G) energy transfer rate constant can beexpressed as [136,137]

kHG ¼ cGð1 =Cþ 1= MÞ ð50Þ

where cG is the mole guest concentration.Unfortunately, most experiments utilized in energy

transfer studies yield only the motion-related primary para-meter. In this respect, time-resolved spectroscopy has theadvantage of yielding two primary experimental parametersassociated with the rate137, 138). In contrast to common picture of the host–guestenergy transfer to be motion-controlled, the capture processhas been suggested as a rate limiting step. For example, inthe case of tetracene-doped anthracene crystal, at leastat T > 60 K, the energy transfer rate has been thought ascapture limited because the estimated exciton motiontime 1=M < 2.3 10�14 s appeared to be much shorterthan the measured value of cG=kHGffi 3 10�13 s at room




of energy transfer (see e.g., Refs.

temperature [137]. This conclusion has been made on thebasis of the experimentally determined temperature depen-dence of the constant kHG and singlet exciton annihilationrate constant, gSS, in a neat anthracene crystal, the point tobe addressed later in Sec. 2.5.1.

The process of reabsorption of emitted photons is impor-tant at long distances (more than 10 nm from the site of exci-tation). In this process, emission originates from a donor andreabsorbed by the acceptor. The net effect of reabsorption in asingle component solid is to lengthen the apparent lifetime ofthe emitting states [139], their spatial distribution and result-ing shape of the emission spectrum [56]. Also, it has beenemployed to determine the spatial distribution of emittingspecies produced in the recombination electroluminescencein single organic crystals (see Chapter 3). The non-radiativeenergy transfer (and migration) will be discussed in thefollowing two sections.

2.4.1. Excitonic Motion

Exciton migration can be described as a random walk and, inthe limit of many steps, this can be described by a diffusionformalism. The form of the diffusion coefficient depends onthe size of the mean free path [140]. If the mean free pathis of the order of the nearest-neighbor intermolecular dis-tance, the exciton hops incoherently between molecules andis scattered at each molecule. The diffusion coefficient is thenexpressed in terms of the nearest-neighbor molecular spacingand exciton hopping time. If the mean free path is greaterthan the nearest-neighbor distance, the exciton moves coher-ently over several intermolecular spacings before being scat-tered and it is more appropriate to use an exciton bandmodel. The diffusion coefficient can then be expressed interms of free path and the exciton velocity. For singlet excitonmigration in typical organic solids at room temperature, theincoherent hopping model is generally thought to be appropri-ate. In ultrapure crystals at low temperatures, where neitherimpurities nor phonons are effective in limiting the excitonmean free path, it may be possible to detect some coherent




exciton motion [140,141]. The kinetic equation for excitondiffusion is given by

@nex

@t¼ GðtÞ � bexnex þDH2nex ð51Þ

where nex is the concentration of excitons generated at a rateG(t), bex is their monomolecular decay rate constant, and D isthe exciton diffusion coefficient which is assumed to be isotro-pic. The energy transfer steps are due to the excitation cap-ture rate by neighbor molecules of radius R. Its secondorder rate constant can be expressed as a time-dependent fluxthrough the spherical surface [142,143]

gD ¼ 4pDR2 @ns=@rð Þ R ¼ 4pDR 1þ R pDtð Þ�1=2h i ð52Þ

which is equivalent to the transfer rate

kDðtÞ ¼ gDN ¼ 4pDRN 1þ R pDtð Þ�1=2h i

ð53Þ

where N is the concentration of molecules. Equation (53)holds for a d-function excitation at t¼ 0 and a single energyacceptor molecule. The latter can be a dopant molecule. Then,R must be replaced by its radius RA, which, in general,differs from R, and N from the dopant concentration, NA. Theboundary condition nex(RA)¼ 0 and the choice of RA define thetrapping mechanism. Although from high-resolutiontime-dependent studies of sensitized fluorescence, a time-dependent rate kD(t) has been established [138,144], all theexperimental data for kD(t), within the limits of the timeresolution > 10 ps, can be explained on the basis of a time-independent energy transfer rate [137]. This suggests D >10�3 cm2=s, which, for typically Rffi 1 nm, makes the transi-ent term in Eq. (53) negligible relative to unity. If the scatter-ing length of an exciton l > R, Eq. (53) will not hold and atransfer rate constant can be considered proportional to sv,where v is the velocity of the exciton and s is the cross-sectionof capture

kD ¼ gDN ¼ svN ð54Þ




In the random walk description, the energy transfer rate con-stant is related to the number of hops made by the excitonwithout revisiting any site in its lifetime. The nearest-neigh-bor random walk in an isotropic medium may be approxi-mated by a random walk on a simple cubic lattice [145]

D ¼ ð1=6Þc2t�1h ð55Þ

where c is the lattice spacing and th is the mean time betweensteps of length c.

If an exciton hops about, starting from some initial siteand ends up at another site at the time of its disappearancefor one reason or another, the linear distance between thesesites is called the diffusion length, ld. The diffusion length isrelated to the diffusion coefficient D through the exciton life-time t:

ld ¼ffiffiffiffiffiffiffiffiffiffiZDtp

ð56Þ

where Z¼ 6 for three dimensions, 4 for strictly two-dimensional motion and 2 for one-dimensional diffusion [26].Reported values of D vary by a factor of about 2 because ofthe inconsistency existing in the literature concerning thevalues of Z; usually Z is taken to be unity. The diffusionlength of excitons can be determined experimentally fromthe luminescence surface quenching or excitonic carrier injec-tion experiments. For singlet excitons in anthracene,ldffi 40 nm and tffi 10 ns yield Dffi l2d=tffi 2 10�3 cm2 s [146].A similar value of ldffi 30 nm has been obtained for TPD[147] and ldffi 10–30 nm for Alq3 [16,148–150]. Taking theexperimental values of the intrinsic lifetime of singlet exci-tons ffi1 and ffi15 ns, respectively, allows to evaluate theirDffi 3.5 10�3 cm2=s for TPD, and Dffi 6 10�5 cm2=s forAlq3 solid films. The latter value is much lower than thosefor anthracene and TPD. This implies a long hopping timeas calculated from Eq. (55), identifying c with the averageintermolecular distance rffi 0.8 nm as estimated from themolecular density of Alq3 (Nffi 2 1021 cm�3). The hoppingtime and some other migration parameters for singlet andtriplet excitons in these important materials are compared




in Table 2. It is interesting to note that the total distance cov-ered by the exciton in the random walk, l¼ ( t= th) c, which bymany orders of magnitude exceeds the diffusion length incrystals, is mostly much shorter in amorphous solids as forexample in Alq3. The l =ld ratio can be a measure of the prob-ability to transfer energy to a structural and=or chemicalimperfection of the molecular system; the greater the ratiois the exciton visits more sites, the probability to encountera defect increases. Thus its large values for crystals makethem particularly well suited for excitonic energy transferto even small amounts of defects or intentionally incorporateddopants. From the definitions of l and ld, it follows that theirratio, l=ld¼ (6t =th)1=2, is determined by the ratio t= th whichcontains characteristics of individual molecules through theexciton lifetime (t), and intermolecular interactions throughthe energy transfer time th. In the strong coupling limitth¼ (�h =4jJj) [157,158], and is proportional to the third powerof the intermolecular separation (R) for dipole–dipole interac-tions, as mentioned already in the context of the exciton loca-lization concept (see Sec. 2.4). The weak coupling limit implies[159]

t�1h ¼

2prn�h

b2elx ð57Þ

where rn is the vibronic state density, x is the vibrationaloverlap (Franck-Condon factor), and bel is the electronic inter-action matrix between the excitonic initial and final states.The total interaction between a vibrationally unrelaxed low-est excited electronic state of a donor molecule (M�1) and anunexcited acceptor molecule (Ma) may be partitioned intoCoulombic and electron exchange terms [160]. The Coulombicinteraction can be expressed as a multipole–multipole expan-sion, the leading term of which is dipole–dipole. This termrepresents the interaction between Md!M�d and Ma!M�atransition dipole moments, ~mm1, ~mm2, yielding

bel �~mm1~mm2

r3ð58Þ




Table 2 Various Singlet and Triplet Exciton Migration Paramete rs in Some Organic Solids

Material

Intermoleculardistance a

c (nm)Exciton spinmultiplicity

Lifetimet (s)

Diffusionlengthld (nm)

DiffusioncoefficientD (cm 2=s)

Hoppingtime th (s)

Total distancecoveredl (nm) l =ld

Anthracene(crystal)

0.5 Singlet 10� 8 40 b 2 � 10 � 3 2 � 10 � 13 2.5 � 10 4 600Triplet 10� 2 10 4c 10 � 4 4.2 � 10 �13 1.2 � 10 10 1.2 � 10 6

Tetracene(crystal)

0.7 Singlet 2 � 10� 10 12 d 7.2 � 10 �3 1.1 � 10 �13 1.3 � 10 2 10Triplet 10� 5 300e 7.9 � 10 �5 6 � 10 � 11 1.2 � 10 5 400

TPD (film) 0.9 Singlet 10� 9 30 f 3.5 � 10 �3 4 � 10 � 13 2.3 � 10 3 80Alq3 (film) 0.8 Singlet 1.5 � 10 � 8 23 g 30h 6 � 10 � 5 1.8 � 10 �11 7 � 10 2 30

Triplet 2.5 � 10 � 5 14 i 8 � 10 � 8 1.3 � 10 �8 1.5 � 10 3 107

aCalculated from c ¼ (M=NA �r) 1= 3, where M is the molecular weight, NA is Avogadro’s number, and r is the mass density of the solid. Typi-cally, r¼ (1.2�1.5) g cm�3; r¼1.3 g cm�3 for Alq3

bFrom Ref. 146.cFrom Ref. 152.dFrom Ref. 153.eFrom Ref. 154.fFrom Ref. 147.gFrom Ref. 155.hFrom Ref. 150.iFrom Ref. 156.

72

Organ

icLigh

tEm

ittingDiodes


has been taken in this calculation (see Ref. 151).

Higher multipole–multipole interaction terms decrease athigher inverse powers of the intermolecular separation, butbecome important when the dipole–dipole interaction is sym-metry forbidden, e.g., in benzene where the octupole–octupoleinteraction is dominant [161]. The electron-exchange interac-tion requires overlap of the electronic wave functions of M�dand Ma, and it is therefore of short range (�1.5 nm). Due toan exponential decrease in the overlap of electronic wavefunctions with intersite distance, the energy transfer rate isexpected to decrease more rapidly and, in fact, it can be

t�1h ¼ t�1

tot exp g 1� r=r0ð Þ½ � ð59Þ

Here ttot is the lifetime of the energy donating molecule,g¼ 2r0=L, where a constant L (called the effective Bohrradius) falls in the 0.1–0.2 nm range, and r0 is defined by

t�1h ðr0Þ ¼ t�1

TOT ð60Þ

which means that at r¼ r0 the rate of energy transfer equalsthe rate of total (radiative and non-radiative) deactivation ofthe excited state.

The exchange term is usually dominant at close approachof M�d and Ma, and allows triplet exciton transfer to occur whenthe donor and acceptor transitions are spin-forbidden. There-fore, four energy transfer processes from a singlet (1M�d)excited molecule and triplet (3M�

d) excited molecule to anunexcited molecule in the singlet state (1Ma) are possible:

1M�d þ 1Ma ! 1Md þ 1M�a ð61aÞ

1M�d þ 1Ma ! 1Md þ 3M�a ð61bÞ

3M�d þ 1Ma ! 1Md þ 3M�a ð61cÞ

3M�d þ 1Ma ! 1Md þ 1M�a ð61dÞ

The latter is of particular importance for improving the ELefficiency by introduction of highly fluorescent molecules into




expressed as (see e.g., Ref. 162)

a poor emitter where triplet excitons are produced efficientlyin the bimolecular electron–hole recombination process[163,164].

2.4.2. Long-range Energy Transfer

Long-range energy transfer is defined by the very weak-coupling case of energy transfer as discussed at the beginningof Sec. 2.4. The excited states are well-localized and the inter-molecular coupling is very weak. This type of energy transferis referred to by several different names including quantummechanical resonance, inductive resonance or Forster–Dextertransfer [135,138]. The mathematical description of the long-range energy transfer was originally developed by Forster[134] for dipole–dipole interactions and later extended byDexter [160] to include exchange and higher multipole inter-actions, which may be important at small separations. Thelong-range energy transfer is the most important mechanismfor singlet excited states in a molecular system coupled bydipole–dipole interactions.

The rate constant of energy transfer between a donor andan acceptor separated by a distance r (isolated single D–Apair) and coupled by the dipole–dipole interaction of ran-domly oriented transition dipoles can be expressed as (see

kD--A ¼1

tR0

r

� �5

¼ 1

tD

R0

r

� �6

ð62Þ

where t is the observed lifetime of the excited state beingrelated to the radiative donor lifetime, tD, through the fluor-escence yield of the donor in the absence of the acceptor,jFL, t¼jFL�tD, and

R0 ¼ 3=4pð ÞZ

c=n0oð Þ4FD oð ÞsA oð Þdo� �1=6

ð63Þ

is a critical transfer distance at which the energy transferrate from D to A is equal to the radiative decay rate. Accor-ding to Eq. (62), R0 ¼ j1=6

FL R0 defines a characteristic




e.g., Ref. 26)

donor–acceptor distance at which transfer competes equallywith the total rate of removal of energy from D by any othermeans such as radiative or radiationless decay or hoppingaway (in the case of single component materials). Typicalvalues of R0 for organic systems are ffi3 nm. The critical dis-tance R0 (63) depends on the overlap integral between thenormalized fluorescence emission spectrum of the donor,FD(o), and absorption spectrum of the acceptor, hereexpressed by the normalized acceptor absorption cross-sec-tion, sA(o) in units cm2 [sA (cm2)¼ 3.82 10�21 E A (liter-molecm�1), where EA is the molar absorption coefficient]. The ointegration is over all (angular) frequencies. The index ofrefraction of the medium is n0, and c is the speed of light invacuum. Equations (62) and (63) demonstrate that no transferis possible unless the donor fluorescence and acceptor absorp-tion spectra overlap.

In the case of triplet energy transfer where electronexchange is the dominant interaction, Dexter has expressedthe transfer rate as

kD�A ¼ 2p=�hð Þ bDAj j2Z

FDðEÞFAðEÞdE ð64Þ

where bDA is the exchange energy interaction between mole-cules, E is the energy, FD(E) and FA(E) are, respectively,the normalized phosphorescence spectrum of the donor andnormalized absorption spectrum of the acceptor molecule.These spectra can be used if the radiative transitions givingrise to these spectra gain their singlet character by a spin-orbit coupling mechanism that is not vibrationally induced[165].

Many tests have been made of the validity of Forster–Dexter transfer in doped organic solids. A typical exampleis the classic solid solution study of anthracene and tetra-cene dissolved in naphthalene [26,166]. Energy originallyabsorbed by anthracene (donor) was shown to be transferredwith high efficiency to tetracene (acceptor) by measuring thetetracene fluorescence. In these studies, the anthracene:tetracene ratio was 1:1 and the mol fraction of the guests




was varied from 2 10�5 to 10�3. The experimental resultsdescribed in terms of the Forster non-radiative transfermechanism gave R0¼ 4.4 nm. The Forster triplet–singletenergy transfer appeared to be an important factor ofimproving the EL efficiency of organic light-emitting diodes[167]. In the course of electron–hole recombination process,usually, much more triplets than singlets are created (seeSec. 1.4). The triplets as a rule are lost for the optical outputbecause their radiative decay is spin-symmetry forbidden. Togain them over to the luminous performance of the ELdevice, the transfer of their energy to a phosphorescentmolecule is required (process (61c) in Sec. 2.4.1). A furtherimprovement of the EL quantum efficiency could be reachedif an effective triplet–singlet energy transfer from this phos-phorescent molecule to another-highly fluorescent moleculewere possible. Such a process has been observed with arange of phosphorescent donors and fluorescent acceptorsin transparent rigid media at 77 or 90 K. Large transfer dis-tances have been found; for example with triphenylamine asthe donor and chrysoidine as the acceptor, the interactionrange is 5.2 nm [168]. However, incorporating directly afluorescent acceptor into a phosphorescent donor materialeliminates the long-range triplet–singlet energy transferbecause due to the close proximity of the donor and acceptormolecules, increases the likelihood of the short-range Dextertransfer between the donor and acceptor triplets. So pro-duced triplets of the fluorescent material are lost for theemission because of their extremely inefficient radiativedecay. To avoid these losses, the phosphorescent donor andfluorescent acceptor must be doped into a conductive matrixenabling the generation of its molecular excited states byelectron–hole recombination. The phosphor then sensitizesthe energy transfer from the matrix to the fluorescent accep-tor, the whole process forms an energy transfer cascade.Cascade Forster energy transfer has been demonstrated forfluorescent materials [121]. A combined version triplet–tri-plet and triplet–singlet energy transfer cascade is shown inFig. 31. The overall quantum efficiency from such a phos-phor sensitized system depends on the efficiency of Forster




energy transfer from the phosphorescent donor [here PtOEPor Ir (ppy)] to the fluorescent acceptor (here DCM2)

ZDA ¼kDA

kDA þ kr þ knrð65Þ

where kr and knr are the radiative and non-radiative decayrates of the phosphorescent (donor) molecule. For highlyphosphorescent molecules (kr�knr) the energy transfer rate(kDA) can be an efficient process, and with kDA > kr and ahighly fluorescent dopant, the EL efficiency of the systemwill exceed that with the phosphorescent dopant solely.Wherever, the phosphorescence efficiency (jPH) of the sensi-tizer is higher or even comparable with the fluorescence effi-ciency of the doped dye (jFL), the emission will be dominated

Figure 31 Emission from an organic phosphorescent (hnph) orsensitized fluorescent (hnfl) LED, utilizing triplet–triplet andtriplet–singlet energy transfer. Three times more non-emittingtriplets are created in the host emitter material (Alq3). They arerecovered for the emission through the triplet–triplet energy trans-fer to PtOEP or Ir(ppy)3, and=or through triplet–singlet energytransfer to DCM2. For further explanations, see text.




by the radiation from the phosphorescent molecules (seeexamples in Sec. 5.4).

2.4.3. Effect of Disorder

disorder [38]. While in the regular molecular structure, theexciton hopping frequency is time independent, there appearsto be a distribution of event times of the form f(t)� t�(1þ b) in adisordered material. The exciton motion is slowed down astime proceeds, energy transfer becomes a dispersive process.It can be described in terms of the continuous time randomwalk concept applied successfully to treat hopping across aspatially random array of iso-energetic hopping sites (off-diagonal disorder) [32,169]. The degree of dispersion isexpressed in terms of the dispersion parameter related to bothdensity of hopping sites and wave function overlap. If hopsare thermally activated from traps exponentially distributedin energy b¼ T= Tc, where Tc is the trap distribution para-meter [170], for site energies distributed in energy accordingto a Gaussian function characterized by the distributionwidth s, the variation of the dispersion parameter with thewidth s can be approximated by Eq. (9). For hopping acrossan array of discrete energy levels b¼ 1, for large dispersion,b approaches zero. The time evolving hopping time impliesthe time-dependent diffusion coefficient of exciton as it doesin the case of the carrier transport [see Eq. (8)]. The equiva-lence of description of disorder affected carrier hopping andhopping of triplets [see Eq. (59)] seems to be quite obvioussince both are determined by exchange interactions resultingin an exponential distance dependence of the coupling matrixelement. The question arises as to whether it can be applied totransport of singlet excitons. In this case, energy transferoccurs via dipole coupling, the rate for an individual jumpfrom a donor site to an acceptor site is given by Eq. (62).The average time required for a single transfer step becomesth¼ k�1

DA¼ tD[hri= r0]6, where hri is the average hopping dis-tance [138]. Thus, the singlet exciton can be considered as a




Like charge carrier transport in molecular solids (cf. Secs. 1.3and 4.6), the energy migration can be impeded by structural

quasi-particle hopping between molecular sites distributedrandomly in space and energy. A measure of its migrationability is the total distance covered during the lifetime. Basedon simulations of transport of an elementary excitation acrossan array of hopping sites with diagonal disorder [171], thetotal distance covered by a singlet exciton ( ldis) during itslifetime (ts) can be expressed using the dispersion parameter,b, as

ldis ¼hrib

ts

th

� �b

¼ 1

bts

th

� �b�1

l ð66Þ

where l is the total distance covered by the exciton in a disor-der-free medium, realizing a non-dispersive motion.

Taking as an example of disordered solids evaporatedfilms of Alq3 and assuming sffi 0.1 eV typical for organicglasses [29], yield bffi 0.5 [see Eq. (9)] and ldisffi 0.23 l followsfrom Eq. (66). If the data in Table 2 represent dispersivetransport of singlet excitons in Alq3, ldis¼ 700 nm, and theirmigration distance in the disorder-free solid Alq3, as extractedfrom Eq. (66), would be lffi 3 103 nm, that is a factor of 4longer than that in real disordered samples. This correspondsto the reduced hopping time thffi 4 10�12 s or, in other words,the presence of the diagonal disorder with s¼ 0.1 eV elongatesthe hopping time by a factor of 4.5. For larger values of b (lessdisordered systems), as found from the fluorescence studiesfor 9,10-diphenylanthracene b¼ 0.7 (Ref. 172) and for polyvi-nylcarbazole (PVK) b¼ 0.77 (Refs. 38 and 173), l would appearto be significantly shorter (lffi 153 nm and lffi 125 nm, respec-tively) and the disorder-induced increase in the hopping timeroughly doubled. It is understood that a reduction in the aver-age hopping distance to only one intermolecular spacingbreaks the condition for the very weak approximation, mak-ing the resonance energy between a molecular pair (J) higherthan the critical limit Jcritffi 15 cm�1, we pass to the weakcoupling case characterized by the nearest-neighbor excitonrandom walk that is to the short-range energy transfer

disorder. For example, the ldis=lffi 3 10�4, corresponding to




mechanism (cf. early stage of Sec. 2.4). It is still affected by

sffi 0.1 eV, can be deduced from chemiluminescent experi-ments for triplets in PVK films [174]. In applying the simula-tion approach (66) to the disorder effects on energy transfer,some complications could arise from neglecting structuraland chemical traps as well as from ignoring cluster formation.For example, the above mentioned very small ldis =l ratio maybe due to defect sites as the disorder effect on triplet motioninferred otherwise from a difference between the triplet diffu-sion coefficient ( DT) in disordered films and single tetracenecrystal falls within an order of magnitude only. The valueDTffi 2 10�4 cm2=s found for the films [175] falls betweenDc0

T ffi 8 10�5 cm2=s for the triplet exciton motion alongthe crystallographic direction c0 (Ref. 154) and Dab

T ffi4 10�3 cm2=s for the exciton moving within the crystal (ab)plane [176]. Formation of clusters eliminates, at least partly,the randomness of the system, that would formally appear ina reduced value of s.

2.5. EXCITONIC INTERACTIONS

The mobility of excited states, imposed by intermolecularinteractions (see Sec. 2.4), can lead to their collision with eachother and=or with other types of excited states as well astrapped or free carriers generated in an organic solid. Suchcollision processes, realizing various excitonic interactions,may result in annihilation of the excitons and=or their trans-formation into another set of particles and quasi-particles. Asdifferent types of excitonic interactions show up in differentoptical and electrical phenomena, we divide them into twocategories corresponding to the interaction between quasi-particles (exciton–exciton interactions) and to the interactionbetween quasi-particles and particles (exciton–charge carrierinteractions).

2.5.1 Exciton–exciton Interactions

2.5.1.1 Singlet–singlet Interactions

The singlet–singlet collision process is often referred to assinglet exciton fusion. The end result of such a fusion reaction




is the production of a highly excited (hot) singlet state (S�n)which can autoionize forming charge carriers (e, h), relax toa vibrationally relaxed emitting singlet state (S1) or fissioninto two triplet excitons:

Experimentally this process can be observed as a quadraticlight intensity dependent photoconduction [177–180] andexternal photoemission of electrons [181–183] or fluorescencequenching [148,155,184–186].

This kinetic analysis of the singlet exciton fusion processis provided by the equation

dS1

dt¼ aIðx; tÞ � S1

tS� gSSS

21 ð68Þ

where tS is the singlet exciton lifetime including radiative andall non-radiative decay pathways except for singlet–singletannihilation, and gSS is the second order rate constant ofthe annihilation process. The exciting light quantal intensityI(x,t) (ph=cm2 s) is a function of time (t) and is assumed topenetrate a flat sample perpendicular (x) to its parallel planesat a depth xa¼ la¼ a�1 determined by its linear absorptioncoefficient a defined by the absorption exponential lawI(t)¼ I(t,x¼ 0) exp(�ax).

At low excitation intensities, the quadratic term in (68)can be neglected, and the PL efficiency

jð0ÞPL ¼ jð0ÞFL ffi tS=tr ð69Þ

given by the ratio of the measured (tS) and radiative (tr) life-times of singlets is a characteristic material parameter inde-pendent of excitation intensity. On the other extreme, at




high excitation intensities, the exciton annihilation domi-nates the singlet exciton lifetime, and

jFL ffijð0ÞFL

tS

ffiffiffiffiffiffiffiffiffiffiffiffiagSS I

p ð70Þ

becomes a decreasing function of light intensity. Therefore, adouble logarithmic plot of jFL = j

ð0ÞFL against I will give

a straight line of slope (�1 =2) in which the intercept atjFL ¼ j

ð0ÞFL yields gSS ffi 1= a Icr t2

S. Icr is the critical excitationintensity, where the exciton kinetics changes from first to sec-ond order. Some examples are shown in Fig. 32. It may beseen that the intercept point moves towards high intensitieswhen passing from anthracene through quasi-amorphousAlq3 to pyrene crystals. The physical meaning of this observa-tion is that the critical concentration of singlets required toswitch their mono-molecular decay to a decay dictated bythe annihilation increases in this material sequence. Theannihilation rate constant decreases accordingly:gSSffi 1 10�8 cm3=s for anthracene, gSSffi 1 10�10 cm3=s forAlq3, and gSSffi 5 10�15 cm3=s for pyrene determined fromrespective values of Icr, show a monotonic degression in theexciton annihilation ability.

The theory of isotropic three-dimensional diffusionallows gSS to be expressed by a product of the exciton diffusioncoefficient DS and the effective annihilation capture radius RS

[189],

gSS ¼ 8 pDS RS ð71Þ

where

RS ¼ rcf ðz0Þ ð72Þ

is an increasing function of the ratio of the hopping ratebetween nearest neighbor sites [t�1

h in (55)] and the donoracceptor rate constant (62)

z0 ffi1

tS

R0

rc

� ��6DS

r2c

� �� 1=2

ð73Þ




The rc represents the capture radius determined by the accep-tor sink efficiency:

rcd S

d r

r¼rc

¼ x SðrcÞ ð74Þ

where the factor x is a measure of the concentration (S)gradient of singlet excited states at r¼ rc; x!0 means

Figur e 32 Relative fluorescence quantum efficiency jFL =jFL(0) as a

3

evaporated on four different material substrates as specified right by

imation behavior according to Eq. (70) implying the log–log plots to bestraight lines with the slope (�1=2). Their intersections (Icr) with thejFL=j

ð0ÞFL ¼ 1 line enable the calculation of the annihilation rate

constant gSS. The values of the gSS for these samples are given in thetext. They were calculated using relevant absorption coefficients (a)and low-intensity determined singlet exciton lifetime, tS. For anthra-cene, a¼ 5 104 cm�1 [187], tS¼ 10 ns [139]; for pyrene,a¼ 1.2 104 cm�1 (at lexc¼ 350 nm) [188], tS¼ 112 ns [184]; for Alq3,a¼ 4 104 cm�1 (at lexc¼ 351, 353 nm) [155], tS¼ 15 ns [148].




function of quantal excitation intensity I for anthracene (see Ref. 184a)and pyrene crystals (see Ref. 184), and quasi-amorphous film of Alq

the curve (see Ref. 155). Dashed lines show the high-intensity approx-

the diffusion flux to an occupied center equals 0, they can bequenched only by a long-range energy transfer process with arate given by Eq. (62).

For z0�1

gSS ¼ 4 p Gð3=4Þ=Gð5=4Þ½ �D3=4S R

3 =20 =t1=4

S ð75Þ

where G(v) is the gamma function. According to Eq. (75), thefusion of excitons is governed by their motion reflected in thediffusion coefficient DS. This case is called diffusion approxi-mation which breaks down as DS increases. Increasing DS

leads to decreasing z0 and RS. At RSffi rc, the condition forthe diffusion approximation would no loger be valid, and forz0�1

gSS ffi 4p =3 tSð Þ R60 =r

3c

� �ð76Þ

i.e., gSS does not depend on DS, defining the capture-controlledannihilation limit.

The transition region from (75) to (76) is defined byRS¼ rAD¼ c or in terms of a diffusion length [190],

ld ¼ffiffiffiffiffiffiffiffiffiffiffiDStS

pffi 0:7R0 R0=rDAð Þ2 ð77Þ

For anthracene crystal, with ldffi 40 nm and rDA¼ 0.5 nm(see Table 2), this condition requires R0ffi 2.5 nm, the valuein good agreement with R0ffi 2.8 nm obtained from indepen-dent data on singlet exciton energy transfer to tetracenemolecules embedded into the anthracene crystal matrix[138]. The agreement suggests both diffusion and collisioncross-section to contribute comparably to the singlet–singletannihilation process in anthracene crystal. Indeed, rc calcu-lated from Eq. (76), representing the capture-controlledlimit, gives unreasonably small value ffi0.2 nm. The formalinteraction radius RS in (71) should here be considered asa sum [190],

RS ffi rDA þ R�S ð78Þ

where

R�S ffi 0:7 R60=tSDS

� �1=4 ð79Þ




which is a function of the diffusion coefficient DS as well asthe long-range energy transfer parameter R0. Solving Eqs.(71), (78) and (79) for anthracene with the above deter-mined gSS, R0 and tSffi 10 ns allow the real diffusion coeffi-cient of singlet excitons to be calculated. Its rough valueis DSffi 10�5 cm2=s.

The diffusion approximation is often used to describeexcitonic motion in single component organic solids. The reso-nance energy of a molecular pair, dominated by a dipole–dipole nearest-neighbor interactions, reduces the hoppingrate between sites separated by two or more intermolecularspacings (r 2rDA) to less than 1% of that for hops betweennearest-neighbor molecules (rffi rDA), and the exciton motionis treated in the weak-coupling limit. Then the singlet–singletannihilation rate constant allows direct calculation ofDSffi gSS=8 p rDA. Such a treatment gives DSffi 1 10�2 cm2=sfor anthracene, DSffi 3 10�9 cm2=s for pyrene, andDSffi 6 10�5 cm2=s for Alq3. The big difference between DS

for anthracene and pyrene crystals has been attributed tothe difference in the nature of excitons: whereas in anthra-cene singlet excitons are assumed to be single moleculeexcited states, in pyrene, the energy transfer is due to themuch less mobile excimers [184]. An example with anthra-cene shows that an apriori assumption that the exciton migra-tion is diffusion-limited ( RS¼ rDA) leads to a largelyoverestimated value DS. In conclusion, for the interpretationof the measured singlet–singlet annihilation rate constants,both diffusion and long-range energy transfer should be takeninto consideration as for many molecular systems the ratio z0

(73) is close to unity, and a combined diffusion and Forsterenergy transfer theory applies.

The relatively low values of gSS and DS in quasi-amorphous solids might be underlain by disorder (see Sec.2.4.3) and=or a contribution of triplet excitons in quenching

cient of triplets is expected to be lower than of singlets sinceboth energy donor and acceptor transitions are disallowed.A low value of gSS has been found for the triplet–tripletannihilation rate constant from biexcitonic quenching




of fluorescent singlets (cf. Sec. 2.5.1.2). The diffusion coeffi-

experiments, gTTffi (3 � 1)10�14 cm3=s (Ref. 167) in 8%PtOEP:CPB molecular system [CPB stands for the (4,40-N,N0-dicarbazole-biphenyl) compound; for the molecular

of singlet exciton quenching by singlet–triplet interaction hasbeen presented based on the excitation intensity dependenceof the time resolved relative fluorescence yield in crystallineanthracene [185] and will be discussed in some detail inSec. 2.5.1.3.

2.5.1.2. Triplet–triplet Interaction, Singlet ExcitonFission

Colliding triplet excitons are said to undergo triplet–tripletfusion. If they belong to the same species, the process is calledhomofusion. The collision of triplets belonging to differentspecies is called heterofusion. The final products of the tri-plet–triplet interaction process are preceded by intermediatecomplex pair states:

K1 is the rate of encounter of two triplets to form theintermediate triplet–triplet complex [T1��T1

0], KðSÞ2 and K

ðTÞ2

are the dissociation rates of the complex into a pair of




structure of PtOEP, see Fig. 31] (cf. Sec. 2.5.1.2). The evidence

uncorrelated species (singlets and triplet–singlet, respec-tively), and K�1 is the dissociation rate of the complex into apair of uncorrelated triplets. gðSÞTT and gðTÞTT are the overall sec-ond order rate constants for the creation of singlet (80) andtriplet (81) final states. If the energy of the final states andtheir lifetimes are appropriate, the complex state and twoinitial triplets can be restored with a rate K�2 followed byK�1 (the overall rate constant g0S). This process is the inverseof triplet exciton fusion and is called fission of the localizedexcited state into two triplets. Thermodynamic considerationsof the process imply the fission (g0S) and fusion [gðSÞTT] rate con-stants to obey the relation [191]

g0S=gðSÞTT ¼ 9 exp½�ð2ET � ESÞ=kT� ð82Þ

where 2ET (or ETþET0) is the sum of the energy of triplet exci-tons (identical or different excited species), ES is the energy ofa singlet exciton.� The fission of the T�n state, though energe-tically feasible, practically does not occur due to its fastrelaxation to the lowest triplet excited state T1.

The Hamiltonian of the intermediate complex [T1��T10] of

triplets is, in general, a function of intermolecular distance,the mutual orientation of the two molecules, and the spin. Thetotal intermolecular interaction is separated into two parts.One is the dipolar spin–spin interaction, which is smaller inmagnitude than the intra-molecular interactions between mag-netic moments of electrons. The other term is the electrostatic,intermolecular interaction which, like the former, depends onthe geometry of the complex, intermolecular distance and thetotal spin. The intermolecular interaction may be of an exchangeand=or charge-transfer nature. Nine possible collision complexstates, designated by l¼ 1,2, . . . ,9 are possible, whose wavefunctions are eigenstates of Hamiltonian, and may be written as

ci ¼ jSClSjSi þ jTC

lTjTi þ jQC

lQjQi ð83Þ

� The pre-exponential factor depends on the definition of g and can amount9=2 if in the triplet–triplet annihilation pathway for decay of tripletexcitons a factor of 1=2 is introduced [192].




where j designates the orbital part of the wave functions, andjSi, jTi and jQi the spin parts. The coefficients Cl

S, ClT and Cl

Qare the spin amplitudes of the singlet, triplet, and quintet inthe pair state, and they satisfy the closure relationships

X9

l¼1

ClS

2¼ 1;X9

l¼1

ClT

2¼ 3 andX9

l¼1

ClQ

2¼ 5 ð84Þ

Quintet states on a single molecule require the simultaneousexcitation of two electrons and are, therefore, energetically inac-cessible (at least in aromatics in the solid phase). This is the rea-son for which the quintet states in the final products of reactions(80) and (81) have been omitted. Any of the nine pair states isformed with equal probability since the individual triplet exci-tons are in thermal equilibrium. Thus the rate of formation ofeach of the nine l states is (1=9) K1, and K

ðSÞ2 Cl

S

2, and

KðTÞ2 Cl

T

2 are the rate transitions to energetically accessible finalsinglet and triplet states, respectively. The fraction

KðSÞ2 Cl

S

2= K�1 þ ClS

2KðSÞ2

� is just the probability of the lth pair

state giving rise to a singlet. Thus, weighted average over all pos-sible pair states yields the desired expression for gðSÞTT,

gðSÞTT ¼1

9K1

X9

l¼1

2S ClS

21þ 2S Cl

S

2 ð85Þ

and for gðTÞTT ,

gðTÞTT ¼1

9K1

X9

l¼1

2T ClT

21þ 2T Cl

T

2 ð86Þ

where 2 and 20 stand for the branching ratios

2S¼ KðSÞ2 =K�1 and 2T¼ K

ðTÞ2 =K�1 ð87Þ

Similar considerations for the stationary state imply the fissionrate constant

g0S ¼X9

l¼1

K�2 ClS

21þ 2 Cl

S

2; ð88Þ




where K�2 C lS

2 represents the rate of formation of the lthtriplet pair state from the singlet manifold. The absence ofthe 1=9 factor in (88) as compared to the stationary stateequation for gðSÞTT occurs because there is only one initial

state, for each state C lS 2

the dissociation rate K�1 is low as compared with KðSÞ2

and KðTÞ2 , 2s, 2r�1, and gðSÞTT¼g

ðTÞTTffi 1/3, the fusion of triplets

is governed solely by their collision probability. This is the

case often assumed in the kinetics of triplet excitons inorganic LEDs.

Since the transition from initial to final singlet states isspin-conserving, it has been postulated that gðSÞTT is larger thegreater the number of pair states with singlet character,i.e., the greater the number of terms in (85) with C lS 6¼ 0[193]. The effect of an external magnetic field on gðSÞTT (thuson gS) may be understood on this basis (see Sec. 2.5.3.1).

Experimentally, the triplet exciton fusion shows up inthe delayed fluorescence, and singlet exciton fission in alow strongly temperature-dependent fluorescence efficiency.The study, under spatially uniform excitation, of the phaseof the first harmonic of delayed fluorescence as a function ofthe intensity of the rectangular waveform exciting light I0(t)allows to determine the product agðTOTÞ

TT for a material,where a is the absorption coefficient of the exciting light.To get an uniform distribution of the excited triplets, theexciting photons with energy (hnex) smaller than the firstexcited singlet energy ðES1

Þ can be used. Then, triplet exci-tons are produced by the weak direct S0!T1 transitionsreflected in a low absorption coefficient a¼ aT. When diffu-sion effects can be neglected, the rate equation for tripletexciton concentration (T) can be written as

dT

dt¼ aTI0ðtÞ � T=tT � gðTOTÞ

TT T2 ð89Þ

with tT standing for the effective triplet exciton lifetimedetermined by all monomolecular decay pathways, andgðTOTÞ

TT accounting for all triplet–triplet annihilation channels,which, when governed by the triplet collision frequency, give




¼ 1=3 [cf. relationships (84)]. If

gðTOTÞTT ffi 3 gðSÞTT. Delayed fluorescence photon flux per unit

volume of the material is defined by

FðtÞ ¼ jr gðSÞTT T

2 ð90Þ

where jr is the radiative decay efficiency of the created singletexcitons. Under a square-wave excitation of angular fre-quency o, the phase shift y of the first harmonic of delayedfluorescence waveform can be approximated by [194]

tan y ¼ o

½ t�1T þ aT tT g

ðTOTÞTT I0�

ð91Þ

Thus, the inverse of tan y vs. I0 is expected to give a straightline with the product of its slope and intercept yieldingaT� gðTOTÞ

TT . Figure 33 shows some examples, anthracene, andpyrene single crystals. The straight line intercepts withthe axis of ordinates at I0¼ 0 give tTffi 21 ms for anthraceneand tTffi 7 ms for pyrene crystal. Deduced value of aT g

ðTOTÞTT

allows to calculate gðTOTÞTT ¼ 5 10�11 cm3s�1 for anthracene,

assuming aT¼ 2.7 10�4 cm�1 in good agreement with thevalue obtained previously from the excitation spectrum ofanthracene [195]. gðTOTÞ

TT ¼ 7.5 10�12 cm3s�1 has been evalu-ated employing the ratio of steady-state fluorescence signals ofpyrene to that of anthracene at low excitation intensity with-out knowledge of aT. As expected, gTT� gSS for anthracene, butthe opposite relation holds for pyrene crystal (see Sec. 2.5.1.1).This striking difference can be explained by the different nat-ure of singlet and triplet excited states in crystalline pyrene.In contrast to singlets, which were shown to be excimeric innature, the triplet state in crystalline pyrene appears to be amonomeric localized excited state as comes from the mirrorsymmetry between phosphorescence and S0!T1 absorptionspectrum [196]. Thus, the triplet exciton in pyrene crystalshould behave like triplet molecular excitons in other aro-matic crystals which do not have a dimeric structure. Indeedthe gðTOTÞ

TT for pyrene and anthracene differ by a factor of 2only, the difference to be associated with a lower triplet exci-ton mobility in pyrene, such a difference may be expected onthe basis of the much smaller Davydov splitting [197] as




compared with that for anthracene [198] or possibly non-localscattering being the predominant mechanism for triplet exci-ton transport in pyrene crystals [199].

The singlet exciton fission [g0S in Eq. (80)] is a processreducing the concentration of singlet excitons, thus, it shouldshow up in a low fluorescence efficiency of a material. Accord-ing to Eq. (82) the materials with 2ET less or comparable withES are expected to reveal an efficient fission process. Suchrelations hold for example in solid pentacene (ES1

ffi 1.9 eV,

Figure 33 Experimental data of the phase shift y of the delayedfluorescence with respect to the square-wave excitation as a func-tion of the quantal exciting light intensity, plotted in the(tan y)�1–I0 scale (squares, triangles) to compare with Eq. (91) (solidlines) reflecting triplet kinetics expressed by Eq. (89). Wavelengthof the excitation l¼ 514.5 nm (2.41 eV), angular chopping frequencyo¼ 157.0 s�1. The data are taken for (ab)-cleaved pyrene andanthracene single crystals excited with light polarized along thea crystallographic axes. The overall triplet–triplet annihilationrate constants gðTOTÞ

TT are deduced from the slope-ordinate intersec-tion products of the straight-line plots. The data adapted fromRef. 194.




ET1ffi 0.9 eV), tetracene (ES1

ffi 2.37 eV, ET1ffi 1.27 eV) and

rubrene ( ES1ffi 2.33 eV, ET1

ffi 1.2 eV), and their fluorescencequantum yield is known to be very low at room temperature,strongly increasing as temperature decreases. Examples areshown in Fig. 34. In the case of neat tetracene and rubrene,the fluorescence efficiency increases as the temperature islowered because of the suppression of the thermally activatedsinglet exciton fission channel [cf. g0S

Using the temperature dependence of the fission rate[26,200,203],

kf ¼ k0 expð� DE = kTÞ ð92Þ

Figur e 34 The relative fluorescence intensity plotted as a func-




tion of temperature, for crystalline tetracene (see Ref. 200), rubrene

emission component as shown in the inset) (see Ref. 202).(see Ref. 201) and tetracene doped with pentacene green and red

in (80) and (82)].

where k0¼ kf at T!1 (or DE¼ 0), the prompt fluorescenceintensity can be expressed as

FEL ¼ ISkr

kS þ k0 expð�DE=kTÞ ð93Þ

where IS is the excitation rate per unit area, kS is the sum ofthe rate constants for all decay channels including radiativedecay (kr) for S1 but exclusive of singlet fission. The latter iscontained in the last term of the denominator of Eq. (93). Thisterm dominates in the high-temperature region, where theArrhenius plot log[FFL(T)=FFL(293 K)] vs. (103=T) allows DEto be determined. DEffi 0.16 eV for tetracene [200], andDEffi 0.07 eV for rubrene [201] are consistent with the predic-tions (2ET1

�ES1) based on the first triplet and singlet energy

levels (ET1, ES1

). A tendency to saturation of the fluorescenceefficiency at low temperatures indicates suppression of theexciton fission and practically temperature-independent rates(kS) of other decay channels of S1. From the fit of (93) and themagnetic field-induced enhancement of the fluorescence in theentire temperature range applied, k0ffi 0.5 1012 s�1, andg0S(1)¼ k0=Sffi 1.5 10�10 cm3 s�1 follow with the molecularconcentration of tetracene S0¼ 3.4 1021 cm�3 [200]. It givesg0S(293 K)¼ g0S(1) exp(�DE=kT)ffi 2 10�13 cm3 s�1 in goodagreement with the value 1.5 10�13 cm3 s�1 obtained byGroff et al. [192] and kfffi 109 s�1 comparable with the appar-ent decay rate t�1

S ffi 3 109 s�1 of tetracene singlet excitons[204]. The radiative rate constant is much lower and can beestimated from the absolute quantum fluorescence efficiencyjPL¼ kr=ktotffi tS=trffi 0.002 at room temperature [205]. Ityields krffi 2 106 s�1 with ktotffi kf. A rather large scatter inthe literature data on g0S is noted due to its critical dependenceon DE¼ 2ET�ES. For example, the value g0S¼ 1.510�12 cm3 s�1 have been obtained with DEffi 0.2 eV andkf¼ 5 109 s�1, the latter based on the fluorescence efficiencyratio at 77 and 300 K, varying strongly with different crystalsamples [203]. This certainly affects the value of g0S as calcu-lated from the relationship (82). It gives g0Sffi 7 10�12 cm3 s�1

with DE¼ 0.16 eV, and g0Sffi 10�12 cm3 s�1 with DE¼ 0.2 eV,




using the gðSÞTT¼ 4.8 10�10 cm3 s�1 [203]. These values become

even higher if gðSÞTTffi 7 10�10 cm3 s�1 is used [206] (see alsoSec. 2.5.1.3). If the encounter limit for triplet–triplet interac-

tion is assumed, gðTOTÞTT ffi 3 gðSÞTT with the above literature data

for gðSÞTT, the values of gðTOTÞTT for tetracene range between 10�9

and 2 10�9 cm3s�1 that is they are about two orders of mag-nitude larger than in anthracene, and three orders of magni-tude larger than in pyrene (see Fig. 33). However,gðTOTÞ

TT ffi 5 10�11 cm3s�1, identical with that for anthracene,is obtained, using gðSÞTT following from the relationship (82)and the above estimated g0S(1) . Interestingly, the tempera-ture decrease of the fluorescence intensity for the green(tetracene host) emission component is much weaker thanthat for the red (pentacene guest) emission component inpentacene-doped tetracene crystal. This is a signature of thepentacene singlet hetero-fission, that is the fission of excitedsinglets of pentacene into one triplet of tetracene and anotherone of pentacene molecules [206a]. In a pentacene-doped tetra-cene crystal with a low concentration of pentacene (here<100 ppm), the exciting light of wavelength 405 nm is com-pletely absorbed by the host molecules. Singlet energy trans-fer in the host lattice produces the excited guest pentacenemolecules. A kinetic scheme taking into account the abovedifference in the excitation modes of tetracene and pentacenesinglet excited states yields the host fluorescence intensityFFL(green) as

FFLðgreenÞ ¼

ISkrg

kSg þ gtrS0ðpentÞ þ gð1ÞS S0ðtetrÞ expð�DE=kTÞð94Þ

and the guest fluorescence intensity FEL(red) as

FFLðredÞ ¼

ISkrrgtrS0ðpentÞ

kSr þ g0ð1ÞHF S0ðpentÞ expð�DEHF=kTÞFFLðgreenÞ

ð95Þ




Here gtr¼ kD–A= S0(pent) is a bimolecular rate constant forenergy transfer from the host donor (D) to the guest acceptor(A) molecule populated with S0(tetr)¼ 3.4 1021 cm�3 andS0(pent) (here about 1017 cm�3), respectively. The radiativeand total decay rates for the host are krg, ksg, and for the questkrr, ksr. The thermally activated homofission process of hostmolecules ( g0S) and heterofission process of quest molecules( g0HF) are separated from other non-radiative singlet excitondecay channels. Since both the molecular and crystal struc-tures of tetracene and pentacene are similar, the guestmolecules are expected to enter the tetracene lattice substitu-tionally. Since there are two inequivalent orientations of mole-cules in the tetracene crystal lattice [207], two inequivalentpositions of the pentacene molecule can assume in the crystalelementary cell. The two activation energies for the heterofis-sion will correspond to these two different crystallographicsites, DEHF(I) and DEHF(II). Assuming, the red component tobe a simple sum of the contributions from both sites with g0HFfrom sites I and II, and taking into account that gtr is also tem-perature-dependent, gtr¼ gtr(1) exp(�DEtr = kT), Eqs. (94) and(95) can be fitted to the experimental results of Fig. 34 (‘‘red’’and ‘‘green’’ curves) with DEIffi 0.13 eV, DEII¼ 0.06 eV andDEtr¼ 0.18 eV [208]. The difference in the activation energiesas compared with that for homofission in neat tetracenereflects the difference in energies of singlets and tripletsand may also indicate either some local distorsion of thelattice, and=or non-substitutional entry of pentacene intotetracene lattice. The origin of the activation energy, DEtr,is unclear but could arise from the lattice distortions(shallow traps) and=or electronic polarization energy with asmall lattice relaxation contribution. Based on low-tempera-ture singlet exciton lifetime measurements, t�1(tetr)¼ g0SS0(tetr)þ kSg, and t�1(pent)¼ g0HF S0(pent)þ kSr, g0S(1)¼2 10�9 cm3 s�1 and g0HF(1)¼ 4.7 10�10 cm3 s�1 have beeninferred [208]. The inferred heterofission rate constantg0S(1) is smaller than g0S(1) deduced above for neattetracene and for the tetracene singlet fission in penta-cene-doped tetracene. This would suggest a larger singletcomponent of the triplet pair state [T1��T1

0] in the case of




homofission than in the case of heterofission. On the basisof the magnetic field-dependent fluorescence measurements,it has also been demonstrated that tetracene triplet–penta-cene triplet interaction (triplet–triplet heterofusion) takesplace in pentacene-doped tetracene crystals [209] (see alsoSec. 2.5.3.1). The anthracene host–tetracene quest triplet–triplet heterofusion follows from the time evolution of thedelayed fluorescence and its magnetic field dependence intetracene-doped anthracene crystals [210,211] (see alsoSec. 2.5.3.1).

It should be kept in mind that guest molecules can pro-vide additional recombination centers in the case of electrolu-minescence. For example, tetracene added to anthraceneintroduces electron and hole traps at depths 0.2 and0.42 eV, respectively, with holes being more effectively cap-tured at the guest sites. Thus, the trapped hole can capturea mobile electron, forming a tetracene molecular singlet ortriplet excited state. This contributes to the tetracene guestemission in addition to tetracene singlets excited by energytransfer from singlet excitons of anthracene [210,212]. Someother examples are described in Sec. 5.2.

The coexistence of thermally induced singlet excitonfission and triplet–triplet fusion can only be observed iftemperature is high enough to activate the fission processover the energy barrier resulting from the difference(2ET�ES) for vibrationally relaxed triplet (ET) and singlet(ES) excited states. At low temperatures, where the ther-mally activated fission process is suppressed, fission from‘‘hot’’ exciton level S1

� should be observable by monitoringthe relative fluorescence quantum efficiency as a functionof excitation wavelength. Even though the lifetime S�1 isonly 10�13–10�12 s, this process is feasible and has beenreported as a sharp 8% fluorescence intensity drop athc=lf ffi 2.5 eV (lf ffi 496 nm) for tetracene with 2ETffi 2.4 eV[153], and as a small magnetic field effects (ffiþ0.5%) onthe prompt fluorescence of anthracene crystals excited withphotons above hc=lf¼ 4 eV in energy (lf � 310 nm), where2ET ffi 3.66 eV [213]. The optically induced fission, that isthe fission of hot singlet excitons, S1

�, is not as effective




as the thermally induced fission, the explanation of thisdifference being still an open question.

The fusion of two triplets may give rise to autoionizationas observed in the case of singlet exciton fusion (67)

The vibrationally excited singlet S1� and triplet T1

�, expectedupon the annihilation of the lowest excited triplets T1, T1

0,have an energy below the autoionization threshold of typicalaromatic crystals [26], thus, no intrinsic photoionization hasbeen observed in these solids. However, the presence of inten-tional or non-intentional admixtures can allow the triplet–tri-plet interaction-induced photoionization forming a freecarrier in the matrix and a trapped carrier on an admixturemolecule. Also, such a process has been reported for the CTtriplet states localized on the donor molecule, e.g. in polycrys-talline samples of CT complex anthracene-tetracyanoben-zene, where the triplets are localized on the anthracenedonor (3D1). Annihilation of 3D1 results in the population ofnon-relaxed excited states of the complex 1(DþA�)n and3(DþA�)n, dissociation of which may lead to the formation offree charges Dþ [214].

2.5.1.3 Singlet–triplet Interaction

Singlet excitons can be destroyed by triplets in the singlet–tri-plet collision process




This process is fully allowed and may be treated as an energytransfer promotion of T1 to higher (hot) triplet states, T2

� andT3� ( T1! T2 or T3 are spin-allowed processes). The reverse

reaction, however, is spin forbidden. If the spin-symmetryrule for some reasons (e.g. spin-orbit coupling) is broken this

The role of singlet–triplet exciton annihilation in redu-cing the fluorescence efficiency of organic solids is well

the singlet–singlet annihilation process (67) by studyingthe time-resolved intensity dependence of the fluorescenceyield. A value gST¼ (5� 3) 10�9 cm3 s�1 has been obtainedfrom such a dependence for the slow component of thefluorescence of a single anthracene crystal [185]. This resultis to be compared with theoretical values based on theenergy transfer notions expressed by Eq. (71). An attempthas been made using its diffusion approximation (75) [215].For the evaluation of gST in anthracene, these authors assu-med R0¼ RST

0 ¼ 3.2 nm, DS! D¼ DSþ DT¼ 3.6 10�3 cm3 s�1,tS¼ 4 ns, and G(3=4)= G(5=4)ffi 0.676. They interpreted RST

0

as a critical singlet-triplet distance at which the energytransfer rate of the singlet is equal to all other rates ofsinglet decay, and D as the sum of the diffusion coefficientsof the singlet and triplet excitons. The obtained value wasgST¼ 2.8 10�9cm3s�1. Though in good agreement with theabove cited experimental data, it is open for criticismbecause of uncertain values of D and tS, but first of allbecause the diffusion approximation for anthracene maynot be valid (see Sec. 2.5.1.1). Employing the capture-con-trolled annihilation limit (76) with R0¼ 3.2 nm andrc¼ 0.5 nm yields gST¼ 4 10�9 cm3s�1 even more consistentwith experiment.

An obvious expectation is that singlet–triplet annihila-tion process will dominate under high concentration of tri-plet excitons which can occur as a result of the efficientsinglet ! triplet fission [cf. Scheme accompanyingthe passage of high-energy radiation through an organicsolid [216–218] or effective recombination of charge carriersinjected from electrodes into solid-state samples as in the




documented (see e.g. Ref. 26). It can be distinguished from

process becomes active as well (cf. Sec. 2.4.2).

(67)],

case of organic LEDs. One of the most characteristic resultsis the excitation intensity dependence of the relative fluore-scence intensity in tetracene crystals (Fig. 35). The relativefluorescence efficiency initially increases, reaches a broadmaximum and decreases thereafter. In the lower intensityregime (�1016 quanta=cm2 s), the dominating triplet–tripletinteraction produces an increasing number of singlet exci-tons in addition to those created directly by the excitinglight, the fluorescence efficiency increases. At higher excita-tion intensities, the singlet–triplet annihilation process setsin leading to quenching of singlet excitons. A balancebetween the singlet exciton surplus resulting from the tri-plet–triplet annihilation and its reduction due to singletexciton quenching by triplets holds the relative fluorescenceefficiency on a constant level within about two orders ofmagnitude of the exciting flux. At still higher excitationintensities, the quenching of singlets by triplets becomes adominating process and the fluorescence efficiency decreases.For steady-state excitation, with weakly absorbed light, theeffects of exciton diffusion can be neglected, and the rateequations giving the singlet and triplet populations S(x)

Figure 35 Relative fluorescence efficiency as a function of thequantal exciting intensity for a ffi 200 mm-thick tetracene crystalexcited with the 325 nm line of a He-Cd laser. The increasing seg-ment shows the triplet–triplet fusion contribution to the fluores-cence (delayed fluorescence); the decrease at high excitation levelsis attributed to quenching of the singlets by singlet–triplet annihila-tion. Experimental data are represented by points, theoretical fits,as described in text, by the solid line. Adapted from Ref. 206.




and T(x), at a distance x from the illuminated surface canbe written as

aI0 expð�a xÞ þ gðSÞTT T2 � S =tST � gST S � T ¼ 0 ð98aÞ

gS= tS � T =tT � gðTOTÞTT T2 ¼ 0 ð98bÞ

and the fluorescence quantum efficiency

jFL ¼ krZ1

0

Sð xÞ=I0 expð�a xÞ½ �dx ð99Þ

In Eqs. (98) and (99), g is the average number of tripletsgenerated by the decay of one singlet (if t�1

S ffi kf , as isthe case of tetracene crystals, g¼ 2), the meaning of othersymbols is the same as given already in Secs. 2.5.1.1 and2.5.1.2.

Taking as a reference level, the fluorescence quantumefficiency of the crystal in the absence of triplet exciton inter-actions, j0

FL ¼ kr tS, the relative quantum efficiency can bedefined by the ratio jFL= jFL(0).

In the low excitation region, the term gST S�T in Eq. (98a)can be neglected, Eqs. (98) and (99), with the assumption

gðTOTÞTT ffi 3gðSÞTT, lead to

jFL =jFLð0Þ ¼ 3 1� ð1þ pI0Þ1 =2 � lnð1þ pI0Þ1 =2 � 1

ð3 =8ÞpI0

" #

ð100Þ

where

p ¼ 8

3 agðTOTÞ

TT t2T ð101Þ

Due to the contribution of delayed fluorescence from singletsproduced in the triplet–triplet fusion, the overall fluorescenceefficiency increases to the value jFL =jFL(0)¼ 3. The best fitof Eq. (100) (solid line below 1017 quanta=cm2 s in Fig. 35)




was obtained for p¼ 1.6 10�13 cm2 s. From this value of pand measured triplet exciton lifetime (tT¼ 5 10�4 s) andabsorption coefficient of the exciting light (a¼ 6 102 cm�1),

one obtains gðTOTÞTT ¼ (2.2 � 0.5) 10�9 cm3s�1, as mentioned

already in Sec. 2.5.1.2.The solution of Eq. (98a) with the term gST S�T and of

(98b) where T=tT has been neglected yields to a first approx-imation (for not too high intensities)

jFL =jFLð0Þ ffi 3 1� r9

pI0ð Þ1 =2h i

ð102Þ

where p is defined by (101), and the parameter r¼ gST tS =3 tT

gðTOTÞTT contains the singlet–triplet annihilation rate constantgST. Equation (102) predicts a decrease of jFL= jFL(0) withintensity I0 from the value 3 reached with the saturation ofthe contribution of the delayed fluorescence. Its reasonablefit to the experimental data (solid line within the high inten-sity regime in Fig. 35) has been obtained using the previousvalue of p, and the value r¼ 3 10�5. Based on the aboveevaluated constant gðTOTÞ

TT and taking for the ratio tS= tT thevalue 10�6, one arrives at gSTffi 2 10�7 cm3 s�1. This valuecan be in error by one order of magnitude in view of the uncer-tainties as to the actual intensity distribution of the focusedlaser beam throughout the bulk of the sample and as to thereliability of the value of tS = tT

process has been inferred indirectly from studies of intrinsicphoto-carrier generation in anthracene [219]. In this process,intrinsic charge carriers are produced by autoionization of anexcited state degenerated with the continuum of states in thefree carrier bands [the upper pathway of the singlet–triplet

ble if the sum of energies of one singlet (ES) and one triplet(ET) exciton is larger than or at least comparable with theenergy gap, Eg. In the case of anthracene crystal, ESþET¼(3.15þ 1.8) eV¼ 4.95 eV > Eg

its efficiency is determined by competition with other exci-tonic interactions and monomolecular decay pathways.




ffi 4.0 eV (see e.g. Ref. 26), and

(cf. discussion in Sec.2.5.1.2). The existence of a singlet–triplet exciton annihilation

annihilation process in Scheme (97)]. It is energetically feasi-

2.5.2. Exciton–charge Carrier Interactions

2.5.2.1. Singlet Exciton Annihilation byParamagnetic (Doublet) Species

In this process, singlet excitons may be annihilated by thespin �1=2 particles (doublets D�1=2) represented by eitherradicals and free or trapped electrons and holes:

Interactions of singlet excitons with these species lead to theirannihilation, and thus to a decreased fluorescence quantumyield. Quenching of singlets by impurity centers, which wereproduced by ionizing radiation, has been reported [220–222].Experimental evidence for the destruction of singlet excitonsby charge carriers injected into anthracene has also been pre-sented [85,223–225]. By irradiating crystalline samples ofvarious hydrocarbons with X-rays or high energy electrons,quenching centers are introduced. If their concentrationinduced by one rad amounts N [(cm3 rad)�1], the fluorescencequantum efficiency has been found to decrease with the radia-tion dose (R) as follows:

jFLðRÞ ¼jFL

1þ gSqNtSRð104Þ

Here jFL and tS are the fluorescence quantum efficiency andmeasured singlet exciton lifetime, respectively, of thesamples before irradiation, and gSq is a constant characteriz-ing the singlet exciton-quenching center energy transfer effi-ciency [the second order singlet exciton-quenching centerinteraction rate constant (cm3=s)]. Interestingly, the mea-sured jFL(R) dependence deviates from the function (104)within the long-wavelength part of the fluorescence spectrum




[226,227]. A formal modification of this function has been pro-posed replacing the denominator of Eq. (104) by (1þ gSq N t SRZ), where Z varies with the range of the emission spectrum.For example, Z¼ 1 for the short wavelength emission wingand drops down to 0.3 at the long-wavelength emission tailof stilbene (references as above). This modification does nothave any physical meaning, and the reason for the deviationeffects is still an open question, though one can speculate thatthey are associated with energy-dependent product of gSq � tS

[note that tS in Eq. (104) is an average singlet exciton life-time]. Due to the complexity of the radiation-induced damage,inferring about the nature of the quenching centers is verydifficult. But to a large extent, they seem to have a physicalorigin since their annealing has been successfully observed[222]. The singlet exciton quenching by impurity centers isof crucial importance for the stability and quantum efficiencyof organic LEDs. The quenching centers can be producedwithin their emitter layers due to chemical instability of lightemitting molecules under ambient conditions or their ionicspecies formed by excess charge carriers injected from electro-des into EL structures. External factors that can inducedegradation of the emitter are oxidation, photo-oxidation,diffusion of the electrode material, and heating effects (for

photo-oxidation process, high-energy irradiation induces p top� and s to s� transitions, creating free radicals in the mate-rial. C–C, C–N, and C–O low-energy bonds can also bedamaged under irradiation. The created defects are subjectto chemical reactions with the atmospheric oxygen or moist-ure, and lead to oxidation of the sample. The instability ofAlq3

þ cations formed by injection of holes into common Alq3

emitter-based organic LEDs is believed to influence thedegradation rate, the degradation products act as fluores-cence quenchers [228,229]. The EL intensity decreases intime during device operation (Fig. 36a) indicating a decreasein the EL quantum efficiency that reflects the intrinsic degra-dation behavior. Associated with the decrease in EL duringdevice aging, the decrease in PL intensity is observed, whichreflects a decrease in the PL quantum efficiency of Alq3, thus




a recent review of degradation effects see Ref. 3). In the

Figure 36 Quenching effects on photoluminescence (PL) and elec-troluminescence (EL) of fluorescent Alq3 and phosphorescentIr(ppy)3 emitters due to aging by operation of an Alq3-based LEDat 50 mA=cm2 (a) and by exposing a 150 nm-thick Ir(ppy)3 film tothe UV-radiation (¼313 nm) under ambient conditions (b). The dataof part (a) have been obtained with the EL structure as shown in theinset ITO=N,N0-di(naphthalene-1-yl)-N=N0-diphenyl-benzidine(NPB)(40 nm)=triphenyl-triazine(TPT)(40 nm)=Mg=Ag by Aziz et al.[230] (Copyright 2001 SPIE). The Ir(ppy)3 results in part (b) areunpublished data of Mezyk and Kalinowski.




revealing degradation in the Alq3 layer. Exposing some emit-ter materials to the UV radiation under ambient conditionsleads also to a decrease in the PL quantum efficiency. Anexample is shown in Fig. 36b, where the PL intensity of aphosphorescent Ir complex is plotted vs. exposition time.

