Organic Light-Emitting Diodes: Principles, Characteristics & Processes

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DK1217_half 10/6/04 3:32 PM Page 1

Organic Light-Emitting Diodes Principles, Characteristics, and Processes

Copyright © 2005 by Marcel Dekker

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OPTICAL ENGINEERING Founding Editor Brian J. Thompson University of Rochester Rochester, New York

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Electron and Ion Microscopy and Microanalysis: Principles and Applications, Lawrence E. Murr Acousto-Optic Signal Processing: Theory and Implementation, edited by Nor man J. Berg and John N. Lee Electro-Optic and Acousto-Optic Scanning and Deflection, Milton Gottlieb, Clive L. M. Ireland, and John Martin Ley Single-Mode Fiber Optics: Principles and Applications, Luc B. Jeunhomme Pulse Code Formats for Fiber Optical Data Communication: Basic Principles and Applications, David J. Morris Optical Materials: An Introduction to Selection and Application, Solomon Musikant Infrared Methods for Gaseous Measurements: Theory and Practice, edited by Joda Wormhoudt Laser Beam Scanning: Opto-Mechanical Devices, Systems, and Data Storage Optics, edited by Gerald F. Marshall Opto-Mechanical Systems Design, Paul R. Yoder, Jr. Optical Fiber Splices and Connectors: Theory and Methods, Calvin M. Miller with Stephen C. Mettler and Ian A. White Laser Spectroscopy and Its Applications, edited by Leon J. Radziemski, Richard W. Solarz, and Jeffrey A. Paisner Infrared Optoelectronics: Devices and Applications, William Nunley and J. Scott Bechtel Integrated Optical Circuits and Components: Design and Applications, edited by Lynn D. Hutcheson Handbook of Molecular Lasers, edited by Peter K. Cheo Handbook of Optical Fibers and Cables, Hiroshi Murata Acousto-Optics, Adrian Korpel Procedures in Applied Optics, John Strong

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62. Computational Modeling of Vision: The Role of Combination, William R. Uttal, Ramakrishna Kakarala, Spiram Dayanand, Thomas Shepherd, Jagadeesh Kalki, Charles F. Lunskis, Jr., and Ning Liu 63. Microoptics Technology: Fabrication and Applications of Lens Arrays and Devices, Nicholas Borrelli 64. Visual Information Representation, Communication, and Image Processing, edited by Chang Wen Chen and Ya-Qin Zhang 65. Optical Methods of Measurement, Rajpal S. Sirohi and F. S. Chau 66. Integrated Optical Circuits and Components: Design and Applications, edited by Edmond J. Murphy 67. Adaptive Optics Engineering Handbook, edited by Robert K. Tyson 68. Entropy and Information Optics, Francis T. S. Yu 69. Computational Methods for Electromagnetic and Optical Systems, John M. Jarem and Partha P. Banerjee 70. Laser Beam Shaping, Fred M. Dickey and Scott C. Holswade 71. Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition, Revised and Expanded, edited by Michel J. F. Digonnet 72. Lens Design: Third Edition, Revised and Expanded, Milton Laikin 73. Handbook of Optical Engineering, edited by Daniel Malacara and Brian J. Thompson 74. Handbook of Imaging Materials: Second Edition, Revised and Expanded, edited by Arthur S. Diamond and David S. Weiss 75. Handbook of Image Quality: Characterization and Prediction, Brian W. Keelan 76. Fiber Optic Sensors, edited by Francis T. S. Yu and Shizhuo Yin 77. Optical Switching/Networking and Computing for Multimedia Systems, edited by Mohsen Guizani and Abdella Battou 78. Image Recognition and Classification: Algorithms, Systems, and Applications, edited by Bahram Javidi 79. Practical Design and Production of Optical Thin Films: Second Edition, Revised and Expanded, Ronald R. Willey 80. Ultrafast Lasers: Technology and Applications, edited by Martin E. Fermann, Almantas Galvanauskas, and Gregg Sucha Copyright © 2005 by Marcel Dekker

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81. Light Propagation in Periodic Media: Differential Theory and Design, Michel Nevière and Evgeny Popov 82. Handbook of Nonlinear Optics, Second Edition, Revised and Expanded, Richard L. Sutherland 83. Polarized Light: Second Edition, Revised and Expanded, Dennis Goldstein 84. Optical Remote Sensing: Science and Technology, Walter Egan 85. Handbook of Optical Design: Second Edition, Daniel Malacara and Zacarias Malacara 86. Nonlinear Optics: Theory, Numerical Modeling, and Applications, Partha P. Banerjee 87. Semiconductor and Metal Nanocrystals: Synthesis and Electronic and Optical Properties, edited by Victor I. Klimov 88. High-Performance Backbone Network Technology, edited by Naoaki Yamanaka 89. Semiconductor Laser Fundamentals, Toshiaki Suhara 90. Handbook of Optical and Laser Scanning, edited by Gerald F. Marshall 91. Organic Light-Emitting Diodes: Principles, Characteristics, and Processes, Jan Kalinowski 92. Micro-Optomechatronics, Hiroshi Hosaka, Yoshitada Katagiri, Terunao Hirota, and Kiyoshi Itao 93. Microoptics Technology: Second Edition, Nicholas F. Borrelli

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Organic Light-Emitting Diodes Principles, Characteristics, and Processes

Jan Kalinowski Technical University of Gda´nsk Gda´nsk, Poland

MARCEL

MARCEL DEKKER DEKKER

Copyright © 2005 by Marcel Dekker

NEW YORK

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-5947-8 This book is printed on acid-free paper. Headquarters Marcel Dekker, 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800-228-1160; fax: 845-796-1772 World Wide Web http:==www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales=Professional Marketing at the headquarters address above. Copyright # 2005 by Marcel Dekker, All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10

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Preface

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

Copyright © 2005 by Marcel Dekker

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Preface

Supplying electrical energy with insulating or non-injecting electrodes using voltage waves or pulses imposes fieldinduced creation of excited states (high-field EL as shown in Fig. 1a) or the generation of charge carriers inside the EL material, 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 recombination processes, the carriers being injected either at a semiconductor p–n junction (Fig. 1c) or from metallic contacts to a luminescent material (Fig. 1d). Although high-field and impact EL mechanism have been utilized in pioneer works on organic EL to explain emission properties of films and powders [1,4–7] as well as crystals [8–11] and fluorescent liquid solutions [12,13], only a scant attention has been given to them after more exact examination of EL in organic single crystals [14] and recent successful fabrication of EL devices comprised of multi-layers of evaporated low-molecular-weight organic materials [15,16] and polymeric systems prepared via precursor polymerization [17,18] or casting from solution without subsequent processing or heat treatment [19,20]. Their EL properties are now commonly ascribed to the formation of emissive states via the recombination of charge carriers injected from the electrodes (Fig. 1d). In general, only a part of the injected carriers undergoes recombination in emitter bulk, the remainder is discharged at the counter electrical contacts, forming the leakage currents. Obviously, the proportion between the recombination and leakage currents determines the light output from EL devices. Studying the kinetics of injected free carriers, this proportion can be translated into the recombination probability PR ¼ (1 þ trec=tt)1, where trec is the carrier recombination time and tt is the time required for a carrier to traverse the inter electrode distance d. Two limiting cases of the recombination EL have been distinguished based on the value of the recombination-to-transit time ratio: (i) volumecontrolled 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 probability PR ¼ 0.5 stands for a demarcation value when the rate of Copyright © 2005 by Marcel Dekker

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monomolecular decay (leakage current) and the rate of bimolecular decay (recombination current) of the carriers are equal to each other. High recombination EL efficiency requires the trec-to-tt ratio to be kept at a minimum, then PR ! 1. To exploit this principle for LED optimizing, one needs to understand the processes that control this ratio: (i) the injection of charge carriers, (ii) their transport, and (iii) recombination. Furthermore, the overall quantum EL efficiency as well as spectral features of the emitted light depend on the type and decay pathways of the excited states. It is the purpose of this book to give an outline of the problems underlying the function of organic LEDs utilizing bimolecular charge recombination as a generation process of emitting states. ACKNOWLEDGEMENTS This book, reflecting the skills and interests of its author, is underlain by a remote but still inspiring experience of scientific and personal contacts of the author with Professor Martin Pope (New York University), which played an important role in the author’s understanding of electronic phenomena in organic solids. The author acknowledges the invaluable contribution of his past and present coworkers of the Gdan´sk and Bologna LED groups. In the first instance, the author’s thanks are due to Dr. Piergiulio Di Marco who invited him to work for more than five years with Molecular Electronics Group at CNR Center in Bologna, where the main body of the author’s work on thin film organic LEDs has been developed. Fully as important as the scientific contribution of my coworkers in completing the book have been the patience and sacrifice of my wife Krystyna who made the work much more efficient. Her and the author’s son Sebastian assistance in technical preparing the manuscript are recognized with deep appreciation.

Copyright © 2005 by Marcel Dekker

Contents

Preface . . . . iii 1. Generation of Excited States by Charge Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Introduction . . . . 1 1.2. Initial and Volume-Controlled Recombination . . . . 3 1.3. Langevin and Thomson Recombination . . . . 5 1.4. Multiplicity of Excited States in the Recombination Process . . . . 8 2. Types and Decay Pathways of Excited States . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Introduction . . . . 13 2.2. Optical Spectroscopy . . . . 15 2.3. Monomolecular and Bimolecular Excited States . . . . 22 2.4. Energy Transfer By Excited States . . . . 61 2.5. Excitonic Interactions . . . . 80 2.6. Electric Field-Assisted Dissociation of Excited States . . . . 135

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Contents

3. Spatial Distribution of Excited States . . . . . . . 147 3.1. Introduction . . . . 147 3.2. Photoexcitation . . . . 150 3.3. Recombination Radiation. Recombination Zone . . . . 156 4. Electrical Characteristics of Organic LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 4.1. Introduction . . . . 171 4.2. Current–Voltage Characteristics . . . . 171 4.3. Space-Charge- and Injection-Controlled Currents . . . . 177 4.4 Diffusion-Controlled Currents (DCC) . . . . 227 4.5. Double Injection . . . . 229 4.6. Charge Carrier Mobility . . . . 236 5. Optical Characteristics of Organic LEDs . . . . . 273 5.1. Introduction . . . . 273 5.2. Emission Spectra . . . . 275 5.3. Light Output . . . . 344 5.4. Quantum EL Efficiency . . . . 376 6. Summary and Final Remarks

. . . . . . . . . . . . . . 423

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

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1 Generation of Excited States by Charge Recombination

1.1. INTRODUCTION The charge recombination process can be defined as a fusion of a positive (e.g. hole) and a negative (e.g. electron) charge carrier into an electrically neutral entity though the positive and negative charge centers on it do not necessarily coincide. The radiative decay of such an entity or following its evolution successive excited states produces light called recombination radiation. This underlies directly recombination EL, the EL type depicted in Fig. 1c,d to be compared with other types of EL phenomena (Figs. 1a, b) in which the recombination radiation still can participate as mentioned in Preface. The initial (or geminate) recombination and volume-controlled recombination can be distinguished on the basis of charge carrier origin.

1

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Figure 1 The schematic representation of various electronic excitation mechanisms due to ac or dc external electric fields: (a) the tuneling electrons from the valence band (VB) to the conduction band (CB) and ionization of an acceptor state (--) (Zener effect) followed by electron–hole recombination, indicated by horizontal and vertical arrows, respectively; (b) excitation or ionization by electron impact; (c) recombination of electrons () and () holes at a semiconductor p–n junction; and (d) bulk recombination of electrons and holes injected from electrodes. Adapted from Ref. 2

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1.2. INITIAL AND VOLUME-CONTROLLED RECOMBINATION The initial or geminate recombination (IR or GR) is the recombination process following the initial carrier separation from an unstable locally excited state, forming a nearest-neighbor charge-transfer (CT) state. It typically occurs as a part of intrinsic photoconduction phenomena in organic solids due to generation of charge from light-excited molecular states (see Fig. 2). The probability of the GR can 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 Z0 O

ð1Þ

Since the probability of the initial recombination can be expressed by the separation step rates, the natural way of its determination is to measure the bulk-generated photocurrent. However, one should keep in mind that the measured photocurrent contains carrier mobilities in addition to the effective separation probability (Z0O). The carrier mobilities

Figure 2 Initial recombination (IR) of a geminate (eh) pair formed by absorption of light (hn exc). Adapted from Ref. 21a. Copyright © 2005 by Marcel Dekker

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and their possible field dependence must be, therefore, determined independently. Moreover, other mechanisms of charge generation such as injection or photoinjection from the electrodes may lead to grave errors in evaluation of Z0O. Another possibility to determine PGR, which is free of these drawbacks, is electric-field modulation (EFM) of photoluminescence (PL). Electric-field effect on the effective charge separation efficiency (Z0O) shows up in the varying population of CT states, and consequently, in the varying concentration of the emitting states. It is expected that the field-induced increase in the charge separation efficiency would translate into PL quenching. The ratio (d) of the PL efficiency in the presence (jPL(F)) and in the absence (jPL(0)) of an external electric field (F) would give directly PGR d ¼ jPL ðFÞ=jPL ð0Þ ¼ 1 Z0 O

ð2Þ

A more detailed discussion of the GR and experimental examples of its manifestation are presented in Sec. 2.6. If the oppositely charged carriers are generated independently far away of each other (e.g. injected from electrodes) volume-controlled recombination (VR) takes place, the carriers are statistically independent of each other, the recombination process is kinetically bimolecular. It naturally proceeds through a Coulombically correlated electron–hole pair (e h) leading to various emitting states in the ultimate recombination step (mutual carrier capture) (Fig. 3; for more details, see Figs. 11 and 27 in Sec. 2.3). As a result, the overall recombination probability becomes a product of the probability of the pair formation, PR(1) ¼ (1 þ tm=tt)1, and the capture probability, PR(2) ¼ (1 þ tc=td)1, ð1Þ

ð2Þ

PR ¼ PR PR ¼ ð1 þ tm =tt Þ1 ð1 þ tc =td Þ1 ;

ð3Þ

where td is the dissociation time for the pair. There are two limiting cases of the VR: (i) the Langevin-like, and (ii) the Thomson-like recombination. Copyright © 2005 by Marcel Dekker

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Figure 3 Recombination of oppositely charged, statistically independent carriers (e, h) can lead to the creation of an emitting excited state through a Coulombically correlated charge pair (eh). The charge pair formation time (diffusion motion time) and its capture time are indicated in the figure as tm and tc, respectively. The excited states decay radiatively (hn) with the rate constant kf and non-radiatively with an overall rate constant kn. After Ref. 21a.

1.3. LANGEVIN AND THOMSON RECOMBINATION The classic treatment of carrier recombination can be related to the notion of the recombination time. The recombination time 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 radius rC ¼ e2=4pe0ekT), and the elementary capture time (tc) for the ultimate recombination event (actual annihilation of 1 1 ¼ tm þ tc1 (cf. Fig. 3). Following the charge carriers), trec traditional description of recombination processes in ionized gases, a Langevin-like [22] and Thomson-like [23] recombination can be defined if tc tm and tc tm, respectively. In solid-states physics, these two cases have been distinguished Copyright © 2005 by Marcel Dekker

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from each other by a comparison of the mean free path for optical phonon emission, l, with the average distance (4rC=3) across a sphere of critical radius rC [24,25]. One has Thomson recombination if l rC and Langevin recombination if l rC. Two subcases should be considered when l ¼ (Dt0)1=2, and l ¼ 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 lifetime of p and E charge carrier states, respectively, and vth is the thermal velocity of the carriers. Due to the low carrier mobility (m) in organic solids, one would expect to deal with the first subcase with m ¼ 1 cm2=V s (D ¼ mkT=e) and ˚ . This value mean free path for elastic scattering l ¼ 10 A ˚ of l is clearly much lower than rC ﬃ 150 A (e 4), strongly suggesting a Lengevin-like model to be appropriate to describe the recombination process in organics. Its signature is a field and temperature-independent ratio [26] geh =mm ¼ e=e0 e ¼ const;

ð4Þ

where geh is the bimolecular (second order) recombination rate constant, mm the sum of the carrier mobilities, and e is the dielectric constant. The essence of Eq. (4), derived from the Smoluchowski expression relating geh to the sum particle diffusion coefficient, D, and their interaction radius R via geh ¼ 4pDR, if one identifies R with the Coulombic capture radius RC and assumes the validity of Einstein’s relation, eD ¼ mkT, is that in the long-time limit, charge recombination is a process controlled by diffusion. For molecular solids with typically e ¼ 4, geh=m ¼ 4.5 107 V cm which span ge–h between 4.5 105 and 4.5 1017 cm3=s, the range corresponding to the limiting values of the carriers mobility from about 102 cm2=V s in the case of some aromatic crystals at low temperatures [27,28] down to about 1010 cm2=V s in the case of polymeric films [29]. The kinetic description of bimolecular reactions in condensed media, based on the solution of Smoluchowski Copyright © 2005 by Marcel Dekker

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equation, leads to the time(t)-dependent rate constant [30,31] gðtÞ ¼ 4pDR½1 þ R=ðpDtÞ1=2

ð5Þ

Equation (5), seemed to be consistent with experimental data on time evolution of many chemical reactions, in liquids, is not adequate to describe the reaction kinetics in disordered solids. In disordered solids, the carrier motion is only partially diffusion controlled, carrier hopping across a manifold of statistically distributed in energy and space molecular sites must be defined and taken into account [32–34]. Assuming that the carrier hopping sites are subject to an energy Gaussian distribution r(E) ¼ (2ps2)1=2 exp(E2=2s2), and introducing the average length of hops d, yields the average hopping frequency [35,36] 91 8 > > < ZCðtÞ = 2 2 exp½ðE=kTÞ ðE =2s Þ dE nðtÞ ¼ n 0 expð2d=d0 Þ > > : ; 0

ð6Þ where n 0 is the effective preexponential factor, d0 the charge localization radius [37] at a hopping site, and C(t) ¼ kT ln[s2n 0t=(kT)2] being only a weakly varying function of time (t). By substituting Eq. (6) into expression for the diffusion coefficient D ¼ d2 nðtÞ

ð7Þ

one obtains DðtÞ ¼ D0 ðn 0 tÞ1þb

ð8Þ

with the dispersion parameter b bearing a weak functional time dependence of the expression for C(t) and possible for an approximation by the time-independent empirical relationship [36] b1 ¼ 1 þ s2 =4kT Copyright © 2005 by Marcel Dekker

ð9Þ

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As long as s2=4kT > 1, b < 1, and D(t) is a decreasing function of time. The Monte Carlo simulation study of dispersive transport in organic solids [38,39] has shown that Eq. (9) is applicable for s=kT ranging from 1 up to 20. However, s=kT ¼ 1–5 may be too small for getting accurate estimations by means of Eqs. (8) and (9). The long-time balance between recombination and drift of carriers as expressed by the g=m ratio has been analyzed using a Monte Carlo simulation technique and shown to be independent of disorder [40]. Consequently, the Langevin formalism would be expected to obey recombination in disordered molecular systems as well. However, the time evolution of g is of crucial importance if the ultimate recombination event proceeds on the time scale comparable with that of carrier pair dissociation (tc=td 1). The recombination rate constant becomes then capture—rather than diffusion-controlled, so that Thomson-like model would be more adequate than Langevin-type formalism for the description of the recombination process (cf. Sec. 5.4).

1.4. MULTIPLICITY OF EXCITED STATES IN THE RECOMBINATION PROCESS The multiplicity of an electronic state is defined by its spin quantum number (s) as 2s þ 1. The most often occurring singlet, doublet and triplet states are defined by their spin quantum numbers 0, 1=2, and 1, respectively. When an electron and a hole, representing doublet species, recombine in an organic solid, an excited state of either singlet or triplet character is formed. If both carriers are free, three times more triplets than singlets are produced due to spin statistics. This means that the creation probability of singlets PS ¼ 1=4, and PT ¼ 3=4 for triplets. This holds as long as the conduction gap (Eg) or the electron–hole energy gap, Eeh, is larger than or comparable with excited singlet energy (ES). Since only singlets fluoresce, the singlet fraction is required to calculate the efficiency limit for fluorescent organic EL materials. The statistical upper limit of the electrofluorescence (EF) Copyright © 2005 by Marcel Dekker

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quantum efficiency (jEL) is obviously 25%, provided all excited singlets decay radiatively. Triplet states can contribute to the recombination radiation either by phosphorescence (PH) or delayed fluorescence due to thermal activation of triplets to singlets and or triplet–triplet annihilation (cf. Sec. 2.5.1). The latter is expected to improve electrofluorescence jEL up to 35%, on the basis of triplet spin statistics. However, the spin statistics of doublet species, here charge carriers, breaks down if one of the two recombining carriers is trapped (Fig. 4). Let, for illustration, the depth of a discrete electron trap be Et, then the generation of singlets requires a thermal activation energy DE ¼ Et (Eg ES) > 0, and 1 PSt ¼ exp ½Et ðEg ES Þ =kT 4 1 ¼ exp½ðES Eeh Þ=kT < PS 4

ð10Þ

Figure 4 Triplet–triplet annihilation contribution to the emitting singlet states in the absence (a) and in the presence (b, c) of carrier traps. A 100% radiative decay is assumed for excited singlets in the evaluation of jEL. Copyright © 2005 by Marcel Dekker

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On the extreme, when the electron–hole energy is much lower than the excited singlet energy due for example to deep trapping of electrons only triplets are energetically feasible and possible emission is purely phosphorescence or delayed fluorescence. In the latter case, the recombination yield of singlet production drops down to 12.5% (Fig. 4c). Phosphorescence, neglecting triplet–triplet annihilation, would give the emission yield limited only by phosphorescence quantum yield; for all emitting triplets, it would be as much as 100%. Therefore, unexpectedly, to further improve the EL quantum yield, a highly phosphorescent material with deep one carrier traps must be applied as an emitter in organic LEDs. The triplet–triplet interaction, postulated to explain increased quantum yield of thin film organic LEDs, has been well known in EF of organic single crystals [2,21,41]. One of the most spectacular manifestation of this type excitonic interactions is spatial distribution of EL emission (see Sec. 3.3). Interestingly, the EL light output resulting from the free-trapped carrier recombination ðFtEL Þ with respect to that underlain by free carriers recombination (FEL) does not depend on the trap depth [2] FtEL =FEL ¼ ð1=2ÞðHte;h =Neff Þ exp½ðEg ES Þ=kT

ð11Þ

but is a function of trapped electron or hole concentration Hte,h, density of states (Neff) and the difference between the energy gap and excited singlet energy (Eg ES). From Eq. (11), it is seen that for a given Eg ES, that is for a given material, the EL flux depends solely on the concentration of trapped carriers. Its value Hte;h ¼ 2Neff exp½ðEg ES Þ=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 in composite materials where intentionally introduced or uncontrolled 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 the PL spectrum, have been assigned to the trap-enhanced Copyright © 2005 by Marcel Dekker

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production of triplets emitting phosphorescent light. [42] An attempt to detect the singlet-to-triplet branching ratio from the electrofluorescence to electrophosphorescence ratio of the archetype organic LED’s emitter aluminum (8-hydroxyqninoline) (Alq3) doped with a phosphorescent dye, 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine platinum (II) (PtOEP) led to a singlet exciton fraction (22 3)% [43]. It is, within the experimental accuracy, in accordance with the spin statistics ratio 25%. However, this result can be questioned due to the neglection of the direct exciton formation by the electron recombination on PtOEP molecule-trapped holes and possible triplet quenching by charge carriers (cf. Secs. 2.5.2 and 5.4). Therefore, it remains an open question whether or not the spin statistics predicted branching ratio is firmly established. Another reason for breaking the simple spin statistics for recombining carriers is that the capture time in the formation of singlet states ðtSc Þ can be different from that in the formation of three equivalent triplet exciton states ðtTc Þ (cf. Fig. 3). This is underlain by the fact that the volume recombination process proceeds through an intermediate unstable encounter complex (e h) being a quantum mechanical mixture of the overall eigenstate c(0) ¼ ce þ ch of the initial reactant species (jcei, jchi) and the overall eigenstate cf ¼ (cS=cT) þ cG of the final products of the capture, with (cS=cT) being either a singlet or triplet excited state of one participant, and jGi being the ground state of the other participant. For a non-zero electroncorrelation, valid particularly for p-conjugated polymers, the ce and ch states are no longer single configurations [44], but represent superpositions of multiple configurations involving low occupied or high unoccupied one-electron levels. It has been argued that the formation cross-section of singlet excited states, sS ðtSc Þ1 , is larger than that for triplet states, sT ðtTc Þ1 because the correlated singlet excitons have 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 absorption detected magnetic resonance (PADMR) techniques [47]. These techniques have been used to measure the ratio sS=sT Copyright © 2005 by Marcel Dekker

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for a series of p-conjugated polymers and oligomers, showing its strong (non-monotonic) dependence on the optical gap, ES. The sS=sT ratio decreases from 5 for ES ﬃ 1.8 eV [poly(thienylene vinylene)] to a minimum value of 1.8 for ES ﬃ 2.3 eV (a-hexathiophene), and increases again up to 4.0 for ES ¼ 3 eV (polyfluorene) [45]. The value of 2.2 found for the sS=sT in poly(phenylene-vinylene) (PPV) (E ﬃ 2.4 eV) leads to jEL of 42% in agreement with the data for jEL measured directly from PPV LED operation [48,49]. Understanding and quantifying such experimental observations by deriving an analytical relationship between the ratio sS=sT and interrelated positions of various electronic levels, and its possible dependence on electric field is a challenge for future work, though the simple spin statistics has been recently applied to interpret the excitonic singlet–triplet ratios for both low-molecular weight materials and conjugated polymers [50]. The singlet–triplet ratios for Alq3 and poly[2methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEHPPV) were found to be (20 1)% and (20 4)%, respectively, using a technique based on reverse bias measurements of photoluminescent efficiency from organic LEDs.

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2 Types and Decay Pathways of Excited States

2.1. INTRODUCTION The excited states of molecular solids are traceable to properties of individual molecules. However, the energy of interaction between the molecules imposes a communal response upon the molecular behavior in the condensed phase; the collective response is embodied in an entity called an exciton (see Sec. 2.4.1). A molecular (localized) exciton model is applicable to van der Waals force-bonded solids (e.g. polyacenes, rare gases or polymers) [26,51]. In contrast to the Mott–Wannier excitons in tightly bonded inorganic semiconductors, the molecular excitons are usually located much below the lower edge of the conduction band being, in essence, an ionized state stabilized by a polarization energy (cf. Fig. 1d). Its narrowness makes the carriers highly localized at room temperature and the traditional one-electron band picture is inadequate for a description of the conducting properties of the overwhelming majority of organic solids. It is for this reason that 13

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the term ‘‘conduction level’’ is sometimes used instead of the usual ‘‘conduction band’’ designation. On the other hand, as in the case of inorganic semiconductors, the positive ion in molecular solids is referred to as a ‘‘hole’’ since it is an electron vacancy. The band designation can be used for the higherenergy conducting states because of the greater delocalization of charge carriers. Such a higher conduction band has been suggested to exist in anthracene crystal in order to explain its EL properties as being due to electron impact excitation [8]. Superimposed on the conduction levels are the higher neutral excitonic levels. Their quantum-mechanical coupling provides an additional (auto-ionization) channel for the decay of the neutral excited states. Due to the same reason, electron–hole recombination leads to creation of neutral excitons. However, optical transitions occur mostly from the relaxed lowest excited singlet because of fast internal conversion within the singlet manifold relative to the rate of radiative decay and auto-ionization from higher, excited singlet states. The energy of a localized (Frenkel type) exciton may be split into as many components (Davydov splitting) as there are individual molecules per unit cell in an organic crystal. This splitting is in addition to the level splitting produced by the interaction between two adjacent identical molecules. The Davydov splitting (D ¼ 2jL12(k ¼ 0)j) depends upon the resonance interactions between molecules that are translationally inequivalent, whereas the mean energy displacement downward (L11) depends on resonance interactions between translationally equivalent molecules. The wave vector selection rule k ﬃ 0 imposes the direct transitions to occur only between the bottom states of the exciton bands. The exciton band dispersion can be expressed as EðkÞ ¼ Eg D L11 ðkÞ L12 ðkÞ

ð13Þ

where D is the gas (Eg)-to-crystal shift term arising from the non-resonant interaction between an excited molecule and its surrounding medium. The Davydov splitting, as small as 10 cm1 for triplet states due to the short range of exchange Copyright © 2005 by Marcel Dekker

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interactions, can vary from a few hundred cm1 to several thousands cm1 for highly excited singlet states. In addition to this spectral splitting, the Davydov components have different polarization properties [52].

2.2. OPTICAL SPECTROSCOPY Optical spectroscopy is a natural tool for investigating photo-excited states. While absorption spectroscopy provides information about the excited states as they are created, luminescence spectroscopy reflects properties of relaxed excited states. In general, absorption and emission spectra of organic solids are complex compositions of various electronic transitions and their analysis can be a complicated task. For example, the presence of Davydov components can be observed in the absorption or emission spectrum of organic solids, although their identification is not necessarily straightforward because of an overlap with vibronic bands and disorder broadening of the bands. In Fig. 5, the Davydov splitting is apparent in the absorption spectrum of a polycrystalline tetracene film, a-polarized component at ﬃ505 nm and b-polarized component at ﬃ520 nm; D ﬃ 600 cm1 (see also Refs. 54 and 55). In the front recorded emission spectrum at room temperature, the b-polarized transition appears at 535 nm implying a large Stokes shift (ﬃ500 cm1) between the 0–0 transition absorption and fluorescence. This shift reduces to typical 260 cm1 for the emission spectrum corrected for spatial distribution of excitons (Fig. 5b), illustrating how the exciton dynamics combined with the internal absorption and reflectance can influence the shape of the spectrum [56]. Such effects contribute to a variety of losses attenuating light leaving EL cells. Thus, the external EL quantum efficiency differs from the internal quantum efficiency as discussed in Sec. 5.4. The large Stokes shift can be due to conformational changes of molecules upon excitation. An excellent example is provided by the PL and EL spectra of Alq3 [the aluminum (III) 8-hydroxyquinoline complex] one of the most used materials in organic EL diodes [16,57,58]. A large Stokes Copyright © 2005 by Marcel Dekker

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Figure 5 (a) Absorption (a) and emission (PL) polarized spectra of tetracene: kb and ?b Davydov splitting components of a tetracene single crystal seen in the absorption spectrum of a polycrystalline tetracene layer (upper full curve) as double features at ﬃ505 and ﬃ520 nm; the PL spectrum (1) as measured, the PL spectrum (2) corrected for the spatial distribution of excitons in the crystal as shown in part (b). (b) The spatial distribution of singlet excitons [f(x)] in a 4.7 mm-thick tetracene single crystal, obtained according to the procedure described elsewhere [53] (see also Sec. 3.1).

shift (0.4–0.7 eV) between the broad emission and the first absorption transition in Alq3 has been ascribed to the structural distortion of the molecule, leading to deep localization of the first excited singlet [58,59]. Copyright © 2005 by Marcel Dekker

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Another reason for optical spectra to differ from those determined by well-defined molecular energy levels is the structural disorder in organic solids [38]. Depending on the degree of disorder, one can distinguish two limiting cases: completely random systems (strong disorder) characteristic of high-molecular weight organic solids (mostly polymers) and systems exhibiting long-range order, typical for perfect single organic crystals. It is, however, easily conceivable and experimentally confirmed that a large group of organic solids displays an intermediate degree of disorder, characterized by the presence of aggregates whose structure is similar to the crystal structure. Static and=or dynamic statistical fluctuations of the molecular coordinates, the degree of which depends on the formation conditions of the solid, cause a splitting of the exciton bands into a distribution of localized states and the spectral profiles map the energy distribution of the absorbing or emitting sites. Davydov splitting, which must vanish in a completely random system because the average over the intermolecular energies is 0, appears in solids composed of highly asymmetric molecules where the intermolecular potential is such as to favor certain molecular configurations. Some of these can lead to the formation of incipient dimers responsible for excimer emission [60–63]. A general feature of the disorder-affected spectra is their large width and extended long-wavelength tail due to a high density of defects resulting from structural inhomogeneities. All of these features are exemplified in Figs. 6 and 7 by absorption (A) and emission (PL) spectra of some materials used extensively in organic EL devices. The structural disorder formalism has been mostly utilized to discuss electronic transport in organic solids [29,38] (cf. Sec. 4.6), and only a few works show its applicability to interpret optical spectra [62,67], and, recently, quantum efficiency of organic LEDs [68]. The absorption spectrum of an organic material with impurities disorder, local electric fields, or strong exciton–phonon coupling exhibits an exponential tail, commonly referred to as the Urbach tail [69,70]. Such a spectrum can often be decomposed into broad bands featuring Copyright © 2005 by Marcel Dekker

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Figure 6 Absorption (A) and photoluminescence (PL) roomtemperature spectra of SL and DL thin film structures based on materials described in the upper part of the figure. The small green luminescence contribution of Alq3 (emission maximum at ﬃ520 nm) to the blue luminescence of TPD (emission maxima at ﬃ400 and ﬃ420 nm) for the DL film structure TPD=Alq3 excited through the TPD layer reflects the filtering action of the TPD layer for the exciting light lexc ¼ 355 nm. For more details, see Ref. 57.

" Figure 7 Absorption (A) and photoluminescence (PL) roomtemperature spectra of (a) thin films of polyvinylcarbazole (PVK), [64] (b) a-sexithiophene (a-6T) [65], and (c) poly-(p-phenylene vinylene) (PPV) [66].

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Gaussian profiles (Fig. 8). Gaussian profiles are ascribed to the Gaussian distribution of energies (e) of the emitting states: gðeÞ ¼ ð2ps2 Þ1=2 expðe2 =2s2 Þ

ð14Þ

The distribution parameter s reflects the root-mean square standard deviation of the non-resonance interaction energy D [cf. Eq. (13)] corresponding to the polarization energy of a charge carrier in a medium (cf. Sec. 2.3.1). The essential contribution to D is the difference of the van der Waals energies between an unexcited and excited molecule embedded in a medium of polarizability a.

Figure 8 The absorption spectrum and its decomposition into Gaussian profiles for a pentacene film deposited at 80 K, and the spectrum recorded at 240 K. The main S0 ! S1 transition hn 0(1) is accompanied by the upper Davydov component hn 0(2), in the crystal spectrum, its first vibronic band, hn 0vibr, and a defect band hn 0D. Adapted from Ref. 67. Copyright © 2005 by Marcel Dekker

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

X

r6 ik

ð15Þ

i6¼k

Variation of the intermolecular distances by hDr=ri causes an average relative fluctuation of the D-term by s=D ¼ 6hDr=ri

ð16Þ

For D ﬃ 0.3 eV, the level splitting s exceeds the exciton bandwidth, 0.01 eV [52] if hDr=ri > 0.6%. This in the case exemplified by disordered tetracene and pentacene films for which the width of the Gaussian to fit the S0 ! S1 0–0 transition varies between 0.037 eV (ﬃ300 cm1) and 0.08 eV (ﬃ650 cm1) depending on film formation conditions [67] (cf. Fig. 8). All disordered organic solids investigated so far show broad fluorescence spectra red-shifted with respect to the absorption spectra (cf. Fig. 7). They reveal the radiative decay of single molecule based excited states [71–74] but are strongly characteristic of excimers (double-molecule-based excited states) [62,72,74,75]. A typical example is shown in Fig. 9, where Gauss-analysis of the emission spectrum of a tetracene layer evaporated on a cold glass substrate is presented. Two dominating Gaussian bands (III, IV), ascribed to excimeric emission, are accompanied by a weaker band II underlain by the monomer (defect) emission, and a weak band V reflecting emission of an additional (low-populated) excimer. Such an assignment is confirmed by different decay time constants, t1 ﬃ 7 ns for monomeric component, and t2 ﬃ 21 ns for excimeric emission centered near 610 nm. The appearance of both, monomer and excimer emission bands in emission spectra of organic films, demonstrates that lacking long-range order (crystal) structure they contain short-range order imposing local molecular pair configuration similar to that in the corresponding crystal. The dominating excimer emission suggests important role of two moleculesunderlain excited states (bimolecular excited states) (see Sec. 2.3). Furthermore, since the originally excited singlet Copyright © 2005 by Marcel Dekker

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Figure 9 The emission spectrum of a tetracene film evaporated onto a glass substrate kept at 89 K and the emission monitored at 180 K (full circles). Its decomposition into Gauss profiles (II, III, IV, V) is shown by solid lines. The dashed curve is the sum of the gaussians. The lacking band I (ﬃ540 nm) is characteristic of the monomer emission from crystalline films formed at T > 140 K. Adapted from Ref. 72.

state does not fluoresce (the lacking band I in Fig. 9), rapid energy transfer to both monomeric defects and incipient dimers (closely spaced parallel molecular pairs) capable to excimer formation must exist (see Secs. 2.3.1 and 2.4). 2.3. MONOMOLECULAR AND BIMOLECULAR EXCITED STATES The excitons in the weak coupling limit are practically localized on one molecule, forming monomolecular (monomeric) Copyright © 2005 by Marcel Dekker

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excited states. If, for some reasons, as for example energy or charge exchange, a nearest-neighbor molecule becomes involved to form the excited state, a bimolecular excited state is created. Its properties are different from those of monomeric states and depend on electronic structure of interacting molecules. 2.3.1. Single Component Emitters In addition to the localized (monomeric) excited states (M ) (cf. Sec. 2.4.1), the locally excited pair states of excimer jM Miloc, charge-transfer excimer jMþMiCT, and electromer (Mþ–M) states can be created by light or electron–hole recombination in single component organic solids (Figs. 10 and 11). The term single component solids means that except for unavoidable chemical impurities, only one sort of molecules is present. The electronic structure of an excimer can be approximated by a linear combination of locally excited, jM Miloc, and charge-transfer (CT), jM MiCT, configurations of complexing species [76]: jM Mi ¼ ajM Miloc þ bjMþ M iCT

ð17Þ

The coefficients, a and b, determine the extent of mixing between local and CT configurations. Their binding energies differ because the binding energy of the local configuration is due to excitation resonance (M M $ MM ) and that of the CT configuration to charge resonance (MþM $ MMþ) effects. The relative contribution of the two configurations (a=b), depends on the intermolecular separation, with the charge resonance contribution increasing with decreasing distance of separation [77–79]. This is illustrated in Fig. 12. The large bandwidth of the excimer luminescence is caused by radiative transitions to a steep-rising, repulsive, ground-state potential curve. The spectral region of the emission band (f(l)) is correlated with the amount of charge resonance character on the one hand, and the vertical transition energy, on Copyright © 2005 by Marcel Dekker

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Figure 10 Light-generated excited states in single component organic solids.

the other. The relatively low quantum yield of emission (jPL ﬃ 0.3) suggests that the triplet state of the molecular sandwich pair is formed with high efficiency or internal conversion to the ground state is a dominant photophysical process (for a more detailed discussion, see Ref. 80). Copyright © 2005 by Marcel Dekker

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Figure 11 Excited states created by bimolecular electron–hole recombination in single component organic solids. In contrast to photo-excitation (Fig. 10), recombination of oppositely charged, statistically independent carriers (e, h) leads to molecular and bimolecular excited states through unavoidable Coulombically correlated electron–hole pairs (eh).

The energy of an excited pair state of identical molecules (M) can be expressed as (see e.g. [81]) m2 1;3 1 ;3 2 EðMMÞ ¼ EM 3 cos a 3 cos y EMþ M r ð18Þ where 1,3EM are zero-point singlet or triplet (1 or 3 superscript, respectively) excitation energies of individual molecules. The interaction between an excited (M ) and unexcited (M) molecule leads to exciton resonance splitting dependent on their intermolecular distance, r, and the relative orientation. The intermolecular orientation in (18) is represented by the angle a between the dipole M ! M transition moments, m, and the angle y between the transition moments and the line of centers of the two interacting molecules. Configuration interaction of each exciton-resonance state (the two terms in the square brackets) with the corresponding charge-resonance state of energy 1;3

EMþ M ¼ I A Ec ðrÞ

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ð19Þ

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Figure 12 Potential energy diagram correlating the spectral region of the emission band, f(l) with the amount of charge resonance character (b) of the wave function in Eq. (17) with interplanar separation, r, of the molecules forming excimer. Adapted from Ref. 80.

yields two additional energy sublevels of mixed singlet or triplet bimolecular excited states. In the absence of orbital overlap between the two molecules, the four charge-resonance states (18) are degenerate with a common energy of an electron–hole pair (19), where I is the molecular ionization potential, A is the electron affinity, and Ec(r) ¼ e2=4pe0er is the isotropic Coulombic interaction potential with e being the Copyright © 2005 by Marcel Dekker

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dielectric constant of the material (or solvent) and e standing for the electronic charge. The states with a negative chargetransfer-resonance component have the lowest energies. The equilibrium separation of the molecules in a typical aromatic excimer is ﬃ0.33 nm. In anthracene and its derivatives, the strong 1La–1A transition dipole is polarized along the line joining the 9- and 10-carbon positions in the first excited singlet state, S1 (1La in the Platt notation), so that m is directed along the short molecular axis and lies in the molecular plane. The two anthracene molecules in a parallel overlapping arrangement with the meso-positions adjacent to each other (a ¼ 0, y ¼ 0) are prepared to form the photodimer-dianthracene (M2) with the 0.16 nm long 9 to 90 and 10 to 100 C–C bonds (Ref. 76 and references therein). The formation of the exact sandwich dimer, named otherwise incipient dimer [82,82a], shows up in a long-lived (ﬃ200 ns) red excimer emission with a maximum at lmax ﬃ 575 nm. It occurs in rigid environments where the sandwich pair cannot evolve to a more energetically favored configuration with the molecules ‘‘slided’’ over each other. Such a red excimer emission has been observed in the crystal of dianthracene in which regular close packing of dianthracene molecules does not allow the photochemically produced sandwich pair to move to configurations of lower repulsion energy [83,84]. Its broad spectrum is shown in Fig. 13 (curve 4). For anthracene molecules incorporated in rigid low-temperature glasses, the excimer emission has two components, one red and the other green [84]. The proportions of these components vary somewhat from sample to sample because their microscopic structures vary from amorphous-like to crystalline-like depending on preparation conditions, and the green emission disappears at higher temperatures than the red emission. Blue and green emission components have been distinguished in the fluorescence of non-crystalline anthracene films [75]. The difference between the red, the green and the blue emission has been ascribed to different excimer conformations. Possible anthracene excimer conformations and their spectral consequences are presented in Fig. 13. It is commonly accepted that the rigidity and size of the environmental cage play a major role Copyright © 2005 by Marcel Dekker

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Figure 13 Possible anthracene excimer conformations (a), and their spectral features (b). (a) (i) Exact parallel overlapping arrangement (incipient dimer) with the angles a ¼ 0 and y ¼ p=2 [cf. Eq. (18)]; (ii) parallel molecules ‘‘slided’’ slightly over each other (a ¼ 0, y 6¼ p=2); (iii) parallel molecules with one benzene ring displacement along the long molecular axis (a ¼ 0, y 6¼ p=2); (iv) parallel overlapping arrangement with the short molecular axes forming an angle about 60 (a 6¼ 0, y 6¼ p=2). (b) 1 represents the long wavelength tail of the fluorescence spectrum, F(l), of a 34 nm-thick sublimation grown anthracene single crystal excited at 366 nm; 2 and 3 are the time-resolved fluorescence spectra of non-crystalline anthracene films sublimed onto a 89 K glass substrate (see Ref. 75); 4 is the fluorescence spectrum of the anthracene excimer emission produced by the photocleavage of dianthracene (A2) crystal with 254 nm light at 10 K (see Ref. 84); 5 represents the relative difference DF=F0 in the fluorescence of the single anthracene crystal as in 1, taken in the absence (F0) and in the presence (F) of the positive charge injected from an electrode into its emitting zone (limited by the penetration depth ﬃ 0.2 mm) of the exciting light 366 nm [85]. The spectra 2, 3, 4 are normalized to the 4 band maximum. The spectral slit in measurements of the charge modulated fluorescence (5) increases towards long wavelength region up to ﬃ20 nm. For explanations, see text. Copyright © 2005 by Marcel Dekker

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in determining the type of excimer. The appearance of the green emission in a solid methylcyclohexane solution, and the green and blue emission in non-crystalline anthracene films (curves 2 and 3 in Fig. 13) indicates that the relaxation of the environmental cage allows the molecules to move over each other yielding more stable excimer conformations. Excimer conformations (ii)–(iv) have been suggested to be responsible for the blue and green emissions in non-crystalline anthracene films [75]. The large width of the green emission band, 3, has been ascribed to a statistical fluctuation in conformational 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 to form a separate red emission band observed from anthracene excimers generated by photo cleavage of dianthracene crystal (curve 4 in Fig. 13). Band 2 and a more blue-shifted band peaking at 457 nm (not shown in Fig. 13) have been assigned to well-defined (more stable) structures (iii) and (iv), respectively, by an analogy to anti-[2,2](1,4)anthracenophane forming an excimer with lmax ¼ 450 nm [87]. Another configuration of anthracene dimer has been proposed on the basis of absorption and fluorescence spectra of methylcyclohexane rigid glasses containing dianthracene irradiated with 254 nm light [88]. This is so called ‘‘55 dimer’’ in which the short molecular axes make an angle of (55 5 ) with each other while the long axes are parallel (Fig. 14a). Its 0–0 emission peak (ﬃ420 nm) falls within 0–1 vibronic component of anthracene crystal, thus lies far beyond long-wavelength excimer emissions [60]. Two anthracene molecules linked chemically can still form excimer-like pairs though their formation competes with the formation of zero-overlap excited anthracene units. An example is 1,1-di(9-anthryl)alkane, which, in addition to the short-wavelength structured excitonic emission of the compound, reveals unstructured red-shifted components characteristic of charge-transfer type (Fig. 14b) and excimer-type (Fig. 14c) anthracene unit pairs [89]. It has been pointed out that the molecular arrangements in the solid solution of anthracene are similar to those of two Copyright © 2005 by Marcel Dekker

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Figure 14 Schematic representation of anthracene dimers with no parallel molecular planes: (a) ‘‘55 dimer’’ (see Ref. 88); (b) zero overlap twisted intramolecular charge-transfer type pair; and (c) large overlap excimer-type conformation of anthracene units in 1,1-di(9-anthryl)alkane (see Ref. 89).

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molecules in the unit cell of the crystal [60,88]. They can be matched by a structural imperfection of the crystal, leading to an effective trap for the excitation energy and emission features characteristic of either the excimer configurations (Fig. 13a) and the stable dimers like ‘‘55 dimer’’ (Fig. 14a). Such features, observed naturally in full defect microcrystalline films [60,88,90], can be found even in sublimation grown good quality single anthracene crystals. A strong maximum at ﬃ465 nm, and weak shoulders at ﬃ500 nm and ﬃ575 nm, of the long-wavelength tail of the emission spectrum of such a crystal (Fig. 13b, curve 1), suggest emission from various excimer conformations, including that of the exact overlapping arrangement of the ‘‘incipient dimer’’ (Fig. 13a). Also, the crystal sites, at which the configuration of adjacent molecules differs from the regular lattice structure, form charge carrier traps. 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 excited states in traps (St) and, consequently, their contribution to the crystal emission, are controlled by the filling factor given by the ratio of trapped charge of concentration nt to the total concentration of defects Sot. The fractional change dt in the trap fluorescence due to the presence of trapped charge is thus given by dt ﬃ nt=Sot. The observed fluorescence variation due to the positive charge (holes) photoinjected from aqueous electrodes into anthracene crystals confirms this supposition [85]. An example is shown in Fig. 13b (curve 5). The relative increase in the fluorescence intensity in the absence of charge (F0) to that in its presence (F) shows maxima within the spectral ranges corresponding to the emission of different excimer conformations, the effect over 5% observed for the emission by incipient dimers. This indicates that the concentration of crystal sites enabling formation of the exact parallel arrangement molecular pairs is lower than that for defects leading to the formation of weaker overlapping molecular pairs (see Fig. 13a). The average trapped charge concentration within the emission region (<0.3 mm from the illuminated water electrode) can be evaluated from the intensity (I0) of the excited light and the Mott–Gurney function describing the charge Copyright © 2005 by Marcel Dekker

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Figure 15 The kinetic scheme illustrating the interplay between exciton (S) and charge carrier (q) trapping by crystal defects (Sot). The PL spectrum of the crystal contains the excitonic emission (kr, hn M) and the trap center emission (ktr , hn t), the latter being controlled by the number of the defect sites available for excitation. The exciton capture process (gst) competes directly with charge carrier trapping (gqt). The defects filled with charge reduce the emission resulting from radiative relaxation of the excited states produced at defect sites. For further explanations, see text.

distribution injected at the water=crystal contact [85,91]. For I0 ¼ 4 1015 quanta=cm2 s (lex ¼ 366 nm), nt ﬃ 2 1014 cm3 which with dt ¼ 5% gives Sot ﬃ 4 1016 cm3. This means that a fraction Sot=S0 ¼ 4 1016=4 1021 ¼ 0.001% of crystal sites forms defects enabling formation of the incipient dimers (S0 ﬃ 4 1021 cm3 is the concentration of molecules in anthracene crystal). The defects leading to formation of partial overlap excimer configurations [(ii)–(iv) in Fig. 13a] are populated by approximately one order of magnitude more (dt 1%). One should keep in mind that there exists a group of aromatic crystals in which adjacent parallel molecules have a large overlap and are relatively closely spaced, as in pyrene [92]. Their emission spectra are structureless, reveal a large Stokes shift, and are characteristic of the excimer [93]. Copyright © 2005 by Marcel Dekker

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However, the more common aromatic crystals show spectral properties resembling those of anthracene. Substitution in the 9- and=or 10-positions in anthracene introduces steric hindrance to the approach of the two molecules and thereby modifies the photodimerization and excimer fluorescence behavior. The steric hindrance to the close approach of the pair molecules reduces or prevents photodimerization but not excimer formation. The fluorescence spectra of such substituted anthracenes are broad, structureless bands, similar to the excimer, with maxima at ﬃ489 nm for 9-methylanthracene, at ﬃ494 nm for 9-chloroanthracene at ﬃ495 nm for 9-bromoanthracene [88]. Even anthracene-substituted large molecules reveal the excimer-like PL spectra of anthracene (Fig. 16). ANTPEP in dilute solution exhibits a structured violet fluorescence emission band, with a 0–0 transition at lM ﬃ 398 nm, characteristic of the excited molecule A . The concentration quenching of the molecular fluorescence is accompanied by the appearance of an increasing broad structureless blue fluorescence, with the peak intensity at ﬃ470 nm being red-shifted by about 0.5 eV as compared to the A transition. This structureless emission band is due to the fluorescence of excimers produced by the interaction between excited and unexcited units of A in the A-based supramolecules of ANTPEP. It corresponds well to the emission band at ﬃ465 nm observed from non-crystalline films and perturbed regions of anthracene crystals, which has been assigned to the excimer conformation presented in Fig. 13a as (iv). The autoionization of optically excited states (Ms , M s in Fig. 10) or bimolecular charge recombination (Fig. 11) processes lead to direct formation of nearest-neighbor electron–hole pairs (Mþ–M) which can realize a cross-radiative transition, producing light within the long-wavelength tail of the emission spectrum. They must not be confused with the CT excimer, jMþMiCT, which requires short intermolecular distances (<0.4 nm) and a large overlap intermolecular conformation in the A –A interaction process. A new name for such a pair, ‘‘electromer’’ (EM) , has been, therefore, proposed [74]. It is understood that the electromer emission will Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

Figure 16 The PL spectra of anthracene (A) 10-substituted with a long molecular thread (ANTPEP:10-[3,5-di(terbutyl)phenoxy]decyl2-(f2-[(9-anthrylcarbonyl)amino]gacetate)) in a bisphenol A polycarbonate (PC) matrix at different concentrations shown in the figure. The PL spectrum in the dilute solution of dichloromethane (DCM) is displayed for comparison (curve 4). Molecular structures of the chemical compounds are shown in the upper part of the figure. Adapted from Ref. 94.

appear preferably in the recombination radiation when, due to structural defects, the carriers are not available for intermolecular transfer until a delay time of a carrier pair has Copyright © 2005 by Marcel Dekker

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elapsed. In fact, the electromer emission, absent in the PL spectra, appears in the recombination EL spectra of polycarbonate (PC) dispersion of anthracene (Fig. 17). It is represented by the EM band (ﬃ540 nm) emerging on the longwavelength tail of the broad band emanated from a series of anthracene intermolecular excimers (EXs) emitting at 457, 465 and 510 nm dependent on the degree of the p orbital overlap within molecular pairs (see Fig. 13). Yet, the strongest radiative transitions in molecular excitons are apparent on the structureless band of the excimer emission (cf. the PL spectrum in Fig. 13). A most striking example of the electromer emission has been reported in the EL emission of thin films of 1,1-bis(di-4-tolyloamino=phenyl) cyclohexane (TAPC) [74]. The EL and PL spectra of TAPC appear to be completely different (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 lex ¼ 330 nm, and the EL spectra recorded at two different voltages applied to the film, as given in the figure. The absorption spectrum (OD) of the film is shown for comparison. Adapted from Ref. 94. Copyright © 2005 by Marcel Dekker

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

maxima at ﬃ370 and 450 nm, a strong regular band at 580 nm is characteristic of the EL spectra. In contrast to PL, which is composed of molecular exciton (monomer) (370 nm) and excimer (450 nm) emission, EL is underlain by emission of electromers formed by electrons and holes trapped on tritolylamine subunits of different TAPC molecules. However, intramolecular excimer formation cannot be excluded due to the molecule folding imposed by opposite charges located on tritolylamine subunits at one TAPC molecule. Intramolecular formation of Copyright © 2005 by Marcel Dekker

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excited complexes is known in bichromophoric compounds [89] and random copolymers [95], treated as single component materials (cf. Fig. 14). Since, however, in the latter case, the excited-state complexes are formed between electron donor and electron acceptor moieties constituting pendant groups to the polymer chain, they should be considered as hetero-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 rigid glasses at 77 K [97,98]. The compounds exhibit normal molecular (3M ) phosphorescence but there appears broad emission band peaking below the 0–0 band of the molecular phosphorescence spectrum, ascribed to triplet excimers. The emission decays non-exponentially with a half-lifetime of <1 ms, its excitation spectrum corresponds to the absorption spectrum of molecular species and can be detected when excited directly into their lowest triplet state T1 [98]. Excimer phosphorescence from crystals of three halobenzenes is facilitated by their crystal structure enabling excimer formation. Translationally equivalent molecules in the crystal lattice are spaced closely along the c-axis in such a manner as to maximize the hydrogen–hydrogen and p–p intermolecular overlap implying intermolecular charge–resonance interactions within the crystal to dominate in the stabilization of the triplet excimers [96]. Formation of triplet excimers, and dimers, has been recently observed in organic neat films of the phosphorescent molecule: platinum (II) (2-(40 ,60 -difluorophenyl)pyridinato-N,C2)acetyl acetate [99]. Its square planar structure allows it to facially pack in a crystal with an intermolecular separation of only 0.34 0.01 nm, thereby facilitating excimer formation between adjacent molecules. While triplet excimers could be excited efficiently at either optical or electrical excitation, the emitting triplet dimer states were detected only under electrical pumping in a light-emitting device based on this organic phosphor (see Sec. 5.2.2). Interestingly, the dimer emission spectrum shows no structure, which, as compared with the vibronic progression clearly resolved in the monomer spectrum, provides Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

evidence that the ground state of this aggregate is only weakly bound. The dimer state is not apparent in the optical pumping experiments because of a low efficiency of the monomer triplet exciton transfer to low populated molecular pairs with configurations where the Pt–Pt contact promotes its formation. The conformation of the excimer and electromer forming molecular pairs is reflected in the temporal behavior of the emission. Their luminescence response function for high concentration systems can be expressed by the luminescence rate (cf. Ref. 76) as FðtÞ ﬃ

et=t et=tf t tf

ð20Þ

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

hn 3 i n3 jmtr j2

ð21Þ

is the luminescence lifetime. The value of t is determined by the mean value hn 3i of n 3 over the luminescence spectrum given by the quantal flux F(n)[s1] as a function of light frequency (n), the mean refractive index (n) of the solvent (matrix) over the luminescence band, and the mean electronic transition moments for excimer mtr ¼ hM Mj^ mEX jMMi

ð22Þ

or electromer mtr ¼ hMþ M j^ mEM jMMi;

ð23Þ

where m^EX and m^EM are excimer and electromer dipole moment operators, respectively. Some examples of the time evolution of PL for excimeremitting organic films are presented in Fig. 19. A very short formation time, falling within the rise time of the exciting flash, is observed for ANTPEP films (Fig. 19a) while it is apparently larger for the layers of TAPC (Fig. 19b) revealing the excimer emission at ﬃ450 nm (see Fig. 18). It is likely that Copyright © 2005 by Marcel Dekker

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Figure 19 Time-dependent PL intensity of ANTPEP (a) (see Fig. 16) and TAPC (b) (see Fig. 18) solid films. (a) The PL excited at lex ¼ 350 nm and detected at 500 nm, the curves approximated by two exponentials for short- and long-time behavior with the decay times t1 and t2, respectively (dashed and dotted lines). Single exponential decay with t ﬃ 3.2 ns is observed in a dilute (105 M in DCM) ANTPEP solution (solid line). (b) The PL excited at lex ¼ 337 nm and detected in various emission spectral regions (cf. absorption and PL spectra in Fig. 18): (1) 370 nm (t < 1 ns); (2) 450 (t ¼ 2.3 ns); (3) 525 nm (4.8 ns) and (4) 580 nm (t ¼ 6.4 ns) (after Ref. 74).