Quenching of singlets by trapped holes injected from anelectrolytic contact has been demonstrated for anthracene[85,91,231]. The effect, described by the schemes in Fig. 15and (103), apparent already in the short-wavelength regionof the charge-induced decrease in the fluorescence intensityof anthracene in Fig. 13b (curve 5), is extended towards theshorter-wavelength emission range in Fig. 37. Increasingwavelength (lo) translates into the thickness of the observedslab (l0¼ a�1

0 ) at the injecting contact through the absorptioncoefficient of the emitted light (a0). Its extent monotonicallyincreases from l0¼ 23 nm at l0¼ 394 nm, up to l0 exceeding

Figure 37 Charge carrier-induced quenching of prompt fluores-cence from a 75mm-thick anthracene crystal as a function of theemission wavelength (l0). The charge is injected from the illumi-nated water=crystal interface. The excitation intensityI0¼ (4 � 2) 1015 quanta=cm2 s. Adapted from Ref. 231.




the crystal thickness above l0¼ 425 nm. The experimentallyobserved fluorescence intensity can be expressed as

F ¼Z2 x1 =2

0

SðxÞ expð�x =l0Þdx ð105Þ

where x1=2 is a distance counted from the illuminated contactinto the bulk of the crystal which determines the region fromwhich a half of all fluorescence photons of energy hc= l0 origi-nate. The exponential factor exp(�x =l0) is the probability for aphoton to leave the crystal when emitted at the distance xfrom the illuminated interface. In any thin section of the sam-ple at a distance x from the injecting electrode, the singletexciton concentration S(x) may be described by

Ið xÞ=la þ DS@2 SðxÞ@ x2

� Sð xÞ=tS � gSq nhð xÞ Sð xÞ ¼ 0 ð106Þ

Thus, neglecting the diffusion term, the coordinate-dependentconcentration of singlet excitons takes on the form

SðxÞ ffi I0 expð�x= laÞla t�1

S þ gSq nhðxÞ� � ð107Þ

where la is the penetration depth of the exciting light whichfor lex¼ 366 nm (unpolarized) amounts to about 0.5 mm. Holeinjection into anthracene crystals is achieved utilizing excitonreactions at the illuminated water electrode. The distributionof injected holes is given by the Mott–Gurney function [91]

nhð xÞ ¼ nhð0Þ½ x0 =ðx0þxÞ2� ð108Þ

where x0¼ [e2nh(0)=2e0ekT]�1=2 is the characteristic Debyelength dependent on the concentration of holes at the inject-ing interface. In the example presented in Fig. 37,x0ffi 0.12mm with nh(0)ffi 7 1014 cm�3 and e¼ 4.5 at roomtemperature. Clearly, the average hole concentration, nh,decreases as the extent of the observation slab increasesfollowing the increase of the emission wavelength (l0). The




fractional change (d) of the fluorescence intensity (for not toohigh quenching),

d ¼ FU � F U¼0

FU¼0ffi gSqnh tS ð109Þ

upon applying a sufficiently high external voltage ( U ), revealsthe fluorescence increase since the concentration of homoge-neously distributed holes under saturation current,nh( U)ffi 1012 cm�3, is much smaller than the average hole con-centration within the layer of thickness la in the absence of anexternal voltage (U¼ 0). We note that FU corresponds to thefluorescence intensity in the absence (F0), and F U¼0 corre-sponds to the fluorescence intensity in the presence (F) ofcharge in the excited layer of the crystal (cf. Fig. 37). Ascri-bing appropriate values of nh to increasing x1=2 (read l0),one arrives at the spatial distribution of d( x). From the iden-tification of such obtained d(x) with the nh(x) (108), andusing tSffi 10 ns [232], gSq¼ (3� 1.5) 10�9 cm3 s�1 has beendeduced based on Eq. (109) [231]. If the annihilation constantgSq was determined by the excitonic diffusion, its value couldbe simply related to the singlet–singlet exciton annihilationrate constant (71) as gSSffi 2 gSqffi (0.6 � 0.3) 10�8 cm3 s�1

which agrees well with the value 10�8 cm3 s�1 determinedfrom the excitation intensity dependence of the anthracenefluorescence (see Sec. 2.5.1.1). Also, the value of gSqffi 10�9–10�10 cm3 s�1, deduced from the PL quenching upon injectionof holes and electrons into a 100 nm-thick film of Alq3 [233],compares with gSSffi 1.3 10�10 cm3 s�1 for this Al complex(see Sec. 2.5.1.1), though the upper limit of gSq suggests somedifferences in quenching mechanisms of singlets by other sing-lets, and by charge carriers. This question has been recentlyaddressed in the context of the field-dependent EL quantumefficiency from the Alq3-based organic LEDs (see Sec. 5.4).

2.5.2.2. Triplet Exciton Reactions with DoubletSpecies

The triplet exciton quenching by doublet species is well estab-lished. Annihilation of triplet excitons has been observed on




either radiation-induced centers [234] or free [235–239] andtrapped charge carriers [91,231,238–249]. The triplet–doubletinteraction process consists of the collision of a triplet and adoublet species to form a singlet and a doublet state throughan intermediate pair state, [T1�� D�1=2],

where S0� is a vibrational state of the ground state singlet, T1

is a triplet exciton, and D�1=2is a spin � 1 =2 paramagneticcenter. While K1 represents the rate of encounter of tripletswith charge carriers, K2 is the dissociation rate of the pairstate complex into a singlet doublet pair and K�1 its dissocia-tion into the original triplet doublet pair. gTq denotes the over-all annihilation (quenching) rate constant for the reaction.The dissociation rate constant K�1 can be considered as ascattering process and need not be spin-conserving, althoughthe quenching process (the transition rate to final state, K2)conserves spin. Hence only those pair spin states with doubletcharacter can undergo quenching, since the final state of thereaction is a pure doublet. The species in the intermediatecomplex [T1�� D�1=2] are correlated in a sense that they caninteract with each other. The interaction energy is deter-mined by the dipolar spin–spin interaction (dependent onthe intermolecular distance as r�3) and the electrostatic inter-molecular interaction which like spin–spin coupling dependson the geometry of the complex, intermolecular distance andthe total spin. The six spin states jcli, l¼ 1��6 of the[T�� D�1=2] complex are in general doublet–quartet mixtureswith a doublet spin component jhcljD�1=2ij � jD�l j. The spincorrelation properties make the doublet component of theintermediate complex to be affected by an external magneticfield (see Sec. 2.5.3.1).

The determination of the triplet exciton-trapped holeoverall rate constant (gTq) was initially made by measuring




of decay rate of the delayed singlet exciton fluorescence uponthe introduction of excess positive charges into a samplethrough an ohmic hole-injecting contact [236,238,243,244].The emitting singlet excitons were generated by the fusionof triplet excitons excited directly from the ground state withuniformly absorbed chopped, long wavelength light. The life-times were determined by measuring the decay rate of thedelayed fluorescence during the dark period of the choppedexcitation sequence. For low intensity exciting light, neglect-ing diffusion, the decay of triplet exciton population can bedescribed by

aI0 � T=tT�gTq � nhT ¼ 0 ð111Þ

where aI0 denotes the generation rate of triplet excitons usinglight of intensity I0 and absorption coefficient a for S0!T1

absorption, nh is the total concentration of holes. This equa-tion is analogous to Eq. (106) except that la for the S0!S1

transition has been replaced by a�1 for the S0!T1 transition,tS by tT, and gSq by gTq. The slope of the plot of the delayedfluorescence intensity vs. time yields the effective triplet exci-ton lifetime for any given value of nh

1

teff¼ 1

tTþ gTqnh ð112Þ

The total concentration of holes nh is a sum of the concentrationof trapped (nht) and free (nhf) carriers. However, oftennhf=nht!0, nhffinht due to a large concentration of traps. Then,the excitons are quenched by trapped carriers and the annihila-tion rate constant gTq is equivalent to the mobile exciton-immo-bile (trapped) charge carrier interaction rate constant gTq.Under space-charge-limited conditions, the concentration ofcharge is simply proportional to the applied voltage (U),nht¼ (3=2)e0eU=ed2, where d is the sample thickness, e is theelectronic charge, e is the dielectric constant of the sample mate-rial, and e0 is the permittivity of free space. Thus, it may be seenthat the fractional change in the triplet exciton decay rate

DbbT

¼ tT

teff� 1 ffi e0etT

ed2gðtÞTqU ð113Þ




varies linearly with the external voltage U and decreases as d�2.This is the case for anthracene crystal with CuI hole injectingelectrode (Fig. 38). From the slopes of the Db=bT(U) straightlines in Fig. 38a, gðtÞTq¼ (0.7 � 0.2) 10�11 cm3 s�1 follows. The




non-linear voltage increase of D b= bT in the case of a crystal withthe hole injecting contact Aþ (Fig. 38b) suggests triplet excitonsto be quenched by free holes. In such a case

b ffi bT þ gðfÞTq nhf þ gðtÞTq nht ð114Þ

where gðfÞTq and gðtÞTq are the second order rate constants for tripletsinteracting with free and trapped carriers, respectively. Theconcentration of free holes, defined by the current densityj¼ emhnhf U=d, where mh is the hole mobility, allows Eq. (114)to be expressed in the form

b� bTð Þ=U ¼ D b =U ¼ 3

2

e0 eed2

gðtÞTq þd

e mh

gðfÞTq

j

U2

� �ð115Þ

This equation fits well the experimental data of Fig. 38b.From the linear dependence of Db =U vs. j=U2 both gðtÞTq¼(0.5 � 0.2) 10�11 cm3 s�1 and gðfÞTq¼ (2 � 1) 10�9 cm3 s�1 were

calculated [238]. A much larger value of gðfÞTq would indicate a

much larger effective diffusion coefficient of the interacting tri-plet (DT) and mobile hole ( Dh), Deff ¼ DTþ Dh, and=or theirmuch larger capture radius. The diffusion-controlled excitonic

interactions [cf. Eqs. (52) and (71)] imply gðfÞTq¼ (1=2) gðTOTÞTT ffi

2.5 10�11 cm3 s�1 with gðTOTÞTT ¼ 5 10�11 cm3 s�1 (Fig. 33),

exceeding the above value of gðtÞTq by a factor of 5. Despite the

two fold difference in DT¼ gðtÞTq =4pRffi 0.4 10�4 cm2 s�1 (R¼0.5 nm) and DT¼ 10�4 cm2 s�1 obtained from the triplet–tripletannihilation experiment (see Table 2), both of them are negligi-

Figur e 38 Relative increase in the monomolecular decay rate con-stant ( Db =bT) (decrease in the lifetime) of triplet excitons in threedifferent anthracene crystals under the positive voltage applied totwo different hole injecting electrodes: CuI (a) and anthracene posi-tive ions (Aþ) in nitromethane (b). bT¼ t�1

T is the triplet decay rateconstant with no voltage: bT¼ 239 s�1 for the d¼ 350 mm-thick crys-tal, bT¼ 175 s�1 for anthracene with d¼ 625 mm (from Ref. 243);bT¼ 200 s�1 for the d¼ 320 mm-thick crystal, Aþ injecting contact

2

is presented (points) to be compared with Eq. (115) (solid line).

J




(see Ref. 238). In the right-top scale in part (b) the Db =U vs. j=U

ble as compared with Deffffi Dh¼ gðfÞTq =4pRffi 3.3 10�3 cm2 s�1.Assuming the Einstein relation to hold, Dh¼ mhkT = e, mhffi0.13 cm2=V s follows from this value of Dh. Though in the sameorder of magnitude, it is a factor of 6 lower than the lowesttime-of-flight measured mobility of holes in the c0 crystallo-graphic direction of anthracene at room temperature mh(c0)¼0.85 cm2=V s [101]. However, the values of mh as low as0.4 cm2=V s (Refs. 250 and 251) or even 5 10�3 cm2=V s(Ref. 252) have been reported in early mobility works. Thediscrepancies in mh obtained by different researchers [253] canbe attributed to differences in the crystal samples and causedby the accuracy of the apparatus setups. Therefore, it is not

excluded that the above value of gðfÞTq, when assumed to be gov-

erned by the diffusion of free holes, reflects the chemical andstructural imperfection of the crystals studied. On the other

hand, gðfÞTq < 4pDTR could mean that the reaction is not comple-

tely diffusion limited with R < 0.5 nm. The latter would indicatethat not all T– qf encounter events lead to the triplet quen-ching. Like in anthracene, the free hole–triplet exciton quen-ching has not been observed for pyrene crystal providedwith a hole-injecting CuI anode. From the straight line Db = bT

vs. U plots, the triplet-trapped hole annihilation rate constant

has been deduced, gðtÞTq¼ 4.5 10�11 cm3 s�1 [244], This is a value

six times larger than that for anthracene, and an order of

magnitude larger than the diffusion-controlled value gðtÞTq¼(1=2)

gðTOTÞTT ¼ 0.4 10�11 cm3 s�1 resulting from gðTOTÞ

TT ¼ 0.7510�11 cm3 s�1 for pyrene (Fig. 33). A possible reason for the dis-

crepancy between gðtÞTq and gðTOTÞTT is that the former contains a

contribution from the triplet exciton-free charge carrier inter-action, neglected in the discussion of the results on triplet-charge carrier quenching experiments [244]. Another possibilityto explain this discrepancy can be associated with different pre-ferential sites and directions for triplet–triplet and triplet-charge carrier interactions, thus, following different compo-nents of the triplet diffusivity tensor in pyrene crystal [254].The triplet–triplet annihilation occurring within the pyrenecrystal dimer on molecules 0.35 nm apart, with DT¼ 0.3




10�4 cm2 s�1 in the ac0-plane, leads to gðTOTÞTT ¼ 8pDTR¼ 2.5

10�11 cm3 s�1 which within the experimental accuracy forgðTOTÞ

TT (� 0.410�11 cm3s-�1) and DT (� 0.1 10�4 cm2 s�1)

approaches the experimental value of gðTOTÞTT . On the other hand,

DT¼ (1.2 � 0.3) 10�4 cm2 s�1 along the b-axis and R¼ 0.5 nm

[255], yields gðtÞTt ¼ 4p DTR¼ 7.5 10�11 cm3 s�1 near its experi-mental value. The triplet-trapped charge carrier interactionleads to increasing concentration of free carriers observed asphoto-enhanced currents [238,256–259]. The detrapped carrierscontribute, in turn, to triplet exciton quenching. This contribu-tion can be essential if the exciton-free charge carrier interactionrate constant exceeds that for the exciton-trapped carrier inter-action constant, due to high diffusivity of free carriers. From the

linear increase of the triplet quenching rate, kTq¼ [gðtÞTqþYgðfÞTq] nht, with the ratio of free to total concentration of holes

(Y¼ nhf= nh), the triplet-free hole interaction rate constant foranthracene, gðfÞTq¼ (2 � 1) 10�10 cm3 s�1, follows [236]. This

value is an order of magnitude lower than that resulting from

the data of Fig. 38, and could be attributed to a combination oftriplet-trapped charge carrier and triplet–singlet interactions.A similar value was obtained for the triplet-trapped hole inter-action in tetracene, gðtÞTq¼ (1.5 � 0.5) 10�10 cm3 s�1 [260]. In

the framework of the diffusion-controlled excitonic interactions,one would expect gðTOTÞ

TT 2gðtÞTqffi 3 10�10 cm3 s�1 which is one

order of magnitude lower that the experimental value of gðTOTÞTT

discussed in Sec. 2.5.1.2. The neglection of the singlet–tripletinteraction and unjustified assumption about ohmic properties

the above discrepancy. In fact, a method avoiding these short-comings allowed the determination of gðtÞTq¼ (5 � 2)10�9 cm3 s�1 for tetracene [245], comparable with gðTOTÞ

TT ffi 210�9 cm3 s�1 (see Sec. 2.5.1.2). The method employed the high

intensity (I0) dependence of the saturation current (jþS ) due tohole injection from the H2O=tetracene positively biased contactby triplet excitons. Their successively increasing quenching byinjected holes leads to sublinear increase jþS (I0) which yieldsthe current dependent diffusion length of triplet excitons. From




of gold=tetracene contact (cf. Ref. 257) may be the reason for

the latter gðtÞTq has been determined. The quenching of tripletexcitons by the spatially distributed trapped carriers at thewater=tetracene contact has been used to deduce the triplet-trapped charge carrier interaction rate constant as describedalready for singlet excitons in anthracene (see Sec. 2.5.2.1).The obtained value gðtÞTq¼ (2 � 1.5) 10�9 cm3 s�1 (Ref. 91) corre-

sponds, within the experimental error, to the prediction of thediffusion-controlled interaction process gðtÞTq¼ (1 =2) gðTOTÞ

TT ffi(0.5–1) 10�9 cm3 s�1

It is obvious that triplet-charge carrier interactionsmight be of crucial importance in organic LEDs, where tripletemitting states are generated in the high charge carrier con-centration regions due to the electron–hole recombinationprocess [261]. Their role in organic electrophosphorescentLEDs is discussed in Secs. 5.3 and 5.4.

2.5.3. Magnetic Field Effects

There are various classes of phenomena that can lead to mag-netic field-imposed changes in EL efficiency of organic LEDs:(I) the first class phenomena are subject to fine structure mod-ulation (FSM) and require fields of 10 mT to 0.1 T [262]. Thisclass includes singlet exciton fission ( S� ! Tþ T), triplet–tri-plet fusion (T–T) and triplet-charge carrier (generally, doub-let species, D� 1=2) annihilation ( T– D�1=2) (cf. Secs. 2.5.1.2

electronic Zeeman effect and hyperfine modulation (HFM),and fields only 1 mT are required [263]. The key examplesare photoconduction [264–268] and photochemical reactions[269–272] involving an intermediate charge-transfer state.

2.5.3.1 Exciton Fine Structure Effects

Due to the spin conserving rule, the rate constants of someexcitonic interactions are subject to modulation by weak mag-netic fields (less than 1 T). The magnetic field modulation of

experimentally observed as a magnetic field effect on promptfluorescence [192,200,201,273–278]. The magnetic field sensi-tive triplet–triplet (80) and triplet–doublet (110) annihilation




(cf. Sec. 2.5.1.2).

and 2.5.2.2). (II) The second class phenomena are subject to

the singlet exciton fission rate [see Scheme (80)] can be

rate constants show up as magnetic field effects ondelayed fluorescence [209,234,256,279–282], photoconduction[238,241,248,256,283–285] and photovoltaic parameters [286]of organic solids. Since all these excitonic interactions areexpected to occur in organic LEDs, the magnetic field effectson their EL output [287] and=or double injection currents[259] can be utilized to infer about their presence andaltering processes that underlie the LED’s performance.Figure 39 illustrates an experimental arrangement for mea-suring of three-dimensional anisotropy of the magnetic fieldeffect (MFE) on photoconduction. The magnetic field can berotated in any plane perpendicular to the ab-plane of the crys-tal. The orientation of the magnetic field with respect to thecrystallographic axes is represented by angles W and j. Fora fixed field strength and crystal orientation j, the photocur-rent shows one or two maxima as W varies between 0 and180 (Fig. 40a). The maxima (or minima) in the MFE as afunction of the orientation of the magnetic field with respectto the crystal axes are characteristic also for prompt and

tropy of the MFE on delayed fluorescence in anthracene crys-

crystallographic structure of the organic system, and dependson the range of the magnetic field strength. At low fields(B < 0.1 T), the anisotropy is slightly more complex, with

bisect the angular separation between the high-field maxima(or minima) positions (see e.g., the minima of the MFE ondelayed fluorescence in anthracene). For a fixed field-crystalorientation, the MFE on either fluorescence or photocurrentshows non-monotonic behavior as seen in Fig. 41 for thephotocurrent in Au=Tetracene crystal=Au system. Qualita-tively, a similar result has been found for the fluorescence(also for other organic crystals), although the position of theminimum (or maximum in the case of delayed fluorescence)and the field at which the effect vanishes are different.

The above characteristics of the MFEs on fluorescence,photoconduction, and photovoltaic parameters can beexplained by class (I) phenomena based on the magnetic field




delayed fluorescence intensity (for a three-dimensional aniso-

new maxima (or minima) appearing for field directions that

tal, see Refs. 281, 282). Their positions are determined by

Figure 39 (a) Schematic representation of an experimental setupfor measuring of three-dimensional anisotropy of the magnetic fieldeffect on photoconductivity (C—crystal, M—mirror). (b) Orientationof the magnetic field B with respect to the crystal axes (a0, b, c0).From Ref. 248.




modulation of the spin components of the intermediate pairstates formed in the course of the exciton fission and fusion[(80), (81)] as well as exciton-doublet interaction (110). Themost comprehensive theory of the MFEs is that includingthe effects of the spatial variation of the triplet exciton wavefunctions [288]. However, for the general understanding ofthe phenomenon, it is sufficient to analyze the complete spindensity matrix of the intermediate pair states with spatialvariables of the excitons to be neglected [280]. As discussedin Secs. 2.5.1.2 and 2.5.2.2, two triplet excitons or one tripletand one doublet species can form correlated pair states withtheir pair spin wave functions containing a certain degree ofindeterminacy. They are coupled to the exciton reservoir by

Figur e 40 Three-dimensional anisotropy of the magnetic fieldeffect on photoconduction of a 7 mm-thick tetracene single crystalilluminated through a semitransparent gold evaporated anode (cf.Fig. 39a). (a) Relative increase of the photocurrent (iph) when amagnetic field B¼ 0.5 T is rotated perpendicular to the ab-planefor different orientations of the crystal j. The maximum relativeincrease amounts to about 10%. (b) Orientation (j) dependent posi-tions of the maxima in the magnetic field effect vs. direction of themagnetic field (W). Circles: experimental data; solid line: theoreticalprediction according to Eq. (121). After Ref. 248.




two phenomenological constants K�1 and K2 (K�1 in thekinetic schemes stands for the source term). It is essentialto remark again that the overall reaction is spin-conserving,in contrast to the scattering process K�1 for which there areno spin selection rules. The spin of the intermediate pairstates is described by the complete spin density matrix,(9 9) for the correlated triplet pair [ T1�� T1

0] and (6 6) forthe triplet–doublet pair [T1�� D1=2]. In general, the annihila-tion (9 9) matrix consists of a sum of three terms represent-ing the singlet, triplet, and quintet final state channels [seeEq. (83)]. Explicit calculations for the gðSÞTT or g�S constantsrequire the knowledge of the number of pair states with sing-let character ( Cl

S 6¼ 0). In order to evaluate different spinamplitudes, the spin Hamiltonian of the intermediatecomplex [ T1�� T1

0] must be defined. It has been assumed tobe a simple sum of the Hamiltonians for two triplets forming

Figur e 41 The influence of the magnetic field strength (B) on thehigher maximum of the MFE for the photocurrent (see Fig. 40a) in atetracene crystal with various orientations of the magnetic field (cf.Fig. 39). Crystal is the same as in Fig. 40. From Ref. 248.




the complex

bHHðSÞcomplex ¼ bHHSSð1Þ þ bHHZð1Þh i

þ bHHSSð2Þ þ bHHZð2Þh i

ð116Þ

with bHHSS and bHHZ representing the zero-field and ZeemanHamiltonians for the individual excitons T1(1) and T1

0(2).The zero-field term of (116) can be expressed as

bHHSSð1 ;2Þ ¼ bHHSSð1Þ þ bHHSSð2Þ ¼ D1bSS 2

1 z �1

3bSS2

1

� �

þ E1bSS2

1x � bSS2

1 y

� þ D2

bSS 2

2 z �1

3bSS2

2

� �þ E2

bSS2

2x � bSS 2

2 y

�

ð117Þ

where D1, D2 and E1, E2 are the zero-field splitting para-meters (D of the order �0.1 cm�1, and E =D��0.1). The

squared spin of each of the triplet exciton ( bSS2

1 ;bSS2

2 ) commutes

with the spin projections on the molecular axes ( bSSx, bSS y, bSS z),but does not commute with the Hamiltonian [289]. Therefore,the eigenstates of the Hamiltonian (117), jiji (quantized alongthe molecular axes i,j¼ x,y,z), are not the eigenstates of thetotal spin bSS 2. The pure singlet state jS(0)i(B¼ 0) can beobtained by diagonalizing the bSS2 matrix,

jSð0Þi ¼ 3�1=2ðj x01 x02i þ jy01 y

02i þ jz01 z

02iÞ ð118Þ

where the primed coordinate system x0, y0, z0 is a system ofcoordinates in which bHHSS(1,2) [Eq. (117)] is diagonal. In zerofield, there are only three states with singlet character,

namely jx xi, j y yi, jz zi, pair states jx yi and jy xi, jy zi and

j z yi, jx zi and j z xi are degenerate. This degeneracy is liftedby the weak inter-triplet interaction, giving a set of nine pairstates of which three are singlet–quintet mixtures jx xi, jy yiand jz zi, three are pure quintets and three are pure triplets

Zeeman term

bHHZð1;2Þ ¼ gbBðS1 þ S2Þ ð119Þ

of the pair state adds to the zero-field Hamiltonian (117).




(see e.g., Ref. 262). When a magnetic field B is applied, the

At relatively low-field strengths when gbB�D, the 9 9matrix describing the pair spin state in the basis of the pairstates functions ji ji will, in general, have non-zero off-diago-nal matrix elements which will mix the pair states. Thus, inthis limit, there will be more states with singlet characterand, for example, gS [see Eq. (83)] will be larger than at zerofield. Consequently, the prompt fluorescence from directlyexcited singlets will decrease, while the delayed fluorescencedue to triplet–triplet generated singlets will increase. In thehigh-field limit, when gbB�D, the pair states are approxi-mately described by the spin eigenstates jþ1, �1i, j�1, þ1i,j0, 0i, j0, þ1i, jþ1, 0i, etc. of triplet excitons 1 and 2 in thecomplex with spin angular momentum quantized along theexternal field B. Only the first three of the nine pair stateshave singlet character, and the pure singlet is

jSðHÞi ¼ 3�1=2ðj0;0i � j þ 1;�1i � j � 1;þ1iÞ ð120Þ

In general, the magnitude of the amplitudes ClS, and therefore

gS and gðSÞTT depend on D and E, the applied field B, the energyspread in the manifold of states cl(DEQS, DETS), the relativeorientation of T1 and T1

0 and the branching ratio K2=K�1.For high magnetic fields (B> 0.1 T) with an arbitrary

orientation with respect to the crystallographic axes, onlytwo pair states, j0 0i and 2�1=2(jþ1, �1i þ j�1, þ1i), havesinglet character with fractional singlet component 1=3 and2=3, respectively, as may be seen by projecting these functionsonto the pure singlet state (120). Thus, the rate constant gðSÞTT(85) and g0s (88) are smaller than in zero field, a decrease indelayed, and an increase in prompt fluorescence occurs forsuch magnetic fields. In crystals, when the directions of mole-cular axes are fixed, there exist special orientations of themagnetic field for which the j0 0i state is degenerate withthe jþ1, �1i and j�1, þ1i states. At these orientations,level-crossing resonances occur, since there is only one statewith singlet character which is the pure singlet (120). Equa-tions (85) and (88) thus have only one term for whichCl

S 6¼ 0, gðSÞTT and g0S exhibit a minimum. Within the contextof the theory [234,280], the positions of level-crossing




resonances are determined by the equation

D cos2 g1 þ cos2 g2 �2

3

� �

þ Eðcos2 a1 þ cos2 a2 � cos2 b1 � cos2 b2Þ ¼ 0

ð121Þ

where cos a, cos b and cos g are the direction cosines of B withrespect to the molecular axes of the two inequivalent mole-cules x1, y1, z1 and x2, y2, z2.

The Hamiltonian describing the intermediate state[T1��D�1=2] in the triplet–doublet interaction process (110) is

bHH ¼ gebB � r þ gbB � bSSþ bHHSS ð122Þ

where ge is the radical (electron, hole) g-factor, assumed iso-tropic, and rr and bSS are the spin operators for the doubletand triplet species, respectively. The bHHSS has been definedby (117). As for the exciton–exciton interaction, the total spinoperator, (bSSþ rr)2, does not commute with bHH, and thereforespin pair functions, cl are doublet–quartet mixtures. Inzero-field, the pure doublet is

jD�1=2ð0Þi ¼ 3�1=2ðjz;�1=2i � jx;�1=2i þ ijy;�1=2ið123Þ

where i¼ffiffiffiffiffiffiffi�1p

, and jxi, jyi, jzi are the zero-field eigenfunctionsof the triplet quantized along crystalline axes (the triplet exci-ton fine structure tensor), and j � 1=2i are the doublet entityspin states. Each of the six eigenstates forming the puredoublet state (123) has doublet character D� ¼ hD�1=2(0)jx,� 1=2i¼ hD�1=2(0)jy, � 1=2i¼ hD�1=2(0)jz, � 1=2 i¼ 3�1=2.The dissociation rate gTq is proportional to the number of stateswith the amplitude of the mS¼ � 1=2 doublet component,D�l ¼hcljD�1=2i as predicted by the theory [234],

gTq ¼1

6K1

X6

l¼1

K Dþl 2þ D�l

2�

K�1 þ K Dþl 2þ D�l

2� ð124Þ

where the quenching process occurs with the transition rate to




final state, K2¼ Kðj Dþl j2 þ jD�l j

2Þ. Hence only those pair spinstates with doublet character can undergo quenching sincethe final state of the reaction is a pure doublet. It is importantto note that, in contrast to gðSÞTT and g0S, the quenching rate con-stant, gTq, decreases monotonically with increasing appliedmagnetic field. This follows from the properties of the eigen-functions of the Hamiltonian (122) at B 6¼ 0, non all of themhaving doublet character. At high fields, g bB� D, only fournon-degenerate states have doublet character. Thus, in agree-ment with Eq. (124), for any magnetic field B 6¼ 0, the inter-action rate constant should be smaller than for B¼ 0.

In addition to this general decrease in the quenching ratewith field, one would expect high-field anisotropies due tolevel-crossing resonances of the pair states similar to thoseobserved in the delayed fluorescence of anthracene and tetra-cene, and in tetracene prompt fluorescence. These resonancesoccur when j0, � 1 =2i and j�1, � 1=2i are degenerate, respec-tively, with j1, �1 =2i and j0, �1=2i. These special orientationsof the magnetic field result from the equality of their energies,namely W0,�1=2¼ Wþ1,�1=2, and W�1,þ1=2¼ W0,�1 =2. The pairenergies are determined by the sum of the triplet excitonenergies W0, Wþ1, W�1, and of the doublets W� 1=2¼ � ge

b B=2. These conditions reduce to the same equations whenapplied to fission or fusion, Eq. (121). A good agreement ofthe experimental data with the theoretical predictions isapparent from Fig. 40b for the MFE on photoconduction dueto triplet exciton-trapped hole interaction in triclinic tetra-cene crystal if two translationally inequivalent crystallo-graphic positions of tetracene molecules [207], thus twoappropriate sets of the angles a1, b1, g1, and a2, b2, g2 are usedin solving Eq. (121). In monoclinic crystals like anthraceneand naphthalene, the crystal b-axis coincides with one ofthe molecular axis, which is taken to be z-axis. The y- andx-axes lie in the ac-plane, which is a mirror plane (see e.g.

due to the developed ab-plane in solution- and sublimation-grown thin crystals, the high-field resonances occur at� 23.5 with respect to the b-axis [238,280]. On the basis ofEq. (124), the interaction rate constant for zero field [gTq(0)],




Ref. 52). When B is rotated in the ab-plane, as often met

and B 6¼ 0 at the resonance [gðrezÞTq ( B)] and off-resonance

[ gðoffÞTq (B)] field directions can be calculated and compared to

each other [238]:

gTqð0Þ ¼1

3 KK1ð1þ K =3Þ�1 ð125Þ

gðoffÞTq ð BÞ ¼

1

3 KK1

1þ ð4=9Þ Kð1þ 2K =3Þð1þ K =3Þ ð126Þ

and

gðresÞTq ðBÞ ¼

1

3 KK1ð1þ KÞ�1 ð127Þ

From the ( ab)-plane anisotropy of the MFE on the photocur-rent in anthracene crystal gðoffÞ

Tq = gTq¼ 0.965 has been found.Dividing Eq. (126) by Eq. (125), one obtains gðoffÞ

Tq ( B)=gTq(0)¼[1þ (4=9) K ][1þ (2=3) K ]�1 which compared with the aboveexperimental value yields K¼ 0.17. Then, from Eq. (125),and the above value of K, K1ffi 20 gTq (0) follows, and identify-ing gTq(0) with gðtÞTq¼ (0.5 � 0.2) 10�11 cm3 s�1 (see Sec.2.5.2.2), K1¼ (1.0 � 0.5) 10�10 cm3 s�1 is obtained. This isan order of magnitude larger than a triplet exciton diffu-sion-controlled process (see Sec. 2.5.2.2) and may indicatethe exciton capture radius by a trapped hole to remarkablyexceed the nearest-neighbor intermolecular distance. In spiteof this, simple scattering of the triplet by a trapped hole seemsto be a quite frequent process, since K¼K2=K�1ffi 0.17, that isthe annihilation rate K2 constitutes only about 15% of thetotal rate of the decay of the [T1��D�1=2] pair state, onlyweakly competing with its backwards to the reacting sepa-rated species (K�1). The latter, as obtained from fitting ofthe general shape of the high-field anisotropy curve to beK�1¼ (1.25 � 0.3) 109 s�1, determines the lifetime of a cor-related triplet-trapped hole pair in anthracene, K�1

�1 ffi 0.8 ns[238]. The magnetic field effects on excitonic interactions inamorphous or highly defected solids are difficult to quantita-tive description, because the intermediate pairs of theinteracting species may assume a variety of collisional config-urations, and the Hamiltonian and coordinate system in







which pure singlet (120) or pure doublet (123) is defined, arenot constant. Thus, their MFE characteristics may be comple-tely different from those for single crystals. For example, ithas been shown that the triplet–triplet fusion rate constant,gðSÞTT, in solutions decreases monotonically with increasingmagnetic field, and it does not exhibit the inversion at lowfields which is characteristic for crystals [290]. Such an inver-sion can be observed as a transition from the low-fieldenhancement to the high-field reduction in the intensity ofthe delayed fluorescence and as an opposite effect for promptfluorescence if the singlet exciton fission process is feasibleenergetically. An excellent illustration of these phenomenais presented in Fig. 42, where the MFE on prompt anddelayed fluorescence from tetracene crystal is plotted as afunction magnetic field strength at a fixed field direction(Fig. 42a) and a fixed value of field as a function of its direc-tion (Fig. 42b). Coexistence of the thermally mediated singletexciton fission and triplet–triplet fusion is clearly demon-strated [cf. Eq. (82)]. The fitting of the theory to the experi-mental data of the MFE anisotropy of prompt fluorescenceallows various reaction parameters for excitonic interactionsin tetracene to be evaluated. Such a procedure applied to tet-racene crystal at low (ffi0.1 MPa) and high (ffi 300 MPa) hydro-static pressures has shown how they are modified by smallchanges in the crystal lattice (Table 3). For example, the life-time of the [T1�� T1

0] pair complex increases from 0.2 ns at nor-mal pressure to 0.33 ns at 290 MPa. At the same time, thetriplet annihilation [K

ðSÞ2 ] and singlet fission (K�2) rates

decrease by a factor of 2 and 1.3, respectively. In the frames

Figure 42 Magnetic field dependence of prompt and delayedfluorescence intensities in a tetracene crystal as a function of themagnetic field strength (a) and field orientation (b) at different tem-peratures. The curves in part (a) have been obtained with the fieldoriented at �20 with respect to the b-axis in the ab-plane of thecrystal, corresponding to one of the resonance directions shown inpart (b) presenting the MFE anisotropy with the magnetic fieldB¼ 0.4 T rotated in the (ab)-plane of the crystal. From Ref. 192.Copyright 1970 American Physical Society.

J




of Merrifield’s [280] and Suna’s [288] theories, these changescan be interpreted as a pressure improvement of the two-dimensional character of the triplet exciton movement. Thepressure modification of constants K�1 and K2 allows to inferabout relative pressure changes in the cc component ( Dcc) ofthe diffusion tensor of triplet excitons in tetracene, namely(D Dcc =Dcc) =D p¼ 1.3 10�3=MPa�1—the number being abouttwo times of that in anthracene [292] and consistent withthe relation of pressure gradients of other quantities foranthracene and tetracene [200,292]. Interestingly, a promptfluorescence-like inversion in the MFE has also been observedwith the MFE on photoconduction in tetracene crystal(Fig. 41). Its appearance depends on the crystal orientationand suggests singlet excitons to be involved in generation ofthe photocurrent. They can increase the concentration of freecarriers by the interaction with trapped carriers injected initi-ally from the electrode and=or increase the injection currentdue to increasing singlet exciton flux reaching the electrode.In both cases, the MFE on photocurrent should follow exactlythe MFE on prompt fluorescence reflecting the magnetic fieldmodulation of the singlet exciton concentration within theabsorption depth of the exciting light. The magnetic fielddependence of the photocurrent of a thin tetracene film illu-minated either by a non-injecting (Al) or hole injecting (Au)anode is shown in Fig. 43a. Only in the high electric-field case(F¼ 100 V=2mm¼ 5 105 V cm�1) for the non-injecting anode(curve 2), the (Dj=j) (B) follows qualitatively the magnetic

Table 3 Singlet Exciton Fission Parametersa for a TetraceneSingle Crystal at Two Different Hydrostatic Pressures

p¼ 0.1 MPa p¼ 290 MPa

E¼K2=K1¼ 0.52 E¼ 0.45K�1¼ 3.3 109 s�1 K�1¼ 2.1 109 s�1

K�2¼ 1.3 10�12 cm3 s�1 K�2¼ 1.0 10�12 cm3 s�1

KðSÞ2 ¼ 1.72 109 s�1 K

ðSÞ2 ¼ 0.95 109 s�1

K1¼ 1.7 10�12 cm3 s�1 K1¼ 0.88 10�12 cm3 s�1

t¼ (K�1þK2)�1¼ 2 10�10 s t¼ (K�1þK2)�1¼ 3.3 10�10 s

aAccording to Scheme (80). The data from Ref. 291.




field-induced prompt fluorescence changes (DF=F) (B). Thismight be ascribed to the injection of holes by singlet excitonsreaching the Alþ anode. However, as for the values, Dj=j (B) isroughly twofold lower than DF=F (B). There must then be anadditional charge generation process whose efficiencydiminishes in a magnetic field. The injection of holes by tripletexcitons seems to be a natural candidate since they are effi-ciently produced in the fission and have much longer diffusionlength [l

ðTÞD ffi 300 nm] [154] as compared with singlet excitons

[lðSÞD ffi 12 nm] [153]. The former is even larger than the pene-

tration depth of the exciting light in tetracene films(laffi 150 nm at la¼ 470 nm) [286]. Since the concentration of

Figure 43 (a) Experimental curves of the magnetic field-inducedpercentage changes of the photocurrent, Dj=j (1,2,3), and promptfluorescence, DF=F (4), in a 2 mm-thick polycrystalline layer ofvacuum-evaporated tetracene sandwiched between Al and Au elec-trodes. Curves 1 and 2—illumination through Alþ at two differentvoltages, and 3—illumination through Auþ. Excitation light oflexc¼ 470 nm and intensity I0¼ 1013 quanta=cm2 s was used. (b)Hypothetical change in the observed photocurrent if the triplet exci-ton concentration were determined by the magnetic field inhibitionof the triplet–charge carrier interaction process (A), inhibition ofsinglet exciton fission and reabsorption (B), and simultaneousoperation of both processes (C). The absolute values of Dj=j mustnot be compared with those in part (a) since the analysis in part(b) has been performed for a resonance direction of single tetracenecrystal and not averaged for a random distribution of microcrystal-lites in a polycrystalline sample as should be done to quantitativelycompare with the results of part (a). From Ref. 293.




triplet excitons decreases at high magnetic fields due to themagnetic field inhibition of the fission process, the triplet exci-ton flux reaching the electrode diminishes. The resultinginjection current occurs as a result of increasing injection bysinglets and decreasing injection by triplets. At low magneticfields, an increase in the triplet exciton concentration accom-panies the increased singlet exciton fission rate, the decreasein the singlet exciton flux is compensated in part by theincreased triplet exciton flux towards the anode, and thelow-field minimum becomes shallower as compared with thatfor prompt fluorescence. The magnetic field change in the photo-current can be coupled to the magnetic field change in promptfluorescence (DF= F) by an approximate relationship [293]

D jjffi

jS=T þ FS =Tð0ÞðDF= Fþ 1ÞjS =T þ FS=Tð0Þ

� 1 ð128Þ

where jS=T¼ jS= jT is the ratio of injection efficiencies of holesby singlet ( jS) and triplet (jT) excitons, and FS=T is the ratioof the singlet [FS(0)] and triplet [ FT(0)] exciton fluxes reachingthe anode at zero magnetic field. The predictions of Eq. (128)agree with experiment for jSTffi 16 which is in the rangejS=T > 10 predicted previously for the contact Al =anthracenecrystal [294]. At lower voltages, the (Dj=j) (0) does not exhibitthe characteristic for (DF=F) (B) low magnetic field minimum,being a monotonically increasing function of B (curve 1 inFig. 43a). This behavior can be rationalized by subjecting thetriplet exciton flux (thus FS=T) to the magnetic field modulation.The exciton flux towards the anode increases with elongation ofthe exciton diffusion length. Due to triplet-charge carrier inter-action, the triplet lifetime and its diffusion length are shorterthan in the absence of charge [cf. Eq. (114)]. Upon the magneticfield-induced monotonic decrease of the rate of this interaction, amonotonic increase in the triplet exciton diffusion length isexpected which would enhance the charge injection by tripletexcitons. Thus, the low magnetic field increase of the photocur-rent (within the minimum for DF=F) is caused simultaneouslyby two factors, first, the increased concentration of tripletsdue to the magnetic field inhibition of the singlet fission, and




secondly, by magnetic field-induced elongation of their diffusionlength. It suppresses the photocurrent decrease due to injectionby a decreasing number of singlets, the resulting photocurrentincreases monotonically with magnetic field (Fig. 43b). Thiseffect is well pronounced at lower voltages when the concentra-tion of charge in the near-electrode region is high enough tomodulate the triplet exciton diffusion length [see Eq. (108) andthe following discussion]. The role of triplet excitons is evenmore remarkable when hole injecting anode (e.g. Au) is providedto highly charge trapping polycrystalline or amorphous sampleof tetracene (Fig. 43a, curve 3). The MFE on the photocurrent athigh fields is here suppressed by a reduction in the effectivedetrapping of holes by triplet excitons, since the photocurrentis largely due to excitonic detrapping of the holes injected initi-ally from the electrode. The MFE on the photocurrent in theAu=Tetracene crystal =Au system may not follow this patternespecially for high structural quality single crystals whenconcentration of trapped holes is not as high as in solid films.This is the case in Fig. 41, where a high-quality thin (7 mm-thick)tetracene sublimation flake has been studied.

2.5.3.2. Hyperfine vs. Zeeman Interactions

Eectroluminescence from typical organic LEDs is the result ofthe formation of emissive states via the recombination ofoppositely charged carriers (electrons, e, holes, h) injectedfrom electrodes (see Chapters 1 and 5). The injected carriersare free (statistically independent of each other), the recombi-nation process is kinetically bimolecular but naturally pro-ceeds through a Coulombically correlated charge pair state(e��h) prior to the electron–hole localization on one moleculeor closely spaced two molecules, forming molecular or bimole-cular final emissive states (see Sec. 2.3). The spin dynamics ofcharge pairs are sensitive to external applied magnetic fields,which permit the manipulation of both the charge pair life-times and the yields of products arising from charge pairdecay. The effect appeared to be a powerful tool in the elucida-tion of chemical reactions occurring through radical pairs[272,295–298], and assigned for the purpose of this book as




class (II) phenomena. Application of a magnetic field as smallas 10 mT lowers the yield of complex excited triplets within aphotosynthetic bacteria by about 40% [299], and by as muchas 50% of anthracene triplets produced through dye-anthracene charge-transfer (CT) state [300]. As illustrated inFig. 44, in the phenomena of class (II) external magnetic fieldcontrols, the conversion rate between singlet and tripletstates of a pair of oppositely charged carriers when the energy

Figure 44 The energy level scheme diagram (not to scale) andelectronic transitions leading to fluorescent (S1) and phosphores-cent (T1) molecular states produced in the bi-molecular eþh recom-bination process (VR) with suitable rate constants (k1, k�1, k3, k�3,k(S), k(T)). The singlet [1(e��h)] and triplet [3(e��h)] states of the pair(e��h) undergo mixing with the rate constants kST and kTS; theS1!T1 intersystem crossing is characterized by the rate constantkISC. The overlapping Gaussian energy bands of the (e��h) pairsdue to static and dynamic disorder in non-crystalline organic solids




are indicated by dashed curves (cf. Sec. 2.4.3).

separation between their singlet and triplet ground states,j2Jj, is comparable or smaller than the difference betweenthe Zeeman energies of the pair components or theirhyperfine energies. These effects can be classified into threetypes [269,270,296]: (A) the electronic Zeeman effect (DgbB),where Dg¼ ge� gh 6¼ 0 is the difference between electron (ge)and hole (gh) g-factors of the carriers forming pairs, (B) thehyperfine interaction effect, and (C) the mixed effect. SinceDg is usually a small quantity, the first type effect is notexpected to occur at very low magnetic fields, and, for the pairlifetime tCP�2�h=DgbB, the relative change in the yield of thecarrier capture products is proportional to B2 at low fields andB1=2 at higher fields, and saturates at high fields [269,296]. Ifge¼ gh (Dg¼ 0), magnetic field effects (MFEs) on the productyield still exist due to the hyperfine coupling of the paircarriers. The Hamiltonian of the charge pair comprises of

three terms: bHH¼ bHHe–hþ bHHZeemanþ bHHhyperfine, where bHHZeeman¼gbB( bSSeþ bSSh) with bSSe, bSSh representing the spin operators for

the electron and hole, respectively; bHHhyperfine ¼P

l;m albSSm

bIIl

represents the hyperfine interaction between l nuclei (often

protons) interacting with the relevant electrons m, bII1 being

the nuclear spin operator of the lth nucleus (proton) and bSSm

the electron spin operator of the mth electron. The bHHe–h term

relates to the exchange interaction �hJ[(1=2)� 2 bSSebSSh] provided

by a separation (r) exchange parameter J(r)¼J0 exp(�ar)with characteristic constants J0 [J(r) with r!0] and a¼ 2=r0

with J(r)¼ 0.135J0 at r¼ r0. The eigenfunctions of the CPHamiltonian include the singlet states, jSi, which are odd,and triplet states, jTþi,jT0i,jT�i, which are even under theinterexchange of the two particles [289]. The bHHhyperfine pro-vides the necessary unsymmetrical term in the Hamiltonianwhich gives rise to singlet–triplet mixing, the odd singletstates are subject to upconversion to even triplet states[263]. An external magnetic field partially restores the sym-metry of the total CP Hamiltonian because the ZeemanHamiltonian, bHHZeeman, is even under exchange of the twoparticles, and reduces the mixing rate, implying a change inthe triplet-to-singlet products of the recombined CPs. The




effective value of the hyperfine coupling constant, a, can beevaluated from the observed anisotropy of HFM employinghighly ordered systems, and has been found on the order ofa =g bffi 1 mT for a dye-anthracene crystal (D��Aþ) system[300]. Thus, again, the MFE due to the HFM of the CP pairstates is expected to occur at very low magnetic fields andsaturate at high fields when the Zeeman term exceeds thehyperfine interaction energy, bHHhyperfine. Finally, a combina-tion of the Zeeman (D gb B) and hyperfine ( bHHhyperfine) interac-tion defines the third type of a mixed effect which willresult in a non-monotonous dependence of the relative yieldof the recombination products as magnetic field strengthincreases. In this case, an initial low-field increase in the yieldbecomes followed by its decrease at higher fields and can endwith negative values at still higher fields [270]. The situationbecomes more complex if the e–h interaction energy (spin–spin and electrostatic exchange) is not negligible. This wouldbe of importance for the short inter-carrier distances (r) whenJ(r) becomes fairly large (larger and=or comparable withD gb B and bHHhyperfine), and can be considered as class (III) ofmagnetic field sensitive phenomena. If the degenerate tripletstates fall much above the singlet pair state, the splitting ofjTþi and jT�i sub-states in moderate magnetic field strengthsis not sufficient to level jT�i and jSi states, the hyperfineinteraction can be unable to mix these states, no MFE onthe recombination products is expected. However, at a level-crossing field, Bc¼ j2 Jj= g b, the hyperfine interaction-inducedmixing of these states suddenly sets in, and a sharp change ofthe product yield follows. As the field increasing proceeds,the jT�i sub-state moves below the jSi level, one would expecta decrease in the mixing rate. The final result is 0 or a resi-dual MFE signal transforming into a non-monotonous fieldevolution with an extremum at Bc. The second and thirdclass of the phenomena should be considered as a reason forthe MFEs on the emission from organic LEDs since theiremissive states originate from the e–h recombination possiblyinvolving long-living e��h pair states as their precursors.

The DL LED with Alq3 emitter, placed in a steady-statemagnetic field ( B) (Fig. 45), shows the light output following




the bell-shaped function of B as it increases from 0 to 0.5 T. Amaximum value of the MFE is about 5% and appears at a fieldffi300 mT (Fig. 46a). A similar behavior has also been reportedfor EPH LEDs, where the magnetic-field-induced increase inthe EPH efficiency up to 6% at about 500 mT and driving cur-rent jffi 3 mA=cm2 was followed by a high field decrease. Stillpositive effect continued to the highest accessible field ofabout 0.6 T (Fig. 46b). This suggests the strong redissociationlimit of the formation of triplet excitons (k�1�k(S), kST;k�3�k(T), kTS), and a magnetic field shift of the state jT�itowards the state jSi of the (e��h) pairs, leading to the

Figure 45 Schematic drawing of the experimental setup to mea-sure EL output in magnetic field (B). This is a topical view of anAlq3 emitter based LED placed between the pole pieces (N, S) ofan electromagnet in a way that magnetic field is parallel to the sur-face of the sandwich DL EL cell, and the electrofluorescence flux(hnfl) leaves the cell perpendicular to B. Adapted from Ref. 301.




Figure 46 Experimental results of the magnetic field dependenceof the MFEs on the EL output from a DL electrofluorescent LED,ITO=75% TPD:25% PC(60 nm)=Alq3(60 nm)=Ca=Ag (a), and a DLelectrophosphorescent LED, ITO=6 wt% Ir(ppy)3:74 wt% TPD:20wt% PC (60 nm)=100% PBD(50 nm)=Ca=Ag (b). The data taken attwo different applied voltages and corresponding current densitiesgiven in the insets. Part (a) adapted from Ref. 301. Part (b) takenfrom Ref. 301a.




reversed trend in the mixing at Bffi 0.5 T. The broad bell-shaped curves ( Dj = j) as a function of B are indicative of a dis-tribution of the inter-carrier distances dictated by a randomnature of the recombination process, and both static anddynamic disorder in the emitters.

2.6. ELECTRIC FIELD-ASSISTED DISSOCIATIONOF EXCITED STATES

The quantum EL efficiency of organic LEDs is known to be afunction of their operation voltage (see Sec. 5.4). The field-assisted exciton dissociation has been invoked to explain itshigh-field drop [68,302–306]. The existence of such a processresulting in the intrinsic production of charge carriers shouldbe directly observed as photoconduction (PC) and=or electricfield-induced luminescence quenching. The dissociationability depends on the type of excited state, weaker boundedstates expected to dissociate easier. Since in the recombina-tion EL, the final emitting states (mostly localized Frenkeltype excitons) are by definition formed through the intermedi-ate CT state of a Coulombically correlated electron–hole pair(see Fig. 3), there can be sufficient thermal energy to dissoci-ate such a pair, reducing the number of final emitting states.The field-assisted dissociation of the localized Frenkel exci-tons may occur as well, though with a lower efficiency. Sucha process has been proposed to explain PC and electromodu-lated fluorescence characteristics of thin films of Alq3

[305,306]. Figure 47 shows the fluorescence (FL) quenchingefficiency (Fig. 47a) and dc photocurrent jph (Fig. 47b) as afunction of the applied electric field at two different excitationwavelengths. A possible mechanism for the photogenerationof carriers in solid Alq3 is that excited singlet states (Alq3)may dissociate into separated electrons and holes, in additionto the radiative relaxation producing fluorescence, h nfl. Thisis shown in some detail in Fig. 48. The initial separation stepinvolves a charge-transfer state (CT) formed with a field-independent probability, Z0 and field-depending CT dissocia-tion process (O) into separated charge carriers (eþh). Thus,




the photocurrent can be expressed as

jph ¼ eZI0 ð129Þ

where Z is the overall probability for excited states to dissoci-ate into separated charge carriers, and I0 is the quantalexciting light intensity (photons=cm2 s). At low fields, theexperimental photogeneration efficiency (jexp=eI0) is very

Figure 48 Photo-excitation and dissociation of Alq3, leading to thecharge transfer state (CT) and electron–hole pairs, the latter givingrise to photocurrent flowing in solid Alq3.

Figure 47 Fluorescence quenching efficiency (a) and steady-statephotocurrent (b) as a function of electric field at two different excita-tion wavelengths. From Ref. 306. Copyright 2002 American Insti-tute of Physics.




low, extrapolated to F¼ 0 gives Z(0) < 10�6 (Fig. 47). Thefluorescence intensity at F¼ 0, FL(0), would decrease underan electric field F applied to the Alq3 film FL(F)ffiFL(0)[1� Z(F)]. The experimental ratio [FL(0)�FL(F)] =FL(0)ffi Z(F) is a measure of the field-induced fluorescencequenching. The functional shape of the overall dissociationprobability Z(F) depends on the physical mechanism under-lying the charge separation. In the Poole–Frenkel (PF)framework [307,308], the field dependence of the overallquantum photogeneration yield is given by

ZPF ¼ Z0

expðbPF F1 =2Þ

APF þ expðbPF F1=2Þ ð130Þ

where bPF¼ ( e3= pe0k2 T2)1=2¼ 1.5 10�2 (cm=V)1=2 with e¼ 3.8

[309], and APF expresses the recombination-to-generationrate constants ratio at F¼ 0.

The PF formalism treats the electron–hole pair dissocia-tion as a one step carrier escapes from the Coulomb field ofthe countercharge due to external field-assisted thermal acti-vation over the barrier. The two steps in the formation of afree carrier pair, as shown in Fig. 48, are undistinguishable.In other models of the exciton dissociation process, thesetwo steps are separable, and the overall quantum efficiencyexpressed by the product

ZðFÞ ¼ ZCTðFÞOðFÞ ð131Þ

where

ZCTðFÞ ¼�kkCTðFÞ

�kkCTðFÞ þ kf þ kn

ð132Þ

stands for the quantum yield of CT states. kCT is the primaryescape rate constant averaged over all solid angles due to itsdependence on the electron jump direction with respect to theapplied electric field. The field dependence of Z(F) comes fromthe field-dependent rate constant kCT(F) and O(F); kf and kn

represent the rate constants of radiative and non-radiative,respectively, decays of the excited states.




It is often assumed that the rate constant for carrier pro-duction is characterized by an exponential function [310,311]

k ¼ k0 exp½ðF=F0Þ cosY� ð133Þ

where k0 and F0 are constants which may depend on tempera-ture, and Y is the direction of the carrier escape with respectto the applied field.

The physical meaning of expression (133) has been dis-cussed. Originally considered as due to the primary one-stepcharge-carrier separation to form a CT exciton [310,312],was later proposed to reflect charge-carrier hopping betweenlocal sites (microtraps) forming the core (pinning trap) of aspatially extended defect (macrotrap) localizing primaryexcited states [313].

If by definition, the average of kCT(F) were

�kkCTðFÞ ¼1

2

Z1

�1

dðcosYÞk0 expðF cosY=F0Þ

¼ k0sinhðF=F0Þ

F=F0ð134Þ

the average quantum yield of CT states would read

ZCTðFÞ ¼sinhðbCTFÞ=bCTF

Aþ sinhðbCTFÞ=bCTFð135Þ

where

bCT ¼ F�10 and A ¼ ðkf þ knÞ=k0 ð136Þ

The probability of the dissociation of the CT state into a pairof separated carriers, and its functional form is determined bythe mechanism of final charge separation [O(F)]. Besides theone-step PF dissociation process (130), the Onsager formalismis often used to describe O(F) [314,315]

OOnsðFÞ ¼Z

gðr;YÞf ðr;YÞdt ð137Þ

where g(r,Y) is the probability per unit volume of finding the




ejected electron in a volume element dt at Y, r for the specificionization process, and

f ðr; YÞ ¼ exp½�ð Aþ BÞ�X1m

X1n¼0

Am

m!

B mþn

ð mþ nÞ! ð138Þ

with A¼ 2 q= r, B¼ br(1þ cos Y), q¼ e2=8p e0e kT, b¼ eF=2 kT.The field dependence of OOns( F) appears in a complex

manner through the parameter B which determines theexpansion terms of the infinite series in Eq. (138). The expan-sion coefficients in Eq. (138) are governed by the so-called‘‘Onsager radius’’ at which the Coulombian attraction is equalto the thermal energy, kT

rC ¼ e2 =4 pe0 ekT ð139Þ

and a distribution of thermalization length, r. The latter cor-responds to the initial electron–hole separation (CT diameter)which has been approximated by either an exponential orGaussian function [316,317], but it is usually assumed totake a discrete value r0 defined by a delta function, g(r)¼d(r� r0)=4 p r2

0

Another interpretation for the rate constant (133) comesfrom the ‘‘macrotrap model’’ [313,317a] which assumes theexcited states to move to the macrotraps defined as spatiallyextended domains arising from physical perturbation of crys-tal lattice [318] or from local structure different from the basicenvironment including disordered solids [319]. The macro-traps consist of local states (microtraps) with energy (E) dis-tributed in space (r) such that E¼ (3kT=s)ln(r0=r), where sis a characteristic parameter of the exponential energy distri-bution function and r0 is the radius of the macrotrap. Theexcited state generated within the macrotrap can dissociateby hopping within the pinning trap according to Eq. (133)with F0¼ kT=ed, where d is the hopping distance of a carrier

plify a theoretical description of the exciton dissociation pro-cess: (i) the primary step separation limit with O(F)¼ const(or slowly varying function of F), and (ii) the dissociation limitwith ZCT(F)¼ const. By these definitions, it is clear that limit




(see e.g., Ref. 26).

e (cf. Sec. 4.6). Two limiting cases can be distinguished to sim-

(i) corresponds to Z(F)ffi ZCT(F) as expressed by Eq. (135), andlimit (ii) corresponds to Z(F)ffi Z0OOns( F) as comes from Eqs.(131), (137), and (138). These both approaches have beenemployed to fit experimental results. For example, thethree-dimensional Onsager theory [limit (ii)] with Z0¼ consthas been extensively applied in works on charge photogenera-tion in organic crystalline materials [65,305,306,316,320,321]and partially or completely amorphous polymers [322–324].Some additional circumstances such as formation of excimers[323,324], field-dependent mobility [65], or space charge [306]have been invoked to account for experimental data. The fielddependence of the primary charge separation step [limit (i)]has been suggested to underlie the charge photogenerationin single component sandwich cells [302,311,313] and electrontransfer in electron donor–electron acceptor molecularsystems [325]. Figure 49 shows the electric field dependenceof photogeneration efficiency for the commonly used organicLED emitter Alq3. The low-field values of Z(F) have beendeduced from the PC and high-field values from the electromo-dulated fluorescence experimental data of Fig. 47. Differenttheoretical models such as Poole–Frenkel, Onsager or thatbased on the macrotrap concept, cannot account for the experi-mental data for Z(F) (Fig. 49a). Excellent agreement withexperiment is provided by the 3D-Onsager theory of geminaterecombination combined with volume (bimolecular) recombi-nation (VR) of the photogenerated space charge (Fig. 49b),

ZðFÞ ¼ Z0OOnsðFÞ 1� ZVRðFÞ½ � ð140Þ

The bimolecular recombination efficiency (ZVR) is determinedby the recombination time, trec, and transit time tt, of thecarriers to the electrodes, as defined in Preface and Sec. 5.4,

ZVR ¼ ð1þ trec=ttÞ�1 ð141Þ

We note that at high electric fields (>105 V cm�1), the space-charge correction to Z(F) can be neglected and the 3D-Onsa-ger model alone fits well the experimental data. Thus, onewould expect this model to be sufficient for describing thehigh-field reduction in PL and EL efficiency. As a matter of




Figur e 49 Electric field dependence of carrier generation effi-ciency ( Z) for eight different samples of Alq3. The low-field values( < 105 V cm�1) are extracted from the steady-state PC, and high-field values from fluorescence quenching measurements displayedin Fig. 47. The lines represent theoretical predictions of Z( F) for dif-ferent charge separation models (a), and the conventional 1938Onsager model [Eqs. (137)–(139)] with g(r)¼ d(r� r0)=4pr2 , assum-ing r0¼ 1.5 nm and Z¼ 0.8 and taking into account the bimolecularrecombination according to Eq. (140) (The field dependence of thebimolecular recombination efficiency (ZVR) and total concentrationof holes (nh) as given in the inset was used in the fitting procedure(b). From Ref. 305.




fact, its application to phosphorescent complex of Ir(ppy)3

shows good agreement with the experimental data of theelectric field-induced quenching of its phosphorescence (PH)and electrophosphorescence (EPH) (see Fig. 50). The failureof the Poole–Frenkel approach is apparent by comparisonits fit to experiment. In contrast, the fit Z( F)¼ Z0OOns( F)resulting from the Onsager theory is accurate for the firstrun and reasonably good for the second run in measuringthe EPH quantum efficiency for the same diode. The curva-ture of the d( F) plot is a function of two parameters, r0 andF0. The fit for the two consecutive measurement runs for

Figur e 50 Quenching efficiency ( d) as a function of dc electric fieldapplied to the electrophosphorescent (EPH) and phosphorescentsystem. The curves are fits to the Poole–Frenkel (see lower inset)and Onsager (see upper inset) models for charge pair dissociationin external electric fields. The quenching efficiency is defined as arelative difference between the emission efficiency at a given fieldF[F(F)] and at a field F0[F(F0)] where a decrease in the EPH effi-ciency becomes observed (d¼ [F(F0)� F(F)]=F(F0); F0

3

cular structures of TPD and PC are given in Figs. 6 and 16. FromRef. 304. Copyright 2002 American Physical Society.




< F) (cf. Sec.5.4). For the molecular structure of Ir(ppy) , see Fig. 36; the mole-

the EPH device was made for the same r0¼ 3.5 nm andF0¼ 8.55 105 V cm�1. This value of r0 stands for a lowerlimit of the electron–hole distance in the charge pair (CP)as the curvature of the d(F) function in the Onsager formal-ism becomes insensitive to r0 above 3.5 nm [304]. Thus, theaverage initial e–h distance of the CPs formed in the bi-mole-cular recombination can be larger, that is re–h 3.5 nm. Theexcellent fit of the phosphorescence quenching data withthe field-assisted dissociation as described by the Onsagertheory is obtained with r0¼ rCT¼ (1.8� 0.1) nm andF0¼ 8.55 105 V cm�1. The roughly twofold decrease in r0

accompanying the observed diminution in the quenching effi-ciency when passing from EPH to PH systems illustrates thedifferent origin of the CP states. Whereas Coulombically cor-related e–h pairs in the EPH device originate in the mutualapproaching process of statistically independent carriersfrom the electrodes, CT states produced under photoexcita-tion originate from the electron–hole separation process ofthe initially excited molecular excitons. From the abovevalues of r0, the zero-field dissociation efficiency is found todiffer by about two orders of magnitude for the bimolecularlyformed CPs, Ze–h(F¼ 0)ffi 4 10�3, and for CT states,ZCT(F¼ 0)ffi 3 10�5, as calculated with rc¼ 19 nm, andZ0¼ 1 and Z0¼ 0.9, respectively. If r0 is large ( >4 nm), its fielddependence may contribute to the field dependence of theoverall dissociation efficiency of an excited state. The fielddependence of r0 is then a consequence of a hot carrier driftduring its thermalization [326]. The effective thermalizationlength increases to rth¼ r0þ mFtth, where m is the carriermobility, and tth is the thermalization time of the carrier.The modified function OOns(F) (137) leads to a more steepdependence of Z on electric field, predicting well the Z(F)behavior in pentacene films as shown in Fig. 51. It is seenthat both rth and r0ffi rth (r0� mFtth) increase with photonenergy, leading to large values of rth (up to 12 nm) and sup-porting the ballistic model for autoionization process inwhich the excess kinetic energy of the carrier is directly pro-portional to the incident photon energy. The evaluation of rth

can be based either on the theoretical fit of Z(hn) with




Ztheor(hn)ffiA(F,T) (hn�Eg)5=2 (Eg—energy gap) [327]; A(F,T)—

hn-independent constant) being proportional to OOns, or on theArrhenius plot of Zexp(T) yielding the activation energyEa¼ e2=4pe0erth. However, as comes from Fig. 51b, the fieldeffect on r0 is negligible whenever its values are lower than4 nm characteristic for the first absorption band of the mate-rial. Due to improvement of sample preparation, especiallyfor high quality single crystals, the low-field increase in r0

and field dependence of r0 may become of importance becauseof remarkable increase in the carrier mobility. For example,the hole mobility m�h¼ 0.4 cm2=V s assumed to calculate theZ(F) curves in Fig. 51b for polycrystalline pentacene filmsincreases up to over 3 cm2=V s for single pentacene crystals.