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Organic Light Emitting Diodes

the long-time parts of the PL response curves belong to excimers in both cases, but their lifetimes in ANTPEP (t2 ¼ 40 ns) and TAPC (t ﬃ 6.4 ns) are largely different. The energy (thus n) shift in the emission maximum from 470 to 450 nm, respectively (cf. Figs. 16 and 18), is insufficient to explain such a big difference according to Eq. (21). A twofold larger electronic transition dipole moment (22) for TAPC would, thus, be expected to yield the observed difference in the decay rate constants. The large values of mtr (23) for electromers could strongly influence their lifetime. But, on the other hand, the electromer lifetime has its upper limit due to the excimer formation process. Activated diffusion implies that carriers will not be available for intermolecular transfer until a delay time after formation of a carrier pair has elapsed. For the electric field-assisted thermal activation, the electron hopping time is given by thop ¼ t0 exp½ðDE erFÞ=kT

ð24Þ

where t0 ¼ n 01 (n 0—frequency factor), r is the intermolecular (inter-ion) distance, and DE is the height of the barrier due to the localization energy of the electron. The situation is schematically depicted in Fig. 20. The electron transport (LUMO ! LUMO electron transition) dominates in unperturbed environment resulting in dominating monomer and excimer emission of the e–h pair. The electron localization on a defect site impedes electron transport and increases the probability for the excess electron to recombine directly with a HOMO-located hole on the other molecule of the ion pair. If such a cross-transition occurs radiatively, a longwavelength EM emission can be observed. Its time constant tEC has an upper limit determined by the electron hopping time (24). Furthermore, the steric hindrance to the close approach of the ion pair can drastically impede formation of excimer, the emission will be dominated by electromer pairs. Such a situation has been reported for macromolecules of the methyl-exopyridyne-anthracene rotaxane (EPAR-Me), where anthracene molecule plays a chromophore role as pendant group located close to a large macrocycle of a more complex Copyright © 2005 by Marcel Dekker

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

supramolecular structure (Fig. 21). In contrast to ANTPEP, both PL and EL spectra of EPAR-Me practically coincide suggesting a common emission species [94]. The PL lifetime (ﬃ20 ns) is by a factor ﬃ0.5 shorter than that for the longwavelength (500 nm) of ANTPEP (see Fig. 19a). The explanation was based on the kinetic scheme presented in Fig. 22. The electromer pair (Mþ–M) can be formed by approaching Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

Figure 21 Absorption (A) photoluminescence (PL) and electroluminescence (EL) spectra of EPAR-Me-doped PC (75 wt%) (molecular structures of EPAR-Me and PC are given in the upper part of this figure and Fig. 16, respectively). The ANTPEP unit in EPAR-Me is shown in bold. Adapted from Ref. 94.

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Figure 22 The kinetic scheme used to describe the electromer (EC) emission (hn EM) excited with light (a) and resulting from volume recombination of statistically independent holes and electrons (b). The low-efficient processes are indicated by the crosses in bold.

ions of a geminate ion pair (MþM) preceded by the encounter complex of molecular exciton (M ) and ground-state molecule (M) or from the encounter ion pair (MþM) produced in the course of the volume recombination of statistically independent holes and electrons (e.g. injected from electrodes). Due to the steric hindrance by the macrocycle, the optically excited singlet cannot approach close enough to form an excimer, the encounter complex (M M) decays predominantly by electron transfer from M to M creating a separated electron– hole pair (MþM) which is likely to relax to the electromer, i.e. a pair of closer located ions (Mþ–M). In the volume Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

recombination process, the EC state comes into existence naturally by the diffusion approaching of independent charge carriers. Its formation competes with the generation processes of M and (MM ). The latter become very inefficient for large inter-ion separations as for the system in Fig. 21, where the anthracene units are, in average, r ﬃ 1.2 nm apart, that is the distance between them is much larger than that in anthracene crystal (r ﬃ 0.6 nm) and even that in the solid PC: ANTPEP solution (r ﬃ 1 nm) [94]. Consequently, the nonradiative relaxation and formation of electromers kfEM are dominating decay channels for encounter ion pairs. One of the important premises in understanding the notion of electromer is that electromer species are formed at molecular separations and relative orientations as to maximize the rate of the radiative cross-transitions. They are different than those resulting from statistical averages for molecular dispersion, but yet undergo some statistical fluctuation which must be reflected in the shape and width of the electromer emission band. The electromer spectra presented in Fig. 21 are largely dominated by the broad electromer band at l ﬃ 540 nm, and a weak monomer emission around 400 nm. An apparently stronger monomer emission in the PL spectrum than that in the EL spectrum reflects the radiative decay of photo-excited molecular species (M ) to be a competitive process to the diffusion-controlled formation of the encounter complex (M M). A very weak monomer component in the EL spectrum supports an assumption that the formation rate of M from the ion pairs (MþM) is negligibly small (cf. Fig. 22). The large width (ﬃ0.6 eV) of the electromer band suggests that this emission stems from electromers whose conformational parameters are subject to a statistical distribution. The optimized intermolecular distance for the EM emitting entities (rEM) can be estimated from the general relationship between the EC transition energy (hn EM equivalent to hn EC) and the first molecular excited state energy EA ﬃ 3.3 eV [76], hn EM ﬃ EA 2DE Ec

ð25Þ

where DE is the localization energy (see Fig. 20) and Ec ¼ e2=4pe0erEM is the isotropic Coulomb attraction energy Copyright © 2005 by Marcel Dekker

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within the electromer. The localization energy can be estimated from the lifetime data using Eq. (24). For EPARMe:PC, tEM ﬃ thop ﬃ 20 ns, which with t0 ﬃ 1012 s (resulting from the commonly used value of the frequency factor n 0 ¼ 1012 s1), and T ¼ 300 K yields DE ﬃ 0.25 eV at F ¼ 0 (photoexcitation). A reduction in the hopping barrier in the electric field applied to the EL emitting sample and suggested to enhance slightly formation rate of the excimer component in A:PC system (see Fig. 17) does not seem to be of importance for the transition energy hn EM since the dominating features of the PL and EL spectra of the EPAR-Me:PC system are quasi-identical (see Fig. 21). Using this value of DE and e ¼ 3, Eq. (25) yields Ec ﬃ 0.5 eV and REM ¼ 1.0 nm. The photon energies at the half-width (0.6 eV) limits of the EC spectrum give the distance range (0.7–2.4) nm corresponding well to the optimum value of the rEM estimated from the lifetime data. These values for rEC are too large to enable formation of an excimer. A comment should be made regarding the interrelation between the electron–hole pair energy (19) and the transition energy (25). They are different because unrelaxed ion pairs, formed either optically or by approaching of uncorrelated carriers, have different energy than that of relaxed emitting EC states. Like charge-transfer (CT) excitons in aromatic crystals, the charge pair states are vibrationally excited states, the vibrational energy for CT pairs in anthracene, as inferred from electro-absorption measurements, is Ev ﬃ 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’’) band ¼ 4:1 0:1 eV for anthracene crystal, and can account gap Eel g for the difference between EEC and hn EC in non-crystalline solids and concentrated molecular solid solutions.

We note that the notions ‘‘optical’’ and ‘‘electrical’’ gap are here used in the context of the classical band theory of solids and can be confusing in application to molecular (van der Waals bonded) solids, where they have the opposite meaning: the ‘‘optical gap’’ reflects the energy of excitonic (localized) states, while the ‘‘electrical gap’’ stands for the lowest energy between free carrier states.

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Organic Light Emitting Diodes

The solid-state values of the ionization potential (I) and the electron affinity (A) in (19) are related to their values in the gas phase (Ig, Ag) through the polarization energies of positive (Pþ) and negative (P) carriers, thus Eq. (19) may be replaced by the relationship EEM ¼ Ig Ag 2P EC Ev

ð26Þ

where Pþ ¼ P ¼ P has been assumed. From (26), it follows that P ﬃ 1.9 0.1 eV is required to identify EEM with hn EM ¼ 2.3 eV for the A:PC (Fig. 17) and EPAR-Me:PC (Fig. 21) solid solutions. Ig ¼ 7.5 eV, Ag ¼ 0.6 eV [26], and the above discussed values of Ev ¼ 0.3 eV and Ec ¼ 0.5 eV have been assumed in this evaluation. The value of P ¼ 1.9 eV falls within the 1–3 eV range of the polarization energies determined experimentally by ultraviolet photoelectron spectroscopy for a broad spectrum of various organic compounds [26], and equal to P ¼ 1.7 0.1 eV for solid anthracene, as calculated from P ¼ Ig Ic with the ionization energy of the crystalline anthracene Ic ¼ 5.8 eV [101]. The quasi-one dimensional (quasi-1D) nature of some polymeric semiconductors used in EL cells is the source of differences in description of excited states as compared with those in conventional organic solids. In such polymers, if there is no empty level below the conduction band, the excess electron will cause a chain deformation about 20 sites long called a polaron (see e.g., Refs. 26, 102, and 103). In the deformation process, a level is pulled out of the valence band with its two electrons and a level is pulled out of the conduction band. Two levels in the gap are created, the lower one filled with the two electrons brought up from the valence band, the upper containing the added electron. Although its energy levels are in the gap, the polaron can move freely on its own chain, its lattice distortion moving with it. When in a conventional organic solid, an electron and a hole move freely, contributing to transport, until they recombine forming a stable exciton, in quasi-1D polymer the added electron and hole can in addition create a pair of polarons, one positively charged, the other negatively charged, in the manner Copyright © 2005 by Marcel Dekker

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described above. If these polarons meet, they recombine. An exception to this behavior is trans-polycetylene, in which solitons, a different type of excitation from polarons, are formed. At high carrier concentrations, when the polarons come close together, the charge carriers donated to the chain are housed in bipolaron states. Summarizing, the formation of solitons, polarons, or bipolarons introduces states in the band gap of the quasi-1D polymers (Fig. 23). Charged excited states have been detected through the sub-gap (<Eg) optical transitions and electron spin resonance technique. The question of interest here is whether, and if so, how these gap states show up in electroluminescence. The injected carriers are transported as singly charged polarons or bipolarons. Their combination may form singlet polaronic excitons (Fig. 23) which decay radiatively producing electroluminescence with energy quanta hn < Eg. Since singlet excitons in conventional organic solids fall also below Eg, this fact cannot be taken as an experimental evidence for the existence of polaronic excitons. A theoretical reasoning pointing a difference between electron screening suggests different origin of the EL emission.

Figure 23 Energy levels of various types of elementary excitations in quasi-1D conjugated polymers. Adapted from Ref. 21. Copyright © 2005 by Marcel Dekker

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The central issue relates to the strength of the electron–electron interactions and the spatial extent of the excited state wave function. Strong electron–electron interactions (electron–hole attraction) lead to the creation of highly localized and strongly correlated electron–hole pairs (excitons); wellscreened electrons and holes are more appropriately described using a band picture [104,105]. It seems, however, that this difference has a quantitative character rather than a fundamental significance for electronic processes in EL. For example, it is not quite clear what should be the exact relation between electron–phonon coupling and electron– electron interaction in order to distinguish between band picture and molecular model of organic solids (cf. discussion in Sec. 5.2.2). 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 account in the formation process of excited states. Of particular interest are interactions between electron donor molecules (D) and electron acceptor molecules (A) characterized by partial or complete electron transfer from D to A. The degree of electron transfer depends on the ionization potential (ID) of the donor and the electron affinity (AA) of the acceptor. A 1:1 DA complex is formed by the reversible process D þ A ! ðDAÞ

ð27Þ

The molecular equilibrium constant Keq ¼ [DA]=[D][A], where square brackets indicate molar concentrations of donors, [D], acceptors, [A], and complex [DA]. The theory of donor–acceptor interaction has been developed by Mulliken [106,107] and followed by many researchers in interpretation of results on optical spectra of D–A molecular mixtures (a comprehensive overview of past works is given by Birks [76]). The ground-state function of the DA complex may be written as jD; Ai ¼ ajDAi þ bjDþ A i

Copyright © 2005 by Marcel Dekker

ð28Þ

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where jDAi is the non-bond wave function of the DA structure, and jDþAi is the dative-bond wave function of the DþA structure, in which an electron is transferred from D to A. The corresponding wave function of the excited state of the DA complex is jD; Ai ¼ a jDþ A i b jDAi

ð29Þ

The coefficients a, b, a and b determine the extent of mixing between different electronic configurations of donor and acceptor molecules. For a weak DA complex, a ﬃ a ¼ 1 and b ﬃ b ﬃ 0. The jD,Ai ! jD,Ai transitions are thus appropriately described by a charge-transfer transition, since it corresponds approximately to a jDAi ! jDþAi transition. It is, however, incorrect to describe the ground-state DA complex as a charge-transfer (CT) complex. The ground-state electronic configuration is a result of the interaction between the p-orbitals of the components and can be considered as a van der Waals complex ‘‘prepared’’ for charge transfer before excitation. The ratio l¼

b2 a2 þ b2

ð30Þ

determines the fractional contribution of the DþA to the ground state and this fractional ionic character can vary from l ¼ 0 for no charge transfer to l ¼ 1 for complete electron transfer. The coefficients a, b, a and b for various DA complexes have been evaluated from their dipole moments. In a complex of a nonpolar donor with a nonpolar acceptor, the non-bond structure DA has a negligible dipole moment m0 ﬃ 0, but the dative bond structure DþA has a finite dipole moment m1 ﬃ erDA, directed from D to A, where e is electronic charge, and rDA is the equilibrium separation of the two components in the complex. The analysis of coefficients describing configuration interaction mixing in the ground state indicates a minor admixture of CT configuration (<0.005) that is a=b > 15. The energy of intermolecular Copyright © 2005 by Marcel Dekker

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interactions in the ground-state configuration (DA) can be expressed as EðDAÞ ¼ Ev dW ðDAÞ þ Eel ðDAÞ

ð31Þ

where Ev dW is the energy of van der Waals interactions and Eel is the energy of electrostatic interactions between the net charges on the two molecules. The energy of the CT configuration (DþA) is EðDþ A Þ ¼ ID AA EC þ Ev dW ðDAÞ

ð32Þ

where EC is the Coulomb interaction in the (DþA) configuration which is formed upon electron transfer from the highest occupied molecular orbital (HOMO) of the donor to the lowest unoccupied molecular orbital (LUMO) of the acceptor, and EC ¼

e2 4pe0 erDA

ð33Þ

Coupling between the CT state and ground electronic state is expressed by the matrix element of the Hamiltonian (H) of the system (A,D) and shown to be proportional to the overlap integral (S): hDþ A jHjDAi ¼ 21=2 KS

ð34Þ

where S ¼ hDþ A jDAi

ð35Þ

and the K is a constant dependent on chemical nature of the interacting moities [108]. The formation of molecular complexes in the ground state 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 wavelength than those of the components. The longest wavelength absorption band of the complex (DA) corresponds to an electronic transition, which, in the first approximation, can be Copyright © 2005 by Marcel Dekker

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described as a CT transition jDAi ! jDþAi. An example is shown in Fig. 24. The energy ECT of the maximum of the jDAi ! jDþAi CT absorption transition is given by a difference between the energies of the DA complex in the excited (Eex) and ground (Eg) states at the equilibrium separation (rDA) of the ground-state DA complex: ECT ¼ Eex Eg

ð36Þ

Figure 25 shows diagramatically the potential energy curves of a DA complex as a function of the intermolecular distance r. The curves EDA(r) and EDþA(r) represent the energies of the DA and DþA structures, respectively. ECT corresponds to the vertical Franck-Condon Eg ! Eex transition. The ground and excited state energies of the DA complex are given by Mulliken [106,107] Eg ¼ EDA

ðH01 EDA SÞ2 ðEDþ A EDA Þ

ð37Þ

Figure 24 The CT absorption band in solid anthracene–trinitrobenzene complex (1). Solid state absorption spectra of anthracene (2) and trinitrobenzene (3) are shown for comparison. After Ref. 109. Copyright © 2005 by Marcel Dekker

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

and Eex ¼ EDþ A

ðH01 EDþ A SÞ2 þ ðEDþ A EDA Þ

ð38Þ

where H01 ¼ hDþAjHjDAi. Equation (36) can thus be rewritten as ECT ¼ EDþ A EDA þ

ðH01 EDþ A SÞ2 þðH01 EDA SÞ2 ðEDþ A EDA Þ ð39Þ

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From the diagram ECT ¼ Eex Eg ¼ ID AA ðDEex DEg Þ

ð40Þ

where DEex and DEg are the energies of formation of the DA complex in the excited and ground states, respectively. A molecular complex may be dissociated in the ground state, and yet be associated in an excited electronic state. An excited molecular complex of defined stoichiometry, which dissociates 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 a donor molecule D and an acceptor molecule A has a general form jDAi ¼ C1 jDþ A i þ C2 jD Aþ i þ C3 jD Ai þ C4 jDA i ð41Þ Exciplex formation in the excited singlet state manifests itself in the fluorescence spectrum. An example is given in Fig. 26. The fluorescence of the TPD donor (D) is quenched by the PBD acceptor (A) (the latter is not practically excited by the 360 nm exciting light) and a new broad and structureless emission band appears at longer wavelength. This new emission is ascribed to an exciplex, formed in the excited singlet state according to TPD ð1 D Þ

1

þ

1

PBD ð1 AÞ

!

1

ðPBD TPDÞ 1 ðADÞ

ð42Þ

As there is no corresponding change in the absorption spectrum, the complex, evidently, is not formed in the ground state. Exciplexes formed between relatively strong donors and acceptors are preferably represented by 1(ADþ), expressing the fact that the excited state is a singlet CT state [the coefficients C2, C3 and C4 in (41) are negligibly small]; the emission of the complex, therefore, corresponds to the CT transition, the reverse of the CT absorption, jDþAi ! jDAi. The energy of the pure CT state, jDþAi, in the gas phase relative to Copyright © 2005 by Marcel Dekker

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

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the ground state, A þ D, is given by Eq. (32). Therefore, in the first approximation, the energy of the CT emission band, hn max EX , should be linearly correlated with ID and AA, which, in turn, are related to the polarographic oxidation potential of the donor, Eox D , and to the polarographic reduction potential , respectively. Such linear correlations of the acceptor, Ered A ox red and E E have been found for more between hn max EX D A than 160 exciplexes in a non-polar solvent (hexane) (see e.g., Ref. 113), ox red hn max EX ¼ ED EA D

ð43Þ

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 measurements) is evidently due to the fact that the solvation energy in a polar matrix of the separate ions, Dþ and A, is of the same order and depends on the size of the ions in the same way as the Coulomb term EC. Applying Eq. (43) to the (TPD:PBD:PC) film in Fig. 26, yields hn max EX ¼ 2.6 0.1 eV (476 15 nm) in excellent agreement with the experimentally observed location of the PL spectrum maximum using Eox (TPD) ¼ 0.35 eV [114] and Ered(PBD) ¼ 2.4 eV [115]. This indicates the exciplex (42) to have a strong CT character. The exciplexes with D values >0.2 eV and dipole moments which are smaller than those of the CT exciplexes are formed as a result of interactions between the CT state 1 (ADþ) and non-polar (locally) excited complex states such as 1(A D) and 1(AD ) leading to stabilization of the CT state and to lowering of the dipole moment [116]. The coefficients C1 or C2, and C3 and C4 in the wave function (41) can be of comparable magnitude for such exciplexes. The value of D ﬃ 0.3 eV follows for the exciplex formed by the TPOB acceptor [1,3,5-tris(4-fert-butylphenyl-1,3,4-oxadiazolyl)benzene] with the TCTA donor [4,40 ,400 -tri(N-carbazolyl) triphenylamine] based on EDox ¼ 0.69 eV and EAred ¼ 2.1 eV, and the Copyright © 2005 by Marcel Dekker

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position of its emission band, hn max EX ¼ 2.48 eV, observed from a TPOB:TCTA equimolar mixture prepared in a form of spincoated films [117]. This value of D implies a relatively small energy gap between CT singlet and locally excited singlet states, so that their mixing cannot be neglected forming an excited complex termed the intermediate exciplex. These interactions are even more important with typical excimers where D > 0.6 eV and zero dipole moment (cf. Sec. 2.3.1). Analogous to fluorescence from the singlet CT state, phosphorescence from the triplet CT state may be expected if this state 3(ADþ) is energetically below the locally excited triplet states, 3(A D) and 3(AD ). Under this condition, the energy gap between CT singlet and locally excited singlet states is large, so that their mixing will be small or even negligible. The singlet–triplet splitting, DST, for the CT state (ADþ) can be expressed as [108] DST ¼ 1 E1 ðA Dþ Þ 3 E1 ðA Dþ Þ ﬃ 102 S2 ðeVÞ

ð44Þ

where S represents the overlap between the HOMO of the donor and the LUMO of the acceptor. For typically S ﬃ 0.01, DST ﬃ 0.01 eV is very small, and in fact, will be 0 for the zero-order CT state. Exciplex phosphorescence can be studied with complexes which are present in the ground state [118]. Equation (43) and its corollaries with respect to variations in D are applicable also to exciplex phosphorescence. For example, positive deviations (D > 0.18 eV) which have been found in the phosred E > 2.75 eV are phorescence of complexes with Eox D A ascribed to the stabilizing interaction between the triplet CT state and energetically higher locally excited triplet states [108,119]. Contrary to the photodissociation, where electron–hole pairs originate from photoexcited localized states, the charge pair states constitute primary species for final emitting states in the bimolecular recombination process (see Fig. 27). The injected carriers (e, h), by diffusing together will form an encounter complex, i.e. a Coulombically correlated ion pair (ADþ). This ion pair comprises a large number of Copyright © 2005 by Marcel Dekker

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Figure 27 Molecular (D ), exciplex [(D A) þ (ADþ)CT], chargetransfer (A–Dþ) excited species as generated by photo-excitation and electron–hole recombination processes in electron acceptor (A)–electron donor (D) molecular systems. hn D, hn EX, and hn EC are corresponding transition energies to the ground state, to be observed as different emission bands.

configurations of A relative to Dþ, which differ from the specific configuration of A and Dþ in the hetero-excimer [charge resonance component (ADþ)CT of the exciplex: (D A) þ (ADþ)CT]. Like in excimer, in the exciplex, the molecular planes of A and Dþ are parallel or nearly parallel to each other with an interplanar separation of 0.3–0.4 nm, and with no matrix molecules in between (cf. Figs. 13 and 14 in Sec. 2.3.1). As a consequence, only a fraction of the correlated (ADþ) pairs leads to formation of exciplexes, the reminder should result in the formation of molecular excited states of either donors or acceptors. However, the formation process of the molecular excited state is inhibited by an energy barrier for the excess electron located on the acceptor molecule to pass on the donor molecule. Possible electron pathways between molecules PBD and TPD are shown in Fig. 28. The finite electron transit time in process 1 opens Copyright © 2005 by Marcel Dekker

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

an additional relaxation pathway for the excessive electron on the molecule A, which is the cross-transition to the hole located on the HOMO of the donor (process 3). This resembles the cross-transition between energetically inequivalent molecules in single component materials, considered as a relaxation of the specific excited state called electromer (see Fig. 20 and Sec. 2.3.1). The term ‘‘electroplex’’ (EC) becomes often used to characterize a charge pair (A–Dþ) with charge carriers spaced by a distance rðA Dþ Þ ¼ rEC > rðA Dþ Þcr but rEC < r(ADþ). It has been first introduced to explain the green emission band in the emission spectrum of the organic Copyright © 2005 by Marcel Dekker

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LED based on the PTOPT=PBD junction [121]. This band located between the monomolecular red emission band from a conjugated polymer (PTOPT) and the molecular exciton violet-blue emission from PBD, has been ascribed to a sort of ‘‘cross-reaction’’ between the LUMO of PBD and HOMO of PTOPT (Fig. 29). Its occurrence in this system shows that the cross-transition does not necessarily require the hole transporting material (HTM) to have an electron affinity lower than that of the electron transporting material (ETM). This would suggest that the electron transition from the LUMO of ETM to the LUMO of HTM can be simply considered as a hopping process across a disordered organic solid with the high-field (F > 105 V cm1) activation energy D(F) ¼ D0(1 F=F0), where D0 is the Arrhenius zero-field activation energy and F0 is a constant dependent on the intersite distance and disorder parameters. At F F0, D(F) 0, the transport properties of the system are determined by electron–phonon interactions. For a 0.1% triphenylamine (TPA) dispersion in polycarbonate (PC), D0 ﬃ 0.58 eV and F0 ¼ 3.3 106 V cm1 was found. These parameters change with concentration of the dopant [122]. The Arrhenius-type behavior of carrier transport can be considered as an approximation of a non-Arrhenius-type temperature dependence of carrier motion among transporting states which are subject to Gaussian distribution of energies (14), implying D0 ¼ (8=9)s2=kT and F0 D0=r (cf. Sec. 4.6). Thus, the transport properties reveal a recurrent pattern of features for a broad class of disordered materials independent of their chemical composition and impurity effects [39]. Consequently, the rate of electron transfer from the LUMO of an acceptor to the LUMO of a donor (route 1 in Fig. 28) is determined by the disorder parameter, s, of the system rather than by the chemical nature of the interacting molecules. The field lowering of the intermolecular barrier for electron transport implies a field-dependent branching ratio between formation of molecular excited states and electroplexes, the competition to be extended to the formation of exciplexes (cf. Fig. 27). A relatively weak, but well-discernable Copyright © 2005 by Marcel Dekker

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

feature at lEC ﬃ 564 nm in the EL spectra of the (TPD:PBD:PC) film (Fig. 26), has been assigned to the electroplex emission [112,120]. It can be separated as a Gaussian band which in a combination with other two Gaussian Copyright © 2005 by Marcel Dekker

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bands, corresponding to the monomolecular emission of TPD and exciplex emission of 1(PBD TPD) , reproduces well the experimental EL spectrum (Fig. 30a). The contribution of these bands to the spectrum changes with applied voltage as shown in Fig. 30b. From these results, it is apparent that the low-voltage EL spectrum is dominated by the exciplex (60%) and electroplex (40%) emissions, the monomolecular emission from TPD being practically negligible. The electroplex emission drops down at increasing voltages (<30% at 18 V) while both monomolecular and exciplex emissions increase (3% and 70%, respectively, at 18 V). The counterbalance between these changes suggests that the increasing production of excited molecular donors (D ) and exciplex (ADþ) occurs on the expense of the formation efficiency of electroplexes from their common precursor of Coulombically correlated ion pair (ADþ) (cf. Fig. 27). This is consistent with the above premise predicting the enhanced formation of molecular excited states and exciplexes due to the field-induced lowering of the LUMO ! LUMO or HOMO HOMO intermolecular electron-transfer barrier (Fig. 28). It is to be expected that the radiative rate constants for spontaneous emission of exciplexes and electroplexes will resemble those for excimer and electromers [see discussion of Eqs. (20) and (21) in Sec. 2.3.1)]. This implies that, dependent on the intermolecular configuration, the fluorescence lifetimes of exciplexes range between 10 and 200 ns, and that the emission lifetime of electroplexes is limited by the intermolecular electron hopping time. Though there are no at present direct lifetime measurements on electroplexes, the measurements on a series of donor–acceptor species in solidstate 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 recombination event in an organic solid creates an electronic excitation, Copyright © 2005 by Marcel Dekker

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Figure 30 (a) The experimental EL spectrum of a (TPD:PBD:PC) film (d ¼ 60 nm) (solid line) deconvoluted into three Gaussian components (1, 2, 3), corresponding to its wavelength representation I in Fig. 26. The dashed curve represents the best fit to the experimental spectrum. (b) The voltage evolution of the Gaussian components of the EL emission. A1, A2, A3 correspond to the contributions of the EL components related by the area under the Gaussian profiles peaking at hn 1 ¼ 2.99 eV (l1 ¼ 415 nm; molecular exciton emission of TPD), hn 2 ¼ 2.6 eV (l2 ¼ 477 nm; TPD–PBD exciplex emission), and hn 3 ¼ 2.2 eV (l3 ¼ 564 nm; electroplex emission). After Ref. 120. Copyright 2000 Institute of Physics (GB).

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Table 1 Fluorescence Band Locations (lmax) and Lifetimes (t) of some Electron Donor and Electron Acceptor Molecules-doped Solid PC films (from Kalinowski, Cocchi, Virgili, Di Marco and Fattori, to be published) Films (d ¼ 60 nm)b Single-dopant films TPD 75%:PC 25% PBD 75%:PC 25% m-MTDATA 75%:PC 25% TCTA 75%:PC 25% Exciplexes in films of TPD 40%:PBD 40%:PC 20% m-MTDATA 75%:PBD 40%:PC 20% TCTA 40%:PBD 40%:PC 20%

lmax (nm)

t (ns)

415 390 420 390

<1c <1c 1.3d 1.1c

464 535 445

44e 145f 37e

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

b

which, dependent on the strength of the intermolecular interactions (intermolecular coupling), has different degree of delocalization. It is considered as a communal response of a molecular aggregate, forming a quasi-particle called exciton. 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 the wave functions of all excited molecules in the domain have a uniquely defined relationship to each other, the resulting Copyright © 2005 by Marcel Dekker

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excitation moves in a wavelike manner and the exciton is said to be free or coherent. Its mixture with exciting photons in the medium is called polariton (see e.g., Ref. 126). In this case, the quantum numbers characterizing the exciton do not change; for example, the wave vector k~ is a good quantum number and the direction of exciton propagation is fixed. Because of interactions with phonons and imperfections, transitions are induced among the various states accessible to the excitons and the coherence of the exciton is lost. The time for which the exciton remains coherent is called its coherence time, tcoh, and for organic materials tcoh at room temperature is generally much less than 1013 s because of the large exciton– phonon interaction energies characteristic of these solids [127]. For times greater than tcoh, the exciton moves incoherently and generally is viewed as a localized excitation undergoing a random hopping like motion. The exciton wave vector k~ is no longer a good quantum number, the large spread in k~, dk~, limits the exciton size which is inversely proportional to the dk~ [e.g., the extent along the x-axis dx ﬃ (dkx)1]. The average value of dkx, evaluated from Boltzmann’s statistics through the relationship h2(dkx)2=2me ﬃ (3=2)kT, is on the order of dkx ﬃ 2 106 cm1 for T ¼ 300 K and me ¼ rest mass of the electron. Resulting dx ﬃ 5 nm indicates the localization of the exciton within a few neighboring molecules, we deal with a small radius (Frenkel type) exciton. Its application to organic crystalline solids was initially given by Davydov [128] (see also Ref. 129). The spread in k~ imposes a spread in vg ¼ h1dE(k~)=dk~ is the group energy dE(k~) ¼ h~ vg(k~)dk~, where ~ velocity of the packet representing a localized exciton. This must not be confused with the width of the exciton band, DEb ¼ 4jbj, which is determined by the energy of interaction between neighboring molecules b which can be either positive or negative. For triplet excitons in 1,2,4,5-tetrachlorobenzene, b ¼ þ0.34 cm1 [130], whereas, for triplet excitons in 1,4-dibromonaphthalene, b ¼ 6.7 cm1 [131]. In conventional solid-state physics, an exciton is considered as an electron–hole pair separated by a medium with a well-defined dielectric constant, e. The time-independent Schro¨dinger equation with the inter-carrier Coulomb Copyright © 2005 by Marcel Dekker

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potential (e2=4pe0er) is solved leading to a series of discrete hydrogen atom-like, energies (see e.g., Ref. 132) En ðk~Þ ¼

1 h2 k2 þ 2 h2 ð4pe0 eÞ2 n2 2ðme þ mh Þ mr e4

ð45Þ

and corresponding electron–hole distances an ¼

4pe0 h2 e 2 n e2 mr

ð46Þ

in which n is an integer (n ¼ 1,2,3, . . . ), and mr ¼ me mh =ðme þ mh ) is the reduced mass of the electron (me ) and hole (mh ) effective masses. The binding energy of the exciton is given by the difference between the energy gap and the energy values of (45), DEex ¼ Eg En(k~). This type of exciton is envisaged by Wannier [125] and Mott [132a], thus known commonly as a Wannier-Mott exciton. In this exciton, the electron and the hole revolve around each other resembling the simple (Bohr) structure of the hydrogen atom. The energies (45) and inter-carrier distances (46) can, therefore, be readily related to the discrete energy 4 h2 ð4pe0 Þ2 n2 and radii of electron spectrum ½EH n ¼ me e =2 H 2 orbits ðan ¼ a0 n Þ in this atom. Neglecting kinetic energy, one arrives at EH mr n En ¼ 2 e me

ð47Þ

and an ¼ a0

me en2 mr

ð48Þ

where a0 ¼ 0.053 nm is the atomic (Bohr) radius. The exciton binding energy is related directly to the ionization energy of the hydrogen atom, IH ¼ 13.5 eV, according to 13:5 mr ½eV ð49Þ DEex ðnÞ ¼ 2 2 e n me Copyright © 2005 by Marcel Dekker

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The smaller the reduced mass of the exciton and higher dielectric constant of the material is, the larger is the exciton radius and weaker exciton binding. For example, the ground excitonic state (n ¼ 1) is characterized by a1 only about 0.4 nm and DEex (n ¼ 1) as high as 0.4 eV for low-dielectric constant materials (e ¼ 4) and me ¼ mh ¼ me (mr ¼ 0.5), whereas for higher excitonic levels (say n ¼ 5), and high-dielectric constant materials (say e ¼ 12), the electron–hole distance as large as 32 nm but the carriers are loosely bounded with DEex(n ¼ 5) ﬃ 4 meV. In the first case, we deal with a smallradius (Frenkel) exciton typical for organics, in the latter with the large-radius exciton characteristic of inorganic semiconductors (see e.g., Ref. 133). The intermediate size excitons have been discussed in Sec. 2.3.1 under the name of coulombically correlated electron–hole pairs or charge-transfer states. The existence of the finite exciton bandwidth implies the kinetic energy of the exciton and exciton–phonon coupling to be accounted for in a more realistic description of excited states. For most materials, there is a dense system of vibrational states that is strongly coupled to the electronic states. The exciton–phonon coupling strength, relative to the intermolecular interactions, has been used as another criterion for localization of excitons. If the strength (J) of the interaction between an excited molecule (energy donor) and a ground-state molecule (energy acceptor) greatly exceeds the vibrational bandwidth (DEv) of the acceptor electronic state (jJj DEv), we deal with the strong exciton coupling limit. In this limit, the energy transfer is coherent, the exciton is said to be a free exciton. For dipole–dipole interactions, J r3, where r is the mean separation between donor (MD) and acceptor (MA) molecules, the time for excitation energy to pass from MD to MA, t(MD ! MA) r3. It strongly depends on r and is shorter than the vibrational relaxation time of molecules [t(MD ! MA) < h]. This condition is, however, generally, not met in DEv= practice. If jJj is much greater than the width of a single vibronic level, the condition termed the medium interaction case, the exciton is said to be an intermediate exciton. On Copyright © 2005 by Marcel Dekker

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the other extreme, a localized exciton is defined by the weak-coupling condition jJj < DEv. The very weak-coupling case is commonly distinguished jJj DEv, the limit often encountered in practice and called long-range or Fo¨rster energy transfer [134,135]. There is a lack of consistency in the terminology of energy transfer. In further considerations, the term of energy transfer will be used to describe a process that involves one donor molecule and one acceptor molecule, whereas energy migration will refer to the process of motion of the exciton. Typically, migration involves a series of transfers if no intervening trap halts the process. The final step in the migration process is then designated as trapping. If the trap is due to a guest molecule allowing the excess energy to be released by a radiative decay, we deal with the quest- (or dopant-) sensitized luminescence. Two primary experimentally measured parameters are necessary to characterize this phenomenon: (i) the motion time (1=M), i.e., the time to get the exciton within the capture radius of a guest molecule, and (ii) the elementary capture time (1=C). Thus, the host (H)–guest (G) energy transfer rate constant can be expressed as [136,137] kHG ¼ cG ð1=C þ 1=MÞ

ð50Þ

where cG is the mole guest concentration. Unfortunately, most experiments utilized in energy transfer studies yield only the motion-related primary parameter. In this respect, time-resolved spectroscopy has the advantage of yielding two primary experimental parameters associated with the rate of energy transfer (see e.g., Refs. 137, 138). In contrast to common picture of the host–guest energy transfer to be motion-controlled, the capture process has been suggested as a rate limiting step. For example, in the case of tetracene-doped anthracene crystal, at least at T > 60 K, the energy transfer rate has been thought as capture limited because the estimated exciton motion time 1=M < 2.3 1014 s appeared to be much shorter than the measured value of cG=kHG ﬃ 3 1013 s at room Copyright © 2005 by Marcel Dekker

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temperature [137]. This conclusion has been made on the basis of the experimentally determined temperature dependence of the constant kHG and singlet exciton annihilation rate constant, gSS, in a neat anthracene crystal, the point to be addressed later in Sec. 2.5.1. The process of reabsorption of emitted photons is important at long distances (more than 10 nm from the site of excitation). In this process, emission originates from a donor and reabsorbed by the acceptor. The net effect of reabsorption in a single component solid is to lengthen the apparent lifetime of the emitting states [139], their spatial distribution and resulting shape of the emission spectrum [56]. Also, it has been employed to determine the spatial distribution of emitting species produced in the recombination electroluminescence in single organic crystals (see Chapter 3). The non-radiative energy transfer (and migration) will be discussed in the following two sections. 2.4.1. Excitonic Motion Exciton migration can be described as a random walk and, in the limit of many steps, this can be described by a diffusion formalism. The form of the diffusion coefficient depends on the size of the mean free path [140]. If the mean free path is of the order of the nearest-neighbor intermolecular distance, the exciton hops incoherently between molecules and is scattered at each molecule. The diffusion coefficient is then expressed in terms of the nearest-neighbor molecular spacing and exciton hopping time. If the mean free path is greater than the nearest-neighbor distance, the exciton moves coherently over several intermolecular spacings before being scattered and it is more appropriate to use an exciton band model. The diffusion coefficient can then be expressed in terms of free path and the exciton velocity. For singlet exciton migration in typical organic solids at room temperature, the incoherent hopping model is generally thought to be appropriate. In ultrapure crystals at low temperatures, where neither impurities nor phonons are effective in limiting the exciton mean free path, it may be possible to detect some coherent Copyright © 2005 by Marcel Dekker

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exciton motion [140,141]. The kinetic equation for exciton diffusion is given by @nex ¼ GðtÞ bex nex þ DH2 nex @t

ð51Þ

where nex is the concentration of excitons generated at a rate G(t), bex is their monomolecular decay rate constant, and D is the exciton diffusion coefficient which is assumed to be isotropic. The energy transfer steps are due to the excitation capture rate by neighbor molecules of radius R. Its second order rate constant can be expressed as a time-dependent flux through the spherical surface [142,143] h i ð52Þ gD ¼ 4pDR2 ð@ns =@rÞ R ¼ 4pDR 1 þ RðpDtÞ1=2 which is equivalent to the transfer rate h i kD ðtÞ ¼ gD N ¼ 4pDRN 1 þ RðpDtÞ1=2

ð53Þ

where N is the concentration of molecules. Equation (53) holds for a d-function excitation at t ¼ 0 and a single energy acceptor 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. The boundary condition nex(RA) ¼ 0 and the choice of RA define the trapping mechanism. Although from high-resolution time-dependent studies of sensitized fluorescence, a timedependent rate kD(t) has been established [138,144], all the experimental data for kD(t), within the limits of the time resolution > 10 ps, can be explained on the basis of a timeindependent energy transfer rate [137]. This suggests D > 103 cm2=s, which, for typically R ﬃ 1 nm, makes the transient term in Eq. (53) negligible relative to unity. If the scattering length of an exciton l > R, Eq. (53) will not hold and a transfer rate constant can be considered proportional to sv, where v is the velocity of the exciton and s is the cross-section of capture kD ¼ gD N ¼ svN Copyright © 2005 by Marcel Dekker

ð54Þ

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In the random walk description, the energy transfer rate constant is related to the number of hops made by the exciton without revisiting any site in its lifetime. The nearest-neighbor random walk in an isotropic medium may be approximated by a random walk on a simple cubic lattice [145] D ¼ ð1=6Þc2 t1 h

ð55Þ

where c is the lattice spacing and th is the mean time between steps of length c. If an exciton hops about, starting from some initial site and ends up at another site at the time of its disappearance for one reason or another, the linear distance between these sites is called the diffusion length, ld. The diffusion length is related to the diffusion coefficient D through the exciton lifetime t: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð56Þ ld ¼ ZDt where Z ¼ 6 for three dimensions, 4 for strictly twodimensional motion and 2 for one-dimensional diffusion [26]. Reported values of D vary by a factor of about 2 because of the inconsistency existing in the literature concerning the values of Z; usually Z is taken to be unity. The diffusion length of excitons can be determined experimentally from the luminescence surface quenching or excitonic carrier injection experiments. For singlet excitons in anthracene, ld ﬃ 40 nm and t ﬃ 10 ns yield D ﬃ l2d =t ﬃ 2 103 cm2 s [146]. A similar value of ld ﬃ 30 nm has been obtained for TPD [147] and ld ﬃ 10–30 nm for Alq3 [16,148–150]. Taking the experimental values of the intrinsic lifetime of singlet excitons ﬃ1 and ﬃ15 ns, respectively, allows to evaluate their D ﬃ 3.5 103 cm2=s for TPD, and D ﬃ 6 105 cm2=s for Alq3 solid films. The latter value is much lower than those for anthracene and TPD. This implies a long hopping time as calculated from Eq. (55), identifying c with the average intermolecular distance r ﬃ 0.8 nm as estimated from the molecular density of Alq3 (N ﬃ 2 1021 cm3). The hopping time and some other migration parameters for singlet and triplet excitons in these important materials are compared Copyright © 2005 by Marcel Dekker

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in Table 2. It is interesting to note that the total distance covered by the exciton in the random walk, l ¼ (t=th)c, which by many orders of magnitude exceeds the diffusion length in crystals, is mostly much shorter in amorphous solids as for example in Alq3. The l=ld ratio can be a measure of the probability to transfer energy to a structural and=or chemical imperfection of the molecular system; the greater the ratio is the exciton visits more sites, the probability to encounter a defect increases. Thus its large values for crystals make them particularly well suited for excitonic energy transfer to even small amounts of defects or intentionally incorporated dopants. From the definitions of l and ld, it follows that their ratio, l=ld ¼ (6t=th)1=2, is determined by the ratio t=th which contains characteristics of individual molecules through the exciton lifetime (t), and intermolecular interactions through the energy transfer time th. In the strong coupling limit h=4jJj) [157,158], and is proportional to the third power th ¼ ( of the intermolecular separation (R) for dipole–dipole interactions, as mentioned already in the context of the exciton localization concept (see Sec. 2.4). The weak coupling limit implies [159] t1 h ¼

2prn 2 b x h el

ð57Þ

where rn is the vibronic state density, x is the vibrational overlap (Franck-Condon factor), and bel is the electronic interaction matrix between the excitonic initial and final states. The total interaction between a vibrationally unrelaxed lowest excited electronic state of a donor molecule (M 1) and an unexcited acceptor molecule (Ma) may be partitioned into Coulombic and electron exchange terms [160]. The Coulombic interaction can be expressed as a multipole–multipole expansion, the leading term of which is dipole–dipole. This term represents the interaction between Md ! M d and Ma ! M a transition dipole moments, ~ m1, ~ m2, yielding bel

~ m1~ m2 r3

Copyright © 2005 by Marcel Dekker

ð58Þ

72

Table 2

Various Singlet and Triplet Exciton Migration Parameters in Some Organic Solids

Material Anthracene (crystal) Tetracene (crystal) TPD (film) Alq3 (film)

Intermolecular distancea c (nm) 0.5 0.7 0.9 0.8

Exciton spin multiplicity Singlet Triplet Singlet Triplet Singlet Singlet Triplet

Lifetime t (s) 108 102 2 1010 105 109 1.5 108 2.5 105

Diffusion length ld (nm)

Diffusion coefficient D (cm2=s)

Hopping time th (s)

Total distance covered l (nm)

40b 104c 12d 300e 30f 23g 30h 14i

2 103 104 7.2 103 7.9 105 3.5 103 6 105 8 108

2 1013 4.2 1013 1.1 1013 6 1011 4 1013 1.8 1011 1.3 108

2.5 104 1.2 1010 1.3 102 1.2 105 2.3 103 7 102 1.5 103

l=ld 600 1.2 106 10 400 80 30 107

a

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Organic Light Emitting Diodes

Calculated from c ¼ (M=NAr)1=3, where M is the molecular weight, NA is Avogadro’s number, and r is the mass density of the solid. Typically, r ¼ (1.2 1.5) g cm3; r ¼ 1.3 g cm3 for Alq3 has been taken in this calculation (see Ref. 151). b From Ref. 146. c From Ref. 152. d From Ref. 153. e From Ref. 154. f From Ref. 147. g From Ref. 155. h From Ref. 150. i From Ref. 156.