As comes from the above discussion, both r0(F) and O(F)must be taken into account for the general case of the field-assisted dissociation of excited states. Then, Z(F) can be

Figure 51 (a) Intrinsic photocurrent quantum efficiency inpentacene films (1–3 mm thick) induced by light at hn¼ 2.6 eV as afunction of electric field at two different temperatures (T¼ 330 K—crosses; T¼ 250 K—squares). Theoretical predictions: Onsager1938 with Z0¼ 0.5; r0(F)¼ const¼ 5.3 nm (dashed curves), Onsager1938 modified by r0¼ rth(F) according to Eq. (142) (solid lines). (b)Variation of rth with electric field for two pentacene films (1–5mmthick—filled circles; 1.65mm—open circles) at T¼ 205 K and selectedenergies of exciting photons (from 2.3 to 2.8 eV). Adapted from Ref. 326.




expressed by the relationship [326]

Z r0ðhn;FÞ;F;T½ �

¼ ð1=2ÞZ0 expð�bmFtthÞZþ1

�1

exp �ð2q=sÞ�bs�br0 cosY½ �

X1n¼0

X1m¼0

bmþnsþmFtthþ r0 cosY

smð2qÞm

m!ðmþnÞ!dðcosYÞ

ð142Þ

where s¼ [r20þ (mFtt)

2þ 2r0mFtth cosY]1=2, and other quanti-ties as defined in Eq. (138). Equation (142) is reduced to theOnsager approach if r0(F)¼ r0¼ const.




3

Spatial Distribution of Excited States

3.1. INTRODUCTION

When describing the characteristics of a system of emittingspecies in a macroscopic object, one important property tobe considered is the spatial distribution of the species. It isrecognized, for example, that optical confinement, followingthe location of the recombination-generated emitting states,is an important requirement for achieving high-efficiencyemission and lasing in organic LEDs. The detected emissionefficiency of a radiating object is determined by: (i) the origi-nal population of the emitting species; (ii) the lifetime of theparticles radiated; and (iii) the absorption properties of theobject investigated. It is markedly modified if the object sub-stance can absorb the emitted radiation or the excited speciesare quenched inhomogeneously within the object (e.g.strongly annihilating on its boundaries). Thus, the radiationflux spectrum is deformed and this deformation can be usedto derive information about the spatial distribution of emit-ting species. The situation for the one-dimensional case withemitting species distributed along the x-axis inside a slab

147



object is illustrated in Fig. 52. The measured radiation flux inthe direction �x, F1 differs, in general, from that in the direc-tion þx, F2, due to a difference in the absorption of radiationoriginating at a distance x in two flat layers of different thick-nesses x and (d� x), respectively.

The spectral dependence of the ratio of the flux F2(l) tothe flux F1(l) can be used as an experimental probe for deter-mining the spatial distribution of the emitting species, c(x)[53]. The ratio Rj(lj) obtained for a finite set of wavelengths,lj ( j¼ 1,2,3, . . . ,m) is given within the error of known magni-tude DRj(lj) and

CjðEjÞRd0

cðxÞpðd� x; ljÞdx

Rd0

cðxÞpðx; ljÞdx¼ RjðljÞ � DRjðljÞ ð143Þ

where Cj(lj) is a quantity responsible for possible differencesin optical pathways in detection systems, and p(x, lj) and

Figure 52 Spatial variation of emitting species (c(x)) for the one-dimensional case and schematic illustration of experimental config-uration of two detectors of the radiation emitted from the object inthe direction �x(f1) and þx(f2). From Ref. 53.




p (d � x , lj) are the probabilities that a photon emitted from adistance x and (d � x ), respectively, will reach suitable detec-tor (1 or 2). In the case of infinite lifetime of photons, they aredetermined by the absorption properties of the material onrespective optical pathways

p ðx ; lj Þ ¼ exp½�m ðl j Þx � and p ðd � x; lj Þ¼ exp½�m ðlj Þðd � xÞ� ð144Þ

Equation (143) can be transformed into a linear Fredholmequation of the first kind [328]

Zd

0

cð xÞ Cj ðl j Þp ðd � x; lj Þ þRj ð lj Þ 1 � p ðx ; l j Þ� ��

d x

¼ Rj ð lj Þ � D Rj ðl j Þ ð145Þ

with the kernel

K ðx ; lj Þ ¼ C ð lj Þ pð d � xÞ þ Rj ð lj Þ 1 � p ðx ; lj Þ� �

ð146Þ

The integral equation (145) presents a classic example of an‘‘ill-posed’’ problem, by which one means that the solutionc (x ) does not depend continuously on the data function R( l).In the above formulation of the problem, R(l ) is known onlyfor l 2fljg ( j ¼ 1,2, . . . , m) and the data are given with knownerrors DRj( lj ). With these inadequate data, it is extremely dif-

possible approach is to apply the statistical regularizationmethod (STREG) [330].

This probabilistic method gives the best solution of equa-tions of the type (145) and has been applied successfully to asimilar problem in the past [328,331]. This method consists ofintroducing a priori information about the unknown functionc (x ). It can be the assumption about the smoothness and non-negativity of the solution. Then, using the apparatus of math-

332), we obtain a ‘‘regularized’’ solution and its rms errors.The details of this procedure are given in Appendix A inRef. 328 and testing of the method discussed in the appendix

Chapter 3. Spatial Distribution of Excited States 149



ficult, in general, to solve Eq. (145) (see e.g. Ref. 329). One

ematical statistics known as Bayesian strategy (see e.g. Ref.

of Ref. 53. The application of the method to extract the spatialdistribution of emitting states under different type of excita-tion is described in the following two sections.

3.2. PHOTOEXCITATION

The spatial distribution profile of photoexcited states does notcoincide, in general, with the light absorption profile given bya simple exponential function I (x) ¼ I0(x) exp(�x= la), wherela (l) ¼ m �1a ( l) defines its penetration depth using the linearabsorption coefficient, ma(l). There are several reasons forthat, including: (1) exciton diffusion, (2) internal surfacereflection of emitted photons and= or excitons, (3) host–guestexciton transfer with a finite probability of activation to freehost exciton state from a guest molecule, (4) guest–guest exci-ton transfer with the final step of activation to free host exci-ton state, and (5) host–guest and guest–guest reabsorptionwith the final step of activation to free host exciton state. Inthe last three cases, the guest can be a structural defect form-ing a more or less deep exciton trap. We illustrate the pre-sence of these effects in the spatial distribution of singletexcitons S( x) generated by the exciting light I( x) in the moststudied aromatic crystals of anthracene and tetracene, usingthe semiempirical method described at the beginning of thepresnet chapter. The starting point is Eq. (145) which isapplicable to plate-shaped crystals excited perpendicularlyto their front surface as shown in Fig. 53. Highly absorbedpolarized light is shone on the one side of the crystal andthe fluorescence flux is measured from both sides using thetwo suitably placed quartz plate splitters, an experimentalarrangement corresponding to the one-dimensional configura-tion assumed in Fig. 52. To avoid complications connectedwith differences in separated measurements for the front(Ff) and rear (Fr) emission fluxes, both are measured withthe same detection system. Concurrently with the excitationof the crystal by light (from an HBO 200 lamp in Fig. 53a),a shutter could be placed into one of two different positions.It is arranged so that the photon counts accumulated with




the shutter in position 1 originate from the illuminated sur-face (Ff), and those accumulated in position 2 come from therear (Fr) of the crystal. This gives us the experimental function

Rðm�1Þ ¼ FrðlaÞ=Ff ðlaÞ ¼ Frðm�1Þ=Ff ðm�1Þ ð147Þ

Figure 53 (a) Schematic drawing of the experimental arrange-ment permitting spectral measurements of the radiation originat-ing from two sides of a crystal, to be performed with the sameoptical and detection systems. M1, M2, monochromators. (b) Experi-mental dependence of the rear (fr) to front (ff) photoluminescenceratio as a function of observation depth (l¼m�1) for two differentwavelengths (la) of the exciting light. �, la1¼ 366nm; �, la2¼297nm; in order to better distinguish between the plot for la1 andla2 the latter is averaged by the solid line. After Ref. 53. Copyright1979 Institute of Physics (GB), with permission.




with l ¼ m� 1( l) standing for the ‘‘observation depth’’ that isthe average path traversed by emitted light of wavelengthl . Its value determines directly the probability of emittedphoton to leave the crystal through the front or rear surfacelimiting the plate-shaped crystal [cf. Eqs. (143)–(146)].

Using the experimental points of R(l) with their knownerrors DR(l) and applying the STREG procedure for solutionof (145) with (144) and (146), we obtain the spatial distributionfunction S(x) � c (x) for singlet excitons generated by radiationwith a given la. Two examples are shown in Fig. 54. It is appar-ent that the concentration of excitons deeply within the crys-tals is comparable with that at distances determined by thepenetration depth of the exciting light. In addition, a finite con-centration of excitons appears in front of the rear surface of thecrystal. The latter is by an order of magnitude lower as com-pared with that at the front illuminated surface, but it shouldbe taken into account in all types of interface detector quantumyield experiments regarding the determination of the excitondiffusion length [285] or determining real photoluminescencespectra [56]. The effect of the crystal surface treatment, seenin Fig. 55, confirms the role of its reflectance properties forthe actual distribution of the emitting states. A strong roll-offin the singlet exciton concentration is observed with the illumi-nated metal (Ag, Au) and semiconductor (CuI) coated frontcrystal surface, indicating strong quenching of singlet excitonsnear-by these contacts (Fig. 55a). The penetration depth andthe second rear contact exciton concentration maximumbecome strongly reduced by surface roughening with a streamof carborundum powder (Fig. 55b).

The fluorescence spectra are subject to substantial deforma-tion due to such a broad spatial distribution of emitting species.Two exampl e s ar e shown i n Fig. 56. The real fluoresc enc e spect ra�3 have been obtained from the apparent spectra�1 based onthe spatial distribution of singlet excitons, S(x), from Fig. 54,using the following expression for the fluorescence intensity:

FðlÞ ¼ AjðlÞZd

0

SðxÞ exp½�mðlÞx�dx ð148Þ




Figur e 54 Spatial dist ributions S( x) of sing let exc itons in a 35 m m-thick ant hracene (a), and 4.7 mm-t hick tetracen e (b) singl e cryst alrefer red to the front face cryst allographic plane ( ab ) placed atx ¼ 0. The result s obtained accord ing to the proce dure described inSec. 3.2 wit h the experim ental data collec ted by Glin ski andKalinowski [56] using the experimental arrangement fromFig. 53. A strongl y absorbed light , polarized to the b cryst allo-graphic axis has been used to excite the fluorescence in both cases.The absorption profiles (straight lines) are shown for comparison.




Here, j (l) is the re al e mis si on s pe ct r um t o be d et er mine d , m (l )denotes the absorption coefficient of the fluorescent l ight and Astands for an apparat us factor. The experiment al termexp[�m (l )x] represents t he photon (hc =l ) escape probability ata distance x from the observed crystal illuminated surface. Theintegral runs along the whole thi ckness d of the c rystal. With asimpli fying assumption S(x) ¼ S(0) exp(�max), where ma is theabsorption coefficient of the exciting light (la), the solution ofEq. (148) f or j (l ) on the basis of experimentally known F (l )and ma may b e found and the resul ts a re shown i n F i g. 5 6.

Figure 55 (a) Spatial distributions S(x) of singlet excitons withina 30 mm range from the illuminated front free surface of eight differ-ent anthracene crystals�1 and crystals coated with a semitran-sparent layers of Ag�2 , Au�3 , and CuI�4 , the penetration ofthe exciting light (bk polarized lex¼ 366nm), I0 exp(�x=la) is shownfor comparison (dashed curve). (b) Singlet exciton concentrationprofiles in a 25 mm-thick anthracene crystal before (�) and after (�)roughening the rear surface (x¼ 25mm) of the crystal. After Ref. 285.




The procedure for determining the actual fluorescence spectra,j (l), involves dividing F (l) by

R d0 S ðx Þ exp ½� mð lÞx � d x , the inte-

gral obtained by numerical calculations. In spite of the fact thatt h e emi tt ed l ight, F (l ), was collected from the same crystal facethat was excited, we c an see the blue shift of 2 nm for anthr aceneand as large as 10 nm for t etracene between t he fir st 0–0 fluores-cenc e bands for j (l ) c orrected for r eabsorpt ion and spatial distri-buti on of e x ci to ns . H owe v er , the mo st s t ri ki ng ef fe ct c a us e d byf re e ing the a p par ent sp e ct ra fr om re abs or p ti on and s pat ial ex ci -ton distribution is the sharply increasing intensity of the fluores-c e nc e w it hi n the 0–0 band . The r ef or e, c ry st a l l umines c enc e

Figure 56 The fluorescence spectra from the illuminated free sur-face of plate-shaped anthracene (A) and tetracene (B) crystals, cor-rected for the real spatial distribution of singlet excitons fromFi g. 54 �3 , and that appro xi mated by the e xponential lawS(x)¼S(0) exp(�max)�2 .�1 represents the apparent spectra of fluor-escence. The x are experimental data for anthracene, corrected forreabsorption according to the usual calculation procedure [232,233].




spectra and luminescence spectra f rom c rystal ( the lat ter, as ar ul e , meas ur e d in n or mal e xp e ri ments ) a r e not to b e take n assynonymous.

3.3. RECOMBINATION RADIATION.RECOMBINATION ZONE

The spatial distribution of emitting species produced in theelectron–hole recombination process is one of important rea-sons for a difference between the PL and EL spectra, and acharacteristic determining the EL quantum efficiency. Theself-absorption of the short-wavelength part of the fluores-cence can be utilized for determining the spatial distributionof EL. The principle of the method, as discussed in Sec. 3.1and used for photoexcited states in Sec. 3.2, has been adaptedto the recombination radiation as follows [41]: the unknownspatial distribution of the EL light intensity, c (x ) from aplate-shaped emitting sample, is related to the experimen-tally observed EL signal, FEL (l0), by the expression

FEL ðl0 Þ ¼ Að l0 ÞZd

0

c ðx Þ expð�x =l0 Þ dx ð 149Þ

where exp(�x =l0) stands for the photon escape probabilitywhen its emission takes place at a distance x from the observedcrystal surface (x ¼ 0). l0 ¼ m�10 is the observation depth definedalready as the reciprocal of the linear absorption coefficient m0of the fluorescent light. The integral runs along the thicknessof the crystal, d. The quantity A(l0) is independent of x andcontains characteristics of the emission and some apparatusfactors. A(l0) can be eliminated by measuring the crystal PLunder the same detection conditions (Fig. 57):

FPLðl0Þ ¼ Aðl0ÞZd

0

SðxÞ expð�x=l0Þdx ð150Þ

The ratio FEL(l0)=FPL(l0)¼F(l0), which is a function of l0, con-tains a difference between c(x) and S(x). The condition that




permits the experimental ratio F(l0) to be used for determina-tion of c(x) is to know S(x), which, in general, is modified byreabsorption, and combined reflectance and interferenceeffects as already discussed in Sec. 3.2. Knowing S(x), c(x)follows from a solution of the integral equation based onexpressions (149) and (150):

Zd

0

cðxÞ expð�x=l0Þdx ¼ Fðl0ÞZd

0

SðxÞ expð�x=l0Þdx ð151Þ

Figure 57 Scheme of the experimental arrangement permittingthe spectral measurements of EL and PL to be performed withthe same optical and detection systems. Adapted from Ref. 41.




For a rough analysis, S(x) can be approximated by an exponen-tial function S(x)¼S(0) exp(�x=la), and a set of Eq. (151) fordiscrete variable l0 and given la, solved for c(x) by the methodof statistical regularization [330]. An example of the spatialdistribution of the EL intensity from a 90mm-thick tetracenecrystal is shown in Fig. 58. In contrast to the theoretical pre-dictions of the recombination zone to be located within thecathode region for a trap free tetracene crystal (see discussionof the recombination zone below), comparable intensityregions appear nearby the electrode contacts, and a thirdmuch weaker emission region can be distinguished in the1=3 crystal thickness distance from the anode at a high vol-tage. Important aspects of such a spatial distribution of the

Figure 58 The spatial distribution of the EL intensity in a 90 mm-thick tetracene crystal at two different voltages: U¼ 750V (�) andU¼ 950V (�). The semi transparent hole-injecting Au anode islocated at x¼ 0, and a thick layer of a Na=K alloy forms the elec-tron-injecting contact at the rear crystal side, x¼d¼ 90 mm. Theblack field patterns simulate the light intensity distribution forthese two voltages. The upper part illustrates the position andwidth of the recombination zone as predicted by Eq. (155) for atrap-free tetracene crystal and ohmic contacts. From Refs. 2, 51.




excited singlets can be mapped onto a trap-dependentelectron–hole recombination process involving excitonic inter-actions at the interface and in the bulk of the crystal [41]. Thestratification of the observed EL emission zone into anodeand cathode subzones suggests that trapping is involved inEL processes. The initial recombination leading to emittingsinglets presumably occurs on deeply trapped carriers, holestrapped adjacent to the anode and electrons trapped adjacentto the cathode. On the time scale, the average release time ofcarriers from the traps is much longer than the average recom-bination time, and these two times are much longer that theaverage trapping time. This, however, does not explain theevolution of the EL spatial distribution pattern with appliedvoltage. A well-pronounced drop in the EL intensity close tothe anode at high voltages can be attributed to singlet excitonquenching by high density trapped holes. At a lower concen-tration of holes (at lower voltages), a weaker drop in the sing-let exciton concentration can be observed there. The singletexciton quenching at the cathode is practically absent due tomuch lower concentration of trapped electrons. To understandthe origin of the splitting in the anode EL zone at a high vol-tage, the delayed component of the EL and triplet exciton-trapped charge carrier interaction must be taken into consid-eration. The delayed EL originates from emission of singletexcitons created in the process of triplet–triplet fusion (cf.

efficiently in the singlet exciton fission into two triplets atroom temperature (Sec. 2.5.1.2) add to triplets originateddirectly from the electron–hole recombination process. In theabsence of space charge, the spatial distributions of singletand triplet excitons coincide. A spatially inhomogeneous dis-tribution of high-density trapped holes adjacent to the inject-ing anode causes the triplets to be quenched with the rateincreasing towards the contact. As a result, the position ofthe maximum concentration of the two triplet-created singletexcitons will shift towards the bulk of the crystal observedas a second emission region separated from the anode.

At first glance, the low-field spatial EL pattern apparentin Fig. 58 resembles the spatial distribution of singlet excitons




Secs. 1.4 and 2.5.1.2). In tetracene, triplet excitons produced

generated in single crystals by a strongly absorbed light (Fig.54a). However, the underlying physics is completely differentfor these two pictures. While the rear surface-located maxi-mum of the exciton population in the case of photoexcitationis due to reabsorption of light reflected from the rear crystal-= air interface, the near-cathode maximum of EL shows up asa result of the recombination between trapped electrons andholes arrived from the injecting anode. Though in both casesexcitons concentrate near the principal crystal walls, the rearsurface population of photoexcited states is much lower anddisappears when the surface roughness increases (Fig. 55b).In contrast, the near-anode and near-cathode concentrationsof excitons in the EL spatial distribution pattern are compar-able, illustrating the location of the most efficient recombina-tion regions. It is interesting to note that the overallrecombination zone width producing majority of excited statescan be limited to about 20% of the total crystal thickness if thecontribution to the EL intensity from a threefold droppedexciton concentration is neglected.

The width of the recombination zone is directly related tothe EL efficiency of LEDs, through its definition as a distancetraversed by a carrier during the recombination time,� trec [2]

w ¼ me ; h F t rec ð 152Þ

where me,h is the carrier (electron or hole) mobility and F isthe field within the recombination zone of an EL device. Com-bining (152) and the carrier transit time between electrodes(d), tt ¼ d =m h,eF , yields t rec= tt ¼ w= d, and the recombination

connected with the recombination zone width, w,

PR ¼ 1þw

d

� ��1ð153Þ

Thus, PR extracted from the measured EL efficiency allows

�We note that such defined recombination zone width must not be identi-fied with the geometrical limits imposed on the charge recombination bythe device structure.




probability (see Preface and Chapter 1) becomes directly

the determination of the recombination zone width (seeSec. 5.4). The two limiting operational modes of the EL cell

for w: w > d for the ICEL and w < d for the VCEL opera-tional modes. When we apply Langevin’s theory of recombina-tion [Eq. (4)], substituting at the same time the above definedexpressions for trec and t t , for a comparable contribution tothe current of holes and electrons, we obtain

w ffi ½2 e0 eme m h =ðm e þ m h Þ�ðF 2 =j Þ ð154Þ

Accordingly, the recombination zone generally varies withelectric field. For a strongly field-dependent injection-limited-currents (ILC) (Sec. 4.3.2), w j � 1. Equation (154)predicts a field-independent w if ohmic injection occurs atthe contacts and carrier mobilities are independent of electricfield

w ¼ 2 me mh d =ð me þ m h Þm eff ð155Þ

which in the case of negligible space-charge overlap( meff ffi me þ m h) gives the width of the recombination zonederived from the analysis of the recombination-induced coor-dinate variation of the currents [21,334] (see also Secs. 4.3.2and 4.5). In reality, the recombination rate constant (geh ) isfinite and a certain space-charge overlap occurs. The totalcurrent is composed of hole and electron currents

j ¼ jh þ je ¼ ½mh n h ðx Þ þ me ne ðx Þ�eF ð156Þ

independent of x. In the recombination region w located atx ¼ xr (Fig. 59), the hole current density decreases withincreasing x as

d jhd x¼ e mh

d nh

d x¼ �e geh nh n e ð157aÞ

The analogous relation obeys for electron current density

d jed x¼ eme

d ne

d x¼ egeh n e n h ð157bÞ

The electric field can be assumed constant throughout the




(see Preface and Sec. 5.4) lead to important consequences

sample if the recombination zone is thin compared to thesample thickness, d. Combining Eqs. (156) and (157) yields

dne

dx¼ gehne

meFj

eFmh� ne

memh

� �ð158Þ

Its solution gives a spatial distribution of the electron concen-tration within the recombination zone:

neðxÞ ¼ne;1

1þ exp jgeh=eF2memhð Þ dh � xð Þ½ � ð159Þ

where ne,1 is the electron concentration out of the recombina-

Figure 59 Location (xr) and width (w) of the recombination zonefor a small space-charge overlap in a plate shaped EL material ofthickness d, provided with two injecting ohmic electrodes (anode,cathode). dh and de denote the penetration depths of injected holesand electrons, respectively. We note that xrffidh, dh=deffi mh=me, anddhþdeffid for w! 0.




tion zone,� and dh is the penetration depth of holes includingthe charge overlap region. The recombination width may bedefined as twice of the reciprocal of the exponent factor pre-ceding (dh � x ):

w ¼ 2 eF 2 me m h =jg eh ð160Þ

In other words, the recombination width constitutes the dou-ble penetration distance of the electron current into the over-lap region. Inserting appropriate expressions for the shallow-trap SCL current density, j ¼ (9=8)e0e( me h 2

eh

w ffi 2 me mh d =ð me þ m h Þm eff ð161Þ

an expression identical to that of (155). Whenever w � dh, de ,the ratio dh=d e ffi mh =m e determines the position of the recombi-nation zone (in Fig. 59, xr ¼ d h þ w=2 ffi d h). Such a case hasbeen assumed in the evaluation of the position ( mh= me ) ffi 2.8and width (161) of the recombination zone for the tetracenecrystal in Fig. 58, using independent data for the electron( me ffi 0.3 cm2= V s) and hole ( mh ffi 0.85 cm2= V s) mobilities inthe c0 crystallographic direction [335]. To be more precise, aspatial variation of the electric field within the sample should

FðxÞ ¼ ð3=2ÞðU=dÞðx=dÞ1=2 ð162Þ

and its averaged value F¼ (3=2)U=d inserted into Eq. (160).Then the recombination width doubles:

w ¼ 4memhd=ðme þ mhÞmeff ð163Þ

It is clear from Eq. (163) that w¼ 4(me,h=mh,e) d < d being sim-ply determined by the electron to hole mobility ratiome,h=mh,e�1, and wmax¼d for me¼ mh.

The above discussion has been limited to a considerationof field-independent mobilities, an assumption relatively

� The coordinate dependence of ne,1 resulting from the charge-density inho-mogeneity of one-carrier SCL current flow is assumed here to be negligible.




be taken into account (see e.g. Ref. 334),

þ m )F =d (cf. Sec.4.3.1), and g (4), we arrive at

well justified for single organic crystals [27]. On thecontrary, there are numerous experimental data for thefield dependence of the carrier mobility in amorphous and

Consequently, the recombination width must be consideredas a field-dependent quantity whenever the field dependenceof the mobility for electrons differs from that for holes. A typi-cal experimentally obtained relationship m ¼ m (0) exp(bm F 1=2)yields w ¼ 4d [me,h(0) =m h,e(0)] exp[(b me,h � bmh,e )F 1=2 ] for sub-stantially different mobilities of holes and electrons. Thus,the recombination zone width can either increase or decreasewith electric field depending on the relation between the char-acteristic parameter bm for electrons and for holes injectedunder SCL conditions.

In the case where the current flowing through the sam-

width becomes a complex function of applied field because thefield decreasing F2 =j factor in Eq. (154) adds to the field-dependent mobility of w and often can dominate the electric

The recombination width can be minimized by the con-finement of the recombination process at the interface oftwo organic materials as typically occurs in double- andmulti-layer organic LEDs [2] (see also Chapter 5). The pene-tration depths of holes and electrons can then be identifiedwith thicknesses of hole and electron transporting layers,respectively, and their mobilities used to calculate the recom-bination width. A good example of such a situation is therecombination process in the most studied double-layerLED, ITO=TPD=Alq3=Mg=Ag. The free carrier kinetics atthe TPD=Alq3 interface after an abrupt switch of the voltageoff takes on a simple form

dn

dt¼ �gehn2 ð164Þ

where n¼nhffine represents the equal concentrations of holes(nh) and electrons (ne). A solution of this equation leads to afunction describing the temporal (t) evolution of these




polycrystalline materials (see e.g. Ref. 29; cf. also Sec. 4.6).

ple is injection limited (cf. Sec. 4.3.2), the recombination zone

field-induced changes in the recombination zone (cf. Sec. 5.4).

concentrations

1

n¼ 1

n0þ geht ð165Þ

which can be translated to the EL intensity decay [FEL(t)] inthe form [309]

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiFELðtÞ

p ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijPLPSgeh

pn0

þffiffiffiffiffiffiffiffiffiffiffiffiffiffigeh

jPLPS

rt ð166Þ

assuming FEL¼jPL PS geh[n(t)]2, where jPL is the emission

efficiency of excited states, and PS is the probability of thecreation of an emitting singlet excited state of Alq3

EL)�1=2 vs. time plot of the experi-

mentally observed decay of the EL intensity at the fallingedge of a 25V rectangular voltage pulse for such an LED, fol-

Figure 60 The EL decay at the falling edge of a 25V pulse plottedin F�1=2EL against time scale to compare with the bimolecular kineticsbehavior. Here, t¼ 0 corresponds to the voltage fall of the pulse. Thedata are fitted (full straight line) to the function expressed by Eq.(166). The FEL(t) decay curve is shown in the inset for comparison.After Ref. 309. Copyright 1998 American Institute of Physics.




lowing the behavior predicted by Eq. (166). A single straight

(cf. Sec.1.4). Figure 60 shows the (F

line fitted to the experimental data with n0 ¼ (2j= eg edd )1= 2dependent on the steady-state current density j ffi je ffi jh (at25 V) allows geh ¼ (1.1 � 0.5) � 10 �10 cm3= s to be determinedfrom its slope to intercept ratio [309]. This value seems to sup-port the Langevin recombination mechanism, givingme þ m h ffi ( e0e =e )geh ffi 3 � 10� 4 cm 2=V s with e ¼ 3.8 based onEq. (4). Since the electron mobility in the electron-transport-ing layer of Alq3, m e ffi 10� 5 2

is much lower than the above value of the effective mobility,it has been ascribed to the zero-field hole mobility in TPD[mh(0) ffi 6 � 10� 4 cm2= V s [338]. Under these conditions, thewidth of the recombination zone can be approximatedby the expression w ffi 4[mh(TPD)=m e (Alq3)](d= 2), where d =2corresponds to the position of the interface with the identicalthickness of hole (TPD) and electron (Alq3)-transportinglayers, d= 2. Taking a high-field ( F ffi 106 V =cm) values ofthe hole mobility in TPD, mh(TPD) ffi 10� 3 cm 2=V s [338], andme(Alq3)ffi 5� 10�5 cm2=Vs (Ref. 337) for a TPD=Alq3 func-tion-based diode with d¼ 120nm (Ref. 309), we arrive atw ffi 12 nm (w=d ffi 0.2 close to such a ratio discussed abovefor the tetracene crystal from Fig. 58). This value appears tobe quite independent on electric field since mh(F) for TPDand me(F) for Alq3 vary in a similar manner [339–341]. Onthe other hand, the recombination zone width shows up as amarkedly decreasing function of applied electric field for thinfilm organic LEDs operating in the ICEL mode (Sec. 5.4).

The above discussed methods for determining spatial dis-tributions of excited states, based on the reabsorption ofemitted light, are expected to break down in thin organic filmsand weakly absorbed light within their emission spectrumrange. Other particular features of organic LEDs such asthe EL anisotropy [342] or differences in emission spectra[343,344] of consecutive LED emitter component layers havebeen utilized to infer the spatial extent of the recombinationzone. The latter will be illustrated in Sec. 5.4 since it isdirectly connected with quantum EL efficiency. The EL aniso-tropy, defined as the relative light output polarized parallel(Ik) and perpendicular (I?) to the direction of preferentialmolecular alignment (S¼ Ik=I?), can be accomplished either




cm = V s (see Refs. 309, 336, 337)

by stretching substrates or by means of Langmuir–Blodgetttechnique. The EL anisotropy as high as S ¼ 3 has beenobtained with stretch-oriented poly(3-octylthiophene)(P3OT)[345]. The Langmuir–Blodgett (LB) technique has beenapplied for the preparation of LEDs based on soluble poly(p -phenylene)(PPP) derivatives [346,347]. This technique allowsfor complete three-dimensional control of the film structureincluding the macroscopic alignment of the rigid macromole-cules, and polarized EL has been observed from LEDs basedon LB films of PPP [348]. In the LB film, the rigid rod-likepolymers lie flat on the substrate and posses a preferentialorientation in the plane of the layer parallel to the dippingdirection. For a distribution in the conjugation length of poly-mer chains, long conjugation chains are oriented, whereasshorter conjugation chains are randomly oriented. This leadsto a reduction of the EL anisotropy. S ¼ 1.3 has been found forpoly(3-alkylthiophene) (P3AT) derivatives-based LB LEDs[349]. By analyzing degree of polarization of an LB LED con-sisting of two layers with two different (mutually perpendicu-lar) orientations, it is possible to determine the spatial profileof its emission. Such a procedure has been applied to a rangeof LED devices based on PPD LB films [342]. Schematic repre-sentation of such LEDs is shown in Fig. 61. The iso-pentoxysubstituted PPP polymers were deposited in such a way asto form two orthogonal orientation regions with a varyingratio of the monomolecular layer numbers at a constant over-all thickness of d¼ 120nm, which corresponds to the typicalfilm thickness in polymer LEDs. The parallel orientationrefers to the direction of preferential alignment of the layernext to the Al cathode. Therefore, Ik > I? means that mostof the emission originates from the parallel layer (and viceversa for Ik < I?). Increasing the number of monolayers ofparallel orientation (n) and correspondingly decreasing thenumber of monolayers of perpendicular orientation (100�n)increase the anisotropy of the EL emission S2¼ Ik=I?) (thesubscript 2 indicates Ik and I? are obtained from the tworegion LED). Since increasing n translates directly throughthe monolayer thickness ( 1.2 nm) into the thickness of theregion located next to the Al cathode (L), the dichroic ratio




(Ik=I?)2 should be an increasing function of L. One has to keepin mind that due to a two-dimensional orientational distribu-tion function of the in-plane molecular alignment, the contri-bution of Ik normalized to the total intensity Ikþ I?,a¼ Ik=(Ikþ I?) differs from one even for a homogeneouslyoriented device, as for example a¼ 0.75 with S¼ 3. It is clearthat the experimentally observed EL anisotropy plottedagainst the distance, x, from the Al cathode (located atx¼ 0), and identified with varying thickness (L) of paralleloriented n monolayers, contains the EL emission profiledetermined by the spatial distribution of emitting states, w(x):

Zx

0

wðx0Þdx0 ¼ f ðxÞ ¼ SS2ðxÞ � 1

ðS� 1Þ½S2ðxÞ þ 1� ð167Þ

Figure 61 Polymeric Langmuir–Blodgett LED devices used forthe determination of the EL profile by observation of the degree ofpolarization of the light output. The chemical structure of the poly-mer is given in the circular inset. After Ref. 342. Copyright 1997Wiley-VCH, with permission.




Equation (167) has been derived assuming the dichroic ratioS2(x) to be independent of the absorption coefficient of thepolymer, and S2 per monolayer to be constant for any locationwithin the LED, assumptions which may not always be justi-fied. The relative EL output as a function of the distance fromthe Al cathode can thus be obtained by differentiation of themeasured relative emission from the parallel organized layer,f(x), as given by the right-hand side of Eq. (167). The calcula-tion of Df(x)=Dx, made with Dx¼ 12nm (10 monolayers) for theITO=PPP=Al devices with x varying between 0 and 120nm, isshown in Fig. 62. Such a calculated profile, like that in single

Figure 62 The spatial distribution of the EL emission repre-sented by the amount of emission from a block of 10 monolayersas a function of its distance from the Al electrode in a PPP LED:ITO=PPP (120nm)=Al. The experimental data are indicated bythe bars. The curves are exponential functions illustrating an expo-nentially decreasing penetration of electrons injected from Al intothe PPP film for a set of fixed values of the penetration depthsse¼ 10, 20, 30nm. After Ref. 342. Copyright 1997 Wiley-VCH, withpermission.




aromatic crystals (see Fig. 58), shows the exciton quenchingnear the metal electrode, but unlike single aromatic crystals,possesses only one maximum (at 30 nm in Fig. 62) in thecathode region of the LED. The decreasing emission intensityfor x> 30nm has been ascribed to decreasing concentration ofelectrons injected from the Al cathode, the holes assumed tobe distributed homogeneously throughout the PPP film.Nearly 90% of the EL is generated in a 60nm thick zonewhich can be regarded as the width of the recombinationzone. In addition, the width has been found not to dependon the overall thickness of the LED [342]. The message thatfollows from these results is that the recombination processin the ITO=PPP=Al LEDs is determined by unbalanced injec-tion conditions far from space charge and trapping effects sostrongly apparent in the EL emission profiles of aromatic sin-gle crystals [41].




4

Electrical Characteristics ofOrganic LEDs

4.1. INTRODUCTION

Light emission from a thin film organic LED is underlain by acomplex combination of various electronic processes, one ofthem being charge injection and following it electrical currentflowing through the device.

4.2. CURRENT–VOLTAGE CHARACTERISTICS

The non-linearity is recurrent feature of current–voltagecharacteristics of all operating organic LEDs, independentof the number and configuration of organic layers (Fig. 63).It is associated with the fact that the driving them currentis due to injection of charge at the electrodes: holes at theanode and electrons at the cathode (and not being a resultof the bulk generated carriers). Double logarithmic plots ofthe current vs. applied voltage allow to distinguish the power

171



law behavior of the current. From the examples shown inFig. 64 for the LEDs based on single aromatic crystals, themoderate field (104 V= cm < F < 5 � 105 V= cm) straight-linesegments of such plots suggest the power law j � Un to obeyfor unipolar and double-injection currents for tetracene butnot for anthracene crystals. The current–voltage characteris-tics in single organic crystals, measured over many orders ofmagnitude in applied field (10–106 V =cm), exhibit severalwell-pronounced regimes [318,350,350a]. An example pre-sented in Fig. 65 shows the low-field value n ¼ 1 to approachn ¼ 2 for moderate and high fields. They are thought to repre-sent the low-field Ohmic conduction and SCL conduction inthe presence of shallow traps followed by the free-trap con-duction (or saturation of injection) in the upper limit of the

Figure 63 (a) Double-layer (DL), (b) Triple-layer (TL) and (c)Multi-layer (ML) configurations for organic LEDs. In the (a)and (c) configurations of either electron-transporting layers(ETLs) or hole-transporting layers (HTLs) can serve as emit-ting layers (EMLs), which are indicated in brackets besidetheir description. After Ref. 2. Copyright 1999 Institute ofPhysics (GB).




applied field. Similar behavior has been observed for thin filmorganic systems provided with Ohmic injecting electrodesthough the deep exponentially distributed traps regionis usually considered to occur at moderate electric fields(Figs. 66 and 67). Three general regimes can be distinguishedas indicated in Fig. 67: (A) leakage or diffusion-limitedcurrent, (B) volume-controlled current with an exponentialdistribution of traps, and (C) volume-controlled current withfilled traps. From the slopes in the regime (B) and the

Figure 64 Current–voltage characteristics for single-layer (SL)EL cells based on anthracene (a) and tetracene (b) single crystalswith unipolar and double injection contacts. Na=K–Na=K: mono-negative carrier injection, Au–H2O: mono-positive carrier injection,Au–Na=K: double injection. The crystal thicknesses are 98 and 108mm for anthracene and tetracene, respectively. The slopes of thestraight-line segments for tetracene characteristics are givennearby the curves. After Ref. 51.

Chapter 4. Electrical Characteristics of Organic LEDs 173



Figure 65 Unipolar (electron) current vs. electric field for a0.1 cm-thick naphthalene single crystal provided with silver electro-des. Several different regimes can be distinguished: (i) the low-fieldlinear increase of the current (Ohmic regime); (ii) the SCLC in thepresence of shallow traps (DE < kT); (iii) the trap-filled limit atFTFL; and (iv) the SCLC with filled traps (no trapping). Adaptedfrom Ref. 350a.

Figure 66 The architecture and energy levels of a four-layerorganic LED (a) and its current–voltage characteristics with pulsedbias applied at high current density as indicated in part (b). Thechemical structures of the materials used are shown in part (c).After Ref. 351. Copyright 2002 American Physical Society.

"







trap-filled-limit field, FTFL ¼ 8 � 10 5 V =cm, the total concen-tration of traps H ¼ (3=2)e0eF TFL =ed ¼ 3 � 10 19 cm� 3 and theirenergy (E ) distribution h (E ) ¼ ( H=lkT) exp(�E =lkT) withl ¼ 2.9 follow. However, there is an interesting differencebetween j(U) curves for single crystals (Fig. 65) and thin filmLEDs (Figs. 66 and 67). A well-resolved sharp current jump atU ¼ UTEL (F TFL ), seen for single crystals, practically does notappear for thin film LEDs. Although further studies are

Figur e 67 The current -field charact eristics of a DL electr opho-sphor escen t orga nic LED based on the metallo -organi c phosp horIr(ppy)3 (for the molecu lar structure’ see Fig. 31). The energy levelsof the LED structure are given in the inset. The j(F) curves are wellreproduced from run to run except the lowest field region, where thebuilt in electric field (Fbi¼ 2� 105 V=cm), due to the difference inthe work functions of the electrodes, becomes comparable with theapplied field. After Ref. 304. Copyright 2002 American PhysicalSociety.




needed to establish the exact reason for this difference, thestrong temperature dependence of the current–voltage char-acteristics and their linear scaling with U=d for both typesSL [352–355] and DL [356] organic LEDs suggest the devicecurrent to be injection limited rather than SCLC (for a

teristics for the SL, ITO=TPD(90 nm)= Al, and DL,ITO= TPD(27 nm)=Alq3(55 nm)=Mg:Ag, LEDs at varyingtemperature, and Fig. 69 their variation with sample thick-ness for other SL, Al= Alq3= Ca, and DL, ITO=TPD(20 nm)= Gaq3(10–80 nm)= Mg:Ag, organic LEDs. A moredetailed study of the interrelation between thickness of theHTL and ETL using a molecularly doped layer as the HTLshows no direct correlation of the current to either componentlayers and total thickness of the LEDs (Fig. 70). Since theinjection-limited current, by definition, should not exhibitany sample thickness dependence, the observed variation ofj (V) characteristics with film layer thickness would suggestthe film formation process (including the formation timeand thus, film thickness) to affect the carrier injection at itsinterface and=or trap-free SCLC to be modified by the fielddependence of carrier mobilities. All these options are dis-cussed in Secs. 4.3–4.6.

4.3. SPACE-CHARGE- AND INJECTION-CONTROLLED CURRENTS

Unlike in inorganic semiconductors, impurities normally actas traps for charge carriers rather than as sources of chargecarriers. An exception from that rule are conjugated poly-mers. For example, polyphenylenevinylene (PPV) fabricatedvia a special precursor route may turn out to be p-doped withdoping concentrations in the order of 1017 cm�3. In that case,a Schottky-type depletion zone can be established near ametal contact [358]. However, in vast majority of cases, theconcentration of impurities is small enough not to perturbthe electric field distribution inside a solid-state sample




Organic solids are usually insulators (see e.g. Ref. 357).

discussion, see Sec. 4.3). Figure 68 shows j –U charac-

Figure 68 Current–voltage characteristics of SL and DL ELdevices at various temperatures. (a) A 6.8mm2-area deviceITO=TPD (90nm)=Al from Ref. 356a; (b) a 0.01mm2-active areadevice ITO=TPD (27nm)=Alq3 (55nm)=Mg:Ag; inset: temperaturedependence of the straight-line slopes (precisely, n� 1); afterRef. 356. Copyright 1996 American Institute of Physics, withpermission.




[359]. In those cases, the dark electrical conduction is verylow, the solids are considered as good insulators. Yet, suchsolids can be made to conduct a relatively large current ifthe contacts permit the introduction in them an excess of freecarriers [360]. If the carriers enter through a surface bound-ary, the process is referred to as charge injection. The chargeinjected conduction is governed by charge injection barriers atthe electrode contacts and charge transport properties ofmaterials. For electrons, the injection barrier is given byDEe¼Wc�A, and for holes by DEh¼ I�Wa, where Wa andWc are the work functions of anode and cathode, and I andA are ionization potential and electron affinity of the solidstate. Depending on the charge injection efficiency and mobi-lity of charge carrier, the current is space-charge limited(SCLC) [26,334] or injection limited (ILC) [360,361].

Figure 69 Variation of the current with applied voltage, recordedin a range of thickness between 10 and 300nm. (a) SL sandwich filmsystem of Al=Alq3(d)=Ca; adapted from Ref. 355. (b) DL LED,ITO=TPD(20 nm)=Gaq3(10–80nm)=Mg:Ag with varying emitterlayer of 8-hydroxyquino-line gallium complex (Gaq3); after Ref.356. Copyright 1996 American Institute of Physics.




Figure 70 Influence of thickness of the anodic (75% TPD:PC) (a)and cathodic (Alq3) (b) layers (HTL and ETL, respectively), givenin the figure, on the j(F) characteristics of the DL LEDs ITO=75%TPD:PC=Alq3=Mg=Ag. The low-field (S1) and high-field (S2) slopesdiffer in general except for the thinnest layers (35 nm). The thick-ness of the ETL (60nm) and HTL (60nm) were kept constant inpanel (a) and (b), respectively. After Ref. 303. Copyright 2001 Insti-tute of Physics (GB).




4.3.1. Space-charge-limited Conduction (SCLC)

An indispensable condition for the occurrence of SCLC is thatthe electrode can supply more carriers per unit time than canbe transported through the insulating sample. A contact thatbehaves in that way is called Ohmic contact. At an idealOhmic contact, the electric field vanishes (F ¼ 0) because ofscreening by the injected space charge (the charge concentra-tion n !1). In practice, an electrode can only be Ohmic if theinjection barrier is small enough to ensure that no field-assisted barrier lowering is required to maintain a sufficientlyhigh injection rate. In that case, a virtual electrode is estab-lished close to the geometrical contact that serves as a chargecarrier reservoir [362]. At low fields, the virtual electrodemoves into the bulk of the sample so far that a large numberof the carriers injected at the geometrical contact do not reachthe opposite electrode, and the current becomes limited bytrapping before reaching the in-bulk barrier formed by thesuperposition of the image Coulombic, space charge andexternal potential [257]. This situation relates to the injec-tion-limited currents discussed later on in Sec. 4.3.2. The cri-tical value of the injection barrier height depends ontransport properties of the adjacent insulator. It can be higherfor low mobility, and lower for high mobility materials. A fewtenths of an eV will be an upper limit in cases of practicalinterest. For a perfectly ordered or disordered insulatingmaterials, or those containing very shallow traps (DE�kT),the SCL current in a sample of thickness d obeys Child’s

jSCL ¼9

8e0em

F2

dð168aÞ

In the presence of discrete traps

jSCL ¼9

8e0eYm

F2

dð168bÞ

where m is the microscopic mobility of the carriers, e thedielectric constant, e0 the dielectric permittivity, and Y isthe fraction of free (nf) to trapped (nt) space charge.




law (see e.g. Ref. 334)

If local traps are distributed in energy (E), they will befilled from bottom to top as electric fields, F, increase. Thequasi-Fermi level will scan the distribution shifting towardsthe transport band, and Yffinf=nt will become a function of F.A general form of nt¼nt(nf) relation can be obtained from adetailed balance equation as [363]

nt ¼ nfusZ1

0

hðEÞn expð�E=kTÞ þ nfus

dE ð169Þ

where u is the thermal velocity of free carriers, s the capturecross-section, and the term n exp(�E=kT) expresses the rateof thermal release of charge from all trap energies E distrib-uted according to a function h(E).

In studies of low-mobility insulators, two types of contin-uous trap distributions are commonly used: the exponentialdistribution of traps [364] and the Gaussian distribution oftraps [365].

The problem has been solved analytically for an exponen-tial distribution of traps

hðEÞ ¼ ðH=lkTÞ expð�E=lkTÞ ð170Þ

where H is the total concentration of traps, and l is a charac-teristic distribution parameter which can be replaced by acharacteristic distribution temperature Tc¼ lT. E¼ kTc

stands for a measure of the average trap depth of a given trapdistribution. Inserting (170) into (169) and substitutingn=vs¼Neff, where n is the common frequency factor and Neff

the effective density of states in the transport band, andassuming l¼Tc=T > 1 and nf=Neff� 1, yield

ntffiH

l

nf

Neff

� �1=l

pcosecðp=lÞ� ðNeff=nf Þ1�1=lð1�1=lÞh i�1� �

ð171Þ

On the basis of Eq. (171), a solution to the current

j ¼ nf ðxÞemðFÞ ð172Þ




and Poisson’s equation

dFðxÞdx

¼ e

e0entðxÞ ð173Þ

with

U ¼Zd

0

FðxÞdx ð174Þ

and the boundary condition F(0)¼ 0 (SCLC) can be found:

jg ¼NeffemHl

e0ee

� �l l2 sin p=l½ �lþ 1ð Þp

� �l2lþ 1

lþ 1

� �lþ1Ulþ1

d2lþ1 ð175Þ

This general solution is usually approximated by Mark andHelfrich [366]

j ffi NeffemHl

e0ee

l

lþ 1

� �l 2lþ 1

lþ 1

� �lþ1Ulþ1

d2lþ1 ð176Þ

when a¼ jg=j¼ [l sin(p=l)=p]l ! 1, i.e. for large values of l.However, for an exponential distribution of shallow traps,expression (176) overestimates the current. For example,l¼ 1.05 gives affi 0.04 that is the current density calculatedaccording to Eq. (176) is overestimated by a factor of 25( jffi 25jg). For the typical range of l at room temperature(1.5 < l < 20), the factor a changes from 0.25 to 1 (Ref. 363)so that applying Eq. (176) instead of Eq. (175) leads to a max-imum difference not exceeding a factor of 4. At sufficientlyhigh injection levels, the traps are completely filled; they nolonger influence the carrier transport, and the samplebehaves as an ideal SCL conductor. This occurs at a voltage

UTFL ¼en0d

2

e0en0

Neff

� �H

n0

� �l 9

8

lþ 1

l

� �l lþ 1

2lþ 1

� �lþ1" #1= l�1ð Þ

ð177Þ

where n0 is the thermally generated background free chargedensity. Since n0 is negligible in comparison to the injected




charge density, it can be easily eliminated from Eq. (177). Ifthe trap distribution is of Gaussian rather than exponentialshape, jSCL (F ) no longer obeys a power law. Instead@ ln j=@ ln F increases with increasing field [367–369]. In mostcases in organic solids, it is difficult to distinguish experimen-tally between a Gaussian distribution of traps

h Eð Þ ¼ Hffiffiffiffiffiffiffiffiffiffiffi2 ps 2p exp �ðE � Em Þ2 = 2 s2

h ið 178Þ

where s characterizes the dispersion of trap energies aroundEm, and E m is the position of the maximum of the distribution,and the exponential one given in Eq. (170) because of a finite(not too wide) range in voltage applied to the studied samples.It usually remains within a factor of 10 4. For this relativechange in trapped charge concentration (169), the quasi-Fermi level ( EF ) would move a distance of 0.23 eV. Therefore,under normal experimental conditions, EF will move no morethan 0.2–0.3 eV from the deepest trapping level, Ed, towardthe band edge and will only probe traps in this energy range.For E not differing greatly from Ed, Eq. (177) can be writtenas [370]

h ðE Þ ¼ h ðEd Þ exp½�ðE � E d Þ= lkT � ð179Þ

where

lkT ¼ s2 =ð Ed � E m Þ ð180ÞThe functional shapes of Eqs. (179) and (170) become

identical, and, therefore, the exponential and Gaussian trapdistributions have approximately identical current–voltagecharacteristics [26]. There are experimental current–voltageplots which can be approximated by a sequence of power typefunctions j � Un with varying n (see Figs. 70 and 71). They canbe interpreted in terms of the voltage-induced movement ofthe quasi-Fermi level through a set of Gaussian distributionsof local traps dispersed around consecutive discrete traps[368] or explained by the lowering of the potential barrier ofa spatially extended trap (macrotrap) pinned on structuralor chemical defect [318]. Each macrotrap consists of local




(point) traps distributed and limited in energy and space. Itcan be characterized by a spherical-symmetry cage of radiusr0 and energy distribution in space

EðrÞ ¼ 3 lkT lnðr0=rÞ ð181Þ

where r is a distance from the center of the pinning trap ofradius rb� r0. The potential shape (181) is a result of theexponential energy distribution of point traps (170) and itsrelation to their caging in macrotraps,

hðEÞdE ¼ �4pr2NmN0 dr ð182Þ

where Nm is the concentration of molecules, andN0 is the con-centration of macrotraps. The integrating within the energyrange (1,0), and distance (0,r0), respectively, yields themacrotrap radius

r0 ¼3H

4pN0Nm

� �1=3

ð183Þ

which shows an expected tendency to increase with decreas-ing molecular density (Nm) and the macrotrap-to-microtrapconcentration ratio (N0=H). There is no exact knowledgeabout the nature of pinning traps but it is easily conceivablethat they originate from small clusters of dimers or non-inten-tional polar dopants [371]. Such dimer clusters or polardopants distort their environment in a certain region, produ-

Figure 71 Current density as a function of electric field for twosolution-grown anthracene crystals at room temperature. Electro-des: copper iodide (CuJ); crystal thickness: d¼ 66mm (a), d¼ 49 mm(b). After Ref. 317a.




cing and=or aggregating local defects with energy states dis-tributed in space according to a decreasing function givenfor instance by Eq. (181). Thus, it is not unreasonable to spec-ulate that macrotraps constitute cluster of incipient dimers ofvarying sizes formed preferentially at dislocations as it hasbeen already suggested to explain evolution of an SCLCregime in organic crystals [372]. Furthermore, the macrotrappotential could be, in principle, considered as the strainenergy in a dislocation itself. Based on a distance (r) fromthe dislocation, two contributing terms of this energy areusually distinguished (Fig. 72). For distances larger than r2,there is E(1)(r), the elastic (continuum) strain energy, andfor distances smaller than r2 (but larger than rb ), one hasE(2)(r), the core energy, which, in contrast to E(1)(r), cannotbe evaluated from elastic approximation because the strains

Figure 72 A two-dimensional representation of a two-componentpotential of a macrotrap. Adapted from Ref. 317a.




are too large [26]. The dimers created along dislocation lineswould still form the pinning traps for the macrotraps. Theradius r0 of a spherical macrotrap, which in this case is a termsomewhat ill-defined, expresses the Burgers vector averageddistance at which the effect of the dislocation on intermolecu-lar orientations and distances lies within kT of the effect oftemperature on these parameters. The dislocation back-ground of the macrotrap explains in a natural way two repro-ducible branches of the potential:

E ðr Þ ¼3 l1 kT lnð r01 = rÞ for r01 � r � r13 l2 kT lnð r02 = rÞ for r1 � r � r b

�ð184Þ

The weak-gradient part (l1 ffi 1) is due to weak strains createdat distances larger than r2, and strong gradient part (e.g.l2 ffi 3) resulted from large strains occurring in the rangerb < r < r2. Since dislocations are typical extended faultsarising in crystal lattice during crystal preparation and sub-sequent handling, one would expect them to be commonlyobserved with different techniques. The discrete trap depthsEt ¼ 0.53–0.60 eV are, for example, detected in anthracenecrystal with TSC techniques [373–375]. The same valuescan be found by an analysis of steady-state SCLC j–U charac-teristics based on the concept of the macrotrap potential givenby Eq. (184) (see also Fig. 69). For a discrete set ( N0) of macro-traps, a general solution to Eqs. (171)–(174) with one-branchpotential (181) takes on the form [318]

j ¼ Neff

N0

e0em2þ 3l

2:7er03lkT

� �3l 3þ 3l

2þ 3l

� �2þ3lexpð�Et=kTÞ

U2þ3l

d3þ3l

ð185Þ

which like Eqs. (175) and (176) gives a power-type function ofj vs. U, j�Un, with n¼ 2þ 3l > 2. However, it can beexpressed by a quadratic dependence typical for discrete traps(168) with a field-dependent Y factor

Y ¼ nf

nt¼ Neff

N0

2:7er03lkT

� �3l U

d

� �3l

expð�Et=kTÞ ð186Þ




Equation (185) reads then as

j ¼ e0 em2 þ 3l

3 þ 3 l2 þ 3 l

� �2þ3 lYU 2

d 3 ð 187Þ

The conductivity and j–U characteristic given by Eq. (187) issimilar to the result following the Poole–Frenkel effect onSCL currents [376,377]. Such a situation is clearly notexpected in the case of the standard solution for trappingby a discrete set of separated microtraps expressed byEqs. (167) and (168). This is the case if one extrapolatesEq. (185) to l ! 0, with Y ¼ (Neff= N0) exp(�Et=kT). The physicalmeaning of this extrapolation is that we deal with one discretetrap level (Et), the trap potential being the infinitely sharppoint well for which the barrier lowering can be neglected.

Due to the functional form of Eq. (185), which, except forthe constant coefficient, is identical to the SCL j –U character-istics for a continuous exponential distribution of the form(175) or (176) derived in the case of the infinitely sharp pointtraps, the experimental data arising from the discrete macro-trap background can, without scrutiny, be mistakenly attrib-uted to the continuous exponential distribution of point traps.The transition from the low-to high-field regions of thecurrent occurs at a voltage (see Fig. 71)

UðaÞtr ¼

3lkTd

2:7er0

9l

8

� �1=3l ð2=lþ 3Þ1þ1=l

ð3=lþ 3Þ1þ2=3lð188Þ

which, having l from log j–logU slope, allows macrotrapdimension r0 to be determined, and then from the relationr0¼ (1=2pNeff)

1=3, Neff to be calculated. We note that theUtr 6¼UTFL as given by Eq. (177). The latter supplies an infor-mation about the total concentration of local (point) trapsrather than the density of states, Neff. From the above, it isevident that the experimental form of j–U curves is not suffi-cient to unambiguously identify the trap distribution underly-ing the SCLC flow. Even the steep rise in the current withincreasing voltage, typically associated with the trap filledlimit, is not unambiguous, as it can be due to the voltageUðbÞtr (Fig. 71) which lowers the macrotrap barrier at the




rm( b), where the microtrap distribution changes steeply its lfrom the actual value l1 to l2 (cf. Fig. 69). The macrotrap(defect cage) concept has been successfully applied in the pastto explain the quenching of luminescence [263,311,313,378],field-dependent mobility [319] (see Sec. 4.6), and current–vol-tage characteristics in organic solids. Figure 71 shows typicalhole j –U characteristics for two of over 20 solution grownanthracene crystals, within the broad current range (overeight decades) allowing to yield substantial information aboutthe concentration and distribution of traps. Both the tradi-tional approach using Eq. (176) based on the quasi-continuousexponential distribution of point traps, and the macrotrapconcept were employed in the analysis of the data above thetransition field F (a ) [318]. The segment of the j– F curvesbelow F ¼ F (a) is most probably governed by the carrier diffu-sion (see Sec. 4.4). According to the first approach, Regions I,II and III, should be ascribed to filling exponentially distribu-ted point traps (I), trap-filled limit (II) and electrode-limitedcurrent (III). From the trap-filled limit voltage UTFL ¼ U

ð bÞtr

(177) for both crystals, the total concentration of trapsH ¼ nt ffi (3= 2)e0e UTFL = ed

2 ffi 10 13 cm� 3 follows. This low con-centration of hole point traps disagree with H ffi 1017 cm �3 ascalculated from the current j ¼ jb using Eq. (176) withNeff ¼ 4�1021 cm� 3 (the molecular density in anthracene),mh ffi 1 cm2=V s and e ¼ 3. The macrotrap concept resolves theabove inconsistency. The results summarized in Table 4 showthat the total energy of a hole in the macrotrap is the sum ofthe two terms as given by Eq. (184) (cf. Fig. 72). The key dif-ference between the standard SCLC j– U characteristic inter-pretation and that resulting from the macrotrap model is thatwhile in the first case, the plot follows the position of thequasi-Fermi level sweeping consecutive microtrap levels, inthe second case, it is due to lowering of the barrier with thequasi-Fermi level moving below the trapping level. The vol-tage at which a sharp increase in the current appears, for-merly referred to as the trap-filled limit voltage or possibleas a step-increased value of l voltage, now corresponds to astep change in the macrotrap potential gradient withincreased l. The reduction of the barrier height at high fields




Table 4 Trapping Parameters as Determined from Applying the Discrete Macrotraps Concept

Parameter l1 l 2

r01(A )

Et

(eV)r02(A )

r2(A )

rb(A )

Et

(eV)E1

(eV)Neff

(cm� 3 )S ¼ pr 201(cm 2)

nth(s �1 )

Crystal �1 �2 �3 �4 �5 �6 �7 �8 �9 �10 �11 �12d ¼ 49 m m 1.00 0.26 711 0.55 229 60 30 0.57 0.6 6.7 � 1014 9.5 � 10 � 11 1.3 � 1012d ¼ 66 mm 1.10 3.03 550 0.55 456 201 35 0.57 0.6 1.4 � 1015 1.6� 10�10 9.9� 1011

�1 �2 Taken from the slopes (n ) of suitable segments (I and II) in Fig. 71 . According to (185) n ¼ 2 þ 3 l.�3 Calculated from (188) at the transition voltage a (see Fig. 71), using�1 .

�4 Obtained from (185), using�3 and�1 or�2 , and making the assumption neff¼N0.

�5 Obtained from (85) with�2 , using�4 .

�6 Calculated from (181) at the transition voltage b by equating (3l1 kT) ln(r01=r2)¼ (3l2 kT) ln(r02=r2).

�7 Calculated from (181), using�2 and�4 .

�8 �9 Obtained from equating DEH (187) to Et, and substituting, respectively, first l1 and r01, and then l2 and r02 (W¼ 0 in both cases).In the calculation, the field (F) corresponding to the crossing point between Child’s law curve and suitable extrapolated segmentsof the experimental curve has been substituted in (189).

�10 Calculated from (183), assuming Neff¼N0 and H0¼Nm, and using�3 .

�11 Obtained with values of r01 as given in�3 .

�12 Calculated with the assumption Neff¼N0, v¼ 107 cm=s, and using�11 .

190

Organ

icLigh

tEm

ittingDiodes

5647-8

Kalin

owsk

iCh04

R2090804


is given by Kalinowski et al. [318]

D EH ¼ 3 lkT 1 þ lneFr0 cos W

3lkT

� �� ð189Þ

whereas

D EL ¼ eFr0 ð190Þ

at low fields.The potential energy maximum

Vmax ¼ 3 lkT 1 þ ln r0rm

� �ð191Þ

occurs at

rm ¼3 lkT

eF cos W ð192Þ

with the field orientation W (note differences with the Coulom-bic barrier position in the Schottky’s and Poole–Frenkel’smodels discussed in Sec. 4.3.2).

The experimental results with a large number of solutiongrown anthracene crystals including those from Fig. 71 showthe trap parameter l1 ¼ 1.0 0.2, l2 ¼ 3.3 0.5, andEt ¼ 0.60 0.05 eV to be well reproducible from crystalto crystal, but the macrotrap radius varying between 10and 100 nm. As the macrotrap depth increases with r0 accor-ding to E (r0) ¼ 3lkT ln(r 0=r b)[see Eq. (181)], it is possible toreconcile this apparent discrepancy by allowing for variationin the radius of the based pinning trap rb. The valuesrb ffi 3–4 nm (see Table 4) seem to be reasonable sizes for smallclusters of the dimers which are expected to involve a fewpairs of molecules [372]. At this point, we want to stress thatthe results of Table 4 are selfconsistent under the conditionsNeffffiN0 and NmffiH. They impose all molecules to beinvolved in formation of macrotraps, the macrotraps toucheach other occupying approximately the whole volume of thecrystal. This makes the carriers hopping from one to anothermacrotrap, the number of states available per 1 cm3 (Neff)equals the density of macrotraps in contrast to the standard




interpretation in which Neff is usually identified with themolecular density Nm (note that Neff ffi Nm results directlyfrom Neff ffi (2p r30 )

� 1, as discussed above, if for r0 the moleculardimension is substituted). Since the capacitor charge per unitarea ( CU= e) < N0 in Table 4 within the entire range of theapplied voltage, the TFL conditions for macrotraps cannotbe fulfilled. In general, however, Neff > N0, N0 < (CU = e),and TFL is attainable. The data for naphthalene crystal seemto provide an example, where the trap concentrations deter-mined from the TFL voltage and from the temperature depen-dence of Y for point traps with Neff ¼ Nm differ by about fiveorders of magnitude [350a]. This discrepancy is readilyresolved by the macrotrap concept as the trap concentrationobtained from the TFL voltage can be identified with the con-centration of macrotraps (N0) and Neff ¼ Y N0

exp(�Et =kT) � Nm as calculated on the basis of the experi-mental value of Y. Summarizing the results, it must bepointed out that the presence of macrotraps can be seen inthe shape of j– U characteristics only in relatively high perfec-tion crystals for which ( N0)

� 1=3 � 2r 01. In poor-quality crystals(thus, polycrystalline films), only two straight-line segmentsof log j–log U plot should be observed; the second one withthe slope reflecting most probably a continuous energy distri-bution of microtraps dispersed homogeneously in space due toformation of macrotrap assemblies throughout the crystal. Incontrast, in high perfection crystals, one would expect at leastthree segments suggesting the current to be controlled by acomplex of potential discrete macrotraps distributed ran-domly in space. The reason for the fourth segment (in Fig.71, n ¼ 3.4, with the crystal d ¼ 66 m m) can have several ori-gins. It may be associated with a transition to the electrode-limited current (see Sec. 4.3.2), but it is also possible thatafter filling the macrotraps each with one carrier, next trap-ping events proceed through the capture of the second carrierby the already charged macrotraps. The Coulombic repulsionof the two one-macrotrap located carriers makes the macro-trap to be shallower, which shows up as a decrease in theslope of the log j–logU plot. Such a multi-charge carrier trap-ping has been demonstrated by the voltage-induced step-like




changes in the triplet exciton lifetime in anthracene and

Ref. 2).

4.3.2. Injection-limited Conduction (ILC)

The current becomes limited by injection when the averagecharge density in the sample (n� ) approaches n(0)—the chargedensity at the injecting contact. The injecting contact can nolonger act as a reservoir and thus ceases to be Ohmic. Thecurrent from such an electrode will saturate at sufficientlyhigh voltages. On the other hand, very high electric fieldscan make some contacts Ohmic by causing a strong injectionvia tunneling or other mechanisms superlinear with electricfield. Though the average charge density in the sample iscomparable with the charge density at the contact, both ofthem should be much smaller than the capacitor chargerelated to unit volume (e0eF=d). Thus, the condition for thecurrent to be injection limited can be expressed by the follow-ing inequality:

e0eFd nf þ ntð Þe ð193Þ

Combining inequality (193) with the current density given by

j ¼ nfemF ð194Þ

yields a modified condition for the injection-limited current(ILC)

e0eFd j

YmFð195Þ

where Yffinf=nt

From condition (195), it follows that ILC will be observedonly for relatively low currents at high electric fields withhigh mobility and large values dielectric permittivity (e) mate-rials formed into high chemical and structural perfection(large value of Y) thin layers. These are often met featuresof thin organic films sandwiched between metals or semicon-ductors with moderate work functions. The measured current




fluorescence intensity of tetracene crystals [247] (see also

( j) is determined by the source current ( js), the diffusioncurrent ( jdf) and the drift current ( jd). The source currentis a result of the balance between the primary injectioncurrent ( jp) and geminate recombination with the imagecharge at the electrode current ( jr ). The current balance atthe electrode obeys the continuity equation, which, in the caseof one-dimensional injection for steady-state flows, is given by

d

dxjp ð xÞ þ j r ð xÞ þ js ð xÞ

�¼ 0 ð 196Þ

To explain the behavior of the current flowing through thesample, the functional dependence js(x ) must be introducedas a boundary condition into the model describing injectioncurrents in insulators.

In the case of the primary injection due to hot carriers,js (x ) is determined by mechanisms of their thermalization[379–383]. The exponential character of js(x) is apparent in

a d function has also been used in analyses of some photoinjec-tion experiments [385]. The exponential shape of js(x) is a con-sequence of an exponential function defining the probabilitythat a carrier injected in a small escape cone will reach adistance x from the contact

PðxÞ ¼ expð�x=lÞ ð197Þ

where l is an average penetration depth of the carrier. Thereare various physical mechanisms that can be responsible forthe value of the penetration depth of the carrier into an insu-lator. A simple trajectory approach [386–388] assumes l to bea mean free path for carrier scattering on phonons or struc-tural and chemical defects. The process of carrier emission fol-lowing more scattering events may result in l being a measureof the carrier thermalization length. Alternatively, chargecarrier injection can be considered as damping of the metalelectron wave functions. The carriers enter the forbiddengap of the adjacent insulating material as damped one-dimen-sional Bloch waves which for a rectangular potential barrier(threshold) are given by c(x)¼A exp(�x=l) with A being their




some photoinjection experiments (see e.g. Ref. 384) although

amplitude and l the damping length either for electrons l ¼le ¼ ð�h= 2

ffiffiffi2pÞðm�e we Þ

�1 =2 or holes l ¼ lh ¼ ð�h= 2ffiffiffi2pÞðm�h w h Þ

�1 =2 ,wh ere m�e and m

�h , are the effective masses of electron (e) and

hole (h), respectively, and we and w h are their injection barriers.The probability per unit length of finding a charge carrier at adistance x defined by j c(x)j2 leads then to an equationP(x) ¼ jAj2 ex p( �x= le,h) equivalent to expression (197) [21].The range (‘‘schubweg’’) in the carrier diffusion process maybe determined by traps immobilizing charge carriers [257].

The collected current, i.e. current ( j) flowing through theinsulating sample, can be expressed as follows:

j ¼ js xð Þ þ em n xð Þ F � e

16p e0 e x2

� �� eDd n xð Þ

d x ð198Þ

Here, n( x) is the coordinate ( x) dependent concentration offree charge carriers and D is the microscopic diffusion coeffi-cient of the carriers, which is directly related to the carriermobility ( m) through the Einstein relation D ¼ mkT =e . Equa-tion (198) is composed of a hot carrier stream of js( x) andtwo additional terms representing the current flow due tothermalized carriers. The thermalized carriers flow is gov-erned by macroscopic diffusion proportional to the concentra-tion gradient [�dn(x)=dx], the image force (�e=16pe0ex2) andthe applied electric field (F). The latter two form a potentialbarrier located at x¼ xm (Fig. 73). If the diffusion current com-ponent is negligible, the drift current in the combined imageand external fields dominates the collected current which isdetermined by those carriers that escape over the image forcebarrier

j ¼ j0 expð�xm=lÞ ð199Þ

where j0 is the current which would flow for l!1 (e.g. in theabsence of scattering processes). The field dependence of thecollected current in Eq. (199) enters through the field-depen-dent position of the barrier

xm ¼ b=g ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

e

16pe0eF

rð200Þ




expressed with two additional convenient variables

g ¼ eF

kTand b ¼ e2

16pe0ekTð201Þ

Thus,

j ¼ j0 exp �c=F1=2� �

ð202Þ

where c¼ l�1(e=16pe0e)1=2 for hot carriers penetrating the mate-

rial with the mean free path, l, or c¼ (2 p=h)(e m�wc=2pe0e)

1=2

assuming the carriers to be one-dimensional Bloch wavesdampedwithin the potential threshold (wc is the injection barrierreferred to the Fermi level of the injecting electrode). These two

Figure 73 Formation of the potential barrier at the injectingmetal contact (x¼ 0) with an exponential distribution of the sourcecurrent js(x) penetrating the insulator sample to the l¼ 1nm. Thepotential, F(x), calculated with e¼ 4 and F(x)¼ const¼ 106V=cm,has its maximum at about xm¼ 0.9 nm. After Ref. 21. Copyright1996 Gordon & Breach.




cases can be distinguished by an examination of the c ur rent–voltage characteristics varying work functions of the injectingmetal; the i nj ection barrier dependent carri er penetration depthwill show the constant c to vary with wc for the dampinglength, whereas for s imple scattering l should be independentof wc.

When js (x) is a strongly decreasing function of x( l � xm ) all hot carriers entering the sample are thermalizedat a distance l , and only their fraction due to thermalactivation over the barrier can contribute to the collectedcurrent

j ¼ AF 3 =4 exp aF 1 = 2� �

ð203Þ

where A(F ) ¼ const, A ¼ j0(el = kT)3= 4 exp[�2(b= l) 1=2], and

a ¼ 2 b ekT

� �1 =2

¼ 1

kT

e 3

4p e0 e

� �1= 2

ð204Þ

This is the injection current limited by a field-assisted separa-tion of charge from its mirror image in the injecting contact.Since the preexponential factor is a relatively slowly varyingfunction of F, and the constant a identical with the Schottkyparameter, aS , Eq. (203) can fairly be approximated by thestraight-line plot log j � F1 =2, and often interpreted in termsof the Schottky injection into carrier conducting bands (see

that the Schottky approach assumes the activated carriersto occupy allowed free electron states within wide conductingband materials. Its application to narrow band insulators (anoverwhelming majority of organics) can be misleading.Although much similarity can be seen in the description ofILC for both wide- and narrow-band insulators, there is animportant difference in the mechanisms by which charge car-riers surmount the barrier. This difference is apparent inFig. 74.

In contrast to the wide-band materials, where suffi-ciently high activated carriers can overcome the barrierdirectly (path 1), in the narrow-band case, the only practical




the discussion in Ref. 361). One should, however, remember

way to reach its maximum is diffusion against the field direc-ted towards the injecting contact. This leads to importantconsequences in the description of the current-field character-istics in wide- and narrow-band insulators. While for thewide-band materials, the only condition for the carrier toenter a conducting band is to be excited to its lower edge

Figure 74 Comparison of field-assisted thermionic injectionmechanisms in wide- (a) and narrow-band (b) materials. An x0 closeto the geometrical contact region is distinguished where Eq. (198) isnot applicable. The inapplicability can be associated with field orcoordinate dependence of m, D and e or the coexistence of some otherprocesses such as bimolecular or tunneling recombination whichare not included in Eq. (198). After Ref. 361. Copyright 1989 Jpn.JAP, with permission.




(Schottky injection), in the case of narrow-band materials, theinjected real charge has to be separated by diffusion from itsmirror image and, therefore, should be considered in the con-text of a one-dimensional Onsager-type formalism [382]. Inthe former, electric field increase in the current is due tothe electric field-induced lowering of the barrier ( Ecoul inFig. 74), in the latter, the current increases because an exter-nal electric field reduces the geminate recombination rate ofthe carrier at the injecting contact. It has been shown thatthe one-dimensional Onsager model for carrier injectionappears to be a particular solution of Eq. (198) for a weak gra-dient function js(x) and=or x0! 0 [361]. The field dependenceof the collected current is determined by the relation betweenthe barrier location xm, and thermalization length, l, and dif-fers for high and low electric fields. It is, with the accuracy tothe preexponential factors, identical to the function (203)for xm l and the high-field regime [2(bg)1=2 > 1;F > 5.2eT2 (V=m)], but j varies linearly with F for low fields[2(b) 1=2 < 1; F < 5.2eT2 (V=m)],

j ffi j0 el2=bkT�

exp �b=lð Þ �

F ð205Þ

For xm� l, the current saturates, j¼ j0, independent of thefield regime (unless F!0; the condition xm� l cannot thenbe fulfilled with a finite value of l, since xm!1). It is inter-esting to note that the low-field regime for room-temperatureand materials with 2 < e < 15 falls in the 9� 103–7� 104V=cm range, an estimation useful in the analysis ofthe current–voltage behavior of the injection currents. How-ever, one should keep in mind that this demarcation valueof F can be as low as 2V=cm atffi 4K (e¼ 2) and as high as8� 105V=cm atffi 103K (e¼ 15). In summary, the generallyvalid equation (198) governing injection-limited current flowin insulators can be reduced to a description of the drift cur-rent that evolves with electric field taking on various func-tional shapes dependent on the primary carrier injectionand motion mechanisms in the insulator. But even for a giventype injection process, the current-field dependence variespassing from low- to high-electric field regimes. For instance,




thermionic injection of charge reveals a linear increase of thecurrent density with applied voltage at low fields (205), andfollows an exponential function at high fields (203). The latteris illustrated in Fig. 75 for three different SL LEDs based onmolecularly doped polymers. For all three devices, the cur-rent-field [ j(F)] curves can be reasonably approximated bythe straight-line log( j=F3=4) vs. F1=2 plots, their slopes yield-ing the characteristic parameter a in Eq. (203). The differencebetween their slopes can be ascribed to different dielectricconstants of the samples (e1¼ 4.5, e2¼ 2.3, e3¼ 1.7) and does

Figure 75. Thermionic injection currents in three different SLLEDs following Eq. (203) as represented by the straight-linelog( j=F3=4)�F1=2 plots: (1) ITO=(25% TPD:25% Alq3:50% PC)(60 nm)=Mg; (2) ITO=(50% TPD:30% Alq3:20% PC) (60nm)=Mg; (3)ITO=(70% TPD:10% T50hex:20%PC) (70nm)=Ca. The slopes of thestraight-line plots, a1¼ 0.7� 10�2 (cmV�1)1=2, a2¼ 1.15� 10�2

(cmV�1)1=2 and a3¼ 1.01� 10�2 (cmV�1)1=2 reflect differences inthe composition of the LEDs. After Ref. 389. Copyright 2001 Insti-tute of Physics (GB), with permission.




not exceed 35% as compared with predictions of the theory(204) with e¼ 3. Similar straight-line plots for a series of DLLEDs, shown in Fig. 76, yield the slopeffi 1.4� 10�2

(cm=V) 1=2ffi 2aS. There are at least two reasons for the discre-pancy between experimental values of aexp and aS. First, dueto accumulation of majority positive carriers at theTPD=emitter (DPP:Alq3) interface, the field in the anodiccompartment of the device is much lower than the nominalapplied field [2,303,390], and second, due to disorder, theCoulombic potential at the interface is affected by the near

Figure 76 Log( j=F3=4)–F1=2 plots for DL organic LEDs ITO=TPD(30–49nm)=Alq3:% DPP (33–62nm)=MgAg with different concen-trations of diphenylpentacene (DPP) in the electron-transportinglayer. After Ref. 68. Copyright 2001 American Institute of Physics.




surface splitting of the conducting level into an extended bandformed by a spread of energy and space of the carrier hoppingsites [391,392]. The maximum anodic field screening can beestimated, neglecting disorder effects, by comparing theexperimental and theoretical values of the Schottky para-meter a . The anode screening factor is then given byk1 ¼ (a theor = a)2 ffi 0.4, assuming the average value for all thesamples in Fig. 76, a ¼ aexp ffi 1.45 � 10� 2 (cm=V) 1=2. Thismeans that the electric field within the HTL of thickness d1

constitutes about 40% of the nominal field (F1 ¼ k 1F) andthe cathodic compartment (d2) field F 2 ¼ k 2F becomesenhanced by a factor k2 ¼ ( d= d 2)[1�k1( d1= d )] ffi 1.4 determinedfrom simple electrostatics arguments for averaged values ofd1 and d 2, and d for the samples in Fig. 76. The applied field(F ¼ U= d) is defined by the applied voltage (U) ratio to thetotal thickness of the device kept at an approximately con-stant value d ffi 115 nm [68]. The apparent decrease in theparameter a (204) for the devices with doped emitters sug-gests that the dopant reduces the positive charge at theHTL= emitter (also ETL) interface, so that the anodic compart-ment field would increase to about 46% of the nominal field,and an increasing trend in the injection current should beexpected. Instead, except for the lowest doped emitter device(0.25 mol%), the current decreases at variance with the aboveprediction (cf. Fig. 76). This contradiction can be resolved byassuming the measured current to be composed of the hole-injection current and recombination current at the interface.The recombination current defined by the number of holesrecombining per unit time is proportional to the interfacialdensity of electrons. The latter, in turn, appears to be a func-tion of dopant concentration as comes out from the concentra-tion dependence of the EL efficiency (see Sec. 5.4). The higherconcentration decrease in the EL efficiency can be related to adecrease in the recombination current, thus observed as adecrease in the total device current. This reasoning is sup-ported by the variation of the straight-line log( j=F3=4)�F1=2

plots with concentration of the hole accepting TPD moleculesin the TPD doped PC HTLs (Fig. 77). Increasing concentra-tion of TPD leads to increasing hole-injection efficiency at




the ITO=(TPD:PC) interface� (Ref. 393), the differencebetween anodic (F1) and cathodic (F2) compartment fieldsincreases. From simple electrostatics, it follows that the(TPD:PC)=Alq3 interfacial charge concentration is propor-tional to the electric field across the interface, which for the

Figure 77 Current-field characteristics [in log( j) F3=4) againstF1=2 representation] of the DL LEDs consisting of variable concen-tration of TPD HTL (%TPD:PC)(70 nm) and a 100% evaporatedAlq3 ETL (60 nm) sandwiched between an ITO anode and a Mgcathode. The slopes of straight lines approximating the experimen-tal plots (points), a, in (cm=V)1=2 are given in the bottom-rightcorner. After Ref. 303. Copyright 2001 Institute of Physics (GB).

� A recent study of the TPD concentration effect in PC on charge injectionfrom ITO [394] neglected the injection enhacement due to the increasingdensity of electron donor molecules of TPD (thus, js) and explained theTPD concentration increase of the electric conduction in terms of SCL cur-




rents modified by the field-dependent mobility (cf. Sec. 4.6).

majority charge carriers reads

ni ¼e0 ee d

F1 � F 2ð Þ ð206Þ

Here d is the thickness of the interfacial layer, where therecombination occurs predominantly among the interfacialcharges. It can be identified with the recombination zonewidth. Assuming for a while d (F ) ¼ const, ni andD Fi ¼ (F 1 � F 2) would be expected to increase with the hole-injection efficiency, and, as a consequence, the recombinationcurrent to increase. The latter reduces the electric fieldscreening at the electrodes [(F1 � F 2) decreases]. Sinceaexp > atheor , the screening effects must prevail over therecombination-induced reduction in the interfacial spacecharge and increasing of a with the hole injection efficiencyis observed. Even at the lowest concentration of TPD (33%in Fig. 77) aexp=atheorffi 1.3, the screening factork1=k2¼F1=F2ffi 0.7 indicating the cathode field to exceed astronger screened anodic field by a factor of 1.5. For highinjection levels (75% and 100% TPD in the HTL),k1=k2¼F1=F2ffi 0.1, the cathodic field becomes an order ofmagnitude larger than in the anodic LED compartment.Any field dependence of the recombination zone width, d, willmodify the balance between ni and (F1�F2), the log( j=F3=4)vs. F1=2 plots will deviate from the straight-line behavior.Such a deviation apparent in Fig. 77 for the 50% and 33%TPD samples indicates the high-field narrowing of d as pre-dicted (Sec. 3.3) and verified experimentally (Sec. 5.4) forICEL mode operating LEDs. The field distribution amongthe totally vacuum evaporated TPD (100%) HTL and Alq3(100%) ETL has been inferred from the analyses of transientcurrents [395] and electroabsorption experiments [396]. Theelectric field within the TPD (100%) HTL was generallyfound to be lower than that in the Alq3 (100%) ETL, suggest-ing more effective accumulation of holes than electrons atthe TPD=Alq3 interface. The screening factor F1=F2

depended slightly on the applied voltage and varied betweenffi0.35 for a weakly injecting Al cathode and ffi0.8 for a




strongly injecting LiF= Al cathode at high applied fieldsF ffi 2 � 106 V cm� 1.

The thermionic emission currents provide a plausiblealternative for the current–voltage characteristics of organicsolids, discussed in terms of SCL conduction. For example,the strong power function plots with two different powers inthe low- and high-field regions of the applied field (Fig. 70)can be replaced by the straight-line log( j=F3=4) vs. F1=2 plots(Fig. 78) characteristic of the thermionic injection expressedby Eq. (203). Due to the reasonable straight-line approxima-tion of the log( j=F3=4)–F1=2 plots, the screening of the appliedfield within the HTL is fairly independent of the proportionsbetween thicknesses of the hole-transporting (75% TPD:PC)(d1) and electron-transporting (100% Alq3)( d2) layers, andequals k1¼ (atheor=aexp)

2ffi 0.2. On the other hand, theenhancement factor for the cathodic field increases withincreasing ratio d1=d2, k2¼ (1þd1=d2)� k1(1þd2=d1), so thatthe screening factor k1=k2 decreases from k1=k2ffi 0.14 ford1=d2 (or d2=d1)¼ 35=60nm, down to k1=k2ffi 0.08 for d1=d2

Figure 78 Thermionic injection current-field characteristics forthe ITO=75% TPD:PC= Alq3=Mg=Ag devices with different propor-tions of the hole transporting to electron-transporting layer thick-nesses as described previously in Fig. 70. The slopes in (cm=V)1=2

of the straight lines log( j=F3=4) vs. F1=2 approximating the resultsaccording to Eq. (203) are given in the bottom-right corners of thefigures. After Ref. 303. Copyright 2001 Institute of Physics (GB).




(or d2= d1 ) ¼ 120=60 nm. This is an interesting observation,suggesting that increasing the total thickness of the device(d1 þ d 2) either by increasing d1 or d 2, it is possible to enhancethe electron injection due to the increasing field in the ETL,F2. However, it should be kept in mind that large values ofthe field F2 are derived from the positive space charge onthe TPD side of the TPD=Alq3 junction. If there is a compar-able negative space charge on the Alq3 side of the junction,one has to take into account the screening of the cathodic fielddue to this charge. As a result, F1 and F 2 may not differ toomuch, and the screening factor F1= F 2 may approach unity(but F1, F2 < F ). Employing SL LEDs allows to avoid the fielddistribution problem and makes the verification of injectionmechanisms straightforward. The current–voltage character-istics for the SL LEDs based on TPD and Alq3 films are shownin Fig. 79. In Fig. 79a, the j (F ) curves from Fig. 68a arereplotted in the log( j= T2) vs V1= 2=T (parametric in tempera-ture). Except for the low temperature plots (50 and 90 K), theyare fairly well approximated by the straight lines reflectingthe Schottky-type injection described by Eq. (208) withj0 ¼ A� T 2 [ A� (T,F ) ¼ const] and a S ¼ (1=kT )( e3 =4 pe 0ed )1= 2 [cf.Eq. (204)]. No difference in the current density at any appliedfield for the samples of different thickness led Campbell et al.[397] to the conclusion that the current observed for theITO= TPD=Al is due to thermally activated injection of bothholes from ITO and electrons from Al into TPD sandwichedbetween these two electrodes. However, quantitative differ-ences have been noted concerning the RS coefficient, theprefactor current, and the injection barrier.

In contrast, t he quasi-straight-line log j–log U plots f orthe Al=Alq3=Ca s y st em fr o m Fi g. 69a, r ep l ot te d i n t heSchottky-type coordi nates in Fig. 79b, deviate apparently fromthe straight lines, and the current decreases with the samplethickness. Moreover , the thickness dependence of t he currentdensity obeys the d� 1 law f or d > 125 nm (Fig. 80) suggestingthe free-carrier SCLC (168a) to underlie the current flow inthis system. The fitti ng of the experimental data with thepower l aw Fn (n > 3) seen in Fig.69a has been explai ned bythe field-dependent mobility [ 355]. (see also Sec . 4.6).




The shape of the current–voltage characteristics athigh fields can be dominated by the tunneling carrierinjection through the narrow triangular barrier [21,397a]when its position [see Eq. (200)] approaches the geometricalcontact. In Fig. 81, the tunneling injection is comparedwith the thermionic injection treated as the classicRichardson–Schottky (RS) electron emission at the metal=insulator interface. In the RS emission, the Coulombicenergy barrier

D EC ¼ e F x ¼ x mð Þ � F x ¼ lð Þ½ � ¼ e2

16pe0 el � e3 F

4 pe0 e

� �1 = 2

ð207Þ

has to be overcome by a carrier in order to contribute to thecollected current

j � exp �DEC =kTð Þ ¼ j0 exp aS F 1 =2

� �ð208Þ

Figur e 79 Current–v oltage charact eristics for ITO =TPD =Al (a)and Al =Alq3 =Ca (b) from Figs . 68a and 69 a, respectivel y, replottedin the scales correspo nding to the strai ght-line be havior accordi ngto Eq. (208). The curves in pa rt (a) are parame tric in temp eratureas in Fig. 68a, and in part (b) are parame tric in thickn ess as givenin the figure. Adapted from Campbell et al. [356a] and Bruttinget al. [355] and respectively.




where j0 is the injection current density at F¼ 0, and aS�ais given by Eq. (204). Electrons entering the insulator aremost likely thermalized at a distance l < xm from the inter-face, where their energy, determined by the Coulombicinteraction with the image charge, Ec (x¼ l)¼ e2=16 p e0el,is lower than Ec at x¼ xm. However, they can reach xm bythermally activated diffusion. The activation energy is iden-tical with the Coulombic binding energy (207), the square-root term accounting for barrier lowering by the externalfield (field-assisted thermal escape). Such carriers contri-bute to the collected current following the straight-line rela-tionship ln j vs. F1=2 (208).

Figure 80 Thickness dependence of the injection current in theAl=Alq3=Ca system at a constant electric field F¼ 0.5MV=cm. A pro-nounced deviation from the d�1 behavior for thin samples is seen ford < 125nm. Adapted from Ref. 355.




Figur e 81 Comparis on of the fie ld-assisted therm al activ ation ofan electr on ove r the Coulo mbic barrier located at x ¼ xm (cf. Fig.74 ) (a) and tun neling throug h the barrier wit h xm! 0 (b), at ametal=insulator interface. The potential F(x) calculated with e¼ 4,and F(x)¼ const¼ 106V=cm. Adapted from Ref. 21.




In the high-field limit (xm ! 0), the carrier injection canbe considered as tunneling through the Coulombic barrierreduced to a triangular shape (Fig. 81b) into continuum ofstates [397a] disregarding tunneling of hot electrons (cf.Fig. 73). This is the classic Fowler–Nordheim (FN) treatment[398] leading to the collected current approximated by

j ¼ BF 2 exp �b =Fð Þ ð209Þ

with B (F ) ¼ const, and

b ¼ 4 2m�ð Þ1 =2

3 �hew3 =2b ð 210Þ

where wb is the injection barrier and m� is the effective massof electron inside the barrier. Support for the applicabilityof the FN concept to injection into organic LEDs comesfrom injection studies upon varying the injection barrier[398–400]. The temperature independence of the injectioncurrent observed in systems with large barrier for hole injec-tion lent further support to the concept [400]. At lower fieldsdeviations from FN-behavior are usually noted, though, andcurrents become temperature-activated, suggesting that atlower fields thermionic emission prevails. The applicabilityof the FN vs. RS charge injection model has been studied indetail on the Al=Alq3= Mg:Ag system [401]. Although the cur-rent–voltage characteristics bears out a high power-law beha-vior ( j � U7 at 295 K and j � U12 at 133 K), similar to that inFig. 68b for the DL LEDs based on the TPD=Alq3 junction,indicative of the trap-controlled SCLC flow, the current hasbeen considered as ILC rather because of too high injectionbarriers at both contacts. The measured injection currentsin Fig. 82 clearly show inapplicability of the FN model, whiletheir good qualitative agreement with the RS concept isapparent from the straight-line plots log j vs. F1= 2. Yet, quan-titative differences concerning the characteristic model para-meters have been observed. In Fig. 83, high-fielddependencies of the injection current into TPD- and Alq3-based SL EL devices are presented in different scales to testthe validity of different injection models. Though they can




be approximated by a power function j � F n with n ¼ 2.9 and2.3 for TPD and Alq3 film, respectively, deviating from thisbehavior at ‘‘lower fields’’, the non-linear field increase in

is well approximated by the RS thermionic emission model,and the high-field segment (F > 1MV=cm) by either FN orhot carrier description of the injection. From the linearregimes of the plots in three different scales (Fig. 83b), appar-ent injection parameters can be inferred that differ signifi-cantly from expected ones (Table 5). Even with a largeuncertainty, the values of the energy barrier wb at theITO= TPD and Mg= Alq3 interface appear unreasonably low,compared with 0.6 and 0.65 eV resulting from the energy dia-gram for these interfaces (Fig. 84). Therefore, tunnelingthrough triangular barrier can be ruled out as the carrieremission process at high fields though it has been consideredas a limiting case for thermally assisted hopping within a

Figure 82 Fowler–Nordheim (a) and Richardson–Schottky (b)representations of the current-field dependence in anAl=Alq3(150nm)=Mg:Ag device at various temperatures. After Ref.401. Copyright 1999 American Physical Society, with permission.




their brightness rules out the current to be SCL (cf. Sec.5.3). Instead, the low-field region behavior ( F < 1.0 MV=cm)

superimposed Coulombic and external potential [402]. Thedata of Table 5 suggest primary (hot) carrier penetration overthe image force barrier to be the most probable injectionmechanism at high electric fields. From the asymptotichigh-field slope of log j vs. F�1=2 plots, we obtain the meanfree path of primary holes injected into TPD, lh¼ 0.26nm,and electrons injected into Alq3, le¼ 0.45nm [cf. Eq. (202)].These are figures corresponding to less than one molecularlayer. Though they seem relatively small, their goodcorrespondence to the value (0.22 0.03) nm found for a

Figure 83 The high-field regime log–log current-field characteris-tic (a), replotted in three different representations (b) forITO=TPD(130 nm)=Mg=Ag (left) and ITO=Alq3(140 nm)=Mg=Ag(right) EL diodes. The plots log j vs. F�1=2, log j vs F1=2 and log jvs. F�1 allow to test hot carrier, thermionic, and tunneling modelsfor carrier injection, respectively. Adapted from Ref. 57.




Table 5 Various Charge Injection Paramete rs for SL EL Devices, Extracted from the Plots of Fig. 83

Structure a (cm1=2V�1=2) a=atheora b (V cm�1) wb (eV) c (V1=2 cm�1=2) wc (eV) l(A)

SL Alq3 1.9� 10�3 0.25 1.15� 106 0.07 2.1� 103 0.04 4.5SL TPD 2.8� 10�3 0.26 1.95� 106 0.09 3.6� 103 0.14 2.6

aatheor¼ (e=kT)(e=4pe0e)1=2¼7.6�10�3 cm1=2V�1=2 with e¼ 4.

Note: The energy barriers (wb, wc) have been calculated by assuming that the carriers’ effective mass equals the rest mass of the electron.

Chap

ter4.Electrical

Characteristics

ofOrgan

icLED

s213

5647-8

Kalin

owsk

iCh04

R2090804


characteristic distance of the charge transfer reaction at theanthracene=metal interface [384] does not exclude their relia-bility. However, on the quantum mechanical ground, consid-ering l as the average penetration depth of electron wavesinto a rectangular potential barrier, the experimental valuesof c yield wc apparently smaller than the actual barriers,although its value for the Alq3=Mg interface is much largerthan wb. A much better agreement of these numbers canbe reached if the Schottky reduction (DECoul) of the energybarrier and disorder-induced broadening of the HOMOlevel in TPD will be taken into account. At fieldstrengths F > 106V=cm, DECoul¼ (e3 F=4p e0 e)

1=2 > 0.2 eVand DEdisorderffi 2 sp 0.2 eV typically for amorphous solids

Figure 84 Energy level scheme and EL emission from a DLdevice: ITO=TPD=Alq3=Mg. Note that the injection barriers at theITO=TPD (DEh) and Mg=Alq3(DEe) bear some uncertainty due tothe inaccuracy in determination of both energy levels in organicsas well as in the work functions of ITO and Mg. DEh < DEe in thefigure, may thus be replaced by DEhffiDEe or even DEh > DEe,dependent on the choice of the literature data for these energylevels. After Ref. 57.




value of wc and relatively large value of le for the Mg =Alq3interface would suggest classical propagation of electrons inthe Alq3 image force potential well between the emitter andthe potential maximum.

Analyzing the RS portion of j (F ) curves yields a signifi-cantly smaller than atheor (204) calculated with e ¼ 4. It hasbeen suggested that a < atheor can be the result of the chargetrapped near the contact along linear imperfections [403].Both, experimental observations and theoretical considera-tions show that the distribution of imperfections can be linearin crystals [82,404–406], and linear macrotraps formed by anarray of dipolar microtraps [371]. Then [403],

a

atheor¼ 1 � 16tD0

e ð211Þ

where t is the linear density of charge along the trapping lineparallel to and located from the surface at a distance D0, and eis the elementary charge. The experimental data from Table5, a = atheor¼ 0.25, require tD0=effi 0.05. This means that thelinear density of the trapped charge at a distanceD0¼ 10nm amounts t=e¼ 0.005 e=nm, that is one elementarycharge carrier occurs in the trap array every 200nm (roughlyevery 20 intermolecular distances). The linear traps more dis-tant from the surface would create the same difference in a atlower charge density (t=e�D�10 ). If the charge trappingdomain is planar, the current becomes a more complex func-tion of applied field, it cannot be anymore approximated bythe linear plot of log j vs. F1=2. The same occurs, in general,if the deep discrete traps are split in a series of localized statesdistributed in energy according to the Gaussian function witha width s. The charge transport among a Gaussian shapeddensity of states (DOS) becomes of importance for the carrierescape from the near-contact Coulombic well [392]. Sincethe primary charge injection probability from the metal tothe insulator depends whether the carrier jumps into anupper or lower part of the Gaussian profile (upward anddownward carrier jumps), the collected current and its field




with diagonal disorder (cf. Secs. 2.4.3 and 4.6). A very low

evolution are strongly dependent on the injection barrier(thus, the metal work function). The higher the barrier is,the j (F) behavior more and more resembles the Schottky-typestraight-line plot ln j vs. F1=2 (see Fig. 85). Yet, @ ln j=@F1=2

approximately is larger by a factor of 2 and has been ascribedto a roughly doubled energy barrier the carrier has to sur-mount to reach the transport level and to escape from the well

Figure 85 The broad range injection current densities plotted vs.F1=2 for different injection barriers, D (given in the inset). The ana-lytic theory results (lines) compared with Monte Carlo simulations(points) according to Ref. 392.




formed by a superposition of the Coulomb field of the imagecharge and the external field. The Gaussian DOS can be con-sidered as a particular case of an additional potential loca-lized between the contact and the position of the Coulombic(Schottky-type) barrier [361]. It creates an additional electricfield (Ft ) which should be included into the drift component ofthe current

j ¼ en xð Þm F þ Ft �e

16p e0 ex 2

� �� mkT dn xð Þ

d t ð212Þ

Solving the differential equation in n( x) in the high-fieldregime yields

j ¼ B eF= kTð Þ þ at½ �3= 4 exp 2 b eF = kT þ atð Þ½ �1= 2n o

ð213Þ

where the parameter at ¼ eFt =kT is a measure of the trappotential shape and its influence on the j( F) dependenceappears in a deflection from the linearity of the plot log j vs.F 1= 2. In Fig. 86, a hypothetical trap potential is presentedand current-field characteristics following Eq. (213) areplotted in the log j vs. F1=2 scale for different values of theparameter at. The external electric field combined with thetrap field (Ft) and the image charge field (�e=16pe0ex2) formstwo energy barriers. Their height ratio depends on the exter-nal field strength (1 and 2 in Fig. 86b illustrate the potentialat low- and high-electric fields, respectively). The dashed linesin Fig. 86c represent non-linear portions of the log j–F1=2 plot.It is seen that for at¼ 5 � 105 cm�1, the plot gives a straightline in the entire field range 104–1.2� 105V=cm consideredin calculations. The straight-line behavior appears also forother values of at > 5 � 105 cm�1, but the lower limit of theelectric field at which it starts increases with increasing at.For at < 5 � 105 cm�1, the plot becomes non-linear in theabove field range. We note that at a given at, the trap depthincreases with the trap dimension (d0) according toEt ¼

R d0

0 Ftedx ¼ atkTd0. A relatively shallow trap Etffi 0.1 eVfollows for d0¼ 10nm and at¼ 4 � 106 cm�1 at room tempera-ture. It is comparable with typical Gaussian shaped DOSwidths. The presence of a traps in the near-electrode




Coulombic well may change the function (213) to include anadditional probability factor (P) allowing for the carrier toreach the potential maximum [257,361]

P ¼ exp �xm=lq�

ð214Þ

Figure 86 Hypothetical trap potentials localized at the electrode inthe absence (a) and in the presence (b) of image and external electricfields. Dashed lines represent a linear approximation of the trappotential in (a), and the potentials in the absence of trap in (b). Plotsof log j vs. F1=2 according to Eq. (213) (c) parametric in at:4� 106 cm�1 (1), 2� 106 cm�1 (2), 106 cm�1 (3), 5� 105 cm�1 (4) andat¼ 0 (5). After Ref. 361. Copyright 1989 Jpn. JAP, with permission.




Here lq is the diffusion length (‘‘schubweg’’) of free car-riers. Then, for low values of at [�(e F =kT)], Eq. (213)reduces to

j ffi j0 exp aU 1 = 2 � bU �1 =2� �

ð215Þ

where a ¼ aS d� 1= 2 [aS defined by Eq. ( 204)], and b ¼ (b d=t cm) 1=2with b defined in (201) and tc standing for the carrier lifetime,is the constant which must not be confused with that of Eq.(209). The second term in the exponential function of (215)can dominate low-field current behavior when the Coulombicbarrier is located far from the contact (large xm). Indeed, fromthe example given in Fig. 87, it is seen that j ( U) follows wellthe function exp(�bU�1=2) in the low-field regime, andswitches to exp(aF1=2) behavior at high fields. The straight-line plot log j vs. the complex variable (aU1=2� bU�1=2) canbe obtained in the entire voltage range applied to the samplewithin a broad range of current densities (six orders of mag-nitude). The presence of a large concentration surface trapsas determined from the lqffi 30nm following the experimentalvalue of b¼ 1.5V1=2, seems to influence the constant a which(as often happens) exceeds its theoretical value by a factor of2. In closing, it should be pointed out that a similaritybetween the function exp(�bU�1=2) and that given by Eq.(202) comes from the identical definition of the probabilityof a carrier to surmount the Coulombic barrier [cf. Eqs.(199) and (214)]. However, the physical background is differ-ent for these two cases. Whereas, Eq. (199) relates to thescattering of hot carriers within a narrow Coulombic well(small xm), Eq. (214), in contrast, describes the motion ofthermalized carriers in a relatively extended Coulombic well.Thus, the first occurs at high, and second at low electricfields. It is important to remember that the injection currentflow will be modified by the space charge reducing the near-electrode field, which in the extreme case (for low injectionbarriers) renders the current to be SCL (cf. Ifthe space charge occurs as a result of trapping, its concentra-tion can be reduced by illumination of the sample. Photons orlight-produced excitons, releasing charge carriers from traps,




Sec. 4.3.1).

increase the free-to-trapped concentration ratio, Y, alleviat-ing the ILC condition (195) to be fulfilled. One would expect,such a photo-enhanced current easier to attain the ILC thanthat produced under dark injection condition. An excellent

Figure 87 log j–(aU1=2–bU�1=2) dependence (solid line) calculatedfrom (215) with corresponding experimental points (open circles) forthe photocurrent in a 22mm-thick tetracene single crystal illumi-nated through a semitransparent gold anode. (a) log j–U�1=2 and(b) log j–U1=2 plots are shown in the insets. The calculations havebeen done with a¼ 0.42 and b¼ 1.5. After Ref. 257. Copyright1979 Wiley-VCH, with permission.




illustration of this prediction are current–voltage character-istics for the hole injection from a semitransparent gold elec-trode into a tetracene single crystal shown in Fig. 87. A steeppower-like j– U dark current characteristic (resembling theSCLC flow) converts into S-shaped curves under illumination(Fig. 88a). Two, low- and high-field segments can be distin-guished at sufficiently intensive illumination (> 1012 quan-ta=cm2 s): the first following the function exp(�bU�1=2) andthe second following the function exp(aU1=2)(cf. also Fig.87). It is clearly seen that increasing light intensity (reducingthe near-contact space charge) elongates the straight-linebehavior of the log j vs. (aU1=2� bU�1=2) plot characteristicof the ILC in accordance with Eq. (215).

Until now, a recombination velocity of thermalized aswell as hot carriers has been directly introduced in variousmodels as a boundary condition independent of the carrierposition in an insulator. This corresponds to the assumptionjr(x)¼ const, and from Eq. (196), js¼ j0a1 exp(�a1 x), for theexponential character of the primary injection currentjP¼ j0 exp(�a1 x), follows. The source carriers are being ther-malized with a probability n (per unit time) and rate en N(x)equal to the carrier injection rate,

enN xð Þ ¼ j0a1 exp �a1xð Þ ð216Þ

where N(x) is the concentration of charge at x of non-therma-lized carriers. Since, by definition,

js xð Þ ¼ enZ1

0

N xð Þdx ð217Þ

from (216)

js xð Þ ¼ j0 exp �a1xð Þ ð218Þ

that is the source current coincides with the primary injectioncurrent jp.

Without an applied electric field, the source current iscompensated by opposite in direction the surface recombina-tion current js� jr¼ 0. An assumption has been made that




Figure 88 Current–voltage characteristics for a 12 mm-thick tet-racene crystal in the dark (I0¼ 0) and under increasing illuminationup to 1014 quanta=cm2 s. (lex¼ 550nm; penetration depthla¼ 7.27 mm) through a semitransparent gold anode as shown inpart (a), where the j–U dependence is plotted in a log j–logV scale.It is replotted in other three different scales: (b) log j–U�1=2, (c) log j–U1=2, and (d) log j–(aU1=2–bU�1=2). After Ref. 257. Copyright 1979Wiley-VCH, with permission.




this balance takes place at a distance x ¼ xc ¼ rc =4, whererc ¼ e 2=4 pe 0ekT is known as Coulomb radius defined by iden-tifying the intercarrier binding energy with thermal energykT [407]. Furthermore, these authors assumed the recombi-nation rate to be underlain by the hopping process towardsthe surface. Based on these assumptions, they arrived at anet current which is lower as compared to the injection cur-rent neglecting the surface recombination for either low andhigh electric field regimes. This simple description can be gen-eralized on the expense of the simplicity of the resulting cur-rent-field relationship. A physically probable tunnelingrecombination process at the interface has been discussedpreviously in detail [361]. The recombination rate has beenassumed to take an exponential form

Zr xð Þ ¼ Zr 0ð Þ exp �a2 xð Þ ð219Þ

where Zr (0) ¼ Z r (x) at x ¼ 0, and a 2 is a characteristic tunnelingparameter dependent on the type of the interface. Now,Eq. (196) takes on the form

d jp ð xÞd x

� eN ðx ÞZr ðx Þ � e n N ðx Þ ¼ 0 ð220Þ

and combining Eqs. (196) and (217)–(220) yields

js ð xÞ ¼ j0 a 1

Z1

0

expð�a1 x Þ dx1 þ Zr ð 0Þ=n expð�a 2 xÞ½ � ð221Þ

Expression (221) allows us to solve the problem only inthe approximation of the one-dimensional Onsager modelbut not in the approximation of the strong gradient js(x).But, even in the first case, an approximated solution becomesexpressed by a first order modified Bessel functions and

describe the one-dimensional motion of thermal carriers nearthe injecting contact, we can define the transition probabilityfrom a position x to a position xþ l and x� l, corresponding tothe carrier motion in and against the external electric fielddirection, respectively. Assuming the carrier to realize a




requires summation procedures (see Ref. 361). However, to

diffusion motion, they are given by Godlewski et al. [408].

Px�lðFÞ ¼1

6expð�eFl=kTÞ and PxþlðFÞ

¼ 1

62� expð�eFl=kTÞ½ �

ð222Þ

The parameter l represents a field-independent scatteringlength of the carriers. The factor 1=6 is included to accountfor the statistical distribution of motion directions. The netcarrier flux in field direction is

F ¼ nðx� lÞuthPxþlðFÞ � nðxþ lÞuthPx�lðFÞ ð223Þ

where n(x� l) and n(xþ l) are charge concentrations at posi-tions (x� l) and (xþ l), respectively, and uth is the thermalvelocity of the carriers. If there are sinks for carriers at boththe origin [emitter: js(x)] and the collecting electrode at x¼d,and if the concentration functions n(x� l) and n(xþ l),expanded in Taylor series about x, are truncated after thefirst expansion term, the collected current will have the form

j ¼ eFþ jsðxÞ ¼1

3euthnðxÞ 1� expð�e FðxÞj jl=kTÞ½ �

� FðxÞFðxÞj j �

1

3uthl

dnðxÞdxþ jsðxÞ

ð224Þ

It corresponds to the standard equation (198) with

1

3uth

el

kT¼ m ð225Þ

FðxÞ ¼ kT

eðg� b

x2Þ ð226Þ

and

D ¼ 1

3uthl ð227Þ

The field-dependent drift velocity

uðFÞ ¼ 1

3uth 1� expð�eFl=kTÞ½ � ð228Þ




saturates at high fields, approaching umax ( F !1 ) ¼ (1=3)u th .On the other hand, for eFl � kT (low-field regionor l ! 0)

u ðF Þ ¼ 1

3 u th

eFl

kTffi m F ð229Þ

giving Eq. (225).Equation (224) may be solved numerically, leading to

more or less steep current-field characteristics dependent onthe carrier scattering length, l. Examples are shown inFig. 89. The curve with the lowest l ¼ 0.01 nm is adjusted toreproduce one-dimensional Onsager approximation. The lar-gest value of l¼ 2nm is chosen at the upper limit of the applic-ability of the field-controlled diffusion jump model. It is seenthat increasing l reduces the steep rise of current with field,a tendency to saturation appears for l > 0.1nm andF0 > 105V=cm. The scattering length 0.5 nm correspondsroughly to the shortest distance between molecules of anthra-cene. We note, however, that the scattering length has notnecessarily to be identical with the intermolecular distance.Charge carrier scattering in molecular solids occurs at atomsof vibrating and rotating molecules, the scattering lengthindicating an average distance between sites of two consecu-tive scattering events. Such a distance can be shorter thanthe lattice constant or intermolecular distance. The differenceis expected to be well pronounced in case of large moleculesforming disordered solids, e.g. polymers. This is reflected ina difference between the hopping and intermolecular dis-tances. However, one has to distinguish between the kineticmodel and a hopping model for charge carrier motion.While hopping in molecular systems must include a disorderleading to a field-induced modification of effective hoppingdistances, the kinetic model describes the carrier motion witha field-independent scattering length. Moreover, and moreimportant, the dwell time in hopping motion is much longerthan the scattering event time. Equation (221) inserted intoEq. (224) allowed to test the effect of the tunneling recombina-tion at the interface (219) on the current-field characteristics.




In Fig. 90 emission-limited currents vs. applied field fordifferent surface recombination efficiency are presented.A slight change in the shape of the j(F ) curves (particu-larly for l < 0.1 nm) is accompanied by a substantialdecrease in the current following an increasing rate of recom-bination.

The above considerations show that the identification ofthe injection mechanism based upon the shape of a j( F) curveonly is highly uncertain and conclusions must be drawn withgreat caution.

Figure 89 Current-field characteristics, plotted in a log–log scale,as calculated numerically from Eq. (224) parametric in scatteringlength. Calculation was performed with a1¼ 20nm�1, T¼ 300K,e¼ 3, d¼ 10 mm, and for the case no surface recombination. The cur-rent values are normalized to j0. After Ref. 408. Copyright 1994Wiley-VCH, with permission.




4.4 DIFFUSION-CONTROLLED CURRENTS(DCC)

Charge carrier injection from a metallic electrode is said to bediffusion-controlled if space-charge effects can be neglected(see Sec. 4.3.1) and the diffusion term in Eq. (198) [or Eq.(224)] is comparable or exceeding the drift current flow. Sol-ving Eq. (198) for n (x ) in the case of a strong-gradient js (x )for the low-field regime [2 (bg) 1=2 < 1] yields [361]

jDCC ffi m enðx Þ expð�b = x0 Þ½ �F ð230Þ

where n( x0) is the charge concentration at x ¼ x 0.For the high-field case [2(bg) 1=2 > 1], the solution is

jDCC ffi m enðx 0 Þ expð�gx 0 � b= x 0 Þp �1 =2 ðkT = eb Þ1 =4 F 3= 4

� exp 2 ðb e= kT Þ 1= 2 F 1= 2h i

ð231Þ

Figur e 90 Inj ection-limit ed current j (norm alize d to j0 ) vs. appliedelectr ic field F0 for (a) l ¼ 0.01, and (b) 0.5 nm , and different surfacerecombination rates Zr(0)=n (as given in the figure). The tunnelingconstant for the surface recombination a2¼ 10 nm�1, other para-meter s as in Fig. 87. After Ref. 408. Cop yright 1994 Wi ley-VCH,with permission.




To the constant factor (with g x0 � 1), they are identicalwith Eqs. (18) and (19) in Ref. 409, respectively, derived fordiffusion-limited Schottky emission of electrons from a metal-lic cathode into the conduction band of an insulator. Also, theyresemble the general drift current solutions (203) and (205),though an important difference can be noted due to the mobi-lity appearing in Eqs. (230) and (231). This would be of crucialimportance if the mobility were an electric field-dependent

the extreme case in which the current in the insulator is diffu-sion controlled, while the drift current, Eq. (203), representsthe greatest current that can flow across the interface. Theratio of these two currents, j= jDCC , must be greater than unityfor the current to be diffusion controlled. Using Eqs. (203) and(231) for the high-field current regimes with a strong-gradientsource currents, js (x ), this condition can be expressed throughthe minimum carrier injection rate

Zinj ¼j0

en x0ð Þl >

mkT

e p 1= 2 b 1= 4 l 7= 4 exp 2 b= lð Þ1 = 2�gx0 � b= x0

h i

ð 232Þ

As expected, the limiting value of Zinj strongly dependson the relation between b , l and x0 and increases with increas-ing mobility and temperature. For typical room-temperaturemobilities on the level of 10� 4 cm2= V s, b ¼ 4.7 nm [resultingfrom (201) with e ¼ 3], l ¼ 0.2 nm (cf. Table 5) and x0¼ 1nm(one molecular distance, roughly), the minimum injection rateZðlimÞinj ffi 4� 108 s�1. The physical meaning of the condition (232)consists in the formation of the sufficient carrier concentra-tion gradient [�dn(x)=dx] in order that diffusion currents playthe dominating role in Eq. (198). But, it cannot be too largethat not to make the current space-charge-limited. We notethat the limiting value of Zinj [Eq. (232)] contains the strengthof the electric field applied to the sample through the quantityg (201). In the above calculation example, F¼ 106V=cm hasbeen used. It follows readily from (232) that for lower fields(lower g), the limiting value of Zinj increases (ZðlimÞinj ffi 1010 s�1

at F¼ 105V=cm). A larger injection efficiency is needed in




quantity (cf. Sec. 4.6). Equation (231) gives the current for

order that the drift current exceeds the DCC at low fields. Thefield dependence of ZðlimÞinj follows from the functional shape ofjDCC (231) which shows that, in general, log j DCC vs. F

1= 2 plotmay not be a straight line, and only for gx0 � 1, this might bethe case. This condition with x0 < 0.25 nm at F ¼ 106 V = cmand T ffi 300 K leads to a very low value of ZðlimÞinj . Summarizing,we have seen that the carrier diffusion can change theSchottky (one-dimensional Onsager)-type behavior of theinjection current-field characteristic (203) by a field-depen-dent factor exp(�gx0) ¼ exp[�( eF=kT ) x 0] (unless g x0 � 1),and this could be one of the reasons of the high-field regimedeviations of the experimental plots of log ( j= F3= 4) vs. F1= 2

from the theoretical predictions of Eq. (203). Another reasonfor them would be a field-dependent mobility m (F ), the casediscussed in Sec. 4.6.

4.5. DOUBLE INJECTION

To manufacture an organic LED functioning on the basis ofelectron–hole recombination processes, a system of organicfilms has to be provided with two injecting contacts, one inject-

of electrical properties of such systems is much more complexthan that for systems with one injecting contact (see Secs. 4.3and 4.4) because the recombination current adds to the driftand diffusion currents flowing between electrodes throughthe sample [410]. The total current density may be orders ofmagnitude larger than with single injection, although thepositive and negative net space charges situated at the respec-tive electrodes are roughly equal to the one-carrier spacecharge connected with current flow. The generally valid equa-tion governing double-injection current in the presence ofspace charge has been derived by Parmenter and Ruppel[411]. They solved the system of the following equations:

j ¼ e meneðxÞ þ mhnhðxÞ½ �FðxÞ ¼ independent of x

e0edF

dx¼ eðnh � neÞ ð233Þ




ing electrons, another injecting holes (cf. Sec. 4.2). Description

med

dxðneFÞ ¼ �mh

d

dxðnhFÞ ¼ gehnenh

Zd

0

FðxÞdx ¼ U ð234Þ

where subscripts e and h for carrier concentrations ne andnh refer to electrons and holes, respectively. Except for Eq.(234), all these equations have their analogs in unipolarinjection. For two Ohmic contacts, that is with the boundaryconditions

Fð0Þ ¼ FðdÞ ¼ 0; nhð0Þ ¼ neðdÞ ¼ 1 ð235Þ

and for trap-free (or shallow trap) case, the current densityfulfilling Eqs. (233) and (234) may be written as [334]

j ¼ 9

8e0 e meffF

2=d ð236Þ

It is identical with Eq. (168a) except for the mobility whichin the double-injection case is a complex combination of indi-vidual electron (me) and hole (mh) mobilities, including socalled recombination mobility (m0),

meff ¼ m0nenh2

3

� �2 ð3=2Þ ne þ nh½ � � 1ð Þ!ð3=2Þne � 1ð Þ! ð3=2Þnh � 1ð Þ!

� �2

� ne � 1ð Þ!ðnh � 1Þ!ðne þ nh � 1Þ!

� �3 ð237Þ

The term m0, having dimension of the mobility, is definedby

m0 ¼e0egeh2e

ð238Þ

and the dimensionless parameters ne and nh are defined by

ne ¼ me=m0 and nh ¼ mh=m0 ð239Þ

Let us note that the introduction of m0 accounts for therecombination effect on the current. Its relation to the carrier




mobilities allows to distinguish three limiting cases for theSCL double-injection current flow. These are

(i) Injected plasma (or weak recombination) case forne 1 and n h 1, with a large space-charge overlap, interpe-netrating electrons and holes mostly reach opposite electro-des. Equation (237) reduces to

meff ffi2

32 p me m h = m0ð Þðme þ m h Þ½ �1 = 2 ð240Þ

An organic LED operating under such conditions shouldshow emission from the entire emitter bulk as the recombina-tion occurs on the total carriers paths equal to the emitterthickness, d . The recombination zone width w � d (see Sec.3.3).

(ii) Volume-controlled current (or strong recombinationcase) for ne�1 and nh�1. This is the case of negligiblespace-charge overlap with

meff ffi me þ mh ð241Þ

Here, the requirement of high values of the electron–holerecombination coefficient requires double injection from twoOhmic contacts to produce two SCL currents meeting andannihilating each other somewhere in the emitter within anarrow recombination zone (w�d).

(iii) One-carrier SCLC flow for ne1, nh�1 (or ne�1,nh 1). Equation (237) may then be reduced to

meff ffi me ðor mhÞ ð242Þ

dependent on which of the above inequality pairs are ful-filled. The current is practically one-carrier SCL current,the less mobile carriers recombining very near the electrodefrom which they are injected. The recombination zone isexpected to locate towards the low mobility carrier injectingelectrode.

It is interesting to note that in the Langevin recombina-tion mechanism with the geh expressed by the sum of the indi-vidual carrier mobilities (4), the interrelation between ne,hand m0 switches to the relations between electron and hole




mobilities themselves. For instance, the strong recombinationcase can be defined by either

ne ¼mem0¼ 2

1 þ mh =m e� 1 that is

mhme 1

or

nh ¼mhm0¼ 2

1 þ me = mh� 1 that is

memh 1

ð 243Þ

if the expression (4) for geh is inserted into Eqs. (238) and(239). This means that the strong-recombination case can beobserved whenever me differs substantially from mh. Forme ¼ m h, n e (n h ) ¼ 1, we deal with an intermediate case between(i) and (ii). An excellent system to observe the strong recombi-nation double injection is a DL LED with an interface block-ing passage of charge carriers across the LED. For example,the confinement of the recombination to a narrow zone locatedin the Alq3 close to the TPD=Alq 3 interface of the TPD HTLand Alq3 ETL based LED makes the current flowing throughthe device equivalent to the recombination current suppliedby two quasi-Ohmic electrodes injecting holes at theITO= TPD and electrons at the Mg= Alq3 contacts, as discussedalready in Sec. 3.3. Even better example is given by an elec-trophosphorescent DL LED with a strongly hole blockinglayer described in Fig. 67. The high-field segment of its cur-rent-field characteristic can be approximated by Eq. (236)with e¼ 3 and meff¼ 3.7� 10�6 cm2=Vs¼ const throughoutthe square field dependence of the current. Since the EL spec-trum of this LED is underlain by the emission of Ir(ppy)3 dis-persed in its HTL [6% Ir(ppy)3:20% PC:74% TPD] [304], therecombination zone is most probably located in the HTL closeto the interface with the PBD ETL. From the energy levelscheme, it follows that molecules of Ir(ppy)3 do not form holetraps so that the hole mobility in the HTL should be on theorder of hole mobility of a film composed of 74% of TPD and26% of PC. The time-of-flight mobility data give an order of10�4 cm2=Vs for films between 50% and 80% content of TPDat room temperature [338] is two orders of magnitude higherthan the above calculated meff. This would suggest that




molecules of the organic phosphor Ir(ppy)3 act as polar specieswhich increase disorder parameters of the organic film, redu-cing strongly the hole mobility (see Sec. 4.6).

The presence of active charge traps can change the abovepicture entirely. Of importance becomes the relation betweenthe average trapping time (tt) of the carriers, the averagethermal release time (trel ) of the carriers from traps and theiraverage recombination time (trec). For active (sufficientlydeep) traps, the condition trel tt is usually fulfilled, other-wise trapping would be negligible. Three extreme cases canbe considered taking in addition various relations of thesetimes with respect to trec:

(A) trec trel , tt . In this case, the Parmenter–Ruppelequation (236) is still basically valid provided the mobilitiesare replaced by effective mobilities controlled by discretetraps, meff ¼ Y m. If each of single-carrier currents are charac-teristic of an exponential trap distribution [Eq. (175)], thedoubly injected current varies in the same way but is largerby orders of magnitude (see e.g. Fig. 64b). Moreover, thethickness dependence of the current does not follow thatresulting from Eq. (175). It is usually less steep than d �(2n � 1)

with n determined by the voltage dependence of j � Un (Refs.412 and 413) or j does not show any monotonic decrease withd [414,415]. Figure 91 shows an example for anthracene crys-tals provided with different hole injecting anodes and electroninjecting cathodes. The main problem in verifying the thick-ness dependence of the double (also single) injection currentis dealing with different samples which can differ in the con-centration of traps and trap distribution function, and sepa-rately deposited injection contacts with injection efficiencieswhich may differ from sample to sample. The example inFig. 91 seems to alleviate this problem since a number of par-allel diodes were made by cleaving a number of ‘‘staircaseshaped’’ single crystal specimens from the same Bridgmanmethod grown boule. A common indium anode contact wasused on each specimen and individual sodium–anthracenecomplex cathodes prepared by dropping a small quantity ofthe sodium complex in solution onto the crystal under anargon atmosphere (sideways spreading was constrained by a




ridge of nitrocellulose applied prior to dropping the solution).In the moderate field regime j � Un was found with the expo-nent ranged from 6 to 12 for a series of cells employing botha carbon fiber and anthracene–sodium complex cathode. Inthe high-field regime j � U3= d 4. Clearly, the relation Un=d 2n� 1

[cf. Eq. (175)] is not obeyed. Also, a weak thickness depen-dence of the double injection current within the moderate

414). This would support a conclusion that even individuallystrong injecting electrodes are unable to supply volume-controlled currents in a double contact combination to anthra-cene or Alq3. Indeed, the j(F) dependence for double-injectioncurrents using ITO=TPD=Alq3: DPP=Mg LEDs can be well

Figure 91 (a) Current–voltage characteristics of double injectioncurrents for a single anthracene crystal diode employing a carbonfibre cathode (�), and partly oxidized sodium anthracene cathode(o). (b) Thickness dependence of the current for anthracene crystalsprovided with indium anode and sodium anthracene cathode. AfterRef. 412.




field regime has been observed (see Fig. 69b; see also Ref.

described by ILC flow as presented in Fig. 76 and discussed inSec. 4.6. An alternative would be the application of the macro-trap model for carrier trapping, which predicts j � Un=d nþ 1

(185) with n reflecting the macrotrap potential shape. Thispotential consists of two branches (Fig. 72) reflected in theexperiment by two different steeps of the log j –log U plots ascan be seen in Figs. 71 and 91 (the low-field linear part dueto the Ohmic conduction precedes superlinear segments). Incontrast to anthracene, j( F) curves for double injectioncurrent into tetracene crystals follow well SCLC behavior

high-field regime, they can be well described by the relation-ship j � Fn =d n� 1 with n ffi 5 either for KI= I2 (positive)–Mg(OH)(negative) contacts [416] and Au (positive)–Na= K (negative)contacts [41]. This seems to be readily associated with a lowerinjection barrier for holes from gold (Au) into tetracene;D Eh ¼ I � WAu

anthracene DEh ffi 0.6 �� 1.12 eV with I ¼ 5.9 eV (for the values

Ref. 417). However, similar concentrations and energy distri-butions for electrons and holes in this crystal might be ofimportance for the voltage evolution of the double injectioncurrent

ð BÞ trel trec t trap and ðC Þ trel ; ttrap trec

In these two deep trapping cases, the trap filled limits in

the recombination zone in two layers in front of the electrodesin case (B) anticipated. The situation becomes even more com-plex if traps are concentrated in front of the electrodes, thecase very probable due to the exposition of sample surfaceto the ambient atmosphere during sample handling anddeposition of the electrodes. A striking example of a complexrecombination zone due to inhomogeneous trapping effectsin organic crystals can bee seen in Fig. 58. A more detaileddiscussion of the spatial distribution of the EL emission,from organic crystals, and its evolution with applied fieldand injection efficiency of the contacts has been given byKalinowski [41].




¼ [5.4 � (4.78�� 5.3)] eV ffi 0.1�� 0.62 eV than into

of I, see Ref. 26; the work functions for gold are taken from

the SCLCs would be expected (cf. Sec. 4.3.1), and a splitting of

for single injection (see Fig. 64, also Refs. 41 and 416). In the

Unfortunately, however, though some electrical and opti-cal characteristics can be explained or made plausible by qua-litative considerations, ‘‘proofs’’ on this basis are very difficultas the identification of the terms in the equations selected isoften not unique and the results obtained depend upon theparticular assumptions and simplifications made.

4.6. CHARGE CARRIER MOBILITY

Electrical characteristics of organic LEDs are inevitably asso-ciated with mobility of charge carriers in materials used fortheir fabrication. The mobility defined as a carrier drift velo-city (v) per unit applied electric field

me;h ¼ ue;h=F ð244Þ

can be determined from various experiments, the time-of-flight (TOF) technique being most commonly used as itdirectly provides drift velocities [250,418–421]. In the TOFmethod charge carriers pairs are created in a photoconductor,near the surface of a plane-parallel sample sandwichedbetween two planar electrodes, by absorption of a short pulseof light of sufficient photon energy, admitted through thesemitransparent front electrode. Depending on the polarityof the field established (F¼U=d) by applying a voltage differ-ence (U) between the front and rear electrode (separated by adistance d), a ‘‘sheet’’ of electrons or holes is pulled across thesample at a velocity ve,h. In the external circuit, the driftingcharge, q, is manifested as a constant current, ie,h¼ qme,hF=dflows, coupled by the displacement current, which drops to 0when moving carriers have been collected (or stopped near) bythe rear electrode. The average travel time, tt, read from theduration of an (ideally) rectangular TOF pulse on an oscillo-scope display, is thus direct measure of the average drift velo-city ve,h of the carriers, ve,h¼d=te,h. From the current pulseamplitude, the charge generation efficiency, Zq¼ q=eI0, canalso be derived, if the excitation intensity, I0, is not too highas to deform the electric field within the sample through theinjected charge. For a strongly absorbed light pulse of




duration dt� tt, and fast carrier generation process, the car-rier sheet has a width dl�d. This width is increased duringtravel by diffusion and Coulombic repulsion broadening[422]. If trapping losses of carriers on their way to the collect-ing electrode are not too severe, an arrival kink on the TOFpulse will still be seen and used to determine the travel timeof the carrier sheet. Strong deviations from ideal rectangularpulse are frequently observed with disordered solids becausecarriers propagating through the solid experience a distribu-tion of hopping times. Then, the current pulse is character-ized by a rather featureless decay. The featureless currentpulse indicates a widespread of the carrier packet as it arrivesat the collecting electrode. In fact, it is so wide that it nolonger exhibits the Gaussian spread but is asymmetricallyskewed, with a leading edge penetrating into the bulk and asharp cut off on the backside of the packet. Such currenttraces have become known as being indicative of ‘‘dispersivetransport’’. A successful interpretation of dispersive transporthas been presented by Scher and Montroll [32]. They assumeda carrier hopping in a three-dimensional random array ofisoenergetic sites, and derived the time dependence of thetransient current in the form

iðtÞ � t�ð1�aÞ for t < ttt�ð1þaÞ for t > tt

�ð245Þ

with the temperature (T) and sample thickness (d) dependenttransit time

tt � d=lðFÞ½ �1=a expðD0=kTÞ ð246Þ

where 0 < a, l is a dispersion parameter (denoted earlier by band discussed in Sec. 1.3). The more disordered system, thesmaller the a-value and from Eqs. (245) and (246), the moredispersive the current shape and the stronger the thicknessand field dependence, the latter entering Eq. (246) throughthe field-dependent mean displacement l(F) in field directionper hop. The natural consequence of relations (245) are tworegimes of slopes (1� a) and (1þ a) that occur on log–log dis-plays of current against time. Because a is a constant with




respect to applied field and specimen thickness, this charac-teristic implies universality of pulse shape on normalized cur-rent and time axes. Since, by definition, the hopping is athermally activated process, the transit time decreases withtemperature, thus, the carrier mobility increases with thezero-field activation energy, D0. A spread of the activationenergy of the hopping carriers, resulting from the diagonaldisorder (see discussion later on), implies a temperaturedependence of the dispersion parameter [see Eq. (9)]. Withtemperature decreasing, one expects from (245) and (246),and (9) the shape of the transient current pulse to becomemore dispersive (more featureless). Observations consistentwith all the above expectations are presented in the wide-spread literature for both organic and inorganic solids. A typi-cal example is shown in Fig. 92. Almost non-dispersivetransport of holes in amorphous selenium at room tempera-ture becomes dispersive at lower temperatures. For example,the highly dispersive transport at 123 K, which does not cre-ate any particular feature on the current pulse in the linearscale, shows a pronounced bend at t ¼ tt in the double loga-rithmic scale, dividing the current decay into two branchesaccording to relations (245). A recently published work onAlq3 shows the importance of traps produced by oxygen andimpurities for the transient current shape [423]. In Fig. 93,TOF electron transients in a linear and double logarithmicscale representations are shown for diverse samples of Alq3.The samples as-received from the supplier and exposed toambient behave highly dispersive, after purification exhibitswell-resolved features of non-dispersive transport. The mobi-lity has been determined from the relationship (244) withve¼d=tt, where tt is the transit time taken as the time atwhich the photocurrent dropped to half of its plateau value[421] for non-dispersive transients (purified sample), andfrom the inflection point on a log i–log t plot [424] for disper-sive transients with the as-received Alq3 sample. Interest-ingly, the mean values and the Poole–Frenkel like fielddependence of such determined mobility are in both casesidentical except for a stronger degree of variation insuccessive experiments with the as-received material. The




experimental data fulfilled the Poole–Frenkel type functionme ¼ meo exp(bm F 1= 2) with meo ¼ 2.9 � 10� 9 cm2= v s and b m ¼7.3 � 10� 3 (cm= V)1=2 in accordance with some other literaturevalues [336,340,341,425].