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Higher multipole–multipole interaction terms decrease at higher inverse powers of the intermolecular separation, but become important when the dipole–dipole interaction is symmetry forbidden, e.g., in benzene where the octupole–octupole interaction is dominant [161]. The electron-exchange interaction requires overlap of the electronic wave functions of M d and Ma, and it is therefore of short range (1.5 nm). Due to an exponential decrease in the overlap of electronic wave functions with intersite distance, the energy transfer rate is expected to decrease more rapidly and, in fact, it can be expressed as (see e.g., Ref. 162) 1 t1 h ¼ ttot exp½gð1 r=r0 Þ

ð59Þ

Here ttot is the lifetime of the energy donating molecule, g ¼ 2r0=L, where a constant L (called the effective Bohr radius) falls in the 0.1–0.2 nm range, and r0 is defined by 1 t1 h ðr0 Þ ¼ tTOT

ð60Þ

which means that at r ¼ r0 the rate of energy transfer equals the rate of total (radiative and non-radiative) deactivation of the excited state. The exchange term is usually dominant at close approach of M d and Ma, and allows triplet exciton transfer to occur when the donor and acceptor transitions are spin-forbidden. Therefore, four energy transfer processes from a singlet (1M d ) excited molecule and triplet (3Md ) excited molecule to an unexcited molecule in the singlet state (1Ma) are possible: 1

Md þ 1 Ma ! 1 Md þ 1 Ma

ð61aÞ

1

Md þ 1 Ma ! 1 Md þ 3 Ma

ð61bÞ

3

Md þ 1 Ma ! 1 Md þ 3 Ma

ð61cÞ

3

Md þ 1 Ma ! 1 Md þ 1 Ma

ð61dÞ

The latter is of particular importance for improving the EL efficiency by introduction of highly fluorescent molecules into Copyright © 2005 by Marcel Dekker

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a poor emitter where triplet excitons are produced efficiently in the bimolecular electron–hole recombination process [163,164]. 2.4.2. Long-range Energy Transfer Long-range energy transfer is defined by the very weakcoupling case of energy transfer as discussed at the beginning of Sec. 2.4. The excited states are well-localized and the intermolecular coupling is very weak. This type of energy transfer is referred to by several different names including quantum mechanical resonance, inductive resonance or Fo¨rster–Dexter transfer [135,138]. The mathematical description of the longrange energy transfer was originally developed by Fo¨rster [134] for dipole–dipole interactions and later extended by Dexter [160] to include exchange and higher multipole interactions, which may be important at small separations. The long-range energy transfer is the most important mechanism for singlet excited states in a molecular system coupled by dipole–dipole interactions. The rate constant of energy transfer between a donor and an acceptor separated by a distance r (isolated single D–A pair) and coupled by the dipole–dipole interaction of randomly oriented transition dipoles can be expressed as (see e.g., Ref. 26) 5 1 R0 1 R0 6 ¼ ð62Þ kD--A ¼ t r tD r where t is the observed lifetime of the excited state being related to the radiative donor lifetime, tD, through the fluorescence yield of the donor in the absence of the acceptor, jFL, t ¼ jFLtD, and 1=6 Z 4 ð63Þ R0 ¼ ð3=4pÞ ðc=n0 oÞ FD ðoÞsA ðoÞ do is a critical transfer distance at which the energy transfer rate from D to A is equal to the radiative decay rate. Accor1=6 ding to Eq. (62), R0 ¼ jFL R0 defines a characteristic Copyright © 2005 by Marcel Dekker

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donor–acceptor distance at which transfer competes equally with the total rate of removal of energy from D by any other means such as radiative or radiationless decay or hopping away (in the case of single component materials). Typical values of R0 for organic systems are ﬃ3 nm. The critical distance R0 (63) depends on the overlap integral between the normalized fluorescence emission spectrum of the donor, FD(o), and absorption spectrum of the acceptor, here expressed by the normalized acceptor absorption cross-section, sA(o) in units cm2 [sA (cm2) ¼ 3.82 1021 E A (liter-mole cm1), where EA is the molar absorption coefficient]. The o integration is over all (angular) frequencies. The index of refraction of the medium is n0, and c is the speed of light in vacuum. Equations (62) and (63) demonstrate that no transfer is possible unless the donor fluorescence and acceptor absorption spectra overlap. In the case of triplet energy transfer where electron exchange is the dominant interaction, Dexter has expressed the transfer rate as hÞjbDA j kDA ¼ ð2p=

2

Z

FD ðEÞFA ðEÞ dE

ð64Þ

where bDA is the exchange energy interaction between molecules, E is the energy, FD(E) and FA(E) are, respectively, the normalized phosphorescence spectrum of the donor and normalized absorption spectrum of the acceptor molecule. These spectra can be used if the radiative transitions giving rise to these spectra gain their singlet character by a spinorbit coupling mechanism that is not vibrationally induced [165]. Many tests have been made of the validity of Fo¨rster– Dexter transfer in doped organic solids. A typical example is the classic solid solution study of anthracene and tetracene dissolved in naphthalene [26,166]. Energy originally absorbed by anthracene (donor) was shown to be transferred with high efficiency to tetracene (acceptor) by measuring the tetracene fluorescence. In these studies, the anthracene: tetracene ratio was 1:1 and the mol fraction of the guests Copyright © 2005 by Marcel Dekker

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was varied from 2 105 to 103. The experimental results described in terms of the Fo¨rster non-radiative transfer mechanism gave R0 ¼ 4.4 nm. The Fo¨rster triplet–singlet energy transfer appeared to be an important factor of improving 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 (see Sec. 1.4). The triplets as a rule are lost for the optical output because their radiative decay is spin-symmetry forbidden. To gain them over to the luminous performance of the EL device, the transfer of their energy to a phosphorescent molecule is required (process (61c) in Sec. 2.4.1). A further improvement of the EL quantum efficiency could be reached if an effective triplet–singlet energy transfer from this phosphorescent molecule to another-highly fluorescent molecule were possible. Such a process has been observed with a range of phosphorescent donors and fluorescent acceptors in transparent rigid media at 77 or 90 K. Large transfer distances have been found; for example with triphenylamine as the donor and chrysoidine as the acceptor, the interaction range is 5.2 nm [168]. However, incorporating directly a fluorescent acceptor into a phosphorescent donor material eliminates the long-range triplet–singlet energy transfer because due to the close proximity of the donor and acceptor molecules, increases the likelihood of the short-range Dexter transfer between the donor and acceptor triplets. So produced triplets of the fluorescent material are lost for the emission because of their extremely inefficient radiative decay. To avoid these losses, the phosphorescent donor and fluorescent acceptor must be doped into a conductive matrix enabling the generation of its molecular excited states by electron–hole recombination. The phosphor then sensitizes the energy transfer from the matrix to the fluorescent acceptor, the whole process forms an energy transfer cascade. Cascade Fo¨rster energy transfer has been demonstrated for fluorescent materials [121]. A combined version triplet–triplet and triplet–singlet energy transfer cascade is shown in Fig. 31. The overall quantum efficiency from such a phosphor sensitized system depends on the efficiency of Fo¨rster Copyright © 2005 by Marcel Dekker

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Figure 31 Emission from an organic phosphorescent (hn ph) or sensitized fluorescent (hn fl) LED, utilizing triplet–triplet and triplet–singlet energy transfer. Three times more non-emitting triplets are created in the host emitter material (Alq3). They are recovered for the emission through the triplet–triplet energy transfer to PtOEP or Ir(ppy)3, and=or through triplet–singlet energy transfer to DCM2. For further explanations, see text.

energy transfer from the phosphorescent donor [here PtOEP or Ir (ppy)] to the fluorescent acceptor (here DCM2) ZDA ¼

kDA kDA þ kr þ knr

ð65Þ

where kr and knr are the radiative and non-radiative decay rates of the phosphorescent (donor) molecule. For highly phosphorescent molecules (kr knr) the energy transfer rate (kDA) can be an efficient process, and with kDA > kr and a highly fluorescent dopant, the EL efficiency of the system will exceed that with the phosphorescent dopant solely. Wherever, the phosphorescence efficiency (jPH) of the sensitizer is higher or even comparable with the fluorescence efficiency of the doped dye (jFL), the emission will be dominated Copyright © 2005 by Marcel Dekker

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by the radiation from the phosphorescent molecules (see examples in Sec. 5.4). 2.4.3. Effect of Disorder Like charge carrier transport in molecular solids (cf. Secs. 1.3 and 4.6), the energy migration can be impeded by structural disorder [38]. While in the regular molecular structure, the exciton hopping frequency is time independent, there appears to be a distribution of event times of the form f(t) t(1þb) in a disordered material. The exciton motion is slowed down as time proceeds, energy transfer becomes a dispersive process. It can be described in terms of the continuous time random walk concept applied successfully to treat hopping across a spatially random array of iso-energetic hopping sites (offdiagonal disorder) [32,169]. The degree of dispersion is expressed in terms of the dispersion parameter related to both density of hopping sites and wave function overlap. If hops are thermally activated from traps exponentially distributed in energy b ¼ T=Tc, where Tc is the trap distribution parameter [170], for site energies distributed in energy according to a Gaussian function characterized by the distribution width s, the variation of the dispersion parameter with the width s can be approximated by Eq. (9). For hopping across an array of discrete energy levels b ¼ 1, for large dispersion, b approaches zero. The time evolving hopping time implies the time-dependent diffusion coefficient of exciton as it does in the case of the carrier transport [see Eq. (8)]. The equivalence of description of disorder affected carrier hopping and hopping of triplets [see Eq. (59)] seems to be quite obvious since both are determined by exchange interactions resulting in an exponential distance dependence of the coupling matrix element. The question arises as to whether it can be applied to transport of singlet excitons. In this case, energy transfer occurs via dipole coupling, the rate for an individual jump from a donor site to an acceptor site is given by Eq. (62). The average time required for a single transfer step becomes 6 th ¼ k1 DA ¼ tD[hri=r0] , where hri is the average hopping distance [138]. Thus, the singlet exciton can be considered as a Copyright © 2005 by Marcel Dekker

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

hri ts b 1 ts b1 ¼ ¼ l b th b th

ð66Þ

where l is the total distance covered by the exciton in a disorder-free medium, realizing a non-dispersive motion. Taking as an example of disordered solids evaporated films of Alq3 and assuming s ﬃ 0.1 eV typical for organic glasses [29], yield b ﬃ 0.5 [see Eq. (9)] and ldis ﬃ 0.23 l follows from Eq. (66). If the data in Table 2 represent dispersive transport of singlet excitons in Alq3, ldis ¼ 700 nm, and their migration distance in the disorder-free solid Alq3, as extracted from Eq. (66), would be l ﬃ 3 103 nm, that is a factor of 4 longer than that in real disordered samples. This corresponds to the reduced hopping time th ﬃ 4 1012 s or, in other words, the presence of the diagonal disorder with s ¼ 0.1 eV elongates the hopping time by a factor of 4.5. For larger values of b (less disordered systems), as found from the fluorescence studies for 9,10-diphenylanthracene b ¼ 0.7 (Ref. 172) and for polyvinylcarbazole (PVK) b ¼ 0.77 (Refs. 38 and 173), l would appear to be significantly shorter (l ﬃ 153 nm and l ﬃ 125 nm, respectively) and the disorder-induced increase in the hopping time roughly doubled. It is understood that a reduction in the average hopping distance to only one intermolecular spacing breaks the condition for the very weak approximation, making the resonance energy between a molecular pair (J) higher than the critical limit Jcrit ﬃ 15 cm1, we pass to the weak coupling case characterized by the nearest-neighbor exciton random walk that is to the short-range energy transfer mechanism (cf. early stage of Sec. 2.4). It is still affected by disorder. For example, the ldis=l ﬃ 3 104, corresponding to Copyright © 2005 by Marcel Dekker

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s ﬃ 0.1 eV, can be deduced from chemiluminescent experiments for triplets in PVK films [174]. In applying the simulation approach (66) to the disorder effects on energy transfer, some complications could arise from neglecting structural and chemical traps as well as from ignoring cluster formation. For example, the above mentioned very small ldis=l ratio may be due to defect sites as the disorder effect on triplet motion inferred otherwise from a difference between the triplet diffusion coefficient (DT) in disordered films and single tetracene crystal falls within an order of magnitude only. The value DT ﬃ 2 104 cm2=s found for the films [175] falls between 0 DcT ﬃ 8 105 cm2=s for the triplet exciton motion along the crystallographic direction c0 (Ref. 154) and Dab T ﬃ 4 103 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 in a reduced value of s. 2.5. EXCITONIC INTERACTIONS The mobility of excited states, imposed by intermolecular interactions (see Sec. 2.4), can lead to their collision with each other and=or with other types of excited states as well as trapped or free carriers generated in an organic solid. Such collision processes, realizing various excitonic interactions, may result in annihilation of the excitons and=or their transformation into another set of particles and quasi-particles. As different types of excitonic interactions show up in different optical and electrical phenomena, we divide them into two categories corresponding to the interaction between quasiparticles (exciton–exciton interactions) and to the interaction between quasi-particles and particles (exciton–charge carrier interactions). 2.5.1 Exciton–exciton Interactions 2.5.1.1 Singlet–singlet Interactions The singlet–singlet collision process is often referred to as singlet exciton fusion. The end result of such a fusion reaction Copyright © 2005 by Marcel Dekker

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

Experimentally this process can be observed as a quadratic light intensity dependent photoconduction [177–180] and external photoemission of electrons [181–183] or fluorescence quenching [148,155,184–186]. This kinetic analysis of the singlet exciton fusion process is provided by the equation dS1 S1 gSS S21 ¼ aIðx; tÞ dt tS

ð68Þ

where tS is the singlet exciton lifetime including radiative and all non-radiative decay pathways except for singlet–singlet annihilation, and gSS is the second order rate constant of the annihilation process. The exciting light quantal intensity I(x,t) (ph=cm2 s) is a function of time (t) and is assumed to penetrate a flat sample perpendicular (x) to its parallel planes at a depth xa ¼ la ¼ a1 determined by its linear absorption coefficient a defined by the absorption exponential law I(t) ¼ I(t,x ¼ 0) exp(ax). At low excitation intensities, the quadratic term in (68) can be neglected, and the PL efficiency ð0Þ

ð0Þ

jPL ¼ jFL ﬃ tS =tr

ð69Þ

given by the ratio of the measured (tS) and radiative (tr) lifetimes of singlets is a characteristic material parameter independent of excitation intensity. On the other extreme, at Copyright © 2005 by Marcel Dekker

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high excitation intensities, the exciton annihilation dominates the singlet exciton lifetime, and ð0Þ

jFL

jFL ﬃ ﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ tS agSS I

ð70Þ

becomes a decreasing function of light intensity. Therefore, a ð0Þ double logarithmic plot of jFL =jFL against I will give a straight line of slope (1=2) in which the intercept at ð0Þ jFL ¼ jFL yields gSS ﬃ 1=aIcr t2S . Icr is the critical excitation intensity, where the exciton kinetics changes from first to second order. Some examples are shown in Fig. 32. It may be seen that the intercept point moves towards high intensities when passing from anthracene through quasi-amorphous Alq3 to pyrene crystals. The physical meaning of this observation is that the critical concentration of singlets required to switch their mono-molecular decay to a decay dictated by the annihilation increases in this material sequence. The annihilation rate constant decreases accordingly: gSS ﬃ 1 108 cm3=s for anthracene, gSS ﬃ 1 1010 cm3=s for Alq3, and gSS ﬃ 5 1015 cm3=s for pyrene determined from respective values of Icr, show a monotonic degression in the exciton annihilation ability. The theory of isotropic three-dimensional diffusion allows gSS to be expressed by a product of the exciton diffusion coefficient DS and the effective annihilation capture radius RS [189], gSS ¼ 8 p DS RS

ð71Þ

where RS ¼ rc f ðz0 Þ

ð72Þ

is an increasing function of the ratio of the hopping rate between nearest neighbor sites [t1 h in (55)] and the donor acceptor rate constant (62) 1 R0 6DS 1=2 z0 ﬃ ð73Þ tS rc r2c Copyright © 2005 by Marcel Dekker

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Figure 32 Relative fluorescence quantum efficiency jFL=jFL(0) as a function of quantal excitation intensity I for anthracene (see Ref. 184a) and pyrene crystals (see Ref. 184), and quasi-amorphous film of Alq3 evaporated on four different material substrates as specified right by the curve (see Ref. 155). Dashed lines show the high-intensity approximation behavior according to Eq. (70) implying the log–log plots to be straight lines with the slope (1=2). Their intersections (Icr) with the ð0Þ jFL =jFL ¼ 1 line enable the calculation of the annihilation rate constant gSS. The values of the gSS for these samples are given in the text. They were calculated using relevant absorption coefficients (a) and low-intensity determined singlet exciton lifetime, tS. For anthracene, a ¼ 5 104 cm1 [187], tS ¼ 10 ns [139]; for pyrene, a ¼ 1.2 104 cm1 (at lexc ¼ 350 nm) [188], tS ¼ 112 ns [184]; for Alq3, a ¼ 4 104 cm1 (at lexc ¼ 351, 353 nm) [155], tS ¼ 15 ns [148].

The rc represents the capture radius determined by the acceptor sink efficiency: dS ð74Þ rc ¼ x Sðrc Þ dr r¼rc where the factor x is a measure of the concentration (S) gradient of singlet excited states at r ¼ rc; x ! 0 means Copyright © 2005 by Marcel Dekker

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the diffusion flux to an occupied center equals 0, they can be quenched only by a long-range energy transfer process with a rate given by Eq. (62). For z0 1 3=4

3=2

1=4

gSS ¼ 4p½Gð3=4Þ=Gð5=4Þ DS R0 =tS

ð75Þ

where G(v) is the gamma function. According to Eq. (75), the fusion of excitons is governed by their motion reflected in the diffusion coefficient DS. This case is called diffusion approximation which breaks down as DS increases. Increasing DS leads to decreasing z0 and RS. At RS ﬃ rc, the condition for the diffusion approximation would no loger be valid, and for z0 1 ð76Þ gSS ﬃ ð4p=3tS Þ R60 =r3c i.e., gSS does not depend on DS, defining the capture-controlled annihilation limit. The transition region from (75) to (76) is defined by RS ¼ rAD ¼ c or in terms of a diffusion length [190], pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð77Þ ld ¼ DS tS ﬃ 0:7 R0 ðR0 =rDA Þ2 For anthracene crystal, with ld ﬃ 40 nm and rDA ¼ 0.5 nm (see Table 2), this condition requires R0 ﬃ 2.5 nm, the value in good agreement with R0 ﬃ 2.8 nm obtained from independent data on singlet exciton energy transfer to tetracene molecules embedded into the anthracene crystal matrix [138]. The agreement suggests both diffusion and collision cross-section to contribute comparably to the singlet–singlet annihilation process in anthracene crystal. Indeed, rc calculated from Eq. (76), representing the capture-controlled limit, gives unreasonably small value ﬃ0.2 nm. The formal interaction radius RS in (71) should here be considered as a sum [190], RS ﬃ rDA þ RS

ð78Þ

where 1=4 RS ﬃ 0:7 R60 =tS DS Copyright © 2005 by Marcel Dekker

ð79Þ

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which is a function of the diffusion coefficient DS as well as the long-range energy transfer parameter R0. Solving Eqs. (71), (78) and (79) for anthracene with the above determined gSS, R0 and tS ﬃ 10 ns allow the real diffusion coefficient of singlet excitons to be calculated. Its rough value is DS ﬃ 105 cm2=s. The diffusion approximation is often used to describe excitonic motion in single component organic solids. The resonance energy of a molecular pair, dominated by a dipole– dipole nearest-neighbor interactions, reduces the hopping rate between sites separated by two or more intermolecular spacings (r 2rDA) to less than 1% of that for hops between nearest-neighbor molecules (r ﬃ rDA), and the exciton motion is treated in the weak-coupling limit. Then the singlet–singlet annihilation rate constant allows direct calculation of DS ﬃ gSS=8prDA. Such a treatment gives DS ﬃ 1 102 cm2=s for anthracene, DS ﬃ 3 109 cm2=s for pyrene, and DS ﬃ 6 105 cm2=s for Alq3. The big difference between DS for anthracene and pyrene crystals has been attributed to the difference in the nature of excitons: whereas in anthracene singlet excitons are assumed to be single molecule excited states, in pyrene, the energy transfer is due to the much less mobile excimers [184]. An example with anthracene shows that an apriori assumption that the exciton migration is diffusion-limited (RS ¼ rDA) leads to a largely overestimated value DS. In conclusion, for the interpretation of the measured singlet–singlet annihilation rate constants, both diffusion and long-range energy transfer should be taken into consideration as for many molecular systems the ratio z0 (73) is close to unity, and a combined diffusion and Fo¨rster energy transfer theory applies. The relatively low values of gSS and DS in quasiamorphous solids might be underlain by disorder (see Sec. 2.4.3) and=or a contribution of triplet excitons in quenching of fluorescent singlets (cf. Sec. 2.5.1.2). The diffusion coefficient of triplets is expected to be lower than of singlets since both energy donor and acceptor transitions are disallowed. A low value of gSS has been found for the triplet–triplet annihilation rate constant from biexcitonic quenching Copyright © 2005 by Marcel Dekker

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experiments, gTT ﬃ (3 1) 1014 cm3=s (Ref. 167) in 8% PtOEP:CPB molecular system [CPB stands for the (4,40 N,N0 -dicarbazole-biphenyl) compound; for the molecular structure of PtOEP, see Fig. 31] (cf. Sec. 2.5.1.2). The evidence of singlet exciton quenching by singlet–triplet interaction has been presented based on the excitation intensity dependence of the time resolved relative fluorescence yield in crystalline anthracene [185] and will be discussed in some detail in Sec. 2.5.1.3. 2.5.1.2. Triplet–triplet Interaction, Singlet Exciton Fission Colliding triplet excitons are said to undergo triplet–triplet fusion. If they belong to the same species, the process is called homofusion. The collision of triplets belonging to different species is called heterofusion. The final products of the triplet–triplet interaction process are preceded by intermediate complex pair states:

K1 is the rate of encounter of two triplets to form the ðSÞ ðTÞ intermediate triplet–triplet complex [T1T10 ], K2 and K2 are the dissociation rates of the complex into a pair of Copyright © 2005 by Marcel Dekker

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uncorrelated species (singlets and triplet–singlet, respectively), and K1 is the dissociation rate of the complex into a ðSÞ ðTÞ pair of uncorrelated triplets. gTT and gTT are the overall second order rate constants for the creation of singlet (80) and triplet (81) final states. If the energy of the final states and their lifetimes are appropriate, the complex state and two initial triplets can be restored with a rate K2 followed by K1 (the overall rate constant g0S ). This process is the inverse of triplet exciton fusion and is called fission of the localized excited state into two triplets. Thermodynamic considerations ðSÞ of the process imply the fission (g0S ) and fusion [gTT ] rate constants to obey the relation [191] ðSÞ

g0S =gTT ¼ 9 exp½ð2ET ES Þ=kT

ð82Þ

where 2ET (or ET þ ET0 ) is the sum of the energy of triplet excitons (identical or different excited species), ES is the energy of a singlet exciton. The fission of the Tn state, though energetically feasible, practically does not occur due to its fast relaxation to the lowest triplet excited state T1. The Hamiltonian of the intermediate complex [T1T10 ] of triplets is, in general, a function of intermolecular distance, the mutual orientation of the two molecules, and the spin. The total intermolecular interaction is separated into two parts. One is the dipolar spin–spin interaction, which is smaller in magnitude than the intra-molecular interactions between magnetic moments of electrons. The other term is the electrostatic, intermolecular interaction which, like the former, depends on the geometry of the complex, intermolecular distance and the total spin. The intermolecular interaction may be of an exchange and=or charge-transfer nature. Nine possible collision complex states, designated by l ¼ 1,2, . . . ,9 are possible, whose wave functions are eigenstates of Hamiltonian, and may be written as ci ¼ jS ClS jSi þ jT ClT jTi þ jQ ClQ jQi

ð83Þ

The pre-exponential factor depends on the definition of g and can amount 9=2 if in the triplet–triplet annihilation pathway for decay of triplet excitons a factor of 1=2 is introduced [192].

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where j designates the orbital part of the wave functions, and jSi, jTi and jQi the spin parts. The coefficients ClS , ClT and ClQ are the spin amplitudes of the singlet, triplet, and quintet in the pair state, and they satisfy the closure relationships 9 X Cl 2 ¼ 1;

9 X Cl 2 ¼ 3 and T

l¼1

l¼1

S

9 X l 2 CQ ¼ 5

ð84Þ

l¼1

Quintet states on a single molecule require the simultaneous excitation of two electrons and are, therefore, energetically inaccessible (at least in aromatics in the solid phase). This is the reason for which the quintet states in the final products of reactions (80) and (81) have been omitted. Any of the nine pair states is formed with equal probability since the individual triplet excitons are in thermal equilibrium. Thus the rate of formation of 2 ðSÞ each of the nine l states is (1=9) K1, and K2 ClS , and 2 ðTÞ K2 ClT are the rate transitions to energetically accessible final singlet and triplet states, respectively. The fraction l 2 ðSÞ ðSÞ l 2 K2 CS = K1 þ CS K2 is just the probability of the lth pair state giving rise to a singlet. Thus, weighted average over all posðSÞ sible pair states yields the desired expression for gTT , 2 9 X 2S ClS 1 ðSÞ ð85Þ gTT ¼ K1 2 9 l l¼1 1þ 2S C S

and for

ðTÞ gTT ,

ðTÞ gTT

2 9 X 2T ClT 1 ¼ K1 2 9 l l¼1 1þ 2T CT

ð86Þ

where 2 and 20 stand for the branching ratios ðSÞ

2S ¼ K2 =K1

and

ðTÞ

2T ¼ K2 =K1

ð87Þ

Similar considerations for the stationary state imply the fission rate constant g0S

2 9 X K2 ClS ¼ l 2 ; l¼1 1þ 2 C S

Copyright © 2005 by Marcel Dekker

ð88Þ

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2 where K2 ClS represents the rate of formation of the lth triplet pair state from the singlet manifold. The absence of the 1=9 factor in (88) as compared to the stationary state ðSÞ equation for gTT occurs because there is only one initial 2 state, for each state ClS ¼ 1=3 [cf. relationships (84)]. If ðSÞ the dissociation rate K1 is low as compared with K2 ðTÞ ðSÞ ðTÞ and K2 , 2s, 2r 1, and gTT ¼gTT ﬃ 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 in organic LEDs. Since the transition from initial to final singlet states is ðSÞ spin-conserving, it has been postulated that gTT is larger the greater the number of pair states with singlet character, i.e., the greater the number of terms in (85) with ClS 6¼ 0 ðSÞ [193]. The effect of an external magnetic field on gTT (thus on gS) may be understood on this basis (see Sec. 2.5.3.1). Experimentally, the triplet exciton fusion shows up in the delayed fluorescence, and singlet exciton fission in a low strongly temperature-dependent fluorescence efficiency. The study, under spatially uniform excitation, of the phase of the first harmonic of delayed fluorescence as a function of the intensity of the rectangular waveform exciting light I0(t) ðTOTÞ for a material, allows to determine the product agTT where a is the absorption coefficient of the exciting light. To get an uniform distribution of the excited triplets, the exciting photons with energy (hn ex) smaller than the first excited singlet energy ðES1 Þ can be used. Then, triplet excitons are produced by the weak direct S0 ! T1 transitions reflected in a low absorption coefficient a ¼ aT. When diffusion effects can be neglected, the rate equation for triplet exciton concentration (T) can be written as dT ðTOTÞ ¼ aT I0 ðtÞ T=tT gTT T 2 dt

ð89Þ

with tT standing for the effective triplet exciton lifetime determined by all monomolecular decay pathways, and ðTOTÞ gTT accounting for all triplet–triplet annihilation channels, which, when governed by the triplet collision frequency, give Copyright © 2005 by Marcel Dekker

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ðTOTÞ

ðSÞ

gTT ﬃ 3gTT . Delayed fluorescence photon flux per unit volume of the material is defined by ðSÞ

FðtÞ ¼ jr gTT T 2

ð90Þ

where jr is the radiative decay efficiency of the created singlet excitons. Under a square-wave excitation of angular frequency o, the phase shift y of the first harmonic of delayed fluorescence waveform can be approximated by [194] tan y ¼

o ðTOTÞ

½t1 T þ aT tT gTT

I0

ð91Þ

Thus, the inverse of tan y vs. I0 is expected to give a straight line with the product of its slope and intercept yielding ðTOTÞ aTgTT . Figure 33 shows some examples, anthracene, and pyrene single crystals. The straight line intercepts with the axis of ordinates at I0 ¼ 0 give tT ﬃ 21 ms for anthracene ðTOTÞ and tT ﬃ 7 ms for pyrene crystal. Deduced value of aTgTT ðTOTÞ allows to calculate gTT ¼ 5 1011 cm3s1 for anthracene, assuming aT ¼ 2.7 104 cm1 in good agreement with the value obtained previously from the excitation spectrum of ðTOTÞ anthracene [195]. gTT ¼ 7.5 1012 cm3s1 has been evaluated employing the ratio of steady-state fluorescence signals of pyrene to that of anthracene at low excitation intensity without knowledge of aT. As expected, gTT gSS for anthracene, but the opposite relation holds for pyrene crystal (see Sec. 2.5.1.1). This striking difference can be explained by the different nature of singlet and triplet excited states in crystalline pyrene. In contrast to singlets, which were shown to be excimeric in nature, the triplet state in crystalline pyrene appears to be a monomeric localized excited state as comes from the mirror symmetry between phosphorescence and S0 ! T1 absorption spectrum [196]. Thus, the triplet exciton in pyrene crystal should behave like triplet molecular excitons in other aromatic crystals which do not have a dimeric structure. Indeed ðTOTÞ for pyrene and anthracene differ by a factor of 2 the gTT only, the difference to be associated with a lower triplet exciton mobility in pyrene, such a difference may be expected on the basis of the much smaller Davydov splitting [197] as Copyright © 2005 by Marcel Dekker

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Figure 33 Experimental data of the phase shift y of the delayed fluorescence with respect to the square-wave excitation as a function of the quantal exciting light intensity, plotted in the (tan y)1–I0 scale (squares, triangles) to compare with Eq. (91) (solid lines) reflecting triplet kinetics expressed by Eq. (89). Wavelength of the excitation l ¼ 514.5 nm (2.41 eV), angular chopping frequency o ¼ 157.0 s1. The data are taken for (ab)-cleaved pyrene and anthracene single crystals excited with light polarized along the a crystallographic axes. The overall triplet–triplet annihilation ðTOTÞ rate constants gTT are deduced from the slope-ordinate intersection products of the straight-line plots. The data adapted from Ref. 194.

compared with that for anthracene [198] or possibly non-local scattering being the predominant mechanism for triplet exciton transport in pyrene crystals [199]. The singlet exciton fission [g0S in Eq. (80)] is a process reducing the concentration of singlet excitons, thus, it should show up in a low fluorescence efficiency of a material. According to Eq. (82) the materials with 2ET less or comparable with ES are expected to reveal an efficient fission process. Such relations hold for example in solid pentacene (ES1 ﬃ 1.9 eV, Copyright © 2005 by Marcel Dekker

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ET1 ﬃ 0.9 eV), tetracene (ES1 ﬃ 2.37 eV, ET1 ﬃ 1.27 eV) and rubrene (ES1 ﬃ 2.33 eV, ET1 ﬃ 1.2 eV), and their fluorescence quantum yield is known to be very low at room temperature, strongly increasing as temperature decreases. Examples are shown in Fig. 34. In the case of neat tetracene and rubrene, the fluorescence efficiency increases as the temperature is lowered because of the suppression of the thermally activated singlet exciton fission channel [cf. g0S in (80) and (82)]. Using the temperature dependence of the fission rate [26,200,203], kf ¼ k0 expðDE=kTÞ

ð92Þ

Figure 34 The relative fluorescence intensity plotted as a function of temperature, for crystalline tetracene (see Ref. 200), rubrene (see Ref. 201) and tetracene doped with pentacene green and red emission component as shown in the inset) (see Ref. 202). Copyright © 2005 by Marcel Dekker

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where k0 ¼ kf at T ! 1 (or DE ¼ 0), the prompt fluorescence intensity can be expressed as FEL ¼ IS

kr kS þ k0 expðDE=kTÞ

ð93Þ

where IS is the excitation rate per unit area, kS is the sum of the rate constants for all decay channels including radiative decay (kr) for S1 but exclusive of singlet fission. The latter is contained in the last term of the denominator of Eq. (93). This term dominates in the high-temperature region, where the Arrhenius plot log[FFL(T)=FFL(293 K)] vs. (103=T) allows DE to be determined. DE ﬃ 0.16 eV for tetracene [200], and DE ﬃ 0.07 eV for rubrene [201] are consistent with the predictions (2ET1 ES1 ) based on the first triplet and singlet energy levels (ET1 , ES1 ). A tendency to saturation of the fluorescence efficiency at low temperatures indicates suppression of the exciton fission and practically temperature-independent rates (kS) of other decay channels of S1. From the fit of (93) and the magnetic field-induced enhancement of the fluorescence in the entire temperature range applied, k0 ﬃ 0.5 1012 s1, and g0S (1) ¼ k0=S ﬃ 1.5 1010 cm3 s1 follow with the molecular concentration of tetracene S0 ¼ 3.4 1021 cm3 [200]. It gives g0S (293 K) ¼ g0S (1) exp(DE=kT) ﬃ 2 1013 cm3 s1 in good agreement with the value 1.5 1013 cm3 s1 obtained by Groff et al. [192] and kf ﬃ 109 s1 comparable with the appar9 1 of tetracene singlet excitons ent decay rate t1 S ﬃ 3 10 s [204]. The radiative rate constant is much lower and can be estimated from the absolute quantum fluorescence efficiency jPL ¼ kr=ktot ﬃ tS=tr ﬃ 0.002 at room temperature [205]. It yields kr ﬃ 2 106 s1 with ktot ﬃ kf. A rather large scatter in the literature data on g0S is noted due to its critical dependence on DE ¼ 2ET ES. For example, the value g0 S ¼ 1.5

1012 cm3 s1 have been obtained with DE ﬃ 0.2 eV and kf ¼ 5 109 s1, the latter based on the fluorescence efficiency ratio at 77 and 300 K, varying strongly with different crystal samples [203]. This certainly affects the value of g0S as calculated from the relationship (82). It gives g0S ﬃ 7 1012 cm3 s1 with DE ¼ 0.16 eV, and g0S ﬃ 1012 cm3 s1 with DE ¼ 0.2 eV, Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes ðSÞ

using the gTT ¼ 4.8 1010 cm3 s1 [203]. These values become ðSÞ even higher if gTT ﬃ 7 1010 cm3 s1 is used [206] (see also Sec. 2.5.1.3). If the encounter limit for triplet–triplet interacðTOTÞ ðSÞ tion is assumed, gTT ﬃ 3gTT with the above literature data ðSÞ

ðTOTÞ

for gTT , the values of gTT for tetracene range between 109 and 2 109 cm3s1 that is they are about two orders of magnitude larger than in anthracene, and three orders of magnitude larger than in pyrene (see Fig. 33). However, ðTOTÞ gTT ﬃ 5 1011 cm3s1, identical with that for anthracene, ðSÞ is obtained, using gTT following from the relationship (82) and the above estimated g0S (1) . Interestingly, the temperature decrease of the fluorescence intensity for the green (tetracene host) emission component is much weaker than that for the red (pentacene guest) emission component in pentacene-doped tetracene crystal. This is a signature of the pentacene singlet hetero-fission, that is the fission of excited singlets of pentacene into one triplet of tetracene and another one of pentacene molecules [206a]. In a pentacene-doped tetracene crystal with a low concentration of pentacene (here <100 ppm), the exciting light of wavelength 405 nm is completely absorbed by the host molecules. Singlet energy transfer in the host lattice produces the excited guest pentacene molecules. A kinetic scheme taking into account the above difference in the excitation modes of tetracene and pentacene singlet excited states yields the host fluorescence intensity FFL(green) as FFL ðgreenÞ ¼ IS

kSg þ gtr S0 ðpentÞ þ

krg ð1Þ gS S0 ðtetrÞ expðDE=kTÞ

ð94Þ

and the guest fluorescence intensity FEL(red) as FFL ðredÞ ¼ IS

kSr þ

krr gtr S0 ðpentÞ FFL ðgreenÞ 0ð1Þ gHF S0 ðpentÞ expðDEHF =kTÞ ð95Þ

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Here gtr ¼ kD–A=S0(pent) is a bimolecular rate constant for energy transfer from the host donor (D) to the guest acceptor (A) molecule populated with S0(tetr) ¼ 3.4 1021 cm3 and S0(pent) (here about 1017 cm3), respectively. The radiative and total decay rates for the host are krg, ksg, and for the quest krr, ksr. The thermally activated homofission process of host molecules (g0S ) and heterofission process of quest molecules (g0HF ) are separated from other non-radiative singlet exciton decay channels. Since both the molecular and crystal structures of tetracene and pentacene are similar, the guest molecules are expected to enter the tetracene lattice substitutionally. Since there are two inequivalent orientations of molecules in the tetracene crystal lattice [207], two inequivalent positions of the pentacene molecule can assume in the crystal elementary cell. The two activation energies for the heterofission will correspond to these two different crystallographic sites, DEHF(I) and DEHF(II). Assuming, the red component to be a simple sum of the contributions from both sites with g0HF from sites I and II, and taking into account that gtr is also temperature-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 DEI ﬃ 0.13 eV, DEII ¼ 0.06 eV and DEtr ¼ 0.18 eV [208]. The difference in the activation energies as compared with that for homofission in neat tetracene reflects the difference in energies of singlets and triplets and may also indicate either some local distorsion of the lattice, and=or non-substitutional entry of pentacene into tetracene 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 a small lattice relaxation contribution. Based on low-temperature singlet exciton lifetime measurements, t1(tetr) ¼ g0S S0(tetr) þ kSg, and t1(pent) ¼ g0HF S0(pent) þ kSr, g0 S(1) ¼ 2 109 cm3 s1 and g0 HF(1) ¼ 4.7 1010 cm3 s1 have been inferred [208]. The inferred heterofission rate constant g0S (1) is smaller than g0 S(1) deduced above for neat tetracene and for the tetracene singlet fission in pentacene-doped tetracene. This would suggest a larger singlet component of the triplet pair state [T1T10 ] in the case of Copyright © 2005 by Marcel Dekker

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homofission than in the case of heterofission. On the basis of the magnetic field-dependent fluorescence measurements, it has also been demonstrated that tetracene triplet–pentacene triplet interaction (triplet–triplet heterofusion) takes place in pentacene-doped tetracene crystals [209] (see also Sec. 2.5.3.1). The anthracene host–tetracene quest triplet– triplet heterofusion follows from the time evolution of the delayed fluorescence and its magnetic field dependence in tetracene-doped anthracene crystals [210,211] (see also Sec. 2.5.3.1). It should be kept in mind that guest molecules can provide additional recombination centers in the case of electroluminescence. For example, tetracene added to anthracene introduces electron and hole traps at depths 0.2 and 0.42 eV, respectively, with holes being more effectively captured at the guest sites. Thus, the trapped hole can capture a mobile electron, forming a tetracene molecular singlet or triplet excited state. This contributes to the tetracene guest emission in addition to tetracene singlets excited by energy transfer from singlet excitons of anthracene [210,212]. Some other examples are described in Sec. 5.2. The coexistence of thermally induced singlet exciton fission and triplet–triplet fusion can only be observed if temperature is high enough to activate the fission process over the energy barrier resulting from the difference (2ET ES) for vibrationally relaxed triplet (ET) and singlet (ES) excited states. At low temperatures, where the thermally activated fission process is suppressed, fission from ‘‘hot’’ exciton level S1 should be observable by monitoring the relative fluorescence quantum efficiency as a function of excitation wavelength. Even though the lifetime S 1 is only 1013–1012 s, this process is feasible and has been reported as a sharp 8% fluorescence intensity drop at hc=lf ﬃ 2.5 eV (lf ﬃ 496 nm) for tetracene with 2ET ﬃ 2.4 eV [153], and as a small magnetic field effects (ﬃ þ0.5%) on the prompt fluorescence of anthracene crystals excited with photons above hc=lf ¼ 4 eV in energy (lf 310 nm), where 2ET ﬃ 3.66 eV [213]. The optically induced fission, that is the fission of hot singlet excitons, S1 , is not as effective Copyright © 2005 by Marcel Dekker

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as the thermally induced fission, the explanation of this difference being still an open question. The fusion of two triplets may give rise to autoionization as observed in the case of singlet exciton fusion (67)

The vibrationally excited singlet S1 and triplet T1 , expected upon the annihilation of the lowest excited triplets T1, T10 , have an energy below the autoionization threshold of typical aromatic crystals [26], thus, no intrinsic photoionization has been observed in these solids. However, the presence of intentional or non-intentional admixtures can allow the triplet–triplet interaction-induced photoionization forming a free carrier in the matrix and a trapped carrier on an admixture molecule. Also, such a process has been reported for the CT triplet states localized on the donor molecule, e.g. in polycrystalline samples of CT complex anthracene-tetracyanobenzene, where the triplets are localized on the anthracene donor (3D1). Annihilation of 3D1 results in the population of non-relaxed excited states of the complex 1(DþA)n and 3 (DþA)n, dissociation of which may lead to the formation of free charges Dþ [214]. 2.5.1.3 Singlet–triplet Interaction Singlet excitons can be destroyed by triplets in the singlet–triplet collision process

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This process is fully allowed and may be treated as an energy transfer promotion of T1 to higher (hot) triplet states, T2 and T3 (T1 ! T2 or T3 are spin-allowed processes). The reverse reaction, however, is spin forbidden. If the spin-symmetry rule for some reasons (e.g. spin-orbit coupling) is broken this process becomes active as well (cf. Sec. 2.4.2). The role of singlet–triplet exciton annihilation in reducing the fluorescence efficiency of organic solids is well documented (see e.g. Ref. 26). It can be distinguished from the singlet–singlet annihilation process (67) by studying the time-resolved intensity dependence of the fluorescence yield. A value gST ¼ (5 3) 109 cm3 s1 has been obtained from such a dependence for the slow component of the fluorescence of a single anthracene crystal [185]. This result is to be compared with theoretical values based on the energy transfer notions expressed by Eq. (71). An attempt has been made using its diffusion approximation (75) [215]. For the evaluation of gST in anthracene, these authors assu3 cm3 s1, med R0 ¼ RST 0 ¼ 3.2 nm, DS ! D ¼ DS þ DT ¼ 3.6 10 tS ¼ 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 energy transfer rate of the singlet is equal to all other rates of singlet decay, and D as the sum of the diffusion coefficients of the singlet and triplet excitons. The obtained value was gST ¼ 2.8 109cm3s1. Though in good agreement with the above cited experimental data, it is open for criticism because of uncertain values of D and tS, but first of all because the diffusion approximation for anthracene may not be valid (see Sec. 2.5.1.1). Employing the capture-controlled annihilation limit (76) with R0 ¼ 3.2 nm and rc ¼ 0.5 nm yields gST ¼ 4 109 cm3s1 even more consistent with experiment. An obvious expectation is that singlet–triplet annihilation process will dominate under high concentration of triplet excitons which can occur as a result of the efficient singlet ! triplet fission [cf. Scheme (67)], accompanying the passage of high-energy radiation through an organic solid [216–218] or effective recombination of charge carriers injected from electrodes into solid-state samples as in the Copyright © 2005 by Marcel Dekker

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case of organic LEDs. One of the most characteristic results is the excitation intensity dependence of the relative fluorescence intensity in tetracene crystals (Fig. 35). The relative fluorescence efficiency initially increases, reaches a broad maximum and decreases thereafter. In the lower intensity regime (1016 quanta=cm2 s), the dominating triplet–triplet interaction produces an increasing number of singlet excitons in addition to those created directly by the exciting light, the fluorescence efficiency increases. At higher excitation intensities, the singlet–triplet annihilation process sets in leading to quenching of singlet excitons. A balance between the singlet exciton surplus resulting from the triplet–triplet annihilation and its reduction due to singlet exciton quenching by triplets holds the relative fluorescence efficiency on a constant level within about two orders of magnitude of the exciting flux. At still higher excitation intensities, the quenching of singlets by triplets becomes a dominating process and the fluorescence efficiency decreases. For steady-state excitation, with weakly absorbed light, the effects of exciton diffusion can be neglected, and the rate equations giving the singlet and triplet populations S(x)

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

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and T(x), at a distance x from the illuminated surface can be written as ðSÞ

aI 0 expðaxÞ þ gTT T 2 S=tST gST S T ¼ 0 ðTOTÞ

gS=tS T =tT gTT

T2 ¼ 0

ð98aÞ ð98bÞ

and the fluorescence quantum efficiency jFL ¼ kr

Z1

½SðxÞ=I0 expðaxÞ dx

ð99Þ

0

In Eqs. (98) and (99), g is the average number of triplets generated by the decay of one singlet (if t1 S ﬃ kf , as is the case of tetracene crystals, g ¼ 2), the meaning of other symbols is the same as given already in Secs. 2.5.1.1 and 2.5.1.2. Taking as a reference level, the fluorescence quantum efficiency of the crystal in the absence of triplet exciton interactions, j0FL ¼ kr tS , the relative quantum efficiency can be defined by the ratio jFL=jFL(0). In the low excitation region, the term gST ST in Eq. (98a) can be neglected, Eqs. (98) and (99), with the assumption ðTOTÞ ðSÞ gTT ﬃ 3gTT , lead to "

ð1 þ pI 0 Þ1=2 lnð1 þ pI 0 Þ1=2 1 jFL =jFL ð0Þ ¼ 3 1 ð3=8ÞpI 0

#

ð100Þ where 8 ðTOTÞ p ¼ agTT t2T 3

ð101Þ

Due to the contribution of delayed fluorescence from singlets produced in the triplet–triplet fusion, the overall fluorescence efficiency increases to the value jFL=jFL(0) ¼ 3. The best fit of Eq. (100) (solid line below 1017 quanta=cm2 s in Fig. 35) Copyright © 2005 by Marcel Dekker

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was obtained for p ¼ 1.6 1013 cm2 s. From this value of p and measured triplet exciton lifetime (tT ¼ 5 104 s) and absorption coefficient of the exciting light (a ¼ 6 102 cm1), ðTOTÞ one obtains gTT ¼ (2.2 0.5) 109 cm3s1, as mentioned already in Sec. 2.5.1.2. The solution of Eq. (98a) with the term gST ST and of (98b) where T=tT has been neglected yields to a first approximation (for not too high intensities) h i r jFL =jFL ð0Þ ﬃ 3 1 ð pI 0 Þ1=2 9

ð102Þ

where p is defined by (101), and the parameter r ¼ gST tS=3 tT ðTOTÞ gTT contains the singlet–triplet annihilation rate constant gST. Equation (102) predicts a decrease of jFL=jFL(0) with intensity I0 from the value 3 reached with the saturation of the contribution of the delayed fluorescence. Its reasonable fit to the experimental data (solid line within the high intensity regime in Fig. 35) has been obtained using the previous value of p, and the value r ¼ 3 105. Based on the above ðTOTÞ and taking for the ratio tS=tT the evaluated constant gTT value 106, one arrives at gST ﬃ 2 107 cm3 s1. This value can be in error by one order of magnitude in view of the uncertainties as to the actual intensity distribution of the focused laser beam throughout the bulk of the sample and as to the reliability of the value of tS=tT (cf. discussion in Sec. 2.5.1.2). The existence of a singlet–triplet exciton annihilation process has been inferred indirectly from studies of intrinsic photo-carrier generation in anthracene [219]. In this process, intrinsic charge carriers are produced by autoionization of an excited state degenerated with the continuum of states in the free carrier bands [the upper pathway of the singlet–triplet annihilation process in Scheme (97)]. It is energetically feasible if the sum of energies of one singlet (ES) and one triplet (ET) exciton is larger than or at least comparable with the energy gap, Eg. In the case of anthracene crystal, ES þ ET ¼ (3.15 þ 1.8) eV ¼ 4.95 eV > Eg ﬃ 4.0 eV (see e.g. Ref. 26), and its efficiency is determined by competition with other excitonic interactions and monomolecular decay pathways. Copyright © 2005 by Marcel Dekker

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2.5.2. Exciton–charge Carrier Interactions 2.5.2.1. Singlet Exciton Annihilation by Paramagnetic (Doublet) Species In this process, singlet excitons may be annihilated by the spin 1=2 particles (doublets D1=2) represented by either radicals and free or trapped electrons and holes:

Interactions of singlet excitons with these species lead to their annihilation, and thus to a decreased fluorescence quantum yield. Quenching of singlets by impurity centers, which were produced by ionizing radiation, has been reported [220–222]. Experimental evidence for the destruction of singlet excitons by charge carriers injected into anthracene has also been presented [85,223–225]. By irradiating crystalline samples of various hydrocarbons with X-rays or high energy electrons, quenching centers are introduced. If their concentration induced by one rad amounts N [(cm3 rad)1], the fluorescence quantum efficiency has been found to decrease with the radiation dose (R) as follows: jFL ð104Þ jFL ðRÞ ¼ 1 þ gSq NtS R Here jFL and tS are the fluorescence quantum efficiency and measured singlet exciton lifetime, respectively, of the samples before irradiation, and gSq is a constant characterizing the singlet exciton-quenching center energy transfer efficiency [the second order singlet exciton-quenching center interaction rate constant (cm3=s)]. Interestingly, the measured jFL(R) dependence deviates from the function (104) within the long-wavelength part of the fluorescence spectrum Copyright © 2005 by Marcel Dekker

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[226,227]. A formal modification of this function has been proposed replacing the denominator of Eq. (104) by (1 þ gSq N tS RZ), where Z varies with the range of the emission spectrum. For example, Z ¼ 1 for the short wavelength emission wing and drops down to 0.3 at the long-wavelength emission tail of stilbene (references as above). This modification does not have any physical meaning, and the reason for the deviation effects is still an open question, though one can speculate that they are associated with energy-dependent product of gSq tS [note that tS in Eq. (104) is an average singlet exciton lifetime]. Due to the complexity of the radiation-induced damage, inferring about the nature of the quenching centers is very difficult. But to a large extent, they seem to have a physical origin since their annealing has been successfully observed [222]. The singlet exciton quenching by impurity centers is of crucial importance for the stability and quantum efficiency of organic LEDs. The quenching centers can be produced within their emitter layers due to chemical instability of light emitting molecules under ambient conditions or their ionic species formed by excess charge carriers injected from electrodes into EL structures. External factors that can induce degradation of the emitter are oxidation, photo-oxidation, diffusion of the electrode material, and heating effects (for a recent review of degradation effects see Ref. 3). In the photo-oxidation process, high-energy irradiation induces p to p and s to s transitions, creating free radicals in the material. C–C, C–N, and C–O low-energy bonds can also be damaged under irradiation. The created defects are subject to chemical reactions with the atmospheric oxygen or moisture, and lead to oxidation of the sample. The instability of Alq3þ cations formed by injection of holes into common Alq3 emitter-based organic LEDs is believed to influence the degradation rate, the degradation products act as fluorescence quenchers [228,229]. The EL intensity decreases in time during device operation (Fig. 36a) indicating a decrease in the EL quantum efficiency that reflects the intrinsic degradation behavior. Associated with the decrease in EL during device aging, the decrease in PL intensity is observed, which reflects a decrease in the PL quantum efficiency of Alq3, thus Copyright © 2005 by Marcel Dekker

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Figure 36 Quenching effects on photoluminescence (PL) and electroluminescence (EL) of fluorescent Alq3 and phosphorescent Ir(ppy)3 emitters due to aging by operation of an Alq3-based LED at 50 mA=cm2 (a) and by exposing a 150 nm-thick Ir(ppy)3 film to the UV-radiation (¼313 nm) under ambient conditions (b). The data of part (a) have been obtained with the EL structure as shown in the inset 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) are unpublished data of Me˛z˙yk and Kalinowski.

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revealing degradation in the Alq3 layer. Exposing some emitter materials to the UV radiation under ambient conditions leads also to a decrease in the PL quantum efficiency. An example is shown in Fig. 36b, where the PL intensity of a phosphorescent Ir complex is plotted vs. exposition time. Quenching of singlets by trapped holes injected from an electrolytic contact has been demonstrated for anthracene [85,91,231]. The effect, described by the schemes in Fig. 15 and (103), apparent already in the short-wavelength region of the charge-induced decrease in the fluorescence intensity of anthracene in Fig. 13b (curve 5), is extended towards the shorter-wavelength emission range in Fig. 37. Increasing wavelength (lo) translates into the thickness of the observed slab (l0 ¼ a1 0 ) at the injecting contact through the absorption coefficient of the emitted light (a0). Its extent monotonically increases from l0 ¼ 23 nm at l0 ¼ 394 nm, up to l0 exceeding

Figure 37 Charge carrier-induced quenching of prompt fluorescence from a 75 mm-thick anthracene crystal as a function of the emission wavelength (l0). The charge is injected from the illuminated water=crystal interface. The excitation intensity I0 ¼ (4 2) 1015 quanta=cm2 s. Adapted from Ref. 231. Copyright © 2005 by Marcel Dekker

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the crystal thickness above l0 ¼ 425 nm. The experimentally observed fluorescence intensity can be expressed as 2x1=2

F¼

Z

SðxÞ expðx=l0 Þdx

ð105Þ

0

where x1=2 is a distance counted from the illuminated contact into the bulk of the crystal which determines the region from which a half of all fluorescence photons of energy hc=l0 originate. The exponential factor exp(x=l0) is the probability for a photon to leave the crystal when emitted at the distance x from the illuminated interface. In any thin section of the sample at a distance x from the injecting electrode, the singlet exciton concentration S(x) may be described by IðxÞ=la þ DS

@ 2 SðxÞ SðxÞ=tS gSq nh ðxÞSðxÞ ¼ 0 @ x2

ð106Þ

Thus, neglecting the diffusion term, the coordinate-dependent concentration of singlet excitons takes on the form SðxÞ ﬃ

I expðx=la Þ 0 la t1 S þ gSq nh ðxÞ

ð107Þ

where la is the penetration depth of the exciting light which for lex ¼ 366 nm (unpolarized) amounts to about 0.5 mm. Hole injection into anthracene crystals is achieved utilizing exciton reactions at the illuminated water electrode. The distribution of injected holes is given by the Mott–Gurney function [91] nh ðxÞ ¼ nh ð0Þ½x0 =ðx0 þxÞ2

ð108Þ

where x0 ¼ [e2nh(0)=2e0ekT]1=2 is the characteristic Debye length dependent on the concentration of holes at the injecting interface. In the example presented in Fig. 37, x0 ﬃ 0.12 mm with nh(0) ﬃ 7 1014 cm3 and e ¼ 4.5 at room temperature. Clearly, the average hole concentration, nh , decreases as the extent of the observation slab increases following the increase of the emission wavelength (l0). The Copyright © 2005 by Marcel Dekker

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fractional change (d) of the fluorescence intensity (for not too high quenching), d¼

FU FU¼0 ﬃ gSq nh tS FU¼0

ð109Þ

upon applying a sufficiently high external voltage (U ), reveals the fluorescence increase since the concentration of homogeneously distributed holes under saturation current, nh(U) ﬃ 1012 cm3, is much smaller than the average hole concentration within the layer of thickness la in the absence of an external voltage (U ¼ 0). We note that FU corresponds to the fluorescence intensity in the absence (F0), and FU¼0 corresponds to the fluorescence intensity in the presence (F) of charge in the excited layer of the crystal (cf. Fig. 37). Ascribing appropriate values of nh to increasing x1=2 (read l0), one arrives at the spatial distribution of d(x). From the identification of such obtained d(x) with the nh(x) (108), and using tS ﬃ 10 ns [232], gSq ¼ (3 1.5) 109 cm3 s1 has been deduced based on Eq. (109) [231]. If the annihilation constant gSq was determined by the excitonic diffusion, its value could be simply related to the singlet–singlet exciton annihilation rate constant (71) as gSS ﬃ 2gSq ﬃ (0.6 0.3) 108 cm3 s1 which agrees well with the value 108 cm3 s1 determined from the excitation intensity dependence of the anthracene fluorescence (see Sec. 2.5.1.1). Also, the value of gSq ﬃ 109– 1010 cm3 s1, deduced from the PL quenching upon injection of holes and electrons into a 100 nm-thick film of Alq3 [233], compares with gSS ﬃ 1.3 1010 cm3 s1 for this Al complex (see Sec. 2.5.1.1), though the upper limit of gSq suggests some differences in quenching mechanisms of singlets by other singlets, and by charge carriers. This question has been recently addressed in the context of the field-dependent EL quantum efficiency from the Alq3-based organic LEDs (see Sec. 5.4). 2.5.2.2. Triplet Exciton Reactions with Doublet Species The triplet exciton quenching by doublet species is well established. Annihilation of triplet excitons has been observed on Copyright © 2005 by Marcel Dekker

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either radiation-induced centers [234] or free [235–239] and trapped charge carriers [91,231,238–249]. The triplet–doublet interaction process consists of the collision of a triplet and a doublet species to form a singlet and a doublet state through an intermediate pair state, [T1D1=2],

where S0 is a vibrational state of the ground state singlet, T1 is a triplet exciton, and D1=2is a spin 1=2 paramagnetic center. While K1 represents the rate of encounter of triplets with charge carriers, K2 is the dissociation rate of the pair state complex into a singlet doublet pair and K1 its dissociation into the original triplet doublet pair. gTq denotes the overall annihilation (quenching) rate constant for the reaction. The dissociation rate constant K1 can be considered as a scattering process and need not be spin-conserving, although the quenching process (the transition rate to final state, K2) conserves spin. Hence only those pair spin states with doublet character can undergo quenching, since the final state of the reaction is a pure doublet. The species in the intermediate complex [T1D1=2] are correlated in a sense that they can interact with each other. The interaction energy is determined by the dipolar spin–spin interaction (dependent on the intermolecular distance as r3) and the electrostatic intermolecular interaction which like spin–spin coupling depends on the geometry of the complex, intermolecular distance and the total spin. The six spin states jcli, l ¼ 16 of the [TD1=2] complex are in general doublet–quartet mixtures with a doublet spin component jhcljD1=2ij jD l j. The spin correlation properties make the doublet component of the intermediate complex to be affected by an external magnetic field (see Sec. 2.5.3.1). The determination of the triplet exciton-trapped hole overall rate constant (gTq) was initially made by measuring Copyright © 2005 by Marcel Dekker

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of decay rate of the delayed singlet exciton fluorescence upon the introduction of excess positive charges into a sample through an ohmic hole-injecting contact [236,238,243,244]. The emitting singlet excitons were generated by the fusion of triplet excitons excited directly from the ground state with uniformly absorbed chopped, long wavelength light. The lifetimes were determined by measuring the decay rate of the delayed fluorescence during the dark period of the chopped excitation sequence. For low intensity exciting light, neglecting diffusion, the decay of triplet exciton population can be described by aI0 T=tT gTq nh T ¼ 0

ð111Þ

where aI0 denotes the generation rate of triplet excitons using light of intensity I0 and absorption coefficient a for S0 ! T1 absorption, nh is the total concentration of holes. This equation is analogous to Eq. (106) except that la for the S0 ! S1 transition has been replaced by a1 for the S0 ! T1 transition, tS by tT, and gSq by gTq. The slope of the plot of the delayed fluorescence intensity vs. time yields the effective triplet exciton lifetime for any given value of nh 1 1 ¼ þ gTq nh teff tT

ð112Þ

The total concentration of holes nh is a sum of the concentration of trapped (nht) and free (nhf) carriers. However, often nhf=nht ! 0, nh ﬃ nht due to a large concentration of traps. Then, the excitons are quenched by trapped carriers and the annihilation rate constant gTq is equivalent to the mobile exciton-immobile (trapped) charge carrier interaction rate constant gTq. Under space-charge-limited conditions, the concentration of charge is simply proportional to the applied voltage (U), nht ¼ (3=2)e0eU=ed2, where d is the sample thickness, e is the electronic charge, e is the dielectric constant of the sample material, and e0 is the permittivity of free space. Thus, it may be seen that the fractional change in the triplet exciton decay rate Db tT e0 etT ðtÞ ¼ 1ﬃ g U bT teff ed2 Tq Copyright © 2005 by Marcel Dekker

ð113Þ

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varies linearly with the external voltage U and decreases as d2. This is the case for anthracene crystal with CuI hole injecting electrode (Fig. 38). From the slopes of the Db=bT(U) straight ðtÞ lines in Fig. 38a, gTq ¼ (0.7 0.2) 1011 cm3 s1 follows. The

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non-linear voltage increase of Db=bT in the case of a crystal with the hole injecting contact Aþ (Fig. 38b) suggests triplet excitons to be quenched by free holes. In such a case ðf Þ

ðtÞ

b ﬃ bT þ gTq nhf þ gTq nht ðf Þ

ð114Þ

ðtÞ

where gTq and gTq are the second order rate constants for triplets interacting with free and trapped carriers, respectively. The concentration of free holes, defined by the current density j ¼ emhnhfU=d, where mh is the hole mobility, allows Eq. (114) to be expressed in the form 3 e0 e ðtÞ d ðf Þ j ðb bT Þ=U ¼ Db=U ¼ g þ g ð115Þ 2 ed2 Tq emh Tq U 2 This equation fits well the experimental data of Fig. 38b. ðtÞ From the linear dependence of Db=U vs. j=U2 both gTq ¼ ðf Þ 11 3 1 9 3 1 cm s and gTq ¼ (2 1) 10 cm s were (0.5 0.2) 10 ðf Þ calculated [238]. A much larger value of gTq would indicate a much larger effective diffusion coefficient of the interacting triplet (DT) and mobile hole (Dh), Deff ¼ DT þ Dh, and=or their much larger capture radius. The diffusion-controlled excitonic ðf Þ ðTOTÞ interactions [cf. Eqs. (52) and (71)] imply gTq ¼ (1=2) gTT ﬃ ðTOTÞ 2.5 1011 cm3 s1 with gTT ¼ 5 1011 cm3 s1 (Fig. 33), ðtÞ exceeding the above value of gTq by a factor of 5. Despite the ðtÞ

two fold difference in DT ¼ gTq =4pR ﬃ 0.4 104 cm2 s1 (R ¼ 0.5 nm) and DT ¼ 104 cm2 s1 obtained from the triplet–triplet annihilation experiment (see Table 2), both of them are negligiJ Figure 38 Relative increase in the monomolecular decay rate constant (Db=bT) (decrease in the lifetime) of triplet excitons in three different anthracene crystals under the positive voltage applied to two different hole injecting electrodes: CuI (a) and anthracene positive ions (Aþ) in nitromethane (b). bT ¼ t1 T is the triplet decay rate constant with no voltage: bT ¼ 239 s1 for the d ¼ 350 mm-thick crystal, bT ¼ 175 s1 for anthracene with d ¼ 625 mm (from Ref. 243); bT ¼ 200 s1 for the d ¼ 320 mm-thick crystal, Aþ injecting contact (see Ref. 238). In the right-top scale in part (b) the Db=U vs. j=U2 is presented (points) to be compared with Eq. (115) (solid line). Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes ðf Þ

ble as compared with Deff ﬃ Dh ¼ gTq =4pR ﬃ 3.3 103 cm2 s1. Assuming the Einstein relation to hold, Dh ¼ mhkT=e, mh ﬃ 0.13 cm2=V s follows from this value of Dh. Though in the same order of magnitude, it is a factor of 6 lower than the lowest time-of-flight measured mobility of holes in the c0 crystallographic direction of anthracene at room temperature mh(c0 ) ¼ 0.85 cm2=V s [101]. However, the values of mh as low as 0.4 cm2=V s (Refs. 250 and 251) or even 5 103 cm2=V s (Ref. 252) have been reported in early mobility works. The discrepancies in mh obtained by different researchers [253] can be attributed to differences in the crystal samples and caused by the accuracy of the apparatus setups. Therefore, it is not ðf Þ excluded that the above value of gTq , when assumed to be governed by the diffusion of free holes, reflects the chemical and structural imperfection of the crystals studied. On the other ðf Þ hand, gTq < 4pDTR could mean that the reaction is not completely diffusion limited with R < 0.5 nm. The latter would indicate that not all T– qf encounter events lead to the triplet quenching. Like in anthracene, the free hole–triplet exciton quenching has not been observed for pyrene crystal provided with a hole-injecting CuI anode. From the straight line Db=bT vs. U plots, the triplet-trapped hole annihilation rate constant ðtÞ has been deduced, gTq ¼ 4.5 1011 cm3 s1 [244], This is a value six times larger than that for anthracene, and an order of ðtÞ magnitude larger than the diffusion-controlled value gTq ¼(1=2) ðTOTÞ ðTOTÞ gTT ¼ 0.4 1011 cm3 s1 resulting from gTT ¼ 0.75

1011 cm3 s1 for pyrene (Fig. 33). A possible reason for the disðtÞ ðTOTÞ crepancy between gTq and gTT is that the former contains a contribution from the triplet exciton-free charge carrier interaction, neglected in the discussion of the results on tripletcharge carrier quenching experiments [244]. Another possibility to explain this discrepancy can be associated with different preferential sites and directions for triplet–triplet and tripletcharge carrier interactions, thus, following different components of the triplet diffusivity tensor in pyrene crystal [254]. The triplet–triplet annihilation occurring within the pyrene crystal dimer on molecules 0.35 nm apart, with DT ¼ 0.3

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113

104 cm2 s1 in the ac0 -plane, leads to gTT ¼ 8pDTR ¼ 2.5

1011 cm3 s1 which within the experimental accuracy for ðTOTÞ ( 0.4 1011 cm3s-1) and DT ( 0.1 104 cm2 s1) gTT ðTOTÞ approaches the experimental value of gTT . On the other hand, 4 2 1 DT ¼ (1.2 0.3) 10 cm s along the b-axis and R¼ 0.5 nm ðtÞ [255], yields gTt ¼ 4pDTR ¼ 7.5 1011 cm3 s1 near its experimental value. The triplet-trapped charge carrier interaction leads to increasing concentration of free carriers observed as photo-enhanced currents [238,256–259]. The detrapped carriers contribute, in turn, to triplet exciton quenching. This contribution can be essential if the exciton-free charge carrier interaction rate constant exceeds that for the exciton-trapped carrier interaction constant, due to high diffusivity of free carriers. From the ðtÞ linear increase of the triplet quenching rate, kTq ¼ [gTq þ ðf Þ YgTq ] nht, with the ratio of free to total concentration of holes (Y ¼ nhf=nh), the triplet-free hole interaction rate constant for ðf Þ anthracene, gTq ¼ (2 1) 1010 cm3 s1, 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 of triplet-trapped charge carrier and triplet–singlet interactions. A similar value was obtained for the triplet-trapped hole interðtÞ action in tetracene, gTq ¼ (1.5 0.5) 1010 cm3 s1 [260]. In the framework of the diffusion-controlled excitonic interactions, ðTOTÞ ðtÞ one would expect gTT 2gTq ﬃ 3 1010 cm3 s1 which is one ðTOTÞ order of magnitude lower that the experimental value of gTT discussed in Sec. 2.5.1.2. The neglection of the singlet–triplet interaction and unjustified assumption about ohmic properties of gold=tetracene contact (cf. Ref. 257) may be the reason for the above discrepancy. In fact, a method avoiding these shortðtÞ comings allowed the determination of gTq ¼ (5 2)

ðTOTÞ 109 cm3 s1 for tetracene [245], comparable with gTT ﬃ 2

109 cm3 s1 (see Sec. 2.5.1.2). The method employed the high intensity (I0) dependence of the saturation current (jþ S ) due to hole injection from the H2O=tetracene positively biased contact by triplet excitons. Their successively increasing quenching by injected holes leads to sublinear increase jþ S (I0) which yields the current dependent diffusion length of triplet excitons. From

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Organic Light Emitting Diodes ðtÞ

the latter gTq has been determined. The quenching of triplet excitons by the spatially distributed trapped carriers at the water=tetracene contact has been used to deduce the triplettrapped charge carrier interaction rate constant as described already for singlet excitons in anthracene (see Sec. 2.5.2.1). ðtÞ The obtained value gTq ¼ (2 1.5) 109 cm3 s1 (Ref. 91) corresponds, within the experimental error, to the prediction of the ðtÞ ðTOTÞ diffusion-controlled interaction process gTq ¼ (1=2)gTT ﬃ (0.5–1) 109 cm3 s1 (cf. Sec. 2.5.1.2). It is obvious that triplet-charge carrier interactions might be of crucial importance in organic LEDs, where triplet emitting states are generated in the high charge carrier concentration regions due to the electron–hole recombination process [261]. Their role in organic electrophosphorescent LEDs 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 magnetic field-imposed changes in EL efficiency of organic LEDs: (I) the first class phenomena are subject to fine structure modulation (FSM) and require fields of 10 mT to 0.1 T [262]. This class includes singlet exciton fission (S ! T þ T), triplet–triplet fusion (T–T) and triplet-charge carrier (generally, doublet species, D 1=2) annihilation (T–D1=2) (cf. Secs. 2.5.1.2 and 2.5.2.2). (II) The second class phenomena are subject to electronic Zeeman effect and hyperfine modulation (HFM), and fields only 1 mT are required [263]. The key examples are 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 some excitonic interactions are subject to modulation by weak magnetic fields (less than 1 T). The magnetic field modulation of the singlet exciton fission rate [see Scheme (80)] can be experimentally observed as a magnetic field effect on prompt fluorescence [192,200,201,273–278]. The magnetic field sensitive triplet–triplet (80) and triplet–doublet (110) annihilation Copyright © 2005 by Marcel Dekker

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rate constants show up as magnetic field effects on delayed 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 are expected to occur in organic LEDs, the magnetic field effects on their EL output [287] and=or double injection currents [259] can be utilized to infer about their presence and altering processes that underlie the LED’s performance. Figure 39 illustrates an experimental arrangement for measuring of three-dimensional anisotropy of the magnetic field effect (MFE) on photoconduction. The magnetic field can be rotated in any plane perpendicular to the ab-plane of the crystal. The orientation of the magnetic field with respect to the crystallographic axes is represented by angles W and j. For a fixed field strength and crystal orientation j, the photocurrent shows one or two maxima as W varies between 0 and 180 (Fig. 40a). The maxima (or minima) in the MFE as a function of the orientation of the magnetic field with respect to the crystal axes are characteristic also for prompt and delayed fluorescence intensity (for a three-dimensional anisotropy of the MFE on delayed fluorescence in anthracene crystal, see Refs. 281, 282). Their positions are determined by crystallographic structure of the organic system, and depends on the range of the magnetic field strength. At low fields (B < 0.1 T), the anisotropy is slightly more complex, with new maxima (or minima) appearing for field directions that bisect the angular separation between the high-field maxima (or minima) positions (see e.g., the minima of the MFE on delayed fluorescence in anthracene). For a fixed field-crystal orientation, the MFE on either fluorescence or photocurrent shows non-monotonic behavior as seen in Fig. 41 for the photocurrent in Au=Tetracene crystal=Au system. Qualitatively, a similar result has been found for the fluorescence (also for other organic crystals), although the position of the minimum (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 be explained by class (I) phenomena based on the magnetic field Copyright © 2005 by Marcel Dekker

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

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Figure 40 Three-dimensional anisotropy of the magnetic field effect on photoconduction of a 7 mm-thick tetracene single crystal illuminated through a semitransparent gold evaporated anode (cf. Fig. 39a). (a) Relative increase of the photocurrent (iph) when a magnetic field B ¼ 0.5 T is rotated perpendicular to the ab-plane for different orientations of the crystal j. The maximum relative increase amounts to about 10%. (b) Orientation (j) dependent positions of the maxima in the magnetic field effect vs. direction of the magnetic field (W). Circles: experimental data; solid line: theoretical prediction according to Eq. (121). After Ref. 248.

modulation of the spin components of the intermediate pair states formed in the course of the exciton fission and fusion [(80), (81)] as well as exciton-doublet interaction (110). The most comprehensive theory of the MFEs is that including the effects of the spatial variation of the triplet exciton wave functions [288]. However, for the general understanding of the phenomenon, it is sufficient to analyze the complete spin density matrix of the intermediate pair states with spatial variables of the excitons to be neglected [280]. As discussed in Secs. 2.5.1.2 and 2.5.2.2, two triplet excitons or one triplet and one doublet species can form correlated pair states with their pair spin wave functions containing a certain degree of indeterminacy. They are coupled to the exciton reservoir by Copyright © 2005 by Marcel Dekker

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

two phenomenological constants K1 and K2 (K1 in the kinetic schemes stands for the source term). It is essential to remark again that the overall reaction is spin-conserving, in contrast to the scattering process K1 for which there are no spin selection rules. The spin of the intermediate pair states is described by the complete spin density matrix, (9 9) for the correlated triplet pair [T1T10 ] and (6 6) for the triplet–doublet pair [T1D1=2]. In general, the annihilation (9 9) matrix consists of a sum of three terms representing the singlet, triplet, and quintet final state channels [see ðSÞ Eq. (83)]. Explicit calculations for the gTT or g S constants require the knowledge of the number of pair states with singlet character (ClS 6¼ 0). In order to evaluate different spin amplitudes, the spin Hamiltonian of the intermediate complex [T1T10 ] must be defined. It has been assumed to be a simple sum of the Hamiltonians for two triplets forming Copyright © 2005 by Marcel Dekker

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the complex h i h i bðSÞ b b b b H complex ¼ H SS ð1Þ þ H Z ð1Þ þ H SS ð2Þ þ H Z ð2Þ

ð116Þ

bZ representing the zero-field and Zeeman bSS and H with H Hamiltonians for the individual excitons T1(1) and T10 (2). The zero-field term of (116) can be expressed as 2 1 b2 b b b b H SS ð1; 2Þ ¼ H SS ð1Þ þ H SS ð2Þ ¼ D1 S1z S1 3 2

2 2 2 2 1 2 þ E1 Sb1x Sb1y þ D2 Sb2z Sb2 þ E2 Sb2x Sb2y 3 ð117Þ where D1, D2 and E1, E2 are the zero-field splitting parameters (D of the order 0.1 cm1, and E=D 0.1). The 2 2 squared spin of each of the triplet exciton (Sb1 ; Sb2 ) commutes with the spin projections on the molecular axes (Sbx, Sby, Sbz), but does not commute with the Hamiltonian [289]. Therefore, the eigenstates of the Hamiltonian (117), jiji (quantized along the molecular axes i,j ¼ x,y,z), are not the eigenstates of the total spin Sb 2. The pure singlet state jS(0)i(B ¼ 0) can be obtained by diagonalizing the Sb 2 matrix, jSð0Þi ¼ 31=2 ðjx01 x02 i þ jy01 y02 i þ jz01 z02 iÞ

ð118Þ

where the primed coordinate system x0 , y0 , z0 is a system of bSS(1,2) [Eq. (117)] is diagonal. In zero coordinates in which H field, there are only three states with singlet character, namely jx xi, jy yi, jz zi, pair states jx yi and jy xi, jy zi and jz yi, jx zi and jz xi are degenerate. This degeneracy is lifted by the weak inter-triplet interaction, giving a set of nine pair states of which three are singlet–quintet mixtures jx xi, jy yi and jz zi, three are pure quintets and three are pure triplets (see e.g., Ref. 262). When a magnetic field B is applied, the Zeeman term bZ ð1; 2Þ ¼ gbBðS1 þ S2 Þ H

ð119Þ

of the pair state adds to the zero-field Hamiltonian (117). Copyright © 2005 by Marcel Dekker

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At relatively low-field strengths when gbB D, the 9 9 matrix describing the pair spin state in the basis of the pair states functions ji ji will, in general, have non-zero off-diagonal matrix elements which will mix the pair states. Thus, in this limit, there will be more states with singlet character and, for example, gS [see Eq. (83)] will be larger than at zero field. Consequently, the prompt fluorescence from directly excited singlets will decrease, while the delayed fluorescence due to triplet–triplet generated singlets will increase. In the high-field limit, when gbB D, the pair states are approximately described by the spin eigenstates jþ1, 1i, j1, þ1i, j0, 0i, j0, þ1i, jþ1, 0i, etc. of triplet excitons 1 and 2 in the complex with spin angular momentum quantized along the external field B. Only the first three of the nine pair states have singlet character, and the pure singlet is jSðHÞi ¼ 31=2 ðj0; 0i j þ 1; 1i j 1; þ1iÞ

ð120Þ

In general, the magnitude of the amplitudes ClS , and therefore ðSÞ gS and gTT depend on D and E, the applied field B, the energy spread in the manifold of states cl(DEQS, DETS), the relative orientation of T1 and T10 and the branching ratio K2=K1. For high magnetic fields (B > 0.1 T) with an arbitrary orientation with respect to the crystallographic axes, only two pair states, j0 0i and 21=2(jþ1, 1i þ j1, þ1i), have singlet character with fractional singlet component 1=3 and 2=3, respectively, as may be seen by projecting these functions ðSÞ onto the pure singlet state (120). Thus, the rate constant gTT (85) and g0 s (88) are smaller than in zero field, a decrease in delayed, and an increase in prompt fluorescence occurs for such magnetic fields. In crystals, when the directions of molecular axes are fixed, there exist special orientations of the magnetic field for which the j0 0i state is degenerate with the jþ1, 1i and j1, þ1i states. At these orientations, level-crossing resonances occur, since there is only one state with singlet character which is the pure singlet (120). Equations (85) and (88) thus have only one term for which ðSÞ ClS 6¼ 0, gTT and g0S exhibit a minimum. Within the context of the theory [234,280], the positions of level-crossing Copyright © 2005 by Marcel Dekker

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resonances are determined by the equation 2 2 2 D cos g1 þ cos g2 3

ð121Þ

2

2

2

2

þ Eðcos a1 þ cos a2 cos b1 cos b2 Þ ¼ 0 where cos a, cos b and cos g are the direction cosines of B with respect to the molecular axes of the two inequivalent molecules x1, y1, z1 and x2, y2, z2. The Hamiltonian describing the intermediate state [T1D1=2] in the triplet–doublet interaction process (110) is bþH b ¼ ge bB r þ gbB S bSS H

ð122Þ

where ge is the radical (electron, hole) g-factor, assumed isob are the spin operators for the doublet ^ and S tropic, and r bSS has been defined and triplet species, respectively. The H by (117). As for the exciton–exciton interaction, the total spin b þr b, and therefore ^)2, does not commute with H operator, (S spin pair functions, cl are doublet–quartet mixtures. In zero-field, the pure doublet is jD1=2 ð0Þi ¼ 31=2 ðjz; 1=2i jx; 1=2i þ ijy; 1=2i ð123Þ pﬃﬃﬃﬃﬃﬃﬃ where i ¼ 1, and jxi, jyi, jzi are the zero-field eigenfunctions of the triplet quantized along crystalline axes (the triplet exciton fine structure tensor), and j 1=2i are the doublet entity spin states. Each of the six eigenstates forming the pure doublet state (123) has doublet character D ¼ hD1=2(0)jx, 1=2i ¼ hD1=2(0)jy, 1=2i ¼ hD1=2(0)jz, 1=2 i ¼ 31=2. The dissociation rate gTq is proportional to the number of states with the amplitude of the mS ¼ 1=2 doublet component, D l ¼ hcljD1=2i as predicted by the theory [234], 2 þ D 2 6 K Dþ X l l 1 ð124Þ gTq ¼ K1 6 þ 2 þ D 2 l¼1 K1 þ K Dl l where the quenching process occurs with the transition rate to Copyright © 2005 by Marcel Dekker

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2 2 final state, K2 ¼ KðjDþ l j þ jDl j Þ. Hence only those pair spin states with doublet character can undergo quenching since the final state of the reaction is a pure doublet. It is important ðSÞ to note that, in contrast to gTT and g0S , the quenching rate constant, gTq, decreases monotonically with increasing applied magnetic field. This follows from the properties of the eigenfunctions of the Hamiltonian (122) at B 6¼ 0, non all of them having doublet character. At high fields, gbB D, only four non-degenerate states have doublet character. Thus, in agreement with Eq. (124), for any magnetic field B 6¼ 0, the interaction rate constant should be smaller than for B ¼ 0. In addition to this general decrease in the quenching rate with field, one would expect high-field anisotropies due to level-crossing resonances of the pair states similar to those observed in the delayed fluorescence of anthracene and tetracene, and in tetracene prompt fluorescence. These resonances occur when j0, 1=2i and j1, 1=2i are degenerate, respectively, with j1, 1=2i and j0, 1=2i. These special orientations of the magnetic field result from the equality of their energies, namely W0, 1=2 ¼ Wþ1,1=2, and W1,þ1=2 ¼ W0,1=2. The pair energies are determined by the sum of the triplet exciton energies W0, Wþ1, W1, and of the doublets W 1=2 ¼ ge bB=2. These conditions reduce to the same equations when applied to fission or fusion, Eq. (121). A good agreement of the experimental data with the theoretical predictions is apparent from Fig. 40b for the MFE on photoconduction due to triplet exciton-trapped hole interaction in triclinic tetracene crystal if two translationally inequivalent crystallographic positions of tetracene molecules [207], thus two appropriate sets of the angles a1, b1, g1, and a2, b2, g2 are used in solving Eq. (121). In monoclinic crystals like anthracene and naphthalene, the crystal b-axis coincides with one of the molecular axis, which is taken to be z-axis. The y- and x-axes lie in the ac-plane, which is a mirror plane (see e.g. Ref. 52). When B is rotated in the ab-plane, as often met due to the developed ab-plane in solution- and sublimationgrown thin crystals, the high-field resonances occur at 23.5 with respect to the b-axis [238,280]. On the basis of Eq. (124), the interaction rate constant for zero field [gTq(0)],

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ðrezÞ

and B 6¼ 0 at the resonance [gTq (B)] and off-resonance ðoff Þ [gTq (B)] field directions can be calculated and compared to each other [238]: 1 gTq ð0Þ ¼ KK1 ð1 þ K =3Þ1 3

ð125Þ

1 1 þ ð4=9ÞK ðoffÞ gTq ðBÞ ¼ KK1 3 ð1 þ 2K =3Þð1 þ K =3Þ

ð126Þ

1 ðresÞ gTq ðBÞ ¼ KK1 ð1 þ KÞ1 3

ð127Þ

and

From the (ab)-plane anisotropy of the MFE on the photocurðoff Þ rent in anthracene crystal gTq = gTq ¼ 0.965 has been found. ðoff Þ Dividing Eq. (126) by Eq. (125), one obtains gTq (B)=gTq(0) ¼ 1 [1 þ (4=9) K ][1 þ (2=3) K ] which compared with the above experimental value yields K ¼ 0.17. Then, from Eq. (125), and the above value of K, K1 ﬃ 20 gTq (0) follows, and identifyðtÞ ing gTq(0) with gTq ¼ (0.5 0.2) 1011 cm3 s1 (see Sec. 2.5.2.2), K1 ¼ (1.0 0.5) 1010 cm3 s1 is obtained. This is an order of magnitude larger than a triplet exciton diffusion-controlled process (see Sec. 2.5.2.2) and may indicate the exciton capture radius by a trapped hole to remarkably exceed the nearest-neighbor intermolecular distance. In spite of this, simple scattering of the triplet by a trapped hole seems to be a quite frequent process, since K ¼ K2=K1 ﬃ 0.17, that is the annihilation rate K2 constitutes only about 15% of the total rate of the decay of the [T1D1=2] pair state, only weakly competing with its backwards to the reacting separated species (K1). The latter, as obtained from fitting of the general shape of the high-field anisotropy curve to be K1 ¼ (1.25 0.3) 109 s1, determines the lifetime of a cor1 ﬃ 0.8 ns related triplet-trapped hole pair in anthracene, K1 [238]. The magnetic field effects on excitonic interactions in amorphous or highly defected solids are difficult to quantitative description, because the intermediate pairs of the interacting species may assume a variety of collisional configurations, and the Hamiltonian and coordinate system in Copyright © 2005 by Marcel Dekker

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which pure singlet (120) or pure doublet (123) is defined, are not constant. Thus, their MFE characteristics may be completely different from those for single crystals. For example, it has been shown that the triplet–triplet fusion rate constant, ðSÞ gTT , in solutions decreases monotonically with increasing magnetic field, and it does not exhibit the inversion at low fields which is characteristic for crystals [290]. Such an inversion can be observed as a transition from the low-field enhancement to the high-field reduction in the intensity of the delayed fluorescence and as an opposite effect for prompt fluorescence if the singlet exciton fission process is feasible energetically. An excellent illustration of these phenomena is presented in Fig. 42, where the MFE on prompt and delayed fluorescence from tetracene crystal is plotted as a function magnetic field strength at a fixed field direction (Fig. 42a) and a fixed value of field as a function of its direction (Fig. 42b). Coexistence of the thermally mediated singlet exciton fission and triplet–triplet fusion is clearly demonstrated [cf. Eq. (82)]. The fitting of the theory to the experimental data of the MFE anisotropy of prompt fluorescence allows various reaction parameters for excitonic interactions in tetracene to be evaluated. Such a procedure applied to tetracene crystal at low (ﬃ0.1 MPa) and high (ﬃ 300 MPa) hydrostatic pressures has shown how they are modified by small changes in the crystal lattice (Table 3). For example, the lifetime of the [T1T10 ] pair complex increases from 0.2 ns at normal pressure to 0.33 ns at 290 MPa. At the same time, the ðSÞ triplet annihilation [K2 ] and singlet fission (K2) rates decrease by a factor of 2 and 1.3, respectively. In the frames J Figure 42 Magnetic field dependence of prompt and delayed fluorescence intensities in a tetracene crystal as a function of the magnetic field strength (a) and field orientation (b) at different temperatures. The curves in part (a) have been obtained with the field oriented at 20 with respect to the b-axis in the ab-plane of the crystal, corresponding to one of the resonance directions shown in part (b) presenting the MFE anisotropy with the magnetic field B ¼ 0.4 T rotated in the (ab)-plane of the crystal. From Ref. 192. Copyright 1970 American Physical Society. Copyright © 2005 by Marcel Dekker

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Table 3 Singlet Exciton Fission Parametersa for a Tetracene Single Crystal at Two Different Hydrostatic Pressures p ¼ 0.1 MPa E ¼ K2=K1 ¼ 0.52 K1 ¼ 3.3 109 s1 K2 ¼ 1.3 1012 cm3 s1 ðSÞ K2 ¼ 1.72 109 s1 K1 ¼ 1.7 1012 cm3 s1 t ¼ (K1 þ K2)1 ¼ 2 1010 s

p ¼ 290 MPa E ¼ 0.45 K1 ¼ 2.1 109 s1 K2 ¼ 1.0 1012 cm3 s1 ðSÞ K2 ¼ 0.95 109 s1 K1 ¼ 0.88 1012 cm3 s1 t ¼ (K1 þ K2)1 ¼ 3.3 1010 s

a

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

of Merrifield’s [280] and Suna’s [288] theories, these changes can be interpreted as a pressure improvement of the twodimensional character of the triplet exciton movement. The pressure modification of constants K1 and K2 allows to infer about relative pressure changes in the cc component (Dcc) of the diffusion tensor of triplet excitons in tetracene, namely (DDcc=Dcc)=Dp ¼ 1.3 103=MPa1—the number being about two times of that in anthracene [292] and consistent with the relation of pressure gradients of other quantities for anthracene and tetracene [200,292]. Interestingly, a prompt fluorescence-like inversion in the MFE has also been observed with the MFE on photoconduction in tetracene crystal (Fig. 41). Its appearance depends on the crystal orientation and suggests singlet excitons to be involved in generation of the photocurrent. They can increase the concentration of free carriers by the interaction with trapped carriers injected initially from the electrode and=or increase the injection current due to increasing singlet exciton flux reaching the electrode. In both cases, the MFE on photocurrent should follow exactly the MFE on prompt fluorescence reflecting the magnetic field modulation of the singlet exciton concentration within the absorption depth of the exciting light. The magnetic field dependence of the photocurrent of a thin tetracene film illuminated either by a non-injecting (Al) or hole injecting (Au) anode is shown in Fig. 43a. Only in the high electric-field case (F ¼ 100 V=2 mm ¼ 5 105 V cm1) for the non-injecting anode (curve 2), the (Dj=j) (B) follows qualitatively the magnetic Copyright © 2005 by Marcel Dekker

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Figure 43 (a) Experimental curves of the magnetic field-induced percentage changes of the photocurrent, Dj=j (1,2,3), and prompt fluorescence, DF=F (4), in a 2 mm-thick polycrystalline layer of vacuum-evaporated tetracene sandwiched between Al and Au electrodes. Curves 1 and 2—illumination through Alþ at two different voltages, and 3—illumination through Auþ. Excitation light of lexc ¼ 470 nm and intensity I0 ¼ 1013 quanta=cm2 s was used. (b) Hypothetical change in the observed photocurrent if the triplet exciton concentration were determined by the magnetic field inhibition of the triplet–charge carrier interaction process (A), inhibition of singlet exciton fission and reabsorption (B), and simultaneous operation of both processes (C). The absolute values of Dj=j must not be compared with those in part (a) since the analysis in part (b) has been performed for a resonance direction of single tetracene crystal and not averaged for a random distribution of microcrystallites in a polycrystalline sample as should be done to quantitatively compare with the results of part (a). From Ref. 293.

field-induced prompt fluorescence changes (DF=F) (B). This might be ascribed to the injection of holes by singlet excitons reaching the Alþ anode. However, as for the values, Dj=j (B) is roughly twofold lower than DF=F (B). There must then be an additional charge generation process whose efficiency diminishes in a magnetic field. The injection of holes by triplet excitons seems to be a natural candidate since they are efficiently produced in the fission and have much longer diffusion ðTÞ length [lD ﬃ 300 nm] [154] as compared with singlet excitons ðSÞ [lD ﬃ 12 nm] [153]. The former is even larger than the penetration depth of the exciting light in tetracene films (la ﬃ 150 nm at la ¼ 470 nm) [286]. Since the concentration of Copyright © 2005 by Marcel Dekker

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triplet excitons decreases at high magnetic fields due to the magnetic field inhibition of the fission process, the triplet exciton flux reaching the electrode diminishes. The resulting injection current occurs as a result of increasing injection by singlets and decreasing injection by triplets. At low magnetic fields, an increase in the triplet exciton concentration accompanies the increased singlet exciton fission rate, the decrease in the singlet exciton flux is compensated in part by the increased triplet exciton flux towards the anode, and the low-field minimum becomes shallower as compared with that for prompt fluorescence. The magnetic field change in the photocurrent can be coupled to the magnetic field change in prompt fluorescence (DF=F) by an approximate relationship [293] Dj jS=T þ FS=T ð0ÞðDF=F þ 1Þ ﬃ 1 j jS=T þ FS=T ð0Þ

ð128Þ

where jS=T ¼ jS=jT is the ratio of injection efficiencies of holes by singlet (jS) and triplet (jT) excitons, and FS=T is the ratio of the singlet [FS(0)] and triplet [FT(0)] exciton fluxes reaching the anode at zero magnetic field. The predictions of Eq. (128) agree with experiment for jST ﬃ 16 which is in the range jS=T > 10 predicted previously for the contact Al=anthracene crystal [294]. At lower voltages, the (Dj=j) (0) does not exhibit the characteristic for (DF=F) (B) low magnetic field minimum, being a monotonically increasing function of B (curve 1 in Fig. 43a). This behavior can be rationalized by subjecting the triplet exciton flux (thus FS=T) to the magnetic field modulation. The exciton flux towards the anode increases with elongation of the exciton diffusion length. Due to triplet-charge carrier interaction, the triplet lifetime and its diffusion length are shorter than in the absence of charge [cf. Eq. (114)]. Upon the magnetic field-induced monotonic decrease of the rate of this interaction, a monotonic increase in the triplet exciton diffusion length is expected which would enhance the charge injection by triplet excitons. Thus, the low magnetic field increase of the photocurrent (within the minimum for DF=F) is caused simultaneously by two factors, first, the increased concentration of triplets due to the magnetic field inhibition of the singlet fission, and Copyright © 2005 by Marcel Dekker

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secondly, by magnetic field-induced elongation of their diffusion length. It suppresses the photocurrent decrease due to injection by a decreasing number of singlets, the resulting photocurrent increases monotonically with magnetic field (Fig. 43b). This effect is well pronounced at lower voltages when the concentration of charge in the near-electrode region is high enough to modulate the triplet exciton diffusion length [see Eq. (108) and the following discussion]. The role of triplet excitons is even more remarkable when hole injecting anode (e.g. Au) is provided to highly charge trapping polycrystalline or amorphous sample of tetracene (Fig. 43a, curve 3). The MFE on the photocurrent at high fields is here suppressed by a reduction in the effective detrapping of holes by triplet excitons, since the photocurrent is largely due to excitonic detrapping of the holes injected initially from the electrode. The MFE on the photocurrent in the Au=Tetracene crystal=Au system may not follow this pattern especially for high structural quality single crystals when concentration 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 of the formation of emissive states via the recombination of oppositely charged carriers (electrons, e, holes, h) injected from electrodes (see Chapters 1 and 5). The injected carriers are free (statistically independent of each other), the recombination process is kinetically bimolecular but naturally proceeds through a Coulombically correlated charge pair state (eh) prior to the electron–hole localization on one molecule or closely spaced two molecules, forming molecular or bimolecular final emissive states (see Sec. 2.3). The spin dynamics of charge pairs are sensitive to external applied magnetic fields, which permit the manipulation of both the charge pair lifetimes and the yields of products arising from charge pair decay. The effect appeared to be a powerful tool in the elucidation of chemical reactions occurring through radical pairs [272,295–298], and assigned for the purpose of this book as Copyright © 2005 by Marcel Dekker

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Figure 44 The energy level scheme diagram (not to scale) and electronic transitions leading to fluorescent (S1) and phosphorescent (T1) molecular states produced in the bi-molecular e þ h recombination process (VR) with suitable rate constants (k1, k1, k3, k3, k(S), k(T)). The singlet [1(eh)] and triplet [3(eh)] states of the pair (eh) undergo mixing with the rate constants kST and kTS; the S1 ! T1 intersystem crossing is characterized by the rate constant kISC. The overlapping Gaussian energy bands of the (eh) pairs due to static and dynamic disorder in non-crystalline organic solids are indicated by dashed curves (cf. Sec. 2.4.3).

class (II) phenomena. Application of a magnetic field as small as 10 mT lowers the yield of complex excited triplets within a photosynthetic bacteria by about 40% [299], and by as much as 50% of anthracene triplets produced through dyeanthracene charge-transfer (CT) state [300]. As illustrated in Fig. 44, in the phenomena of class (II) external magnetic field controls, the conversion rate between singlet and triplet states of a pair of oppositely charged carriers when the energy Copyright © 2005 by Marcel Dekker

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separation between their singlet and triplet ground states, j2Jj, is comparable or smaller than the difference between the Zeeman energies of the pair components or their hyperfine energies. These effects can be classified into three types [269,270,296]: (A) the electronic Zeeman effect (DgbB), where Dg ¼ ge gh 6¼ 0 is the difference between electron (ge) and hole (gh) g-factors of the carriers forming pairs, (B) the hyperfine interaction effect, and (C) the mixed effect. Since Dg is usually a small quantity, the first type effect is not expected to occur at very low magnetic fields, and, for the pair h=DgbB, the relative change in the yield of the lifetime tCP 2 carrier capture products is proportional to B2 at low fields and B1=2 at higher fields, and saturates at high fields [269,296]. If ge ¼ gh (Dg ¼ 0), magnetic field effects (MFEs) on the product yield still exist due to the hyperfine coupling of the pair carriers. The Hamiltonian of the charge pair comprises of bZeeman þ H bhyperfine, where H bZeeman ¼ b¼H be–h þ H three terms: H gbB(Sbe þ Sbh) with Sbe, Sbh representing the spin operators for bhyperfine ¼ P al Sbm Ibl the electron and hole, respectively; H l;m represents the hyperfine interaction between l nuclei (often protons) interacting with the relevant electrons m, Ib1 being the nuclear spin operator of the lth nucleus (proton) and Sbm be–h term the electron spin operator of the mth electron. The H relates to the exchange interaction hJ[(1=2) 2SbeSbh] provided by a separation (r) exchange parameter J(r) ¼ J0 exp(ar) with characteristic constants J0 [J(r) with r ! 0] and a ¼ 2=r0 with J(r) ¼ 0.135 J0 at r ¼ r0. The eigenfunctions of the CP Hamiltonian include the singlet states, jSi, which are odd, and triplet states, jTþi,jT0i,jTi, which are even under the bhyperfine prointerexchange of the two particles [289]. The H vides the necessary unsymmetrical term in the Hamiltonian which gives rise to singlet–triplet mixing, the odd singlet states are subject to upconversion to even triplet states [263]. An external magnetic field partially restores the symmetry of the total CP Hamiltonian because the Zeeman bZeeman, is even under exchange of the two Hamiltonian, H particles, and reduces the mixing rate, implying a change in the triplet-to-singlet products of the recombined CPs. The Copyright © 2005 by Marcel Dekker

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effective value of the hyperfine coupling constant, a, can be evaluated from the observed anisotropy of HFM employing highly ordered systems, and has been found on the order of a=gb ﬃ 1 mT for a dye-anthracene crystal (DAþ) system [300]. Thus, again, the MFE due to the HFM of the CP pair states is expected to occur at very low magnetic fields and saturate at high fields when the Zeeman term exceeds the bhyperfine. Finally, a combinahyperfine interaction energy, H bhyperfine) interaction of the Zeeman (DgbB) and hyperfine (H tion defines the third type of a mixed effect which will result in a non-monotonous dependence of the relative yield of the recombination products as magnetic field strength increases. In this case, an initial low-field increase in the yield becomes followed by its decrease at higher fields and can end with negative values at still higher fields [270]. The situation becomes more complex if the e–h interaction energy (spin– spin and electrostatic exchange) is not negligible. This would be of importance for the short inter-carrier distances (r) when J(r) becomes fairly large (larger and=or comparable with bhyperfine), and can be considered as class (III) of DgbB and H magnetic field sensitive phenomena. If the degenerate triplet states fall much above the singlet pair state, the splitting of jTþi and jTi sub-states in moderate magnetic field strengths is not sufficient to level jTi and jSi states, the hyperfine interaction can be unable to mix these states, no MFE on the recombination products is expected. However, at a levelcrossing field, Bc ¼ j2Jj=gb, the hyperfine interaction-induced mixing of these states suddenly sets in, and a sharp change of the product yield follows. As the field increasing proceeds, the jTi sub-state moves below the jSi level, one would expect a decrease in the mixing rate. The final result is 0 or a residual MFE signal transforming into a non-monotonous field evolution with an extremum at Bc. The second and third class of the phenomena should be considered as a reason for the MFEs on the emission from organic LEDs since their emissive states originate from the e–h recombination possibly involving long-living eh pair states as their precursors. The DL LED with Alq3 emitter, placed in a steady-state magnetic field (B) (Fig. 45), shows the light output following Copyright © 2005 by Marcel Dekker

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Figure 45 Schematic drawing of the experimental setup to measure EL output in magnetic field (B). This is a topical view of an Alq3 emitter based LED placed between the pole pieces (N, S) of an electromagnet in a way that magnetic field is parallel to the surface of the sandwich DL EL cell, and the electrofluorescence flux (hn fl) leaves the cell perpendicular to B. Adapted from Ref. 301.

the bell-shaped function of B as it increases from 0 to 0.5 T. A maximum value of the MFE is about 5% and appears at a field ﬃ300 mT (Fig. 46a). A similar behavior has also been reported for EPH LEDs, where the magnetic-field-induced increase in the EPH efficiency up to 6% at about 500 mT and driving current j ﬃ 3 mA=cm2 was followed by a high field decrease. Still positive effect continued to the highest accessible field of about 0.6 T (Fig. 46b). This suggests the strong redissociation limit of the formation of triplet excitons (k1 k(S), kST; k3 k(T), kTS), and a magnetic field shift of the state jTi towards the state jSi of the (eh) pairs, leading to the Copyright © 2005 by Marcel Dekker

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Figure 46 Experimental results of the magnetic field dependence of 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 DL electrophosphorescent LED, ITO=6 wt% Ir(ppy)3:74 wt% TPD:20 wt% PC (60 nm)=100% PBD(50 nm)=Ca=Ag (b). The data taken at two different applied voltages and corresponding current densities given in the insets. Part (a) adapted from Ref. 301. Part (b) taken from Ref. 301a.

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reversed trend in the mixing at B ﬃ 0.5 T. The broad bellshaped curves (Dj=j) as a function of B are indicative of a distribution of the inter-carrier distances dictated by a random nature of the recombination process, and both static and dynamic disorder in the emitters.

2.6. ELECTRIC FIELD-ASSISTED DISSOCIATION OF EXCITED STATES The quantum EL efficiency of organic LEDs is known to be a function of their operation voltage (see Sec. 5.4). The fieldassisted exciton dissociation has been invoked to explain its high-field drop [68,302–306]. The existence of such a process resulting in the intrinsic production of charge carriers should be directly observed as photoconduction (PC) and=or electric field-induced luminescence quenching. The dissociation ability depends on the type of excited state, weaker bounded states expected to dissociate easier. Since in the recombination EL, the final emitting states (mostly localized Frenkel type excitons) are by definition formed through the intermediate CT state of a Coulombically correlated electron–hole pair (see Fig. 3), there can be sufficient thermal energy to dissociate such a pair, reducing the number of final emitting states. The field-assisted dissociation of the localized Frenkel excitons may occur as well, though with a lower efficiency. Such a process has been proposed to explain PC and electromodulated fluorescence characteristics of thin films of Alq3 [305,306]. Figure 47 shows the fluorescence (FL) quenching efficiency (Fig. 47a) and dc photocurrent jph (Fig. 47b) as a function of the applied electric field at two different excitation wavelengths. A possible mechanism for the photogeneration of carriers in solid Alq3 is that excited singlet states (Alq3) may dissociate into separated electrons and holes, in addition to the radiative relaxation producing fluorescence, hn fl. This is shown in some detail in Fig. 48. The initial separation step involves a charge-transfer state (CT) formed with a fieldindependent probability, Z0 and field-depending CT dissociation process (O) into separated charge carriers (e þ h). Thus, Copyright © 2005 by Marcel Dekker

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Figure 47 Fluorescence quenching efficiency (a) and steady-state photocurrent (b) as a function of electric field at two different excitation wavelengths. From Ref. 306. Copyright 2002 American Institute of Physics.

the photocurrent can be expressed as jph ¼ eZI0

ð129Þ

where Z is the overall probability for excited states to dissociate into separated charge carriers, and I0 is the quantal exciting light intensity (photons=cm2 s). At low fields, the experimental photogeneration efficiency (jexp=eI0) is very

Figure 48 Photo-excitation and dissociation of Alq3, leading to the charge transfer state (CT) and electron–hole pairs, the latter giving rise to photocurrent flowing in solid Alq3. Copyright © 2005 by Marcel Dekker

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low, extrapolated to F ¼ 0 gives Z(0) < 106 (Fig. 47). The fluorescence intensity at F ¼ 0, FL(0), would decrease under an electric field F applied to the Alq3 film FL(F) ﬃ FL(0)[1 Z(F)]. The experimental ratio [FL(0) FL(F)]= FL(0) ﬃ Z(F) is a measure of the field-induced fluorescence quenching. The functional shape of the overall dissociation probability Z(F) depends on the physical mechanism underlying the charge separation. In the Poole–Frenkel (PF) framework [307,308], the field dependence of the overall quantum photogeneration yield is given by ZPF ¼ Z0

expðbPF F 1=2 Þ APF þ expðbPF F 1=2 Þ

ð130Þ

where bPF ¼ (e3=pe0k2T2)1=2 ¼ 1.5 102 (cm=V)1=2 with e ¼ 3.8 [309], and APF expresses the recombination-to-generation rate constants ratio at F ¼ 0. The PF formalism treats the electron–hole pair dissociation as a one step carrier escapes from the Coulomb field of the countercharge due to external field-assisted thermal activation over the barrier. The two steps in the formation of a free carrier pair, as shown in Fig. 48, are undistinguishable. In other models of the exciton dissociation process, these two steps are separable, and the overall quantum efficiency expressed by the product ZðFÞ ¼ ZCT ðFÞOðFÞ

ð131Þ

where

kCT ðFÞ ZCT ðFÞ ¼ kCT ðFÞ þ kf þ kn

ð132Þ

stands for the quantum yield of CT states. kCT is the primary escape rate constant averaged over all solid angles due to its dependence on the electron jump direction with respect to the applied electric field. The field dependence of Z(F) comes from the 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. Copyright © 2005 by Marcel Dekker

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It is often assumed that the rate constant for carrier production is characterized by an exponential function [310,311] k ¼ k0 exp½ðF=F0 Þ cos Y

ð133Þ

where k0 and F0 are constants which may depend on temperature, and Y is the direction of the carrier escape with respect to the applied field. The physical meaning of expression (133) has been discussed. Originally considered as due to the primary one-step charge-carrier separation to form a CT exciton [310,312], was later proposed to reflect charge-carrier hopping between local sites (microtraps) forming the core (pinning trap) of a spatially extended defect (macrotrap) localizing primary excited states [313]. If by definition, the average of kCT(F) were 1 kCT ðFÞ ¼ 2

Z1

dðcos YÞk0 expðF cos Y=F0 Þ

1

¼ k0

sin hðF=F0 Þ F=F0

ð134Þ

the average quantum yield of CT states would read ZCT ðFÞ ¼

sin hðbCT FÞ=bCT F A þ sin hðbCT FÞ=bCT F

ð135Þ

where bCT ¼ F01

and A ¼ ðkf þ kn Þ=k0

ð136Þ

The probability of the dissociation of the CT state into a pair of separated carriers, and its functional form is determined by the mechanism of final charge separation [O(F)]. Besides the one-step PF dissociation process (130), the Onsager formalism is often used to describe O(F) [314,315] Z ð137Þ OOns ðFÞ ¼ gðr; YÞf ðr; YÞ dt where g(r,Y) is the probability per unit volume of finding the Copyright © 2005 by Marcel Dekker

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ejected electron in a volume element dt at Y, r for the specific ionization process, and f ðr; YÞ ¼ exp½ðA þ BÞ

1 X 1 X Am Bmþn m! ðm þ nÞ! m n¼0

ð138Þ

with A ¼ 2q=r, B ¼ br(1 þ cos Y), q ¼ e2=8pe0ekT, b ¼ eF=2kT. The field dependence of OOns(F) appears in a complex manner through the parameter B which determines the expansion terms of the infinite series in Eq. (138). The expansion coefficients in Eq. (138) are governed by the so-called ‘‘Onsager radius’’ at which the Coulombian attraction is equal to the thermal energy, kT rC ¼ e2 =4pe0 ekT

ð139Þ

and a distribution of thermalization length, r. The latter corresponds to the initial electron–hole separation (CT diameter) which has been approximated by either an exponential or Gaussian function [316,317], but it is usually assumed to take a discrete value r0 defined by a delta function, g(r) ¼ d(r r0)=4pr20 (see e.g., Ref. 26). Another interpretation for the rate constant (133) comes from the ‘‘macrotrap model’’ [313,317a] which assumes the excited states to move to the macrotraps defined as spatially extended domains arising from physical perturbation of crystal lattice [318] or from local structure different from the basic environment including disordered solids [319]. The macrotraps consist of local states (microtraps) with energy (E) distributed in space (r) such that E ¼ (3kT=s)ln(r0=r), where s is a characteristic parameter of the exponential energy distribution function and r0 is the radius of the macrotrap. The excited state generated within the macrotrap can dissociate by hopping within the pinning trap according to Eq. (133) with F0 ¼ kT=ed, where d is the hopping distance of a carrier e (cf. Sec. 4.6). Two limiting cases can be distinguished to simplify a theoretical description of the exciton dissociation process: (i) the primary step separation limit with O(F) ¼ const (or slowly varying function of F), and (ii) the dissociation limit with ZCT(F) ¼ const. By these definitions, it is clear that limit Copyright © 2005 by Marcel Dekker

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(i) corresponds to Z(F) ﬃ ZCT(F) as expressed by Eq. (135), and limit (ii) corresponds to Z(F) ﬃ Z0OOns(F) as comes from Eqs. (131), (137), and (138). These both approaches have been employed to fit experimental results. For example, the three-dimensional Onsager theory [limit (ii)] with Z0 ¼ const has been extensively applied in works on charge photogeneration 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 field dependence of the primary charge separation step [limit (i)] has been suggested to underlie the charge photogeneration in single component sandwich cells [302,311,313] and electron transfer in electron donor–electron acceptor molecular systems [325]. Figure 49 shows the electric field dependence of photogeneration efficiency for the commonly used organic LED emitter Alq3. The low-field values of Z(F) have been deduced from the PC and high-field values from the electromodulated fluorescence experimental data of Fig. 47. Different theoretical models such as Poole–Frenkel, Onsager or that based on the macrotrap concept, cannot account for the experimental data for Z(F) (Fig. 49a). Excellent agreement with experiment is provided by the 3D-Onsager theory of geminate recombination combined with volume (bimolecular) recombination (VR) of the photogenerated space charge (Fig. 49b), ZðFÞ ¼ Z0 OOns ðFÞ½1 ZVR ðFÞ

ð140Þ

The bimolecular recombination efficiency (ZVR) is determined by the recombination time, trec, and transit time tt, of the carriers to the electrodes, as defined in Preface and Sec. 5.4, ZVR ¼ ð1 þ trec =tt Þ1

ð141Þ

We note that at high electric fields (>105 V cm1), the spacecharge correction to Z(F) can be neglected and the 3D-Onsager model alone fits well the experimental data. Thus, one would expect this model to be sufficient for describing the high-field reduction in PL and EL efficiency. As a matter of Copyright © 2005 by Marcel Dekker

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Figure 49 Electric field dependence of carrier generation efficiency (Z) for eight different samples of Alq3. The low-field values ( < 105 V cm1) are extracted from the steady-state PC, and highfield values from fluorescence quenching measurements displayed in Fig. 47. The lines represent theoretical predictions of Z(F) for different charge separation models (a), and the conventional 1938 Onsager model [Eqs. (137)–(139)] with g(r) ¼ d(r r0)=4pr2 , assuming r0 ¼ 1.5 nm and Z ¼ 0.8 and taking into account the bimolecular recombination according to Eq. (140) (The field dependence of the bimolecular recombination efficiency (ZVR) and total concentration of holes (nh) as given in the inset was used in the fitting procedure (b). From Ref. 305.