Figur e 92 Typi cal tran sient current pulses for ho les in amorp hous

the degree of the dispers ion in carrie r transport . Left: linear current( i ) and time ( t) axes; righ t: normaliz ed value s in loga rithmic axeslog (i =i0 ) vs. log ( t=t 0 ). The arrow s i ndicate the posit ion of the ‘‘knee’ ’div iding the two reg imes of loga rithmic depend ence. Similar beha-




seleniu m (see Ref. 422a) , illustr ating the effect of temperatur e on

vio r can be observed in organ ic solid s (see e.g. Ref. 422b).

The xerographic discharge modification of the TOFtechnique is often used for the samples prepared in the formof thin films cast or evaporated on conductive substrates

a corona to surface potential V0, and the change in the sur-face potential V(t) following a flash of strongly absorbedlight is observed. The absorbed photons generate chargecarriers in a thin layer close to the charged surface, wherethey can decay in the bimolecular recombination process orneutralize the surface charge due to opposite free carriersdrifting to the substrate. At low light intensities (the changein the surface potential is small compared to V0), the initialrate of the potential change (dV=dt)t¼ 0¼ ZqeI0=C (C is thecapacitance of the sample) provides a direct measure ofthe injection quantum efficiency (Zq) that is the number offree carriers emitted into the sample bulk per absorbedphoton. To obtain the drift mobility from a xerographic dis-

Figure 93 Transient photocurrent signals (i) for 8 mm thick Alq3layers sandwiched between the ITO anode and Al cathode. Lightpulses entered the samples through the ITO anode. The changefrom the dispersive transport for Alq3 as-received from the supplier(circles) to the non-dispersive transport with purified (squares) Alq3samples. It can be seen in both linear (a) and double logarithmic (b)plots. In the inset of part (a) electric field dependence of mobility isshown, in part (b) the TOF transient for as-received Alq3 exposed toambient is added (diamonds). After Ref. 423. Copyright 2003 Amer-ican Institute of Physics, with permission.




(see e.g. Ref 424). The free sample surface is charged with

charge measurement, the photoinduced discharge has to bedriven under SCLC conditions, that is the number ofinjected carriers has to be approximately equal to the capa-citor charge CV0. The motion of the space charge makes theelectric field F (d ,t) on the exit electrode (x ¼ d ) to increaseabove its initial value F0(d ,t¼0) ¼ U= d. Combining the driftand displacement currents with the Poisson equation, yields[426,427]

F ðd ; t Þ ¼ 2 d

m1

2t0 � t ð247Þ

where

t0 ¼ d 2 = mU ð248Þ

is the transit time of carriers traversing a sample thicknessd , with applied voltage U, in the absence of space charge.The time t1 when the front arrives at this electrode isobtained from the equation

R t10 m F ð d; tÞ d t ¼ d which after

integration with (247) yields t1 ffi 0.8t0. As expected, the t 1is shorter than the transit time t0 (248) in the absence ofspace charge. Using Eq. (247), the time evolution of the cur-rent density for t < t1 can be obtained in the followingform:

jð tÞ ¼ 2d e0 em

1

ð 2t0 � tÞ 2 ð249Þ

Comparison with Child’s current (168a), here denoted asj1, shows that current begins with j(t¼ 0)¼ 0.44 j1 and risesto j(t¼ t1)¼ 1.21j1. Since the current for t > t1 has to drop toj1, its time evolution should show a spike at t¼ t1 as illu-strated in Fig. 94. We note that the SCL charge injection tran-sients can be induced either by a strong light flash generatedcarriers or a step-like voltage applied to the injecting (Ohmic)electrode in the dark. The latter is exemplified by the topcurve of Fig. 94b. For comparison, a small signal light-induced transient current shown in the bottom of this figureexhibits a shape typical for non-dispersive transport of holes




Figur e 94 (a) The SCL transien t current s for various no rmalizedtrapp ing times ( R ¼ ttrap 0

R¼1 denotes the trap-free case; j1 is the steady-state currentwithout trapping. (b) t1: trap-free SCL transient current injectedfrom ITO under a positive step voltage applied to anITO=PPV=TPD:PC=Al device: jSCL corresponds to j1 in part (a). Bot-tom: TOF photocurrent transient for holes generated by a lightpulse at the Al=(TPD:PC) interface (the negative polarity appliedto ITO). (From Ref. 428).




= t ) as calcula ted from theory (se e Ref. 26);

in TPD:PC systems. This indicates the TPD dispersed in thePC matrix to form almost trap-free organic films, and, there-fore, the SCL transient current in Fig. 94b (top) can be consid-ered as an example of trap-free SCL currents predicted by thetheoretical curve with R¼1 in Fig. 94a. From the same fig-ure, one can see that the stronger trapping (decreasing R) isthe discontinuity of pulse slope becoming less and less pro-nounced, disappearing when the trapping time drops below0.5t0. In other words, the current decay under strong trapping(but negligible detrapping) means the carrier schubweg to beshorter than the sample thickness. A completely differentsituation arises if both trapping and detrapping are much fas-ter than free carrier transit. Then the current transient isdetermined by the effective mobility meff¼Ym with the possi-ble exception of a very short ‘‘trap-free’’ interval at the begin-ning where a peak might appear if a duration of light flashesare comparable to the trapping time. The SCL transientsshould be distinguished from SCL sheet currents that iscurrent flows after momentary Ohmic injection which mayoccur if a flash of duration much shorter than the transit timeis used for introducing carriers (short-lived Ohmic contacts).The density of the sheet current is given then by Helfrich[334] and Schwartz and Hornig [429]

jðtÞ ¼ 1

4e0 e m

U2

d3expðt=t0Þ ð250Þ

for t < t2—the time at which the leading front of the space-charge sheet reaches the exit electrode. It has been shownthat t2ffi 0.8t0 (Ref. 429) which may lead to a confusion withSCL current transients. Though in both cases a current cuspappears at tffi 0.8t0, the difference is apparent in the func-tional shape of the current increase for t < 0.8 t0.

Time-of-flight experiments have been used for over threedecades to characterize carrier mobilities in crystal, andpolycrystalline and disordered organic solids includingmolecularly doped polymers and molecular glasses[28,424,430,431]. Relatively high values (up to several hun-dreds cm2=Vs) and hot carrier effects have been observed in




single van der Waals bonded crystals [420,432–436].Characteristic is a strong electric-field dependence of themobility. Figure 95 shows a few examples of the drift velocity(vdrif) as a function of electric field (F) at different tempera-tures. At low-fields vdrift depends linearly on F, increases sub-linearly at intermediate fields, and saturates at high electricfields. This means the low-field constant mobility, as followsfrom the definition Eq. (244), to decrease with increasing field.The sublinear dependence of vdrift can be associated withacoustic phonon scattering of carriers; the model predicting[420]

udrift ¼ m0ffiffiffi2p

F 1þ 1þ 3p8

m0FC1

� �2" #1=2

8<:

9=;�1=2

ð251Þ

where C1 is the longitudinal sound velocity and m0 is the low-field mobility.

The high-field saturation of the carrier velocity can havevarious origins, e.g. a finite bandwidth of a non-parabolictransporting (here valence) bands, or the emission of opticalphonons. It is believed that the high-field saturation of thedrift carrier velocity in the crystal directions where the bandmodel concept can be applied is due to the first one. Then[420],

uðsatÞdrift ¼ 0:724Wa0

p�hð252Þ

where a0 is the lattice constant in the direction of the chargetransport, and W is the transport bandwidth. On the otherhand, for the transport along narrow-band directions, as forinstance along the c0 direction in anthracene at room tem-perature, it is attributed to the second origin, the charge car-rier is accelerated by the electric field until it has gainedenough kinetic energy m� v2drift=2 (m� is the effective massof the charge carrier) to emit an optical phonon. In the caseof anthracene crystal, this is associated with excitation ofthe intramolecular vibration 395 cm�1 [432]. The tempera-ture dependence of the mobility in two selected organic




(given in the figure). For naphthalene, the drift velocity has beendetermined in the crystallographic a-direction (Eka) and for anthra-cene in crystallographic c0-direction (Ekc0).




(b) ant hracene (se e Ref. 432) crystal s at different temp erature sFigur e 95 (a) Hole drif t vel ocity in naph thalene (see Ref. 28) and

crystals is shown in Fig. 96. At low temperatures, the mobi-lity is dominated by the effect of shallow traps and impurityscattering, and hence a strong dependence on purity andquality of the crystals. The activation energy of thermallyactivated mobilities in the low temperature range can beidentified with discrete trap depths (17.5 meV for electrontraps in perylene, and less than 8 meV for hole traps inanthracene crystals). In the samples with the highest quality,the effect of shallow traps can be excluded and the mobilitylevels off at low temperatures, (open circles in Fig. 96b). Thisindicates scattering at neutral impurities [437]. At highertemperatures, the electron–lattice coupling (a generalizedpolaronic effect) has to be taken into account which leads to

Figur e 96 Tem peratur e depend ence of the charge carrier mobilit yin organic single crystals. (a) The electron mobility in a crystal

electron (m�) and hole (mþ) mobilities in synthetic ultrapurifiedanthracene crystals at an electric field E¼ 2.3�104V=cm directedalong the crystallographic axes b (adapted from Ref. 436a).




grown from moderately purified perylene (see Ref . 28), and (b) th e

the temperature narrowing of the bandwidth according to[438,439]

W ¼ 4 jJ j exp½�g 2 cot hð�ho = 2kT Þ� ð253Þ

where J is the nearest-neighbor transfer integral, g is adimensionless electron–phonon coupling constant, and �h o isthe energy of phonons excited at the temperature T. Clearly,the narrowing of the bandwidth leads to decreasing driftvelocity (252) and mobility defined by Eq. (244). Beyond thetrap-controlled transport region, the temperature depen-dence of the low-field mobility is often found to obey a powerlaw me,h � T �n with 1 < n < 3. [28] (see also examples in Fig.96). Acoustic-phonon scattering in the wide band limit( W > kT ) leads to a T� 1 or T � 1.5 dependence resulting fromthe description of charge carriers as extended Bloch statesrepresented by the electron wave packets, characterized bytheir mean free path exceeding the average distance betweentwo lattice sites (molecules) [440]. The powers �1 and �1.5reflect two different extreme cases for the statistical distribu-tion of electrons, the first for a step-like Fermi–Dirac func-tion, and the second for the Maxwell–Boltzmann function

� n behavior withn > 1.5, the combination of acoustic and optic deformation-potential scattering might be useful [441a].

The band transport picture will break down if the carriertransporting bands become too narrow. The temperaturedependence changes from a power-law to an almost tempera-ture-independent or slightly activated dependence. At hightemperatures, the saturation of the carrier velocity is absent,and dramatic trapping effects on mobility observed even athigh temperatures (see Fig. 97). This is the case when thecharge carriers become localized by the polaronic interactions,and a ‘‘lattice polaron’’ is formed. A transition from coherentbandlike motion to incoherent hopping transport would beexpected from theoretical considerations [435,436]. Theexperimental results do not show such an abrupt transition,the mobility might be seen as a superposition, m¼ mcohþ mincoh,where mcoh is the mobility of the coherent band-like transport,




(see e.g. Ref. 441). To explain the T

and mincoh that of the incoherent hopping motion [443]. Thepresence of traps makes the effective mobility (meff) to bedependent on the time spent by a carrier in the trap andcan be expressed by Karl [28]

meff ¼ Ch½1þ ðCt=ChÞ expðEt=kTÞ�f g�1 ð254Þ

where Et is the depth of traps, and Ch¼Nh=N andCt¼Nt=N denote the fractions of host material molecules(Nh) and traps (Nt) with respect to their total numberN¼NhþNt. For sufficiently deep traps [Et > kT ln (Ch=Ct)],Eq. (254) becomes an Arrhenius-type function with the activa-tion energy corresponding to the depth of traps. This can beseen in Fig. 97b, where the straight-line segments of theArrhenius plots give Et¼ 0.17 eV for electrons andEt¼ 0.42 eV for holes trapped by tetracene molecules incorpo-rated in anthracene crystal lattice. A nearly temperature-independent mobility of both holes and electrons can be foundin polycrystalline films [430,444–446]. Being represented bythe Arrhenius-type function, it exhibits small activation

Figure 97 Arrhenius plot of electron and hole mobilities in thecrystallographic c0 direction of a well-purified anthracene crystal(a) and for a 4� 10�7mol tetracane-doped anthracene crystal (b).After Ref. 442. Copyright 1975 Wiley-VCH, with permission.




energies on the level of tens of millielectronvolts (an exampleis shown in Fig. 98). This temperature behavior in polycrys-talline samples can be interpreted in the general frameworkof the stochastic theory of dispersive transport independentof the details of any specific mechanisms underlying a broaddistribution of event times. These event times can be hoppingtimes, trap release times, or both simultaneously [447]. It hasbeen already discussed above that for the case of hoppingmotion the field and temperature dependence can be relatedto the transit time expressed by Eq. (246), completed by afield-dependent activation energy

D ¼ D0 � eaðtÞF ð255Þ

where the lattice parameter a(T) is only mildly temperaturedependent. D0 is the activation energy extrapolated to zerofield. The effect of electric field on the activation energy forfields F < 105V=cm (as in Fig. 98) and a on the order 1nmdoes not exceed 30%, and falls often in the range of spreadof the experimental values of D for different samples. The

Figure 98 Temperature dependence of TOF-measured hole andelectron mobilities in polycrystalline films of p-terphenyl (a) andp-quaterphenyl (b). The sample thicknesses have been chosen fromthe range 12–18 mm. The values of the activation energy are givenabove each of the Arrhenius plots. After Ref. 430.




mobility data for polycrystalline samples composed of micro-crystallites characterized by broad transporting bands canbe understood in terms of the standard multiple-trap trans-port including a spectrum of release rates (to the band) froma distribution of trap levels and assuming the mean displace-ment between traps equal to the average distance, m0ttrapF,the carrier moves in the band before it is retrapped. This isequivalent to a random walk on a lattice, where the latticespacing in the direction of the electric field is field dependent,namely, a¼ m0ttrapF, where m0 is the microscopic mobility ofcarriers in the band, and ttrap is the free carrier trappingtime. Assuming that all traps have the same capture cross-section, the time evolution of the current, i(t), can be asso-ciated with the distribution function of release times, andexpressed in the form

iðtÞ ¼ i0að1� aÞðnttÞ2aðntÞ�ð1þaÞ ð256Þ

where i0 is the current at t¼ 0, n is the attempt-to-escape rate,and tt is the transit time defined by

Ztt

0

m tð ÞFdt ¼ 1

2d ð257Þ

This equation identifies the transit time as a time atwhich the leading edge of the charge packet reaches the rearcontact located at a distance d from the injecting one, whichoccurs when the center of gravity is roughly halfway across.Equation (256) has been derived with an assumption thatthe trap energies are distributed exponentially below the lim-iting edge of the transporting bands [448]. The dispersionparameter a is then simply related to the distribution para-meter l¼ a�1¼Tc=T [cf. Eq. (170)]. The time dependence inEq. (256) matches the Shear–Montroll result (245). Thelarge-time range TOF experiments show a to be a time-depen-dent parameter [449,450]: affi 0.0 within a short-time regime(0.1ms < t < 10ms), and a! 1 for t < 10ms. The charge oflog i–log t plot slopes is gradual—nearly three orders of mag-nitude. These features indicate a transition in i(t) from a




highly dispersive transport to an essentially non-dispersiveduring a single transit. This, in turn, allows to infer froma(t) information about the real trap distribution. Two exam-ples of such a procedure are described by Muller-Horscheet al. [449] and Di Marco et al. [450]. The procedure is basedon the conjecture that [449]

aðln tÞ ¼ ln hðEdÞ=hðE ¼ 0Þ½ �ln rðEdÞ=n½ � ð258Þ

where h(Ed)¼h(E¼ 0) exp(�a Ed=kT) [cf. Eq. (170)], and

rðEdÞ ¼ n expð�Ed=kTÞ ð259Þ

is the release rate at the demarcation energy

Ed ¼ kT lnðntÞ ð260Þ

which is a time-increasing quantity with n being the attempt-to-escape rate. This energy separates those states above Ed(t)for which the most probable number of release events in thetime t is greater than unity, from the deeper states where acarrier is unlikely to be thermally released in the time t.

Equation (258) relates directly the slope parameter of i(t)and the density of traps h(E). Using the time-dependent tan-gent to the experimental log i(t) vs. log t curves and (Eqs.(258)–(260), h(E) has been calculated for polyvinylcarbazolesolution cast films [449] and vacuum-evaporated polycrystal-line film of thionaphtenoindole [450]. The latter is shown inFig. 99. The general f eatures of t he distribution f (E) ¼ h(E)=h0

are: (i) f(E) is flat (TcT) for E < 0.395 eV, and (ii) there isa cut-off of f(E) at E > 0.4 eV, indicating a quasi-exponentialdecrease of the trap density with kTcffi 0.054 eV. The gradualdecrease in the dispersion of the charge transportcorresponds to the quasi-exponential range of f(E)(0.135 eV > kTc > 0.033 eV) with an energy range less than0.1 eV wide. Weakly dispersive transport takes place over atime range about one decade prior to tt. The restriction ofi(t) measurements to this time range would lead to erroneousconclusion that there is a narrow range of exponentiallydistributed trap energies instead of the broad range with a




cut-off as shown in Fig. 99. The data for polycrystalline filmsof thionaphtenoindole provide an interesting example of theelectric field-decreasing mobility (Fig. 100).

Provided that real polycrystalline samples are subject ofa spatially non-homogeneous distribution of traps near thesample surface and within intergrain boundaries, the pre-transit time averaged carrier flux is composed of two compar-able parts: one due to usual carrier drift in the external field

j ¼ en mdrifteff F � eDeffdn

dx ð 261Þ

where the effective drift mobility mdrifteff , the effective diffusionconstant Deff and the carrier concentration, n , can be treatedas pre-transit time averaged quantities.

The measured effective mobility, meff, can be definedusing Eq. (261) as

meff ¼ m drifteff þ udf F �1 ¼ mdrifteff þ m dfeff ð 262Þ

Figur e 99 The trap distribution fun ction in evaporate d polycry s-talline films of thion aphtenoind ole (TNI), calcu lated from Eq. (25 8),using time- depende nt tang ent of the experim ental log i ( t)–log t plots




(See Ref. 450).

and the second due to carrier diffusion [see Eq. (198) andSec. 4.4]:

where vdf is the macroscopic diffusion velocity of the carriers:

udf ¼ �Deff

n

dn

dx ð263Þ

for sufficiently high electric fields (F !1), the second term inEq. (262) vanishes and meff ! m drifteff . However, in general, andespecially at low fields, the measured mobility meff decreaseswith field as 1= F . We note that the electric field strengthFc ¼�(kT =en)(d n= dx ) ¼ 4.4 � 104 V cm� 1 separates thoseeffective diffusion mobilities which are greater than the effec-tive drift mobility from their values smaller than mdrifteff , andthus

meff ¼ m drifteff 1 þ Fc

F

� �ð264Þ

This result is useful in understanding the variation of thefield dependence of the TOF measured mobility from sampleto sample, following the carrier density gradients( Fc � dn =d x ). For example, the role of the diffusion carrierstream would explain the field dependence of m in single crys-tals whenever their near-surface layer is strongly populated

Figur e 100 Effect ive mobilit y, as measur ed by the TOF techniquein a 10mm thick polycrystalline film of thionophtenoindole, plottedvs. 1=F (points). The solid line drawn according to Eq. (264), extra-




pola ted by the dashed line to F !1 (se e Ref. 450).

would not expect the macroscopic diffusion to affect signifi-cantly the mobility measured in amorphous films. Equation(264) could be successfully applied to the experimentalmobility data for polycrystalline thionaphtenoindole films asillustrated in Fig. 100. From the intersect of the straight-lineplot of log meff vs. F

�1, mdrifteff ¼ 5� 10�5cm2=Vs follows, and itsslope gives vdf¼ 2.2 cms�1.

Numerous measurements over a large range of electricfields and temperatures have established that, in many mate-rials, the carrier mobility can be described by a universal lawbearing the ‘‘Poole–Frenkel’’ like form of the electric fielddependence

m ¼ m0 exp �Y=kTð Þ exp bmF1=2 ð265Þ

where m0exp(�Y=kT) is the zero-field mobility.Various versions of expression (265) can be found in the

literature. The differences are due to the interpretation of theactivation energy Y and the parameter bm. For example, atemperature-independent value of Y and the ‘‘Poole–Frenkel’’factor bm¼B(1=kT� 1=kT0) with constant parameters B andT0, has been assumed by Gill [37], the mobility follows Arrhe-nius-type temperature dependence. The formalism based onthe assumption that charge transfer occurs by hoppingthrough a manifold of localized states characterized by aGaussian distribution of energies and positions has led toEq. (265) with a temperature-dependent activation energyY¼ (2s=3)2=kT and bm¼C[(2s=3kT)2�S2], where the con-stant Cffi 2.9� 10�4 (cm=V)1=2, and s=kT and S are energyand position disorder parameters, respectively [29,39]. Sincethe energy of a molecule in a disordered solid state can berepresented by a matrix in which the diagonal elements indi-cate the site energy of the molecule in the absence of reso-nance interaction with the surrounding medium, and off-diagonal elements represent the strength of resonance inter-action between a molecule and its neighbors, the fluctuationsin the site energies are usually referred to as diagonaldisorder (parameter s=kT) and the fluctuations of the




with deep traps (see e.g. Ref. 451). On the other hand, one

intersite coupling energies as off-diagonal disorder (para-meter S ). The meaning of disorder parameters is associatedwith a random distribution of site energies described by aGaussian function of standard deviation s, and the intermole-cular coupling parameter Gij ¼ Gi þ G ¼ 2g a, being a sum oftwo site specific contributions (Gi, Gj ), each varying randomlyaccording to a Gaussian probability density of standard devia-tion d G . The variance of Gij is S ¼

ffiffiffi2p

dG . The parameter S = 2g adescribes the relative local variations of nearest-neighborintersite distances, or variations of the mutual orientationsof non-spherical molecules. The parameter g has been alreadyintroduced in Sec. 2.4.1 [see Eq. (59)] and characterizes thedegree of the wavefunction overlap between nearest-neighbormolecules separated by a distance a . The temperature depen-dence of the activation energy in this formalism predicts themobility (265) to obey a non-Arrhenius-type temperaturebehavior m � expf� [(2= 3)2 � CF1= 2]( s= kT)2 g. In the last sev-eral years, the mobility has been discussed in terms of the car-rier motion in a spatially correlated random potentialunderlain by the interaction of charge carriers with randomlydistributed permanent dipoles of the dopant or host material[452–460]. The general functional form of Eq. (265) is still pre-served in this model, but the field dependence of m0(F) must beincluded. In the 1D analysis m0 (F ) ¼ m 0(p s= kT) 1=2 � (eFa = kT)1= 4,and Y¼ s2=kT and bm ¼ (2s =kT )(ea= kT) 1=2 The field-independent exp(�Y=kT) in (265) supports thequadratic temperature dependence associated with Gaussiandisorder model, but omits the factor 2=3 that appears in thismodel. Observation of such a behavior of mobility requiresenough energetic disorder so that 2s=kT > (eaF=kT)�1=2. Athigher fields, the mobility will depend more critically on theactual form of the microscopic hopping rate, and on the wayin which detailed balance is implemented.

In the Gaussian disorder model site energies are distrib-uted independently, with no correlations occurring over anylength scale. Consequently, the field dependence in this modelagrees with (265) only over a very narrow range at high fields(F > 3� 105V=cm) [461]. A 3D version of the disorder modelincluding spatial correlations due to charge–dipole interactions




(see e.g. Ref. 458).

leads to Y ¼ (3= 5sd)2= kT , and b m ¼ C0[(s d= kT )3=2 � G](ea=s d)1= 2],

where C0 ¼ 0.78, G ¼ 2 [ 460]. The site energy distribution in thismodel i s shown to be approximat ely Gaussian, wi th width[462,463]

sd ðeV Þ ¼ 7 :04 p = ea 2 ð 26 6 Þ

This parameter characterizes the randomness of the orienta-t io ns o f di p ol e m ome n ts p (inDebye) placed on each site of a cubiclattice of cell spacing a (i n A ). In Fig. 101, the resul ts of Monte-Carlo simulations are presented for the carrier mobility accord-ing to the correlated disorder model along with those based onthe Gaussian disorder model. The main difference between thetwo models is the range of electric fields over which Poole–Fren-kel type behavior occurs. The Gaussian disorder model approxi-mates the PFmobility behavior in the high-field regime (around106V=cm), the former fits to the PF-type function over a widefield range. In the Gaussian disorder model, the mobility atlowfields is almost parabolicwhenplotted vs.F1=2. This suggeststhat at low-to-intermediate fields, the mobility is betterdescribed by a logm�F=kT law rather than by (265) as has beenobserved for somemolecularly doped polymers in the field range(105–5� 105)V=cm [338]. However, substantial deviations fromthis behavior are noted below 105V=cm. A broad field-rangeTOF mobility data in these materials have been successfullyexplained using the macrotrap model discussed in Sec. 4.3.1 inconnection with space-charge-injection currents. The formationof macrotraps can be considered as a result of correlationsbetween individual microtraps (local energy sites) distributedexponentially in energy, creating potential wells described byEq. (181). The potential barrier for the carriers localized in suchneutral macrotraps (spatially extended trapping domains) canbe effectively lowered by an external electric field, making themobility and its thermal activation energy field dependent.The field dependence of the effective mobility in the macrotrapmodel has the following form [319]:

meff � Fm�1 expðaF � b=FÞ ð267Þ




where m ¼ 3 l, a ¼ er =2kT (r—intersite distance), and b ¼3lkT= elD with l being the energy trap di stri bution parameter[see Eq. (179)] and lD standi ng for the di ffusion l ength of ther-mally activated carriers. The constants a and b must not be con-fused with the constants a and b in Eqs. (203) and (209),respectively. The straight-line plots of log meff vs. the complexvariable (aF � b=F) predicted by Eq. (267) fit well the TOFmobi-lity data for a series of molecularly doped polymers, displayed inFig. 102.

Figure 101 Calculated Poole–Frenkel plots according to the cor-related disorder model for different values of sd=kT (from top curvedownward). The calculations according to the Gaussian disordermodel with s=kT¼ 5.10 (the lowest curve) are given for comparison.The value of (eaF=sd)

1=2¼ 1 corresponds to the electric fieldF¼ 106V=cm with sd¼ 0.1 eV and a¼ 1nm. After Ref. 460. Copy-right 1998 American Physical Society.




The contribution of the power factor Fm�1 to the func-tional form of meff(F) appears to be negligible, but it must beaccounted for to match its absolute values. The quantity avaries between 1.8� 10�6 cm=V and b varies between0.7� 105 and 2.7� 105V=cm. For example, for 0.5 TPA=PCsample, a¼ 2� 10�6 cm=V and b¼ 105V=cm which at roomtemperature corresponds to r¼ 1 nm, and lD=l¼ 7.6 whichwith l¼ 0.4nm gives lD¼ 3nm. We note that aF� b=F¼ 0indicates a critical electric field Ftr¼ (b=a)1=2 at which differ-ent components of the exponent in Eq. (267) dominate themobility. In the above example, this transition field valueFtr¼ 2.2� 105V=cm. The Arrhenius-type temperature depen-dence measured at the F¼Ftr provides the activation energywhich can be identified with the sum of the macrotrap energyand the average localization energy of the hopping sites [319].

Figure 102 Field dependence of the effective hole mobility in anumber of polymeric samples for various concentrations (given inthe by curve descriptions) of two molecular dopants [TPA (tripheny-lamine) and TPM (triphenylmethane)] in polycarbonate matrix. Theexperimental data for TPA (full circles) from Ref. 122 and for TPM(open circles) from Ref. 464, plotted in a semilogarithmic scale vs.the complex variable (aF–b=F) with a and b resulting from theslopes of the high- and low-field range separate straight-line plots.After Ref. 319. Copyright 1992 Jpn. JAP, with permission.




In Sec. 4.3.2, a number of examples have been presentedshowing the charge injection current to follow a Schottky (orPoole–Frenkel)-type electric field increase (see Figs. 75––82b)which in some cases could be explained satisfactorily by aclassic thermionic carrier emission mechanism from metalinto insulator, based on Eq. (203) containing an exponentialRichardson–Schottky like factor exp(aF1=2). However, quanti-tative differences in the exponent coefficient atheor (204) aretypically met in the experiment. Often, affi 2atheor, the rela-tion ascribed by some authors to a difference between theactual and nominal electric field (U=d) used as a rule inexperimental current-field plots, suitable especially for DL

rier injection from the Fermi level of electrode into a manifoldof hopping states with a weighted probability density of width100meV [401]. The present section discussion on the field-dependent mobility opens an alternative explanation of thedifference between the measured and calculated values ofthe coefficient a. The Poole–Frenkel type behavior of the cur-rent can now be analyzed in terms of diffusion-controlled cur-rents (Sec. 4.4) which in the high-field regime obeys Eq. (231).If the mobility (m) follows the Poole–Frenkel type field depen-dence (265), the DCC will be represented by a function

jDCC � F3=4 exp 2 be=kTð Þ1=2þbmh i

F1=2n o

ð268Þ

with an effective coefficient [cf. Eqs. (203) and (204)]

a ¼ 2bekT

� �1=2

þbm ¼ atheor þ bm ð269Þ

Clearly, Eq. (268) can be approximated by a Poole–Frenkel-type function with a coefficient a > atheor. The exact value ofa varies from sample to sample dependent on the type andextent of disorder—through the disorder-dependent compo-nent bm. Following an example of electron injection from Alinto Alq3 (d¼ 150nm) (see Fig. 82b), the experimental avalues can be calculated from the slopes of the PF-type plots.As predicted by (204) and (265), they should be temperature




devices (see discussion in Sec. 4.3.2), or to the thermionic car-

dependent and, according to (269), related to the sample dis-order (s , S or sd). These data are plotted in Fig. 103. Theyexceed the theoretical values roughly by a factor of 2, andshow a weaker temperature decrease than that for atheo r.The experimental data in near-room temperature region arewell reproduced by the diffusion-controlled model for theinjection current [Eqs. (268) and (269)] involving the coeffi-cient bm governed by the electron motion within a manifold

Figur e 103 The experim ental value s ( H) of the parame ter a fol-lowi ng from the PF-type plots of the j– F depend ence in Fig. 82bas a functi on of temp erature . The open circles represent the dataobtain ed from Eq. (26 9) desc ribing diffusion–c ontrolle d injec tioncurrent that involve s the electron motio n with in a man ifold of dis-order ed but spatially correlated hopping sites wit h sd ¼ 0.13 eVobtain ed from (269) using p ¼ 4.4 D, e ¼ 3.8, [309] anda ¼ ( M =NA r)

1 =3 ¼ 8.38 A [calc ulated with the molec ula r weightM ¼ 459,4 4 g mol � 1 ; densit y r ¼ 1.3 g =cm3

dro’s number NA¼ 6� 1023mol�1]. The theoretical prediction of a(T)according to Eq. (204) (solid line), and the simulation values at 250and 300K (�) for a hopping system with a Gaussian disorder(s¼ 80meV) are shown for comparison [401].




(see Ref. 151) , and Avoga-

of disordered but spatially correlated hopping sites. The roomtemperature bm ¼ 0.75 � 10� 2 (cm=V)1= 2 obtained from thismodel with sd ¼ 0.13 eV, G ¼ 0 and a ¼ 8.38 A is in excellentagreement with the experimental value bm ¼ (0.75 0.05) �10� 2 (cm=V)1= 2

sured mobility data (filled points in Fig. 104; see also Ref.423). A value 1.65 � 10 �2 (cm= V)1= 2, in excellent agreementwith the experimental value of a at 300 K in Fig. 103, wouldbe obtained if the theoretical value p ¼ 5.3 D of the meridianalisomer of Alq3 calculation of sd. The weakly field-dependent TOF mobilitydata obtained with a DL ITO=Alq3 (150nm)=rubrene(10nm)=Mg:Ag device (open circles in Fig. 104) do not allowto fit the values of a to the experimental points. A Monte-Carlo simulation of carrier injection from metal to an organicinsulator with random (uncorrelated) hopping sites, thoughbrings the value of a closer to the experimental results (twofilled circles in Fig. 103), seems inadequate for the descriptionof electron injection into Alq3. On the other hand, the dipolar

Figure 104 Electric field dependence of TOF-measured electronmobility in thin films of Alq3: the data of Ref. 336 (&), Ref. 425(�), and Ref. 341 (�).




found from the field-dependent TOF-mea-

(see Ref. 465) were used instead 4.4 D in the

nature of Alq3 molecules makes their random aggregation(e.g. evaporated thin solid films [466]) a typical medium inwhich long-range spatial correlations in the random potentialcan be seen by an excess charge carrier [467]. This spatialsmoothing of the energy distribution contrasts the assump-tion of independent site energies that is implicit in the Gaus-sian disorder model [29]. Through a similar reasoning, thecurrent-field characteristic in doped Alq3 films (Fig. 76) canbe ascribed to the diffusion-controlled injection current, aslightly reduced value of a arising from the dopant-inducedmodification of the disorder parameter sd. Yet, apparentdivergence between the model-calculated and experimentaldata for the coefficient a below 200 K (Fig. 103) suggests dis-order to be a temperature-dependent factor. It is conceivablethat the coefficient G in bm, which is analogous to the posi-tional disorder parameter S 2 in the Gaussian disorder model,and at near-room temperatures approaching 0, becomes ofimportance at lower temperatures, leading to lower valuesof bm and thus to a reduction of the coefficient a . This wouldconcur with simulations of the equilibrium orientational dis-tribution of stick-like molecules for a cubic sample[460,468]. For high concentration of dipolar transport sites,like that in Alq3 , a disordered system is assumed to undergoa low-temperature phase transition to partially ordered state.Sterical ordering decreases the effective randomness of thesystem, the effect reducing the role of the disorder parameters . One has to note, however, that the concentration of theoff-diagonal disorder parameter, S , in the purely Gaussiandisorder model, is considered to increase with temperature[29] (see also discussion below). Another possibility toexplain a slower increase of the coefficient a as temperaturedecreases would be increasing the carrier dwell time in thetraps detected by various experiments in Alq3 films[150,469] (see also discussion below). This point requiresfurther studies.

The field-dependent mobility, would obviously modify theshape of the field characteristics of space-charge-limited cur-




original work see Ref. 377]. For example, the Schottky-typerents [cf. Sec. 4.3.1; Eqs. (168), (175), (176) and (185); the first

curves in Fig. 82b can be interpreted in terms of trap-freeSCLC electron currents injected into Alq3 from a Ca cathode,their straight-line segments being directly related to bm [cf.Eq. (265)],

jð F Þ ¼ 9

8 e0 em0 expð�Y= kT Þ expð bm F 1 =2 ÞF 2 = d ð270Þ

The use of the SCL description to those results is supportedby the d� 1 behavior of the current with varying film thick-ness, d , though an apparent deviation from the straight-linej � d �1 relationship can be observed for thin samples (seeFig. 80). Equation (270) is valid as long as the mobility is gov-erned by the dispersive transport yielding its Poole–Frenkel-type behavior as a function of electric field. Since disorder inAlq3 films seems to be associated with the presence in thematerial of oxygen (cf. dispersive and non-dispersive photo-current transients in Fig. 93, and the explanation thereto),one would expect m( F) ¼ const in the oxygen-free Alq3. Thiscould be reached under ultra-high-vacuum conditions. In facta well-defined squared-law dependence of j( F) for the electroninjection from Mg into Alq3 has been observed under a pres-sure less than 10� 9 hPa [470]. A representative result isshown in Fig. 105. Of three voltage regimes (A, B, C), the lat-ter stands for the trap-free SCLC which is well reproduced byEq. (168) with e¼ 3.5 and m on the 10�7 cm2=Vs varying fromsample to sample within one order of magnitude but indepen-dent of electric field. The region of steep current increase (B),moving towards larger electric fields with the time intervalbetween completing fabrication of the device and its charac-terization procedure, indicates increasing the voltage thresh-old of carrier injection caused by an increase of the electrontrap concentration with time. However, electron trapping cen-ters have a relatively well-defined energy with an energeticspread insufficient to produce meaningful disorder. The Aregion is characteristic of bulk generated carriers due to e.g.uncontrollable impurities or corresponds to the diffusion-freelow-field approximation (205) of the solution of Eq. (198). Themost impressive results of the field-dependent mobilitymodified space-charge-limited currents have been obtained




on conjugated polymers [471,472]. Some examples are shownin Fig. 106. The set of experimental j –U characteristics inPPV (Fig. 106a) can be described by Eq. (270) withbm ffi 0.6 � 10� 2 (cm= V)1=2 and e ¼ 3 at room temperature (solidlines). The deviations from the conventional j � U2= d behaviorfor SCLC are, thus, due to the Poole–Frenkel-type fielddependence of the mobility [377]. The straight-line segmentof the jd3=( DU)2 vs. (D U=d )1= 2 plot in Fig. 106b again confirmsthe applicability of Eq. (270) and allows to determine the coef-ficient bm ¼ 0.44 � 10� 2 (cm=V)1= 2 At high electric fields(F > 3 � 106 V= cm), the current approaches a field-indepen-dent mobility trap-free space-charge-limited current. Theanalysis of the trap-free SCLC allows to determine thetemperature and field dependence of the mobility [see

Figure 105 Electron injection current density vs. average electricfield (F¼U=d) for a Mg=Alq3=Mg sandwich device with a 300nm–thick Alq3 film (circles). The dash-dotted line corresponds to aj�U2 dependence; the dashed line represents a linear plot j�U.After Ref. 470. Copyright 2002 American Institute of Physics.




Figure 106 Experimental j–U characteristics of polymer films forvarious temperatures (a) and two different thickness (�,D) samplesat room temperature (b). (a) Steady-state currents in poly(dialkoxy-p-phenylene vinylene) (PPV) (the layer thickness d¼ 125nm). AfterRef. 471. (b) Response current to 10 ms rectangular voltage pulsesin poly[2-5-dimethoxy-1,4-phenylene-1,2-ethenylene-2methoxy-5-(2-ethylhexyloxy)-1,4-phenylene-1,2-ethenylene (M3EH-PPV);DU¼U–Ubi, where U is the applied voltage and Ubi is the built-inpotential due to a difference in the work functions of the electrodes.After Ref. 472. Copyright 2000 American Institute of Physics.




Eq. (168a)]. High values of the hole mobility ( > 102 V =cm 2 s)in high-purity samples at low temperatures support the sup-position that conventional band-theory combined with a tem-perature-dependent coherent bandwidth renormalization dueto electron–phonon interaction is a reasonable approximationto understand the charge transport in good quality organiccrystals at low temperatures. The calculated mean free pathof charge carriers can exceed many lattice constants. Itdecreases to about the lattice constant and the intermoleculardistances with increasing temperature. To distinguish themobility-dependent space-charge-limited (270) from the injec-tion-controlled [e.g. DCC (268)] current flow, the thicknessdependence of the current appears to be a useful criterionas demonstrated in Figs. 80 and 106b.

One should note that the mobility dependent injection-controlled current, like that resulting from the inclusion ofa macroscopic diffusion component to the collected current,can also be described taking into account the surface recombi-nation of injected carriers [see Sec. 4.3.2, and in particularEqs. (224) along with Eq. (221)]. A direct way to follow themobility-dependent charge injection would be measuring theinjection current into organic solid-state samples with inde-pendent controlled variations in the carrier mobility. Suchan experiment has been attempted with the injection of holesfrom ITO into tetraphenyl diamine doped polycarbonate(TPD:PC) films, where the hole mobility was varied from10� 6 to 10 �3 cm2= V s by adjusting the concentration of thehole transport agent, TPD, in the PC matrix from 30% to100% of the TPD content [394]. The results are shown inFig. 107. The measured injection current ( jILC� jINJ) is abouttwo orders of magnitude lower than that expected to flowunder SCLC conditions [the values of jSCL calculated fromEq. (168a)], and is independent of the dopant concentrationas expressed by a constant injection efficiency ( jILC=jSCL) vs.hole mobility. This result is difficult to understand as theinjection efficiency is by definition a function of the numberof the electron donor centers, here identified with the TPDconcentration, and varying between nffi 4� 1019 cm�3 at the30% doping level up to nffi 1.5� 1021 cm�3 for the 100% TPD




sample (calculated with the molecular weight ofTPD:M¼ 516 g=mol, density r¼ 1.2 g=cm3, and Avogadro’snumber A¼ 6� 1023mol�1). If the surface current is governedby the tuneling process, increasing n changes the injectioncurrent according to [393]

j � n�2=3 expð�Q=n1=3Þ ð271Þ

where Q¼ eF=kTþ r�10 with r0 being a critical distanceof a donor molecule from the electrode, which, according totunnel theory, is a function of the injection barrier, DEi,r0¼ �h=2(2m� DEi)

1=2. Assuming the electron effective massm� ¼m (free electron mass), one arrives at r0ffi 1.3 A withDEi¼ 0.6 eV characterizing the TPD=ITO interface [2]. ThusEq. (271) shows, in general, supralinear increase of the cur-rent with n, and explains, among others differences betweenj–F characteristics of DL LEDs using the TPD-doped PC

Figure 107 Mobility-dependent hole injection currents for sixTPD:PC samples at 0.4MV=cm, under space-charge-limited ( jSCL)and injection-controlled ( jINJ) conditions. Inset: mobility depen-dence of the injection efficiency defined by the ratio ( jILC=jSCL).After Ref. 394. Copyright 2001 American Physical Society.




HTLs with different concentrations of TPD (see Fig. 77). Theconcentration independence of the injection efficiency, demon-strated indirectly in the inset of Fig. 107, might have severalreasons of which diffusion of TPD molecules from the bulk tothe surface [473] and different meaning of the linear j vs. mincrease will be here mentioned. The former is based on thesuggestion that the near-contact concentration of TPD mole-cules remains approximately constant independent of theirconcentration in the bulk due to molecular diffusion towardsthe surface, the region which becomes a TPD-depleted layerdue to the conceivable process that TPD sublimes off the sam-ple surface during the metal deposition process. This explana-tion is supported by the time evolution of the hole injectionefficiency from evaporated Au anode into TPD-dopedPC layers [473]. The second possibility is that the linearincrease of j with m reflects simply the identity between theconcentration function of the injection efficiency (301)and the concentration dependence of the mobilitym � n �2= 3 exp[�(2= r0n 1=3 )], where r 0 ffi 1.4 A [338]. While theinjection-controlled current ( jILC ) follows the concentrationincreasing injection efficiency (271), the space-charge-limitedcurrent ( jSCL) is governed by the identically concentrationincreasing mobility m (n ), so that their ratio, jILC =j SCL is con-stant at any concentration of TPD (any value of m ). Some-times, injection currents decrease with applied field or showthe field evolution much weaker than predicted by thePoole–Frenkel-type behavior of the carrier mobility at lowelectric fields. Such a behavior can be seen in Fig. 108, wherethe field-dependent mobility modified SCL currents as a func-tion of electric field (F¼DV=d) are presented for single layersof a conjugated polymer (MEH-PPV). While for two Au con-tacts monopolar (hole-only) injection, the initial strong cur-rent increase is followed by the high-field SCL injectionmodified by the Poole–Frenkel-type evolution of hole mobility,providing the samples with an Al, and especially Ohmic Ca,cathodes makes the current to be a decreasing function inthe low-field regime. One of possible explanations of theseresults could be a field-decreasing mobility of electronsinjected from Al and Ca cathodes. In addition to the discussed




above saturation of the drift velocity or contribution of themacroscopic diffusion to the transient current, the field-decreasing mobility may occur when the off-diagonal disorderdominates over the diagonal disorder [see discussion of bm

Figur e 108 Curr ent–v oltage da ta (point s) from single layers ofpoly [2-methox y,5-(2-et hylhe xoxy)-1 ,4-pheny lene vinylene ] (ME H-PPV ) provide d with Au ano des and diff erent cath odes (Ca, Al, andAu as indicat ed in the figure). The data normaliz ed to the samp lethick ness , d, and the electr ic fie ld accou nted for the bui lt-in poten-tial (Ubi) DU ¼ U � U bi, wher e U is th e applied voltage. Solid linesplotted according to predictions of Eq. (270). After Ref. 474 (see also




Ref . 475). Cop yright 1998 Am erican Phys ical Societ y.

following Eq. (265)]. If S 2 > (s= kT) 2 or G > (sd=kT) 3=2, b m < 0

the mobility becomes a decreasing function of applied field, F .There are several sets of the experimental mobility datashowing such a behavior at both low and high fields[29,476–478]. The field-decreasing mobility is expected to bebetter pronounced at high temperatures alleviating the aboveinequalities to be fulfilled. It is well illustrated by the exampleshown in Fig. 109. The negative field dependencies areobserved within a low-field region (F < 2� 105V=cm) at hightemperatures (T > 240K). The range of fields for which beha-vior is observed increases at low dopant concentrations. Forexample, in the case of 10% pyrazoline-doped PC, the field-decreasing hole mobility is observed up to 106V=cm at hightemperatures [476].

In previous attempts to model carrier transport in disor-dered organic solids, ln mffi f(F)¼ const, and lnm1F relation-ships have been discussed [341,419,447,476,480–482]. Theyhave been rationalized either on the basis of particularexperimental features or a hopping model involving a field-induced reduction in the effective width of the energy distri-bution of hopping sites. For example, the data obtained fromanalysis of the EL decay, in Alq3-based EL devices, have beenascribed to the accumulation of charge rather than to electrontransport and differences in the results for thick and thindevices considered as due to varying film morphology [341].It is difficult to find well-reproducible recurrent features ofnumerous mobility data in a variety of disordered organicsolids since unintentional impurities, including dipolar spe-cies, and molecules forming shallow and deep traps, can mod-ify substantially the carrier transport. In general, the fielddependence of the carrier mobility can be expressed by asum of a number of terms reflecting different structural andchemical features of the samples [460]

lnm � f ðTÞ þ D1ðTÞF1=2 þ A2ðTÞF3=4 þ A3F5=6 þ A4ðTÞF

ð272Þ

This expression imitates the Poole–Frankel-type depen-dence [ln m�A1(T)F

1=2] in a relatively narrow field range




Figure 109 Poole–Frenkel–type plots of the field dependent mobi-lity in a molecular–doped polymer (TAPC:PC) at different tempera-tures. A change from the negative to positive value of bm [see Eq.(265)] is well pronounced at T > 240K. After Ref. 479. Copyright1991 American Institute of Physics.




(Fmax=Fminffi 10), indicating the dispersive dipolar transportcomponent A1(T)F

1=2 to be dominant. The upward or down-ward deviation from the straight-line plot lnm�A1F

1=2 wouldsuggest the higher power terms to contribute to the overallfield dependence of the mobility. They have been assignedto disorder correlated by long-range interactions betweenmolecules possessing quadrupole [A2(T)F

3=4] and octupole[A3F

5=6] electrical moments. The term A4(T)F is a signatureof the presence of deep traps (Ref. 460) or the formation ofpolarons [122]. The deviation trend from the PF-type depen-dence is expected to depend on polarity of materials. Whilefor non-polar materials, the mobility curve convex downwardshould be observed, the upward curve convex would appearfor polar materials.




5

Optical Characteristics of OrganicLEDs

5.1. INTRODUCTION

In organic LEDs, electricity is directly converted into light.Therefore, the evaluation of the overall light output and itsrelation to the driving current are of fundamental interestthough understanding and tailoring of their emission coloralso falls in central device physics and practical applicationproblems. A large amount of effort has been expended prepa-ring various material compositions, particularly of the binaryand ternary systems, and measuring their emission spectrawith the hope of finding new and useful organic LED emit-ters. The following section provides an overview of varioustype of EL spectra and a good sampling of the empiricismwhich characterizes the work at many laboratories. However,the main subject of the present chapter is in correlating theoptical properties of organic LEDs to their electrical charac-teristics.

273






5.2. EMISSION SPECTRA

Published emission spectra of organic LEDs cover a spectralrange from infrared [483–486] to ultraviolet [487] and showeither a shape characteristic of molecules dispersed in an elec-tronically neutral medium, broad maxima from disorderedemitters involving two-molecules underlain excited states,or narrow lines reflecting excitation of metal ions in theircomplexes with organic compounds or microcavity and lasingeffects in the layered structures with strongly injecting elec-

ious types of EL spectra will be presented and their originbriefly discussed in relation to the nature of excited statesdescribed in Chapter 2. Furthermore, since the compositionof the population of emitting excited states produced inmulti-layer EL devices varies with their operation conditions,the voltage evolution of the emission spectra will be demon-strated on selected examples of organic LEDs.

5.2.1. Molecular Emission

If the light emanating from an organic LED originates fromthe radiative decay of locally excited (molecular) states (see

general, differ from those of isolated molecules because thegas-to-solid shift, and resonance interactions must be takeninto account [cf. Eq. (13)]. Moreover, they can reveal widerbands due to dynamical and structural disorder in the solid

Figure 110 Emission spectra of organic LEDs cover the spectralrange between infrared (a) through visible (b) to ultraviolet (c)region of the electromagnetic wavelengths. (a) The absorption(ABS), photoluminescence (PL) and electroluminescence (EL) spec-tra taken from spin-coated layers of a cyano-substituted thienylenephenylene copolymer (reprinted from Ref. 483, Copyright 1995 withpermission from Elsevier); (b) PL spectra of TPD and Alq3 vacuumevaporated films, and EL spectrum of Alq3 dispersed in a TPD:PCmatrix (adapted from Ref. 389); (c) EL spectra of dialkylpolysilanesas indicated in the figure (adapted from Ref. 487).

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Chapter 5. Optical Characteristics of Organic LEDs 275



trodes (Fig. 110). Below, a number of examples of these var-

Fig. 11), we deal with molecular emission spectra. They, in

trum of SL LEDs based on polycrystalline layers of anthra-cene and tetracene-doped anthracene are supposed to reflectradiative decay of singlet excitons located on anthraceneand=or tetracene molecules, the latter populated either bydirect electron–hole recombination and=or Forster energytransfer from anthracene host to tetracene guest molecules(Fig. 111). The molecular emission underlain EL spectra canalso be observed in DL LEDs of which an interesting example

3

hex:PC) stand for the emitters within the green and yellowspectral regions, respectively. Remarkably, EL spectra differfrom the PL spectra either for ITO=TPD:PC=Alq3=Mg=Agand ITO=TPD:T5Ohex:PC=Alq3=Ca structuresThe reason is that optical excitation (lex¼ 350nm) of Alq3(green emission) and T5Ohex (yellow emission) occursthrough the Forster energy transfer from excited singlets of

Figure 111 Emission spectra from the SL LEDs based on anth-racene (A) and tetracene-doped anthracene (T:A) films with twodifferent concentrations of tetracene. Violet anthracene emissiondisappears with increasing concentration of tetracene. The spectrawere taken with the 1 mm-thick films sandwiched between Auanode and Al cathode at the applied field F¼ 106V=cm. AfterRef. 212. Reprinted from Ref. 212. Copyright Springer-Verlag, withpermission.




is shown in Fig. 112. Both ETL (Alq ) and HTL (TPD:T5O-

(Fig. 113).

state (cf. Sec. 2.2). The well-separated maxima in the EL spec-

TPD (violet emission), whereas, electrical excitation is due toelectron–hole recombination within the Alq3 ETL for the firststructure, combined with the electron–hole recombination onT5Ohex molecules of the HTL for the second structure. In the

Figure 112 Molecular structures (a) of the materials used tomanufacture DL LEDs (b) with a molecularly doped hole-trans-porting-layer (HTL) which serves as an emitter (EML) along withthe emitting electron-transporting-layer (ETL).




Figure 113 Normalized PL and EL spectra of DL LEDs. (a) ITO=(75% TPD:25% PC) (60nm)=Alq3 (60 nm)=Mg=Ag; EL spectra takenat different voltages between 8 and 15V do not differ from eachother. (b) ITO=70% TPD:10% T5O hex:20% PC) (60nm)=Alq3(60 nm)=Ca. The EL does not contain the violet emission componentfrom TPD and evolves with applied voltage. All PL spectra inclu-ding that of a TPD film alone [PL(TPD)] were excited through theITO anode with lexcAfter Ref. 303. Copyright Institute of Physics (GB).




¼ 350nm (cf. the absorption spectra in Fig. 6).

second case, electrons injected from the cathode migratewithin the Alq3 ETL and a fraction of them passes theAlq3=(TPD:T5Ohex:PC) interface drifting towards the anode.The number of recombination events within the HTL isobviously a function of the electron stream penetrating thislayer. The latter increases with the voltage applied to theLED. The increasing penetration of electrons into the HTL,which can be considered as an extension of the recombinationzone towards the anode, would be expected to enhance theyellow component in the overall emission spectrum of the

is an example showing the importance of the type of excitationfor the emission spectrum of intentionally (or unintentionally)doped materials. Even traces of fluorescent molecules cangive a substantial (or even dominating) contribution to theoverall emission spectrum of LED structures. It is instructiveto follow the emission spectra of low Alq3-doped and undoped

3

emission peaking at about 520nm is well pronounced in theEL while absent in the PL spectra of a low-doped (10�6MAlq3) TPD layer (Fig. 114a). Furthermore, increasing voltageapplied to the sample quenches the dopant emission asalready demonstrated on vacuum-evaporated neat Alq3 films

tion of Alq3� singlet states [306]. The presence of uninten-

tional admixtures can dominate the EL spectra, while the PLspectra are characteristic of the host material. Such a situa-

an electron acceptor polymer, 2,7-poly(9-fluorenone) (PF), thehigh molecular weight precursor polymer 2,7-poly(spiro[40,40-dioctyl-20,60-dioxocyclohexane-10,9-fluorenone) (POFK) is usedallowing good processability and conversion into insoluble PF[489] (also see the scheme in the top part of Fig. 115). Theoptical properties of POFK and PF differ significantly. ThePOFK shows blue fluorescence (see PL spectrum in Fig. 115b)while the product PF shows a maximum emission at 580nmin the yellow region of the visible spectrum (see Fig. 115c).In the EL spectrum of POFK, a dominating yellow componentappears, suggesting a small amount of the reaction product




LED as, in fact, is observed in experiment (Fig. 113b). This

TPD SL LEDs presented in Fig. 114. The characteristic Alq -

(cf. Fig. 47), the effect ascribed to the field-assisted dissocia-

tion is shown in Fig. 115. In the process of the synthesis of

(PF) to form effective electron–hole recombination centers[488].

An extreme case in the difference between PL and EL

(PBP)-doped TPD layer reveals the PL spectrum belongingtotally to the violet emission of TPD molecules, and ELspectrum originating from radiative transitions of the doped

Figure 114 PL and EL spectra of a vacuum evaporation preparedITO=(TPD:10�6MAlq3) (165 nm)=Mg=Ag SL structure (a). Effect ofapplied voltage on its EL spectra is shown in part (b). Adapted fromRef. 21.




spectra is presented in Fig. 116. A perylene bisimide pigment

Figure 115 Optical spectra of the precursor POFK and the pro-duct PF of the reaction (a). Absorption (left ordinates), PL and EL(right ordinates) spectra of POFK and PF are shown in parts (b)and (c), respectively. The difference between the PL and EL spectraof POFK contrasts a similarity of these spectra for PF (for explana-tions, see text). After Ref. 488. Copyright 2000 Viley-VCH.







molecular of PBP, which falls in the red [490]. This indicatesthe exciton energy transfer TPD!PBP to be veryinefficient and hole recombination on the PBP-trapped elec-trons to dominate the generation process of the excited statesof PBP. We note that the EL spectrum of this system is insen-sitive to the applied voltage. In contrast, voltage-induced colorvariations can be observed from multi-layer white light emit-ting devices based on pyridine-containing conjugated poly-mers and para-sexiphenyl (6P) oligomer [491]. An exampleof a three-layer ITO=PVK=6P=PPy=A device is shown in

ITO-covered glass and recorded from the PVK side show max-ima in different spectral regions that reflect varying contribu-tions of the emission from different layers of the device, theblue–green emission from PPy and PVK becoming dominantat excitation wavelength of 400nm. Increasing contributionof this part of the emission spectrum of the device is seen alsoin the EL spectra as the applied voltage increases.Moreover, a new maximum appears in the EL at about605nm (in the red) and grows with applied voltage (Fig.117B.b) The color coordinates of the EL spectra at 21 and25V are (0.261, 0.245) and (0.298, 0.286), respectively. At27V, the emitted light appears bright white to the eye. Thered-like emission shows up at 31V due to the growing contri-bution of the 605nm peak. Thus, the color coordinates tra-verse along a straight line in the CIE chromaticity diagramas the voltage increases. Though the EL spectra of thisthree-layer device are presented in the molecular emission

Figure 116 Comparison of the PL and EL spectra of PBP (a). (b)PL spectra of PBP and TPD films; their maxima are shifted towardsred and blue, respectively, as compared to the PL maximum of Alq3(just given as a commonly known reference spectrum). For the

3

spectra of the ITO = (TPD:30% PBP) (70 nm) = Mg=Ag SL structure.The by-side arrows indicate the curves recorded at different appliedvoltages. From Ref. 490. Copyright 1998 American Institute ofPhysics.

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Fig. 117. The PL spectra of the device excited through the

molecular structures of TPD and Alq , see Fig. 6. (c) PL and EL




section, they can be only in part rationalized by the molecularemission of the individual component materials. Namely, theemission color is tuned from blue, the molecular emission ori-ginating from para-sexiphenyl, to white to green, the molecu-lar emission from PPy. The voltage evolution of the spectrafrom the emission of 6P to the emission of PPy can be under-stood in terms of asymmetric narrowing of the recombina-tion zone which reduces the recombination radiation in the6P and enhances it in the PPy layer. The gradual shift ofthe maximum recombination efficiency from the HTL toETL in the three-layer ITO=TPD=Alq3=PBP=Mg=Ag LEDhas been employed earlier to explain the field increasing redemission from PBP [490,492]. The origin of the new red-located component is not known and is likely to be associatedwith bimolecular excited states formed at the 6P=PPy inter-

the polymer blends have been employed to manufacturethe voltage-controlled color organic LEDs [121,345,493]. Such

electron acceptor-transporting layer (ETL), and the hole (ITO)and electron (Ca=Al) injecting electrodes reveals voltage-dependent EL spectra While the EL spectra ofthe individual polymers (PCHMT, PTOPT) peak in blue andred, respectively (Fig. 119a), their blend shows the two bands(Fig. 119b) with the blue one increasing with applied voltage.This is explained by the phase separation within the blend

Figure 117 Emission characteristics of a three-layer device basedon the pyridine-contained polymer and para-sexiphenyl oligomer(see (A) Repeat units of the pyridine-containing poly-mers and other materials used in the fabrication of the LED;(a) poly(p-pyridine)(Ppy), (b) poly(N-vinyl carbazole)(PVK), and(c) para-sexiphenyl (6P). (B) Normalized PL spectra of PVK=6P=Ppy with different excitation wavelengths (given in the figure)(a); normalized EL spectra of an ITO=PVK=6P=Ppy=Al device underdifferent applied voltages (given in the figure) (b). The CIE (Com-mision Internationale de l’Eclairage) color coordinates of the ELspectra from part B (b). Adapted from Ref. 491

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a structure (shown in Fig. 118) composed of a polymer blend,

(Fig. 119).

491).Ref.

face (cf. Secs. 2.3 and 5.2.2). The selforganizing properties of

into domain channels connecting the hole injecting ITOand electron transporter PBD (see Fig. 118a). By this,the device becomes a composition of a large number ofparallel submicrometer size ITO=PCHMT=PBD=Ca=Al and

Figure 118 (a) Schematic representation (not to scale) of separatedpolymer channel domains individual submicrometer size LEDs in thepolymer blend (PMCHT:PTOPT)=PBD EL structure. (b) The energylevel structure of the EL device. The data on polymer energy levelstaken fromRef. 345. The hole injection barriers from ITO into PMCHT[DEh(1)ffi 1eV] and PTOPT [DEh(2)ffi 0.6 eV] are indicated in the fig-




ure. For the molecular structure of the polymers, see Fig. 119.

Figure 119 EL spectra of two polymers (a), and their blend in a DLdevice ITO=98%PCHMT:2%PTOPT=Ca=Al at two different voltages(b). (c) The layer configuration in the LED and chemical structures ofthe polymers used: PCHMT (poly(3-cyclohexyl-4-methythiophene)),PTOPT (poly(3-(4-octylphenyl)-2,20-bithiophene)); for the chemical




structure of PBD, see Fig. 26. Adapted from Ref. 121.

ITO=PTOPT=PBD=Ca=Al diodes each emitting its own char-acteristic spectrum. The intensity ratio of the blue(PCHMT-based microLEDs) and red (PTOPT-based micro-LEDs) is determined by the voltage applied to the diode,and the stoichiometry of the polymer blend. As the injectionefficiency increases more rapidly with the applied voltage




for high injection barriers, the contribution of the blue emit-ting PCHMT microLEDs with the hole injection barrierffi1 eV to the overall device spectrum increases with appliedvoltage much steeper than that from the red emitting PTOPTmicroLEDs with the hole injection barrier ffi0.6 eV, and, as aconsequence, the LED color shifts towards blue. One has tokeep in mind that due to singlet energy transfer from PCHMT

tion of PCHMT must highly exceed that of PTOPT in order

this condition.The emission spectra from organic LEDs based on

organic phosphors are determined by properties of their tri-

multi-layer LEDs with organic phosphor-doped HTL and ETLare shown at different voltages. Strong emission is observedfrom the triplet excited states of Ir(ppy)3 at 510 nm (Ref. 304)and PtOEP at 650 nm (Refs. 43 and 493a). Spectral and time-resolved photoluminescence measurements confirm this assi-

3 aremost probably produced by the recombination of TPD-trans-ported holes with Ir(ppy)3-trapped electrons; the LUMO ofIr(ppy)3 is located by about 0.6 eV below the LUMO of TPD,that is molecules of Ir(ppy)3 form effective electron traps indevice I [304]. In contrast, the population of excited tripletsof PtOEP in device II (Fig. 120b) follows the e–h recombina-

Figure 120 The spectra of the two electroluminescent devices (Iand II) containing organic phosphors, Ir(ppy)3 (a) (adapted from

Cop yright 1998 Macm illan Publis hers Lt d. [http: == www .natur e.com =]). The latter is compa red wit h the EL spec trum of a devicewith no phosphor inside (III). For the chemical structures of the

teristic of molecular phosphorescence as clearly seen from theircomparison at different voltages with the PL spectrum (a). TheDCM2-doped Alq3 layer of device III becomes dominated by theirphosphorescene from the PtOEP-doped Alq3 layer in device II.

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to PTOPT (cf. the energy level scheme in Fig. 118b), the frac-

the effect to appear. Indeed, the example in Fig. 119 fulfills

phosphors, see Fig. 31. The spectra from device I and II are charac-

plet states (see Sec. 1.4). In Fig. 120, the emission spectra of

Ref. 304), and PtOEP (b) (see Ref. 493a, reprinted from Ref. 493a,

gnment (see e.g., Ref. 156). Excited triplets in Ir(ppy)

http://www.nature.com





tion on Alq3 and Dexter transfer of triplet energy from Alq3 toPtOEP which does not form efficient carrier traps. A 10nm-thick layer of Alq3 doped with �1% DCM2 placed in the widerecombination zone plays a role of singlet exciton loser of bothLED II and LED III, due to efficient Forster energy transferfrom Alq3 to DCM2 and high radiative decay rate constantof the latter [494]. Since the relative contribution of theDCM2 and Alq3 emission components in both devices (II

excited triplets of PtOEP is Dexter energy transfer fromAlq3 triplet states that have diffused through the DCM2and intervening Alq3 layers. The formation of emitting trip-lets by direct electron–hole recombination on Ir(ppy)3 hasbeen clearly demonstrated in emission properties of triple-layer LED structures ITO=m-MTDATA=CBP(d)=Ir(ppy)3:

function of CBP spacer layer thickness, d. Only Ir(ppy)3 trip-let emission (lmaxffi 515nm; cf. Fig. 120a) is observed ford¼ 0, the contribution from Ir(ppy)3 gradually decreases, acc-ompanied by an increase of blue m-MTDATA fluorescencewith increasing d. Such an evolution of the EL spectra indi-cates the recombination zone to cover both the m-MTDATAHTL and CBP:Ir(ppy)3 ETL. The CBP spacer layer revealsambipolar conduction properties. Thus, for the Ir(ppy)3:CBPdoped slab positioned away from the m-MTDATA=CBPinterface (d¼ 10–40nm), the spectra are composed of both

Figure 121 (a) Electroluminescent spectra of an ITO=m-MTDA-TA(50 nm)=CBP (variable d)=7% Ir(ppy)3:93% CBP(60nm)=MgAgdevice with d varying as indicated. (b) Fluorescence (FL) and phos-phorescence (PH) spectra of CBP and m-MTDATA films (PH at70K). (c) The molecular structures of two of the materials used:4,40,400-tris (3-methylphenylamino)triphenylamine (m-MTDATA)and 4,40-N,N0-dicarbazole-biphenyl (CBP). For the molecular struc-

3

120a. (d) The energy level diagram of the device structure showingrelative positions of the HOMO and LUMO levels of the organiclayers used. Adapted from Ref. 495.

J




and III) is identical (see Fig. 120b), the only way to create

CBP=MgAg [495]. Figure 121 shows their EL spectra as a

ture of Ir(ppy) , see Figs. 31 and 36, and for its emission spectra Fig.

m-MTDATA molecular fluorescence (cf. EL and FL spectra in

3 phosphorescence (cf. PH spectrum in

other hand, only Ir(ppy)3 PH occurs in the overall emissionspectrum, since the recombination zone becomes confined tothe Ir(ppy)3:CBP ETL. The direct contact of the m-MTDATAlayer with the Ir(ppy)3:CBP layer facilitates holes to beinjected on the Ir(ppy)3 HOMO levels, while electron injectioninto m-MTDATA is strongly impeded by a relatively highenergy barrier (ffi1 eV; see Fig. 121d). The lacking emissioncharacteristic of CBP indicates the formation of its singletand triplet excited states to be very inefficient; thus, the emit-ting triplets of Ir(ppy)3 are produced in the Ir(ppy)3 trappedhole-free electron recombination process rather than byCBP! Ir(ppy)3 energy transfer.

The existence of different molecular emissive states inthe Alq3 film has been suggested [496]. They were identifiedon the basis of time-dependent fluorescence studies by meansof the femtosecond fluorescence upconversion technique.Their nature is not quite clear. One hypothesis is that theyreflect a series of excitonic traps [496], assuming the S1 exci-tonic energy to be determined by the long-wavelength edge of

hand, they correspond well to the three closely spaced singletlevels (S1, S2, S3) as calculated for Alq3 using a semiempiricalapproach in agreement with those obtained from deconvolu-tion of the absorption spectrum into Gaussian components,if completed with a constant energy increment DEðtÞn ffi 0.65 eV(see Table 6). Experimental studies of Alq3 have observed alarge shift (0.4–0.7 eV) between the optical absorption spectra

terms of nodal characteristics of the HOMO and LUMOcoupled through skeletal quinolate vibrations [502]. The elec-tronic excitation of the molecule of Alq3, localized on one ofthe three quinolite ligands (for molecular structure of Alq3,

cular geometry, the excited-state relaxation energy predictedtheoretically to be 0.55 eV [502]. This is in good agreementwith the Stokes shift between the absorption and emission




Fig. 121a,b) and Ir(ppy)Fig. 120a). No emission from CBP is observed. At d¼ 0, on the

and emission spectra (see Fig. 6). It has been interpreted in

see Figs. 6 and 110), causes a significant change in the mole-

the absorption at ffi2.65 eV (see e.g., Ref. 59). On the other

spectra of Alq3 and enables the exciton trap states S1 (trap) tobe considered rather as a relaxed series of different S1, S2 andS3 excited singlet states with the lifetime decreasing fromffi10ns (S1), through ffi25 ps (S2) down to ffi1ps [496]. Interest-ingly, this approach has been strongly supported by the ELspectra in Alq3 films separated from the electrodes by insulat-ing layers of SiO2

device ITO=SiO2=Alq3=SiO2=Al observed at different voltages.A broad band blue emission peaking at ffi475nm is observedat high voltages. The high-field EL spectra can be understoodassuming a field-induced change in the emission components,the short-living states (S2, S3) dominating at high fields. Thelong-living (ffi10ns) states are efficiently quenched by the vol-tage-increasing concentration of holes at the SiO2=Alq3 inter-face adjacent to the ITO anode. The excitonic interaction with

Table 6 Some Excited States in Alq3 as Identified by DifferentMethods

Molecularstate

EnergyEðgÞn

a(isolatedmolecule) (eV)

Energy EðsÞn

(solid state)(eV)

DEðsÞn(eV)

DEðtÞn ¼DEðsÞn �DEtrap

S1

(eV)

Lifetime(room

temperature)

S1 3.48 3.00b 10–15nsd

S2 3.59 3.19b 0.19S3 3.67 3.27b 0.08S1 (trap 1) – 2.33c 0.67 10nse

S2 (trap 2) – 2.56c 0.63 25pse

S3 (trap 3) – 2.62c 0.65 1pse

a

b The values resulting from the decomposition of the experimental absorption spec-trum into Gaussian components. The absorption onset Ethrffi2.65 eV to be identifiedwith the LUMO level as related to the ground state S0 (see Ref. 59). Note that theLUMO by definition must not be identified with the position of the electron conduc-tion level which can be determined from combined internal photoemission andphotocurrent vs bias experiments. It has been found to be EA¼ (3.0� 0.1) eV belowthe vacuum level, the value, which substracted from the ionization potential(HOMO) IS¼ (5.6�6.65) eV (see implies the electrical gapEg

c Position of S1 trap levels related to the HOMO level, as determined from the time-resolved PL spectra of Alq3d From Refs. 148 and 149.eFrom Ref. 496.




[503]. Figure 122 shows EL spectra of a

497–501)

The data from semiempirical calculations ZINDO=S (see Ref. 59).

Refs.¼ (2.6�3.65) eV (see Refs. 354–465).

films (see Ref. 496).

charge carriers has been discussed in Sec. 2.5.2, and charac-terized by the second order rate constant gSq which for Alq3has been estimated on the order 10�9–10�10 cm3 s�1 [233].The EL intensity at 475nm of the low-voltage (low carrierconcentration) spectrum constitutes roughly 75% of its maxi-mum at 510–520nm. Therefore, to make them comparable,one has to reduce the concentration of S1 by at least 25%, thatis

DS1

S1¼ gS1qtS1

nq ¼ 0:25 ð273Þ

With gS1qffi 10�9 cm3 s�1, tS1¼ 10ns, this would require

nq¼ 2.5� 1016 =cm�3. This reasonable value, attainable forthe carrier concentration at higher voltages, is not sufficientto quench higher short-living singlets S2 and S3 unless, forsome reasons, the interaction constant for them would bemuch greater. Consequently, the relative contribution of theblue high emitting singlets S2 and S3 increases with the spacecharge at the SiO2=Alq3 where the recombination is expectedto be the most efficient. It is worthwhile to mention about

Figure 122 El spectra of an ITO=SiO2(40nm)=Alq3(50nm)=SiO2(40nm)=Al device at different voltages. Adapted from Ref. 503.




another rather speculative, but intriguing possibility for thefield induced blue shift of the EL spectrum of Alq3 in the pre-sence of SiO2 spacer. The partly nanocrystalline character ofevaporated Alq3 films kept at high temperature and exposedto the bombardment of hot molecules of SiO2 during thedeposition of one of the spacers [503] can undergo a partialnear-surface transformation into the d-phase of Alq3 reveal-ing different molecular structure and the weaker overlap ofthe p orbitals of hydroxyquinoline ligands belonging to neigh-boring Alq3 molecules as compared to usual a and b phases[504]. The different geometry, higher dipole moment and dif-ferent electronic properties lead to its strongly blue-shiftedfluorescence [505]. When at a high electric field, the recombi-nation zone becomes very narrow and located at theAlq3=SiO2 interface, the main contribution to the emissioncould originate from the d-phase, giving the observed shiftof the EL maximum towards the blue.

5.2.2. Broad Band Spectra

In Sec. 2.3, we have seen that both PL and EL spectra showup as broad bands when being underlain by the radiativedecay of bimolecular excited species (excimers, electromers,exciplexes or electroplexes). A number of examples presented

tal basis rationalizing the nature of excited states. The princi-pal concept behind the formation of bi-molecular excitedstates is the competition between electron transport andvertical and cross-radiative transitions. It is illustrated in

roaching oppositely charged carriers (e,h) depends on theirdistance (r) and the positions of the LUMO and HOMO levels,which, in general, are different due to either local environ-ment conditions for identical molecules or differences in ioni-zation potential and electron affinities for chemically differentmolecules. In the latter case, the LUMO and HOMO energylevels can also be modified by local environmental conditions.The electron (e) transport from LUMO2 to LUMO1 leads toformation of the molecular emission from LUMO1, the




in Figs. 16–18, 21, 26, 29 and 30 have served as an experimen-

Fig. 123. The type of excited state created by a pair of app-

process competing with electromer or electroplex emission(hncross). On the other hand, the hole hopping from HOMO1to HOMO2 produces excited states localized on molecule 2,which for a non-zero radiative decay rate can be detected asthe molecular emission characteristic of molecule 2. If theintermolecular separation r between chemically different

h pair becomes a CT exciplex; the localized exciplex or exci-mer (in case of chemically identical molecules) can be formedby the resonance interaction between molecularly excited andground states of molecules 1 and 2. From this general picture,it is apparent that in order to observe electromer or electro-plex emission, the energy barrier DE for carrier transport

Figure 123 The energy level shift between two moleculesenabling formation of electromers and electroplexes, and their opti-cal emission characterized by the energy quanta hncross (cf. similar




schemes in Figs. 10, 11, 20, and 28).

molecules is sufficiently small (<0.4 nm, cf. Sec. 2.3), the e–

must be high enough to make the hopping rate comparablewith spatial crossing transition resulting in an additional fea-ture of the overall emission spectrum. Its spectral positiondepends on the LUMO2–HOMO1 gap (DE21) as comparedwith on molecule located LUMO–HOMO energy separations(DE11, DE22). The case DE11<DE21<DE22 has been illu-

nent to be located between the long-wavelength molecularemission from PTOPT and short-wavelength molecular emis-sion from PBD. The same electron acceptor (PBD) combinedwith another donor molecule (TPD) led to a long-wavelengthelectroplex emission component illustrating another intermo-lecular energy relation DE21<DE11<DE22

the position of trapping levels of anthracene molecules in aPC matrix appeared to be sufficient to produce the electromeremission located in the long-wavelength tail of the overall EL

tion. The molecules and electroplex (electromer) emissioncombined with the exciplex (excimer) emission form a broadband spectrum as demonstrated by the results for an SL elec-tron donor (TPD)–electron acceptor (PBD)-based organic LED

emission spectrum based on the same donor and acceptor sys-tem as in Fig. 26, but detected from a DL device where mole-cules of TPD dispersed in PC, forming the hole-transportinglayer, could be brought into a contact with molecules of PBDevaporated on its top as an electron-transporting and strong

ponents representing different emission species can be distin-guished. An additional A4 component appears as comparedwith the EL spectrum of the TPD and PBD dispersed in PCof an SL device, presented in Fig. 26. It has been assignedto the second electroplex while A1, A2 and A3 componentsare same molecular emission of TPD (A1), exciplex emission(A2), and first (shorter-wavelength) electroplex (A3). Theelectroplex (EC) emission is to a large extent determined bythe intercarrier Coulombic attraction energy, EC¼ e2=4pe0er.The emission energy (hnEC), including the local environmen-




strated in Fig. 29, showing the electroplex emission compo-

(see Fig. 30). Also,

spectrum (see Fig. 17) with the same energy level interrela-

in Fig. 26 and for a single-component emitter in Fig. 17. The

hole-blocking layer, is shown in Fig. 124. Four Gaussian com-

tal shift of LUMOs and HOMOs, DE (cf. Fig. 123), can be

Figure 124 (a) A broad-band emission spectrum from a DLITO=(75%TPD:25% PC)(60nm)=PBD(60nm)=Ca LED at 20V andits Gaussian profile analysis ascribed to molecular TPD singlets(A1), exciplexes (A2) and electroplexes (A3, A4). Solid line: experi-mental curve, dashed line: four gaussian band fit. (b) EL spectrafrom the same device at different voltages. The PL spectrum excited

components related to the total EL emission of the device. A1, A2,A3, A4 correspond to the contributions of the EL components relatedby the area under the Gaussian profiles peaking at l1ffi 415nm(hn1ffi 3 eV), l2ffi 477nm (hn2ffi 2.6 eV), l3ffi 564nm (hn3ffi 2.2 eV),and l4ffi 670nm (hn4ffi 1.85 eV). Adapted from Refs. 112 and 120].




at 360nm of a (40% TPD:40% PBD:20% PC) spin-cast film from Fig.26 is recalled for comparison. (c) The field evolution of the spectral

expressed by

hncross ¼ I � A� 2DE� EC ð274Þ

where I is the ionization potential of molecule 1 (say donor, ID)and A is the electron affinity of molecule 2 (say acceptor, AA).Equation (274) with DE!0, and AA¼ IA�Eopt, where IA isthe ionization potential and Eopt, the optical gap of the accep-tor, has been employed to evaluate the intercarrier distanceusing the experimental values of hnEC. With ID(TPD)¼ 5.5 eV,and AA(PBD)¼ 2.6 eV, E

ð1ÞC ¼ 0.7 eV for electroplex 1 [hnð1ÞEC¼

2.2 eV], and Eð2ÞC ¼ 1.1 eV for electroplex 2 [hnð2ÞEC¼ 1.85 eV] have

been obtained. Then, using e¼ 3, rð1ÞEC¼ 0.68nm and r

ð2ÞEC¼

0.45nm calculated [120]. These values of r are expected torepresent rather a lower limit of electroplex radii becausethe used electron affinity has been assumed at its largestvalue IA�Eopt. On the other hand, DE 6¼ 0 could reduce oreven level off this difference.�

essential difference between PL and EL spectra is seen, andthe red shift of the EL spectra with applied voltage apparent.This can be explained by an electric field-induced differentia-tion of the contribution of four Gaussian components to theoverall EL spectrum. The Gaussian profile analysis of theEL spectra at different electric fields allowed to follow the vol-tage dependence of the contribution of particular emissioncomponents (Fig. 124c). Whereas, the molecular (A1) and sec-ond electroplex emission contribution (A4), though in oppositemanner, change only slightly with applied voltage, the contri-bution of the exciplex emission (A2) decreases and that of theshorter-wavelength electroplex emission (A3) increases signif-icantly at increasing voltage. This behavior can be rationa-lized by a particular location of TPDþPBD� pairs at the

�We note that a substantial dispersion in EC and, consequently in r may beexpected due to differences in the literature values of I and A. For example,A can differ by more than 0.5 eV dependent on whether the optical gap Eopt

has been determined from the long-wavelength absorption edge or theabsorption maximum. Then, for PBD, Eopt(edge)¼ 3.54 eV and Eopt

(max)¼ 4.1 eV, respectively, and DEoptffi 0.56 eV. Thus, A falls in the range2.76–2.2 eV. These values yield 0.54 eV�EC� 1.1 eV, and 1.3nm� r�0.62nm for electroplex 1 formed with the TPD donor.



From part (b) of Fig. 124, the

(TPD:PC)=PBD interface. In contrast to the bulk recombina-

involving random oriented e–h complex dipole moments, thedipole moment of the all e–h pairs at the (TPD:PC)=PBDinterface is directed against the electric field because theholes are located on TPD molecules in the HTL, and counter-part electrons are located on PBD molecules in the ETL of thejunction. Consequently, the increasing forward external elec-tric field (ITOþ, Ca�) may either increase the recombinationrate of the electroplex forming pairs or reduce the electroplexenergy (274) by a term erU=d. In the example presented in

the emission spectrum to the red by about 0.05 eV accordingto the erU=d completed Eq. (274). This is at variance withexperiment showing the shift to reach ffi0.2 eV. Therefore,the field-induced increase of the radiative decay rate of elec-troplex 1 seems to be dominating in red shifting of the ELspectrum. An alternative explanation would be a differencein the field-induced drop of the quantum efficiency at high

the emission of such LEDs. The EL quantum yield typically

imum efficiency field dependent on the device structure. Thequantum efficiency drop for the TPD:PBD:PC SL LED beginsat a much higher electric field than that for the (TPD:PC)=PBD DL LED (Fig. 125). The red shift of the EL maximumfor the DL LED (Fig. 124b) occurs in the voltage range corres-ponding to the high-field decrease in the EL quantum effici-ency (F> 1.25MV=cm; Fig. 125). If a roughly 30% decrease inthe overall EL quantum efficiency, going from 1.25MV=cm to2.0MV=cm, were dominated by the quenching of long-livingexciplexes, a net effect would be the relative increase of theelectroplex component shifting the overall EL spectrum tothe red. Referring the reader to Sec. 5.4 for details of quench-ing mechanisms, here we note this supposition to be consis-tent with a 30% drop in the exciplex contribution inferredfrom the Gaussian profile analysis of the EL spectra at differ-ent electric fields (Fig. 124c) and independent observations ofstrongly electric field-induced quenching of fluorescence origi-




tion process in the SL TPD:PBD:PC structure (see Fig. 26),

Fig. 124b, the voltage increase from 20 up to 28V would shift

fields (Fig. 125) for exciplex and electroplex contributions to

decreases above a certain electric field (cf. Sec. 5.4), the max-

nating from long-living excimers in TAPC [506]. One wouldnot expect a substantial red shift effect from increasing com-ponent A4, due to its relatively small contribution to the over-all output. Its appearance in the EL spectrum follows fromEq. (274) with DE 6¼ 0, that is an electroplex formed on a

Electric field effect on the broad EL spectra has been stu-died earlier with another acceptor, Alq3 [507]. The broad bandEL spectra from a series of ITO=HTL=Alq3=Mg=Ag LEDshave been attributed to the emission from exciplexesformed at the HTL=Alq3of EL spectra from one of these LEDs based on the m-MTDATA=Alq3 junction, with the PL spectra of m-MTDATAand Alq3 films, is presented. They fall beyond the maximaof the PL spectra towards red of the m-MTDATA donorand the Alq3 acceptor, suggesting formation of the [(m-MTDATA�Alq3)þ (m-MTDATAþAlq3

�)CT] exciplex and=or (m-MTDATAþ-Alq3

�) electroplex (cf. Unlike in the

Figure 125 The field dependence of the quantum EL efficiency for

right Institute of Physics (GB).




the LEDs from Fig. 30 (SL) and Fig. 121 (DL). After Ref. 120. Copy-

interface. In Fig. 126, a comparison

Fig.

defect site characterized by the DE.

27).

this structure shift towards blue at increasing voltage.This behavior could reflect a field-mediated competitionbetween the formation of Alq�3 molecular excited singlets

�3 )!HOMO




TPD=PBD junction based LED (Fig. 124b), the EL spectra of

(cf. Sec. 5.2.1) and electroplex decay LUMO (Alq

(m-MTDATAþ). The latter corresponds to hnEC¼ (2.1 �0.1) eV and yields the emission at lEC¼ (590 � 30) nm in goodagreement with experiment. Increasing voltage reduces thehole injection barrier at the interface, the hole charge accu-mulated at the m-MTDATA side of the junction decreases,the rate of cross-transitions of electrons from the Alq3 LUMOto holes located on the m-MTDATA HOMO (electroplex tran-sitions) becomes smaller and, as a consequence, the contribu-tion of the electroplex emission to the overall spectrumdecreases, its maximum shifts towards blue, i.e., approachesthe molecular emission from Alq3. Alternatively, the field-induced quenching of the (m-MTDATAþAlq3

�)CT exciplexescan be considered as a reason for the blue shift of the EL spec-trum.

The exciplex energy can be evaluated from Eq. (43)knowing the polarographic oxidation potential of m-MTDATAand reduction potential of Alq3. Based on the values Eox (m-MTDATA)¼ 0.31 eV (Ref. 508) and Ered(Alq3)¼�1.9 eV (Ref.509), we find hnex¼ (2.1 � 0.1) eV identical to the above esti-mated energy of the electroplex. Its emission, identified as a

the molecular emission from Alq3 in order to understand theblue shift of the overall emission maximum at increasing vol-tage. This could occur for the same reason as the discussedabove step down in the electroplex emission component. Thefield decreasing space charge of holes at the m-MTDATA=Alq3junction causes a gradual reduction in the formation rate of

Figure 126 The 1,3,5-tris(3-methylphenylphenylamino)tripheny-lamine(m-MTDATA)=Alq3 (a) junction based DL LEDs emissionspectra as compared with the PL spectrum of m-MTDATA andAlq3 (b) at different applied voltages (c). The EL spectrum (1) in part(b) taken for the device ITO=m-MTDATA (60nm)=Alq3(60nm)=MgAg at 6V; the PL spectrum of Alq3 given by curve (2) and ofm-MTDATA given by curve (3). The vacuum related LUMO andHOMO levels for the materials used are shown in the right-top cor-ner. The 6V EL spectrum from part (b) shows blue shift as appliedvoltage increases (c). Adapted from Ref. 507.

J




CT transition (cf. Sec. 2.3.2), should decrease with respect to

excited CT states. Also, this would explain the absence of theexciplex emission when m-MTDATA are replaced by TPD inthe DL LED [507]. A relatively low injection barrier of holesfrom TPD to Alq3 (ffi0.3 eV) reduces the concentration of holeson the TPD side of the TPD=Alq3 junction, so that the forma-tion rate of CT states, being proportional to the number ofholes located on the TPD HOMO, becomes negligible withthe radiative decay of excited molecular states of Alq3. Thisreasoning assumes hnEX¼Eox (TPD)�Ered (Alq3)� 0.15¼(2.1� 0.1) eV, obtained with Eox (TPD)¼ 0.35 eV (Ref. 112)and the above cited value of Ered (Alq3)¼�1.9 eV. This wouldlocate the maximum of the exciplex emission at ffi590nm. Onthe other hand, the energy gap between the LUMO (Alq3) andHOMO (TPD) (2.4 � 0.1 eV) would lead to the cross-transition(electroplex) at lffi 510nm falling into the molecular emissionspectrum of Alq3tinguish the molecular from electroplex emission based on theemission maximum position solely. In order to check the roleof TPD on the emission from Alq3, it is useful to compare theEL and PL spectra from pure (100%) Alq3 layers with those

3

EL and PL spectra of a 100% Alq3 film are nearly identical,they differ substantially for a 30% Alq3-doped TPD sample.The broader and slightly red-shifted PL spectrum of themixed sample suggests the formation of locally excited bi-

absorption spectra presented in Fig. 127c, and lacking themolecular emission of TPD in the Alq3:TPD sample [not

they might be 1(Alq�3 TPD) trapped states. Under electricalexcitation, the large populations of TPD-located holes, andAlq3-located electrons, render the electroplex emission to com-pete effectively with the emission underlain by molecular Alq3states including their complexes with TPD. Consequently, thenarrower spectrum becomes dominated by less dispersed inenergy electroplex states. The field-induced reduction of theexciplex emission (thus, relative increase of the electroplex

in the electron hopping rate. The effect is much better




from an Alq :TPD mixture as shown in Fig. 127. While the

shown in Fig. 127b since peaking below 450nm (see Fig. 6)],

emission) evident in Fig. 128 is matched by the enhancement

molecular complex states (see Sec. 2.3.2). In conjunction with

(cf. Sec. 5.2.1). Thus, it is not possible to dis-

pronounced in a single layer (SL) mixture (CBP:PC:PBD)than in the bilayer structure (CBP:PC)=PBD. This can beexplained by a difference in the average distance (r) betweenCBP and PBD molecules in these two structures. A lowervalue of r at the (75% CBP:PC)=100% PBD interface in theDL structure promotes the formation of molecular and exci-plex states, the electroplex component constitutes a smallerpart of the overall emission spectrum. The field-enhancementof the electron escape from a Coulombically correlated charge

Figure 127 (a) PL and EL spectra of a vacuum-evaporated layerof Alq3 in the structure ITO=100% Alq3 (140 nm)=Mg=Ag (see

(b) PL and EL spectra of an Alq3-doped TPD film inthe structure ITO=30% Alq3:TPD (150nm)=Mg=Ag (Cocchi andKalinowski, unpublished). The front PL spectra are recordedthrough the ITO-covered glass substrate, and excited with lexc¼420nm; (c) absorption spectra of Alq3, TPD and Alq3:TPD (3:10)films on quartz. The film thickness d given in the inset (Cocchiand Kalinowski, unpublished).




57);Ref.

carrier pair (CBPþCBP�), equivalent to its field-assisted dis-sociation, is not efficient enough to change the dominatingexciplex emission. On the other hand, more distant CBPþ-CBP� charge carrier pairs in the bulk of the SL LED(Fig. 128a) are subject to a stronger field effect on their




dissociation and, consequently, the relative increase in theradiative decay of Coulombically correlated e–h pairs formingelectroplex species. At sufficiently high fields, the overall emi-ssion spectrum becomes dominated by their emission. The PLspectrum of the (CBP:PC:PBD) sample shows two featurescorresponding to the two closely spaced maxima of the mole-cular emission of CBP and a shoulder at ffi420nm which canbe assigned to the locally excited exciplex 1(CBP PBD)�

formed by the exciton resonance between CBP and PBD mole-cules. This state becomes dominating in the EL emission ofthe DL structure and the low-field EL spectra of the SLdevice. A broad band above 500nm reveals three separablefeatures in the low-field EL spectrum of the SL device. Theprincipal maximum at ffi525nm is assumed to reflect theradiative decay of the unperturbed electroplex composed ofan e–h pair located on PBDþ and CBP� molecules and sepa-rated by a distance r¼ e2=4pe0eECffi 0.48nm, the valueobtained with e¼ 3 and EC¼ ID� IA�hnEC¼ 1.04 eV. TheCoulombic e–h attraction energy,EC, has been calculated fromEq. (274) assuming DE¼ 0, ID¼ 6.0 eV, AA¼ 2.6 eV, and usingthe experimental result for hnECffi 2.36 eV. By analogy withthe lowest-energy band in the electroplex emission in the TPD=PBD system (band A4

can be assigned to trapped electroplexes. Using Eq. (274)allows the energy level shift, due to local environment

Figure 128 The PL and EL spectra of combined compositions of(4,40-N,N0-dicarbazole-biphenyl) (CBP) and 2-(4-biphenyl)-5-(4-tert.-butylphenyl)1,3,4-oxdiazole (PBD) in a form of an SL mixedfilm (40% CPB:20% PC:40% PBD) (a), and a double layer structure(75% CPB:25% PC)=100% PBD (b). The PL spectra of a 100% CBP(PL CBP) and 75% CBP:polycarbonate (PC) film are shown for com-parison. The solid-state energy level scheme of the electronicallyactive materials is shown in the inset of part (a). The differencesbetween PL and EL spectra recorded at different voltages areapparent for both systems. After Cocchi and Kalinowski, unpub-lished.

J




in Fig. 124), the features at ffi600nm(EC2) and ffi700nm (EC3) of the electroplex band in Fig. 128a

conditions, to be estimated on DE (EC1)ffi 0.15 eV, and DE(EC2)ffi 0.3 eV. An alternative interpretation of electroplexes2 and 3 would be the formation of the e–h emitting pairs withdifferent intercarrier separations [120]. Such an approachwould give EC leading to rffi 0.3–0.4 nm, the distances charac-teristic of CT exciplex. The impact of the separation distanceon the nature of excited states and corresponding emissionspectra has been demonstrated on copolymers containingthe electron donor and electron acceptor groups of N-vinylcar-bazole (NVK) and PBD [510]. The carbazole and oxadiazole-containing groups connected to the polymer backbone havebeen spaced by a distance impeding the formation of exci-plexes. The EL spectra of such copolymers have been shownto differ from those of PVK:PBD blends, where the intermole-cular NVK–PBD distance is subject to statistical distributionwhich includes distances below 0.4 nm and molecular orienta-

different ratio PV:PBD blended films show the EL maximumnear 440nm characteristic of exciplexes, the EL spectra of SLcopolymer-based devices are very broad with well-pronouncedthree bands peaking in different spectral regions: one at 370–440nm, a second at 500nm, and a third near 610nm. Theshortest wavelength maximum is a superposition of emissionfrom isolated NVK and exadiazole-containing monomer seg-ments and their excimers. The smallest maximum, near610nm, has been attributed to PVK electromers. But theemission maximum dominating at comparable contents ofNVK and oxadiazole-containing species, and especially athigh electric fields, is to be associated with electroplexessince the topological constraints by the polymer prohibit theformation of exciplexes between sequential donor and accep-tor units.

An interesting case of the electroplex formation may beexpected for the low ionization potential of electron donorand high electron affinity of electron acceptor molecules.The electron transition would then occur at large intermole-cular distances (EC!kT) and the optical cross-transitionappears at hncrossffi ID–AA [cf. Eq. (274) with DE¼ 0]. Thebroad band at ffi550nm in the EL spectrum of a DL LED




tions suitable for the exciplex formation (cf. Sec. 2.3). While

based on the poly(9-tetradecanyl-3,6-(dibutadiynyl)carbazole)(PTD-BC)=hyperbranched polycarbazole (HB PC) seems to bea good illustration of such a situation (Fig. 129). The differ-ence, ID(PTD-BC)ffi 5.4 eV and AA(HBPC)ffi 3.2 eV, giveshncrossffi (2.2 � 0.2) eV (520–620nm) corresponding well tothe broad long-wavelength band in the EL, not observed inthe PL spectrum.

demonstrate the importance of local environment for theenergy of excited states. They have been obtained for amulti-component molecular structure comprising of a Nd3þ

cation surrounded by four negatively charged pyrazoloneligands. The structure has a permanent dipole momentassociated with the hemicyanine unit and this is expected tobe enhanced by the rare-earth-containing anion [512]. The

Figure 129 PL and EL spectra of a DL LED:ITO=PTDBC=HBPC=Al. For chemical names of the hole-transporting layer materialPTDBC and electron-transporting material HB PC, see text. TheLUMO and HOMO energy interrelations in these materials aregiven in the right upper corner. Adapted from Ref. 511.




In contrast to this case, EL spectra presented in Fig. 130

Figure 130 Absorption (A), photoluminescence (PL) and electro-luminescence (EL) spectra of a Langmuir–Bloddgett (LB) film (a)containing a donor-conjugated p-electron system acceptor (D–T–A)molecular cation coupled to a monovalent anion with a trivalentrare-earth (Nd3þ) cation surrounded by four organic singly chargedanionic ligands (b). The two EL spectra have been taken from adevice being run for the first time (EL1), and the emission from adevice that has been cycled several times (EL2). Reprinted fromRef. 512. Copyright 1996 with permission from Elsevier.




molecules formed into an LB film give a centrosymmetricstacking of the monolayers. Application of an external voltageshould thus be expected to cause a molecular re-orientationsimilar to that in conventional second order nonlinear materi-als. The PL spectrum, partly red shifted from the EL spectra,has a peak at 590nm (the spectra are normalized at theirmaximum intensities). The EL spectrum recorded on the firstrun appears broader than the PL emission with a blue-shiftedpeak at ffi570nm and a broad shoulder to the red at ffi670nm.Subsequent EL spectra show a further evolution with the red-shifted component dominating. The explanation for this beha-vior is most likely due to unusual nature of the molecularcomplex used. The EL appears to be characteristic of thehemicyanine counter-ion and not the Nd3þ unlike in lantha-nide complexes (cf. The blue-shifted peak andred-shifted shoulder could be two dipole-split componentsreflecting the specific dipole–dipole interactions throughorientation of the dipoles of the molecular complex in theexternal electric field. Cycling of the device promotes in someunknown yet way the second emission component. The exter-nal bias field may cause not only rearrangement of the dipolesbut could even break up the complex, favoring one of the twotypes emitting species that is locally modifying the emissivemedium.

Also, EL emission from triplet bi-molecular states reveals

emission from the EL device based on the metalorganic com-plex platinum (II) (2-(40,60-difluorophenyl)pyridinato-N,C2)acetyl acetate (FPt1) doped into the host material 3,5-bis(N-carbazolyl)benzene(mCP). The vacuum-evaporated layer of4,40-bis[N-(1-naphthyl)-N-phenyl-amino]biphenyl (NBP) ser-ved as the HTL followed a layer of poly(3,4-ethylenedioxythio-phene):poly(styrene sulfonic acid) (PEDOT=PSS) spun ontothe ITO injecting holes (hþ) electrode. The 50nm-thick2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP) layerfollowed the phosphorescent complex FPt1, and serves as ahole=exciton blocking and electron-transporting layer. Theelectron (e�) injecting electrode consists of LiF and Al. Thebroad EL spectrum of such a device differs completely from




broad band spectra. They are illustrated in Fig. 131 by the

Sec. 5.2.3).

its PL spectra (Fig. 131b), peaking at 1.83 eV (678nm). Themolecular emission spectrum of a neat film of FPt1 with thewell-resolved vibronic structure disappears when sandwichedin the organic heterostructure shown in Fig. 131a. The PL ofthe device contains a large contribution from NPD emissionas indicated, and a broad band emission located at 2.07 eV(599nm). There is an 80nm red shift in the EL maximumfrom the broad band maximum location of the PL spectrumof the device at 290K. Interestingly, two peaks in the low tem-perature (82K) EL spectrum can be resolved (Fig. 131c), one

Figure 131 The EL device used to probe triplet bi-molecularexcited states and molecular structures of FPt1 and mCP (a). Com-parison of the room temperature EL (solid line) and PL (dotted line)spectra of the device with a 30K spectrum of Fpt1 (dashed line) (b).The EL spectrum of the device at different temperatures (c). Rep-rinted from Ref. 99. Copyright 2003 with permission from Elsevier.




at 2.07 eV and the second still dominant at 1.83 eV. Fromtheir lifetimes of (1.6 � 0.3)ms and (800� 80) ns, respectively,these two broad states have been assigned to the triplet exci-mer ð3E�0Þ at 2.07 eV, and to the weakly bound dimer (3D�) at1.83 eV, resulting from Pt–Pt contacts on adjacent moleculesin the neat thin films. The 3D� state is present only duringelectrical excitation [99].

From the above examples, we have seen that the recom-bination of electrons and holes injected into a single- or multi-layer combinations of thin organic films shows a tendencytowards the formation of aggregate excited states that under-lie complex multi-band emission spectra observed with thinfilm organic LEDs. The shape and range of these spectra, thusthe color of such LEDs, can be controlled by aggregate forma-tion. In particular, the contribution of bi-molecular excitedstates depends on the composition, morphology, and electricfield, and manipulating these factors both the color and ELefficiency could undergo desired measures. However, to tailorthese LEDs’ characteristics, the more detailed knowledge onthe nature of the aggregate excited states is necessary.

A transition from the molecular like behavior of localizedexcited states to a collective excitation, similar to that of inor-ganic semiconductors, could be underlain by the formation ofbi-excitonic molecules, electron–hole plasma or liquid at high

ing of the PL spectrum and a cubic dependence of the emis-sion intensity on the excitation intensity are then observed[514,515]. These are characteristics also observed with fuller-enes—particular allotropes of carbon organized in variousclosed structures, the most abundant, C60, being a closed cageicosahedron of 60 sp2 hybridized atoms [516]. At room tem-perature, the C60 crystal structure can be regarded as anexcellent example of cubic close packing of isotropic spheresbecause the molecules have almost total rotational freedomin the fcc lattice [517,518]. The icosahedral ‘‘football’’ likeC60 molecules of diameter 0.7 nm are bound by van der Waalsinteractions with an inter-ball spacing of 0.3 nm. Such adimension relation poses questions as to the degree of inter-vs. intra-molecular interactions in solid state fullerenes.




excitation intensities (see e.g., Ref. 513). A red shift, broaden-

Therefore, it is not surprising that their electronic propertiesdiffer as observed in single crystals, powders, and thin films.For example, a strong dependence of the luminescence onexcitation intensity occurring in powders and crystals is notobserved in films [519]. Three distinct photoexcited speciesin C60 films have been identified: a triplet exciton delocalizedover the C60 molecules, a localized exciton pinned to a five- orsix-membered ring at a local molecular deformation site, andan intermolecular polaron [520]. They are considered tounderlie the low excitation intensity PL spectra, but not high

tion from a weak structured PL spectrum at low excitationlevel, to a broad-band PL spectrum at high excitation inten-sity, peaking at about 900nm, with a concomitant anddramatic increase in the luminescence output, has beenascribed to a transition from the linear to non-linear opticalresponse of the C60 crystal, that is from the molecular likebehavior of localized states to collective excitation of the inter-acting molecules. The general correspondence between thehigh excitation intensity PL and EL spectra in C60 crystalsled to a conclusion that both are underlain by the samemechanism based on the Mott description of inter-carrierinteractions under high carrier concentration conditions. Inthis model, as the density of excitons is increased, the elec-tron–hole interaction is screened by a plasma environmentuntil, at a critical density (nC� 0.01=a3

0, where a0¼ 4pe0e�h2=

mre2 is the exciton radius, e is the dielectric constant , mr is

the reduced mass), they cease to exist. The exchange and cor-relation energies become of importance and they dominateover the exciton binding energy, resulting in the formationof an electron–hole plasma. Using band calculations to obtainmr¼ 0.65me [522], a0¼ 0.35nm is obtained with e¼ 4.3 [523].This value is consistent with the dimensions of a molecularlylocalized exciton and leads to the exciton binding energyDEEX¼ e2=8pe0ea0ffi 0.5 eV being in reasonable agreementwith the separation between the exciton energy level andthe lower edge of the conduction band [524]. The origin ofthe broad blue-shifted EL band from a C60 film and an addi-tional maximum just above 400nm in the single crystal EL




excitation intensity PL, and EL spectra (Fig. 132). The evolu-

Figure 132 A comparison of the EL and PL spectra of C60. (1) the

tation intensity (<1021 quanta cm�2s�1); and (4) the PL spectrum ofthe crystal at high excitation intensity (>1021 quanta cm�2 s�1) (see




EL spectrum of a vacuum-evaporated film of thickness 10nm < d <EL spectrum of a 100 mm-thick single crystal (see Ref. 520a); (2) the

100nm (see Ref. 521); (3) the PL spectrum of the crystal at low exci-

Ref. 519). After Ref. 2. Copyright 1999 Institute of Physics (GB).

spectrum is not clear. One of the possibilities is a combinationof the emission from nitrogen ions (300–500nm) produced bythe spurious glow discharge of small amounts of N2 encapsu-lated on the surface and=or in the bulk of the material duringsample preparation, and the PL excited by the ultravioletradiation emanating from the glow discharge microcavities.

crystal packing (structural defects) cannot be excluded (for a

perfect crystal structure or from perfect randomness of thesample are known to create difficulties in deriving a completepicture of the linear optical and electrical properties of the

therein). It is, however, apparent from the results presentedthat the EL emission from single C60 crystal reveals charac-teristic features of the collective optical response underhigh excitation conditions, even though the applied fields(102–103V cm�1) and currents flowing through the crystallinesamples are rather low as compared with those required for

nic processes in fullerenes and the ongoing discussion of theirtheoretical description. The band vs. localized molecular sta-tes description of electronic properties of C60 resembles thesituation in conjugated polymers [527,528]. Conjugated poly-mers, such as polythiophene (PDT) or polyphenylenevinylene(PPV), in contrast to conventional low-molecular weight solids,show a close correspondence between the long-wavelengthphotoconduction threshold and the optical absorption edge[105,529]. This has been considered as an evidence for theequivalence between electrical and optical gap, i.e., that theCoulombic energy of e��h pairs is negligible as compared withkT, the situation typical for inorganic semiconductors. How-ever, due to strong coupling to lattice modes, electrons canrapidly be localized and form polaronic states [104]. A corre-lated on chain pair of negative and positive polarons is thenconsidered as a neutral polaronic exciton, S1

The identical PL and EL spectra in PPV are thought to origi-nate from the radiative decay of singlet polaronic excitons,




(see Fig. 23).

The recombination of charge carriers on local fluctuations in

more comprehensive discussion, see Ref. 2). Deviations from

solid state of fullerene (see e.g., Refs. 525, 526, and references

high-intensity EL in other organic LEDs (cf. Secs. 5.3 and5.4). This observation confirms the complexity of the electro-

thus, their red shift expected with respect to the absorptionspectrum (Fig. 133a). The emission spectra exhibit a well-pronounced vibronic structure which has been attributed toa coupling of phenylene ring stretching modes of the polymer

Figure 133 Optical absorption (optical density, OD), PL and

permission.




EL spectra for: (a) PPV at room temperature (see Ref. 66); (b) 2,5-dihexoxy-PPA at 20K (see Ref. 530). Copyright 1993 SPIE, with

chain (ffi1600 cm�1) to the electronic transitions between pand p� states [531]. The much broader and blue-shiftedabsorption band proves the participation of different excitedstates which relaxing to the excitonic states produce theobserved Stokes shift. The value of the Coulombic energy ofthe emissive states (the binding energy of a relaxed singletexciton) has been estimated between 0.2 and 0.5 eV. The nat-ure of the primary excited states is still under debate. Thepolaronic exciton seems not to be the only relaxed state cre-ated upon excitation. The ‘‘spatially indirect’’ singlet excitonshave been suggested to occur with a high quantum yield of 0.9on the basis of picosecond photoinduced absorption and sti-mulated emission experiments [532]. These are spatiallyseparated bound polaron pairs resembling CT states descri-bed in Sec. 2.3.1. While very effective in absorbing light, theywere assumed to decay by non-emissive geminate recombina-tion on a 1ns time scale. In injection electroluminescencepolaron pair states can be created by gradual approching ofindividual polarons undergoing non-geminate polaron–polaron recombination. These would correspond to the notionof electromers defined in Sec. 2.3.1. The electromer-like emis-sion seems to occur in the EL spectrum of the 2,5-dialkoxyderivative of poly(p-phenyleneacetylene)(PPA) as a long-wavelength band at about 800nm It is notobserved in its PL spectrum. A strong support for the forma-tion of polaron pairs comes from luminescence-detected mag-

the main narrow PL- and EL-detected resonances of a PPVand a 2,5-dihexoxy-PPA-based SL LEDs at 20K. The contrastbetween the enhancing nature of the PL resonance and thequenching nature of the EL resonance is clearly apparent. Aconsistent explanation of both is based on indirect mechanisminvoking the spin-dependent inter- and intra-chain fusion ofpolarons forming polaron heteropairs (Pþ��P�) and like-charged polaron pairs (bipolarons), BPþþ or BP��, respec-tively [533]. Polarons and long-living bipolarons are widelybelieved to quench emissive singlet excitons, the process cor-responding to exciton-charge carrier interaction described inSec. 2.5.2.1. The enhancing polaron resonance curves reflect




(Fig. 133b).

netic resonance (PLDMR and ELDMR). Figure 134 displays

the microwave-induced transitions between Zeeman sublevelsof polarons in a way increasing the rate of their non-radiativeinter-chain recombination process, the following decrease inthe population of polarons reduces the efficiency of thequenching process and results in the increasing populationof emissive singlets, thus PL intensity. The quenchingpolaron resonance, on the other hand, shows the microwavesresonance enhancement of the bipolaron formation process ofthe intra-chain polaron–polaron fusion. The increased popu-lation of bipolarons leads to an increased rate of singlet exci-ton quenching detected as decreasing emission intensity. Theobserved decrease, however, may be dominated by a decreas-ing ratio of the formation of excited singlets, due to decreasingpopulation of free recombining polarons. The question ariseswhy the polaron pair mechanism plays dominating role inthe PL, and the formation of bipolarons in the ELDMR, atleast at low temperatures (as in Fig. 134). The reason mightbe associated with the nature and energy of the primary

Figure 134 The main narrow PL- and EL-detected magnetic reso-nance of a PPV-based LED at 20K excited at 488nm and operatingat i¼ 0 and i¼ 70 mA currents [PL (a), EL (b)], and of a 2,5-dihexoxy-PPA-based LED [PL (c), EL (d)]. After Ref. 530. Copyright 1993SPIE, with permission.




excited states. For example, the PL quenching polaron reso-nance, similar to the ELDMR, can be observed with an agedPPV film excited at 353nm not observed in pristine highlyordered PPV films. (A. W. Smith quoted in Ref. 533). Thiswould suggest the defect-controlled formation of bipolaronsinvolved in quenching of emissive singlet states. Interest-ingly, the defect located polaron hetero-pairs (‘‘electromers’’)

and 134d). The absence of an observable spin dependence ofthe electromer-like emission is not clearly understood at pre-sent, and speculated as due to rapid spin-lattice relaxation atthe trapping site, or to trapping of excitons rather than polar-ons [530]. The opposite trends in ODMR signals for PL andEL may be considered on the general basis of the differencein the formation of polaron heteropairs and bipolarons. Whilein the PL the primary excited states are efficiently generatedgeminate polaron hetero-pairs, in the EL they, by definition,do not exist, the formation of bipolarons as singlet excitonquenching species dominates being promoted by high concen-trations of one sign charges injected at electrodes. This differ-

DMR signal decreases as the PPV-based LED becomes anoperating device with the driving current i¼ 70mA.

5.2.3. Line-like Emission Spectra

Narrow-band, often line-like, EL emission spectra fromorganic LEDs can have different reasons of which the mostcommon will be addressed in the present section. Generally,two their groups are distinguished due to (i) intrinsic opticalproperties of emissive materials, and (ii) configuration andelectrical characteristics of devices. An excellent example ofthe former are lanthanide metal complexes where metal ionsexhibit extremely sharp emission bands differing completelyfrom emission spectra of organic ligands. Recall that, on thecontrary, the organic ligand emission is characteristic of sucha commonly used complex as Alq3 (Sec. 5.2.1) or somerare-earth complexes as discussed in Sec. 5.2.2. Among thelanthanide metal complexes, europium (Eu) and terbium




do not contribute to the main narrow ELDMR (cf. Figs. 133b

ence is demonstrated in Fig. 134a, where the enhancing PL

(Tb) complexes (Fig. 135) are well known to be strongly fluor-escent at room temperature. Their extremely sharp PL bands[537,538] appear also in the EL spectra of various organic

While Eu complexes exhibit red emission having a strongpeak at ca. 615nm, Tb complexes such as Tb(acac)3 (phen)exhibit green emission sharp bands with a strongest onelocated at ca. 545nm. Despite these differences, the spectrahave the same origin, reflecting the fact that the electronsresponsible for the properties of lanthanide ions are 4f elec-trons. Their 4f orbitals are effectively shielded from the influ-ence of the external forces by the overlapping 5s2 and 5p6

shells, which imply the f n configurations to be relativelyinsensitive to the external fields. Consequently, emission (aswell as absorption) bands (f–f transitions) are extremelysharp when electronic transitions occur from one j state ofan f n configuration to another j state of this configuration.In Fig. 136c, five different intensity EL line-like bands areattributed to such transitions, the strongest one assigned tothe 5D4! 7F5 transition. It is important to note a differencein the excitation mechanism of lanthanide metal ions forming

Figure 135 Molecular structures of lanthanide complexes of euro-pium (Eu), tris (thenoyltrifluoroacetonato) Eu3þ (a), tris(thenoyltri-fluoroacetonato)(monophenanthroline) Eu3þ (b), and terbium (Tb),tris(acetylacetonato) Tb3þ (c) employed as narrow-band emitters




LEDs employing these complexes as emitters (see Fig. 136).

in organic EL devices (see Ref. 19, 425, 534–536 and 539).

complexes with organic ligands and organic dyes includingother metal complexes [537]. In organic fluorescent dyes,the emission of photons is due to the electronic transitionsfrom the singlet excited states (see andOrganic phosphors like benzophenone [540], but mostly heavymetal organic ligand complexes [541], show molecular phos-phorescence underlain by electronic transitions from sing-let–triplet mixed molecular excited states or metal-to-ligandcharge transfer (MLCT) mixed states. Many luminescencestudies have interpreted the results as having competitionbetween MLCT and p–p� ligand-centered (LC) states lyingvery close in energy. For example, the ‘‘metal’’ orbital in Ir–

Figure 136 EL spectra of various organic LEDs employinglanthanide complexes as emitters. (a) ITO=TAD (triphenyldiaminederivative)=Eu(TTA)3(phen)(phen:1,10-phenanthrolineþ 4,7-diphe-nyl-1,10-phenanthroline)=Alq3=MgAg (according to Ref. 425); (b)ITO=Eu (TTA)3:PBD=PBD=LiF=Mg, at the different voltages (afterRef. 539); (c) ITO=TPD=Tb (acac)3=Al, transitions of 4f electrons ofthe terbium Tb3þ ion are indicated on the sharp peak positions ofthis spectrum (after Ref. 19).




ppy complexes (see the emission spectra in Fig. 120) ranges

2.3 5.2.1).Secs.

from 45% to 65% Ir (5d) in character, with the remainder ofthe orbital of ligand p character [542,542a]. In contrast, inlanthanide complexes with p-conjugated ligands such as b-diketonato, the central lanthanide ions are excited via intra-molecular energy transfer from the triplet excited states ofthe ligands [543]. Since the ligand’s triplet states can be effi-ciently populated by the bimolecular e–h recombination pro-cess, the internal efficiencies of devices using these complexesas emitters have been expected to be much higher than the

An alternative way to use inorganic species to narrowingthe emission spectrum from organic containing systems is to

layer being used as a narrow-band emitter and organic ser-ving as carrier transport components. Such a structure basedon a layered perovskite compound (C6H5C2H4NH3)2PbI4(PAPI) (inorganic) combined with an oxadiazole derivative(OXD7) (organic) is shown in Fig. 137. The device driven atliquid-nitrogen temperature shows an intense green emissionpeaking at 520nm. The quasi-identical EL and PL spectra ofthe structure are very narrow (the bandwidthffi 10nm) and

Figure 137 An organic–inorganic heterostructure EL deviceusing a PAPI spin-coated film (a), molecular structure of an oxadi-azole derivative (OXD7) (b), and its emission spectra at 77K (see




Ref. 544). Copyright 1994 American Institute of Physics.

25% limit for molecular electrofluorescence (cf. Sec. 1.4).

fabricate an organic–inorganic layer structure, the inorganic

are attributed to the stable strongly bounded exciton formedin the low-dimensional PAPI semiconductor [544]. The holesinjected from ITO are confined in the PAPI side at thePAPI=OXD7 interface, where they recombine with electronsinjected from the Mg=Ag cathode and arrived at the interfacethrough the electron transporting organic layer of OXD7.

Another property of organic materials that leads tonarrowing of the emission bands is their ability to J-aggrega-tion. J-aggregated dyes, in which dye molecules have a head-

fluorescence reproduced well in their EL spectra 545–547.shows EL and PL spectra of a J-aggregated

cyanine-dye bimolecular layer formed by the Langmuir–Blodgett technique (Fig. 138b). The quasi-identical PL andEL spectra with a sharp maximum at ffi560nm and band-width ffi20nm indicate the identity of emissive states produ-ced on bi-molecular aggregates of the dye either by opticaland electrical excitation.

Sharpening of the emission and spectral tunability canbe achieved by placing an emitter between reflecting plane-parallel mirrors an optical microcavity resonatorwith a mirror spacing comparable to the wavelength dimen-

microcavity structures depends on the intermirror spacing(d) and emission angle (Y) because of interference effects

the summation of the amplitudes of direct emission and emis-sion reflected from the 100% mirror for a given wavelengthand Y. As a consequence, a narrow wavelength-range partof the emitted light shows up as a relatively strong emissioncomponent, sharpening and shifting the overall shape of thespectrum. The enhancement (resonance) condition in themicrocavity can be expressed as

XNi¼1

nidi cosY ¼ ml2

ð275Þ

where ni and di represent the refractive index and thicknessof the ith of N microcavity layers, respectively, Y represents




Figure

to-tail orientation, reveal relatively narrow-band resonance

138a

sions (Fig. 139). The shape of the emission spectra of such

(Figs. 140 and

forming

141). An enhancement of light occurs from

the light propagation angle with respect to the emission sur-

microcavity extending between the metal mirror and the

layers with thickness d1¼ 50nm (Alq3) and d2¼ 50nm(TAD) and the ITO layer with thickness d3¼ 200nm. Thedielectric half-mirror composed of a stack of three pairs ofSiO2=TiO2 layers of thickness d4 is equivalent to the opticalpath length of l=4. An additional optical path length due to

Figure 138 (a) Comparison of EL and PL spectra of a J-aggrega-ted cyanine dye (OCD). The EL spectrum taken from a three-layerLED, ITO=TAD=OCD=PBD=MgAg, as depicted in part (b) includingmolecular structures of the materials used. Adapted from Ref. 546.




face (cf. Fig. 139), and m¼ 1,2, . . . is the mode number. The

dielectric half mirror in Fig. 140 consists of the two organic

the effective penetration depth of the dielectric stack reflectorshould be taken into account. This term can be described asthe effective optical path length n5d5. The shortest value ofthe optical length of these N¼ 5 components forming themicrocavity predicts reasonably well the short-wavelengthpeak position at ffi480nm corresponding to m¼ 2 mode atY¼ 0. An optical refractive index n1¼n2¼ 1.7 was used forboth organic layers. The ITO acts as the electrode and hasbeen treated as a transparent spacer with a refractive indexn¼ 1.72. The additional peak at ffi614nm can be due to thesame mode with a cavity extended by the penetration depthinto the dielectric mirror. The interference among partialfluxes reflected at the dielectric interfaces can also be ofimportance. From classical optics, the angular distribution

Figure 139 Comparison of a microcavity structure (a) and aconventional organic LED (b).




Figure 140 The EL spectra for the two types structures depicted

Alq3(50nm)=In operating at 100mAcm�2; a sputtered TiO2=SiO2

multilayer film formed a half mirror layer in the microcavity struc-ture (a), and the long-wavelength maximum position as a functionof observation angle from the microcavity structure (Fig. 139a)(b). Adapted from Ref. 548.




in Fig. 139, using the following sequence of layers: ITO=TAD(50nm)=

Figure 141 EL spectra from the microcavity (a) and conventionalLED (b) measured at different fixed detection angles (Y). The micro-cavity structure comprised a reflective Ag anode (36 nm), a TADHTL (250nm), an emission dye layer [15nm-thick naphthostyryla-mine (NSD) film], an ETL [240nm-thick oxadiazole derivative(OXD) film], and a reflective MgAg cathode. Note that a 10% trans-mittance Ag layer (36nm) played here a role of a half mirror compo-

film served as the anode in the conventional LED structure (Fig.139b). After Ref. 550. Copyright 1993 American Institute of Physics.




nent in the microcavity structure (cf. Fig. 139a). A transparent ITO

F(Y) of the light intensity emitted from microcavities follows

F ¼ T= 1þ a2Rþ 2affiffiffiffiRp

cos dh i

ð276Þ

The external observation angle, Y, associated with the inter-nal light incidence angle, Yi, through Snell’s law(n1 sinYi¼ sinY) is contained in the expression for the phasedifference

d ¼ 2n1d

l2p cosYi ð277Þ

where d is the microcavity length. T and R in Eq. (276) are thetransmittivity and reflectivity of a ‘‘semi’’-transparent mirror,‘‘a’’ represents the relatively light wave amplitude after eachinternal reflection. It is clear from Eqs. (275)–(277) that uponincreasing the external observation angle, the peak positions

and conventional LED (b) based on the emission from anNSD dye forming a thin emitting layer of a three-organiclayer device. It is apparent that the half-width of emissionspectra from the diode with microcavity is much narrowerthan those from the diode without cavity. With Y¼ 00, forexample, the half-width of the spectrum of the diode withcavity is 24nm whereas that of the sample without cavityincreases to 65nm. According to Eq. (275), the resonancewavelength, l, decreases with an increase of Y in agreementwith the experimental data of Fig. 141. We note that no uni-que resonance condition in the planar microcavity is givendue to broad-band emission spectrum of the NSD emissionlayer. Multiple matching of cavity modes with emission wave-lengths occurs. Thus, a band emission is observed instead asharp emission pattern from the microcavity structure aswould appear when observed with a monochromator; thetotal polychromic emission pattern is a superposition of arange of monochromatic emission patterns. The EL spectra




of the modes shift to a shorter wavelength, as shown in Fig.140b, and angular distribution of light intensity depends on

Figure 141 shows the EL spectra from a microcavity (a)

(see e.g. Ref. 548):

microcavity length [549]. (see also Ref. 2).

were also found to evolve with thickness of the organic layersand observation angle for the diode without a half mirror

and emission reflected from metal electrode=100% mirror.However, the narrowing and shift effects are much weakerthan those for the diode with a half mirror. Nevertheless, theyare strong enough to modify the emission spectra of Alq3 fromone 515nm maximum spectrum for d¼ 76.5nm to a doubleband spectrum revealing maxima at 495 and 590nm for a127.5 nm-thick Alq3 film [551].

Microcavity effects were demonstrated for polymer-based organic LEDs as well [348,493,552]. Electrolumines-cent spectra of single PPV layers of different thickness sand-wiched between two metal electrodes, detected at selected

the intensity in the EL spectra is clearly observed as thick-ness of the PPV layer increases (Fig. 142a). The microcavitymode at 560nm, i.e. the EL emission maximum of PPV,causes substantial narrowing of the emission bandwidth(21nm) close to the theoretical value of 15.6nm. Withdecreasing thickness of the PPV layer, the number of themicrocavity modes in the visible spectral region decreasesaccompanied by an increase in bandwidths of the corre-sponding emission peaks. On the device with a 265nm-thickPPV two microcavity modes (m¼ 2, m¼ 3) are observed. Theassignment of the emission maxima to microcavity modes isverified by the angular dependence of the EL emission (Fig.142b). The microcavity modes are expected to shift towardsshorter wavelengths with increasing detection angle. Indeed,such a shift is apparent for all three peaks in Fig. 142b. Theshape of the PL spectrum measured on the device has beenshown to be nearly identical to the shape of the EL spectrum[348].

microcavity structure. The EL spectrum of the Eu complex-based conventional LED from 136a is compared withthe EL spectrum of the same organic layers system placedin a microcavity formed by the MgAg metal=100% mirror(150nm) and a dielectric half mirror (a quarter-wave stack




(Fig. 141b), due to constructive interference of direct emission

detection angles, are shown in Fig. 142. A redistribution of

Figure 143 illustrates the high spectral selectivity of the

Fig.

composed of four pairs of SiO2=TiO2 layers). While the ELspectrum of the device without microcavity contains a num-ber of small peaks characteristic for the emission from anEu3þ ion in free space, the EL spectrum of the device withmicrocavity consists of a single resonance microcavity line

Figure 142 Normalized EL spectra recorded normally to the sur-face of an Au=PPV(d)=Al microcavity structure with different thick-ness (d) of PPV layer (a). Variation of the EL spectra with detectionangle (Y) for an Au=PPV (400nm)=Al device (b). After Ref. 348.Copyright 1996 American Institute of Physics.




Figure 143 Comparison of EL spectra of an Eu complex forming

MgAg electrode=100% mirror and a stack of SiO2=TiO2 layers=halfmirror (b). Note the disappearance of the small features of the spec-trum in device (a) in the spectrum from the microcavity structure(b). After Ref. 425. Copyright 1998 Taylor & Francis.




an emitter layer in a conventional organic LED from Fig. 135a (a)with the same system placed in a microcavity (Fig. 139a) with a

at the main emission maximum, all other features perfectlydisappear.

The emission from an organic microcavity structure withtwo metal electrode=100% mirrors can be observed from theLED edge [2]. PL and EL from such edge emitting structuresshow much sharper spectra and larger emission densitiesbecause they are a result of the propagation of a waveguidingmode allowed between two parallel mirrors separated by adistance D (Fig. 144). For a particular structure (Au=Ag)=PDA=Alq3=(Mg=Ag), the bandwidth of the edge emitted spec-tra is a factor 1.5–3 narrower (dependent on the thickness ofthe organic layers) as compared to the surface light output

edge emitting LEDs may ultimately enable organic materialsto find practical application in electrically pumped lasers[351]. For electrically pumped lasing, much higher injectionlevels are needed to reach the threshold current densityjTHffi 103A=cm2. Such current densities have been generatedusing two field-effect transistors as injection contacts to asingle tetracene crystal in one of the questioned seriesof works by Schon et al. [554] (see the Beasley Report in

Figure 144 (a) An edge emitting microcavity structure with twometal electrode=100% mirrors, based on the Alq3 emitter and PDAas HTL and (b) the EL spectra of two such different thickness struc-tures: (1) D¼ 350nm and (2) D¼ 160nm, detected at Y¼ 0; the sur-face light output spectrum is shown for comparison (broken line).After Ref. 553. Copyright 1993 SPIE, with permission.




spectrum from a conventional organic LED (cf. Fig. 139). The

News & Events—Lucent Technologies: http: ==www.lucent.com=press=0902=02 0925.blahtml). Narrowing of the 0–1vibronic transition band at ffi575.7 nm from 120 down to1meV has been reported and attributed to laser action. Sur-prisingly, a strong band narrowing has been observed fromthe Nile Blue (NB)-based edge emitting LED at much lowercurrents below 1A cm�2 [555]. The LED structure and itsEL spectra are shown in and respectively.Scientific discussion of the above cited results has includedsignificant attention to whether the observations reflect truelasing or only superluminescence and what is the nature ofemitting species [2,351]. In the case of singlet excitons inorganic crystals, the losses due various excitonic interactions

2

the high values of the optical gain necessary to start the laseraction. The formation of an electron–hole plasma, as assumedto underlie the C60

electrical confinement near an interface, can be consideredas an alternative. The plasma formation process causes thedisappearance of the quasiparticle nature of discrete excitonseliminating many excitonic processes in favor of direct band-to-band recombination at the interface, or other regions (suchas that surrounding a defect) where excitons and carrierswould localize at high densities. For example, singlet–singletannihilation will be replaced by non-radiative Auger pro-cesses in the plasma, which occur with a lower probabilitydue to phase-space filling. The minimum threshold currentdensity for lasing becomes lower and has been evaluated on500A cm�2 [351]. The high-density plasma emission may bereinforced by optical confinement introduced by a secondnon-linear effect: self-focusing due to intensity-dependentsaturation of the anomalous dispersion [556]. Its possible rolerequires further studies in ongoing discussion concerningmechanisms underlying line-like emission spectra fromorganic LEDs. In any case, lasing has not been convincinglydemonstrated in electrically pumped devices, and the mainproblem to be resolved seems to be associated with reducinglosses in the exciton formation zone of high-current operatingdevices.




Figs. 145 146,

crystal EL spectra (Fig. 132), created by

(see Sec. 2.5) at high currents (>10A=cm ) seem to eliminate

http://www.lucent.com

http://www.lucent.com

Figure 145 (a) The cross-section of an edge emitting DL LEDsupposed to act as an electrically pumped organic laser; (b) themolecular structure of Nile Blue (NB); and (c) the energy leveldiagram for the device. Adapted from Ref. 555.