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Figure 50 Quenching efficiency (d) as a function of dc electric field applied to the electrophosphorescent (EPH) and phosphorescent system. The curves are fits to the Poole–Frenkel (see lower inset) and Onsager (see upper inset) models for charge pair dissociation in external electric fields. The quenching efficiency is defined as a relative difference between the emission efficiency at a given field F[F(F)] and at a field F0[F(F0)] where a decrease in the EPH efficiency becomes observed (d ¼ [F(F0) F(F)]=F(F0); F0 < F) (cf. Sec. 5.4). For the molecular structure of Ir(ppy)3, see Fig. 36; the molecular structures of TPD and PC are given in Figs. 6 and 16. From Ref. 304. Copyright 2002 American Physical Society.

fact, its application to phosphorescent complex of Ir(ppy)3 shows good agreement with the experimental data of the electric field-induced quenching of its phosphorescence (PH) and electrophosphorescence (EPH) (see Fig. 50). The failure of the Poole–Frenkel approach is apparent by comparison its fit to experiment. In contrast, the fit Z(F) ¼ Z0OOns(F) resulting from the Onsager theory is accurate for the first run and reasonably good for the second run in measuring the EPH quantum efficiency for the same diode. The curvature of the d(F) plot is a function of two parameters, r0 and F0. The fit for the two consecutive measurement runs for Copyright © 2005 by Marcel Dekker

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the EPH device was made for the same r0 ¼ 3.5 nm and F0 ¼ 8.55 105 V cm1. This value of r0 stands for a lower limit of the electron–hole distance in the charge pair (CP) as the curvature of the d(F) function in the Onsager formalism becomes insensitive to r0 above 3.5 nm [304]. Thus, the average initial e–h distance of the CPs formed in the bi-molecular recombination can be larger, that is re–h 3.5 nm. The excellent fit of the phosphorescence quenching data with the field-assisted dissociation as described by the Onsager theory is obtained with r0 ¼ rCT ¼ (1.8 0.1) nm and F0 ¼ 8.55 105 V cm1. The roughly twofold decrease in r0 accompanying the observed diminution in the quenching efficiency when passing from EPH to PH systems illustrates the different origin of the CP states. Whereas Coulombically correlated e–h pairs in the EPH device originate in the mutual approaching process of statistically independent carriers from the electrodes, CT states produced under photoexcitation originate from the electron–hole separation process of the initially excited molecular excitons. From the above values of r0, the zero-field dissociation efficiency is found to differ by about two orders of magnitude for the bimolecularly formed CPs, Ze–h(F ¼ 0) ﬃ 4 103, and for CT states, ZCT(F ¼ 0) ﬃ 3 105, as calculated with rc ¼ 19 nm, and Z0 ¼ 1 and Z0 ¼ 0.9, respectively. If r0 is large (>4 nm), its field dependence may contribute to the field dependence of the overall dissociation efficiency of an excited state. The field dependence of r0 is then a consequence of a hot carrier drift during its thermalization [326]. The effective thermalization length increases to rth ¼ r0 þ mFtth, where m is the carrier mobility, and tth is the thermalization time of the carrier. The modified function OOns(F) (137) leads to a more steep dependence of Z on electric field, predicting well the Z(F) behavior in pentacene films as shown in Fig. 51. It is seen that both rth and r0 ﬃ rth (r0 mFtth) increase with photon energy, leading to large values of rth (up to 12 nm) and supporting the ballistic model for autoionization process in which the excess kinetic energy of the carrier is directly proportional to the incident photon energy. The evaluation of rth can be based either on the theoretical fit of Z(hn) with Copyright © 2005 by Marcel Dekker

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Figure 51 (a) Intrinsic photocurrent quantum efficiency in pentacene films (1–3 mm thick) induced by light at hn ¼ 2.6 eV as a function of electric field at two different temperatures (T ¼ 330 K— crosses; T ¼ 250 K—squares). Theoretical predictions: Onsager 1938 with Z0 ¼ 0.5; r0(F) ¼ const ¼ 5.3 nm (dashed curves), Onsager 1938 modified by r0 ¼ rth(F) according to Eq. (142) (solid lines). (b) Variation of rth with electric field for two pentacene films (1–5 mm thick—filled circles; 1.65 mm—open circles) at T ¼ 205 K and selected energies of exciting photons (from 2.3 to 2.8 eV). Adapted from Ref. 326.

Ztheor(hn) ﬃ A(F,T) (hn Eg)5=2 (Eg—energy gap) [327]; A(F,T)— hn-independent constant) being proportional to OOns, or on the Arrhenius plot of Zexp(T) yielding the activation energy Ea ¼ e2=4pe0erth. However, as comes from Fig. 51b, the field effect on r0 is negligible whenever its values are lower than 4 nm characteristic for the first absorption band of the material. Due to improvement of sample preparation, especially for high quality single crystals, the low-field increase in r0 and field dependence of r0 may become of importance because of remarkable increase in the carrier mobility. For example, the hole mobility mh ¼ 0.4 cm2=V s assumed to calculate the Z(F) curves in Fig. 51b for polycrystalline pentacene films increases 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 fieldassisted dissociation of excited states. Then, Z(F) can be Copyright © 2005 by Marcel Dekker

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expressed by the relationship [326] Z½r0 ðhn; FÞ; F; T ¼ ð1=2ÞZ0 expðbmFtth Þ

Zþ1

exp½ð2q=sÞ bs br0 cos Y

1

1 X 1 X

s þ mFtth þ r0 cos Y ð2qÞm dðcos YÞ

bmþn sm m!ðm þ nÞ! n¼0 m¼0 ð142Þ 2

1=2

where s ¼ [r20 þ (mFtt) þ 2r0mFtth cos Y] , and other quantities as defined in Eq. (138). Equation (142) is reduced to the Onsager approach if r0(F) ¼ r0 ¼ const.

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3 Spatial Distribution of Excited States

3.1. INTRODUCTION When describing the characteristics of a system of emitting species in a macroscopic object, one important property to be considered is the spatial distribution of the species. It is recognized, for example, that optical confinement, following the location of the recombination-generated emitting states, is an important requirement for achieving high-efficiency emission and lasing in organic LEDs. The detected emission efficiency of a radiating object is determined by: (i) the original population of the emitting species; (ii) the lifetime of the particles radiated; and (iii) the absorption properties of the object investigated. It is markedly modified if the object substance can absorb the emitted radiation or the excited species are quenched inhomogeneously within the object (e.g. strongly annihilating on its boundaries). Thus, the radiation flux spectrum is deformed and this deformation can be used to derive information about the spatial distribution of emitting species. The situation for the one-dimensional case with emitting species distributed along the x-axis inside a slab 147

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object is illustrated in Fig. 52. The measured radiation flux in the direction x, F1 differs, in general, from that in the direction þx, F2, due to a difference in the absorption of radiation originating at a distance x in two flat layers of different thicknesses x and (d x), respectively. The spectral dependence of the ratio of the flux F2(l) to the flux F1(l) can be used as an experimental probe for determining the spatial distribution of the emitting species, c(x) [53]. The ratio Rj(lj) obtained for a finite set of wavelengths, lj ( j ¼ 1,2,3, . . . , m) is given within the error of known magnitude DRj(lj) and Rd Cj ðEj Þ cðxÞpðd x; lj Þ dx 0

Rd

¼ Rj ðlj Þ DRj ðlj Þ

ð143Þ

cðxÞpðx; lj Þdx

0

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

Figure 52 Spatial variation of emitting species (c(x)) for the onedimensional case and schematic illustration of experimental configuration of two detectors of the radiation emitted from the object in the direction x(f1) and þx(f2). From Ref. 53. Copyright © 2005 by Marcel Dekker

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p(d x, lj) are the probabilities that a photon emitted from a distance x and (d x), respectively, will reach suitable detector (1 or 2). In the case of infinite lifetime of photons, they are determined by the absorption properties of the material on respective optical pathways pðx; lj Þ ¼ exp½mðlj Þx and pðd x; lj Þ ¼ exp½mðlj Þðd xÞ

ð144Þ

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

cðxÞ Cj ðlj Þpðd x; lj Þ þ Rj ðlj Þ 1 pðx; lj Þ dx

0

¼ Rj ðlj Þ DRj ðlj Þ

ð145Þ

with the kernel K ðx; lj Þ ¼ Cðlj Þpðd xÞ þ Rj ðlj Þ 1 pðx; lj Þ

ð146Þ

The integral equation (145) presents a classic example of an ‘‘ill-posed’’ problem, by which one means that the solution c(x) does not depend continuously on the data function R(l). In the above formulation of the problem, R(l) is known only for l 2 fljg ( j ¼ 1,2, . . . , m) and the data are given with known errors DRj(lj). With these inadequate data, it is extremely difficult, in general, to solve Eq. (145) (see e.g. Ref. 329). One possible approach is to apply the statistical regularization method (STREG) [330]. This probabilistic method gives the best solution of equations of the type (145) and has been applied successfully to a similar problem in the past [328,331]. This method consists of introducing a priori information about the unknown function c(x). It can be the assumption about the smoothness and nonnegativity of the solution. Then, using the apparatus of mathematical statistics known as Bayesian strategy (see e.g. Ref. 332), we obtain a ‘‘regularized’’ solution and its rms errors. The details of this procedure are given in Appendix A in Ref. 328 and testing of the method discussed in the appendix Copyright © 2005 by Marcel Dekker

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of Ref. 53. The application of the method to extract the spatial distribution of emitting states under different type of excitation is described in the following two sections.

3.2. PHOTOEXCITATION The spatial distribution profile of photoexcited states does not coincide, in general, with the light absorption profile given by a simple exponential function I(x) ¼ I0(x) exp(x=la), where la(l) ¼ m1 a (l) defines its penetration depth using the linear absorption coefficient, ma(l). There are several reasons for that, including: (1) exciton diffusion, (2) internal surface reflection of emitted photons and=or excitons, (3) host–guest exciton transfer with a finite probability of activation to free host exciton state from a guest molecule, (4) guest–guest exciton transfer with the final step of activation to free host exciton state, and (5) host–guest and guest–guest reabsorption with the final step of activation to free host exciton state. In the last three cases, the guest can be a structural defect forming a more or less deep exciton trap. We illustrate the presence of these effects in the spatial distribution of singlet excitons S(x) generated by the exciting light I(x) in the most studied aromatic crystals of anthracene and tetracene, using the semiempirical method described at the beginning of the presnet chapter. The starting point is Eq. (145) which is applicable to plate-shaped crystals excited perpendicularly to their front surface as shown in Fig. 53. Highly absorbed polarized light is shone on the one side of the crystal and the fluorescence flux is measured from both sides using the two suitably placed quartz plate splitters, an experimental arrangement corresponding to the one-dimensional configuration assumed in Fig. 52. To avoid complications connected with differences in separated measurements for the front (Ff) and rear (Fr) emission fluxes, both are measured with the same detection system. Concurrently with the excitation of 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 Copyright © 2005 by Marcel Dekker

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Figure 53 (a) Schematic drawing of the experimental arrangement permitting spectral measurements of the radiation originating from two sides of a crystal, to be performed with the same optical and detection systems. M1, M2, monochromators. (b) Experimental dependence of the rear (fr) to front (ff) photoluminescence ratio as a function of observation depth (l¼m1) for two different wavelengths (la) of the exciting light. , la1 ¼ 366 nm; , la2 ¼ 297 nm; in order to better distinguish between the plot for la1 and la2 the latter is averaged by the solid line. After Ref. 53. Copyright 1979 Institute of Physics (GB), with permission.

the shutter in position 1 originate from the illuminated surface (Ff), and those accumulated in position 2 come from the rear (Fr) of the crystal. This gives us the experimental function Rðm1 Þ ¼ Fr ðla Þ=Ff ðla Þ ¼ Fr ðm1 Þ=Ff ðm1 Þ Copyright © 2005 by Marcel Dekker

ð147Þ

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with l ¼ m1(l) standing for the ‘‘observation depth’’ that is the average path traversed by emitted light of wavelength l. Its value determines directly the probability of emitted photon to leave the crystal through the front or rear surface limiting the plate-shaped crystal [cf. Eqs. (143)–(146)]. Using the experimental points of R(l) with their known errors DR(l) and applying the STREG procedure for solution of (145) with (144) and (146), we obtain the spatial distribution function S(x) c(x) for singlet excitons generated by radiation with a given la. Two examples are shown in Fig. 54. It is apparent that the concentration of excitons deeply within the crystals is comparable with that at distances determined by the penetration depth of the exciting light. In addition, a finite concentration of excitons appears in front of the rear surface of the crystal. The latter is by an order of magnitude lower as compared with that at the front illuminated surface, but it should be taken into account in all types of interface detector quantum yield experiments regarding the determination of the exciton diffusion length [285] or determining real photoluminescence spectra [56]. The effect of the crystal surface treatment, seen in Fig. 55, confirms the role of its reflectance properties for the actual distribution of the emitting states. A strong roll-off in the singlet exciton concentration is observed with the illuminated metal (Ag, Au) and semiconductor (CuI) coated front crystal surface, indicating strong quenching of singlet excitons near-by these contacts (Fig. 55a). The penetration depth and the second rear contact exciton concentration maximum become strongly reduced by surface roughening with a stream of carborundum powder (Fig. 55b). The fluorescence spectra are subject to substantial deformation due to such a broad spatial distribution of emitting species. Two examples are shown in Fig. 56. The real fluorescence spectra 3 have been obtained from the apparent spectra 1 based on the spatial distribution of singlet excitons, S(x), from Fig. 54, using the following expression for the fluorescence intensity: FðlÞ ¼ AjðlÞ

Zd 0

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SðxÞ exp½mðlÞxdx

ð148Þ

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Figure 54 Spatial distributions S(x) of singlet excitons in a 35 mmthick anthracene (a), and 4.7 mm-thick tetracene (b) single crystal referred to the front face crystallographic plane (ab) placed at x ¼ 0. The results obtained according to the procedure described in Sec. 3.2 with the experimental data collected by Glin´ski and Kalinowski [56] using the experimental arrangement from Fig. 53. A strongly absorbed light, polarized to the b crystallographic axis has been used to excite the fluorescence in both cases. The absorption profiles (straight lines) are shown for comparison.

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Figure 55 (a) Spatial distributions S(x) of singlet excitons within a 30 mm range from the illuminated front free surface of eight differ1 and crystals coated with a semitranent anthracene crystals 2 , Au 3 , and CuI 4 , the penetration of sparent layers of Ag the exciting light (bk polarized lex ¼ 366 nm), I0 exp(x=la) is shown for comparison (dashed curve). (b) Singlet exciton concentration profiles in a 25 mm-thick anthracene crystal before () and after () roughening the rear surface (x ¼ 25 mm) of the crystal. After Ref. 285.

Here, j(l) is the real emission spectrum to be determined, m(l) denotes the absorption coefficient of the fluorescent light and A stands for an apparatus factor. The experimental term exp[m(l)x] represents the photon (hc=l) escape probability at a distance x from the observed crystal illuminated surface. The integral runs along the whole thickness d of the crystal. With a simplifying assumption S(x) ¼ S(0) exp(max), where ma is the absorption coefficient of the exciting light (la), the solution of Eq. (148) for j(l) on the basis of experimentally known F(l) and ma may be found and the results are shown in Fig. 56. Copyright © 2005 by Marcel Dekker

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Figure 56 The fluorescence spectra from the illuminated free surface of plate-shaped anthracene (A) and tetracene (B) crystals, corrected for the real spatial distribution of singlet excitons from 3 , and that approximated by the exponential law Fig. 54 2 . 1 represents the apparent spectra of fluorS(x) ¼ S(0) exp(max) escence. The x are experimental data for anthracene, corrected for reabsorption according to the usual calculation procedure [232,233].

The procedure for determining Rthe actual fluorescence spectra, d j(l), involves dividing F(l) by 0 SðxÞ exp½mðlÞx dx, the integral obtained by numerical calculations. In spite of the fact that the emitted light, F(l), was collected from the same crystal face that was excited, we can see the blue shift of 2 nm for anthracene and as large as 10 nm for tetracene between the first 0–0 fluorescence bands for j(l) corrected for reabsorption and spatial distribution of excitons. However, the most striking effect caused by freeing the apparent spectra from reabsorption and spatial exciton distribution is the sharply increasing intensity of the fluorescence within the 0–0 band. Therefore, crystal luminescence Copyright © 2005 by Marcel Dekker

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spectra and luminescence spectra from crystal (the latter, as a rule, measured in normal experiments) are not to be taken as synonymous. 3.3. RECOMBINATION RADIATION. RECOMBINATION ZONE The spatial distribution of emitting species produced in the electron–hole recombination process is one of important reasons for a difference between the PL and EL spectra, and a characteristic determining the EL quantum efficiency. The self-absorption of the short-wavelength part of the fluorescence can be utilized for determining the spatial distribution of EL. The principle of the method, as discussed in Sec. 3.1 and used for photoexcited states in Sec. 3.2, has been adapted to the recombination radiation as follows [41]: the unknown spatial distribution of the EL light intensity, c(x) from a plate-shaped emitting sample, is related to the experimentally observed EL signal, FEL(l0), by the expression FEL ðl0 Þ ¼ Aðl0 Þ

Zd

cðxÞ expðx=l0 Þ dx

ð149Þ

0

where exp(x=l0) stands for the photon escape probability when its emission takes place at a distance x from the observed crystal surface (x ¼ 0). l0 ¼ m1 0 is the observation depth defined already as the reciprocal of the linear absorption coefficient m0 of the fluorescent light. The integral runs along the thickness of the crystal, d. The quantity A(l0) is independent of x and contains characteristics of the emission and some apparatus factors. A(l0) can be eliminated by measuring the crystal PL under the same detection conditions (Fig. 57): FPL ðl0 Þ ¼ Aðl0 Þ

Zd

SðxÞ expðx=l0 Þ dx

ð150Þ

0

The ratio FEL(l0)=FPL(l0) ¼ F(l0), which is a function of l0, contains a difference between c(x) and S(x). The condition that Copyright © 2005 by Marcel Dekker

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

permits the experimental ratio F(l0) to be used for determination of c(x) is to know S(x), which, in general, is modified by reabsorption, and combined reflectance and interference effects as already discussed in Sec. 3.2. Knowing S(x), c(x) follows from a solution of the integral equation based on expressions (149) and (150): Zd

cðxÞ expðx=l0 Þ dx ¼ Fðl0 Þ

0

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Zd 0

SðxÞ expðx=l0 Þ dx

ð151Þ

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For a rough analysis, S(x) can be approximated by an exponential function S(x) ¼ S(0) exp(x=la), and a set of Eq. (151) for discrete variable l0 and given la, solved for c(x) by the method of statistical regularization [330]. An example of the spatial distribution of the EL intensity from a 90 mm-thick tetracene crystal is shown in Fig. 58. In contrast to the theoretical predictions of the recombination zone to be located within the cathode region for a trap free tetracene crystal (see discussion of the recombination zone below), comparable intensity regions appear nearby the electrode contacts, and a third much weaker emission region can be distinguished in the 1=3 crystal thickness distance from the anode at a high voltage. Important aspects of such a spatial distribution of the

Figure 58 The spatial distribution of the EL intensity in a 90 mmthick tetracene crystal at two different voltages: U ¼ 750 V () and U ¼ 950 V (). The semi transparent hole-injecting Au anode is located at x ¼ 0, and a thick layer of a Na=K alloy forms the electron-injecting contact at the rear crystal side, x ¼ d ¼ 90 mm. The black field patterns simulate the light intensity distribution for these two voltages. The upper part illustrates the position and width of the recombination zone as predicted by Eq. (155) for a trap-free tetracene crystal and ohmic contacts. From Refs. 2, 51. Copyright © 2005 by Marcel Dekker

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excited singlets can be mapped onto a trap-dependent electron–hole recombination process involving excitonic interactions at the interface and in the bulk of the crystal [41]. The stratification of the observed EL emission zone into anode and cathode subzones suggests that trapping is involved in EL processes. The initial recombination leading to emitting singlets presumably occurs on deeply trapped carriers, holes trapped adjacent to the anode and electrons trapped adjacent to the cathode. On the time scale, the average release time of carriers from the traps is much longer than the average recombination time, and these two times are much longer that the average trapping time. This, however, does not explain the evolution of the EL spatial distribution pattern with applied voltage. A well-pronounced drop in the EL intensity close to the anode at high voltages can be attributed to singlet exciton quenching by high density trapped holes. At a lower concentration of holes (at lower voltages), a weaker drop in the singlet exciton concentration can be observed there. The singlet exciton quenching at the cathode is practically absent due to much lower concentration of trapped electrons. To understand the origin of the splitting in the anode EL zone at a high voltage, the delayed component of the EL and triplet excitontrapped charge carrier interaction must be taken into consideration. The delayed EL originates from emission of singlet excitons created in the process of triplet–triplet fusion (cf. Secs. 1.4 and 2.5.1.2). In tetracene, triplet excitons produced efficiently in the singlet exciton fission into two triplets at room temperature (Sec. 2.5.1.2) add to triplets originated directly from the electron–hole recombination process. In the absence of space charge, the spatial distributions of singlet and triplet excitons coincide. A spatially inhomogeneous distribution of high-density trapped holes adjacent to the injecting anode causes the triplets to be quenched with the rate increasing towards the contact. As a result, the position of the maximum concentration of the two triplet-created singlet excitons will shift towards the bulk of the crystal observed as a second emission region separated from the anode. At first glance, the low-field spatial EL pattern apparent in Fig. 58 resembles the spatial distribution of singlet excitons Copyright © 2005 by Marcel Dekker

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generated in single crystals by a strongly absorbed light (Fig. 54a). However, the underlying physics is completely different for these two pictures. While the rear surface-located maximum of the exciton population in the case of photoexcitation is due to reabsorption of light reflected from the rear crystal=air interface, the near-cathode maximum of EL shows up as a result of the recombination between trapped electrons and holes arrived from the injecting anode. Though in both cases excitons concentrate near the principal crystal walls, the rear surface population of photoexcited states is much lower and disappears when the surface roughness increases (Fig. 55b). In contrast, the near-anode and near-cathode concentrations of excitons in the EL spatial distribution pattern are comparable, illustrating the location of the most efficient recombination regions. It is interesting to note that the overall recombination zone width producing majority of excited states can be limited to about 20% of the total crystal thickness if the contribution to the EL intensity from a threefold dropped exciton concentration is neglected. The width of the recombination zone is directly related to the EL efficiency of LEDs, through its definition as a distance traversed by a carrier during the recombination time, trec [2] w ¼ me;h F trec

ð152Þ

where me,h is the carrier (electron or hole) mobility and F is the field within the recombination zone of an EL device. Combining (152) and the carrier transit time between electrodes (d), tt ¼ d=mh,eF, yields trec=tt ¼ w=d, and the recombination probability (see Preface and Chapter 1) becomes directly connected with the recombination zone width, w, w1 ð153Þ PR ¼ 1 þ d Thus, PR extracted from the measured EL efficiency allows

We note that such defined recombination zone width must not be identified with the geometrical limits imposed on the charge recombination by the device structure.

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the determination of the recombination zone width (see Sec. 5.4). The two limiting operational modes of the EL cell (see Preface and Sec. 5.4) lead to important consequences for w: w > d for the ICEL and w < d for the VCEL operational modes. When we apply Langevin’s theory of recombination [Eq. (4)], substituting at the same time the above defined expressions for trec and tt, for a comparable contribution to the current of holes and electrons, we obtain w ﬃ ½2e0 eme mh =ðme þ mh ÞðF 2 =jÞ

ð154Þ

Accordingly, the recombination zone generally varies with electric field. For a strongly field-dependent injectionlimited-currents (ILC) (Sec. 4.3.2), w j1. Equation (154) predicts a field-independent w if ohmic injection occurs at the contacts and carrier mobilities are independent of electric field w ¼ 2me mh d=ðme þ mh Þmeff

ð155Þ

which in the case of negligible space-charge overlap (meff ﬃ me þ mh) gives the width of the recombination zone derived from the analysis of the recombination-induced coordinate variation of the currents [21,334] (see also Secs. 4.3.2 and 4.5). In reality, the recombination rate constant (geh) is finite and a certain space-charge overlap occurs. The total current is composed of hole and electron currents j ¼ jh þ je ¼ ½mh nh ðxÞ þ me ne ðxÞeF

ð156Þ

independent of x. In the recombination region w located at x ¼ xr (Fig. 59), the hole current density decreases with increasing x as djh dnh ¼ emh ¼ egeh nh ne dx dx

ð157aÞ

The analogous relation obeys for electron current density dje dne ¼ eme ¼ egeh ne nh dx dx

ð157bÞ

The electric field can be assumed constant throughout the Copyright © 2005 by Marcel Dekker

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

sample if the recombination zone is thin compared to the sample thickness, d. Combining Eqs. (156) and (157) yields dne geh ne j me ¼ ne ð158Þ dx me F eFmh mh Its solution gives a spatial distribution of the electron concentration within the recombination zone: ne ðxÞ ¼

ne;1 1 þ exp½ðjgeh =eF 2 me mh Þðdh xÞ

ð159Þ

where ne,1 is the electron concentration out of the recombinaCopyright © 2005 by Marcel Dekker

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tion zone, and dh is the penetration depth of holes including the charge overlap region. The recombination width may be defined as twice of the reciprocal of the exponent factor preceding (dh x): w ¼ 2eF 2 me mh =jgeh

ð160Þ

In other words, the recombination width constitutes the double penetration distance of the electron current into the overlap region. Inserting appropriate expressions for the shallowtrap SCL current density, j ¼ (9=8)e0e(me þ mh)F2=d (cf. Sec. 4.3.1), and geh (4), we arrive at w ﬃ 2me mh d=ðme þ mh Þmeff

ð161Þ

an expression identical to that of (155). Whenever w dh, de, the ratio dh=de ﬃ mh=me determines the position of the recombination zone (in Fig. 59, xr ¼ dh þ w=2 ﬃ dh). Such a case has been assumed in the evaluation of the position (mh=me) ﬃ 2.8 and width (161) of the recombination zone for the tetracene crystal 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 in the c0 crystallographic direction [335]. To be more precise, a spatial variation of the electric field within the sample should be taken into account (see e.g. Ref. 334), FðxÞ ¼ ð3=2ÞðU=dÞðx=dÞ1=2

ð162Þ

and its averaged value F ¼ (3=2)U=d inserted into Eq. (160). Then the recombination width doubles: w ¼ 4me mh d=ðme þ mh Þmeff

ð163Þ

It is clear from Eq. (163) that w ¼ 4(me,h=mh,e) d < d being simply determined by the electron to hole mobility ratio me,h=mh,e 1, and wmax ¼ d for me ¼ mh. The above discussion has been limited to a consideration of field-independent mobilities, an assumption relatively The coordinate dependence of ne,1 resulting from the charge-density inhomogeneity of one-carrier SCL current flow is assumed here to be negligible.

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well justified for single organic crystals [27]. On the contrary, there are numerous experimental data for the field dependence of the carrier mobility in amorphous and polycrystalline materials (see e.g. Ref. 29; cf. also Sec. 4.6). Consequently, the recombination width must be considered as a field-dependent quantity whenever the field dependence of the mobility for electrons differs from that for holes. A typical experimentally obtained relationship m ¼ m(0) exp(bm F1=2) yields w ¼ 4d[me,h(0)=mh,e(0)] exp[(bme,h bmh,e)F1=2] for substantially different mobilities of holes and electrons. Thus, the recombination zone width can either increase or decrease with electric field depending on the relation between the characteristic parameter bm for electrons and for holes injected under SCL conditions. In the case where the current flowing through the sample is injection limited (cf. Sec. 4.3.2), the recombination zone width becomes a complex function of applied field because the field decreasing F2=j factor in Eq. (154) adds to the fielddependent mobility of w and often can dominate the electric field-induced changes in the recombination zone (cf. Sec. 5.4). The recombination width can be minimized by the confinement of the recombination process at the interface of two organic materials as typically occurs in double- and multi-layer organic LEDs [2] (see also Chapter 5). The penetration depths of holes and electrons can then be identified with thicknesses of hole and electron transporting layers, respectively, and their mobilities used to calculate the recombination width. A good example of such a situation is the recombination process in the most studied double-layer LED, ITO=TPD=Alq3=Mg=Ag. The free carrier kinetics at the TPD=Alq3 interface after an abrupt switch of the voltage off takes on a simple form dn ¼ geh n2 dt

ð164Þ

where n ¼ nh ﬃ ne represents the equal concentrations of holes (nh) and electrons (ne). A solution of this equation leads to a function describing the temporal (t) evolution of these Copyright © 2005 by Marcel Dekker

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concentrations 1 1 þ geh t ¼ n n0

ð165Þ

which can be translated to the EL intensity decay [FEL(t)] in the form [309] rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 1 geh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ þ t ð166Þ j jPL PS geh n0 FEL ðtÞ PL PS assuming FEL ¼ jPL PS geh[n(t)]2, where jPL is the emission efficiency of excited states, and PS is the probability of the creation of an emitting singlet excited state of Alq3 (cf. Sec. 1.4). Figure 60 shows the (FEL)1=2 vs. time plot of the experimentally observed decay of the EL intensity at the falling edge of a 25 V rectangular voltage pulse for such an LED, following the behavior predicted by Eq. (166). A single straight

Figure 60 The EL decay at the falling edge of a 25 V pulse plotted 1=2 in FEL against time scale to compare with the bimolecular kinetics behavior. Here, t ¼ 0 corresponds to the voltage fall of the pulse. The data 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. Copyright © 2005 by Marcel Dekker

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line fitted to the experimental data with n0 ¼ (2j=egedd)1=2 dependent on the steady-state current density j ﬃ je ﬃ jh (at 25 V) allows geh ¼ (1.1 0.5) 1010 cm3=s to be determined from its slope to intercept ratio [309]. This value seems to support the Langevin recombination mechanism, giving me þ mh ﬃ (e0e=e)geh ﬃ 3 104 cm2=V s with e ¼ 3.8 based on Eq. (4). Since the electron mobility in the electron-transporting layer of Alq3, me ﬃ 105 cm2=V s (see Refs. 309, 336, 337) 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 6 104 cm2=V s [338]. Under these conditions, the width of the recombination zone can be approximated by the expression w ﬃ 4[mh(TPD)=me(Alq3)](d=2), where d=2 corresponds to the position of the interface with the identical thickness of hole (TPD) and electron (Alq3)-transporting layers, d=2. Taking a high-field (F ﬃ 106 V=cm) values of the hole mobility in TPD, mh(TPD) ﬃ 103 cm2=V s [338], and me(Alq3) ﬃ 5 105 cm2=V s (Ref. 337) for a TPD=Alq3 function-based diode with d ¼ 120 nm (Ref. 309), we arrive at w ﬃ 12 nm (w=d ﬃ 0.2 close to such a ratio discussed above for the tetracene crystal from Fig. 58). This value appears to be quite independent on electric field since mh(F) for TPD and me(F) for Alq3 vary in a similar manner [339–341]. On the other hand, the recombination zone width shows up as a markedly decreasing function of applied electric field for thin film organic LEDs operating in the ICEL mode (Sec. 5.4). The above discussed methods for determining spatial distributions of excited states, based on the reabsorption of emitted light, are expected to break down in thin organic films and weakly absorbed light within their emission spectrum range. Other particular features of organic LEDs such as the EL anisotropy [342] or differences in emission spectra [343,344] of consecutive LED emitter component layers have been utilized to infer the spatial extent of the recombination zone. The latter will be illustrated in Sec. 5.4 since it is directly connected with quantum EL efficiency. The EL anisotropy, defined as the relative light output polarized parallel (Ik) and perpendicular (I?) to the direction of preferential molecular alignment (S ¼ Ik=I?), can be accomplished either Copyright © 2005 by Marcel Dekker

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by stretching substrates or by means of Langmuir–Blodgett technique. The EL anisotropy as high as S ¼ 3 has been obtained with stretch-oriented poly(3-octylthiophene)(P3OT) [345]. The Langmuir–Blodgett (LB) technique has been applied for the preparation of LEDs based on soluble poly(pphenylene)(PPP) derivatives [346,347]. This technique allows for complete three-dimensional control of the film structure including the macroscopic alignment of the rigid macromolecules, and polarized EL has been observed from LEDs based on LB films of PPP [348]. In the LB film, the rigid rod-like polymers lie flat on the substrate and posses a preferential orientation in the plane of the layer parallel to the dipping direction. For a distribution in the conjugation length of polymer chains, long conjugation chains are oriented, whereas shorter conjugation chains are randomly oriented. This leads to a reduction of the EL anisotropy. S ¼ 1.3 has been found for poly(3-alkylthiophene) (P3AT) derivatives-based LB LEDs [349]. By analyzing degree of polarization of an LB LED consisting of two layers with two different (mutually perpendicular) orientations, it is possible to determine the spatial profile of its emission. Such a procedure has been applied to a range of LED devices based on PPD LB films [342]. Schematic representation of such LEDs is shown in Fig. 61. The iso-pentoxy substituted PPP polymers were deposited in such a way as to form two orthogonal orientation regions with a varying ratio of the monomolecular layer numbers at a constant overall thickness of d ¼ 120 nm, which corresponds to the typical film thickness in polymer LEDs. The parallel orientation refers to the direction of preferential alignment of the layer next to the Al cathode. Therefore, Ik > I? means that most of the emission originates from the parallel layer (and vice versa for Ik < I?). Increasing the number of monolayers of parallel orientation (n) and correspondingly decreasing the number of monolayers of perpendicular orientation (100 n) increase the anisotropy of the EL emission S2 ¼ Ik=I?) (the subscript 2 indicates Ik and I? are obtained from the two region LED). Since increasing n translates directly through the monolayer thickness ( 1.2 nm) into the thickness of the region located next to the Al cathode (L), the dichroic ratio Copyright © 2005 by Marcel Dekker

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

(Ik=I?)2 should be an increasing function of L. One has to keep in mind that due to a two-dimensional orientational distribution function of the in-plane molecular alignment, the contribution of Ik normalized to the total intensity Ik þ I?, a ¼ Ik=(Ik þ I?) differs from one even for a homogeneously oriented device, as for example a ¼ 0.75 with S ¼ 3. It is clear that the experimentally observed EL anisotropy plotted against the distance, x, from the Al cathode (located at x ¼ 0), and identified with varying thickness (L) of parallel oriented n monolayers, contains the EL emission profile determined by the spatial distribution of emitting states, w(x): Zx

wðx0 Þ dx0 ¼ f ðxÞ ¼

0

Copyright © 2005 by Marcel Dekker

SS2 ðxÞ 1 ðS 1Þ½S2 ðxÞ þ 1

ð167Þ

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Equation (167) has been derived assuming the dichroic ratio S2(x) to be independent of the absorption coefficient of the polymer, and S2 per monolayer to be constant for any location within the LED, assumptions which may not always be justified. The relative EL output as a function of the distance from the Al cathode can thus be obtained by differentiation of the measured relative emission from the parallel organized layer, f(x), as given by the right-hand side of Eq. (167). The calculation of Df(x)=Dx, made with Dx ¼ 12 nm (10 monolayers) for the ITO=PPP=Al devices with x varying between 0 and 120 nm, is shown in Fig. 62. Such a calculated profile, like that in single

Figure 62 The spatial distribution of the EL emission represented by the amount of emission from a block of 10 monolayers as a function of its distance from the Al electrode in a PPP LED: ITO=PPP (120 nm)=Al. The experimental data are indicated by the bars. The curves are exponential functions illustrating an exponentially decreasing penetration of electrons injected from Al into the PPP film for a set of fixed values of the penetration depths se ¼ 10, 20, 30 nm. After Ref. 342. Copyright 1997 Wiley-VCH, with permission. Copyright © 2005 by Marcel Dekker

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aromatic crystals (see Fig. 58), shows the exciton quenching near the metal electrode, but unlike single aromatic crystals, possesses only one maximum (at 30 nm in Fig. 62) in the cathode region of the LED. The decreasing emission intensity for x > 30 nm has been ascribed to decreasing concentration of electrons injected from the Al cathode, the holes assumed to be distributed homogeneously throughout the PPP film. Nearly 90% of the EL is generated in a 60 nm thick zone which can be regarded as the width of the recombination zone. In addition, the width has been found not to depend on the overall thickness of the LED [342]. The message that follows from these results is that the recombination process in the ITO=PPP=Al LEDs is determined by unbalanced injection conditions far from space charge and trapping effects so strongly apparent in the EL emission profiles of aromatic single crystals [41].

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4 Electrical Characteristics of Organic LEDs

4.1. INTRODUCTION Light emission from a thin film organic LED is underlain by a complex combination of various electronic processes, one of them being charge injection and following it electrical current flowing through the device.

4.2. CURRENT–VOLTAGE CHARACTERISTICS The non-linearity is recurrent feature of current–voltage characteristics of all operating organic LEDs, independent of the number and configuration of organic layers (Fig. 63). It is associated with the fact that the driving them current is due to injection of charge at the electrodes: holes at the anode and electrons at the cathode (and not being a result of the bulk generated carriers). Double logarithmic plots of the current vs. applied voltage allow to distinguish the power 171

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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 emitting layers (EMLs), which are indicated in brackets beside their description. After Ref. 2. Copyright 1999 Institute of Physics (GB).

law behavior of the current. From the examples shown in Fig. 64 for the LEDs based on single aromatic crystals, the moderate field (104 V=cm < F < 5 105 V=cm) straight-line segments of such plots suggest the power law j Un to obey for unipolar and double-injection currents for tetracene but not for anthracene crystals. The current–voltage characteristics in single organic crystals, measured over many orders of magnitude in applied field (10–106 V=cm), exhibit several well-pronounced regimes [318,350,350a]. An example presented in Fig. 65 shows the low-field value n ¼ 1 to approach n ¼ 2 for moderate and high fields. They are thought to represent the low-field Ohmic conduction and SCL conduction in the presence of shallow traps followed by the free-trap conduction (or saturation of injection) in the upper limit of the Copyright © 2005 by Marcel Dekker

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

applied field. Similar behavior has been observed for thin film organic systems provided with Ohmic injecting electrodes though the deep exponentially distributed traps region is usually considered to occur at moderate electric fields (Figs. 66 and 67). Three general regimes can be distinguished as indicated in Fig. 67: (A) leakage or diffusion-limited current, (B) volume-controlled current with an exponential distribution of traps, and (C) volume-controlled current with filled traps. From the slopes in the regime (B) and the Copyright © 2005 by Marcel Dekker

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Figure 65 Unipolar (electron) current vs. electric field for a 0.1 cm-thick naphthalene single crystal provided with silver electrodes. Several different regimes can be distinguished: (i) the low-field linear increase of the current (Ohmic regime); (ii) the SCLC in the presence of shallow traps (DE < kT); (iii) the trap-filled limit at FTFL; and (iv) the SCLC with filled traps (no trapping). Adapted from Ref. 350a.

" Figure 66 The architecture and energy levels of a four-layer organic LED (a) and its current–voltage characteristics with pulsed bias applied at high current density as indicated in part (b). The chemical structures of the materials used are shown in part (c). After Ref. 351. Copyright 2002 American Physical Society. Copyright © 2005 by Marcel Dekker

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Figure 67 The current-field characteristics of a DL electrophosphorescent organic LED based on the metallo-organic phosphor Ir(ppy)3 (for the molecular structure’ see Fig. 31). The energy levels of the LED structure are given in the inset. The j(F) curves are well reproduced from run to run except the lowest field region, where the built in electric field (Fbi ¼ 2 105 V=cm), due to the difference in the work functions of the electrodes, becomes comparable with the applied field. After Ref. 304. Copyright 2002 American Physical Society.

trap-filled-limit field, FTFL ¼ 8 105 V=cm, the total concentration of traps H ¼ (3=2)e0eFTFL=ed ¼ 3 1019 cm3 and their energy (E) distribution h(E) ¼ (H=lkT) exp(E=lkT) with l ¼ 2.9 follow. However, there is an interesting difference between j(U) curves for single crystals (Fig. 65) and thin film LEDs (Figs. 66 and 67). A well-resolved sharp current jump at U ¼ UTEL(FTFL), seen for single crystals, practically does not appear for thin film LEDs. Although further studies are Copyright © 2005 by Marcel Dekker

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needed to establish the exact reason for this difference, the strong temperature dependence of the current–voltage characteristics and their linear scaling with U=d for both types SL [352–355] and DL [356] organic LEDs suggest the device current to be injection limited rather than SCLC (for a discussion, see Sec. 4.3). Figure 68 shows j–U characteristics for the SL, ITO=TPD(90 nm)=Al, and DL, ITO=TPD(27 nm)=Alq3(55 nm)=Mg:Ag, LEDs at varying temperature, and Fig. 69 their variation with sample thickness for other SL, Al=Alq3=Ca, and DL, ITO= TPD(20 nm)=Gaq3(10–80 nm)=Mg:Ag, organic LEDs. A more detailed study of the interrelation between thickness of the HTL and ETL using a molecularly doped layer as the HTL shows no direct correlation of the current to either component layers and total thickness of the LEDs (Fig. 70). Since the injection-limited current, by definition, should not exhibit any sample thickness dependence, the observed variation of j(V) characteristics with film layer thickness would suggest the film formation process (including the formation time and thus, film thickness) to affect the carrier injection at its interface and=or trap-free SCLC to be modified by the field dependence of carrier mobilities. All these options are discussed in Secs. 4.3–4.6.

4.3. SPACE-CHARGE- AND INJECTIONCONTROLLED CURRENTS Organic solids are usually insulators (see e.g. Ref. 357). Unlike in inorganic semiconductors, impurities normally act as traps for charge carriers rather than as sources of charge carriers. An exception from that rule are conjugated polymers. For example, polyphenylenevinylene (PPV) fabricated via a special precursor route may turn out to be p-doped with doping concentrations in the order of 1017 cm3. In that case, a Schottky-type depletion zone can be established near a metal contact [358]. However, in vast majority of cases, the concentration of impurities is small enough not to perturb the electric field distribution inside a solid-state sample Copyright © 2005 by Marcel Dekker

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Figure 68 Current–voltage characteristics of SL and DL EL devices at various temperatures. (a) A 6.8 mm2-area device ITO=TPD (90 nm)=Al from Ref. 356a; (b) a 0.01 mm2-active area device ITO=TPD (27 nm)=Alq3 (55 nm)=Mg:Ag; inset: temperature dependence of the straight-line slopes (precisely, n 1); after Ref. 356. Copyright 1996 American Institute of Physics, with permission.

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

[359]. In those cases, the dark electrical conduction is very low, the solids are considered as good insulators. Yet, such solids can be made to conduct a relatively large current if the contacts permit the introduction in them an excess of free carriers [360]. If the carriers enter through a surface boundary, the process is referred to as charge injection. The charge injected conduction is governed by charge injection barriers at the electrode contacts and charge transport properties of materials. For electrons, the injection barrier is given by DEe ¼ Wc A, and for holes by DEh ¼ I Wa, where Wa and Wc are the work functions of anode and cathode, and I and A are ionization potential and electron affinity of the solid state. Depending on the charge injection efficiency and mobility of charge carrier, the current is space-charge limited (SCLC) [26,334] or injection limited (ILC) [360,361]. Copyright © 2005 by Marcel Dekker

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Figure 70 Influence of thickness of the anodic (75% TPD:PC) (a) and cathodic (Alq3) (b) layers (HTL and ETL, respectively), given in 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) slopes differ in general except for the thinnest layers (35 nm). The thickness of the ETL (60 nm) and HTL (60 nm) were kept constant in panel (a) and (b), respectively. After Ref. 303. Copyright 2001 Institute of Physics (GB).

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4.3.1. Space-charge-limited Conduction (SCLC) An indispensable condition for the occurrence of SCLC is that the electrode can supply more carriers per unit time than can be transported through the insulating sample. A contact that behaves in that way is called Ohmic contact. At an ideal Ohmic contact, the electric field vanishes (F ¼ 0) because of screening by the injected space charge (the charge concentration n ! 1). In practice, an electrode can only be Ohmic if the injection barrier is small enough to ensure that no fieldassisted barrier lowering is required to maintain a sufficiently high injection rate. In that case, a virtual electrode is established close to the geometrical contact that serves as a charge carrier reservoir [362]. At low fields, the virtual electrode moves into the bulk of the sample so far that a large number of the carriers injected at the geometrical contact do not reach the opposite electrode, and the current becomes limited by trapping before reaching the in-bulk barrier formed by the superposition of the image Coulombic, space charge and external potential [257]. This situation relates to the injection-limited currents discussed later on in Sec. 4.3.2. The critical value of the injection barrier height depends on transport properties of the adjacent insulator. It can be higher for low mobility, and lower for high mobility materials. A few tenths of an eV will be an upper limit in cases of practical interest. For a perfectly ordered or disordered insulating materials, or those containing very shallow traps (DE kT), the SCL current in a sample of thickness d obeys Child’s law (see e.g. Ref. 334) 9 F2 jSCL ¼ e0 em 8 d

ð168aÞ

In the presence of discrete traps 9 F2 jSCL ¼ e0 eYm 8 d

ð168bÞ

where m is the microscopic mobility of the carriers, e the dielectric constant, e0 the dielectric permittivity, and Y is the fraction of free (nf) to trapped (nt) space charge. Copyright © 2005 by Marcel Dekker

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If local traps are distributed in energy (E), they will be filled from bottom to top as electric fields, F, increase. The quasi-Fermi level will scan the distribution shifting towards the transport band, and Y ﬃ nf=nt will become a function of F. A general form of nt ¼ nt(nf) relation can be obtained from a detailed balance equation as [363] nt ¼ nf us

Z1 0

hðEÞ dE n expðE=kTÞ þ nf us

ð169Þ

where u is the thermal velocity of free carriers, s the capture cross-section, and the term n exp(E=kT) expresses the rate of thermal release of charge from all trap energies E distributed according to a function h(E). In studies of low-mobility insulators, two types of continuous trap distributions are commonly used: the exponential distribution of traps [364] and the Gaussian distribution of traps [365]. The problem has been solved analytically for an exponential distribution of traps hðEÞ ¼ ðH=lkTÞ expðE=lkTÞ

ð170Þ

where H is the total concentration of traps, and l is a characteristic distribution parameter which can be replaced by a characteristic distribution temperature Tc ¼ lT. E ¼ kTc stands for a measure of the average trap depth of a given trap distribution. Inserting (170) into (169) and substituting n=vs ¼ Neff, where n is the common frequency factor and Neff the effective density of states in the transport band, and assuming l ¼ Tc=T > 1 and nf=Neff 1, yield h i1 H nf 1=l 11=l pcosecðp=lÞ ðNeff =nf Þ ð11=lÞ nt ﬃ l Neff ð171Þ On the basis of Eq. (171), a solution to the current j ¼ nf ðxÞemðFÞ Copyright © 2005 by Marcel Dekker

ð172Þ

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and Poisson’s equation dFðxÞ e ¼ nt ðxÞ dx e0 e

ð173Þ

with U¼

Zd FðxÞ dx

ð174Þ

0

and the boundary condition F(0) ¼ 0 (SCLC) can be found: l Neff em e0 el l2 sin½p=l 2l þ 1 lþ1 U lþ1 jg ¼ ð175Þ Hl e ðl þ 1Þp lþ1 d2lþ1 This general solution is usually approximated by Mark and Helfrich [366] l Neff em e0 e l 2l þ 1 lþ1 U lþ1 ð176Þ jﬃ e lþ1 lþ1 d2lþ1 Hl when a ¼ jg=j ¼ [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, l ¼ 1.05 gives a ﬃ 0.04 that is the current density calculated according to Eq. (176) is overestimated by a factor of 25 ( j ﬃ 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 maximum difference not exceeding a factor of 4. At sufficiently high injection levels, the traps are completely filled; they no longer influence the carrier transport, and the sample behaves as an ideal SCL conductor. This occurs at a voltage l " #1=ðl1Þ en0 d2 n0 H 9 l þ 1 l l þ 1 lþ1 UTFL ¼ n0 8 l 2l þ 1 e0 e Neff ð177Þ where n0 is the thermally generated background free charge density. Since n0 is negligible in comparison to the injected Copyright © 2005 by Marcel Dekker

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charge density, it can be easily eliminated from Eq. (177). If the trap distribution is of Gaussian rather than exponential shape, jSCL(F) no longer obeys a power law. Instead @ ln j=@ ln F increases with increasing field [367–369]. In most cases in organic solids, it is difficult to distinguish experimentally between a Gaussian distribution of traps h i H ð178Þ hð EÞ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ exp ðE Em Þ2 =2s2 2ps2 where s characterizes the dispersion of trap energies around Em, and Em 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 104. For this relative change in trapped charge concentration (169), the quasiFermi level (EF) would move a distance of 0.23 eV. Therefore, under normal experimental conditions, EF will move no more than 0.2–0.3 eV from the deepest trapping level, Ed, toward the band edge and will only probe traps in this energy range. For E not differing greatly from Ed, Eq. (177) can be written as [370] hðEÞ ¼ hðEd Þ exp½ðE Ed Þ=lkT

ð179Þ

where lkT ¼ s2 =ðEd Em Þ

ð180Þ

The functional shapes of Eqs. (179) and (170) become identical, and, therefore, the exponential and Gaussian trap distributions have approximately identical current–voltage characteristics [26]. There are experimental current–voltage plots which can be approximated by a sequence of power type functions j Un with varying n (see Figs. 70 and 71). They can be interpreted in terms of the voltage-induced movement of the quasi-Fermi level through a set of Gaussian distributions of local traps dispersed around consecutive discrete traps [368] or explained by the lowering of the potential barrier of a spatially extended trap (macrotrap) pinned on structural or chemical defect [318]. Each macrotrap consists of local Copyright © 2005 by Marcel Dekker

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185

Figure 71 Current density as a function of electric field for two solution-grown anthracene crystals at room temperature. Electrodes: copper iodide (CuJ); crystal thickness: d ¼ 66 mm (a), d ¼ 49 mm (b). After Ref. 317a.