Finally, the narrow emission lines can be attributed toexcitation of electrode materials. In fact, such emission lineshave been observed from Al and Mg:Ag cathodes of the PPV-derivatives-based SL LEDs when operated under strong elec-

the reabsorption-shifted characteristic Al emission at 395nmcould explain the relatively narrow line at about 400nmobserved in the Nile Blue (NB)-based edge emitting LED pro-

From the above, it is clear that the modification of theshape of the emission spectra from organic emitters contain-ing systems reflects the variation of the position and widthof the electronic levels involved in optical transitions. There-fore, the ability of a controllable production of quantized dis-crete energy levels in organic materials has become ofnoticeable interest. A way to reach this goal is the confine-ment of carriers in spatial cages formed by extended defectsin the bulk and=or superlattices of ultra-thin organic films[21]. The spatially extended defects can act as multi-chargecarrier trapping centers, leading to quantized internal energylevels [247]. The potential energy of a spatially extendeddomain (macrotrap) described by a spherical symmetry poten-tial of the form (181) is modified by the introduction of N> 1one-sign elementary charges (e) by an additional term reflect-ing the Coulombic repulsion of the N charge carriers:

EðrÞ ¼ 3l kT ln r0=rð Þ þ e2N=4pe0er� �

1� sin FN=2ð Þ½ �ð278Þ

where

FN ¼ arc cos 1� 2=Nð Þ½ � ð279Þ

Figure 146 (a) The narrow-band spectrum at a voltage of 0.4Vand current of 0.11mA across the two organic layers; (b) the sche-matic diagram of the edge emitting device: the thickness of NBlayer is 35–50nm and that of Alq3–NB mixture layer is 45–50nm;(c) the power edge emission as a function of the driving current,threshold current ith¼ 88 mA. Adapted from Ref. 555.

J




vided with an Al cathode as shown in Figs. 145 and 146.

trical pulse excitation [472]. (see also Sec. 5.3). For example,

is the energy quantizing factor because N¼ 1,2,3, . . . are thediscrete numbers of trapped elementary carriers. In otherwords, due to the finite dimensions of the macrotrap andthe discrete increment of the charge, the energy correspond-ing to different carrier populations (N) will form a set of dis-crete levels with an internal spacing that decreases with theincreasing number of captured carriers. A difference betweentwo successive trapping levels, DEt, varies from about 0.2 eVto DEt < kT with N1, for r0¼ 25–100nm [21]. The recom-bination of free oppositely charged carriers on the carrierstrapped on different (quantized) energy levels would leadto a split set of excited states contributing to either extendedemission bands or pronounced features in the long-wave-length wings of the emission spectra. The preference ofthe quantized energy levels has been demonstrated intriplet exciton quenching experiments [247]. If an ohmiccontact is used for charge injection into an organic solidwith macrotraps, the position of the quasi-Fermi level(dependent on the stored charge and hence on applied

of the electronic processes determined by the injected charge.For example, a cascade pattern has been observed in theinjecting-voltage dependence of the triplet exciton lifetimein anthracene 147). The triplet lifetime tTshortens in the presence of charge due to the triplet-chargecarrier interaction process (see decay rateconstant b¼ t�1eff increases with charge concentration accor-ding to Eq. (114) and the increase is proportional to theconcentration of trapped charge (nqt), Db¼ b� bTffi gðtÞTq nqt.Since under ohmic injection

nqt ffi3

2

e0eed2

U ð280Þ

Db is expected to be proportional to the applied voltage, U(cf. dotted curve in Fig. 147). The sequential filling of dis-crete traps by injected carriers produces trap-filled segmentscorresponding to consecutive trapping levels which are




(Fig.

levels, leading to a cascade pattern in various characteristics

exciton

2.5.2). TheSec.

voltage, cf. Sec. 4.3.1) scans sequentially the discrete energy

defined by the position of quasi-Fermi level EF as [334]

Et ¼ EF ¼ kT ln Neff=YntTFLð Þ ð281Þ

where Y is the free-to-trapped charge carrier ratio given byEq. (186). For two adjacent (i,k) levels

DEtik ¼ Eti � Etk ¼ kT lnYkDb

ðkÞTFL

YiDbðiÞTFL

ð282Þ

Furthermore, Yk=Yi¼ (Uk=Ui) [3l] follows from Eq. (186),and

DEt12 ¼ kT ln 1þ DU12

U1

� �3lDbð2ÞTFL

Dbð1ÞTFL

" #ð283Þ

Figure 147 The relative cascade-like pattern of the increase oftriplet excitonmonomolecular decay rate constant (b¼ t�1T ) as a func-tion of charge-injecting voltage in anthracene crystal. Consecutivetrap-filled limits are indicated by UTFL (1), UTFL(2) and UTFL (3).Dotted line indicates the averaged (linear) dependence of Db=b0 asresulted from the standard interpretation assuming a continuousincrease in the charge density proportional to the injecting voltage[334]. Adapted from Ref. 240.




for the first two trapping levels (1,2) can be obtained from(282).

It is thus apparent that both height [Dbð2ÞTFL=Dbð1ÞTFL] and

length (DU12) of the steps in the cascade pattern of the voltagedependence of Db=b are measure of the energy interlevel spa-cing. To have an idea of the values of DEt12, let us assume

U1¼ 300V, DU12¼ 300V, and Dbð2ÞTFL¼ 0.16bT, and Dbð1ÞTFL¼0.08bT. Then (283) yields DEt12¼ 0.2 eV. This value is closeto DEð1�2Þt ¼ 0.22 eV—the energy separation between the one-and two-carrier occupied macrotraps with r0¼ 25nm,rb¼ 1.5 nm and lffi 3 [r0 and rb are the macrotrap radius andradius of the pinning trap, respectively, see discussion ofthe macrotrap concept below Eq. (181)].

Another way to produce quantized electronic levels is theconfinement of carriers in ultrathin organic films in a mannerobserved previously with inorganic semiconductors [557]. If afree particle (say electron) is completely confined to a layer ofthickness Lz (by an infinite potential well) then the energies ofthe bound states are

En ¼ p2n2�h2=2m�L2z ð284Þ

where m� is the effective particle mass, and the integern¼ 1,2,3, . . . specifying the energy values represents thequantum number. The heterostructures (alternating thinlayers of different materials) produce two attractive potentialwells of different depths, one for electrons and one for holes.Coulomb attraction correlates the motion of the carriers inthe x- and y-directions, forming for each n an exciton statepeaking in the optical absorption and emission spectra. Asthe layer thickness decreases (decreasing Lz), the excitonmotion becomes two dimensional. The exciton becomes‘‘squeezed’’ in the potential well, resulting in an increase inthe exciton binding energy. This should produce a blue shiftof the absorption and emission maxima of the structure. Sucha shift observed in a system of alternating layers of 3,4,9,10-pery-lenetetracarboxylic dianhydride (PTCDA) and 3,4,7,8-naphthalenetetracarbozylic dianhydride (NTCDA) [558]; and




typically lffi 3, and use the experimental results of Fig. 147,

TPD and Alq3 (Ref. 149) have been interpreted in terms ofmulti-quantum-well (MQW) properties. The good agreementbetween experiment and theory has been obtained, assumingthe excitons to be Mott–Wannier in nature. This is, however,a hardly accepted assumption since excitons in organic solidsare known to be rather Frenkel-like than Mott–Wannier

like exciton energy expression (13), the observed shift couldbe explained in terms of non-resonance interactions betweenmolecules, D, at the interface between different organic solids[2]. On the boundary (mz¼ 0) of two molecular layers (A andB), a difference in D appears for molecules in the first layerof the solid A, due to a difference in the interaction strengthsbetween the molecules in the bulk (DAA) and at the surface(DBA

S ) [559],

DD ¼ DBAS �DAA ¼

Xmz<0

DABnm �DAA

nm

� �ð285Þ

Thus, if the layer is sufficiently thin, the exciton level shiftshould be seen in the position of the absorption and emissionspectra [cf. Eq. (13)]. Since DE can be positive or negative, onewould expect a blue (DD > 0) or a red (DD < 0) shift depen-dent on the relation between the intermolecular interactionsA–A and A–B. While the blue shift for the superlattice ofPTCDA=NTCDA could be ascribed to stronger interactionsbetween molecules of these two solids, the red shift observedin the emission maximum of tetracene within the superlatticestructure of pentacene=tetracene [560] would correspond tostronger interactions between the tetracene molecules in thebulk. This explanation of spectral shifts in absorption andPL spectra observed experimentally only in a small numberof organic superlattices seems to be more convincing,although the existence of MQWs for organic solids cannot becompletely excluded at present. More experiments on organicmaterials with a well-defined nature of excitonic states areneeded to resolve this ambiguity. The appropriate choice oforganic materials forming superlattices allows the fabricationof EL devices with a confinement of charge carriers and




resembling excited states (see Chapter 2) . Using the Frenkel-

excitons in thin layers of their emitters [560–565]. EL spectraof a conventional DL LED based on the Alq3=PBD junction,and of Alq3=PBD MQW structures are displayed in Fig. 148.The energy levels in the Alq3=PBD multi-layer structureshave been considered to originate from thin (3 nm) Alq3 layersforming quantum wells with finite barrier heights for holesand electrons (Fig. 148b). Narrowing and blue shift of theEL spectra from these structures as compared with thesefor the conventional DL LED have been taken as a proof forsuch an assignment. Even more venturous seems an assump-tion that single molecules can form quantum wells. Such anassumption has been made with rubrene molecules embedded

Figure 148 EL spectra (a) of the PBD and Alq3 (b) based conven-tional DL LED (c) and MQW structures (d) at room temperature.From Ref. 564. Copyright 1998 Institute of Physics (GB).




in an Alq3 thin (3nm) layer by multiple source organic mole-cular beam deposition method [565]. The nearly identical PLand EL spectra of a four-layer structure seen in Fig. 149 arecharacteristic of rubrene. The EL spectra have been reportedto narrow from 220 to 175meV, and their maxima to shift upto 55meV as the thickness of the Rb:Alq3 layer decreasedfrom 60 to 3nm. The interpretation of these observations interms of single (molecular) quantum well is highly unjustifiedfor several reasons, to mention only the lacking relationbetween the thickness of the emitter layer as a whole andextension of the quantum well corresponding to the molecularsize of rubrene or thickness effect on the layer morphology.The doping of emitter layers in organic LEDs has beenrecently shown to affect the type and characteristic para-meters of disorder in conventional organic structures[68,566]. These can markedly influence the shape of both PL

Figure 149 PL and EL spectra of the multi-layer structure shownin the inset. The principal maximum is characteristic of rubrene(Rb) doped in the thin (3 nm) layer of Alq3 [10% Rb:Alq3]. Adaptedfrom Ref. 565.




and EL spectra and must be taken into account before invok-ing the MQW interpretation of the experimental data.

5.3. LIGHT OUTPUT

The photon flux leaving unit area of a planar electrofluores-cent cell of thickness d is

FðextÞEL ¼ xZd

0

YðxÞdx ¼ xkF

Zd

0

SðxÞdx ð286Þ

where Y is the EL yield given by number of photons originat-ing in unit volume of the emitter per unit time (photon=cm3 s).It is important to remember that, generally, only a certainfraction of the light generated in the organic emission layer(EML) is available for the face detection from an organicLED. In a planar LED, a large fraction of the emitted lightis lost to waveguiding modes in the glass, ITO, and organic

the external (measured) EL intensity, FðextÞEL is largely affectedby these modes in addition to natural re-absorption and scat-tering losses. Its ratio to the internally (within EML) gener-ated light intensity, FEL, reflects the overall losses to theexternal modes, and defines the so-called ‘‘light outputcoupling factor’’

x ¼ FðextÞEL =FEL ¼ 1�Rð Þ 1� cosYcð Þ exp �axð Þ ð287Þ

The absorption loss is described here by the factor exp(�ax),where a is the linear absorption coefficient and x is the dis-tance traversed by light on its way from the generation siteto the external glass surface. The loss due to the total internalreflection is given by (1�R)(1� cosYc), where R representsthe reflectance coefficient and Yc¼ arc sin(n�1c ) is the criticalangle determined by the appropriate relative refractive indexnc of the material. The Y(x) in Eq. (286) is expected to be afunction of the distance from the emitting surface due to gen-erally non-uniform distribution of singlet emitting states S(x)




layers due to refractive index mismatching (Fig. 150). Thus

(cm�3

radiative decay of the excited states is characterized by therate constant kF (s�1).

5.3.1. Steady-state EL

In a simplified, often used, picture of homogeneously distrib-uted singlets, their concentration, S, under steady-stateelectron–hole recombination conditions, can be expressed bya simple equation

dS

dt¼ PSgnhne � kSS ¼ 0 ð288Þ

and

S ¼ PSg=kSð Þnhne ð289Þ

where g is the second order recombination rate constant to beidentified with geh defined in Sec. 1.3, kS¼ kFþ kn is the totaldecay rate constant including all non-radiative decays with

Figure 150 Different radiative modes in organic LEDs. Externalmodes available for the face detection ½FðextÞEL ] constitutes only a frac-tion of light generated in the EML, the remainder being lost due tovarious wave guide modes indicated in the figure.




) throughout all the sample thickness (see Sec. 3.3). The

the overall rate constant kn, and PS is the probability that asresult of the e–h recombination event a singlet excited state

The evaluation of FðextÞEL is now straightforward and leadsto

FðextÞEL ¼ xPSjFLgnhned ð290Þ

where the jFL¼ kF=kS determines the relative contribution ofradiative decay events of excited singlet states, identifiedoften with the fluorescence (FL) efficiency.

Equation (290) relates the EL output to the uniformthroughout the emitter concentrations of holes (nh) and elec-trons (ne) . The latter are naturally associated with hole (jhi )and electron (jei ) currents injected at the electrodes throughthe following kinetic equations:

jhied� nh

tht� gnenh ¼ 0 ð291aÞ

jeied� ne

tht� gnenh ¼ 0 ð291bÞ

Here, tt¼d=mF is the carrier transit time dependent on thecarrier mobility, m, and electric field, F, operating in the sam-ple. The bimolecular decay of holes and electrons can beexpressed by the recombination time

te;hrec ¼ gnh;e

� ��1 ð292Þ

to be compared with the monomolecular decay time, tt, ofcarrier discharge at opposite electrodes. Two limiting casesleading to simplified interrelations between FðextÞEL and injec-tion currents have been distinguished based on such acomparison [566a]. These are:

(i) Injection-Controlled EL (ICEL) for tt trec. Then,according to Eqs. (291), nhffi jhi =emhF, ne¼ jei =emeF, and

FðextÞEL ¼ xjFLPSgjei j

hi

e2memhF2d ð293Þ




will be created (see Sec. 1.4).

The important message that follows from Eq. (293) is that thelight output for organic LEDs operating in the ICEL modecannot be related directly to the driving current ( j) whichmust not be identified with the recombination current

jR ¼ gjei j

hi

e2memhF2d ð294Þ

and which is not known from electrical measurements. Forthe ICEL mode, the EL is a ‘‘side’’ effect of the current flowand its intensity is proportional to the product of the electronand hole injection currents. Several subcases of ICEL can beconsidered dependent on the carrier injection mechanisms

(ii) Volume-Controlled EL (VCEL) tt trec. In this case,the first order decay terms in Eqs. (291) can be neglected,the carriers decay totally in the bi-molecular recombinationprocess (a weak leakage of carriers to electrodes), jei¼jhi ¼ j, and

FðextÞEL ¼ xPSjFL

j

eð295Þ

Here, the measured current j is simply the recombination cur-rent, jR, and as long as x, PS and jFL do not depend on j, FðextÞELremains directly proportional to the driving current. The slopeof the linear plot ofFðextÞEL with j determines the product xPSjFL.

The variety of results on EL intensity vs. current flowing

and references therein). The FðextÞEL has been shown to increaseboth linearly and non-linearly with increasing current. Thelatter can be either sublinear and supralinear dependenton the applied voltage range. On the analytic side, the inter-play between the recombination and leakage current seems toaccount for the variety of observations. It is useful todistinguish between SL and DL LEDs because interfacialenergy and mobility barriers at two component organic layersin the DL devices increase largely the recombination current,leading to the VCEL operation mode or at least to itsapproximation. One expects the linear increase of FðextÞEL withincreasing drive current. In SL devices, it is more difficultto avoid the leakage of charge carriers to opposite electrodes,




from the electrodes [21] (see also Sec. 4.3).

through device has been observed experimentally (see Ref. 21

unless perfectly Ohmic electrodes are available. They usuallyoperate in the ICEL mode, and FðextÞEL becomes a complex func-tion of the drive current. A careful analysis of the experimen-tal data allows then to distinguish three segments of such adependence. An example is shown in Fig. 151. The non-linearincrease of the EL intensity vs. j in the low-current regime( j < 5mA=cm2), passes to a linear segment for the intermedi-ate currents regime (5mAcm�2 < j < 15mAcm�2) and tends

Figure 151 EL output as a function of driving current for four dif-ferent SL LEDs. (1) ITO= (25% TPD:25% Alq3:50% PC)(60nm)=Mg,(2) ITO=(50% TPD:30% Alq3:20% PC) (60nm)=Mg, (3) ITO=(70%TPD:10% T5Ohex:20% PC) (70 nm)=Ca, and (4) ITO=(25% TPD:25%Alq3:50% PC) (80nm)=Mg. For the molecular structures of the

tute of Physics (GB).




materials used, see Fig. 112. After Ref. 389 Copyright 2001 Insti-

to saturation at high current densities. This behavior reflectsthe gradual voltage evolution of the recombination to theleakage current ratio ( jR=jL; j¼ jRþ jL). Increasing at low vol-tages and remaining constant at moderate electric fields, itshows remarkable decrease at high voltages (large currentdensities). Deviations from the linear relationship FEL( j) alsooccur in DL organic LEDs. This is illustrated in Fig. 152showing the EL output vs. current density in a double-logarithmic scale for one of the most studied DL organic LEDsbased on the TPD=Alq3 junction. The low-current densitysupralinear increase followed by a slightly current-increasingEL output at moderate currents rolls off smoothly as the cellcurrent exceeds 100mAcm�2. All three segments of theFEL( j) curve have been approximated by the power-typefunctions with the powers given by the logFEL� log jstraight-line plots. This behavior can be explained by theICEL mode operation conditions predicting FEL( j) to follow

Figure 152 EL intensity vs. current density for DL LEDs basedon the TPD=Alq3 junction: (a) ITO=TPD(60nm)=Alq3(60 nm)=Mg=

3




Ag structure (left hand scale in absolute units) (see Ref. 21); (b)ITO=TPD(20 nm)=Alq (40nm)=Mg:Ag (see Ref. 356).

expression (293). By definition, the measured cell currentjffi j

ðeÞi þj

ðhÞi . Thus, Eq. (293) provides the EL output variation

with the measured current density ( j) in a form

FðextÞEL � j2

m�jSCLCð296Þ

where m� ¼ m�1h þ m�1e

� ��1. Since the current increase is

imposed by the increasing voltage applied to the cell, both jand jSCLC are the voltage-increasing quantities. Moreover,since by definition j < jSCLC, the FEL must be a function ofthe injection efficiency, jinj, defined by the ratio

jinj ¼j

jSCLC� 1 ð297Þ

The injection efficiency appears to be a crucial factor for thefunctional shape of FEL( j). Its variation with the applied vol-tage depends on the type and quality of the injection contact

contact ITO=TPD. The irreproducible behavior of theITO=TPD:PC junction is clearly apparent. The contact canrange from Ohmic to strongly blocking with the injection effi-ciency falling or rising with electric field. Moreover, the fall-ing trend can switch to a rising trend for the same sampleat a certain electric field strength. The irreproducible beha-vior of injection contacts enables understanding of the varietyof FEL

strongly increasing jinj at low fields (low current densities)and its much slower increase at high field (high current den-sities above 1mA=cm2). In the upper limit of the attainablecurrents (> 100mA=cm2), the FEL( j) approaches linearityand even a sublinear behavior may be seen from its log–logplot (the data with arbitrary units of FEL). The field-inducedenhancement of the injection efficiency is difficult to rigorousanalytical treatment because different preparation conditionsmodify the contact in microscopically uncontrollable manner.Therefore, the interpretation of the strong initial gradient@FEL( j)=@j remains an open question, though a more detaileddiscussion of the processes that underlie the EL efficiency




as illustrated in Fig. 153 for the commonly used hole injection

( j) characteristics. The data in Fig. 152 would indicate a

explanation for the gradient @FEL( j)=@j¼n< 2 (but n> 1) canbe proposed if a weakly varying jinj( j) and jhffi je obeying thethermionic injection mechanism (203) is assumed in additionto the exponential field increase of the mobility according toEq. (265). Under these premises, with the accuracy to aweakly varying function of F, and with bðeÞm ffi bhm ¼ bm,

FELð jÞ � j2�bm=a ð298Þ

The experimental value (2� bm=a)¼ 1.2 requiresbm¼ 0.76� 10�2 (cm=V)1=2 if a¼ 0.95� 10�2 (cm=V)1=2 isassumed as calculated from Eq. (204) with e¼ 2.4 for TPD(note that a slightly lower value for a is obtained in Alq3due to its higher e; but still the equality j

ðeÞi ¼ j

ðhÞi holds due

to a little difference in the injection barriers at ITO=TPDand Mg=Alq3 m is in good

Figure 153 The injection efficiency as a function of electric fieldfor three different ITO=50% TPD:50% PC=Au devices all preparedunder the same conditions and having similar thickness, dffi 19 mm(see numbers in the inset). Adapted from Ref. 352.




interfaces, cf. Fig. 84). This value of b

facilitates its understanding (see Sec. 5.4). A relatively simple

agreement with the data obtained from the field-dependenceof the TOF-measured mobility for holes [336,340] and elec-

3 inj

could explain a slightly sublinear plot of FEL( j) at high cur-rent densities. Some additional effects such as the currentdecreasing of the light output coupling factor (x) or the emis-sion efficiency (jFL) can contribute effectively to the satura-tion tendency at high voltages. Variations in the factor xcan occur as a result of the field-evolution of the recombina-tion zone. Its high-field (large current densities) confinement

of EL intensities in the direction normal to the substrate faceto that emitted from the edge of the substrate (FðsurfaceÞEL =FðedgeÞEL ). In the example shown in Fig. 154, the emission intothe external modes is roughly 50% larger than the internalmodes, decreasing by about 5% as the drive current increasesfrom 0.1 to 10mA=cm2. Stronger effects onFEL can be expected

Figure 154 The measured surface-to-edge EL intensities as afunction of current density in the DL ITO=a-NPD (50nm)=Alq3(50 nm)=Mg:Ag LED. Inset: experimental configuration of lightdetectors used to obtain data in the figure. Adapted from Ref. 494.




trons [336,425] (cf. Fig. 104) in Alq . A field-decreasing j

in the near-cathode region (cf. Fig. 150) may change the ratio

due to a reduction of jFL, caused by singlet exciton quenchingon charge carriers, structural defects and metallic contact it-self. The quenching of singlet excitons in organic LEDs basedon optimal 60nm-thick Alq3 emitters has been evaluated tocreate emission losses between 8% and 30% [566]. These arecomparable with the losses caused by high-field assisted dis-sociation of singlet excitons or their electron–hole pair precur-sors [302,305,306]. Triplet excitonic interactions have beenrevealed in EL–current relationships for aromatic crystals[2,21]. The total EL flux from these crystals comprises a fastand delayed component attributed to the radiative decay ofthe Prompt (PEL)- and Delayed (DEL)- formed singlet exci-tons. If the DEL component originated from singlet excitonscreated in the process of triplet–triplet annihilation (Sec.2.5.1), a superlinear increase of FEL with increasing currentwould appear even for the VCEL-mode operating devices:

FEL ¼ FPEL þ FDEL ¼ jFLPStS jþjFLg

ðSÞTTt

2T 2PS þ PTð Þe2d

j2

ð299Þ

The effective power of the FEL( j)� jn dependence can varybetween one and two, depending on the prompt and delayedcomponent contributions which are determined by the effec-tive lifetimes of singlet (tS) and triplet (tT) excitons along withthe probabilities of their formation in the e–h recombinationprocess (PS, PT

in addition on the T–T interaction constant [gðSÞTT] leading toa singlet exciton, and the sample thickness, d. The EL inten-sity as a function of the measured current for a number of aro-

EL data followa supra-linear relationship and can be approximated by apower dependence within limited ranges of the current. Theexplanation is that the total EL output reflects the averagedsignals from the PEL and DEL components according to Eq.(299); the increasing DEL increases the power ‘‘n’’. A decreasein the effective power for high currents seen for neat tetra-cene crystals (marked by the vertical arrows in Fig. 155a)would suggest the triplet–triplet and triplet–charge carrier




matic crystals is shown in Fig. 155. All of the F

; cf. Sec. 1.4). The DEL component depends




interactions to reduce the effective triplet exciton lifetimeaccording to

1

tðTÞeff

¼ 1

tTþ gTT � T2 þ gTqnq ð300Þ

In order to explain variations of ‘‘n’’ from crystal to crystal,the PS dependence on the trap depth of one of the recombiningcarriers may be invoked. The deeper trapped is the carrier,the lower is the probability of the formation of singlet excitonsin the electron–hole recombination process [see Eq. (10)].Thus, the plots with high ‘‘n’’ reflect the presence of deeptraps. This is confirmed by the high power of the FEL(l)� jn

dependence in doped tetracene crystals. A strong supportfor the triplet–triplet fusion origin of the DEL comes fromthe magnetic field effect on the EL from tetracene crystalswith different ‘‘n’’ the PL evolution withmagnetic field in tetracene is a consequence of the magneticfield effect on singlet exciton fission into two triplets only,the modifying action of the magnetic field on triplet–chargecarrier interaction can be seen in the magnetic field evolution

sented in Fig. 156 clearly shows that both singlet exciton fis-sion into two triplets and triplet exciton quenching by chargecarriers occur in the EL process. The reduced decrease in ELintensity at low magnetic fields (below 0.5kG) as comparedwith that for PL reflects the EL to contain a DEL component

Figure 155 The EL intensity as a function of the measured cur-rent in neat (a) and doped (b) aromatic crystals. The three curvesin part (a) are obtained for three different origin tetracene crystalsof thickness 16.5 mm (I), 118 mm (II) and 19.5 mm (III). The data forthe tetracene-doped anthracene and pentacene-doped tetracenecrystals are shown in part (b), where the EL intensity was mea-sured at host and guest emission bands (445nm for anthracene,598 and 575nm for tetracene and 620nm for pentacene); the nearcurve numbers denote the slopes of the straight-line log–log plots.Adapted from Ref. 51.

J




(Fig. 156). While

of the EL intensity (cf. Sec. 2.5.3). The shape of the plots pre-

quenched by the triplet–charge carrier interaction process.The overall effect is due to the magnetic field increase of the

in the triplet–doublet interaction rate constant gTq [see

decrease in gTq makes the low-field minimum of the EL(B)curves shallower (Fig. 156a) and leads to its disappearance inthe crystal with a large contribution of DEL (Fig. 156b). At thered edge (B curves), the EL, at least partly, originates fromtrapped states which can undergo fission into two inequiva-lent triplet excitons (heterofission [320]), the process lesssensitive to the magnetic field than the homofission. An anni-

the efficient production of trapped singlets resulting in thelarge DEL component of the red edge EL. Consequently, thelow dip in the magnetic field dependence of EL should bemarkedly reduced or disappear. This is indeed observed forthe crystal in Fig. 156b. The striking is the difference betweenthe power ‘‘n’’ for the host and guest electroluminescence from

Figure 156 A comparison of the magnetic field effects on the EL(curves B and C) of tetracene crystals with (a) low and (b) high

The change of photoluminescence (PL) as a function of B is shownby the broken line (curves A). The effect was measured in two differ-ent wavelength regions: A and B in the red edge and A and C in theshort wavelength and emission maximum. No difference in theshape of field evolution of PL was observed. Reprinted from Ref.287. Copyright 1975 with permission from Elsevier.




DEL component (crystals II and I, respectively, from Fig. 155a).

hilation of inequivalent triplets (see Sec. 2.5.1.2) can lead to

singlet fission g’s [see Scheme (80)], and monotonic decrease

Scheme (110)] as discussed in Sec. 2.5.3.1. The magnetic field

an anthracene crystal doped with a small amount of tetracene

EL( j) behavior in terms oftwo-component emission response according to Eq. (299) clea-rly proves that while the tetracene guest emission originatesfrom the tetracene singlets produced directly in the electron–hole recombination on guest molecules, the anthracene hostemission is dominated by the DEL originating in the course

To obtain the EL intensity (either surface or edge) froman EML constituting a part of a microcavity structure, weneed to know the intrinsic spectrum of the radiation fromthe emissive layer along with its angular intensity pattern,FEL(l,Yi). For a given l,

FEL ¼ 2pZ p=2

0

FEL Yið Þ sinYi dYi ð301Þ

Both, theory [494,567] and experiment [549,550] showFEL(Yi) [thus FEL

structure parameters and emission wavelength, the intensityangular pattern FEL

eral, from the classical Lambertian angular distribution ofradiation [568]. In measured angular depen-dence of monochromatic emission of a cavity and free-cavity

uniform spatial distribution nearly Lambertian can beobserved from the leaky ITO=glass anode device (lacking awell-defined microcavity) at wavelength 500nm close to theemission maximum (see Fig. 141b). The similarity of thefar-field intensity profiles has also been reported with (40–80nm) Alq3 layers for glass=ITO=PVK=Alq3=Mg:Ag=Ag LEDs[567] and in polymer LEDs [49,569,570]. In contrast, emissionfrom the microcavity structure becomes strongly directed ver-tically from a diode surface (Fig. 157a); the angle at the peakintensity varies from Y¼ 0� to Yffi 30� with selected emissionat 505 and 480nm, respectively. Clearly, no unique resonancecondition in the planar microcavity exists when the totalbroad band emission from the emitter is measured. Multiplematching of cavity modes with emission wavelengths occurs.




(Fig. 155b). The treatment of the F

(Y); cf. Fig. 142] to be a function of device

(Y) has been shown to deviate, in gen-

157, theFig.

devices from Fig. 141 are compared. Emission with a quasi-

of the bimolecular fusion of host triplets (see Sec. 2.5.1.2).

Thus, no sharp emission pattern can be expected with theoverall emission spectrum. Nevertheless, assuming the Lam-bertian shape of the emission from microcavity structuresmay lead to an overestimate as large as 30% [571]. Anattempt to compare the measured full spectrum externalemission as a function of the emitter thickness (Alq3) withtheoretical description of microcavity modes has shown sub-stantial disagreement, the theoretical estimates lead to theemission output much below the experimental data, differingby a factor of 2 for a 40nm-thick emitter [567]. The reason for

Figure 157 Radial plots of outer emission intensity from a micro-

ent emission wavelengths as indicated in the figure. After Ref. 550.Copyright 1993 American Institute of Physics.




cavity (a) and microcavity-free (b) structures from Fig. 141 at differ-

this discrepancy seems to be associated with different quench-ing efficiency of singlet excitons at the cathode due to a differ-ent location and width of the recombination zone. This pointis discussed in more detail in Sec. 5.4.

According to Eq. (290), high-brightness LEDs can be fab-ricated using highly fluorescent (high values of jFL) emitters,strongly injecting electrodes (high concentrations of recom-bining holes, nh, and electrons, ne), and minimizing lightlosses (high values of x) . Today, outstanding values exceeding105Cd=m2 for organic EL devices are reached. For example,luminance 1.4� 105Cd=m2 and a maximum EL efficiency2.4 d=A were observed at 12V from one of multilayer yellow-light emitting device structures using a highly fluorescentaluminum complex, tris(4-methyl-8-quinolinato)aluminium(III) Almq3 [572]. These LED structures and their lumi-

est luminance has been obtained with a multilayerITO=CuPc=TPD=coumarin 6:Almq3=Almq3=LiF=Al LED witha coumarin 6-doped Almq3 used as the emitter layer. Thelarge improvement in the device is due not only to dopingAlmq3 with coumarin 6, which is known as a highly fluores-cent laser dye being excited mainly by energy transfer fromthe host material [16], but also balancing the charge carrierinjection by using a 15mm-thick CuPc [573] as a hole-inject-ing contact and a 0.5 nm-thick LiF as an electron injectionelectrode [574]. This electrofluorescent LED also shows a highexternal quantum EL efficiency of 7.1% photon=carrier (for amore detailed discussion of the factors determining the EL

5.3.2. Pulsed EL

When addressing a LED by rectangular voltage pulse, a gra-dual rise of EL intensity is observed that reflects the interpe-

a voltage pulse and corresponding current and EL responsefor ITO=MEH-PPV=Al device. The EL response has beenobserved in selected spectral regions of the overall emissionspectra as shown in the same figure for three different




nance-voltage characteristics are shown in Fig. 158. The high-

netration of the charge carrier clouds. Figure 159 shows such

quantum efficiency see Sec. 5.4).

devices. The short-wavelength narrow bands in the EL spec-tra have been identified as the atomic emission lines of thecathode metal (Al, Mg or Ag), and the red-shifted broad emis-sion bands as being characteristic of excited states of the poly-mer [472]. The observation of polymer emission and cathodemetal emission from the same devices, showing the same tem-poral behavior, has been interpreted as due to hole transportproperties of the polymeric material. The delay time betweenthe onset of voltage pulse and the EL response has been foundto decrease with applied voltage [cf. (6)] in amanner fitting the Poole–Frenkel-type field dependence ofmobility (265) with mh (F¼ 0)¼ 1� 10�8m2=Vs and bm¼0.44� 10�2 (cm=V)1=2 (cf. comparable to thoseobtained previously for holes in PPV [575] and MEH-PPVdevices [356a,576]. This underlies the suggestion that thelight generation occurs in the vicinity of the cathode, the

Figure 158 Brightness vs. voltage applied to four EL devices (a)and molecular structures of organic materials used for their fab-rication (b). The curves correspond to the following structures: (1)ITO=TPD(30nm)=Almq3(70nm)=Mg:Ag, (2) ITO=CuPc(15nm)=TPD(30nm)=Almq3(70nm)=Mg:Ag, (3) ITO=CuPc(15nm)=TPD(30nm)=Almq3(70nm)=LiF(0.5 nm)=Al(100nm), (4) ITO=CuPc(15nm)=TPD(30nm)=coumarin 6(1%)-doped Almq3(15nm)=Almq3(55nm)=LiF(0.5 nm)=Al(100nm). After Ref. [572]. Copyright 1998 AmericanInstitute of Physics.




159(5),Fig.

106b)Fig.

delay between the onset of voltage pulse and the EL responseto be identified with the transit time of holes injected at theITO anode. The decay of the EL signal after the pulse isturned-off must reflect the recombination process inside the

Figure 159 EL spectra (a) and EL transients (b) for SL ITO=Polymer=Metal LEDs: (1) ITO=MEH-PPV=Al; (2) ITO=MEH-PPV=MEH-PPV=(Mg=Ag); (3) ITO=M3EH-PPV=(Mg=Ag). EL spectraare recorded at different voltage pulse amplitudes. Characteristiccathode metal emission lines are indicated along with the positionof broad band-red shifted emission maxima from the polymers. For

The transient current under a 1ms pulse (4) and transientresponse of EL polymer and cathode metal emission spectral regionsat two different pulse amplitudes, 4.3 MV=cm (5) and 6.6MV=cm (6)have been measured on ITO=MEH-PPV=Al device. EL transient arenormalized to the maximum intensity of the polymer emission.After Ref. [472]. Copyright 2000 American Institute of Physics.




chemicalmeaning ofMEH-PPV and ofM3EH-PPV, see Figs. 106 and108.

recombination zone. A somewhat faster decay of the cathodemetal emission than that of the polymer results from differentmechanisms of their excitation. Since the polymer emission isassociated with the electron–hole recombination on polymermolecules, a delay due to the final release time of the carriersfrom possibly existing near-cathode imperfections (traps) maycontribute to the overall decay constant. This is not the casewith the cathode metal emission which is featured of theimpact EL [2]. At high fields, the carriers (holes) gain anenergy exceeding 3 eV sufficient for impact excitation of metalatoms of the cathode [472]. The physical meaning of this pro-cess would be the injection of electron from the cathode to theelectronic states with energies below the polymer HOMOlevel. This process ceases immediately at the voltage pulseend, following the decay of the electric field at the cathode.To excite the Mg atom emission (383nm), a minimum energygain is 3.2 eV. As demonstrated experimentally, this energythreshold can be obtained for electric fields above 6.4 MV=cmif the electron mean free path ffi5nm is assumed. Such a largeelectron mean free path in low-molecular weight organic

ble in conjugated polymers for electrons within long polymerchains characterized by the average conjugation length ofca. eight monomeric segments [577,578].

An open question with SL devices is whether and, if so, towhat extent the accumulation of space charge near weakerinjecting electrodes (i.e., redistribution of the internal electricfield) affects the EL delay time. Such an effect could beexpected if a thin interfacial layer is built up between anorganic EL material and an electrode due to impurities(e.g., oxygen) or its chemical reactions with electrode formingmetals. The presence of the space charge would imply the ELdelay time dependence on offset voltages applied to the LEDbefore admitting the rectangular voltage pulse. In fact, tran-sient experiments for the SL ITO=Alq3=Mg:Ag LED haveshown the EL delay time (td) to be a function of dc bias vol-tages [341]. A detailed analysis of the experimental datahas shown an inverse relationship between td with increasingcurrent (j), the product td � j being of the same order of magni-




materials seems to be unlikely (cf. Sec. 4.6), but it is conceiva-

tude as CAlq3U (a few nAs), where CAlq3 denotes the electricalcapacity of the Alq3 layer. In contrast to the above discussedITO=MEH-PPV=(Mg=Ag) system, the recombination zone ishere located near the ITO anode, the leaking holes form aspace charge near the Mg:Ag cathode, which reduce the elec-tric field inside the Alq3 layer. This picture is consistent withthe fact that the injection barrier for holes from ITO to Alq3 is

the hole mobility being approximately two orders of magni-tude lower than that for electrons in Alq3 [336,579]. Also, itis supported by known ability of Alq3 to react with metalssuch as calcium, magnesium or gold [580–582]. However,the field dependence of me as well as its absolute valuesobtained from TOF and time-resolved EL measurements arecomparable suggesting the internal electric field to be homo-geneous and equal to the nominal value of the applied field[341]. More experimental data would help to resolve theseinconsistencies. The EL decay signal after the voltage pulseis turned off is in general non-exponential, reflecting eithera combination of the RC time of the experiment setup andthe time evolution of the recombination process of the chargeaccumulated in the sample [341], and=or radiative relaxationof the prompt and delayed components of excited singlets[415]. The former has been analyzed in more detail, using

single crystals of tetracene were provided with sodium–potassium alloy cathodes and semitransparent evaporatedgold layer anodes. The EL emission was collected from thegold film covered side of the crystals. Concurrently with thevoltage pulse (amplitude: U –U0¼ 90V; width 75 ms), the ana-lyzing generator was started producing narrow t0¼ 2 ms-dura-tion pulses with varying delay time 0.5 ms< td< 150ms. Thishas made possible to count the EL photons at different timesof the EL relaxation. Various levels of bias voltage (U0) wereapplied from a dc regulated voltage supply to get differentsteady-state current conditions for the pulsed EL. A fast(t< 10ns) and delayed (t> 1ms) components can be distin-guished in the time-evolving EL signal (Fig. 160a). The first




higher than that for electrons from (Mg:Ag) (cf. Fig. 84), and

DL EL devices, in Sec. 3.3 (Fig. 60), the latter is illustratedby the tetracene single crystal data in Fig. 160. Vapor grown

one has been attributed to the prompt fluorescence of singletexcitons produced directly by the electron–hole recombination

ated singlets emitting with a time characteristic of the tripletexciton lifetime (�10ms) [260]. The decay rate of the delayedcomponent is determined by triplet–triplet and triplet–charge

bination of detrapped carriers. Thus, it may differ from crys-tal to crystal and depend on the current flowing through thecrystal. The results presented in Fig. 160b support this con-jecture. Their detailed analysis has shown that while thedelayed EL component in crystal I follows detrapping ofcharge, the effective relaxation time of the delayed EL in crys-tal II is largely determined by the triplet exciton lifetime

Figure 160 Voltage (a) and current (b) dependence of the time-resolved EL in tetracene single crystals. (a) Reading from bottomto top are the bias voltage U0, the rectangular voltage pulses (U–U0), the relaxation curves of electroluminescence (F) referring tothe steady-stale EL level F0, the analyzing voltage pulses withvarying duration time t0 and delay time td. (b) The EL decay fortwo different thickness (d) tetracene crystals (crystal I: d¼ 16.5 mm;mm; crystal II: d¼ 118 mm) under different steady-state current con-ditions (1: j¼ 63 mA=cm2; 2: j¼ 23mA=cm2; 3: j¼ 0.7 mA=cm2; 4:j¼ 28 mA=cm2; 5: 6.1 mA=cm2). Adapted from Ref. [415].




process (cf. Fig. 4), and the second to triplet–triplet fusion cre-

carrier interaction processes (see Sec. 2.5), and by the recom-

reduced by triplet exciton–charge carrier interaction [415].This is consistent with steady-state EL output characteristics

In DL organic LEDs, the recombination zone is oftenlocated at the HTL=ETL interface and the EL delay withrespect to the onset of the rectangular pulse can then beascribed to the time for slower carriers to reach the interface.In Fig. 161, EL evolution in time from a DL LED based on theTPD=Alq3 junction is presented, showing the field-dependentdelay between the onset of a rectangular voltage pulse andthe EL response. The delay time has been attributed to theelectron drift time from the Mg=Ag cathode to the TPD=Alq3interface over the thickness of the Alq3 layer. A high-fieldindependent mobility of electrons meffi 1.2� 10�5 cm2=Vs,results from the linear decrease of the delay time with applied

Figure 161 EL evolution in time (a) and early time regime of theonset of EL (b) from an ITO=TPD(60nm)=Alq3(60 nm)=Mg=Ag DLLED after application of a rectangular voltage pulses as a functionof pulse amplitude (V). The vertical arrows show the EL onset. AfterRef. [309]. Copyright 1998 American Institute of Physics.




of the same crystals presented in Fig. 155.

field between 1.25 and 3.3MV=cm (Ref. 309) in good agree-

with much higher and strongly field-dependent electron mobi-lities obtained on three-layer LEDs of ITO=4,40,400-tris[n-(m-tryl)-N-phenyl-amino]-triphenylamine (MTDATA) (60nm) =TPD(20nm) =Alq3(60nm) =Mg:Ag [583]. Upon turning offthe external field, injection of carriers and the potential insidethe devices change in a way as to force the stored electronsand holes towards each other. The probability of their recom-bination is close to unity under VCEL conditions and the non-exponential decay of the EL signal of the form FEL(t)� tn with

currents as compared with the voltage-on stage, a momentaryincrease of the EL intensity (‘‘the overshoot’’) appears decay-ing by the same reasons as those in VCEL operated devices.The VCEL decay has been observed for an ITO=TPD=Alq3=Mg=Ag DL LED, and shown to be governed by the diffu-sion of holes injected from the ITO anode towards theTPD=Alq3sients with overshoots for a polymer-based DL LED are

with time. Increasing duration of the voltage pulse appliedto the device increases the ratio of peak to EL intensity, indi-cating the time increase of the space charge builtup at theinterface. The appearance of the overshoot effect depends onthe relation between recombination and leakage currentsunder steady-state conditions, thus, on the one hand, depen-dent on the injection efficiency of the electrodes, and, on theother hand, affected by charge transport properties of thematerials forming DL LEDs and energy barriers at theorganic materials junction. Therefore, replacement of thePVK matrix in the LED in Fig. 162 by polycarbonate, whichcauses an increase of the hole mobility, increases the relativeheight of the overshoot spike; the increased leakage currentwith voltage on makes the charge recombination better pro-nounced upon turning the voltage off [528].

Selection and combination of the operating currentmodes of organic LEDs allows to glean important information




shown in Fig. 162. The magnitude of the EL spike evolves

nffi 1 is featured of the Langevin-type recombination (see Sec.

ment with the data of Barth et al. [341], but being at variance,

1.3), and under ICEL conditions, due to the reduced leakage,

interface (see Sec. 3.3, Fig. 60). Typical ICEL tran-

on particular electronic processes underlying their light out-put and=or improve their performance parameters. For exam-ple, alternating current (AC) modulation of the EL intensityfrom LEDs operated in constant (DC) current mode showedwhy and how exciton concentration ratiovaries with injected charge (thus, voltage applied to thedevice). The AC–DC interaction in EL of anthracene crystalscould be observed by the separate light detection channels asshown in The AC modulation characteristics

of different response of two EL components: [584]

FEL ¼ xkF

Zd

0

SðxÞdxþ gðSÞTTk�1S

Zd

0

T2ðx; tÞdx

24

35 ð302Þ

Figure 162 Temporal evolution of the EL intensity from a DLITO=50% poly[1,4-phenylene-1,2-di(4-phenoxy-phenyl)vinylene](DPOP-PPV):50% PVK=20% PBD:80% methylpolystyvene(PS)=AlLED upon application of a rectangular voltage pulse of variableduration marked by the spikes of the overshoot EL signals. Adaptedfrom Ref. 528.




(Fig. 164) of the DC EL output have been analyzed in termsFig.

triplet-to-singlet

163.

decay of singlet excitons produced directly by electron–holerecombination and the second is a delayed component (DEL)arising from singlets created by triplet–triplet annihilation,triplets being produced in electron–hole recombination (see

above discussion of the results inroot-mean-square modulation

brightness jF�j to the steady-state EL intensity (F) decreases

modulation voltage (Fig. 164b), and reveals a maximum at acertain DC bias, except for the lowest frequencies (Fig. 164c).This behavior has been rationalized by a model of sinusoidal

sinusoidal voltage U�¼U0 sin 2pnt (if small as compared witha steady-state voltage bias) to produce the current wave ofwavelength l¼ mF�=n, propagating in the crystal of thicknessd,

~jj x; tð Þ ¼ jþ j0 sin 2p nt� x=lð Þ½ � ð303Þ

Figure 163 Scheme of the experimental arrangement for ACmodulation of EL with DC voltage bias of a crystal LED. The photo-multiplier (PM) signal produced by the emitted light (hn) is detectedeither by a DC or an AC selective milivoltmeter, placing theswitches K1 and K2 into positions 1 and 2, respectively, which corre-spond to the DC(F) or AC(F�)-excited electroluminescence. The HVsupply allows DC bias of the sample under sinusoidal AC excitation.Reprinted from Ref. 584. Copyright 1983 Springer-Verlag, withpermission.




Fig.

The first is a prompt component (PEL) due to the radiative

154, 155, and 159). The

with the modulation frequency (Fig. 164a), increases with the

also1.4,Secs. 2.5.1.2;

current wave [584]. (see also Ref. 2). This model assumes a

where j is the steady-state current flowing through the crystaland F�¼U=d is the average field through the sample. Thecurrent wave represents a carrier flux moving along the fieldlines. The concentrations of singlet S(x) and triplet T(x,t)excitons can be expressed by j~ solving the rate equations:

dS

dtþ kSS ¼ a~jjþ gðSÞTTT

2 ð304aÞ

Figure 164 The AC modulation signal (F�) related to the DC-biassignal (F) from a 32 mm-thick single anthracene-crystal LED [CuIanode=anthracene=(Na=K)cathode] as a function of: (a) AC voltagefrequency (n) at Urms¼ 14V for three different DC bias voltages.Experimental data are given by dots, theoretical fit by solid lines.(b) AC root-mean-square modulation voltage (Urms). Solid lines forn¼ 6kHz , dashed lines for n¼ 6Hz at different bias voltages,U¼ 200V (c), U¼ 500V ( ), and U¼ 700V (�). (c) DC bias voltageat the modulation voltage Urms¼ 14V with different frequencies,n¼ 6Hz (�), n¼ 60Hz ( ), and n¼ 6kHz (`). Reprinted from Ref.584. Copyright 1983 Springer-Verlag, with permission.




dT

dtþ kTT ¼ b~jj� gTTT

2 ð304bÞ

where a¼PS=ew and b¼PT=ew are generation terms of sing-let and triplet excitons within the recombination zone ofwidth w. Note that kT (the effective mono-molecular tripletexciton decay rate constant) and j~ are functions of steady-state voltage U which leads to important consequences inthe interpretation of the DC voltage dependence of the ACmodulation depth jF�=Fj. Solving Eqs. (304) and insertingS(j~) and T(j~) to Eq. (302) yield analytical expressions for bothF and F� as functions of U�, U and n [584]. They predict thegeneral behavior of the jF�=Fj ratio as a function of thesevariables, and allow a quantitative fit to the experimentaldata. The experimental jF�been fitted with optimized triplet exciton lifetimes tT¼ 5.7, 4and 0.8ms going from U¼ 150V, through 300 up to 700V.The triplet exciton lifetime decreases with DC bias voltagebecause of the voltage increasing concentration of charge car-riers which act as effective triplet exciton quenching centers.The shortened triplet exciton lifetime results in a reduction ofthe DEL (but not PEL) intensity [the second term in thesquare brackets of Eq. (302)], and the voltage varying tripletexciton lifetime can account for this behavior. We note thatincreasing U translates into increasing j and current wave-length l in Eq. (303) defining the current wave. Three majorranges in the frequency decrease of the jF�=Fj can be distin-guished: the low-frequency range (<100Hz), where a nearlyconstant high value of MD is observed, the high-frequencyrange (>10Hz) with a nearly constant but much lower MD,and the intermediate frequency range (100Hz–1kHz), wherethe relative modulation signal decreases markedly. The rea-son for such a cascade-like behavior is the changing relationbetween the modulation period (n�1) and the effective tripletexciton lifetime. In the low-frequency range [n< kT(U)], thecharge concentration changes are slow enough for triplet exci-tons to follow them during the triplet lifetime, both PEL andDEL intensities are subject to the AC modulation. For n com-parable with kT, the quenching of triplet excitons and follow-




=Fj ¼ f(n) curves in Fig. 164a have

ing modulation of the DEL component become less efficient,the MD decreases within the intermediate frequency range.As the frequency continues to rise (> 1kHz) only the PELcomponent can be modulated, MD saturates with increasingfrequency. Naturally, the range of both low- and high-fre-quency plateau increases with increasing DC bias voltagebecause the accompanying increase of the concentration ofthe injected charge reduces the lower and upper limits ofthe effective triplet lifetime [cf. Eq. (300)]. Further, one wouldexpect nlimffi kSffi 108Hz to be a limiting frequency of the mod-ulation since for n> nlim the period of U� becomes shorterthan the singlet exciton lifetime tSffi 10ns [333]. This rela-tively high value of n can, however, be effective only in thincrystals or films for which d=mF� < 10ns. This means thatwith F�¼ 104V=cm, dlim¼ 1 mm. For any d=F� < 10�4 (cm=V)dlim(cm), nmax< nlim and should increase, as the DC voltageincreases. These predictions are confirmed by the experimen-

mental values of the effective nmax and those calculated asmF�=d come from the assumption F�¼U=d, which, for spacecharge limited current conditions holding in this experiment,is only a rough approximation. As intuitively understood, themodulation depth increases with U�, a linear increase beingobserved at the highest DC voltages (Fig. 164b). The periodiccarrier injection used above for explaining the U� frequencyand strength modulation of a DC-biased EL signal from ananthracene crystal-based LED is insufficient to understandthe non-monotonic variation of the MD with DC bias voltageapparent at higher frequencies (Fig. 164c). Redistribution ofsinglet to triplet concentration ratio with DC is required toattain this goal. Due to a relatively low concentration of thecharge stored in the crystal, positions of quasi-Fermi levelsare far from suitable free carrier bands (taken to be positivewith the gap-sided edge of the bands) at low voltages andthe probability PS of creation of excited singlets can be verylow because it is to a large extent controlled by the deeplytrapped free charge carrier recombination process describedby Eq. (10). The trapping levels are filled sequentially as Uincreases and the shallow-trapped-free carrier recombination




tal results of Fig. 164a. Some differences between the experi-

dominates the recombination process. Since PT is practicallyindependent of U (can change between 3 =4 and 1; see Sec.1.4), the total voltage dependence of PS=PT proceeds throughPS(U). Thus, modulating AC voltage changes the concentra-

of charge and indirectly by periodic shifting the position ofquasi-Fermi levels among a manifold of deep traps. If at lowvoltages PS is very low, the EL output is dominated by thedelayed EL component proportional to the concentration oftriplets T� jtT. Modulating DEL at low frequency (e.g., 6Hzin the MD jF�=Fj follows roughly the voltagedecreasing triplet exciton lifetime, the effect compensatedpartly by increasing ratio FPEL=FDEL. As a consequence, aslightly decreasing modulation effect is observed. At highervoltages, when FPEL=FDEL ratio becomes established at a con-stant level, reflecting spin statistics in the formation of singletand triplet excitons, the MD follows roughly a decreasingvalue of the triplet exciton lifetime. The same situation occursat higher modulation frequencies in the high-field region.However, a remarkable difference can be seen in the low-vol-tage region. Here, the increasing MD is explained by thedecreasing role of triplet–charge carrier interactions the MDincrease being assigned to the increasing PS=PT ratio.

Charge trapping modifies the overall performance oforganic LEDs significantly [585,586]. The EL output from aDL=LED based on vacuum evaporated blue emitting film ofpara-hexaphenyl has been shown to increase by more thanone order of magnitude as the period of duty cycle of thepulse operated devices increased from tffi 10ms (determinedby the RC time constant of the experimental setup) to

injection enhancement at the Al cathode due to the enhancedfield imposed by the space charge of holes blocked at thePHP=DOB interface. The magnitude of the enhancement isdetermined by the accumulation build-up time on a millise-

bility of organic EL devices driven by different current modes.The device driven by the PC mode shows better stability com-pared with the devices operated in the DC and AC modes.




Fig.

tion of emitting singlets by directly varying the concentration

164c),

500ms (Fig. 165). It has been rationalized in terms of electron

cond time scale [585]. Figure 166 compares the luminance sta-

While the light output decreases to 70% of its initial valueafter 250hr for the DC driven device, this period increasesthrough 500hr for the PC up to 1000hr for AC operateddevices. The origin of these differences is, as yet, not quiteclear although some possibilities, including trapping effects,can be speculated. In general, they must be associated withchemical and morphological changes in the bulk as well asat electrodes during continuous device operation. Chemicalreactions lead to degradation of the emitting layer, producingeffective quenchers of the emitting states. The degree of thedegradation proceeds with the number of charges passedthrough the device (thus, operation time). A likely cause forthe most rapid degradation mechanism (�100hr time scale)of organic device layers is a morphological change of the mate-rial. It is likely that the initial disorder ‘‘frozen’’ in metastablemolecular orientations, relax to a more crystalline stateaffecting carrier transport and shape of the emission spec-trum. This relaxation would occur more rapidly at highertemperatures and high applied fields. The microscopic originof the luminescence loss may be related to a change in the car-rier mobility or carrier injection, which, for example, would

Figure 165 Chemical structures of hexaparaphenyl (PHP) and4,40-diamino-octofluorobiphenyl (DOB) and the device structurebased on these materials (a). The EL output vs. period of appliedvoltage rectangular pulses (Uappl¼ 14V; F¼ 0.7MV=cm; j¼ 11mA=cm2); duty cycle 50% (the dashed line is a guide to the eye) (b). AfterRef. 585. Copyright 1998 Wiley-VCH, with permission.




worsen the carrier balance. In contrast to the LEDs based onlow-molecular weight organic materials (cf. Fig. 166), thelongest term degradation mechanism in polymer LEDs seemsto be independent of the current operation mode. Time for thedevice luminance to drop to half of its value is roughly thesame for the DC and PC driven devices, but decreases largely

that ultimate degradation of these polymeric devices comesmainly from a bulk degradation of the polymer film, resulting

Figure 166 The time dependence of device luminance (a) for athree layer LED (b) operated at a field ca. 1MV=cm as driven bythe direct current (DC), alternating current (AC) and pulsed cur-rent (PC) modes. The frequency of the pulsed excitation was1 kHz for both the AC and DC modes. After Ref. 586. Copyright2000 Jpn. JAP, with permission.




with temperature as shown in Fig. 167. These results suggest

in a loss of luminance, whereas, low-molecular weight mate-rial-based devices seem to include more markedly interfacialdeterioration mechanism such as oxidation and oxides decom-positions at electrodes, diffusion of metals and their reactionswith organic molecules (for a more systematic description ofdegradation mechanisms in organic LEDs the reader isreferred to Nguyen et al. [3]).

Figure 167 Time for the derivative of PPV (OC1C10)-based device,ITO=polyaniline(50 nm)=OC1C10(100 nm)=Ca=Al, to drop to half-luminescence of its initial value plotted as a function of tempera-ture. The circles indicate 3 cm2 single pixel devices driven in DC.Squares indicate data for pixellated displays driven in pulsed mode(1=16 duty cycle, 200Hz, same average luminance as DC devices).Current density for DC driven devices is 8.3mA=cm2. After Ref.587. Copyright 1999 American Institute of Physics, with permission.




5.4. QUANTUM EL EFFICIENCY

The quantum EL efficiency is one of the most importantcritical figures of merit for organic LEDs and by definitionrelates the photon [hn(J)] flux per unit area [FEL¼ IEL=hn(photon=cm2 s), where IEL is the light energy (radiant) fluxper unit area (J=cm2 s)], and the carrier stream per cm2

( j=e) of the device as the ratio

jEL ¼ eFEL=j ðphoton=carrierÞ ð305Þ

This quantity is a measure of the degree of the conversion ofthe current into light. The quantum efficiency (QE) defined byEq. (305) can be associated with other performance para-meters such as the dimensionless energy conversion efficiency

Z ¼ EEL

Uið306Þ

where EEL is the light-energy (radiant) flux (Watt) and Ui isthe electrical power (Watt) supplied to the device

jEL ¼eU

hnZ ð307Þ

It follows from Eq. (307) that for the applied voltages U> 3V,jEL> Z whenever emission occurs within the visible lightrange. We note that the definition equation (305) assumesmonochromatic emission at a constant photon energy, hn.Commonly, the radiant flux IEL is measured over the totalemission band f(hn), and the averaged photon energy hhnimust be used to obtain FEL,

hhni ¼R10 hnf ðhnÞdðhnÞR10 f ðhnÞdðhnÞ

ð308Þ

Furthermore, for the face detected emission (as usually is thecase), the light output coupling factor (287) reduces the mea-sured FEL to FðextÞEL , so that we deal with the external quantumEL efficiency

jðextÞEL ¼ xjEL ¼ eFðextÞEL =j ð309Þ




ciency, jEL (cf. discussion in Also, the angularintensity pattern of the emitted light must be taken intoaccount [cf. Eq. (301)]. So that, the precise estimation of theEL QE requires experimentally measured angular distri-

emission spectrum (note that emission spectra differ ingeneral when measured at different observation angles) (see

EL(hn,Y), and then their summation

jðextÞEL ¼2pxe

R10 IELðhn;YÞ sinYdðhnÞdYR1

0 hnf ðhnÞdðhnÞ.R1

0 f ðhnÞdðhnÞð310Þ

Commonly, the Lambertian emission pattern is assumed, andEq. (310) often approximated by

jðextÞEL ffi pexjhhni

Z 1

0

IELðhnÞdðhnÞ ð311Þ

For the integral in Eq. (311), the total energy flux per unitarea as measured by a radiometer at the normal directionto the emissive surface is substituted. This approximationcan lead to substantial (up to 30%) deviations from the exter-nal value of the EL efficiency expressed and measured accord-ing to Eq. (310) [571].

In optoelectronic applications, photometric quantitiesare often used to express the degree of the current conversioninto light. The luminous efficiency with the Lambertian emis-sion pattern is

jðextÞEL ðLÞ ¼pL0

j

Cd

A

� �ð312Þ

where L0 is the luminance L (Cd=m2) at normal incidence.The luminous efficiency of 1Cd=A corresponds to 4p lm=A.The photopic vision function V(l) must be invoked to translateluminous to physical quantities [588].

jðextÞEL ¼ pexL0

hKm jhhni

Z 1

0

f ðhnÞVðhnÞdðhnÞ ð313Þ




Figs. 140–142); I

Sec.which can be a small fraction of the internal EL quantum effi-

bution of the EL intensities at all wavelengths within the

5.3).

The constant Km¼ 673 lm=W is here the luminous efficiencyat l¼ 555nm, where the function V(l) reaches its maximum.For example, a very high luminous efficiency 28Cd=A�350 lm=A for an electrophosphorescent LED based on the Ir(p-py)3:CBP emitter translates into the power conversionefficiency Zffi 30 lm=W(� 0.056) and the quantum efficiencyjðextÞEL ffi 10% photon=carrier at Lffi 100Cd=m2 [589].

By comparing Eq. (309) with Eq. (295), the external ELquantum efficiency

jðextÞEL ¼ xPjr ð314Þ

can be simply expressed by the probability of creation of asinglet (P¼PS) or triplet (P¼PT) exciton and the efficiencyof their radiative decay (jr). It is important to note that Eq.(295), thus (314), assumes the recombination probabilityPR¼ 1. This is indeed the case when the driving current coin-cides with the recombination current, or in other words, forthe upper limit of the VCEL operating LEDs. Whenever, theLED function obeys the ICEL operation mode, Eq. (295) isno longer valid, and

jðextÞEL ¼ xPPR � jr ð315Þ

where

PR ¼krec

krec þ kt< 1 ð316Þ

is the recombination probability defined by the bimolecularrecombination (krec) and monomolecular (kt) decay first orderrate constants.

To get a better physical picture of the phenomena under-lying PR, it is convenient to replace the rate constants by theirinverses trec¼ k�1rec and tt¼ k�1t which have been defined as therecombination time (292) and carrier transit time (248),respectively. Then,

PR ¼1

1þ trec=ttð317Þ




From Eq. (317), it is clear that maximizing PR (thus j ðextÞEL )

requires minimizing the ratio trec= tt , P R ! 1 as trec =t t ! 0.For trec ¼ tt , PR ¼ 1= 2, and for t rec=t t 1, PR ffi tt = trec . TheICEL and VCEL modes can be redefined on the basis of PR .The ICEL mode, when the major carrier decay is due to theelectrode capture, assumes PR < 1= 2, i.e., t rec= tt > 1; the VCELmode under the carrier decay dominated by the recombina-tion applies for PR > 1= 2 , i.e., trec =t t < 1. The PR and thustrec= tt ratio can be determined from the absolute value ofj ðextÞEL if x, P and jr are provided independently [see Eq.(315)]. Since, typically, j ðextÞEL shows a non-monotonic depen-dence on driving voltage (field applied to a device), the fielddependence of trec= tt has been extracted from such experi-

cence and electrophosphorescence quantum efficiency alongwith the luminescence efficiency are presented, and the fielddependence of trec =t tIndependent of the LED structure, the initial field (or cur-rent) increase in ELQE is followed by the roll off precededby more or less broad maximum dependent on the carrierinjection efficiency from the electrodes and transport proper-ties of the materials forming the EL device. Caution is appro-priate concerning the generalization of some literature results

be simply due to the limited range of the applied field or tomodified external interactions of excitons with metal electro-des (see discussion below). Figure 170c,d shows the variationsof trec=tt with applied field. As expected, the minima occur atthe field strengths corresponding to those for the maxima ofthe ELQE (Fig. 170a,b). The ratio trec=tt exceeds unity withinthe entire range of electric fields attained, though for thehighest concentrations of TPD in the HTL, it approachesunity. This indicates that all these LEDs operate in theICEL regime approaching the demarcation value oftrec=tt¼ 1 (PR¼ 1=2) below which the VCEL mode sets in.The absolute values of the trec=tt ratio as well as their electricfield gradient may be a subject to some uncertainties asso-ciated with the assumption of the field independence of x, P,




mental data. In Fig. 168, several examples of electrofluores-

given in addition in Figs. 169 and 170.

showing the high-field saturated (see e.g., Ref. 474) orincreasing (see e.g., Ref. 397) EL efficiencies, since they can




and jr. However, the apparent trend of the ratio to decreasewith concentration of TPD in HTL suggests its values (thus,jðextÞEL ) to be associated with the injection efficiency of holes.In fact, using the definition equations for trec (292) and tt(248), we find

trectt¼

me;hFgnh;ed

ð318Þ

which for comparable concentrations of holes and electrons(nhffine) translates into

trectt¼

eme;hðme þ mhÞF2

gjd¼ 8

9

e

e0eme;hðme þ mhÞ

meffgjSCLj

ð319Þ

where jSCL=j is the inverse of the injection efficiency definedby Eq. (297) and meff is the effective mobility of the carriers(237) under double injection current ( j). Assuming me,h and g

Figure 168 The EL external quantum efficiency as a function ofapplied field (a) and luminance efficiency as a function of appliedvoltage (b) for various organic LEDs. 1:ITO=[6% wt Ir(ppy)3:74wt% TPD:20wt%PC](50nm)=100%PBD(50nm)=Ca=Ag; 2:ITO=TPD(60 nm)=[0.5wt%quinacridone(QAC):Alq3](50 nm)=Mg; 3:ITO=TPD(60 nm)=Alq3 (60nm)=Al-CsF; 4: ITO=TPD(60nm)=Al-LiF; 5: ITO=TPD(60nm)=Alq3(60nm)=Mg; 6: ITO=(75wt%TPD :PC) (60nm)=Alq3(60nm)=Mg; 7: ITO=(75wt% TPD:PC)(60nm)=Alq3(55nm)=Mg; 8: ITO=TPD(60nm)=(0.5% QAC:Alq3)(50nm)=Al; 9: ITO=polyethylenedioxythiophene(PEDOT)(20nm)=terphenyl-PPV(80nm)=low-work function cathode; 10: ITO=PEDOT(20nm)=polyspiro[2,20,7,70-tetrakis (2,2-diphenylamino)spiro-9,90 bi-fluorene (Spiro-TAD); 2,20,7,70-tetrakis (2,2-diphenylvinyl) spiro-9,90

bifluuorene (Spiro-DPVBi)] (80nm)=low-work function cathode; 11:ITO=PEDOT(20nm)=Spiro-TAD(20nm)=[Alq3:DCM](10nm)=Alq3(30nm)=cathode (not speci-fied); 12: ITO=polystyrene sulphonate(PSS):PEDOT=polyfluorenes or PPV=low-work functionmetal cathode(ink-inject printed organic layers); 13: as in item 12 with the spin coat-ing prepared organic layers; 14: ITO=PEDOT(20nm)=[4wt% PtOEP:(PMMA:Alq3(1:1)) (100nm)]=Ca=Al; 15: ITO=PEDOT(20nm)=[4wt%PtOEP:(PMMA:PBD)(1:1)(100nm)]=Ca=Al.

J




to be field-independent parameters, the ratio trec=tt is inver-sely proportional to the injection efficiency jinj¼ j=jSCL. Thedecreasing tendency in the trec=tt ratio with increasing con-centration of TPD in HTL is compatible with this predictionsince the injection efficiency increases as the concentrationof the electron donor centers (TPD) at the contact with ITOincreases [see discussion of Eq. (271)].

Equation (319) expresses that the field dependence of theratio trec=tt is governed by the field dependence of the mobili-ties, me, mh, recombination coefficient, g, and injection effi-ciency, j=jSCL. For the Langevin recombination mechanism,the g is governed by the carrier motion [see Eq. (4)] so thatEq. (319) can be simplified to

trectt¼ 8

9

me;hmeff

jSCLj

ð320Þ

Two different expressions have been presented for meff in Sec.4.5, for the weak recombination case (240) and for the strong

Figure 169 External quantum efficiency of molecularly doped-

(a), and recombination-to-transit time ratio for three of them,obtained from Eqs. (315) and (317) with P¼PS¼ 0.25, x¼ 0.6 andjr¼ 11% for LEDs 1,2 and 3, respectively (b). After Ref. 389. Copy-right 2001 Institute of Physics (GB), with permission.




polymer-based SL LEDs from Fig. 151 as a function of electric field

recombination case (241). They would correspond to the ICELoperating LED’s ratio

trectt

� �ICEL

ffi 2

3ffiffiffipp

me;hffiffiffiffiffiffiffiffiffiffimemhp

jSCLj

ð321Þ

Figure 170 External EL quantum efficiency plotted against cur-rent density (a) and against applied field (b) driving ITO=(%TPD:PC)(70 nm)=Alq3(60nm)=Mg=Ag DL LEDs with different con-centrations of TPD in the HTL (given in the figure). Correspondingrecombination-to-transit time ratio calculated from Eqs. (315)and (316) using the data for jEL and x¼ 0.6, jr¼ 25% andP¼PS¼ 0.25, and plotted against the current (c) and applied field(d). After Ref. 303. Copyright 2001 Institute of Physics (GB), withpermission.




and to the VCEL operating LED’s ratio

trectt

� �VCEL

ffi 8

9

me ;hme þ m h

jSCLj

ð 322Þ

The experimental values of trec =t texceeding unity, and of jinj ¼ j= jSCLindicate that the ICEL operation mode occurs typically forTPD= Alq3 junction-based LEDs, and t rec=t t should obey Eq.(321). A higher value of j ðextÞEL for the (75% TPD:PC) HTL ascompared with the 100% TPD HTL LED can be explainedby different morphology of recrystallizing pure TPD andTPD mixed with PC binder layers. Due to the mass transportfor crystallization of initially amorphous pure TPD films, bareITO glass islands are formed [596] reducing the effective areafor hole injection. The polymer (PC) suppresses the crystalli-zation process in the (TPD:PC) layers, making them lessrough [597] and covering uniformly accessible area of the sub-strate. Thus the injection current from ITO is a result of tradeoff between the effective injection area and concentration ofelectron donor centers (TPD) in the HTL [303]. Taking

Figur e 171 Comparis on of the electr ic field depend ence of injec-tion efficie ncy for the TPD =Alq3 junction-ba sed DL LEDs usin gthe experim ental data for j publishe d in the literat ure and jSCLC cal-culated from (236) and (241) assumin g meff ¼ me þ m h wit hmh ¼ mh(TPD) þ me(Alq 3) ffi m h(TPD) ffi 5.2 � 10� 4 (cm 2 =V s) exp(0.0 187F 1=2

(1) ITO =75% TPD:PC (60 nm) =Alq3 (35 nm) =Mg =Ag. (2) ITO =75%TPD:PC (60 nm) =Alq3 (55 nm) =Mg =Ag, (3) ITO =75%T PD:PC (60 nm) =Alq3 (120 nm), (4) ITO =75% TPD:PC (60 nm) =Alq 3(60 nm) =Mg =Ag

3

3

3 (8)ITO=100% TPD(60nm)=Alq3(60nm)=Al-LiF AC (see Ref. 590). (b)Theoretical fit (solid lines) according to the diffusion-controlledinjection current DCC (231), j¼ 5� 10�6 exp(0.017 F1=2) andSchottky-type injection current (203), j¼ 5� 10�6 exp(0.0095F1=2).Circles and up triangles are the data 4 and 6 from part (a).

I




if Figs. 169 and 170, all1 as shown in Fig. 171

(See Ref. 303), (5) ITO =100% TPD(60 nm)=Alq (60 nm) =Mg (se e

), and e ¼ 3. (a) The data obtained for the follow ing str uctures:

Ref. 590), (6) ITO = 100% TPD (47 nm) =Alq (62 nm) =Mg:Ag (see Ref.303), (7) ITO =100% TPD (60 nm) =Alq (60nm)=Al-CsF=Al,




(trec= tt ) ffi 5 at 106 V =cm (100% TPD= Alq3 e,h=ffiffiffiffiffiffiffiffiffiffime m hp ffi 10� 2 follows from Eq. (321) using jSCL =j ¼ 1.4 � 103

e h choice forthe me,h in the numerator of the ratio me ; h =

ffiffiffiffiffiffiffiffiffiffiffiffiffime � m hp ¼

ffiffiffiffiffiffiffiffiffiffiffiffime =m h

p,

and me= mh ffi 10� 4. This is not the case neither for m e and m hin Alq3 ( me =m h

2e in Alq 3 and mh in

TPD ( me =m h ffi 10� 2; Refs. 336 and 338). Thus, the only possibi-lity to rationalize this ratio is attributing mh ffi 10� 7 cm 2=Vs toholes in Alq3 and m e ffi 10 �11 cm2= V s to electrons in TPD (atF ¼ 106 V= cm). The latter is a very low value, difficult to mea-sure under usual TOF conditions as reported in the literature[338]. We note that applying Eq. (322) to the same data givesme ffi 10 �2 mh which could relate the electron mobility in Alq 3( ffi 10� 5 2

( ffi 10� 3 cm2= V s; Ref. 338). The latter can be easier acceptablefor the lowest trec =t t ! 1 obtained with the (75% TPD:PC)= Alq3 structure at F ffi 1.4 � 106 V = cm (Fig. 170d) and withjinj ffi 10� 2 (Fig. 171a). An important message follows fromFig. 171b. The figure reveals a distinct difference betweenthe field dependence of the injection efficiency for the currentscontrolled by diffusion (see Sec. 4.4) and those limited by thefield-assisted thermionic injection (see Sec. 4.3.2). Both jDCC

and jILC are proportional to the product F3=4 exp(beffF1=2),

but bDCCeff ¼aþ bm as compared with bILCeff ¼a. Clearly,

bDCCeff > bILCeff because the former contains a term bm character-

istic of the Poole–Frenkel-type electric field increase of thecarrier mobility [cf. Eq. (265)]. The field dependence of thejDCC=jSCL ratio agrees very well with the experimental datafollowing the DCC behavior of j with bðDCCÞ

eff ¼ 0.017 (cm=V)1=2

[68]. This does not exclude the occurrence of the ILCs in otherEL structures. It is worthy to note here that the (trec=tt) ratiodiffers from zero (PR< 1) even for j¼ jSCL. Yet

trectt

� �SCLC

ffi 1

1þ mh;e=me;hð323Þ

according to Eq. (322), and trec=tt! 0 (PRffi 1) only if mh,eme,h. For mh,e¼ me,h, trec=ttffi 1=2 (PRffi 2=3), and for mh,e me,h,




in Fig. 170d) m

from Fig. 171a (curve 4). This implies the m m

ffi 10 ; see Ref. 336) nor m

cm = V s; see Ref. 341) to the hole mobility in TPD

trec= tt ffi 1 (P R ¼ 1 =2). Let us consider the case of an SL LEDbased on TPD, where mh me . Surprisingly, the PR for holesand electrons is different. Equations (323) and (317) yieldtrec= tt ffi 1 and P R ¼ 1 =2 for holes, and t rec= tt ! 0 and P R ffi 1for electrons. However, it can be understood if the spatial dis-tribution of the injected charge will be taken into account. Theformal condition for the SCL current is the concentration ofthe injected charge at the injecting contact to attain infinity

rec ¼ ( gn )� 1 ! 0 only at the contacts.Since fast holes reach the opposite contact (cathode) after ashort time ( tt ! 0 for m h !1), and slower electrons reach theanode after a much longer time (tt !1 for m e ! 0), the ratiotrec= tt for holes equals 1, and tends to 0 for electrons. Thisreflects in the position and width of the recombination zoneas discussed already in Sec. 3.3 and addressed in more experi-mental context later on in this section. It follows from experi-ment that the injection efficiency and carrier mobilitiesincrease or at least not diminish at high electric fields (F >10 5 V =cm) in amorphous or polycrystalline organic layers for-

should give a monotonic decrease in trec= tt (320), unless me,h isa much stronger field increasing function than meff. As a con-sequence PR and j

ðextÞEL are expected to be monotonically inc-

reasing functions of applied field. Indeed, such a behavior canbe observed in the lower-field segment of the jðextÞEL (F ) curves.The question arises what is the reason for the high field dec-rease of j ðextÞEL (F ). One of them could be a transition from theLangevin to Thomson description of the volume recombina-tion process (see Sec. 1.3). The recombination coefficient g inEq. (319) cannot be longer expressed by the mobility of chargecarriers [see Eq. (4)] and trec =t t follows a field increasingfunction of the mobility in the numerator of Eq. (319) or=andfield-decreasing g. The Thomson-like recombination occurswhenever the capture time (tc ) in the ultimate step of therecombination process becomes comparable with the dissocia-tion time (td) of an initial (Coulombically correlated) charge

allows PR to be expressed by Eq. (3). However, to completethis picture, the overall recombination probability should also




ming thin film LEDs (see e.g., Figs. 104, 109, 153, 171a). This

pair (CP). Such a recombination scheme, depicted in Fig. 172,

(cf. Sec. 4.3.1), so that t

include exciton–charge carrier interaction [Pð3ÞR ]. Then

PR ¼ Pð1ÞR P

ð2ÞR P

ð3ÞR ¼ð1þ tmttÞ�1ð1þ tc=tdÞ�1

� ð1þ tS=tSqÞ�1ð324Þ

where Pð3ÞR ¼ (1þ tS=tSq)

�1 for excited molecular singlets isdetermined by the ratio of the singlet exciton lifetime tS totheir quenching time (tSq) due to the interaction with chargecarriers (q) (the direct relaxation of the CP states has beenassumed to be very slow as compared with td and tc). Singletexciton–charge carrier interaction has been considered as theprocess contributing to the electrofluorescence roll off at highelectric fields [566], and has been shown to modify the electricfield-induced PL quenching rate [233]. A comparison of theelectric field dependence of the PL quenching rate in Alq3when using non-injecting Al electrodes [233,302,305,306]and electron injecting Mg:Ag cathode [233] allows to evaluatethe singlet exciton–charge carrier interaction rate constant,gSqwhen the Mg:Ag cathode device is used in the PL quenching

Figure 172 Two-step kinetic scheme of the volume-controlledrecombination (VR), taking into account the motion (tm) of oppo-sitely charged carriers forming a correlated e��h pair (CP) and itsdecay by either the back dissociation (td), direct transition (tCP) tothe molecular ground state or the ultimate capture (tc) of each otherleading to an excited singlet state (S1) which produces electrofluor-escence (hnEL). Note that the capture can create other excited states

with permission.




as indicated in Fig. 11. After Ref. 598. Copyright 2001 Jpn. JAP,

. In Fig. 173, a higher quenching rate of PL is observed

experiment. The difference in the quenching rate Dkqffi 9�106 s�1 at F¼ 1.4� 106V=cm can be ascribed to the quenchingrate of singlet excitons by injected electrons. Thus gSq¼ gSe¼Dkq=neffi 10�9 cm3 s�1 is obtained for neffi j=e meFffi 1016 cm�3,identifying the current as the electron injection current fromthe Mg:Ag cathode. This yields tSqffi 10�7 s. The fluorescencequenching by injected holes has been suggested to occur inthin (�15nm) layers of donor-type materials of tetra(N,N-diphenyl-4-aminophenyl) ethylene (TTPAE) [599]. However,a more exact analysis of the data leads to a conclusion thatthe effect is due to the field-induced dissociation of singletexcited states rather than to their hole quenching. The field-induced dissociation of singlet excitons in Alq3 also seems tobe responsible for the quenching effects in the devices with

Figure 173 Electric field dependence of the PL quenching ratesof two different devices: ITO=Alq3(200 nm)=Mg:Ag ( ) and ITO=Alq3(100 nm)=Al (�) (with a solid line as a guide to eyes). Thenegative values of the electric field indicate the negative bias ofthe ITO electrode. After Ref. 233. Copyright 2001 Jpn. JAP, withpermission.




This point has been discussed and the effect supported by thecharge photogeneration measurements in Sec. 2.6. The field-assisted dissociation seems to commonly appear wheneverthe excited states are produced in the presence of high elec-tric fields regardless of their spin multiplicity (singlets or tri-

and electronic properties of the material (evidence for electricfield-assisted dissociation of excited singlets in conjugated

600–602. Various dissociation models have been discussedto explain the experimental results, but excellent agreementwith experiment is provided by the 3D-Onsager theory of

electric fields. Employing this model to Pð2ÞR and substituting

PRffiPð1ÞR P

ð2ÞR (that is assuming P

ð3ÞR ¼ 1) to (315), the field

dependence of the EL quantum efficiency (QE) can be calcu-lated for different current conditions. The results are pre-

upon Ohmic injection (SCLC in the figure) is to reduce thelow-field constant value of the QE starting from ca. 10% at105V=cm up to an order of magnitude at 5� 106V=cm forr0=rc¼ 0.15 that is for the initial inter-carrier separation ofe��h pairs r0ffi 2.3 nm (rcffi 15nm with e¼ 3.8). In the caseof either diffusion-limited current (DCC) or Schottky-typeinjection current, the low-field decrease in QE is observed,then QE passes through a series of minima and maximawhose positions are sensitive to the average initial intercarrierseparation, r0. For the DCC case, one well-pronounced maxi-mum occurs around 0.8MV=cm, the field evolution above105V=cm resembles typical experimental results presentedin In contrast, only weak features on the QE(F)curves for the Schottky-type injection underlain device cur-rents can be distinguished with a general decreasing trendin QE. This prediction is in reasonable agreement with varia-tion of the relative EL efficiency as a function of applied bias atroom temperature for a 90nm-thick film of TPD provided with

ison between theory and experiment for DL TPD=Alq3




the Al cathode and negatively biased ITO electrode (Fig. 173).

geminate recombination as demonstrated in Fig. 47 for high

sented in Fig. 174. The role of the field-assisted dissociation

Fig. 168.

a weakly injecting Al cathode (Fig. 175). Quantitative compar-

polymers has been reported in several works, see e.g., Refs.

plets), type of excitation (optical or electrical) (cf. Sec. 2.6)

junction-based LEDs indicates that the dissociation quench-ing only is unable to reproduce the functional dependence ofthe QE on applied field but completed withquenching due to singlet exciton–charge carrier interactionyields good agreement (Fig. 176b). The latter can be reachedat tcn0¼ 15, where n0 is the usual frequency factor equal to1012–1013 s�1. This allows to evaluate the capture time tcon 1.5� (10�12–10�11) s scale. The rate constant assumed inthis way, gSqffi 10�9 s, agrees as to the order of magnitude

Figure 174 The field dependence of the EL quantum efficiency(QE) in TPD=Alq3 junction-based LEDs working in the VCEL modeas calculated from Eqs. (315), (322), and (324) with x¼ 0.2,P¼PS¼ 0.25, jr¼ 0.25 and e¼ 3.8 at T¼ 298K. The followingassumptions have been made in the calculation: P

ð1ÞR ¼ (1þ tm=tt)

�1

with tm=ttffi 2mh(Alq3)=mh(TPD)(jSCL=j) and field-dependent mobili-ties mh(Alq3) and mh(TPD) in Alq3 and TPD, respectively, and (jSCL=j)

ð2ÞR ¼ (1þ tc=td)

�1 with tc=td¼ tcn0 OOns(F),OOns(F) given by (137) at different ratios of r0=rctcn0¼ 10. The small circles marked curves are due to the QE deter-mined solely by the P

ð1ÞR . Note the difference in the curve shapes for

three different injection mechanisms (SCLC, DCC, and Schottky-type injection). After Kalinowski and Stampor, unpublished.




taken from Fig. 171b; P

176a),(Fig.

(cf. Sec. 2.6) and

ton–electron interaction in Alq3.The EL quantum efficiency can be connected with the

width of the recombination zone, w (152), using Eq. (153)for the recombination probability along with expression (315)

jðextÞEL ¼ xPjr

1þw=dð325Þ

Recall that, according to the definition equation (152), w mayexceed largely the device thickness, d, leading to a very lowvalue of jðextÞEL ¼ (d=w) xPjr whenever wd. On the otherhand, the upper limit of jðextÞEL ¼ (1þ 2=d)�1 xPjr (nm) is smal-ler than xPjr since due to the discrete structure of materialsw must be limited to ca. 2nm corresponding to an averagedimension of the molecules forming low-molecular weightorganic layers of EL device. The often employed expressionfor jðextÞEL ¼ xPjr assuming PR¼ 1, is unjustified since it wouldrequire w!0, thus, an unphysical assumption of a continu-ous homogeneous medium with the recombination time for

Figure 175 Variation of the relative EL efficiency with appliedbias for the device ITO=TPD(90 nm)=Al at different temperatures(the attainable voltage range 5–25V corresponds to the field range�0.5–3MV=cm. Adapted from Ref. 397.




with that deduced from the data of Fig. 173 for singlet exci-

Figure 176 The field dependence of the EL quantum efficiency(QE) for a diffusion-limited current driven ITO=TPD=Alq3=Mg:AgLED. The lines represent theoretical predictions of QE(F) accordingto Eqs. (315), (322), and (324) with different model parameters(r0=rc; tcn0). The small circle curves show the case with PR¼P

ð1ÞR

only (no quenching). The shaded circles stand for the experimentaldata of Ref. 68.




carriers trec ! 0. It is necessary to point out that thew=d ¼ trec= tt ratio, affecting j ðextÞEL through Eqs. (315), (317)and (325), may differ if different assumptions are made asto the relative contributions of the electron and hole currentsflowing in the device. For example, a difference in the mobilityrelations for the w=d ratio in Eq. (155) and those in Eq. (322)results from the assumption of equal contributions of bothelectron and hole flows (me ne ffi m hnh) for the former, and equalcarrier concentrations (ne ffi n h) for the latter. The qualitativedifference disappears in the case of the above discussedTPD= Alq3-based LEDs, where me (Alq3) mh(TPD). The ratiow=d ffi 2 me(Alq3)= m h(TPD) which follows directly from Eq.(155) is within a factor of 2 identical with the (trec=tt)VCELwhen j¼ jSCL according to Eq. (322). Table 7 demonstrateshow the EL quantum efficiency changes with varying ratio(w=d) of the width of the recombination zone w to an electro-fluorescent (P¼PS¼ 0.25) device thickness d. Limiting theratio w=d to the range 0 (w¼ 0)–1000 (wd) implies varia-tion of jðextÞEL between 1.25% and 10�3% photon=carrier fortypically x¼ 0.2 and jr¼ 0.25. The above described lowerlimit for w¼ 2nm reduces the former value to 1.22% photo-n=carrier for common organic layer thickness d¼ 100nm,but to about 1% photon=carrier for d¼ 10nm. The extensionof the recombination zone over all the device thickness d(w¼d) reduces this value by a factor of 2 (jðextÞEL ffi 0.63% photo-n=carrier). These data indicate that in order to optimize theEL quantum efficiency from a light emitting diode, one hasto minimize the recombination zone width as related to thedevice thickness. Furthermore, if one assumes the recombina-tion zone width to be independent of thickness, d, Eq. (325)provides a simple method to determine w by means of experi-mentally measured jðextÞEL as a function of d. A plot of 1=jðextÞELvs. d�1

1

jðextÞEL

¼ Aþ B

dð326Þ

where A¼ (xPjr)�1 and B¼Aw is then expected to be a

straight line with the slope to intercept ratio yielding directly




Table 7 EL Quantum Efficiencies Calculated According to Eq. (325) as a Function of the RecombinationZone Width to the Sample Thickness Ratio (w=d) at Different Values of x and jr (�jPL).

jðintÞEL

x¼ 1, jPL¼ 1 x¼ 1, jPL¼ 0.25 x¼ 1, jPL¼ 1 x¼ 1, jPL¼ 0.2525% 6.25% 25% 6.25%

w=d jðextÞEL (%) jðextÞEL (%) jðextÞEL (%) jðextÞEL (%)PS¼ 0.25 x¼ 0.2, jPL¼ 1, I x¼ 0.2, jPL¼ 0.25, II x¼ 0.35, jPL¼ 1, III x¼ 0.35, jPL¼ 0.25, IV

0a 5.00a 1.25a 8.75a 2.20a

0.10 4.55 1.14 8.00 2.000.15 4.30 1.09. 7.60 1.910.20 4.17 1.04 7.29 1.830.25 4.00 1.00 7.00 1.760.30 3.85 0.96 6.73 1.690.35 3.70 0.93 6.48 1.630.40 3.57 0.89 6.25 1.570.50 3.33 0.83 5.83 1.470.60 3.13 0.78 5.47 1.380.70 2.94 0.74 5.15 1.290.80 2.78 0.69 4.86 1.220.90 2.63 0.66 4.60 1.161.00b 2.50b 0.63b 4.38b 1.10b

1.10 2.38 0.60 4.17 1.051.20 2.27 0.57 3.97 1.00

(Continued)

Chap

ter5.Optical

Characteristics

ofOrgan

icLED

s395

5647-8

Kalin

owsk

iCh05

R2090804


Table 7 (Continued )

w=d jðextÞEL (%) jðextÞEL (%) jðextÞEL (%) jðextÞEL (%)PS¼ 0.25 x¼ 0.2, jPL¼ 1, I x¼ 0.2, jPL¼ 0.25, II x¼ 0.35, jPL¼ 1, III x¼ 0.35, jPL¼ 0.25, IV

1.50 2.00 0.50 3.50 0.881.80 1.79 0.45 3.13 0.792.00 1.67 0.42 2.92 0.733.00 1.25 0.31 2.19 0.555.00 0.83 0.21 1.46 0.376.00 0.71 0.18 1.25 0.317.00 0.63 0.16 1.09 0.288.00 0.55 0.14 0.97 0.249.00 0.50 0.13 0.88 0.22

10.00 0.45 0.11 0.80 0.2015.00 0.31 0.08 0.54 0.1420.00 0.24 0.06 0.42 0.1030.00 0.16 0.04 0.28 0.0750.00 0.10 0.03 0.17 0.04

100.00 0.05 0.01 0.09 0.021000.00 0.005 0.001 0.008 0.002

aMaximum, w¼0.bw¼d.

396

Organ

icLigh

tEm

ittingDiodes

5647-8

Kalin

owsk

iCh05

R2090804


the width of the recombination zone, w. In addition, the lightoutput coupling factor x can be determined from the interceptat d�1!0, if P and jr are known independently. Thisapproach has been successfully applied to the ITO=TPD(dh)=Alq3(de) =Mg:Ag structures [603]. Figure 177 shows externalquantum efficiency as a function of electric field measuredat various Alq3 thickness. For thin emitting layers(de< 20nm) jðextÞEL appears to be field-independent, whereasfor thick Alq3 films (de> 25nm), a non-monotonic evolutionof jðextÞEL with electric field is observed and is consistent with

ðextÞEL

can be fitted to a straight line plot vs. d�1e (Fig. 177b) giving

Figure 177 The external EL quantum efficiency as a function ofelectric field (a) of the bilayer devices ITO=TPD(dh)=Alq3(de)=Mg:Agof the total thickness d¼dhþde¼ 120nm with varying Alq3 thick-ness (de). (b) The inverse jðextÞEL as a function of the inverse of theemitter thickness (de) at three different electric fields (uptriangles,downtriangles, diamonds). The data fit to Eq. (326) are given bystraight solid lines. (c) The carrier injection efficiency as a functionof applied field for the devices with three different emitter thick-ness. Adapted from Ref. 603.




previous results illustrated in Fig. 168. The inverse of j

the field-dependent w, 70 nm at 0.75MV=cm and 40nm at1MV=cm. The value xffi 0.43 of the light-output coupling fac-tor follows from the intercept A¼ (xPjr)

�1 with P¼PS¼ 0.25and jr¼jPL¼ 25% at F¼ 0.75MV=cm and jr¼ 17% at1.0MV=cm. The reduced value of jr has been used at highfields because of exciton quenching by electric field and inter-action with charge carriers. This value of x is twice as large asthat estimated from classical ray optics to be 1=2n2

[2,569,604], using the refractive index for Alq3, n¼ 1.7. Analternative would be jr¼jPL¼ 25% kept constant, and xvarying with electric field. The physical picture of the carrierrecombination is that it proceeds along the path of holesmigrating through the emitter layer of Alq3 towards theMg:Ag cathode. However, due to the accumulation of bothholes and electrons at the TPD=Alq3 interface, the most effi-cient recombination occurs in the Alq3 region adjacent tothe interface and, whenever w < de forming a sufficientlynarrow zone far from the cathode, the singlet exciton quench-ing by this metallic electrode can be ignored. When Alq3 thick-ness becomes small enough (<25nm), the EL quantumefficiency becomes dominated by the excitonic quenching atthe cathode and it practically does not depend on electric field

ðextÞEL with decreas-

ing de is a drop in the injection efficiency for thin emitterdevices (see Fig. 177c). The drop comes simply from theassumption meff¼ meþ mn when using Eq. (236) for the calcula-tion of jSCL, which is valid only for the strong recombinationcase and should not be applied for thin Alq3 layers whenincreasing leakage of holes towards the cathode renders theflow to be described by the weak-recombination limit ratheras discussed in Sec. 4.5. From the above, it is seen that theEL efficiency is a complex function of thickness interrelations

3

The observed dependence of jEL on the emitter-to-devicethickness ratio [303,605] is difficult to a quantitative interpre-tation and needs further efforts in order to improve its theore-tical description. Furthermore, in more exact considerations,a temperature effect on the EL quantum yield must be takeninto account since the PL quantum efficiency of Alq3 appears




(Fig. 177a). Another reason for decreasing j

in double- and multi-layer Alq -based LEDs (cf. Sec. 4.3.2).

to be reduced at a gradient djPL=dTffi�3.9� 10�3K�1 (Ref.50), not mentioning the temperature dependence of electricalcharacteristics, and the LEDs warm up substantially at lar-ger current densities [606]. A similar analysis can be per-formed for polymer-based LEDs, where EL output has beenshown to be a function of thickness ratio of two componentlayers of bi-layer device structures [607].

Obviously, the recombination zone width can be obtaineddirectly from the experimental value of jðextÞEL using Eq. (325),if the parameters x, P and jr are provided. We note that Eq.(325) applies to the conditions when the field-assisted disso-ciation of excited states and their interaction with charge car-riers can be neglected [P

ð2ÞR ¼P

ð3ÞR ¼ 1 in Eq. (324) ]. Under such

conditions, the field dependence of jðextÞEL (F) is an increasingfunction of F following the field decreasing width of therecombination zone. This approach has been employed tostudy the effect of electric field on the recombination zone

applied field for neat and lightly doped Alq3 emitters shiftstrongly toward high fields and disappear at high dopant con-centrations. Applying Eq. (325) to the increasing segments ofthe jðextÞEL (F) curves enables to find the field dependence ofrecombination zone width, showing the effect of a dye doping.The DPP:Alq3 emitter doped devices show generally therecombination width to be less sensitive to the applied field,but its absolute value reveals a minimum (wffi 2nm) at0.25mol% of DPP in Alq3can be as large as 65nm that is covering the total thicknessof the 0.8%TPP:Alq3 emitter and Alq3 ETL in the case ofthe ITO=TPD(60nm)=0.8% DPP:Alq3(35nm)=Alq3(30nm)=Mg:Ag device. The recombination zone width for the neatAlq3 emitter-based LED decreases from about 50nm at lowfields down to 12nm at a high field (ffi0.7MV=cm). The latteris in good agreement with the same value calculated on thebasis of electron and hole mobilities assuming space-charge-limited injection to the TPD=Alq3 bilayer structure [309].Since all PR values calculated from Eq. (315) on the basis ofthe experimental data for jðextÞEL and the field independent




(Fig. 178). On the other hand, it

width with doped and undoped emitter layers [68,566]. Figure178 shows that the well-resolved maxima of the QE plots vs.

Figure 178 The EL QE and overall recombination probability(PR) (a), and the recombination zone width (b) vs. electric fieldapplied to the EL devices ITO=TPD=% DPP:Alq3=Alq3=Mg:Ag withdifferent mol% concentration of 6,13-diphenlyl pentacene (DPP) inAlq3 as emitter. After Ref. 68. Copyright 2001 American Instituteof Physics, with permission.




x¼ 0.2, P¼PS¼ 0.25 and jr

deal with the VCC mode operating devices and Eq. (322)applies which for jSCL=jffi 103 (see 171) impliesme,h=(meþ mh)1. This means that the hole motion towardthe cathode determines the recombination path (mh=me1in Alq3 and DPP-doped Alq3 layers). mh=meffi 0.4� 10�3 followsfrom Eqs. (317) and (322) with PR¼ 0.7 from Fig. 178a, whichis at least one order of magnitude lower than the hole-to-elec-tron mobility ratio in neat Alq3 measured by means of TOFtechnique [336]. The underestimated lightfactor (x¼ 0.2) and=or chemical hole traps seem to be respon-sible for this difference. Intentional doping of Alq3 with DPPreduces the hole mobility since the HOMO level of DPP islocated by about 0.5 eV above that of Alq3 [608]. Moreover,the carrier mobility changes because the presence of dopants

into account the disorder effect on carrier mobility (265),where Y¼ (2s=3)2=kT and bm¼C[(2s=3kT)2�S2], Eq. (155),approximated by

w ffime;h

me þ mhd ð327Þ

for me,hmh,e (cf. discussion above), predicts that w is, ingeneral, a non-monotonic function of diagonal (s) and non-diagonal (S) disorder parameters. In the above example withthe DPP-doped Alq3 emitters (mhme), wffi (mh=me)de, wherede is the thickness of emitting layers including both thicknessof the emitter layer (EML) and electron transporting layer(ETL). This simple expression allows to explain the variationof the recombination zone width with concentration of the

w reflects variations in mh imposed by doping. Since by defini-tion low doping imposes stronger off-diagonal than diagonaldisorder [29], the field-dependent hole mobility, mh¼ mehexp(�2s=3kT)2 expfC[(2s=3kT)2�S2]F1=2g, will enhancedecreasing tendency of mh due to hole trapping. This leadsto narrowing of the recombination zone. At higher concentra-tions of the dopant, the hole mobility increases because thehole transport becomes dominated by the hopping between




ffi 25%, exceeds 0.5 (Fig. 178a), we

Fig.

output coupling

dopant presented in Fig. 179. The concentration evolution of

modifies disorder parameters s and S (cf. Sec. 4.6). Taking

guest molecules (not via the Alq3 matrix) and by stronglyincreasing diagonal disorder for both electrons and holes withse> sh. The recombination zone is subject to the spatial exten-sion, as observed. Values for the recombination zone width forthe devices with the highest concentrations of dopant are afactor of 1.5–2 larger than the thickness of their EMLs. Thisshould not be surprising since by definition (152) the recombi-nation zone is the path on which all the carriers recombineunder conditions characteristic of EML. The (Alq3þDPP)=Alq3 interface breaks the continuity of the EML med-ium, holes trapped on DPP dopant molecules increase the con-centration of recombination centers in the EML, and stronglyreduce the hole penetration into the pure Alq3 ETL. This iswhy one does not see characteristic emission of Alq3 fromthe ETL and why the recombination zone physically becomeslimited to the geometrical thickness of the EML. The residual

Figure 179 Variation of the recombination zone width as a func-tion of DPP concentration in the Alq3 emitter for selected electric




field strengths as taken from Fig. 178

green emission comes from the EML as a result of the compe-tition between Alq�3!DPP energy transfer and radiativedecay of Alq�3 to the ground state [68]. The role of the pene-tration depth of electrons (le) into a double-emitter-basedpolymeric LED has been reported [344]. It has been identifiedwith the spatial extent of the recombination zone to be com-pared with w. Like in the (DPPþAlq3)=Alq3 junction-basedLED, the w appeared to decrease with applied voltage. This

of the electron penetration depth (le). The lowest value ofle¼ 55 � 10nm at F¼ 2� 106V=cm corresponds well to thevalues of w for the heavily DPP-doped Alq3 emitter system

e has been extracted fromthe experimental ratio of TPS to PPV emission (R), assumingthe recombination probability to be expressed by

PðeÞR ¼

Z d

0

exp �x=leð Þdx ð328Þ

Hence,

R ¼jðTSAÞPL

R d1

d0exp �x=leð Þdx

jðPPVÞPL

R dd1exp �x=leð Þdx

ð329Þ

where jðTSAÞPL and jðPPVÞPL are the PL efficiencies of TSA andPPV, respectively. The results are in good agreement withtheoretical predictions based on Eq. (153), assuming a uni-form distribution of recombination centers (holes) andmh me. The latter, according to Eq. (154), makes wffi [ j

ðeÞSCL=

j]d and PRffi [ jðeÞSCL=j]

�1, where jðeÞSCLffi e0emeF

2=d is the electroninjection SCL current, j is the measured device current domi-nated by holes [ jffi emh�nhF > j

ðeÞSCL], and d¼d0þd1þd2 (see

Fig. 180b). Based on the experimental i(F) curve, the electroninjection efficiency [ j=j

ðeÞSCL] and PR have been calculated para-

metric in the electron mobility. A good fit to the experimentaldata is provided with me¼ 3.3� 10�8 cm2=Vs. Also, it is appar-ent that while in the high-field regime (large current values> 5mA), the electron range le<d corresponding to the VCEL




is illustrated in Fig. 180 by the current (i) decreasing function

in Fig. 178. The electron range l

operation mode, low-current values of le>d correspond toPðeÞR < 0.5 and indicate the ICEL operation conditions.

Like electrofluorescence, electrophosphorescence quan-tum efficiency (EPH QE) depends on the device structure

Figure 180 The range (le) of electrons (right ordinate) and therecombination probability [P

ðeÞR ] for electrons (left ordinate). A com-

parison between the theoretical predictions according to Eqs. (153)and (328) (lines) and experiment (data points) shows good agree-ment for the electron mobility me¼ 3.3� 10�8 cm2=Vs (a). Schematiccross-section of the EL device and monitoring of emission from twodifferent emitters: (PSuþTSA)—a blend of polysulfone (PSu) andtris(stilbene)amine(TSA), and PPV-poly(phenylenevinylene). Theirthicknesses (d1, d2) are subject to variation, d0 is the quenchingzone of excitations by the Ca cathode (b). Adapted from Ref. 344.




and shows, in general, non-monotonic dependence on thedevice current. Some examples are shown in Fig. 181. A twoorders of magnitude increase in the EPH QE can be seenwhen passing from an inefficient device ITO=(TPD:PC)=Ir(ppy)3=Ca=Ag (QEffi 0.1% photon=carrier) to an efficientone with a hole-blocking layer of PBD, ITO=6%Ir(ppy)3:74%TPD:20%PC=100%PBD=Ca=Ag (QEffi 10% photon=carrier). Although no correlation between the QE and its jbehavior is observed, all of them must be a result of the inter-

Figure 181 The external quantum efficiency of devices using[Ir(ppy)3] phosphorescent compound, as a function of the drivingcurrent. The data for 6% [Ir(ppy)3]:CPB (circles) are taken fromRef. 43. The squares show the data for the 6% [Ir(ppy)3] in (TPD:PC)system for the first run, the diamonds are the same system for thesecond run, the down triangles are the data for the(TPD:PC)=[Ir(ppy)3]=PBD system, and the up triangles are the datafor the (TPD:PC)=[Ir(ppy)3] system. The intersection between thecurrent-independent segment of the jðextÞEL (j) plot and its falling partis indicated as PC. After Ref. 304. Copyright 2002 American Physi-cal Society, with permission.




play between processes increasing and decreasing the overallrecombination probability (324) which are not directly asso-ciated with the device structure. In the case of electropho-sphorescence exciton–exciton interaction (see Sec. 2.5.1) canlargely contribute to the reduction of the QE because of thelong lifetime of emitting triplet excitons. The EPH quantumefficiency is proportional to the concentration (T) of tripletexcitons

jðextÞEPH ¼ xjPH

ewe

j

T

tPHð330Þ

where tPH represents the intrinsic triplet exciton lifetime, theexcitons being homogeneously distributed throughout theemission zone of width we. The current dependence of theEPH QE is determined by the current variation of T. The lat-ter comes from the kinetic equations describing formation and

cal excitation conditions, the concentrations of singlet (S)and triplet (T) excitons may be described by the equations:

dS

dt¼ a1 1� Zð Þ j

ewþ gðSÞTTT

2 � kðSÞr þ kISC þ k

ðSÞn

1� ZðSÞex

S ¼ 0

ð331aÞ

dT

dt¼ a2 1� Zð Þ j

ewþ kISCS�

kðTÞr þ k

ðTÞn

1� ZðTÞex

T

� 2gðSÞTT þ gðTÞTT

h iT2 ¼ 0

ð331bÞ

where j is the recombination current density flowing withinthe recombination zone of width w, and the symbol k (s�1)denotes unimolecular rate constants for radiative [k

ðSÞr ,k

ðTÞr ]

and radiationless [kðSÞn ,k

ðTÞn ] singlet and triplet exciton transi-

tions, respectively, and for intersystem crossing singlet–triplet conversion (kISC). It must be pointed out that, unlikeearlier kinetics assuming all the encounter charge pairs(CP) to form molecular excitons [167], Eqs. (331) include their

1 2




decay of excited states (Fig. 182). Under steady-state electri-

spin weights (a , a ; cf. Sec. 1.4) and the reduction factors due

to dissociation processes of CPS (Z¼ Z0O), singlet [ZðSÞex ] and tri-

plet [ZðTÞex

tions are achieved for their solutions if we consider twolimits of low (case I) and high (case II) current level at roomtemperature.

Case I: The triplet exciton concentration is too low to giverise to triplet–triplet fusion and the T2 terms in Eqs. (331) canbe dropped. Then,

T ffi 1� Zð Þjew

a2 þ a2kISC= kðSÞr þ kISC þ k

ðSÞn

h i

kðTÞr þ k

ðTÞn

ð332Þ

if ZðSÞex ffi ZðTÞex ffi Zex is assumed.

Figure 182 Formation of molecular excited states (S1, T1) andcharge pair states [(CP) and (CT)] in the course of bimolecularrecombination (a) and under optical excitation (b). After Ref. 304.Copyright 2002 American Physical Society, with permission.




] molecular excitons (cf. Sec. 2.6). Major simplifica-

The triplet exciton concentration increases linearly withthe recombination current density, j.

Case II: The triplet exciton lifetime is dominated by theT2 term in this regime, and

T ffi 1� Zð Þjew

a2 þ kISCa1 1� ZðSÞex

h i= k

ðSÞr þ kISC þ k

ðSÞn

h i

2gðSÞTT þ gðTÞTT

h i� kISCg

ðSÞTT 1� ZðSÞex

h i= k

ðSÞr þ kISC þ k

ðSÞn

h i8<:

9=;

1=2

ð333Þ

is proportional toffiffijp

.A j-independent and inversely proportional to the root

square of j, jðextÞEPH is expected from Eq. (330) for these two lim-iting cases, the slope of a semilogarithmic plot of jðextÞEPH vs. jshould give 0 and �0.5, respectively. While, roughly, the first

for low- (or moderate-) field regions, a higher slope than�0.5 is typically observed at large current densities (exceptfor one case for not too high currents). This strongly suggeststhe existence of other mechanisms of quenching triplet exci-tons or their precursors. A similar conclusion can be drawnfrom comparison of the current dependence of the EPH QE

straightforward for Eq. (330) replaced by

jðextÞEPH ¼ xa2 1� Zð ÞjPH

ttottPH

ð334Þ

where

t�1tot ¼ t�1PH þ gTqn� �

1� ZðTÞex

h iþ 2gðSÞTT þ gðTÞTT

h iT ð335Þ

represents the effective (total) triplet exciton rate constantincluding all monomolecular and bimolecular quenching pro-cesses such as triplet–charge carrier (gTqn) or triplet–triplet

f[2gðSÞTTþgðSÞTT]Tg annihilation, and jPH¼[kðTÞr =][k

ðTÞr þkðTÞn ]. Assu-

ming that the dissociation efficiencies [Z, ZðTÞex ] are independentof current density, the current dependence of the EPH QE

[jðextÞEPH=( j)] should be projection on that for the effective life-




limit can be recognized in the experimental data of Fig. 181

platinum complex PtOEP (cf. Fig. 31). Such a comparison isand EPH lifetime as shown in Fig. 183 for the phosphorescent

time of triplets [ttot( j)]. The experimental data for the EPHlifetime and quantum efficiency show a remarkable discre-pancy (Fig. 183). The QE drops down by about 90% atjffi 150mA=cm2, whereas the effective lifetime decreases byless than 40% only at the same current density. A decreasingtendency in the phosphorescent lifetime as the photoexcitingenergy pulse increases suggests the EPH quenching to beunderlain by triplet–triplet annihilation process at lower cur-

rent densities. The stronger drop for jðextÞEPH above 10mA=cm2

requires additional quenching channels. An exception is

where the slope approaches �0.5. From its intersection point

Figure 183 Lifetime (open circles) and EPH quantum efficiency(triangles) of the phosphorescent dye 2,3,7,8,12,13,17,18-octaethyl-21H, 23H-porphine platinum (II) (PtOEP) embedded in an Alq3matrix as a function of current density. Two filled circles are thelifetimes of the phosphorescence taken at increasing photoexcita-tion pulse (left: 160 nJ=cm2; right: 16 mJ=cm2). The data adaptedfrom Ref. 493a by Kalinowski et al. [304] Copyright 2002 AmericanPhysical Society, with permission.




observed for the first lower-current range run in Fig. 181,

(PC) with the horizontal line representing jðextÞEPH¼ const¼ 11%photon=carrier, one can evaluate the T–T annihilation rate

constant gTT. At the intersection point jðextÞEPH ( j¼ jcrit)¼ 0.11.

The jðextÞEPH (case II) can be approximated by

jðextÞEPHðIIÞ ¼xjPH

2tPH

ew

jcritgTT

� �1=2

ð336Þ

if Z 1, a2¼ 3=4 and gðSÞTT ffi gTT is assumed and contribution ofthe intersystem crossing transitions is neglected as comparedto the direct e–h recombination forming triplet excitons (cf.

be estimated from Eq. (336) on the basis of the experimentalvalue of jcrit (a value of abscissa at PC) if the recombinationzone width, w, were known. The recombination zone, thoughdifficult to evaluate exactly, can be assumed to be very narrowbecause of the confinement of charge carriers at the[TPD:Ir(ppy)3:PC]=PBD interface, imposed by the relativelyhigh-energy barriers for both holes and electrons. This is con-firmed by the volume-controlled current flow in the device

with the dimension of the two nearest-neighbor molecules(ffi2nm). Thus, gTTffi 10�14 cm3=s follows from Eq. (336) usingxffi 0.2, jPH¼ 40% (Ref. 609), tPH¼ 15ms (Ref. 610), andjcrit¼ 2� 10�3A=cm�2

sonably with that for another organic phosphorescent system,PtOEP:CBP, gTTffi 3� 10�14 cm3=s obtained from the fitting of

the experimental data of jðextÞEPH ( j) to the triplet–tripletquenching mechanism [610]. The physical meaning of thesenumbers has been discussed in Sec. 2.5.1.2.

Let us, now, assume that the greater than �0.5 slope ofthe log jðextÞEPH vs. j plots in Fig. 181 belongs to the dominatingtriplet–charge carrier interaction, that is t�1tot (335) approxi-mated by t�1tot ffi gTq�n, where n is the concentration of chargewhich in the high-field region (SCLC conditions; cf. Fig. 67)can be expressed by nffi (3=2)e0eF=ed. With these assump-tions, Eq. (330) for the external EPH quantum efficiency leads




Fig. 182). The triplet–triplet annihilation rate constant could

(see Fig. 67). Therefore, a lower limit for w can be compared

from Fig. 181. This value agrees rea-

to

j ðextÞEPH ¼2

3

a2 x 1 � Zð ÞjPH ed

e0 egTq t PH F

we

w ð337Þ

where the emission zone width, we , is distinguished from therecombination zone width, w. If the latter is very narrow, asin the present case, the emission zone is larger than w, beinglimited on the large values side by the thickness of the emit-ting layer d =2 ¼ 50 nm. On the basis of Eq. (337), a plot ofj ðextÞEPH vs. F

�1 is expected to give a straight line with the slopedependent on three material ( e, gTq PH ) and device (d ) para-meter of the system. Such straight-line plots poorly approxi-mate experimental data and their slopes yieldgTq ffi 10� 12 cm 3=s for the first run and g Tq ffi 7.5 � 10� 12 cm3= sfor the second run at e ¼ 3, tPH ¼ 15 ms, d ¼ 100 nm, andw ¼ wmin = we ¼ 2 nm=50 nm ¼ 0.04. If one assumes that bothgTT and gTq are governed by the triplet exciton motion, thenthe diffusion coefficient of triplet excitons (DT ) can be calcu-lated from their values, gTq ffi gTT ffi 8p RDT [by analogy toEq. (71) derived for singlet excitons]: 4 � 10� 9 cm2= s � DT �3 � 10� 6 cm 2=s. The capture distance has arbitrarily beentaken as R ffi 1 nm in the calculation. These values of the tri-plet exciton diffusion coefficient are much lower as comparedwith those for molecular singlet excitons ( DS ) (see Sec.2.5.1.1). It is not surprising, the diffusion coefficients of tri-plets are expected to be lower than of singlets since bothenergy donor and acceptor transitions are disallowed [26](also see Sec. 2.4). However, the poor fit between theory andexperiment (Fig. 184), required additional experimentalchecks concerning quenching mechanisms at high currentdensities. The field-increasing dissociation efficiency (Z) of

date reducing significantly the EPH quantum efficiency as theapplied voltage increases [see Eq. (334)]. In the high-fieldlimit, it can be considered as a dominating quenching factor.This means that the ttot(F)=ttot(F0) ratio is a weakly varyingfunction of electric field, close to unity. Since the CP dissocia-tion process is enhanced by the applied field only indirectly by




184)(Fig.

�t

charge pairs (Fig. 182) appears to be a straightforward candi-

the device current, we translate selected curves from Fig. 181into the field dependence of the EPH quantum efficiency inorder to compare with the electric field effect on phosphores-

wich structure Al=100% [Ir(ppyP3]=Al, which does not showany emission (EPH) under action of an electric field only(without photoexcitation), decreases gradually as the appliedfield increases and drops down by as much as 30% at a fieldabout 2� 106V=cm. A decrease of twice as much is observedin the jðextÞEPH (second run) at the same electric field. This sug-gests at least a large part of the reduction in jðextÞEPH to havethe same origin as the electric field-induced quenching ofphosphorescence, and this has been shown to be the elec-tric-field-assisted dissociation of Coulombically correlatedelectron–hole pairs as governed by the 3D Onsager theory

Figure 184 External quantum EPH efficiency data taken fromðextÞEPH�F�1 plot in order to fit with

the triplet–charge-carrier interaction limit for triplet exciton decayaccording to Eq. (337) (solid lines). After Ref. 304. Copyright 2002American Physical Society, with permission.




Fig. 181 and represented by a j

cence (Fig. 185). The phosphorescence output from the sand-

on some other electrophosphorescent LEDs show the low-field

high EPH quantum efficiency has been achieved from a tri-ple-layer LED using bis(2-phenylpyridine) iridium(III)acety-lacetonate [(ppy)2Ir(acac)] phosphor molecule doped into awide energy gap host of 3-phenyl-4-(10-naphthyl)-5-phenyl-1,2,4-triazole (TAZ) as the emitter, 4,40-bis[N,N0-(3-tolyl)a-mino]-3,30-dimethyl biphenyl (HMTPD) [611] as a HTL andAlq3 as an ETL (Fig. 186). A maximum jðextÞEPH was observedat (ppy) 2Ir(acac) concentrations from 5% to 12%, while a sig-nificant decrease in jðextÞEPH was observed at both higher andlower concentrations. In addition, a gradual decrease in the

Figure 185 Phosphorescence (PH) and electrophosphorescence(EPH) efficiency response to the dc applied electric field. The rela-tive PH efficiency at lPH¼ (526 � 6) nm was measured with an exci-tation wavelength of 436nm and an exciting light intensity ofI0ffi 1014 2 s. For the PL and EL spectra of [Ir(ppy)3],see After Ref. 304. Copyright 2002 American PhysicalSociety, with permission.




Fig. 120.quanta=cm

of geminate recombination (Sec. 2.6; Fig. 50). Measurements

external efficiency as high as 20%, but like those in Fig. 181, itdecreases at high current densities (Figs. 186 and 187). The

Figur e 186 (a) The external EL QE [ jðext ÞEL ] and power efficie ncy ofa highly efficie nt EPH LED:IT O=HMTP D(60 nm )=12%(p py)3Ir(aca c):TAZ(2 5 nm) =Alq3 (50 nm) =Mg:Ag. Inset: molec ul ar str uc-ture of the orga nic phosph or (ppy)2 Ir(acac) . (b) Ener gy dia gramsof the device with low- and high- concent ration of the phosp hor inthe emittin g layer (EML). For chemic al nam es of the mater ials

American Institute of Physics, with permission.




form ing orga nic layers, see text. Af ter Ref . 495. Copyr ight 2001

Figure 187 (a) The external quantum efficiency of organic LEDsusing 6.2mol% [Ir(ppy)3]:TCTA as an emitter and three differenthole-blocking materials, vs. device current density. (b) The EPHdevice structure and molecular structures of materials used. (c)The energy level scheme of the EL device part (b). After Ref. 612.Copyright 2001 American Institute of Physics, with permission.




blue emission band from HMTPD was observed with anincrease in (ppy)2Ir(acac) concentration. The energy levelscheme inferred from absorption and PL spectra of (ppy)2Ir(-acac) (cf. 186b) in connection with the concentration evolutionof the EL spectra of the device allowed to distinguish two dif-ferent ways of the formation of emitting states. At low concen-

from the HMTPD into the TAC HOMO is energetically unfa-vorable and carrier recombination partly occurs withinHMTPD leading to the blue HMTPD emission in addition toexciton formation at (ppy)2Ir(acac). At (ppy)2Ir(acac) concen-trations higher than 6% [Fig. 186b(II)], the hole injection fromthe HMTPD into the much higher-located LUMO of the phos-phor molecules embedded in TAZ, the triplet and singletMLCT states are predominantly created via the electron–holerecombination among (ppy)2Ir(acac) molecules. Thus, the blueHMTPD emission practically disappears, and the EL spec-trum reflects an efficient emission from (3MLCT) tripletstates, formed either by on molecule e–h recombination pro-cess or via intersystem crossing from the singlet charge trans-fer state (1MLCT) [495]. A 20% photon=electron external EPHefficiency can also be achieved with [Ir(ppy)3] if ‘‘starburst’’perfluorinated phenylenes layers are used and a hole-transporting material 4,40,400-tri(N-carbazolyl)triphenylamine(TCTA) employed as a matrix for the emitting phosphor mole-cules in multi-layer organic LEDs [612]. The current densitydependence of the external quantum efficiency in such EL

role of X- and Y-shaped C60F42 blocking layers (Fig. 187b,c)is obvious by comparison with the jðextÞEPH( j) dependence forthe LEDs devoided such layers (Fig. 187a).

The high EL quantum efficiency of all types of electro-phosphorescent LEDs is underlain by the efficient productionof emitting triplet (mixed) states, the singlet-to-triplet excitonratio 1:3 being governed by simple spin statistics. Thisassumption implies P¼PT¼ 3=4 in expression (315) for jðextÞEPHwhile PS¼ 1=4 only. It is, therefore, obvious that an increasein the electrofluorescence efficiency would be achieved if anincrease in the PS were possible. Such a possibility appears




trations of the phosphor [< 2% in Fig. 186b (I)], hole injection

structures is shown in Fig. 187a. The efficiency improving

as a result of a quantum mechanical mixing of the electronicwave functions of the initial reactant species (e,h) and those ofthe final products of the e �� h pair capture due to a strongerionic character of singlet than triplet excitons formed in con-jugated polymers (see Sec. 1.4). At low temperatures, as muchas 83 � 7% of excitons can have singlet character as inferredfrom the infrared absorption study in working conjugatedpolymer light-emitting diodes [613]. The stringent test forthe singlet-to-triplet ratio would be a comparison of the fluor-escence and phosphorescence output from the same EL struc-ture. The triplet and singlet state emission have beenobserved from a platinum-containing conjugated polymer[614]. The spin–orbit coupling introduced by the platinumatom allows triplet-state emission in addition to the singletexciton emission originating from the molecular skeleton ofmonomer or conjugated polymer structure. The PL and ELspectra of the monomer and polymer structureshow two characteristic emission bands and different relativecontributions of each band to the total emission output (indi-cated as a percentage in the figure). The low-energy band isassigned to the emission of triplets (T1) and the high-energyband to the emission of singlets (S1) . A greater percentageof the photons from triplet states is observed for the EL spec-trum of monomer, whereas their percentage for both PL andEL spectra is clearly much lower for the polymer. In photolu-minescence, a number of excitons are originally all created inthe singlet S1 state, and from there they can decay radiativelyor non-radiatively to the singlet ground state S0, or undergointersystem crossing to the triplet manifold. Both radiativeand non-radiative decay occur from the triplet state T1 tothe ground state S0

certain fraction of triplet excitons can be created directly by

let-to-triplet emission ratio is high for the PL spectra witheither monomer and polymer samples. In contrast, the sing-let-to-triplet generation ratio in electroluminescence,extracted from the experimental percentage contributions ofsinglet and triplet light outputs accounted for the quantumyields for their radiative decays, amounts to 0.15� 0.01 and




(Fig. 188)

(cf. Fig. 10). For electroluminescence, a

the e–h recombination (cf. Fig. 4). This explains why sing-




0.40� 0.03 for monomer and polymer, respectively, at roomtemperature [614]. There is another approach to explain theincrease in the singlet-to-triplet output ratio under electricalexcitation, namely, the singlet fraction is increased by ISCfrom the triplet manifold after formation at bound neutralexcitons. S1 and S2 excited bound states are formed with theratio 1:3, the energy exchange between these states competeswith triplet exciton cooling, the number of excited S1 statesincreases [615]. At present, no experimental data exist allow-ing the distinction between these mechanisms.

The EL quantum efficiency from organic LEDs based onthe emission of bi-molecular excited states (see Sec. 2.3) isexpected to be low due to increasing rate of their radiationlessrelaxation arising from increased intermolecular phononinteractions, and an overall reduction in the oscillator

the well-known singlet excimer of pyrene molecules, wherethe emission efficiency as high as 75% has been reported[616], the PL quantum efficiency of the emission underlainby bi-molecular excited states falls usually much below thisvalue as for example that of ca. 20% observed with exciplexesformed by the molecules of hole-transporting and electron-transporting materials used in the fabrication of organicLEDs [507,508]. The triplet bi-molecular excited states,expected to show even less efficient emission, have recentlybeen reported to reach 15% for the triplet excimer of a Ptorganometallic phosphor molecule [99]. The radiative decayefficiency (jr) is not, however, the only factor affecting theEL quantum efficiency [see Eq. (315)]. With given jr and x,jðextÞEL can be increased by improving the probability of charge

Figure 188 PL and EL spectra of light-emitting diodes of the pla-tinum-containing monomer and polymer at 290K. The triplet emis-sion is denoted by T1 and the singlet emission by S1 . The percentualnumbers provide the fraction of the numbers of singlet and tripletemitted photons with respect to the totally emitted photons (the lar-ger numbers of S1 and smaller numbers for T1 characterize the PLspectra). Reprinted by permission from Ref. 614. Copyright 2001Macmillan Publishers, Ltd. [http:==www.nature.com=].

J




strength of the dimer (see e.g. Ref 26). Indeed, apart from





carrier recombination (PR) and formation of desired excitedstate (P). An efficient exciplex emitting LED has been fabri-cated improving the recombination efficiency at the m-MTDA-TA=PBD interface where charge carriers become stronglyconfined due to the high energy barriers for the electronand hole transfer toward electrodes. The EL spectrum ofITO=m-MTDATA:PC=PBD=Ca devices is entirely due to exci-plex emission with external quantum efficiencies exceeding1% photon=carrier at a luminance 1000Cd=m2 [508]. Thisvalue as compared to SL devices ITO=m-MTDA-TA:PBD:PC=Ca increases by a factor of 3 and over two ordersof magnitude as compared with TPD-based DL devices (cf.

These relations can be seen inwhere the external EL quantum efficiency as a function ofapplied field for various EL devices is displayed. Anotherway to improve the EL QE is to increase the probability (P)of the formation of the emissive states. Since the exciton for-mation is, in general, spin dependent (see Sec. 1.4), anincrease in the singlet exciton formation rate would increasethe electrofluorescence efficiency, and utilizing the dominat-ing channel of the triplet formation (that is the replacementof PS¼ 1=4 with PT¼ 3=4) leads to increasing electropho-sphorescence efficiency. The latter applies also to bi-molecu-lar triplet states, which, being more efficiently created thantheir singlet counterparts, should lead to an increased EL

Figure 189 (a) External EL quantum efficiency as a function ofapplied field for the SL (1) and DL (2) exciplex emitting organicLEDs. SL LED: ITO=(50%) m-MTDATA: 40% PBD:20%PC)(60nm)=Ca; DL LED: ITO=(75% m-MTDATA:25% PC)(60nm)=100% PBD(60nm)Ca (for chemical names and molecular structures

for the SL and DL LEDs with m-MTDATA replaced by TPD (3,4)

American Institute of Physics, with permission. (b) Luminescenceefficiency and quantum efficiency vs. current density of the molecu-

density (squares) and luminance (line) vs. voltage characteristicsof device in Fig. 131a. Adapted from Ref. 99.

J




Figs. 124–126). Fig. 189a,

of m-MT DATA, see Fig. 126, and of PBD and PC, Fig. 26). The data

are given for comparison (see Fig. 125). After Ref. 508. Copyright

lar aggregates emitting device shown in Fig. 131a. Inset: Current

quantum efficiency of EPH devices. In fact, a roughly three-fold increase in the jðextÞEL can be observed with a triplet exci-

above mentioned singlet exciplex emitting LEDs (cf.Fig. 189a).

From this section, we have seen that the EL quantumefficiency is a function of material parameters and structureof EL systems. Various physical mechanisms must be takeninto account to determine jðextÞEL and its evolution with thevoltage driving organic LEDs.




mer emitting LED (Fig. 189b) as compared with that of the

6

Summary and Final Remarks

Organic electroluminescence (EL) is a broad field with greattechnological implication. However, the current understand-ing of the elementary processes underlying the functioningof organic light-emitting devices (LEDs) is still unsatisfactory.

We have attempted to present the physical mechanismsof the functioning of organic LEDs in a way that reveals thelimitations as well as the strengths of the theoretical models.Because of the complexity of EL phenomena and because ofthe diversity of types of organic compounds that exhibit lumi-nescence, it is clear that there is no single, simple theory ofEL of organic solids. The understanding of EL phenomenaand their appearance in organic LEDs are interwoven withthe theoretical bases of other related branches of physicsand chemistry.

Although the general characteristics of organic LEDs canbe derived from theoretical description of energy supplymodes, excitation mechanisms, and nature of excited states,quantitative properties of specific materials and EL struc-tures can rarely be obtained from one theory alone. For exam-ple, the concept of molecular excitons for excited states is well

423



founded in theory of molecular aggregates and approximatevalues of their energies can be obtained from elaborate calcu-lations of electron orbital theory, but specific intermolecularinteractions and disorder must be invoked to determine exactvalues for particular materials. Let us recall a large group ofluminescent conjugated polymers, where, due to a p-bond net-work, the excited state wave function becomes delocalizedover at least 50 unit cells (ffi40nm) which led to treating theexcitation p–p� as the transition across a free carrier bandgap. However, because of the high degree of intrinsic aniso-tropy in conjugated polymers, disorder-induced localizationof excited electronic states is of major importance. Therefore,dependent on the degree of disorder, either band-based mod-els and localized exciton-based models have been used toexplain optical properties of conjugated polymers. Further-more, specific local intermolecular interactions may causethe formation of bi-molecular and multi-molecular units inthe ground and excited states (dimers or multi-molecularaggregates, excimers, electromers). Their counterparts intwo- and multi-component materials take on the form of het-ero-dimers (hetero-aggregates), exciples, and electroplexes.Obviously, their contribution to the optical emission rendersthe EL to reveal multi-band complex spectra difficult to a sim-ple description impeded in addition by electrical field and sur-face optical modes effects on their shape. Disorder, structural,and chemical defects of materials determine to a large extenttransport and trapping of charge carriers. The recombinationprocess proceeding on trapped carriers may lead to emissionspectra from organic LEDs which differ completely not onlyfrom those of molecularly dispersed materials but also of theirordered or a least partly ordered aggregates. The diversity ofthe emission spectra from organic LEDs is demonstrated bythe numerous examples in the section devoted to optical char-acteristic of organic LEDs. The main difficulty encountered inattempting to rationalize the LED performance is in quantify-ing the effect of injection and transport of charge carrierswithin the device structure. In the application of theoreticalmodels, the choice of appropriate quantities is of great impor-tance. For the EL quantum efficiency, an association of the




recombination probability with the charge injection efficiencyand carrier mobility is essential and has been described in thelast section. This has been done in a unified manner by intro-ducing characteristic times for the carrier recombination,transition across the device structure, and excitonic interac-tions. The predictive power of such an approach has beendemonstrated by its qualitative application to differentorganic LEDs and a quantitative analysis for the modelorganic LED based on the TPD=Alq3 junction. The importantrole of excitonic interactions and electric field assisted disso-ciation of excited states emerges in the explanation of theelectric field evolution of the EL quantum efficiency. Theseeffects should be of particular care in attempts to fabricateelectrically pumped organic laser, though the essential condi-tion of high injection currents must be first fulfilled and exter-nal coupling of the emission of light taken into account. Thepredictive content of theoretical models of organic EL isincreasing, particularly in the conversion of electrical currentinto light and light emission mechanisms themselves.We may yet attain the long-sought goal of the design of newluminescent materials and the prediction of describedcharacteristics of organic EL devices from theoretical consid-erations concerning electronic processes that underlie theirfunctioning.

Chapter 6. Summary and Final Remarks 425



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Organic Light-Emitting Diodes: Principles, Characteristics & Processes

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