(point) traps distributed and limited in energy and space. It can be characterized by a spherical-symmetry cage of radius r0 and energy distribution in space EðrÞ ¼ 3 lkT lnðr0 =rÞ

ð181Þ

where r is a distance from the center of the pinning trap of radius rb r0. The potential shape (181) is a result of the exponential energy distribution of point traps (170) and its relation to their caging in macrotraps, hðEÞ dE ¼ 4pr2 Nm N0 dr

ð182Þ

where Nm is the concentration of molecules, and N0 is the concentration of macrotraps. The integrating within the energy range (1,0), and distance (0,r0), respectively, yields the macrotrap radius 1=3 3H ð183Þ r0 ¼ 4pN0 Nm which shows an expected tendency to increase with decreasing molecular density (Nm) and the macrotrap-to-microtrap concentration ratio (N0=H). There is no exact knowledge about the nature of pinning traps but it is easily conceivable that they originate from small clusters of dimers or non-intentional polar dopants [371]. Such dimer clusters or polar dopants distort their environment in a certain region, produCopyright © 2005 by Marcel Dekker

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cing and=or aggregating local defects with energy states distributed in space according to a decreasing function given for instance by Eq. (181). Thus, it is not unreasonable to speculate that macrotraps constitute cluster of incipient dimers of varying sizes formed preferentially at dislocations as it has been already suggested to explain evolution of an SCLC regime in organic crystals [372]. Furthermore, the macrotrap potential could be, in principle, considered as the strain energy in a dislocation itself. Based on a distance (r) from the dislocation, two contributing terms of this energy are usually distinguished (Fig. 72). For distances larger than r2, there is E(1)(r), the elastic (continuum) strain energy, and for distances smaller than r2 (but larger than rb ), one has E(2)(r), the core energy, which, in contrast to E(1)(r), cannot be evaluated from elastic approximation because the strains

Figure 72 A two-dimensional representation of a two-component potential of a macrotrap. Adapted from Ref. 317a. Copyright © 2005 by Marcel Dekker

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187

are too large [26]. The dimers created along dislocation lines would still form the pinning traps for the macrotraps. The radius r0 of a spherical macrotrap, which in this case is a term somewhat ill-defined, expresses the Burgers vector averaged distance at which the effect of the dislocation on intermolecular orientations and distances lies within kT of the effect of temperature on these parameters. The dislocation background of the macrotrap explains in a natural way two reproducible branches of the potential: 3l1 kT lnðr01 =rÞ for r01 r r1 ð184Þ EðrÞ ¼ 3l2 kT lnðr02 =rÞ for r1 r rb The weak-gradient part (l1 ﬃ 1) is due to weak strains created at distances larger than r2, and strong gradient part (e.g. l2 ﬃ 3) resulted from large strains occurring in the range rb < r < r2. Since dislocations are typical extended faults arising in crystal lattice during crystal preparation and subsequent handling, one would expect them to be commonly observed with different techniques. The discrete trap depths Et ¼ 0.53–0.60 eV are, for example, detected in anthracene crystal with TSC techniques [373–375]. The same values can be found by an analysis of steady-state SCLC j–U characteristics based on the concept of the macrotrap potential given by Eq. (184) (see also Fig. 69). For a discrete set (N0) of macrotraps, a general solution to Eqs. (171)–(174) with one-branch potential (181) takes on the form [318] Neff e0 em 2:7er0 3l 3 þ 3l 2þ3l U 2þ3l expðEt =kTÞ 3þ3l j¼ N0 2 þ 3l 3lkT d 2 þ 3l ð185Þ which like Eqs. (175) and (176) gives a power-type function of j vs. U, j Un, with n ¼ 2 þ 3l > 2. However, it can be expressed by a quadratic dependence typical for discrete traps (168) with a field-dependent Y factor nf Neff ¼ Y¼ nt N0 Copyright © 2005 by Marcel Dekker

2:7er0 3lkT

3l 3l U expðEt =kTÞ d

ð186Þ

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188

Equation (185) reads then as e0 em 3 þ 3l 2þ3l U 2 j¼ Y 3 2 þ 3l 2 þ 3l d

Organic Light Emitting Diodes

ð187Þ

The conductivity and j–U characteristic given by Eq. (187) is similar to the result following the Poole–Frenkel effect on SCL currents [376,377]. Such a situation is clearly not expected in the case of the standard solution for trapping by a discrete set of separated microtraps expressed by Eqs. (167) and (168). This is the case if one extrapolates Eq. (185) to l ! 0, with Y ¼ (Neff=N0) exp(Et=kT). The physical meaning of this extrapolation is that we deal with one discrete trap level (Et), the trap potential being the infinitely sharp point well for which the barrier lowering can be neglected. Due to the functional form of Eq. (185), which, except for the constant coefficient, is identical to the SCL j–U characteristics for a continuous exponential distribution of the form (175) or (176) derived in the case of the infinitely sharp point traps, the experimental data arising from the discrete macrotrap background can, without scrutiny, be mistakenly attributed to the continuous exponential distribution of point traps. The transition from the low-to high-field regions of the current occurs at a voltage (see Fig. 71) 3lkTd 9l 1=3l ð2=l þ 3Þ1þ1=l ðaÞ ð188Þ Utr ¼ 2:7er0 8 ð3=l þ 3Þ1þ2=3l which, having l from log j–log U slope, allows macrotrap dimension r0 to be determined, and then from the relation r0 ¼ (1=2pNeff)1=3, Neff to be calculated. We note that the Utr 6¼ UTFL as given by Eq. (177). The latter supplies an information about the total concentration of local (point) traps rather than the density of states, Neff. From the above, it is evident that the experimental form of j–U curves is not sufficient to unambiguously identify the trap distribution underlying the SCLC flow. Even the steep rise in the current with increasing voltage, typically associated with the trap filled limit, is not unambiguous, as it can be due to the voltage ðbÞ Utr (Fig. 71) which lowers the macrotrap barrier at the Copyright © 2005 by Marcel Dekker

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rm(b), where the microtrap distribution changes steeply its l from the actual value l1 to l2 (cf. Fig. 69). The macrotrap (defect cage) concept has been successfully applied in the past to explain the quenching of luminescence [263,311,313,378], field-dependent mobility [319] (see Sec. 4.6), and current–voltage characteristics in organic solids. Figure 71 shows typical hole j–U characteristics for two of over 20 solution grown anthracene crystals, within the broad current range (over eight decades) allowing to yield substantial information about the concentration and distribution of traps. Both the traditional approach using Eq. (176) based on the quasi-continuous exponential distribution of point traps, and the macrotrap concept were employed in the analysis of the data above the transition field F (a) [318]. The segment of the j–F curves below F ¼ F (a) is most probably governed by the carrier diffusion (see Sec. 4.4). According to the first approach, Regions I, II and III, should be ascribed to filling exponentially distributed point traps (I), trap-filled limit (II) and electrode-limited ðbÞ current (III). From the trap-filled limit voltage UTFL ¼ Utr (177) for both crystals, the total concentration of traps H ¼ nt ﬃ (3=2)e0eUTFL=ed2 ﬃ 1013 cm3 follows. This low concentration of hole point traps disagree with H ﬃ 1017 cm3 as calculated from the current j ¼ jb using Eq. (176) with Neff ¼ 41021 cm3 (the molecular density in anthracene), mh ﬃ 1 cm2=V s and e ¼ 3. The macrotrap concept resolves the above inconsistency. The results summarized in Table 4 show that the total energy of a hole in the macrotrap is the sum of the two terms as given by Eq. (184) (cf. Fig. 72). The key difference between the standard SCLC j–U characteristic interpretation and that resulting from the macrotrap model is that while in the first case, the plot follows the position of the quasi-Fermi level sweeping consecutive microtrap levels, in the second case, it is due to lowering of the barrier with the quasi-Fermi level moving below the trapping level. The voltage at which a sharp increase in the current appears, formerly referred to as the trap-filled limit voltage or possible as a step-increased value of l voltage, now corresponds to a step change in the macrotrap potential gradient with increased l. The reduction of the barrier height at high fields Copyright © 2005 by Marcel Dekker

190

Table 4 Trapping Parameters as Determined from Applying the Discrete Macrotraps Concept l1

l2

Crystal

1

2

3

d ¼ 49 mm d ¼ 66 mm

1.00 1.10

0.26 3.03

711 550

Et (eV)

r02 ˚) (A

r2 ˚) (A

rb ˚) (A

Et (eV)

E1 (eV)

Neff (cm3)

S ¼ pr201 (cm2)

n th (s1)

4

5

6

7

8

9

10

11

12

0.55 0.55

229 456

60 201

30 35

0.57 0.57

0.6 0.6

14

6.7 10 1.4 1015

11

9.5 10 1.6 1010

1.3 1012 9.9 1011

In the calculation, the field (F) corresponding to the crossing point between Child’s law curve and suitable extrapolated segments of the experimental curve has been substituted in (189). 10 Calculated from (183), assuming Neff ¼ N0 and H0 ¼ Nm, and using 3. 11 Obtained with values of r01 as given in 3. 12 Calculated with the assumption Neff ¼ N0, v ¼ 107 cm=s, and using 11 .

Copyright © 2005 by Marcel Dekker

Organic Light Emitting Diodes

1 2 Taken from the slopes (n) of suitable segments (I and II) in Fig. 71 . According to (185) n ¼ 2 þ 3l. 3 Calculated from (188) at the transition voltage a (see Fig. 71), using 1. 4 3 1 2 Obtained from (185), using and or , and making the assumption neff ¼ N0. 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 (W ¼ 0 in both cases).

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Parameter

r01 ˚) (A

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Chapter 4. Electrical Characteristics of Organic LEDs

is given by Kalinowski et al. [318] eFr0 cos W DEH ¼ 3lkT 1 þ ln 3lkT

191

ð189Þ

whereas DEL ¼ eFr0 at low fields. The potential energy maximum r0 Vmax ¼ 3lkT 1 þ ln rm

ð190Þ

ð191Þ

occurs at rm ¼

3lkT eF cos W

ð192Þ

with the field orientation W (note differences with the Coulombic barrier position in the Schottky’s and Poole–Frenkel’s models discussed in Sec. 4.3.2). The experimental results with a large number of solution grown anthracene crystals including those from Fig. 71 show the trap parameter l1 ¼ 1.0 0.2, l2 ¼ 3.3 0.5, and Et ¼ 0.60 0.05 eV to be well reproducible from crystal to crystal, but the macrotrap radius varying between 10 and 100 nm. As the macrotrap depth increases with r0 according to E(r0) ¼ 3lkT ln(r0=rb)[see Eq. (181)], it is possible to reconcile this apparent discrepancy by allowing for variation in the radius of the based pinning trap rb. The values rb ﬃ 3–4 nm (see Table 4) seem to be reasonable sizes for small clusters of the dimers which are expected to involve a few pairs of molecules [372]. At this point, we want to stress that the results of Table 4 are selfconsistent under the conditions Neff ﬃ N0 and Nm ﬃ H. They impose all molecules to be involved in formation of macrotraps, the macrotraps touch each other occupying approximately the whole volume of the crystal. This makes the carriers hopping from one to another macrotrap, the number of states available per 1 cm3 (Neff) equals the density of macrotraps in contrast to the standard Copyright © 2005 by Marcel Dekker

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interpretation in which Neff is usually identified with the molecular density Nm (note that Neff ﬃ Nm results directly from Neff ﬃ (2pr30 )1, as discussed above, if for r0 the molecular dimension is substituted). Since the capacitor charge per unit area (CU=e) < N0 in Table 4 within the entire range of the applied voltage, the TFL conditions for macrotraps cannot be fulfilled. In general, however, Neff > N0, N0 < (CU=e), and TFL is attainable. The data for naphthalene crystal seem to provide an example, where the trap concentrations determined from the TFL voltage and from the temperature dependence of Y for point traps with Neff ¼ Nm differ by about five orders of magnitude [350a]. This discrepancy is readily resolved by the macrotrap concept as the trap concentration obtained from the TFL voltage can be identified with the conand Neff ¼ Y N0 centration of macrotraps (N0) exp(Et=kT) Nm as calculated on the basis of the experimental value of Y. Summarizing the results, it must be pointed out that the presence of macrotraps can be seen in the shape of j–U characteristics only in relatively high perfection crystals for which (N0)1=3 2r01. In poor-quality crystals (thus, polycrystalline films), only two straight-line segments of log j–log U plot should be observed; the second one with the slope reflecting most probably a continuous energy distribution of microtraps dispersed homogeneously in space due to formation of macrotrap assemblies throughout the crystal. In contrast, in high perfection crystals, one would expect at least three segments suggesting the current to be controlled by a complex of potential discrete macrotraps distributed randomly in space. The reason for the fourth segment (in Fig. 71, n ¼ 3.4, with the crystal d ¼ 66 mm) can have several origins. It may be associated with a transition to the electrodelimited current (see Sec. 4.3.2), but it is also possible that after filling the macrotraps each with one carrier, next trapping events proceed through the capture of the second carrier by the already charged macrotraps. The Coulombic repulsion of the two one-macrotrap located carriers makes the macrotrap to be shallower, which shows up as a decrease in the slope of the log j–log U plot. Such a multi-charge carrier trapping has been demonstrated by the voltage-induced step-like Copyright © 2005 by Marcel Dekker

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changes in the triplet exciton lifetime in anthracene and fluorescence intensity of tetracene crystals [247] (see also Ref. 2). 4.3.2. Injection-limited Conduction (ILC) The current becomes limited by injection when the average charge density in the sample (n ) approaches n(0)—the charge density at the injecting contact. The injecting contact can no longer act as a reservoir and thus ceases to be Ohmic. The current from such an electrode will saturate at sufficiently high voltages. On the other hand, very high electric fields can make some contacts Ohmic by causing a strong injection via tunneling or other mechanisms superlinear with electric field. Though the average charge density in the sample is comparable with the charge density at the contact, both of them should be much smaller than the capacitor charge related to unit volume (e0eF=d). Thus, the condition for the current to be injection limited can be expressed by the following inequality: e0 eF

ðnf þ nt Þe d

ð193Þ

Combining inequality (193) with the current density given by j ¼ nf emF

ð194Þ

yields a modified condition for the injection-limited current (ILC) e0 eF j

d YmF

ð195Þ

where Y ﬃ nf =nt From condition (195), it follows that ILC will be observed only for relatively low currents at high electric fields with high mobility and large values dielectric permittivity (e) materials formed into high chemical and structural perfection (large value of Y) thin layers. These are often met features of thin organic films sandwiched between metals or semiconductors with moderate work functions. The measured current Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

( j) is determined by the source current ( js), the diffusion current ( jdf) and the drift current ( jd). The source current is a result of the balance between the primary injection current ( jp) and geminate recombination with the image charge at the electrode current ( jr). The current balance at the electrode obeys the continuity equation, which, in the case of one-dimensional injection for steady-state flows, is given by d

jp ðxÞ þ jr ðxÞ þ js ðxÞ ¼ 0 dx

ð196Þ

To explain the behavior of the current flowing through the sample, the functional dependence js(x) must be introduced as a boundary condition into the model describing injection currents 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 some photoinjection experiments (see e.g. Ref. 384) although a d function has also been used in analyses of some photoinjection experiments [385]. The exponential shape of js(x) is a consequence of an exponential function defining the probability that a carrier injected in a small escape cone will reach a distance x from the contact PðxÞ ¼ expðx=lÞ

ð197Þ

where l is an average penetration depth of the carrier. There are various physical mechanisms that can be responsible for the value of the penetration depth of the carrier into an insulator. A simple trajectory approach [386–388] assumes l to be a mean free path for carrier scattering on phonons or structural and chemical defects. The process of carrier emission following more scattering events may result in l being a measure of the carrier thermalization length. Alternatively, charge carrier injection can be considered as damping of the metal electron wave functions. The carriers enter the forbidden gap of the adjacent insulating material as damped one-dimensional Bloch waves which for a rectangular potential barrier (threshold) are given by c(x) ¼ A exp(x=l) with A being their Copyright © 2005 by Marcel Dekker

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195

amplitude pﬃﬃﬃand l the damping length either for pﬃﬃﬃelectrons l ¼ h=2 2Þðme we Þ1=2 or holes l ¼ lh ¼ ðh=2 2Þðmh wh Þ1=2 , le ¼ ð where me and mh , are the effective masses of electron (e) and hole (h), respectively, and we and wh are their injection barriers. The probability per unit length of finding a charge carrier at a distance x defined by jc(x)j2 leads then to an equation P(x) ¼ jAj2 exp(x=le,h) equivalent to expression (197) [21]. The range (‘‘schubweg’’) in the carrier diffusion process may be determined by traps immobilizing charge carriers [257]. The collected current, i.e. current ( j) flowing through the insulating sample, can be expressed as follows: e d nð xÞ eD ð198Þ j ¼ js ð xÞ þ emnð xÞ F 16pe0 ex2 dx Here, n(x) is the coordinate (x) dependent concentration of free charge carriers and D is the microscopic diffusion coefficient of the carriers, which is directly related to the carrier mobility (m) through the Einstein relation D ¼ mkT=e. Equation (198) is composed of a hot carrier stream of js(x) and two additional terms representing the current flow due to thermalized carriers. The thermalized carriers flow is governed by macroscopic diffusion proportional to the concentration gradient [dn(x)=dx], the image force (e=16pe0ex2) and the applied electric field (F). The latter two form a potential barrier located at x ¼ xm (Fig. 73). If the diffusion current component is negligible, the drift current in the combined image and external fields dominates the collected current which is determined by those carriers that escape over the image force barrier j ¼ j0 expðxm =lÞ

ð199Þ

where j0 is the current which would flow for l ! 1 (e.g. in the absence of scattering processes). The field dependence of the collected current in Eq. (199) enters through the field-dependent position of the barrier rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e ð200Þ xm ¼ b=g ¼ 16pe0 eF Copyright © 2005 by Marcel Dekker

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Figure 73 Formation of the potential barrier at the injecting metal contact (x ¼ 0) with an exponential distribution of the source current js(x) penetrating the insulator sample to the l ¼ 1 nm. The potential, F(x), calculated with e ¼ 4 and F(x) ¼ const ¼ 106 V=cm, has its maximum at about xm ¼ 0.9 nm. After Ref. 21. Copyright 1996 Gordon & Breach.

expressed with two additional convenient variables g¼

eF kT

and b ¼

e2 16pe0 ekT

ð201Þ

Thus, j ¼ j0 exp c=F 1=2

ð202Þ

the matewhere c ¼ l1(e=16pe0e)1=2 for hot carriers penetrating rial with the mean free path, l, or c ¼ (2 p=h)(e m wc=2pe0e)1=2 assuming the carriers to be one-dimensional Bloch waves damped within the potential threshold (wc is the injection barrier referred to the Fermi level of the injecting electrode). These two Copyright © 2005 by Marcel Dekker

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197

cases can be distinguished by an examination of the current– voltage characteristics varying work functions of the injecting metal; the injection barrier dependent carrier penetration depth will show the constant c to vary with wc for the damping length, whereas for simple scattering l should be independent of wc. When js(x) is a strongly decreasing function of x (l xm) all hot carriers entering the sample are thermalized at a distance l, and only their fraction due to thermal activation over the barrier can contribute to the collected current ð203Þ j ¼ AF 3=4 exp aF 1=2 where A(F) ¼ const, A ¼ j0(el=kT)3=4 exp[2(b=l)1=2], and

be a¼2 kT

1=2

3 1=2 1 e ¼ kT 4pe0 e

ð204Þ

This is the injection current limited by a field-assisted separation of charge from its mirror image in the injecting contact. Since the preexponential factor is a relatively slowly varying function of F, and the constant a identical with the Schottky parameter, aS, Eq. (203) can fairly be approximated by the straight-line plot log j F1=2, and often interpreted in terms of the Schottky injection into carrier conducting bands (see the discussion in Ref. 361). One should, however, remember that the Schottky approach assumes the activated carriers to occupy allowed free electron states within wide conducting band materials. Its application to narrow band insulators (an overwhelming majority of organics) can be misleading. Although much similarity can be seen in the description of ILC for both wide- and narrow-band insulators, there is an important difference in the mechanisms by which charge carriers surmount the barrier. This difference is apparent in Fig. 74. In contrast to the wide-band materials, where sufficiently high activated carriers can overcome the barrier directly (path 1), in the narrow-band case, the only practical Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

Figure 74 Comparison of field-assisted thermionic injection mechanisms in wide- (a) and narrow-band (b) materials. An x0 close to the geometrical contact region is distinguished where Eq. (198) is not applicable. The inapplicability can be associated with field or coordinate dependence of m, D and e or the coexistence of some other processes such as bimolecular or tunneling recombination which are not included in Eq. (198). After Ref. 361. Copyright 1989 Jpn. JAP, with permission.

way to reach its maximum is diffusion against the field directed towards the injecting contact. This leads to important consequences in the description of the current-field characteristics in wide- and narrow-band insulators. While for the wide-band materials, the only condition for the carrier to enter a conducting band is to be excited to its lower edge Copyright © 2005 by Marcel Dekker

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199

(Schottky injection), in the case of narrow-band materials, the injected real charge has to be separated by diffusion from its mirror image and, therefore, should be considered in the context of a one-dimensional Onsager-type formalism [382]. In the former, electric field increase in the current is due to the electric field-induced lowering of the barrier (Ecoul in Fig. 74), in the latter, the current increases because an external electric field reduces the geminate recombination rate of the carrier at the injecting contact. It has been shown that the one-dimensional Onsager model for carrier injection appears to be a particular solution of Eq. (198) for a weak gradient function js(x) and=or x0 ! 0 [361]. The field dependence of the collected current is determined by the relation between the barrier location xm, and thermalization length, l, and differs for high and low electric fields. It is, with the accuracy to the 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 expðb=lÞ F ð205Þ For xm l, the current saturates, j ¼ j0, independent of the field regime (unless F ! 0; the condition xm l cannot then be fulfilled with a finite value of l, since xm ! 1). It is interesting to note that the low-field regime for room-temperature and materials with 2 < e < 15 falls in the 9 103– 7 104 V=cm range, an estimation useful in the analysis of the current–voltage behavior of the injection currents. However, one should keep in mind that this demarcation value of F can be as low as 2 V=cm at ﬃ 4 K (e ¼ 2) and as high as 8 105 V=cm at ﬃ 103 K (e ¼ 15). In summary, the generally valid equation (198) governing injection-limited current flow in insulators can be reduced to a description of the drift current that evolves with electric field taking on various functional shapes dependent on the primary carrier injection and motion mechanisms in the insulator. But even for a given type injection process, the current-field dependence varies passing from low- to high-electric field regimes. For instance, Copyright © 2005 by Marcel Dekker

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Organic Light Emitting Diodes

thermionic injection of charge reveals a linear increase of the current density with applied voltage at low fields (205), and follows an exponential function at high fields (203). The latter is illustrated in Fig. 75 for three different SL LEDs based on molecularly doped polymers. For all three devices, the current-field [ j(F)] curves can be reasonably approximated by the straight-line log( j=F3=4) vs. F1=2 plots, their slopes yielding the characteristic parameter a in Eq. (203). The difference between their slopes can be ascribed to different dielectric constants of the samples (e1 ¼ 4.5, e2 ¼ 2.3, e3 ¼ 1.7) and does

Figure 75. Thermionic injection currents in three different SL LEDs following Eq. (203) as represented by the straight-line log( 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) (60 nm)=Mg; (3) ITO=(70% TPD:10% T50hex:20%PC) (70 nm)=Ca. The slopes of the straight-line plots, a1 ¼ 0.7 102 (cm V1)1=2, a2 ¼ 1.15 102 (cm V1)1=2 and a3 ¼ 1.01 102 (cm V1)1=2 reflect differences in the composition of the LEDs. After Ref. 389. Copyright 2001 Institute of Physics (GB), with permission. Copyright © 2005 by Marcel Dekker

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not exceed 35% as compared with predictions of the theory (204) with e ¼ 3. Similar straight-line plots for a series of DL LEDs, shown in Fig. 76, yield the slope ﬃ 1.4 102 (cm=V) 1=2 ﬃ 2aS. There are at least two reasons for the discrepancy between experimental values of aexp and aS. First, due to accumulation of majority positive carriers at the TPD=emitter (DPP:Alq3) interface, the field in the anodic compartment of the device is much lower than the nominal applied field [2,303,390], and second, due to disorder, the Coulombic potential at the interface is affected by the near

Figure 76 Log( j=F3=4)–F1=2 plots for DL organic LEDs ITO=TPD (30–49 nm)=Alq3:% DPP (33–62 nm)=MgAg with different concentrations of diphenylpentacene (DPP) in the electron-transporting layer. After Ref. 68. Copyright 2001 American Institute of Physics. Copyright © 2005 by Marcel Dekker

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surface splitting of the conducting level into an extended band formed by a spread of energy and space of the carrier hopping sites [391,392]. The maximum anodic field screening can be estimated, neglecting disorder effects, by comparing the experimental and theoretical values of the Schottky parameter a. The anode screening factor is then given by k1 ¼ (atheor=a)2 ﬃ 0.4, assuming the average value for all the samples in Fig. 76, a ¼ aexp ﬃ 1.45 102 (cm=V)1=2. This means that the electric field within the HTL of thickness d1 constitutes about 40% of the nominal field (F1 ¼ k1F) and the cathodic compartment (d2) field F2 ¼ k2F becomes enhanced by a factor k2 ¼ (d=d2)[1k1(d1=d)] ﬃ 1.4 determined from simple electrostatics arguments for averaged values of d1 and d2, and d for the samples in Fig. 76. The applied field (F ¼ U=d) is defined by the applied voltage (U) ratio to the total thickness of the device kept at an approximately constant value d ﬃ 115 nm [68]. The apparent decrease in the parameter a (204) for the devices with doped emitters suggests that the dopant reduces the positive charge at the HTL=emitter (also ETL) interface, so that the anodic compartment field would increase to about 46% of the nominal field, and an increasing trend in the injection current should be expected. Instead, except for the lowest doped emitter device (0.25 mol%), the current decreases at variance with the above prediction (cf. Fig. 76). This contradiction can be resolved by assuming the measured current to be composed of the holeinjection current and recombination current at the interface. The recombination current defined by the number of holes recombining per unit time is proportional to the interfacial density of electrons. The latter, in turn, appears to be a function of dopant concentration as comes out from the concentration dependence of the EL efficiency (see Sec. 5.4). The higher concentration decrease in the EL efficiency can be related to a decrease in the recombination current, thus observed as a decrease in the total device current. This reasoning is supported by the variation of the straight-line log( j=F3=4) F1=2 plots with concentration of the hole accepting TPD molecules in the TPD doped PC HTLs (Fig. 77). Increasing concentration of TPD leads to increasing hole-injection efficiency at Copyright © 2005 by Marcel Dekker

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Figure 77 Current-field characteristics [in log( j) F3=4) against F1=2 representation] of the DL LEDs consisting of variable concentration of TPD HTL (%TPD:PC)(70 nm) and a 100% evaporated Alq3 ETL (60 nm) sandwiched between an ITO anode and a Mg cathode. The slopes of straight lines approximating the experimental plots (points), a, in (cm=V)1=2 are given in the bottom-right corner. After Ref. 303. Copyright 2001 Institute of Physics (GB).

the ITO=(TPD:PC) interface (Ref. 393), the difference between anodic (F1) and cathodic (F2) compartment fields increases. From simple electrostatics, it follows that the (TPD:PC)=Alq3 interfacial charge concentration is proportional to the electric field across the interface, which for the A recent study of the TPD concentration effect in PC on charge injection from ITO [394] neglected the injection enhacement due to the increasing density of electron donor molecules of TPD (thus, js) and explained the TPD concentration increase of the electric conduction in terms of SCL currents modified by the field-dependent mobility (cf. Sec. 4.6).

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majority charge carriers reads ni ¼

e0 e ðF1 F2 Þ ed

ð206Þ

Here d is the thickness of the interfacial layer, where the recombination occurs predominantly among the interfacial charges. It can be identified with the recombination zone width. Assuming for a while d(F) ¼ const, ni and DFi ¼ (F1 F2) would be expected to increase with the holeinjection efficiency, and, as a consequence, the recombination current to increase. The latter reduces the electric field screening at the electrodes [(F1 F2) decreases]. Since aexp > atheor, the screening effects must prevail over the recombination-induced reduction in the interfacial space charge and increasing of a with the hole injection efficiency is observed. Even at the lowest concentration of TPD (33% in Fig. 77) aexp=atheor ﬃ 1.3, the screening factor k1=k2 ¼ F1=F2 ﬃ 0.7 indicating the cathode field to exceed a stronger screened anodic field by a factor of 1.5. For high injection levels (75% and 100% TPD in the HTL), k1=k2 ¼ F1=F2 ﬃ 0.1, the cathodic field becomes an order of magnitude larger than in the anodic LED compartment. Any field dependence of the recombination zone width, d, will modify 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 predicted (Sec. 3.3) and verified experimentally (Sec. 5.4) for ICEL mode operating LEDs. The field distribution among the totally vacuum evaporated TPD (100%) HTL and Alq3 (100%) ETL has been inferred from the analyses of transient currents [395] and electroabsorption experiments [396]. The electric field within the TPD (100%) HTL was generally found to be lower than that in the Alq3 (100%) ETL, suggesting more effective accumulation of holes than electrons at the TPD=Alq3 interface. The screening factor F1=F2 depended slightly on the applied voltage and varied between ﬃ0.35 for a weakly injecting Al cathode and ﬃ0.8 for a Copyright © 2005 by Marcel Dekker

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strongly injecting LiF=Al cathode at high applied fields F ﬃ 2 106 V cm1. The thermionic emission currents provide a plausible alternative for the current–voltage characteristics of organic solids, discussed in terms of SCL conduction. For example, the strong power function plots with two different powers in the 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 expressed by Eq. (203). Due to the reasonable straight-line approximation of the log( j=F3=4)–F1=2 plots, the screening of the applied field within the HTL is fairly independent of the proportions between thicknesses of the hole-transporting (75% TPD:PC) (d1) and electron-transporting (100% Alq3)( d2) layers, and equals k1 ¼ (atheor=aexp)2 ﬃ 0.2. On the other hand, the enhancement factor for the cathodic field increases with increasing ratio d1=d2, k2 ¼ (1 þ d1=d2) k1(1 þ d2=d1), so that the screening factor k1=k2 decreases from k1=k2 ﬃ 0.14 for d1=d2 (or d2=d1) ¼ 35=60 nm, down to k1=k2 ﬃ 0.08 for d1=d2

Figure 78 Thermionic injection current-field characteristics for the ITO=75% TPD:PC= Alq3=Mg=Ag devices with different proportions of the hole transporting to electron-transporting layer thicknesses 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 results according to Eq. (203) are given in the bottom-right corners of the figures. After Ref. 303. Copyright 2001 Institute of Physics (GB). Copyright © 2005 by Marcel Dekker

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(or d2=d1) ¼ 120=60 nm. This is an interesting observation, suggesting that increasing the total thickness of the device (d1 þ d2) either by increasing d1 or d2, it is possible to enhance the electron injection due to the increasing field in the ETL, F2. However, it should be kept in mind that large values of the field F2 are derived from the positive space charge on the TPD side of the TPD=Alq3 junction. If there is a comparable negative space charge on the Alq3 side of the junction, one has to take into account the screening of the cathodic field due to this charge. As a result, F1 and F2 may not differ too much, and the screening factor F1=F2 may approach unity (but F1, F2 < F). Employing SL LEDs allows to avoid the field distribution problem and makes the verification of injection mechanisms straightforward. The current–voltage characteristics for the SL LEDs based on TPD and Alq3 films are shown in Fig. 79. In Fig. 79a, the j(F) curves from Fig. 68a are replotted in the log( j=T2) vs V1=2=T (parametric in temperature). Except for the low temperature plots (50 and 90 K), they are fairly well approximated by the straight lines reflecting the Schottky-type injection described by Eq. (208) with j0 ¼ A T2 [A (T,F) ¼ const] and aS ¼ (1=kT)( e3=4pe0ed)1=2 [cf. Eq. (204)]. No difference in the current density at any applied field for the samples of different thickness led Campbell et al. [397] to the conclusion that the current observed for the ITO=TPD=Al is due to thermally activated injection of both holes from ITO and electrons from Al into TPD sandwiched between these two electrodes. However, quantitative differences have been noted concerning the RS coefficient, the prefactor current, and the injection barrier. In contrast, the quasi-straight-line log j–log U plots for the Al=Alq3=Ca system from Fig. 69a, replotted in the Schottky-type coordinates in Fig. 79b, deviate apparently from the straight lines, and the current decreases with the sample thickness. Moreover, the thickness dependence of the current density obeys the d1 law for d > 125 nm (Fig. 80) suggesting the free-carrier SCLC (168a) to underlie the current flow in this system. The fitting of the experimental data with the power law Fn (n > 3) seen in Fig.69a has been explained by the field-dependent mobility [355]. (see also Sec. 4.6). Copyright © 2005 by Marcel Dekker

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Figure 79 Current–voltage characteristics for ITO=TPD=Al (a) and Al=Alq3=Ca (b) from Figs. 68a and 69 a, respectively, replotted in the scales corresponding to the straight-line behavior according to Eq. (208). The curves in part (a) are parametric in temperature as in Fig. 68a, and in part (b) are parametric in thickness as given in the figure. Adapted from Campbell et al. [356a] and Bru¨tting et al. [355] and respectively.

The shape of the current–voltage characteristics at high fields can be dominated by the tunneling carrier injection through the narrow triangular barrier [21,397a] when its position [see Eq. (200)] approaches the geometrical contact. In Fig. 81, the tunneling injection is compared with the thermionic injection treated as the classic Richardson–Schottky (RS) electron emission at the metal= insulator interface. In the RS emission, the Coulombic energy barrier 3 1=2 e2 e F DEC ¼ e½Fðx ¼ xm Þ Fðx ¼ lÞ ¼ 4pe0 e 16pe0 el ð207Þ has to be overcome by a carrier in order to contribute to the collected current j expðDEC =kT Þ ¼ j0 exp aS F 1=2

Copyright © 2005 by Marcel Dekker

ð208Þ

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Figure 80 Thickness dependence of the injection current in the Al=Alq3=Ca system at a constant electric field F ¼ 0.5 MV=cm. A pronounced deviation from the d1 behavior for thin samples is seen for d < 125 nm. Adapted from Ref. 355.

where j0 is the injection current density at F ¼ 0, and aS a is given by Eq. (204). Electrons entering the insulator are most likely thermalized at a distance l < xm from the interface, where their energy, determined by the Coulombic interaction with the image charge, Ec (x ¼ l) ¼ e2=16 p e0el, is lower than Ec at x ¼ xm. However, they can reach xm by thermally activated diffusion. The activation energy is identical with the Coulombic binding energy (207), the squareroot term accounting for barrier lowering by the external field (field-assisted thermal escape). Such carriers contribute to the collected current following the straight-line relationship ln j vs. F1=2 (208). Copyright © 2005 by Marcel Dekker

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Figure 81 Comparison of the field-assisted thermal activation of an electron over the Coulombic barrier located at x ¼ xm (cf. Fig. 74 ) (a) and tunneling through the barrier with xm ! 0 (b), at a metal=insulator interface. The potential F(x) calculated with e ¼ 4, and F(x) ¼ const ¼ 106 V=cm. Adapted from Ref. 21.

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In the high-field limit (xm ! 0), the carrier injection can be considered as tunneling through the Coulombic barrier reduced to a triangular shape (Fig. 81b) into continuum of states [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 expðb=F Þ

ð209Þ

with B(F) ¼ const, and 4ð2m Þ1=2 3=2 wb b¼ 3 he

ð210Þ

where wb is the injection barrier and m is the effective mass of electron inside the barrier. Support for the applicability of the FN concept to injection into organic LEDs comes from injection studies upon varying the injection barrier [398–400]. The temperature independence of the injection current observed in systems with large barrier for hole injection lent further support to the concept [400]. At lower fields deviations from FN-behavior are usually noted, though, and currents become temperature-activated, suggesting that at lower fields thermionic emission prevails. The applicability of the FN vs. RS charge injection model has been studied in detail on the Al=Alq3=Mg:Ag system [401]. Although the current–voltage characteristics bears out a high power-law behavior ( j U7 at 295 K and j U12 at 133 K), similar to that in Fig. 68b for the DL LEDs based on the TPD=Alq3 junction, indicative of the trap-controlled SCLC flow, the current has been considered as ILC rather because of too high injection barriers at both contacts. The measured injection currents in Fig. 82 clearly show inapplicability of the FN model, while their good qualitative agreement with the RS concept is apparent from the straight-line plots log j vs. F1=2. Yet, quantitative differences concerning the characteristic model parameters have been observed. In Fig. 83, high-field dependencies of the injection current into TPD- and Alq3based SL EL devices are presented in different scales to test the validity of different injection models. Though they can Copyright © 2005 by Marcel Dekker

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Figure 82 Fowler–Nordheim (a) and Richardson–Schottky (b) representations of the current-field dependence in an Al=Alq3(150 nm)=Mg:Ag device at various temperatures. After Ref. 401. Copyright 1999 American Physical Society, with permission.

be approximated by a power function j Fn with n ¼ 2.9 and 2.3 for TPD and Alq3 film, respectively, deviating from this behavior at ‘‘lower fields’’, the non-linear field increase in their brightness rules out the current to be SCL (cf. Sec. 5.3). Instead, the low-field region behavior (F < 1.0 MV=cm) is well approximated by the RS thermionic emission model, and the high-field segment (F > 1 MV=cm) by either FN or hot carrier description of the injection. From the linear regimes of the plots in three different scales (Fig. 83b), apparent injection parameters can be inferred that differ significantly from expected ones (Table 5). Even with a large uncertainty, the values of the energy barrier wb at the ITO=TPD and Mg=Alq3 interface appear unreasonably low, compared with 0.6 and 0.65 eV resulting from the energy diagram for these interfaces (Fig. 84). Therefore, tunneling through triangular barrier can be ruled out as the carrier emission process at high fields though it has been considered as a limiting case for thermally assisted hopping within a Copyright © 2005 by Marcel Dekker

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Figure 83 The high-field regime log–log current-field characteristic (a), replotted in three different representations (b) for ITO=TPD(130 nm)=Mg=Ag (left) and ITO=Alq3(140 nm)=Mg=Ag (right) EL diodes. The plots log j vs. F1=2, log j vs F1=2 and log j vs. F1 allow to test hot carrier, thermionic, and tunneling models for carrier injection, respectively. Adapted from Ref. 57.

superimposed Coulombic and external potential [402]. The data of Table 5 suggest primary (hot) carrier penetration over the image force barrier to be the most probable injection mechanism at high electric fields. From the asymptotic high-field slope of log j vs. F1=2 plots, we obtain the mean free path of primary holes injected into TPD, lh ¼ 0.26 nm, and electrons injected into Alq3, le ¼ 0.45 nm [cf. Eq. (202)]. These are figures corresponding to less than one molecular layer. Though they seem relatively small, their good correspondence to the value (0.22 0.03) nm found for a Copyright © 2005 by Marcel Dekker

SL Alq3 SL TPD

a (cm1=2 V1=2)

a=atheora

b (V cm1)

wb (eV)

c (V1=2 cm1=2)

wc (eV)

˚) l(A

1.9 103 2.8 103

0.25 0.26

1.15 106 1.95 106

0.07 0.09

2.1 103 3.6 103

0.04 0.14

4.5 2.6

atheor ¼ (e=kT)(e=4pe0e)1=2 ¼ 7.6 103 cm1=2 V1=2 with e ¼ 4. Note: The energy barriers (wb, wc) have been calculated by assuming that the carriers’ effective mass equals the rest mass of the electron. a

213

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Structure

Various Charge Injection Parameters for SL EL Devices, Extracted from the Plots of Fig. 83

Chapter 4. Electrical Characteristics of Organic LEDs

Table 5

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Figure 84 Energy level scheme and EL emission from a DL device: ITO=TPD=Alq3=Mg. Note that the injection barriers at the ITO=TPD (DEh) and Mg=Alq3(DEe) bear some uncertainty due to the inaccuracy in determination of both energy levels in organics as well as in the work functions of ITO and Mg. DEh < DEe in the figure, may thus be replaced by DEh ﬃ DEe or even DEh > DEe, dependent on the choice of the literature data for these energy levels. After Ref. 57.

characteristic distance of the charge transfer reaction at the anthracene=metal interface [384] does not exclude their reliability. However, on the quantum mechanical ground, considering l as the average penetration depth of electron waves into a rectangular potential barrier, the experimental values of c yield wc apparently smaller than the actual barriers, although its value for the Alq3=Mg interface is much larger than wb. A much better agreement of these numbers can be reached if the Schottky reduction (DECoul) of the energy barrier and disorder-induced broadening of the HOMO level in TPD will be taken into account. At field strengths F > 106 V=cm, DECoul ¼ (e3 F=4p e0 e)1=2 > 0.2 eV and DEdisorder ﬃ 2 sp 0.2 eV typically for amorphous solids Copyright © 2005 by Marcel Dekker

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with diagonal disorder (cf. Secs. 2.4.3 and 4.6). A very low value of wc and relatively large value of le for the Mg=Alq3 interface would suggest classical propagation of electrons in the Alq3 image force potential well between the emitter and the potential maximum. Analyzing the RS portion of j(F) curves yields a significantly smaller than atheor (204) calculated with e ¼ 4. It has been suggested that a < atheor can be the result of the charge trapped near the contact along linear imperfections [403]. Both, experimental observations and theoretical considerations show that the distribution of imperfections can be linear in crystals [82,404–406], and linear macrotraps formed by an array of dipolar microtraps [371]. Then [403], a atheor

¼1

16tD0 e

ð211Þ

where t is the linear density of charge along the trapping line parallel to and located from the surface at a distance D0, and e is the elementary charge. The experimental data from Table 5, a=atheor ¼ 0.25, require tD0=e ﬃ 0.05. This means that the linear density of the trapped charge at a distance D0 ¼ 10 nm amounts t=e ¼ 0.005 e=nm, that is one elementary charge carrier occurs in the trap array every 200 nm (roughly every 20 intermolecular distances). The linear traps more distant from the surface would create the same difference in a at lower charge density (t=e D1 0 ). If the charge trapping domain is planar, the current becomes a more complex function of applied field, it cannot be anymore approximated by the 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 states distributed in energy according to the Gaussian function with a width s. The charge transport among a Gaussian shaped density of states (DOS) becomes of importance for the carrier escape from the near-contact Coulombic well [392]. Since the primary charge injection probability from the metal to the insulator depends whether the carrier jumps into an upper or lower part of the Gaussian profile (upward and downward carrier jumps), the collected current and its field Copyright © 2005 by Marcel Dekker

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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-type straight-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 ascribed to a roughly doubled energy barrier the carrier has to surmount 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 analytic theory results (lines) compared with Monte Carlo simulations (points) according to Ref. 392. Copyright © 2005 by Marcel Dekker

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formed by a superposition of the Coulomb field of the image charge and the external field. The Gaussian DOS can be considered as a particular case of an additional potential localized between the contact and the position of the Coulombic (Schottky-type) barrier [361]. It creates an additional electric field (Ft) which should be included into the drift component of the current e dnð xÞ ð212Þ j ¼ enð xÞm F þ Ft mkT 2 16pe0 ex dt Solving the differential equation in n(x) in the high-field regime yields n o j ¼ B½ðeF=kT Þ þ at 3=4 exp 2½bðeF =kT þ at Þ1=2 ð213Þ where the parameter at ¼ eFt=kT is a measure of the trap potential shape and its influence on the j(F) dependence appears in a deflection from the linearity of the plot log j vs. F1=2. In Fig. 86, a hypothetical trap potential is presented and current-field characteristics following Eq. (213) are plotted in the log j vs. F1=2 scale for different values of the parameter at. The external electric field combined with the trap field (Ft) and the image charge field (e=16pe0ex2) forms two energy barriers. Their height ratio depends on the external field strength (1 and 2 in Fig. 86b illustrate the potential at low- and high-electric fields, respectively). The dashed lines in Fig. 86c represent non-linear portions of the log j–F1=2 plot. It is seen that for at ¼ 5 105 cm1, the plot gives a straight line in the entire field range 104–1.2 105 V=cm considered in calculations. The straight-line behavior appears also for other values of at > 5 105 cm1, but the lower limit of the electric field at which it starts increases with increasing at. For at < 5 105 cm1, the plot becomes non-linear in the above field range. We note that at a given at, the trap depth increases with the trap dimension (d0) according to Rd Et ¼ 0 0 Ft edx ¼ at kTd0 . A relatively shallow trap Et ﬃ 0.1 eV follows for d0 ¼ 10 nm and at ¼ 4 106 cm1 at room temperature. It is comparable with typical Gaussian shaped DOS widths. The presence of a traps in the near-electrode Copyright © 2005 by Marcel Dekker

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Figure 86 Hypothetical trap potentials localized at the electrode in the absence (a) and in the presence (b) of image and external electric fields. Dashed lines represent a linear approximation of the trap potential in (a), and the potentials in the absence of trap in (b). Plots of log j vs. F1=2 according to Eq. (213) (c) parametric in at: 4 106 cm1 (1), 2 106 cm1 (2), 106 cm1 (3), 5 105 cm1 (4) and at ¼ 0 (5). After Ref. 361. Copyright 1989 Jpn. JAP, with permission.

Coulombic well may change the function (213) to include an additional probability factor (P) allowing for the carrier to reach the potential maximum [257,361]

P ¼ exp xm =lq Copyright © 2005 by Marcel Dekker

ð214Þ

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Here lq is the diffusion length (‘‘schubweg’’) of free carriers. Then, for low values of at [(e F=kT)], Eq. (213) reduces to ð215Þ j ﬃ j0 exp aU 1=2 bU 1=2 where a ¼ aS d1=2 [aS defined by Eq. ( 204)], and b ¼ (bd=tcm) 1=2 with 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 Coulombic barrier is located far from the contact (large xm). Indeed, from the example given in Fig. 87, it is seen that j (U) follows well the function exp(bU1=2) in the low-field regime, and switches to exp(aF1=2) behavior at high fields. The straightline plot log j vs. the complex variable (aU1=2 bU1=2) can be obtained in the entire voltage range applied to the sample within a broad range of current densities (six orders of magnitude). The presence of a large concentration surface traps as determined from the lq ﬃ 30 nm following the experimental value of b ¼ 1.5 V1=2, seems to influence the constant a which (as often happens) exceeds its theoretical value by a factor of 2. In closing, it should be pointed out that a similarity between the function exp(bU1=2) and that given by Eq. (202) comes from the identical definition of the probability of a carrier to surmount the Coulombic barrier [cf. Eqs. (199) and (214)]. However, the physical background is different for these two cases. Whereas, Eq. (199) relates to the scattering of hot carriers within a narrow Coulombic well (small xm), Eq. (214), in contrast, describes the motion of thermalized carriers in a relatively extended Coulombic well. Thus, the first occurs at high, and second at low electric fields. It is important to remember that the injection current flow will be modified by the space charge reducing the nearelectrode field, which in the extreme case (for low injection barriers) renders the current to be SCL (cf. Sec. 4.3.1). If the space charge occurs as a result of trapping, its concentration can be reduced by illumination of the sample. Photons or light-produced excitons, releasing charge carriers from traps, Copyright © 2005 by Marcel Dekker

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Figure 87 log j–(aU1=2–bU1=2) dependence (solid line) calculated from (215) with corresponding experimental points (open circles) for the photocurrent in a 22 mm-thick tetracene single crystal illuminated through a semitransparent gold anode. (a) log j–U1=2 and (b) log j–U1=2 plots are shown in the insets. The calculations have been done with a ¼ 0.42 and b ¼ 1.5. After Ref. 257. Copyright 1979 Wiley-VCH, with permission.

increase the free-to-trapped concentration ratio, Y, alleviating the ILC condition (195) to be fulfilled. One would expect, such a photo-enhanced current easier to attain the ILC than that produced under dark injection condition. An excellent Copyright © 2005 by Marcel Dekker

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illustration of this prediction are current–voltage characteristics for the hole injection from a semitransparent gold electrode into a tetracene single crystal shown in Fig. 87. A steep power-like j–U dark current characteristic (resembling the SCLC flow) converts into S-shaped curves under illumination (Fig. 88a). Two, low- and high-field segments can be distinguished at sufficiently intensive illumination ( > 1012 quanta=cm2 s): the first following the function exp(bU1=2) and the second following the function exp(aU1=2)(cf. also Fig. 87). It is clearly seen that increasing light intensity (reducing the near-contact space charge) elongates the straight-line behavior of the log j vs. (aU1=2 bU1=2) plot characteristic of the ILC in accordance with Eq. (215). Until now, a recombination velocity of thermalized as well as hot carriers has been directly introduced in various models as a boundary condition independent of the carrier position in an insulator. This corresponds to the assumption jr(x) ¼ const, and from Eq. (196), js ¼ j0a1 exp(a1 x), for the exponential character of the primary injection current jP ¼ j0 exp( a1 x), follows. The source carriers are being thermalized with a probability n (per unit time) and rate en N(x) equal to the carrier injection rate, enN ð xÞ ¼ j0 a1 expða1 xÞ

ð216Þ

where N(x) is the concentration of charge at x of non-thermalized carriers. Since, by definition, js ð xÞ ¼ en

Z1

N ð xÞ dx

ð217Þ

0

from (216) js ð xÞ ¼ j0 expða1 xÞ

ð218Þ

that is the source current coincides with the primary injection current jp. Without an applied electric field, the source current is compensated by opposite in direction the surface recombination current js jr ¼ 0. An assumption has been made that Copyright © 2005 by Marcel Dekker

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Figure 88 Current–voltage characteristics for a 12 mm-thick tetracene crystal in the dark (I0 ¼ 0) and under increasing illumination up to 1014 quanta=cm2 s. (lex ¼ 550 nm; penetration depth la ¼ 7.27 mm) through a semitransparent gold anode as shown in part (a), where the j–U dependence is plotted in a log j–log V scale. It is replotted in other three different scales: (b) log j–U1=2, (c) log j– U1=2, and (d) log j–(aU1=2–bU1=2). After Ref. 257. Copyright 1979 Wiley-VCH, with permission.

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this balance takes place at a distance x ¼ xc ¼ rc=4, where rc ¼ e2=4 pe0ekT is known as Coulomb radius defined by identifying the intercarrier binding energy with thermal energy kT [407]. Furthermore, these authors assumed the recombination rate to be underlain by the hopping process towards the surface. Based on these assumptions, they arrived at a net current which is lower as compared to the injection current neglecting the surface recombination for either low and high electric field regimes. This simple description can be generalized on the expense of the simplicity of the resulting current-field relationship. A physically probable tunneling recombination process at the interface has been discussed previously in detail [361]. The recombination rate has been assumed to take an exponential form Zr ð xÞ ¼ Zr ð0Þ expða2 xÞ

ð219Þ

where Zr(0) ¼ Zr(x) at x ¼ 0, and a2 is a characteristic tunneling parameter dependent on the type of the interface. Now, Eq. (196) takes on the form d jp ðxÞ eN ðxÞZr ðxÞ en N ðxÞ ¼ 0 dx

ð220Þ

and combining Eqs. (196) and (217)–(220) yields js ðxÞ ¼ j0 a1

Z1 0

expða1 xÞ dx 1 þ ½Zr ð0Þ=n expða2 xÞ

ð221Þ

Expression (221) allows us to solve the problem only in the approximation of the one-dimensional Onsager model but not in the approximation of the strong gradient js(x). But, even in the first case, an approximated solution becomes expressed by a first order modified Bessel functions and requires summation procedures (see Ref. 361). However, to describe the one-dimensional motion of thermal carriers near the injecting contact, we can define the transition probability from a position x to a position x þ l and x l, corresponding to the carrier motion in and against the external electric field direction, respectively. Assuming the carrier to realize a Copyright © 2005 by Marcel Dekker

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diffusion motion, they are given by Godlewski et al. [408]. 1 Pxl ðFÞ ¼ expðeFl=kTÞ and Pxþl ðFÞ 6 1 ¼ ½2 expðeFl=kTÞ 6

ð222Þ

The parameter l represents a field-independent scattering length of the carriers. The factor 1=6 is included to account for the statistical distribution of motion directions. The net carrier flux in field direction is F ¼ nðx lÞuth Pxþl ðFÞ nðx þ lÞuth Pxl ðFÞ

ð223Þ

where n(x l) and n(x þ l) are charge concentrations at positions (x l) and (x þ l), respectively, and uth is the thermal velocity of the carriers. If there are sinks for carriers at both the origin [emitter: js(x)] and the collecting electrode at x ¼ d, and if the concentration functions n(x l) and n(x þ l), expanded in Taylor series about x, are truncated after the first expansion term, the collected current will have the form 1 j ¼ eF þ js ðxÞ ¼ euth nðxÞ½1 expðejFðxÞjl=kTÞ 3 FðxÞ 1 dnðxÞ þ js ðxÞ uth l dx jFðxÞj 3

ð224Þ

It corresponds to the standard equation (198) with 1 el uth ¼m 3 kT kT b ðg 2 Þ FðxÞ ¼ e x

ð225Þ ð226Þ

and 1 D ¼ uth l 3

ð227Þ

The field-dependent drift velocity 1 uðFÞ ¼ uth ½1 expðeFl=kTÞ 3 Copyright © 2005 by Marcel Dekker

ð228Þ

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saturates at high fields, approaching umax (F ! 1 ) ¼ (1=3)uth. On the other hand, for eFl kT (low-field region or l ! 0) 1 eFl ﬃ mF uðF Þ ¼ uth 3 kT

ð229Þ

giving Eq. (225). Equation (224) may be solved numerically, leading to more or less steep current-field characteristics dependent on the carrier scattering length, l. Examples are shown in Fig. 89. The curve with the lowest l ¼ 0.01 nm is adjusted to reproduce one-dimensional Onsager approximation. The largest value of l ¼ 2 nm is chosen at the upper limit of the applicability of the field-controlled diffusion jump model. It is seen that increasing l reduces the steep rise of current with field, a tendency to saturation appears for l > 0.1 nm and F0 > 105 V=cm. The scattering length 0.5 nm corresponds roughly to the shortest distance between molecules of anthracene. We note, however, that the scattering length has not necessarily to be identical with the intermolecular distance. Charge carrier scattering in molecular solids occurs at atoms of vibrating and rotating molecules, the scattering length indicating an average distance between sites of two consecutive scattering events. Such a distance can be shorter than the lattice constant or intermolecular distance. The difference is expected to be well pronounced in case of large molecules forming disordered solids, e.g. polymers. This is reflected in a difference between the hopping and intermolecular distances. However, one has to distinguish between the kinetic model and a hopping model for charge carrier motion. While hopping in molecular systems must include a disorder leading to a field-induced modification of effective hopping distances, the kinetic model describes the carrier motion with a field-independent scattering length. Moreover, and more important, the dwell time in hopping motion is much longer than the scattering event time. Equation (221) inserted into Eq. (224) allowed to test the effect of the tunneling recombination at the interface (219) on the current-field characteristics. Copyright © 2005 by Marcel Dekker

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Figure 89 Current-field characteristics, plotted in a log–log scale, as calculated numerically from Eq. (224) parametric in scattering length. Calculation was performed with a1 ¼ 20 nm1, T ¼ 300 K, e ¼ 3, d ¼ 10 mm, and for the case no surface recombination. The current values are normalized to j0. After Ref. 408. Copyright 1994 Wiley-VCH, with permission.

In Fig. 90 emission-limited currents vs. applied field for different surface recombination efficiency are presented. A slight change in the shape of the j(F) curves (particularly for l < 0.1 nm) is accompanied by a substantial decrease in the current following an increasing rate of recombination. The above considerations show that the identification of the injection mechanism based upon the shape of a j(F) curve only is highly uncertain and conclusions must be drawn with great caution. Copyright © 2005 by Marcel Dekker

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Figure 90 Injection-limited current j (normalized to j0) vs. applied electric field F0 for (a) l ¼ 0.01, and (b) 0.5 nm, and different surface recombination rates Zr(0)=n (as given in the figure). The tunneling constant for the surface recombination a2 ¼ 10 nm1, other parameters as in Fig. 87. After Ref. 408. Copyright 1994 Wiley-VCH, with permission.

4.4 DIFFUSION-CONTROLLED CURRENTS (DCC) Charge carrier injection from a metallic electrode is said to be diffusion-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. Solving 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 menðxÞ½expðb=x0 ÞF

ð230Þ

where n(x0) is the charge concentration at x ¼ x0. For the high-field case [2(bg)1=2 > 1], the solution is jDCC ﬃ menðx0 Þ expðgx0 b=x0 Þp1=2 ðkT =ebÞ1=4 F 3=4 h i exp 2ðbe=kT Þ1=2 F 1=2 ð231Þ

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To the constant factor (with gx0 1), they are identical with Eqs. (18) and (19) in Ref. 409, respectively, derived for diffusion-limited Schottky emission of electrons from a metallic cathode into the conduction band of an insulator. Also, they resemble the general drift current solutions (203) and (205), though an important difference can be noted due to the mobility appearing in Eqs. (230) and (231). This would be of crucial importance if the mobility were an electric field-dependent quantity (cf. Sec. 4.6). Equation (231) gives the current for the extreme case in which the current in the insulator is diffusion controlled, while the drift current, Eq. (203), represents the greatest current that can flow across the interface. The ratio of these two currents, j=jDCC, must be greater than unity for the current to be diffusion controlled. Using Eqs. (203) and (231) for the high-field current regimes with a strong-gradient source currents, js(x), this condition can be expressed through the minimum carrier injection rate Zinj ¼

h i j0 mkT 1=2 > exp 2 ð b= l Þ gx b= x 0 0 enðx0 Þl ep1=2 b1=4 l7=4 ð232Þ

As expected, the limiting value of Zinj strongly depends on the relation between b, l and x0 and increases with increasing mobility and temperature. For typical room-temperature mobilities on the level of 104 cm2=V s, b ¼ 4.7 nm [resulting from (201) with e ¼ 3], l ¼ 0.2 nm (cf. Table 5) and x0 ¼ 1 nm (one molecular distance, roughly), the minimum injection rate ðlimÞ Zinj ﬃ 4 108 s1. The physical meaning of the condition (232) consists in the formation of the sufficient carrier concentration gradient [dn(x)=dx] in order that diffusion currents play the dominating role in Eq. (198). But, it cannot be too large that not to make the current space-charge-limited. We note that the limiting value of Zinj [Eq. (232)] contains the strength of the electric field applied to the sample through the quantity g (201). In the above calculation example, F ¼ 106 V=cm has been used. It follows readily from (232) that for lower fields ðlimÞ (lower g), the limiting value of Zinj increases (Zinj ﬃ 1010 s1 at F ¼ 105 V=cm). A larger injection efficiency is needed in Copyright © 2005 by Marcel Dekker

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order that the drift current exceeds the DCC at low fields. The ðlimÞ field dependence of Zinj follows from the functional shape of jDCC (231) which shows that, in general, log jDCC vs. F1=2 plot may not be a straight line, and only for gx0 1, this might be the case. This condition with x0 < 0.25 nm at F ¼ 106 V=cm ðlimÞ and T ﬃ 300 K leads to a very low value of Zinj . Summarizing, we have seen that the carrier diffusion can change the Schottky (one-dimensional Onsager)-type behavior of the injection current-field characteristic (203) by a field-dependent factor exp(gx0) ¼ exp[(eF=kT) x0] (unless g x0 1), and this could be one of the reasons of the high-field regime deviations of the experimental plots of log ( j=F3=4) vs. F1=2 from the theoretical predictions of Eq. (203). Another reason for them would be a field-dependent mobility m(F), the case discussed in Sec. 4.6.

4.5. DOUBLE INJECTION To manufacture an organic LED functioning on the basis of electron–hole recombination processes, a system of organic films has to be provided with two injecting contacts, one injecting electrons, another injecting holes (cf. Sec. 4.2). Description of electrical properties of such systems is much more complex than that for systems with one injecting contact (see Secs. 4.3 and 4.4) because the recombination current adds to the drift and diffusion currents flowing between electrodes through the sample [410]. The total current density may be orders of magnitude larger than with single injection, although the positive and negative net space charges situated at the respective electrodes are roughly equal to the one-carrier space charge connected with current flow. The generally valid equation governing double-injection current in the presence of space charge has been derived by Parmenter and Ruppel [411]. They solved the system of the following equations: j ¼ e½me ne ðxÞ þ mh nh ðxÞFðxÞ ¼ independent of x dF e0 e ¼ eðnh ne Þ dx Copyright © 2005 by Marcel Dekker

ð233Þ

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me

d d ðne FÞ ¼ mh ðnh FÞ ¼ geh ne nh dx dx

Zd

FðxÞ dx ¼ U

ð234Þ

0

where subscripts e and h for carrier concentrations ne and nh refer to electrons and holes, respectively. Except for Eq. (234), all these equations have their analogs in unipolar injection. For two Ohmic contacts, that is with the boundary conditions Fð0Þ ¼ FðdÞ ¼ 0;

nh ð0Þ ¼ ne ðdÞ ¼ 1

ð235Þ

and for trap-free (or shallow trap) case, the current density fulfilling Eqs. (233) and (234) may be written as [334] 9 j ¼ e0 e meff F 2 =d 8

ð236Þ

It is identical with Eq. (168a) except for the mobility which in the double-injection case is a complex combination of individual electron (me) and hole (mh) mobilities, including so called recombination mobility (m0), 2 2 2 ðð3=2Þ½n e þ n h 1Þ! meff ¼ m0 n e n h 3 ðð3=2Þn e 1Þ!ðð3=2Þn h 1Þ! ð237Þ ðn e 1Þ!ðn h 1Þ! 3 ðn e þ n h 1Þ! The term m0, having dimension of the mobility, is defined by m0 ¼

e0 egeh 2e

ð238Þ

and the dimensionless parameters n e and n h are defined by n e ¼ me =m0

and n h ¼ mh =m0

ð239Þ

Let us note that the introduction of m0 accounts for the recombination effect on the current. Its relation to the carrier Copyright © 2005 by Marcel Dekker

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mobilities allows to distinguish three limiting cases for the SCL double-injection current flow. These are (i) Injected plasma (or weak recombination) case for n e 1 and n h 1, with a large space-charge overlap, interpenetrating electrons and holes mostly reach opposite electrodes. Equation (237) reduces to 2 meff ﬃ ½2pðme mh =m0 Þðme þ mh Þ1=2 3

ð240Þ

An organic LED operating under such conditions should show emission from the entire emitter bulk as the recombination occurs on the total carriers paths equal to the emitter thickness, d. The recombination zone width w d (see Sec. 3.3). (ii) Volume-controlled current (or strong recombination case) for n e 1 and n h 1. This is the case of negligible space-charge overlap with meff ﬃ me þ mh

ð241Þ

Here, the requirement of high values of the electron–hole recombination coefficient requires double injection from two Ohmic contacts to produce two SCL currents meeting and annihilating each other somewhere in the emitter within a narrow recombination zone (w d). (iii) One-carrier SCLC flow for n e 1, n h 1 (or n e 1, n h 1). Equation (237) may then be reduced to meff ﬃ me ðor mh Þ

ð242Þ

dependent on which of the above inequality pairs are fulfilled. The current is practically one-carrier SCL current, the less mobile carriers recombining very near the electrode from which they are injected. The recombination zone is expected to locate towards the low mobility carrier injecting electrode. It is interesting to note that in the Langevin recombination mechanism with the geh expressed by the sum of the individual carrier mobilities (4), the interrelation between n e,h and m0 switches to the relations between electron and hole Copyright © 2005 by Marcel Dekker

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mobilities themselves. For instance, the strong recombination case can be defined by either ne ¼

me 2 m ¼ 1 that is h 1 m0 1 þ mh =me me ð243Þ

or nh ¼

mh 2 m ¼ 1 that is e 1 m0 1 þ me =mh mh

if the expression (4) for geh is inserted into Eqs. (238) and (239). This means that the strong-recombination case can be observed whenever me differs substantially from mh. For me ¼ mh, n e (n h) ¼ 1, we deal with an intermediate case between (i) and (ii). An excellent system to observe the strong recombination double injection is a DL LED with an interface blocking passage of charge carriers across the LED. For example, the confinement of the recombination to a narrow zone located in the Alq3 close to the TPD=Alq3 interface of the TPD HTL and Alq3 ETL based LED makes the current flowing through the device equivalent to the recombination current supplied by two quasi-Ohmic electrodes injecting holes at the ITO=TPD and electrons at the Mg=Alq3 contacts, as discussed already in Sec. 3.3. Even better example is given by an electrophosphorescent DL LED with a strongly hole blocking layer described in Fig. 67. The high-field segment of its current-field characteristic can be approximated by Eq. (236) with e ¼ 3 and meff ¼ 3.7 106 cm2=V s ¼ const throughout the square field dependence of the current. Since the EL spectrum of this LED is underlain by the emission of Ir(ppy)3 dispersed in its HTL [6% Ir(ppy)3:20% PC:74% TPD] [304], the recombination zone is most probably located in the HTL close to the interface with the PBD ETL. From the energy level scheme, it follows that molecules of Ir(ppy)3 do not form hole traps so that the hole mobility in the HTL should be on the order of hole mobility of a film composed of 74% of TPD and 26% of PC. The time-of-flight mobility data give an order of 104 cm2=V s for films between 50% and 80% content of TPD at room temperature [338] is two orders of magnitude higher than the above calculated meff. This would suggest that Copyright © 2005 by Marcel Dekker

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molecules of the organic phosphor Ir(ppy)3 act as polar species which increase disorder parameters of the organic film, reducing strongly the hole mobility (see Sec. 4.6). The presence of active charge traps can change the above picture entirely. Of importance becomes the relation between the average trapping time (tt) of the carriers, the average thermal release time (trel) of the carriers from traps and their average recombination time (trec). For active (sufficiently deep) traps, the condition trel tt is usually fulfilled, otherwise trapping would be negligible. Three extreme cases can be considered taking in addition various relations of these times with respect to trec: (A)trec trel, tt. In this case, the Parmenter–Ruppel equation (236) is still basically valid provided the mobilities are replaced by effective mobilities controlled by discrete traps, meff ¼ Y m. If each of single-carrier currents are characteristic of an exponential trap distribution [Eq. (175)], the doubly injected current varies in the same way but is larger by orders of magnitude (see e.g. Fig. 64b). Moreover, the thickness dependence of the current does not follow that resulting from Eq. (175). It is usually less steep than d(2n1) with n determined by the voltage dependence of j Un (Refs. 412 and 413) or j does not show any monotonic decrease with d [414,415]. Figure 91 shows an example for anthracene crystals provided with different hole injecting anodes and electron injecting cathodes. The main problem in verifying the thickness dependence of the double (also single) injection current is dealing with different samples which can differ in the concentration of traps and trap distribution function, and separately deposited injection contacts with injection efficiencies which may differ from sample to sample. The example in Fig. 91 seems to alleviate this problem since a number of parallel diodes were made by cleaving a number of ‘‘staircase shaped’’ single crystal specimens from the same Bridgman method grown boule. A common indium anode contact was used on each specimen and individual sodium–anthracene complex cathodes prepared by dropping a small quantity of the sodium complex in solution onto the crystal under an argon atmosphere (sideways spreading was constrained by a Copyright © 2005 by Marcel Dekker

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Figure 91 (a) Current–voltage characteristics of double injection currents for a single anthracene crystal diode employing a carbon fibre cathode (), and partly oxidized sodium anthracene cathode (o). (b) Thickness dependence of the current for anthracene crystals provided with indium anode and sodium anthracene cathode. After Ref. 412.

ridge of nitrocellulose applied prior to dropping the solution). In the moderate field regime j Un was found with the exponent ranged from 6 to 12 for a series of cells employing both a carbon fiber and anthracene–sodium complex cathode. In the high-field regime j U3=d4. Clearly, the relation Un=d2n1 [cf. Eq. (175)] is not obeyed. Also, a weak thickness dependence of the double injection current within the moderate field regime has been observed (see Fig. 69b; see also Ref. 414). This would support a conclusion that even individually strong injecting electrodes are unable to supply volumecontrolled currents in a double contact combination to anthracene or Alq3. Indeed, the j(F) dependence for double-injection currents using ITO=TPD=Alq3: DPP=Mg LEDs can be well Copyright © 2005 by Marcel Dekker

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described by ILC flow as presented in Fig. 76 and discussed in Sec. 4.6. An alternative would be the application of the macrotrap model for carrier trapping, which predicts j Un=dnþ1 (185) with n reflecting the macrotrap potential shape. This potential consists of two branches (Fig. 72) reflected in the experiment by two different steeps of the log j–log U plots as can be seen in Figs. 71 and 91 (the low-field linear part due to the Ohmic conduction precedes superlinear segments). In contrast to anthracene, j(F) curves for double injection current into tetracene crystals follow well SCLC behavior for single injection (see Fig. 64, also Refs. 41 and 416). In the high-field regime, they can be well described by the relationship j Fn=dn1 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 lower injection barrier for holes from gold (Au) into tetracene; DEh ¼ I WAu ¼ [5.4 (4.785.3)] eV ﬃ 0.10.62 eV than into anthracene DEh ﬃ 0.61.12 eV with I ¼ 5.9 eV (for the values of I, see Ref. 26; the work functions for gold are taken from Ref. 417). However, similar concentrations and energy distributions for electrons and holes in this crystal might be of importance for the voltage evolution of the double injection current ðBÞ trel trec ttrap

and

ðCÞ trel ; ttrap trec

In these two deep trapping cases, the trap filled limits in the SCLCs would be expected (cf. Sec. 4.3.1), and a splitting of the recombination zone in two layers in front of the electrodes in case (B) anticipated. The situation becomes even more complex if traps are concentrated in front of the electrodes, the case very probable due to the exposition of sample surface to the ambient atmosphere during sample handling and deposition of the electrodes. A striking example of a complex recombination zone due to inhomogeneous trapping effects in organic crystals can bee seen in Fig. 58. A more detailed discussion of the spatial distribution of the EL emission, from organic crystals, and its evolution with applied field and injection efficiency of the contacts has been given by Kalinowski [41]. Copyright © 2005 by Marcel Dekker

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Unfortunately, however, though some electrical and optical characteristics can be explained or made plausible by qualitative considerations, ‘‘proofs’’ on this basis are very difficult as the identification of the terms in the equations selected is often not unique and the results obtained depend upon the particular assumptions and simplifications made. 4.6. CHARGE CARRIER MOBILITY Electrical characteristics of organic LEDs are inevitably associated with mobility of charge carriers in materials used for their fabrication. The mobility defined as a carrier drift velocity (v) per unit applied electric field me;h ¼ ue;h =F

ð244Þ

can be determined from various experiments, the time-offlight (TOF) technique being most commonly used as it directly provides drift velocities [250,418–421]. In the TOF method charge carriers pairs are created in a photoconductor, near the surface of a plane-parallel sample sandwiched between two planar electrodes, by absorption of a short pulse of light of sufficient photon energy, admitted through the semitransparent front electrode. Depending on the polarity of the field established (F ¼ U=d) by applying a voltage difference (U) between the front and rear electrode (separated by a distance d), a ‘‘sheet’’ of electrons or holes is pulled across the sample at a velocity ve,h. In the external circuit, the drifting charge, q, is manifested as a constant current, ie,h ¼ qme,hF=d flows, coupled by the displacement current, which drops to 0 when moving carriers have been collected (or stopped near) by the rear electrode. The average travel time, tt, read from the duration of an (ideally) rectangular TOF pulse on an oscilloscope display, is thus direct measure of the average drift velocity ve,h of the carriers, ve,h ¼ d=te,h. From the current pulse amplitude, the charge generation efficiency, Zq ¼ q=eI0, can also be derived, if the excitation intensity, I0, is not too high as to deform the electric field within the sample through the injected charge. For a strongly absorbed light pulse of Copyright © 2005 by Marcel Dekker

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duration dt tt, and fast carrier generation process, the carrier sheet has a width dl d. This width is increased during travel by diffusion and Coulombic repulsion broadening [422]. If trapping losses of carriers on their way to the collecting electrode are not too severe, an arrival kink on the TOF pulse will still be seen and used to determine the travel time of the carrier sheet. Strong deviations from ideal rectangular pulse are frequently observed with disordered solids because carriers propagating through the solid experience a distribution of hopping times. Then, the current pulse is characterized by a rather featureless decay. The featureless current pulse indicates a widespread of the carrier packet as it arrives at the collecting electrode. In fact, it is so wide that it no longer exhibits the Gaussian spread but is asymmetrically skewed, with a leading edge penetrating into the bulk and a sharp cut off on the backside of the packet. Such current traces have become known as being indicative of ‘‘dispersive transport’’. A successful interpretation of dispersive transport has been presented by Scher and Montroll [32]. They assumed a carrier hopping in a three-dimensional random array of isoenergetic sites, and derived the time dependence of the transient current in the form ð1aÞ for t < tt t ð245Þ iðtÞ ð1þaÞ t for t > tt with the temperature (T) and sample thickness (d) dependent transit time tt ½d=lðFÞ1=a expðD0 =kTÞ

ð246Þ

where 0 < a, l is a dispersion parameter (denoted earlier by b and discussed in Sec. 1.3). The more disordered system, the smaller the a-value and from Eqs. (245) and (246), the more dispersive the current shape and the stronger the thickness and field dependence, the latter entering Eq. (246) through the field-dependent mean displacement l(F) in field direction per hop. The natural consequence of relations (245) are two regimes of slopes (1 a) and (1 þ a) that occur on log–log displays of current against time. Because a is a constant with Copyright © 2005 by Marcel Dekker

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respect to applied field and specimen thickness, this characteristic implies universality of pulse shape on normalized current and time axes. Since, by definition, the hopping is a thermally activated process, the transit time decreases with temperature, thus, the carrier mobility increases with the zero-field activation energy, D0. A spread of the activation energy of the hopping carriers, resulting from the diagonal disorder (see discussion later on), implies a temperature dependence of the dispersion parameter [see Eq. (9)]. With temperature decreasing, one expects from (245) and (246), and (9) the shape of the transient current pulse to become more dispersive (more featureless). Observations consistent with all the above expectations are presented in the widespread literature for both organic and inorganic solids. A typical example is shown in Fig. 92. Almost non-dispersive transport of holes in amorphous selenium at room temperature becomes dispersive at lower temperatures. For example, the highly dispersive transport at 123 K, which does not create any particular feature on the current pulse in the linear scale, shows a pronounced bend at t ¼ tt in the double logarithmic scale, dividing the current decay into two branches according to relations (245). A recently published work on Alq3 shows the importance of traps produced by oxygen and impurities for the transient current shape [423]. In Fig. 93, TOF electron transients in a linear and double logarithmic scale representations are shown for diverse samples of Alq3. The samples as-received from the supplier and exposed to ambient behave highly dispersive, after purification exhibits well-resolved features of non-dispersive transport. The mobility has been determined from the relationship (244) with ve ¼ d=tt, where tt is the transit time taken as the time at which the photocurrent dropped to half of its plateau value [421] for non-dispersive transients (purified sample), and from the inflection point on a log i–log t plot [424] for dispersive transients with the as-received Alq3 sample. Interestingly, the mean values and the Poole–Frenkel like field dependence of such determined mobility are in both cases identical except for a stronger degree of variation in successive experiments with the as-received material. The Copyright © 2005 by Marcel Dekker

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Figure 92 Typical transient current pulses for holes in amorphous selenium (see Ref. 422a), illustrating the effect of temperature on the degree of the dispersion in carrier transport. Left: linear current (i) and time (t) axes; right: normalized values in logarithmic axes log(i=i0) vs. log (t=t0). The arrows indicate the position of the ‘‘knee’’ dividing the two regimes of logarithmic dependence. Similar behavior can be observed in organic solids (see e.g. Ref. 422b).

experimental data fulfilled the Poole–Frenkel type function me ¼ meo exp(bm F1=2) with meo ¼ 2.9 109 cm2=v s and bm ¼ 7.3 103 (cm=V)1=2 in accordance with some other literature values [336,340,341,425]. Copyright © 2005 by Marcel Dekker

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Figure 93 Transient photocurrent signals (i) for 8 mm thick Alq3 layers sandwiched between the ITO anode and Al cathode. Light pulses entered the samples through the ITO anode. The change from the dispersive transport for Alq3 as-received from the supplier (circles) to the non-dispersive transport with purified (squares) Alq3 samples. It can be seen in both linear (a) and double logarithmic (b) plots. In the inset of part (a) electric field dependence of mobility is shown, in part (b) the TOF transient for as-received Alq3 exposed to ambient is added (diamonds). After Ref. 423. Copyright 2003 American Institute of Physics, with permission.

The xerographic discharge modification of the TOF technique is often used for the samples prepared in the form of thin films cast or evaporated on conductive substrates (see e.g. Ref 424). The free sample surface is charged with a corona to surface potential V0, and the change in the surface potential V(t) following a flash of strongly absorbed light is observed. The absorbed photons generate charge carriers in a thin layer close to the charged surface, where they can decay in the bimolecular recombination process or neutralize the surface charge due to opposite free carriers drifting to the substrate. At low light intensities (the change in the surface potential is small compared to V0), the initial rate of the potential change (dV=dt)t ¼ 0 ¼ ZqeI0=C (C is the capacitance of the sample) provides a direct measure of the injection quantum efficiency (Zq) that is the number of free carriers emitted into the sample bulk per absorbed photon. To obtain the drift mobility from a xerographic disCopyright © 2005 by Marcel Dekker

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charge measurement, the photoinduced discharge has to be driven under SCLC conditions, that is the number of injected carriers has to be approximately equal to the capacitor charge CV0. The motion of the space charge makes the electric field F(d,t) on the exit electrode (x ¼ d) to increase above its initial value F0(d,t¼0) ¼ U=d. Combining the drift and displacement currents with the Poisson equation, yields [426,427] F ðd; tÞ ¼

2d 1 m 2t0 t

ð247Þ

where t0 ¼ d2 =mU

ð248Þ

is the transit time of carriers traversing a sample thickness d, with applied voltage U, in the absence of space charge. The time t1 when the front R arrives at this electrode is t obtained from the equation 01 mF ðd; tÞ dt ¼ d which after integration with (247) yields t1 ﬃ 0.8t0. As expected, the t1 is shorter than the transit time t0 (248) in the absence of space charge. Using Eq. (247), the time evolution of the current density for t < t1 can be obtained in the following form: jðtÞ ¼

2de0 e 1 m ð2t0 tÞ2

ð249Þ

Comparison with Child’s current (168a), here denoted as j1, shows that current begins with j(t ¼ 0) ¼ 0.44 j1 and rises to j(t ¼ t1) ¼ 1.21j1. Since the current for t > t1 has to drop to j1, its time evolution should show a spike at t ¼ t1 as illustrated in Fig. 94. We note that the SCL charge injection transients can be induced either by a strong light flash generated carriers or a step-like voltage applied to the injecting (Ohmic) electrode in the dark. The latter is exemplified by the top curve of Fig. 94b. For comparison, a small signal lightinduced transient current shown in the bottom of this figure exhibits a shape typical for non-dispersive transport of holes Copyright © 2005 by Marcel Dekker

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Figure 94 (a) The SCL transient currents for various normalized trapping times (R ¼ ttrap=t0) as calculated from theory (see Ref. 26); R ¼ 1 denotes the trap-free case; j1 is the steady-state current without trapping. (b) t1: trap-free SCL transient current injected from ITO under a positive step voltage applied to an ITO=PPV=TPD:PC=Al device: jSCL corresponds to j1 in part (a). Bottom: TOF photocurrent transient for holes generated by a light pulse at the Al=(TPD:PC) interface (the negative polarity applied to ITO). (From Ref. 428).

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in TPD:PC systems. This indicates the TPD dispersed in the PC matrix to form almost trap-free organic films, and, therefore, the SCL transient current in Fig. 94b (top) can be considered as an example of trap-free SCL currents predicted by the theoretical curve with R ¼ 1 in Fig. 94a. From the same figure, one can see that the stronger trapping (decreasing R) is the discontinuity of pulse slope becoming less and less pronounced, disappearing when the trapping time drops below 0.5t0. In other words, the current decay under strong trapping (but negligible detrapping) means the carrier schubweg to be shorter than the sample thickness. A completely different situation arises if both trapping and detrapping are much faster than free carrier transit. Then the current transient is determined by the effective mobility meff ¼ Ym with the possible exception of a very short ‘‘trap-free’’ interval at the beginning where a peak might appear if a duration of light flashes are comparable to the trapping time. The SCL transients should be distinguished from SCL sheet currents that is current flows after momentary Ohmic injection which may occur if a flash of duration much shorter than the transit time is 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] 1 U2 jðtÞ ¼ e0 e m 3 expðt=t0 Þ 4 d

ð250Þ

for t < t2—the time at which the leading front of the spacecharge sheet reaches the exit electrode. It has been shown that t2 ﬃ 0.8t0 (Ref. 429) which may lead to a confusion with SCL current transients. Though in both cases a current cusp appears at t ﬃ 0.8t0, the difference is apparent in the functional shape of the current increase for t < 0.8 t0. Time-of-flight experiments have been used for over three decades to characterize carrier mobilities in crystal, and polycrystalline and disordered organic solids including molecularly doped polymers and molecular glasses [28,424,430,431]. Relatively high values (up to several hundreds cm2=V s) and hot carrier effects have been observed in Copyright © 2005 by Marcel Dekker

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single van der Waals bonded crystals [420,432–436]. Characteristic is a strong electric-field dependence of the mobility. Figure 95 shows a few examples of the drift velocity (vdrif) as a function of electric field (F) at different temperatures. At low-fields vdrift depends linearly on F, increases sublinearly at intermediate fields, and saturates at high electric fields. This means the low-field constant mobility, as follows from the definition Eq. (244), to decrease with increasing field. The sublinear dependence of vdrift can be associated with acoustic phonon scattering of carriers; the model predicting [420]

udrift

8 9 " #1=2 =1=2 pﬃﬃﬃ < 3p m0 F 2 ¼ m0 2F 1 þ 1 þ : ; 8 C1

ð251Þ

where C1 is the longitudinal sound velocity and m0 is the lowfield mobility. The high-field saturation of the carrier velocity can have various origins, e.g. a finite bandwidth of a non-parabolic transporting (here valence) bands, or the emission of optical phonons. It is believed that the high-field saturation of the drift carrier velocity in the crystal directions where the band model concept can be applied is due to the first one. Then [420], ðsatÞ

udrift ¼ 0:724

Wa0 p h

ð252Þ

where a0 is the lattice constant in the direction of the charge transport, and W is the transport bandwidth. On the other hand, for the transport along narrow-band directions, as for instance along the c0 direction in anthracene at room temperature, it is attributed to the second origin, the charge carrier is accelerated by the electric field until it has gained enough kinetic energy m v2drift =2 (m is the effective mass of the charge carrier) to emit an optical phonon. In the case of anthracene crystal, this is associated with excitation of the intramolecular vibration 395 cm1 [432]. The temperature dependence of the mobility in two selected organic Copyright © 2005 by Marcel Dekker

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Figure 95 (a) Hole drift velocity in naphthalene (see Ref. 28) and (b) anthracene (see Ref. 432) crystals at different temperatures (given in the figure). For naphthalene, the drift velocity has been determined in the crystallographic a-direction (Eka) and for anthracene in crystallographic c0 -direction (Ekc0 ).

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crystals is shown in Fig. 96. At low temperatures, the mobility is dominated by the effect of shallow traps and impurity scattering, and hence a strong dependence on purity and quality of the crystals. The activation energy of thermally activated mobilities in the low temperature range can be identified with discrete trap depths (17.5 meV for electron traps in perylene, and less than 8 meV for hole traps in anthracene crystals). In the samples with the highest quality, the effect of shallow traps can be excluded and the mobility levels off at low temperatures, (open circles in Fig. 96b). This indicates scattering at neutral impurities [437]. At higher temperatures, the electron–lattice coupling (a generalized polaronic effect) has to be taken into account which leads to

Figure 96 Temperature dependence of the charge carrier mobility in organic single crystals. (a) The electron mobility in a crystal grown from moderately purified perylene (see Ref. 28), and (b) the electron (m) and hole (mþ) mobilities in synthetic ultrapurified anthracene crystals at an electric field E ¼ 2.3104 V=cm directed along the crystallographic axes b (adapted from Ref. 436a). Copyright © 2005 by Marcel Dekker

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the temperature narrowing of the bandwidth according to [438,439] ho=2kT Þ W ¼ 4jJ j exp½g2 cot hð

ð253Þ

where J is the nearest-neighbor transfer integral, g is a dimensionless electron–phonon coupling constant, and ho is the energy of phonons excited at the temperature T. Clearly, the narrowing of the bandwidth leads to decreasing drift velocity (252) and mobility defined by Eq. (244). Beyond the trap-controlled transport region, the temperature dependence of the low-field mobility is often found to obey a power law me,h Tn with 1 < n < 3. [28] (see also examples in Fig. 96). Acoustic-phonon scattering in the wide band limit (W > kT) leads to a T1 or T1.5 dependence resulting from the description of charge carriers as extended Bloch states represented by the electron wave packets, characterized by their mean free path exceeding the average distance between two lattice sites (molecules) [440]. The powers 1 and 1.5 reflect two different extreme cases for the statistical distribution of electrons, the first for a step-like Fermi–Dirac function, and the second for the Maxwell–Boltzmann function (see e.g. Ref. 441). To explain the Tn behavior with n > 1.5, the combination of acoustic and optic deformationpotential scattering might be useful [441a]. The band transport picture will break down if the carrier transporting bands become too narrow. The temperature dependence changes from a power-law to an almost temperature-independent or slightly activated dependence. At high temperatures, the saturation of the carrier velocity is absent, and dramatic trapping effects on mobility observed even at high temperatures (see Fig. 97). This is the case when the charge carriers become localized by the polaronic interactions, and a ‘‘lattice polaron’’ is formed. A transition from coherent bandlike motion to incoherent hopping transport would be expected from theoretical considerations [435,436]. The experimental results do not show such an abrupt transition, the mobility might be seen as a superposition, m ¼ mcoh þ mincoh, where mcoh is the mobility of the coherent band-like transport, Copyright © 2005 by Marcel Dekker

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Figure 97 Arrhenius plot of electron and hole mobilities in the crystallographic c0 direction of a well-purified anthracene crystal (a) and for a 4 107 mol tetracane-doped anthracene crystal (b). After Ref. 442. Copyright 1975 Wiley-VCH, with permission.

and mincoh that of the incoherent hopping motion [443]. The presence of traps makes the effective mobility (meff) to be dependent on the time spent by a carrier in the trap and can be expressed by Karl [28] meff ¼ fCh ½1 þ ðCt =Ch Þ expðEt =kTÞg1

ð254Þ

where Et is the depth of traps, and Ch ¼ Nh=N and Ct ¼ Nt=N denote the fractions of host material molecules (Nh) and traps (Nt) with respect to their total number N ¼ Nh þ Nt. For sufficiently deep traps [Et > kT ln (Ch=Ct)], Eq. (254) becomes an Arrhenius-type function with the activation energy corresponding to the depth of traps. This can be seen in Fig. 97b, where the straight-line segments of the Arrhenius plots give Et ¼ 0.17 eV for electrons and Et ¼ 0.42 eV for holes trapped by tetracene molecules incorporated in anthracene crystal lattice. A nearly temperatureindependent mobility of both holes and electrons can be found in polycrystalline films [430,444–446]. Being represented by the Arrhenius-type function, it exhibits small activation Copyright © 2005 by Marcel Dekker

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energies on the level of tens of millielectronvolts (an example is shown in Fig. 98). This temperature behavior in polycrystalline samples can be interpreted in the general framework of the stochastic theory of dispersive transport independent of the details of any specific mechanisms underlying a broad distribution of event times. These event times can be hopping times, trap release times, or both simultaneously [447]. It has been already discussed above that for the case of hopping motion the field and temperature dependence can be related to the transit time expressed by Eq. (246), completed by a field-dependent activation energy D ¼ D0 eaðtÞF

ð255Þ

where the lattice parameter a(T) is only mildly temperature dependent. D0 is the activation energy extrapolated to zero field. The effect of electric field on the activation energy for fields F < 105 V=cm (as in Fig. 98) and a on the order 1 nm does not exceed 30%, and falls often in the range of spread of the experimental values of D for different samples. The

Figure 98 Temperature dependence of TOF-measured hole and electron mobilities in polycrystalline films of p-terphenyl (a) and p-quaterphenyl (b). The sample thicknesses have been chosen from the range 12–18 mm. The values of the activation energy are given above each of the Arrhenius plots. After Ref. 430. Copyright © 2005 by Marcel Dekker

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mobility data for polycrystalline samples composed of microcrystallites characterized by broad transporting bands can be understood in terms of the standard multiple-trap transport including a spectrum of release rates (to the band) from a distribution of trap levels and assuming the mean displacement between traps equal to the average distance, m0ttrapF, the carrier moves in the band before it is retrapped. This is equivalent to a random walk on a lattice, where the lattice spacing in the direction of the electric field is field dependent, namely, a ¼ m0ttrapF, where m0 is the microscopic mobility of carriers in the band, and ttrap is the free carrier trapping time. Assuming that all traps have the same capture crosssection, the time evolution of the current, i(t), can be associated with the distribution function of release times, and expressed in the form iðtÞ ¼ i0 að1 aÞðntt Þ2a ðntÞð1þaÞ

ð256Þ

where i0 is the current at t ¼ 0, n is the attempt-to-escape rate, and tt is the transit time defined by Ztt

1 mðtÞFdt ¼ d 2

ð257Þ

0

This equation identifies the transit time as a time at which the leading edge of the charge packet reaches the rear contact located at a distance d from the injecting one, which occurs when the center of gravity is roughly halfway across. Equation (256) has been derived with an assumption that the trap energies are distributed exponentially below the limiting edge of the transporting bands [448]. The dispersion parameter a is then simply related to the distribution parameter l ¼ a1 ¼ Tc=T [cf. Eq. (170)]. The time dependence in Eq. (256) matches the Shear–Montroll result (245). The large-time range TOF experiments show a to be a time-dependent parameter [449,450]: a ﬃ 0.0 within a short-time regime (0.1 ms < t < 10 ms), and a ! 1 for t < 10 ms. The charge of log i–log t plot slopes is gradual—nearly three orders of magnitude. These features indicate a transition in i(t) from a Copyright © 2005 by Marcel Dekker

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highly dispersive transport to an essentially non-dispersive during a single transit. This, in turn, allows to infer from a(t) information about the real trap distribution. Two examples of such a procedure are described by Muller-Horsche et al. [449] and Di Marco et al. [450]. The procedure is based on the conjecture that [449] aðln tÞ ¼

ln½hðEd Þ=hðE ¼ 0Þ ln½rðEd Þ=n

ð258Þ

where h(Ed) ¼ h(E ¼ 0) exp(a Ed=kT) [cf. Eq. (170)], and rðEd Þ ¼ n expðEd =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 attemptto-escape rate. This energy separates those states above Ed(t) for which the most probable number of release events in the time t is greater than unity, from the deeper states where a carrier 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 tangent to the experimental log i(t) vs. log t curves and (Eqs. (258)–(260), h(E) has been calculated for polyvinylcarbazole solution cast films [449] and vacuum-evaporated polycrystalline film of thionaphtenoindole [450]. The latter is shown in Fig. 99. The general features of the distribution f (E) ¼ h(E)=h0 are: (i) f(E) is flat (Tc T) for E < 0.395 eV, and (ii) there is a cut-off of f(E) at E > 0.4 eV, indicating a quasi-exponential decrease of the trap density with kTc ﬃ 0.054 eV. The gradual decrease in the dispersion of the charge transport corresponds to the quasi-exponential range of f(E) (0.135 eV > kTc > 0.033 eV) with an energy range less than 0.1 eV wide. Weakly dispersive transport takes place over a time range about one decade prior to tt. The restriction of i(t) measurements to this time range would lead to erroneous conclusion that there is a narrow range of exponentially distributed trap energies instead of the broad range with a Copyright © 2005 by Marcel Dekker

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Figure 99 The trap distribution function in evaporated polycrystalline films of thionaphtenoindole (TNI), calculated from Eq. (258), using time-dependent tangent of the experimental log i(t)–log t plots (See Ref. 450).

cut-off as shown in Fig. 99. The data for polycrystalline films of thionaphtenoindole provide an interesting example of the electric field-decreasing mobility (Fig. 100). Provided that real polycrystalline samples are subject of a spatially non-homogeneous distribution of traps near the sample surface and within intergrain boundaries, the pretransit time averaged carrier flux is composed of two comparable parts: one due to usual carrier drift in the external field and the second due to carrier diffusion [see Eq. (198) and Sec. 4.4]: j ¼ enmdrift eff F eDeff

dn dx

ð261Þ

where the effective drift mobility mdrift eff , the effective diffusion constant Deff and the carrier concentration, n, can be treated as pre-transit time averaged quantities. The measured effective mobility, meff, can be defined using Eq. (261) as 1 df ¼ mdrift meff ¼ mdrift eff þ udf F eff þ meff

Copyright © 2005 by Marcel Dekker

ð262Þ

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Figure 100 Effective mobility, as measured by the TOF technique in a 10 mm thick polycrystalline film of thionophtenoindole, plotted vs. 1=F (points). The solid line drawn according to Eq. (264), extrapolated by the dashed line to F ! 1 (see Ref. 450).

where vdf is the macroscopic diffusion velocity of the carriers: udf ¼

Deff dn n dx

ð263Þ

for sufficiently high electric fields (F ! 1), the second term in Eq. (262) vanishes and meff ! mdrift eff . However, in general, and especially at low fields, the measured mobility meff decreases with field as 1=F. We note that the electric field strength separates those Fc ¼ (kT=en)(dn=dx) ¼ 4.4 104 V cm1 effective diffusion mobilities which are greater than the effective drift mobility from their values smaller than mdrift eff , and thus Fc drift meff ¼ meff 1 þ ð264Þ F This result is useful in understanding the variation of the field dependence of the TOF measured mobility from sample to sample, following the carrier density gradients (Fc dn=dx). For example, the role of the diffusion carrier stream would explain the field dependence of m in single crystals whenever their near-surface layer is strongly populated Copyright © 2005 by Marcel Dekker

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with deep traps (see e.g. Ref. 451). On the other hand, one would not expect the macroscopic diffusion to affect significantly the mobility measured in amorphous films. Equation (264) could be successfully applied to the experimental mobility data for polycrystalline thionaphtenoindole films as illustrated in Fig. 100. From the intersect of the straight-line 2 5 plot of log meff vs. F1, mdrift eff ¼ 5 10 cm =V s follows, and its 1 slope gives vdf ¼ 2.2 cm s . Numerous measurements over a large range of electric fields and temperatures have established that, in many materials, the carrier mobility can be described by a universal law bearing the ‘‘Poole–Frenkel’’ like form of the electric field dependence m ¼ m0 expðY=kT Þ exp bm F 1=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 the activation energy Y and the parameter bm. For example, a temperature-independent value of Y and the ‘‘Poole–Frenkel’’ factor bm ¼ B(1=kT 1=kT0) with constant parameters B and T0, has been assumed by Gill [37], the mobility follows Arrhenius-type temperature dependence. The formalism based on the assumption that charge transfer occurs by hopping through a manifold of localized states characterized by a Gaussian distribution of energies and positions has led to Eq. (265) with a temperature-dependent activation energy Y ¼ (2s=3)2=kT and bm ¼ C[(2s=3kT)2 S2], where the constant C ﬃ 2.9 104 (cm=V)1=2, and s=kT and S are energy and position disorder parameters, respectively [29,39]. Since the energy of a molecule in a disordered solid state can be represented by a matrix in which the diagonal elements indicate the site energy of the molecule in the absence of resonance interaction with the surrounding medium, and offdiagonal elements represent the strength of resonance interaction between a molecule and its neighbors, the fluctuations in the site energies are usually referred to as diagonal disorder (parameter s=kT) and the fluctuations of the Copyright © 2005 by Marcel Dekker

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intersite coupling energies as off-diagonal disorder (parameter S). The meaning of disorder parameters is associated with a random distribution of site energies described by a Gaussian function of standard deviation s, and the intermolecular coupling parameter Gij ¼ Gi þ G ¼ 2ga, being a sum of two site specific contributions (Gi, Gj), each varying randomly according to a Gaussian probability pﬃﬃﬃdensity of standard deviation dG. The variance of Gij is S ¼ 2dG. The parameter S=2ga describes the relative local variations of nearest-neighbor intersite distances, or variations of the mutual orientations of non-spherical molecules. The parameter g has been already introduced in Sec. 2.4.1 [see Eq. (59)] and characterizes the degree of the wavefunction overlap between nearest-neighbor molecules separated by a distance a. The temperature dependence of the activation energy in this formalism predicts the mobility (265) to obey a non-Arrhenius-type temperature behavior m expf[(2=3)2 CF1=2](s=kT)2g. In the last several years, the mobility has been discussed in terms of the carrier motion in a spatially correlated random potential underlain by the interaction of charge carriers with randomly distributed permanent dipoles of the dopant or host material [452–460]. The general functional form of Eq. (265) is still preserved in this model, but the field dependence of m0(F) must be included. In the 1D analysis m0(F) ¼ m0(ps=kT)1=2 (eFa=kT)1=4, and Y ¼ s2=kT and bm ¼ (2s=kT)(ea=kT)1=2 (see e.g. Ref. 458). The field-independent exp(Y=kT) in (265) supports the quadratic temperature dependence associated with Gaussian disorder model, but omits the factor 2=3 that appears in this model. Observation of such a behavior of mobility requires enough energetic disorder so that 2s=kT > (eaF=kT)1=2. At higher fields, the mobility will depend more critically on the actual form of the microscopic hopping rate, and on the way in which detailed balance is implemented. In the Gaussian disorder model site energies are distributed independently, with no correlations occurring over any length scale. Consequently, the field dependence in this model agrees with (265) only over a very narrow range at high fields (F > 3 105 V=cm) [461]. A 3D version of the disorder model including spatial correlations due to charge–dipole interactions Copyright © 2005 by Marcel Dekker

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leads to Y ¼ (3=5sd)2=kT, and bm ¼ C0[(sd=kT)3=2 G](ea=sd)1=2], where C0 ¼ 0.78, G ¼ 2 [460]. The site energy distribution in this model is shown to be approximately Gaussian, with width [462,463] sd ðeVÞ ¼ 7:04 p=ea2

ð266Þ

This parameter characterizes the randomness of the orientations of dipole moments p (in Debye) placed on each site of a cubic ˚ ). In Fig. 101, the results of Montelattice of cell spacing a (in A Carlo simulations are presented for the carrier mobility according to the correlated disorder model along with those based on the Gaussian disorder model. The main difference between the two models is the range of electric fields over which Poole–Frenkel type behavior occurs. The Gaussian disorder model approximates the PF mobility behavior in the high-field regime (around 106 V=cm), the former fits to the PF-type function over a wide field range. In the Gaussian disorder model, the mobility at low fields is almost parabolic when plotted vs. F1=2. This suggests that at low-to-intermediate fields, the mobility is better described by a log m F=kT law rather than by (265) as has been observed for some molecularly doped polymers in the field range (105–5 105)V=cm [338]. However, substantial deviations from this behavior are noted below 105 V=cm. A broad field-range TOF mobility data in these materials have been successfully explained using the macrotrap model discussed in Sec. 4.3.1 in connection with space-charge-injection currents. The formation of macrotraps can be considered as a result of correlations between individual microtraps (local energy sites) distributed exponentially in energy, creating potential wells described by Eq. (181). The potential barrier for the carriers localized in such neutral macrotraps (spatially extended trapping domains) can be effectively lowered by an external electric field, making the mobility and its thermal activation energy field dependent. The field dependence of the effective mobility in the macrotrap model has the following form [319]: meff F m1 expðaF b=FÞ Copyright © 2005 by Marcel Dekker

ð267Þ

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Figure 101 Calculated Poole–Frenkel plots according to the correlated disorder model for different values of sd=kT (from top curve downward). The calculations according to the Gaussian disorder model with s=kT ¼ 5.10 (the lowest curve) are given for comparison. The value of (eaF=sd)1=2 ¼ 1 corresponds to the electric field F ¼ 106 V=cm with sd ¼ 0.1 eV and a ¼ 1 nm. After Ref. 460. Copyright 1998 American Physical Society.

where m ¼ 3 l, a ¼ er=2kT (r—intersite distance), and b ¼ 3lkT=elD with l being the energy trap distribution parameter [see Eq. (179)] and lD standing for the diffusion length of thermally activated carriers. The constants a and b must not be confused with the constants a and b in Eqs. (203) and (209), respectively. The straight-line plots of log meff vs. the complex variable (aF b=F) predicted by Eq. (267) fit well the TOF mobility data for a series of molecularly doped polymers, displayed in Fig. 102. Copyright © 2005 by Marcel Dekker

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Figure 102 Field dependence of the effective hole mobility in a number of polymeric samples for various concentrations (given in the by curve descriptions) of two molecular dopants [TPA (triphenylamine) and TPM (triphenylmethane)] in polycarbonate matrix. The experimental 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 the slopes of the high- and low-field range separate straight-line plots. After Ref. 319. Copyright 1992 Jpn. JAP, with permission.

The contribution of the power factor Fm1 to the functional form of meff(F) appears to be negligible, but it must be accounted for to match its absolute values. The quantity a varies between 1.8 106 cm=V and b varies between 0.7 105 and 2.7 105 V=cm. For example, for 0.5 TPA=PC sample, a ¼ 2 106 cm=V and b ¼ 105 V=cm which at room temperature corresponds to r ¼ 1 nm, and lD=l ¼ 7.6 which with l ¼ 0.4 nm gives lD ¼ 3 nm. We note that aF b=F ¼ 0 indicates a critical electric field Ftr ¼ (b=a)1=2 at which different components of the exponent in Eq. (267) dominate the mobility. In the above example, this transition field value Ftr ¼ 2.2 105 V=cm. The Arrhenius-type temperature dependence measured at the F ¼ Ftr provides the activation energy which can be identified with the sum of the macrotrap energy and the average localization energy of the hopping sites [319]. Copyright © 2005 by Marcel Dekker

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In Sec. 4.3.2, a number of examples have been presented showing the charge injection current to follow a Schottky (or Poole–Frenkel)-type electric field increase (see Figs. 75––82b) which in some cases could be explained satisfactorily by a classic thermionic carrier emission mechanism from metal into insulator, based on Eq. (203) containing an exponential Richardson–Schottky like factor exp(aF1=2). However, quantitative differences in the exponent coefficient atheor (204) are typically met in the experiment. Often, a ﬃ 2atheor, the relation ascribed by some authors to a difference between the actual and nominal electric field (U=d) used as a rule in experimental current-field plots, suitable especially for DL devices (see discussion in Sec. 4.3.2), or to the thermionic carrier injection from the Fermi level of electrode into a manifold of hopping states with a weighted probability density of width 100 meV [401]. The present section discussion on the fielddependent mobility opens an alternative explanation of the difference between the measured and calculated values of the coefficient a. The Poole–Frenkel type behavior of the current can now be analyzed in terms of diffusion-controlled currents (Sec. 4.4) which in the high-field regime obeys Eq. (231). If the mobility (m) follows the Poole–Frenkel type field dependence (265), the DCC will be represented by a function nh i o jDCC F 3=4 exp 2ðbe=kT Þ1=2 þbm F 1=2 with an effective coefficient [cf. Eqs. (203) and (204)] 1=2 be þbm ¼ atheor þ bm a¼2 kT

ð268Þ

ð269Þ

Clearly, Eq. (268) can be approximated by a Poole–Frenkeltype function with a coefficient a > atheor. The exact value of a varies from sample to sample dependent on the type and extent of disorder—through the disorder-dependent component bm. Following an example of electron injection from Al into Alq3 (d ¼ 150 nm) (see Fig. 82b), the experimental a values can be calculated from the slopes of the PF-type plots. As predicted by (204) and (265), they should be temperature Copyright © 2005 by Marcel Dekker

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dependent and, according to (269), related to the sample disorder (s, S or sd). These data are plotted in Fig. 103. They exceed the theoretical values roughly by a factor of 2, and show a weaker temperature decrease than that for atheor. The experimental data in near-room temperature region are well reproduced by the diffusion-controlled model for the injection current [Eqs. (268) and (269)] involving the coefficient bm governed by the electron motion within a manifold

Figure 103 The experimental values (H) of the parameter a following from the PF-type plots of the j–F dependence in Fig. 82b as a function of temperature. The open circles represent the data obtained from Eq. (269) describing diffusion–controlled injection current that involves the electron motion within a manifold of disordered but spatially correlated hopping sites with sd ¼ 0.13 eV obtained from (269) using p ¼ 4.4D, e ¼ 3.8, [309] and ˚ [calculated with the molecular weight a ¼ (M=NAr)1=3 ¼ 8.38 A 1 M ¼ 459,44 g mol ; density r ¼ 1.3 g=cm3 (see Ref. 151), and Avogadro’s number NA ¼ 6 1023 mol1]. The theoretical prediction of a(T) according to Eq. (204) (solid line), and the simulation values at 250 and 300 K () for a hopping system with a Gaussian disorder (s ¼ 80 meV) are shown for comparison [401]. Copyright © 2005 by Marcel Dekker

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of disordered but spatially correlated hopping sites. The room temperature bm ¼ 0.75 102 (cm=V)1=2 obtained from this ˚ is in excellent model with sd ¼ 0.13 eV, G ¼ 0 and a ¼ 8.38 A agreement with the experimental value bm ¼ (0.75 0.05) 102 (cm=V)1=2 found from the field-dependent TOF-measured mobility data (filled points in Fig. 104; see also Ref. 423). A value 1.65 102 (cm=V)1=2, in excellent agreement with the experimental value of a at 300 K in Fig. 103, would be obtained if the theoretical value p ¼ 5.3 D of the meridianal isomer of Alq3 (see Ref. 465) were used instead 4.4 D in the calculation of sd. The weakly field-dependent TOF mobility data obtained with a DL ITO=Alq3 (150 nm)=rubrene (10 nm)=Mg:Ag device (open circles in Fig. 104) do not allow to fit the values of a to the experimental points. A MonteCarlo simulation of carrier injection from metal to an organic insulator with random (uncorrelated) hopping sites, though brings the value of a closer to the experimental results (two filled circles in Fig. 103), seems inadequate for the description of electron injection into Alq3. On the other hand, the dipolar

Figure 104 Electric field dependence of TOF-measured electron mobility in thin films of Alq3: the data of Ref. 336 (&), Ref. 425 (), and Ref. 341 (). Copyright © 2005 by Marcel Dekker

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nature of Alq3 molecules makes their random aggregation (e.g. evaporated thin solid films [466]) a typical medium in which long-range spatial correlations in the random potential can be seen by an excess charge carrier [467]. This spatial smoothing of the energy distribution contrasts the assumption of independent site energies that is implicit in the Gaussian disorder model [29]. Through a similar reasoning, the current-field characteristic in doped Alq3 films (Fig. 76) can be ascribed to the diffusion-controlled injection current, a slightly reduced value of a arising from the dopant-induced modification of the disorder parameter sd. Yet, apparent divergence between the model-calculated and experimental data for the coefficient a below 200 K (Fig. 103) suggests disorder to be a temperature-dependent factor. It is conceivable that the coefficient G in bm, which is analogous to the positional disorder parameter S2 in the Gaussian disorder model, and at near-room temperatures approaching 0, becomes of importance at lower temperatures, leading to lower values of bm and thus to a reduction of the coefficient a. This would concur with simulations of the equilibrium orientational distribution 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 undergo a low-temperature phase transition to partially ordered state. Sterical ordering decreases the effective randomness of the system, the effect reducing the role of the disorder parameter s. One has to note, however, that the concentration of the off-diagonal disorder parameter, S, in the purely Gaussian disorder model, is considered to increase with temperature [29] (see also discussion below). Another possibility to explain a slower increase of the coefficient a as temperature decreases would be increasing the carrier dwell time in the traps detected by various experiments in Alq3 films [150,469] (see also discussion below). This point requires further studies. The field-dependent mobility, would obviously modify the shape of the field characteristics of space-charge-limited currents [cf. Sec. 4.3.1; Eqs. (168), (175), (176) and (185); the first original work see Ref. 377]. For example, the Schottky-type Copyright © 2005 by Marcel Dekker

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curves in Fig. 82b can be interpreted in terms of trap-free SCLC electron currents injected into Alq3 from a Ca cathode, their straight-line segments being directly related to bm [cf. Eq. (265)], 9 jðF Þ ¼ e0 em0 expðY=kT Þ expðbm F 1=2 ÞF 2 =d 8

ð270Þ

The use of the SCL description to those results is supported by the d1 behavior of the current with varying film thickness, d, though an apparent deviation from the straight-line j d1 relationship can be observed for thin samples (see Fig. 80). Equation (270) is valid as long as the mobility is governed by the dispersive transport yielding its Poole–Frenkeltype behavior as a function of electric field. Since disorder in Alq3 films seems to be associated with the presence in the material of oxygen (cf. dispersive and non-dispersive photocurrent transients in Fig. 93, and the explanation thereto), one would expect m(F) ¼ const in the oxygen-free Alq3. This could be reached under ultra-high-vacuum conditions. In fact a well-defined squared-law dependence of j(F) for the electron injection from Mg into Alq3 has been observed under a pressure less than 109 hPa [470]. A representative result is shown in Fig. 105. Of three voltage regimes (A, B, C), the latter stands for the trap-free SCLC which is well reproduced by Eq. (168) with e ¼ 3.5 and m on the 107 cm2=V s varying from sample to sample within one order of magnitude but independent of electric field. The region of steep current increase (B), moving towards larger electric fields with the time interval between completing fabrication of the device and its characterization procedure, indicates increasing the voltage threshold of carrier injection caused by an increase of the electron trap concentration with time. However, electron trapping centers have a relatively well-defined energy with an energetic spread insufficient to produce meaningful disorder. The A region is characteristic of bulk generated carriers due to e.g. uncontrollable impurities or corresponds to the diffusion-free low-field approximation (205) of the solution of Eq. (198). The most impressive results of the field-dependent mobility modified space-charge-limited currents have been obtained Copyright © 2005 by Marcel Dekker

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Figure 105 Electron injection current density vs. average electric field (F ¼ U=d) for a Mg=Alq3=Mg sandwich device with a 300 nm– thick Alq3 film (circles). The dash-dotted line corresponds to a j U2 dependence; the dashed line represents a linear plot j U. After Ref. 470. Copyright 2002 American Institute of Physics.

on conjugated polymers [471,472]. Some examples are shown in Fig. 106. The set of experimental j–U characteristics in PPV (Fig. 106a) can be described by Eq. (270) with bm ﬃ 0.6 102 (cm=V)1=2 and e ¼ 3 at room temperature (solid lines). The deviations from the conventional j U2=d behavior for SCLC are, thus, due to the Poole–Frenkel-type field dependence of the mobility [377]. The straight-line segment of the jd3=(DU)2 vs. (DU=d)1=2 plot in Fig. 106b again confirms the applicability of Eq. (270) and allows to determine the coefficient bm ¼ 0.44 102 (cm=V)1=2 At high electric fields (F > 3 106 V=cm), the current approaches a field-independent mobility trap-free space-charge-limited current. The analysis of the trap-free SCLC allows to determine the temperature and field dependence of the mobility [see Copyright © 2005 by Marcel Dekker

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Figure 106 Experimental j–U characteristics of polymer films for various temperatures (a) and two different thickness (,D) samples at room temperature (b). (a) Steady-state currents in poly(dialkoxyp-phenylene vinylene) (PPV) (the layer thickness d ¼ 125 nm). After Ref. 471. (b) Response current to 10 ms rectangular voltage pulses in poly[2-5-dimethoxy-1,4-phenylene-1,2-ethenylene-2methoxy-5(2-ethylhexyloxy)-1,4-phenylene-1,2-ethenylene (M3EH-PPV); DU ¼ U–Ubi, where U is the applied voltage and Ubi is the built-in potential due to a difference in the work functions of the electrodes. After Ref. 472. Copyright 2000 American Institute of Physics.

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Eq. (168a)]. High values of the hole mobility ( > 102 V=cm2 s) in high-purity samples at low temperatures support the supposition that conventional band-theory combined with a temperature-dependent coherent bandwidth renormalization due to electron–phonon interaction is a reasonable approximation to understand the charge transport in good quality organic crystals at low temperatures. The calculated mean free path of charge carriers can exceed many lattice constants. It decreases to about the lattice constant and the intermolecular distances with increasing temperature. To distinguish the mobility-dependent space-charge-limited (270) from the injection-controlled [e.g. DCC (268)] current flow, the thickness dependence of the current appears to be a useful criterion as demonstrated in Figs. 80 and 106b. One should note that the mobility dependent injectioncontrolled current, like that resulting from the inclusion of a macroscopic diffusion component to the collected current, can also be described taking into account the surface recombination of injected carriers [see Sec. 4.3.2, and in particular Eqs. (224) along with Eq. (221)]. A direct way to follow the mobility-dependent charge injection would be measuring the injection current into organic solid-state samples with independent controlled variations in the carrier mobility. Such an experiment has been attempted with the injection of holes from ITO into tetraphenyl diamine doped polycarbonate (TPD:PC) films, where the hole mobility was varied from 106 to 103 cm2=V s by adjusting the concentration of the hole transport agent, TPD, in the PC matrix from 30% to 100% of the TPD content [394]. The results are shown in Fig. 107. The measured injection current ( jILC jINJ) is about two orders of magnitude lower than that expected to flow under SCLC conditions [the values of jSCL calculated from Eq. (168a)], and is independent of the dopant concentration as expressed by a constant injection efficiency ( jILC=jSCL) vs. hole mobility. This result is difficult to understand as the injection efficiency is by definition a function of the number of the electron donor centers, here identified with the TPD concentration, and varying between n ﬃ 4 1019 cm3 at the 30% doping level up to n ﬃ 1.5 1021 cm3 for the 100% TPD Copyright © 2005 by Marcel Dekker

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Figure 107 Mobility-dependent hole injection currents for six TPD:PC samples at 0.4 MV=cm, under space-charge-limited ( jSCL) and injection-controlled ( jINJ) conditions. Inset: mobility dependence of the injection efficiency defined by the ratio ( jILC=jSCL). After Ref. 394. Copyright 2001 American Physical Society.

sample (calculated with the molecular weight of TPD:M ¼ 516 g=mol, density r ¼ 1.2 g=cm3, and Avogadro’s number A ¼ 6 1023 mol1). If the surface current is governed by the tuneling process, increasing n changes the injection current according to [393] j n2=3 expðQ=n1=3 Þ

ð271Þ

where Q ¼ eF=kT þ r1 with r0 being a critical distance 0 of a donor molecule from the electrode, which, according to tunnel theory, is a function of the injection barrier, DEi, h=2(2m DEi)1=2. Assuming the electron effective mass r0 ¼ ˚ with m ¼ m (free electron mass), one arrives at r0 ﬃ 1.3 A DEi ¼ 0.6 eV characterizing the TPD=ITO interface [2]. Thus Eq. (271) shows, in general, supralinear increase of the current with n, and explains, among others differences between j–F characteristics of DL LEDs using the TPD-doped PC Copyright © 2005 by Marcel Dekker

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HTLs with different concentrations of TPD (see Fig. 77). The concentration independence of the injection efficiency, demonstrated indirectly in the inset of Fig. 107, might have several reasons of which diffusion of TPD molecules from the bulk to the surface [473] and different meaning of the linear j vs. m increase will be here mentioned. The former is based on the suggestion that the near-contact concentration of TPD molecules remains approximately constant independent of their concentration in the bulk due to molecular diffusion towards the surface, the region which becomes a TPD-depleted layer due to the conceivable process that TPD sublimes off the sample surface during the metal deposition process. This explanation is supported by the time evolution of the hole injection efficiency from evaporated Au anode into TPD-doped PC layers [473]. The second possibility is that the linear increase of j with m reflects simply the identity between the concentration function of the injection efficiency (301) and the concentration dependence of the mobility ˚ [338]. While the m n2=3 exp[(2=r0n1=3)], where r0 ﬃ 1.4 A injection-controlled current ( jILC) follows the concentration increasing injection efficiency (271), the space-charge-limited current ( jSCL) is governed by the identically concentration increasing mobility m(n), so that their ratio, jILC=jSCL is constant at any concentration of TPD (any value of m). Sometimes, injection currents decrease with applied field or show the field evolution much weaker than predicted by the Poole–Frenkel-type behavior of the carrier mobility at low electric fields. Such a behavior can be seen in Fig. 108, where the field-dependent mobility modified SCL currents as a function of electric field (F ¼ DV=d) are presented for single layers of a conjugated polymer (MEH-PPV). While for two Au contacts monopolar (hole-only) injection, the initial strong current increase is followed by the high-field SCL injection modified 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 in the low-field regime. One of possible explanations of these results could be a field-decreasing mobility of electrons injected from Al and Ca cathodes. In addition to the discussed Copyright © 2005 by Marcel Dekker

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Figure 108 Current–voltage data (points) from single layers of poly[2-methoxy,5-(2-ethylhexoxy)-1,4-phenylene vinylene] (MEHPPV) provided with Au anodes and different cathodes (Ca, Al, and Au as indicated in the figure). The data normalized to the sample thickness, d, and the electric field accounted for the built-in potential (Ubi) DU ¼ U Ubi, where U is the applied voltage. Solid lines plotted according to predictions of Eq. (270). After Ref. 474 (see also Ref. 475). Copyright 1998 American Physical Society.

above saturation of the drift velocity or contribution of the macroscopic diffusion to the transient current, the fielddecreasing mobility may occur when the off-diagonal disorder dominates over the diagonal disorder [see discussion of bm Copyright © 2005 by Marcel Dekker

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following Eq. (265)]. If S2 > (s=kT)2 or G > (sd=kT)3=2, bm < 0 the mobility becomes a decreasing function of applied field, F. There are several sets of the experimental mobility data showing such a behavior at both low and high fields [29,476–478]. The field-decreasing mobility is expected to be better pronounced at high temperatures alleviating the above inequalities to be fulfilled. It is well illustrated by the example shown in Fig. 109. The negative field dependencies are observed within a low-field region (F < 2 105 V=cm) at high temperatures (T > 240 K). The range of fields for which behavior is observed increases at low dopant concentrations. For example, in the case of 10% pyrazoline-doped PC, the fielddecreasing hole mobility is observed up to 106 V=cm at high temperatures [476]. In previous attempts to model carrier transport in disordered organic solids, ln m ﬃ f(F) ¼ const, and ln m1F relationships have been discussed [341,419,447,476,480–482]. They have been rationalized either on the basis of particular experimental features or a hopping model involving a fieldinduced reduction in the effective width of the energy distribution of hopping sites. For example, the data obtained from analysis of the EL decay, in Alq3-based EL devices, have been ascribed to the accumulation of charge rather than to electron transport and differences in the results for thick and thin devices considered as due to varying film morphology [341]. It is difficult to find well-reproducible recurrent features of numerous mobility data in a variety of disordered organic solids since unintentional impurities, including dipolar species, and molecules forming shallow and deep traps, can modify substantially the carrier transport. In general, the field dependence of the carrier mobility can be expressed by a sum of a number of terms reflecting different structural and chemical features of the samples [460] ln m f ðTÞ þ D1 ðTÞF 1=2 þ A2 ðTÞF 3=4 þ A3 F 5=6 þ A4 ðTÞF ð272Þ This expression imitates the Poole–Frankel-type dependence [ln m A1(T)F1=2] in a relatively narrow field range Copyright © 2005 by Marcel Dekker

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Figure 109 Poole–Frenkel–type plots of the field dependent mobility in a molecular–doped polymer (TAPC:PC) at different temperatures. A change from the negative to positive value of bm [see Eq. (265)] is well pronounced at T > 240 K. After Ref. 479. Copyright 1991 American Institute of Physics.

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(Fmax=Fmin ﬃ 10), indicating the dispersive dipolar transport component A1(T)F1=2 to be dominant. The upward or downward deviation from the straight-line plot ln m A1F1=2 would suggest the higher power terms to contribute to the overall field dependence of the mobility. They have been assigned to disorder correlated by long-range interactions between molecules possessing quadrupole [A2(T)F3=4] and octupole [A3F5=6] electrical moments. The term A4(T)F is a signature of the presence of deep traps (Ref. 460) or the formation of polarons [122]. The deviation trend from the PF-type dependence is expected to depend on polarity of materials. While for non-polar materials, the mobility curve convex downward should be observed, the upward curve convex would appear for polar materials.

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5 Optical Characteristics of Organic LEDs

5.1. INTRODUCTION In organic LEDs, electricity is directly converted into light. Therefore, the evaluation of the overall light output and its relation to the driving current are of fundamental interest though understanding and tailoring of their emission color also falls in central device physics and practical application problems. A large amount of effort has been expended preparing various material compositions, particularly of the binary and ternary systems, and measuring their emission spectra with the hope of finding new and useful organic LED emitters. The following section provides an overview of various type of EL spectra and a good sampling of the empiricism which characterizes the work at many laboratories. However, the main subject of the present chapter is in correlating the optical properties of organic LEDs to their electrical characteristics. 273

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5.2. EMISSION SPECTRA Published emission spectra of organic LEDs cover a spectral range from infrared [483–486] to ultraviolet [487] and show either a shape characteristic of molecules dispersed in an electronically neutral medium, broad maxima from disordered emitters involving two-molecules underlain excited states, or narrow lines reflecting excitation of metal ions in their complexes with organic compounds or microcavity and lasing effects in the layered structures with strongly injecting electrodes (Fig. 110). Below, a number of examples of these various types of EL spectra will be presented and their origin briefly discussed in relation to the nature of excited states described in Chapter 2. Furthermore, since the composition of the population of emitting excited states produced in multi-layer EL devices varies with their operation conditions, the voltage evolution of the emission spectra will be demonstrated on selected examples of organic LEDs. 5.2.1. Molecular Emission If the light emanating from an organic LED originates from the radiative decay of locally excited (molecular) states (see Fig. 11), we deal with molecular emission spectra. They, in general, differ from those of isolated molecules because the gas-to-solid shift, and resonance interactions must be taken into account [cf. Eq. (13)]. Moreover, they can reveal wider bands due to dynamical and structural disorder in the solid J Figure 110 Emission spectra of organic LEDs cover the spectral range between infrared (a) through visible (b) to ultraviolet (c) region of the electromagnetic wavelengths. (a) The absorption (ABS), photoluminescence (PL) and electroluminescence (EL) spectra taken from spin-coated layers of a cyano-substituted thienylene phenylene copolymer (reprinted from Ref. 483, Copyright 1995 with permission from Elsevier); (b) PL spectra of TPD and Alq3 vacuum evaporated films, and EL spectrum of Alq3 dispersed in a TPD:PC matrix (adapted from Ref. 389); (c) EL spectra of dialkylpolysilanes as indicated in the figure (adapted from Ref. 487). Copyright © 2005 by Marcel Dekker

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state (cf. Sec. 2.2). The well-separated maxima in the EL spectrum of SL LEDs based on polycrystalline layers of anthracene and tetracene-doped anthracene are supposed to reflect radiative decay of singlet excitons located on anthracene and=or tetracene molecules, the latter populated either by direct electron–hole recombination and=or Fo¨rster energy transfer from anthracene host to tetracene guest molecules (Fig. 111). The molecular emission underlain EL spectra can also be observed in DL LEDs of which an interesting example is shown in Fig. 112. Both ETL (Alq3) and HTL (TPD:T5Ohex:PC) stand for the emitters within the green and yellow spectral regions, respectively. Remarkably, EL spectra differ from the PL spectra either for ITO=TPD:PC=Alq3=Mg=Ag and ITO=TPD:T5Ohex:PC=Alq3=Ca structures (Fig. 113). The reason is that optical excitation (lex ¼ 350 nm) of Alq3 (green emission) and T5Ohex (yellow emission) occurs through the Fo¨rster energy transfer from excited singlets of

Figure 111 Emission spectra from the SL LEDs based on anthracene (A) and tetracene-doped anthracene (T:A) films with two different concentrations of tetracene. Violet anthracene emission disappears with increasing concentration of tetracene. The spectra were taken with the 1 mm-thick films sandwiched between Au anode and Al cathode at the applied field F ¼ 106 V=cm. After Ref. 212. Reprinted from Ref. 212. Copyright Springer-Verlag, with permission. Copyright © 2005 by Marcel Dekker

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Figure 112 Molecular structures (a) of the materials used to manufacture DL LEDs (b) with a molecularly doped hole-transporting-layer (HTL) which serves as an emitter (EML) along with the emitting electron-transporting-layer (ETL).

TPD (violet emission), whereas, electrical excitation is due to electron–hole recombination within the Alq3 ETL for the first structure, combined with the electron–hole recombination on T5Ohex molecules of the HTL for the second structure. In the Copyright © 2005 by Marcel Dekker

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Figure 113 Normalized PL and EL spectra of DL LEDs. (a) ITO= (75% TPD:25% PC) (60 nm)=Alq3 (60 nm)=Mg=Ag; EL spectra taken at different voltages between 8 and 15 V do not differ from each other. (b) ITO=70% TPD:10% T5O hex:20% PC) (60 nm)=Alq3 (60 nm)=Ca. The EL does not contain the violet emission component from TPD and evolves with applied voltage. All PL spectra including that of a TPD film alone [PL(TPD)] were excited through the ITO anode with lexc ¼ 350 nm (cf. the absorption spectra in Fig. 6). After Ref. 303. Copyright Institute of Physics (GB).

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second case, electrons injected from the cathode migrate within the Alq3 ETL and a fraction of them passes the Alq3=(TPD:T5Ohex:PC) interface drifting towards the anode. The number of recombination events within the HTL is obviously a function of the electron stream penetrating this layer. The latter increases with the voltage applied to the LED. The increasing penetration of electrons into the HTL, which can be considered as an extension of the recombination zone towards the anode, would be expected to enhance the yellow component in the overall emission spectrum of the LED as, in fact, is observed in experiment (Fig. 113b). This is an example showing the importance of the type of excitation for the emission spectrum of intentionally (or unintentionally) doped materials. Even traces of fluorescent molecules can give a substantial (or even dominating) contribution to the overall emission spectrum of LED structures. It is instructive to follow the emission spectra of low Alq3-doped and undoped TPD SL LEDs presented in Fig. 114. The characteristic Alq3emission peaking at about 520 nm is well pronounced in the EL while absent in the PL spectra of a low-doped (106 M Alq3) TPD layer (Fig. 114a). Furthermore, increasing voltage applied to the sample quenches the dopant emission as already demonstrated on vacuum-evaporated neat Alq3 films (cf. Fig. 47), the effect ascribed to the field-assisted dissociation of Alq3 singlet states [306]. The presence of unintentional admixtures can dominate the EL spectra, while the PL spectra are characteristic of the host material. Such a situation is shown in Fig. 115. In the process of the synthesis of an electron acceptor polymer, 2,7-poly(9-fluorenone) (PF), the high molecular weight precursor polymer 2,7-poly(spiro[40 ,40 dioctyl-20 ,60 -dioxocyclohexane-10 ,9-fluorenone) (POFK) is used allowing good processability and conversion into insoluble PF [489] (also see the scheme in the top part of Fig. 115). The optical properties of POFK and PF differ significantly. The POFK shows blue fluorescence (see PL spectrum in Fig. 115b) while the product PF shows a maximum emission at 580 nm in the yellow region of the visible spectrum (see Fig. 115c). In the EL spectrum of POFK, a dominating yellow component appears, suggesting a small amount of the reaction product Copyright © 2005 by Marcel Dekker

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Figure 114 PL and EL spectra of a vacuum evaporation prepared ITO=(TPD:106 MAlq3) (165 nm)=Mg=Ag SL structure (a). Effect of applied voltage on its EL spectra is shown in part (b). Adapted from Ref. 21.

(PF) to form effective electron–hole recombination centers [488]. An extreme case in the difference between PL and EL spectra is presented in Fig. 116. A perylene bisimide pigment (PBP)-doped TPD layer reveals the PL spectrum belonging totally to the violet emission of TPD molecules, and EL spectrum originating from radiative transitions of the doped Copyright © 2005 by Marcel Dekker

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Figure 115 Optical spectra of the precursor POFK and the product 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 spectra of POFK contrasts a similarity of these spectra for PF (for explanations, see text). After Ref. 488. Copyright 2000 Viley-VCH. Copyright © 2005 by Marcel Dekker

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molecular of PBP, which falls in the red [490]. This indicates the exciton energy transfer TPD ! PBP to be very inefficient and hole recombination on the PBP-trapped electrons to dominate the generation process of the excited states of PBP. We note that the EL spectrum of this system is insensitive to the applied voltage. In contrast, voltage-induced color variations can be observed from multi-layer white light emitting devices based on pyridine-containing conjugated polymers and para-sexiphenyl (6P) oligomer [491]. An example of a three-layer ITO=PVK=6P=PPy=A device is shown in Fig. 117. The PL spectra of the device excited through the ITO-covered glass and recorded from the PVK side show maxima in different spectral regions that reflect varying contributions of the emission from different layers of the device, the blue–green emission from PPy and PVK becoming dominant at excitation wavelength of 400 nm. Increasing contribution of this part of the emission spectrum of the device is seen also in the EL spectra as the applied voltage increases. Moreover, a new maximum appears in the EL at about 605 nm (in the red) and grows with applied voltage (Fig. 117B.b) The color coordinates of the EL spectra at 21 and 25 V are (0.261, 0.245) and (0.298, 0.286), respectively. At 27 V, the emitted light appears bright white to the eye. The red-like emission shows up at 31 V due to the growing contribution of the 605 nm peak. Thus, the color coordinates traverse along a straight line in the CIE chromaticity diagram as the voltage increases. Though the EL spectra of this three-layer device are presented in the molecular emission

J Figure 116 Comparison of the PL and EL spectra of PBP (a). (b) PL spectra of PBP and TPD films; their maxima are shifted towards red and blue, respectively, as compared to the PL maximum of Alq3 (just given as a commonly known reference spectrum). For the molecular structures of TPD and Alq3, see Fig. 6. (c) PL and EL spectra of the ITO = (TPD:30% PBP) (70 nm) = Mg=Ag SL structure. The by-side arrows indicate the curves recorded at different applied voltages. From Ref. 490. Copyright 1998 American Institute of Physics. Copyright © 2005 by Marcel Dekker

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section, they can be only in part rationalized by the molecular emission of the individual component materials. Namely, the emission color is tuned from blue, the molecular emission originating from para-sexiphenyl, to white to green, the molecular emission from PPy. The voltage evolution of the spectra from the emission of 6P to the emission of PPy can be understood in terms of asymmetric narrowing of the recombination zone which reduces the recombination radiation in the 6P and enhances it in the PPy layer. The gradual shift of the maximum recombination efficiency from the HTL to ETL in the three-layer ITO=TPD=Alq3=PBP=Mg=Ag LED has been employed earlier to explain the field increasing red emission from PBP [490,492]. The origin of the new redlocated component is not known and is likely to be associated with bimolecular excited states formed at the 6P=PPy interface (cf. Secs. 2.3 and 5.2.2). The selforganizing properties of the polymer blends have been employed to manufacture the voltage-controlled color organic LEDs [121,345,493]. Such a structure (shown in Fig. 118) composed of a polymer blend, electron acceptor-transporting layer (ETL), and the hole (ITO) and electron (Ca=Al) injecting electrodes reveals voltagedependent EL spectra (Fig. 119). While the EL spectra of the individual polymers (PCHMT, PTOPT) peak in blue and red, 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

J Figure 117 Emission characteristics of a three-layer device based on the pyridine-contained polymer and para-sexiphenyl oligomer (see Ref. 491). (A) Repeat units of the pyridine-containing polymers 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 under different applied voltages (given in the figure) (b). The CIE (Com´ clairage) color coordinates of the EL mision Internationale de l’E spectra from part B (b). Adapted from Ref. 491 Copyright © 2005 by Marcel Dekker

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Figure 118 (a) Schematic representation (not to scale) of separated polymer channel domains individual submicrometer size LEDs in the polymer blend (PMCHT:PTOPT)=PBD EL structure. (b) The energy level structure of the EL device. The data on polymer energy levels taken from Ref. 345. The hole injection barriers from ITO into PMCHT [DEh(1) ﬃ 1 eV] and PTOPT [DEh(2) ﬃ 0.6 eV] are indicated in the figure. For the molecular structure of the polymers, see Fig. 119.

into domain channels connecting the hole injecting ITO and electron transporter PBD (see Fig. 118a). By this, the device becomes a composition of a large number of parallel submicrometer size ITO=PCHMT=PBD=Ca=Al and Copyright © 2005 by Marcel Dekker

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Figure 119 EL spectra of two polymers (a), and their blend in a DL device ITO=98% PCHMT:2% PTOPT=Ca=Al at two different voltages (b). (c) The layer configuration in the LED and chemical structures of the 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.

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ITO=PTOPT=PBD=Ca=Al diodes each emitting its own characteristic spectrum. The intensity ratio of the blue (PCHMT-based microLEDs) and red (PTOPT-based microLEDs) is determined by the voltage applied to the diode, and the stoichiometry of the polymer blend. As the injection efficiency increases more rapidly with the applied voltage

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for high injection barriers, the contribution of the blue emitting PCHMT microLEDs with the hole injection barrier ﬃ1 eV to the overall device spectrum increases with applied voltage much steeper than that from the red emitting PTOPT microLEDs with the hole injection barrier ﬃ0.6 eV, and, as a consequence, the LED color shifts towards blue. One has to keep in mind that due to singlet energy transfer from PCHMT to PTOPT (cf. the energy level scheme in Fig. 118b), the fraction of PCHMT must highly exceed that of PTOPT in order the effect to appear. Indeed, the example in Fig. 119 fulfills this condition. The emission spectra from organic LEDs based on organic phosphors are determined by properties of their triplet states (see Sec. 1.4). In Fig. 120, the emission spectra of multi-layer LEDs with organic phosphor-doped HTL and ETL are shown at different voltages. Strong emission is observed from the triplet excited states of Ir(ppy)3 at 510 nm (Ref. 304) and PtOEP at 650 nm (Refs. 43 and 493a). Spectral and timeresolved photoluminescence measurements confirm this assignment (see e.g., Ref. 156). Excited triplets in Ir(ppy)3 are most probably produced by the recombination of TPD-transported holes with Ir(ppy)3-trapped electrons; the LUMO of Ir(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 in device I [304]. In contrast, the population of excited triplets of PtOEP in device II (Fig. 120b) follows the e–h recombina-

J Figure 120 The spectra of the two electroluminescent devices (I and II) containing organic phosphors, Ir(ppy)3 (a) (adapted from Ref. 304), and PtOEP (b) (see Ref. 493a, reprinted from Ref. 493a, Copyright 1998 Macmillan Publishers Ltd. [http:==www.nature. com=]). The latter is compared with the EL spectrum of a device with no phosphor inside (III). For the chemical structures of the phosphors, see Fig. 31. The spectra from device I and II are characteristic of molecular phosphorescence as clearly seen from their comparison at different voltages with the PL spectrum (a). The DCM2-doped Alq3 layer of device III becomes dominated by their phosphorescene from the PtOEP-doped Alq3 layer in device II. Copyright © 2005 by Marcel Dekker

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tion on Alq3 and Dexter transfer of triplet energy from Alq3 to PtOEP which does not form efficient carrier traps. A 10 nmthick layer of Alq3 doped with 1% DCM2 placed in the wide recombination zone plays a role of singlet exciton loser of both LED II and LED III, due to efficient Fo¨rster energy transfer from Alq3 to DCM2 and high radiative decay rate constant of the latter [494]. Since the relative contribution of the DCM2 and Alq3 emission components in both devices (II and III) is identical (see Fig. 120b), the only way to create excited triplets of PtOEP is Dexter energy transfer from Alq3 triplet states that have diffused through the DCM2 and intervening Alq3 layers. The formation of emitting triplets by direct electron–hole recombination on Ir(ppy)3 has been clearly demonstrated in emission properties of triplelayer LED structures ITO=m-MTDATA=CBP(d)=Ir(ppy)3: CBP=MgAg [495]. Figure 121 shows their EL spectra as a function of CBP spacer layer thickness, d. Only Ir(ppy)3 triplet emission (lmax ﬃ 515 nm; cf. Fig. 120a) is observed for d ¼ 0, the contribution from Ir(ppy)3 gradually decreases, accompanied by an increase of blue m-MTDATA fluorescence with increasing d. Such an evolution of the EL spectra indicates the recombination zone to cover both the m-MTDATA HTL and CBP:Ir(ppy)3 ETL. The CBP spacer layer reveals ambipolar conduction properties. Thus, for the Ir(ppy)3:CBP doped slab positioned away from the m-MTDATA=CBP interface (d ¼ 10–40 nm), the spectra are composed of both

J Figure 121 (a) Electroluminescent spectra of an ITO=m-MTDATA(50 nm)=CBP (variable d)=7% Ir(ppy)3:93% CBP(60 nm)=MgAg device with d varying as indicated. (b) Fluorescence (FL) and phosphorescence (PH) spectra of CBP and m-MTDATA films (PH at 70 K). (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 structure of Ir(ppy)3, see Figs. 31 and 36, and for its emission spectra Fig. 120a. (d) The energy level diagram of the device structure showing relative positions of the HOMO and LUMO levels of the organic layers used. Adapted from Ref. 495. Copyright © 2005 by Marcel Dekker

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m-MTDATA molecular fluorescence (cf. EL and FL spectra in Fig. 121a,b) and Ir(ppy)3 phosphorescence (cf. PH spectrum in Fig. 120a). No emission from CBP is observed. At d ¼ 0, on the other hand, only Ir(ppy)3 PH occurs in the overall emission spectrum, since the recombination zone becomes confined to the Ir(ppy)3:CBP ETL. The direct contact of the m-MTDATA layer with the Ir(ppy)3:CBP layer facilitates holes to be injected on the Ir(ppy)3 HOMO levels, while electron injection into m-MTDATA is strongly impeded by a relatively high energy barrier (ﬃ1 eV; see Fig. 121d). The lacking emission characteristic of CBP indicates the formation of its singlet and triplet excited states to be very inefficient; thus, the emitting triplets of Ir(ppy)3 are produced in the Ir(ppy)3 trapped hole-free electron recombination process rather than by CBP ! Ir(ppy)3 energy transfer. The existence of different molecular emissive states in the Alq3 film has been suggested [496]. They were identified on the basis of time-dependent fluorescence studies by means of the femtosecond fluorescence upconversion technique. Their nature is not quite clear. One hypothesis is that they reflect a series of excitonic traps [496], assuming the S1 excitonic energy to be determined by the long-wavelength edge of the absorption at ﬃ2.65 eV (see e.g., Ref. 59). On the other hand, they correspond well to the three closely spaced singlet levels (S1, S2, S3) as calculated for Alq3 using a semiempirical approach in agreement with those obtained from deconvolution of the absorption spectrum into Gaussian components, ðtÞ if completed with a constant energy increment DEn ﬃ 0.65 eV (see Table 6). Experimental studies of Alq3 have observed a large shift (0.4–0.7 eV) between the optical absorption spectra and emission spectra (see Fig. 6). It has been interpreted in terms of nodal characteristics of the HOMO and LUMO coupled through skeletal quinolate vibrations [502]. The electronic excitation of the molecule of Alq3, localized on one of the three quinolite ligands (for molecular structure of Alq3, see Figs. 6 and 110), causes a significant change in the molecular geometry, the excited-state relaxation energy predicted theoretically to be 0.55 eV [502]. This is in good agreement with the Stokes shift between the absorption and emission Copyright © 2005 by Marcel Dekker

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Table 6 Some Excited States in Alq3 as Identified by Different Methods ðsÞ

ðtÞ

Energy En DEn ¼ Lifetime ðsÞ ðsÞ (room Molecular (solid state) DEn DEn DEtrap S1 temperature) state molecule) (eV) (eV) (eV) (eV) Energy

ðgÞ En a(isolated

S1 S2 S3 S1 (trap 1) S2 (trap 2) S3 (trap 3)

3.48 3.59 3.67 – – –

3.00b 3.19b 3.27b 2.33c 2.56c 2.62c

10–15 nsd 0.19 0.08 0.67 0.63 0.65

10 nse 25 pse 1 pse

a

The data from semiempirical calculations ZINDO=S (see Ref. 59). The values resulting from the decomposition of the experimental absorption spectrum into Gaussian components. The absorption onset Ethr ﬃ 2.65 eV to be identified with the LUMO level as related to the ground state S0 (see Ref. 59). Note that the LUMO by definition must not be identified with the position of the electron conduction level which can be determined from combined internal photoemission and photocurrent vs bias experiments. It has been found to be EA ¼ (3.0 0.1) eV below the vacuum level, the value, which substracted from the ionization potential (HOMO) IS ¼ (5.6 6.65) eV (see Refs. 497–501) implies the electrical gap Eg ¼ (2.6 3.65) eV (see Refs. 354–465). c Position of S1 trap levels related to the HOMO level, as determined from the timeresolved PL spectra of Alq3 films (see Ref. 496). d From Refs. 148 and 149. e From Ref. 496. b

spectra of Alq3 and enables the exciton trap states S1 (trap) to be considered rather as a relaxed series of different S1, S2 and S3 excited singlet states with the lifetime decreasing from ﬃ10 ns (S1), through ﬃ25 ps (S2) down to ﬃ1 ps [496]. Interestingly, this approach has been strongly supported by the EL spectra in Alq3 films separated from the electrodes by insulating layers of SiO2 [503]. Figure 122 shows EL spectra of a device ITO=SiO2=Alq3=SiO2=Al observed at different voltages. A broad band blue emission peaking at ﬃ475 nm is observed at high voltages. The high-field EL spectra can be understood assuming a field-induced change in the emission components, the short-living states (S2, S3) dominating at high fields. The long-living (ﬃ10 ns) states are efficiently quenched by the voltage-increasing concentration of holes at the SiO2=Alq3 interface adjacent to the ITO anode. The excitonic interaction with Copyright © 2005 by Marcel Dekker

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Figure 122 El spectra of an ITO=SiO2(40 nm)=Alq3(50 nm)= SiO2(40 nm)=Al device at different voltages. Adapted from Ref. 503.

charge carriers has been discussed in Sec. 2.5.2, and characterized by the second order rate constant gSq which for Alq3 has been estimated on the order 109–1010 cm3 s1 [233]. The EL intensity at 475 nm of the low-voltage (low carrier concentration) spectrum constitutes roughly 75% of its maximum at 510–520 nm. Therefore, to make them comparable, one has to reduce the concentration of S1 by at least 25%, that is DS1 ¼ gS1 q tS1 nq ¼ 0:25 S1

ð273Þ

With gS1 q ﬃ 109 cm3 s1, tS1 ¼ 10 ns, this would require nq ¼ 2.5 1016 =cm3. This reasonable value, attainable for the carrier concentration at higher voltages, is not sufficient to quench higher short-living singlets S2 and S3 unless, for some reasons, the interaction constant for them would be much greater. Consequently, the relative contribution of the blue high emitting singlets S2 and S3 increases with the space charge at the SiO2=Alq3 where the recombination is expected to be the most efficient. It is worthwhile to mention about Copyright © 2005 by Marcel Dekker

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another rather speculative, but intriguing possibility for the field induced blue shift of the EL spectrum of Alq3 in the presence of SiO2 spacer. The partly nanocrystalline character of evaporated Alq3 films kept at high temperature and exposed to the bombardment of hot molecules of SiO2 during the deposition of one of the spacers [503] can undergo a partial near-surface transformation into the d-phase of Alq3 revealing different molecular structure and the weaker overlap of the p orbitals of hydroxyquinoline ligands belonging to neighboring Alq3 molecules as compared to usual a and b phases [504]. The different geometry, higher dipole moment and different electronic properties lead to its strongly blue-shifted fluorescence [505]. When at a high electric field, the recombination zone becomes very narrow and located at the Alq3=SiO2 interface, the main contribution to the emission could originate from the d-phase, giving the observed shift of 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 show up as broad bands when being underlain by the radiative decay of bimolecular excited species (excimers, electromers, exciplexes or electroplexes). A number of examples presented in Figs. 16–18, 21, 26, 29 and 30 have served as an experimental basis rationalizing the nature of excited states. The principal concept behind the formation of bi-molecular excited states is the competition between electron transport and vertical and cross-radiative transitions. It is illustrated in Fig. 123. The type of excited state created by a pair of approaching oppositely charged carriers (e,h) depends on their distance (r) and the positions of the LUMO and HOMO levels, which, in general, are different due to either local environment conditions for identical molecules or differences in ionization potential and electron affinities for chemically different molecules. In the latter case, the LUMO and HOMO energy levels can also be modified by local environmental conditions. The electron (e) transport from LUMO2 to LUMO1 leads to formation of the molecular emission from LUMO1, the Copyright © 2005 by Marcel Dekker

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Figure 123 The energy level shift between two molecules enabling formation of electromers and electroplexes, and their optical emission characterized by the energy quanta hn cross (cf. similar schemes in Figs. 10, 11, 20, and 28).

process competing with electromer or electroplex emission (hn cross). On the other hand, the hole hopping from HOMO1 to HOMO2 produces excited states localized on molecule 2, which for a non-zero radiative decay rate can be detected as the molecular emission characteristic of molecule 2. If the intermolecular separation r between chemically different molecules is sufficiently small (<0.4 nm, cf. Sec. 2.3), the e– h pair becomes a CT exciplex; the localized exciplex or excimer (in case of chemically identical molecules) can be formed by the resonance interaction between molecularly excited and ground states of molecules 1 and 2. From this general picture, it is apparent that in order to observe electromer or electroplex emission, the energy barrier DE for carrier transport Copyright © 2005 by Marcel Dekker

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must be high enough to make the hopping rate comparable with spatial crossing transition resulting in an additional feature of the overall emission spectrum. Its spectral position depends on the LUMO2–HOMO1 gap (DE21) as compared with on molecule located LUMO–HOMO energy separations (DE11, DE22). The case DE11 < DE21 < DE22 has been illustrated in Fig. 29, showing the electroplex emission component to be located between the long-wavelength molecular emission from PTOPT and short-wavelength molecular emission from PBD. The same electron acceptor (PBD) combined with another donor molecule (TPD) led to a long-wavelength electroplex emission component illustrating another intermolecular energy relation DE21 < DE11 < DE22 (see Fig. 30). Also, the position of trapping levels of anthracene molecules in a PC matrix appeared to be sufficient to produce the electromer emission located in the long-wavelength tail of the overall EL spectrum (see Fig. 17) with the same energy level interrelation. The molecules and electroplex (electromer) emission combined with the exciplex (excimer) emission form a broad band spectrum as demonstrated by the results for an SL electron donor (TPD)–electron acceptor (PBD)-based organic LED in Fig. 26 and for a single-component emitter in Fig. 17. The emission spectrum based on the same donor and acceptor system as in Fig. 26, but detected from a DL device where molecules of TPD dispersed in PC, forming the hole-transporting layer, could be brought into a contact with molecules of PBD evaporated on its top as an electron-transporting and strong hole-blocking layer, is shown in Fig. 124. Four Gaussian components representing different emission species can be distinguished. An additional A4 component appears as compared with the EL spectrum of the TPD and PBD dispersed in PC of an SL device, presented in Fig. 26. It has been assigned to the second electroplex while A1, A2 and A3 components are same molecular emission of TPD (A1), exciplex emission (A2), and first (shorter-wavelength) electroplex (A3). The electroplex (EC) emission is to a large extent determined by the intercarrier Coulombic attraction energy, EC ¼ e2=4pe0er. The emission energy (hn EC), including the local environmental shift of LUMOs and HOMOs, DE (cf. Fig. 123), can be Copyright © 2005 by Marcel Dekker

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Figure 124 (a) A broad-band emission spectrum from a DL ITO=(75% TPD:25% PC)(60 nm)=PBD(60 nm)=Ca LED at 20 V and its Gaussian profile analysis ascribed to molecular TPD singlets (A1), exciplexes (A2) and electroplexes (A3, A4). Solid line: experimental curve, dashed line: four gaussian band fit. (b) EL spectra from the same device at different voltages. The PL spectrum excited at 360 nm 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 components related to the total EL emission of the device. A1, A2, A3, A4 correspond to the contributions of the EL components related by the area under the Gaussian profiles peaking at l1 ﬃ 415 nm (hn 1 ﬃ 3 eV), l2 ﬃ 477 nm (hn 2 ﬃ 2.6 eV), l3 ﬃ 564 nm (hn 3 ﬃ 2.2 eV), and l4 ﬃ 670 nm (hn 4 ﬃ 1.85 eV). Adapted from Refs. 112 and 120].

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expressed by hn cross 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 AA ¼ IA Eopt, where IA is the ionization potential and Eopt, the optical gap of the acceptor, has been employed to evaluate the intercarrier distance using the experimental values of hn EC. With ID(TPD) ¼ 5.5 eV, ð1Þ ð1Þ and AA(PBD) ¼ 2.6 eV, EC ¼ 0.7 eV for electroplex 1 [hn EC ¼ ð2Þ ð2Þ 2.2 eV], and EC ¼ 1.1 eV for electroplex 2 [hn EC ¼ 1.85 eV] have ð1Þ ð2Þ been obtained. Then, using e ¼ 3, rEC ¼ 0.68 nm and rEC ¼ 0.45 nm calculated [120]. These values of r are expected to represent rather a lower limit of electroplex radii because the used electron affinity has been assumed at its largest value IA Eopt. On the other hand, DE 6¼ 0 could reduce or even level off this difference. From part (b) of Fig. 124, the essential difference between PL and EL spectra is seen, and the red shift of the EL spectra with applied voltage apparent. This can be explained by an electric field-induced differentiation of the contribution of four Gaussian components to the overall EL spectrum. The Gaussian profile analysis of the EL spectra at different electric fields allowed to follow the voltage dependence of the contribution of particular emission components (Fig. 124c). Whereas, the molecular (A1) and second electroplex emission contribution (A4), though in opposite manner, change only slightly with applied voltage, the contribution of the exciplex emission (A2) decreases and that of the shorter-wavelength electroplex emission (A3) increases significantly at increasing voltage. This behavior can be rationalized by a particular location of TPDþPBD pairs at the We note that a substantial dispersion in EC and, consequently in r may be expected 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 the absorption maximum. Then, for PBD, Eopt(edge) ¼ 3.54 eV and Eopt (max) ¼ 4.1 eV, respectively, and DEopt ﬃ 0.56 eV. Thus, A falls in the range 2.76–2.2 eV. These values yield 0.54 eV EC 1.1 eV, and 1.3 nm r 0.62 nm for electroplex 1 formed with the TPD donor.

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(TPD:PC)=PBD interface. In contrast to the bulk recombination process in the SL TPD:PBD:PC structure (see Fig. 26), involving random oriented e–h complex dipole moments, the dipole moment of the all e–h pairs at the (TPD:PC)=PBD interface is directed against the electric field because the holes are located on TPD molecules in the HTL, and counterpart electrons are located on PBD molecules in the ETL of the junction. Consequently, the increasing forward external electric field (ITOþ, Ca) may either increase the recombination rate of the electroplex forming pairs or reduce the electroplex energy (274) by a term erU=d. In the example presented in Fig. 124b, the voltage increase from 20 up to 28 V would shift the emission spectrum to the red by about 0.05 eV according to the erU=d completed Eq. (274). This is at variance with experiment showing the shift to reach ﬃ0.2 eV. Therefore, the field-induced increase of the radiative decay rate of electroplex 1 seems to be dominating in red shifting of the EL spectrum. An alternative explanation would be a difference in the field-induced drop of the quantum efficiency at high fields (Fig. 125) for exciplex and electroplex contributions to the emission of such LEDs. The EL quantum yield typically decreases above a certain electric field (cf. Sec. 5.4), the maximum efficiency field dependent on the device structure. The quantum efficiency drop for the TPD:PBD:PC SL LED begins at a much higher electric field than that for the (TPD:PC)= PBD DL LED (Fig. 125). The red shift of the EL maximum for the DL LED (Fig. 124b) occurs in the voltage range corresponding to the high-field decrease in the EL quantum efficiency (F > 1.25 MV=cm; Fig. 125). If a roughly 30% decrease in the overall EL quantum efficiency, going from 1.25 MV=cm to 2.0 MV=cm, were dominated by the quenching of long-living exciplexes, a net effect would be the relative increase of the electroplex component shifting the overall EL spectrum to the red. Referring the reader to Sec. 5.4 for details of quenching mechanisms, here we note this supposition to be consistent with a 30% drop in the exciplex contribution inferred from the Gaussian profile analysis of the EL spectra at different electric fields (Fig. 124c) and independent observations of strongly electric field-induced quenching of fluorescence origiCopyright © 2005 by Marcel Dekker

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Figure 125 The field dependence of the quantum EL efficiency for the LEDs from Fig. 30 (SL) and Fig. 121 (DL). After Ref. 120. Copyright Institute of Physics (GB).

nating from long-living excimers in TAPC [506]. One would not expect a substantial red shift effect from increasing component A4, due to its relatively small contribution to the overall output. Its appearance in the EL spectrum follows from Eq. (274) with DE 6¼ 0, that is an electroplex formed on a defect site characterized by the DE. Electric field effect on the broad EL spectra has been studied earlier with another acceptor, Alq3 [507]. The broad band EL spectra from a series of ITO=HTL=Alq3=Mg=Ag LEDs have been attributed to the emission from exciplexes formed at the HTL=Alq3 interface. In Fig. 126, a comparison of EL spectra from one of these LEDs based on the mMTDATA=Alq3 junction, with the PL spectra of m-MTDATA and Alq3 films, is presented. They fall beyond the maxima of the PL spectra towards red of the m-MTDATA donor and the Alq3 acceptor, suggesting formation of the [(mMTDATA Alq3) þ (m-MTDATAþAlq3)CT] exciplex and=or (mMTDATAþ-Alq3) electroplex (cf. Fig. 27). Unlike in the Copyright © 2005 by Marcel Dekker

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TPD=PBD junction based LED (Fig. 124b), the EL spectra of this structure shift towards blue at increasing voltage. This behavior could reflect a field-mediated competition between the formation of Alq 3 molecular excited singlets (cf. Sec. 5.2.1) and electroplex decay LUMO (Alq 3 ) ! HOMO

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(m-MTDATAþ). The latter corresponds to hn EC ¼ (2.1 0.1) eV and yields the emission at lEC ¼ (590 30) nm in good agreement with experiment. Increasing voltage reduces the hole injection barrier at the interface, the hole charge accumulated at the m-MTDATA side of the junction decreases, the rate of cross-transitions of electrons from the Alq3 LUMO to holes located on the m-MTDATA HOMO (electroplex transitions) becomes smaller and, as a consequence, the contribution of the electroplex emission to the overall spectrum decreases, its maximum shifts towards blue, i.e., approaches the molecular emission from Alq3. Alternatively, the fieldinduced quenching of the (m-MTDATAþAlq3)CT exciplexes can be considered as a reason for the blue shift of the EL spectrum. The exciplex energy can be evaluated from Eq. (43) knowing the polarographic oxidation potential of m-MTDATA and reduction potential of Alq3. Based on the values Eox (mMTDATA) ¼ 0.31 eV (Ref. 508) and Ered(Alq3) ¼ 1.9 eV (Ref. 509), we find hn ex ¼ (2.1 0.1) eV identical to the above estimated energy of the electroplex. Its emission, identified as a CT transition (cf. Sec. 2.3.2), should decrease with respect to the molecular emission from Alq3 in order to understand the blue shift of the overall emission maximum at increasing voltage. This could occur for the same reason as the discussed above step down in the electroplex emission component. The field decreasing space charge of holes at the m-MTDATA=Alq3 junction causes a gradual reduction in the formation rate of

J Figure 126 The 1,3,5-tris(3-methylphenylphenylamino)triphenylamine(m-MTDATA)=Alq3 (a) junction based DL LEDs emission spectra as compared with the PL spectrum of m-MTDATA and Alq3 (b) at different applied voltages (c). The EL spectrum (1) in part (b) taken for the device ITO=m-MTDATA (60 nm)=Alq3(60 nm)= MgAg at 6 V; the PL spectrum of Alq3 given by curve (2) and of m-MTDATA given by curve (3). The vacuum related LUMO and HOMO levels for the materials used are shown in the right-top corner. The 6 V EL spectrum from part (b) shows blue shift as applied voltage increases (c). Adapted from Ref. 507.

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excited CT states. Also, this would explain the absence of the exciplex emission when m-MTDATA are replaced by TPD in the DL LED [507]. A relatively low injection barrier of holes from TPD to Alq3 (ﬃ0.3 eV) reduces the concentration of holes on the TPD side of the TPD=Alq3 junction, so that the formation rate of CT states, being proportional to the number of holes located on the TPD HOMO, becomes negligible with the radiative decay of excited molecular states of Alq3. This reasoning assumes hn EX ¼ Eox (TPD) Ered (Alq3) 0.15 ¼ (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 would locate the maximum of the exciplex emission at ﬃ590 nm. On the other hand, the energy gap between the LUMO (Alq3) and HOMO (TPD) (2.4 0.1 eV) would lead to the cross-transition (electroplex) at l ﬃ 510 nm falling into the molecular emission spectrum of Alq3 (cf. Sec. 5.2.1). Thus, it is not possible to distinguish the molecular from electroplex emission based on the emission maximum position solely. In order to check the role of TPD on the emission from Alq3, it is useful to compare the EL and PL spectra from pure (100%) Alq3 layers with those from an Alq3:TPD mixture as shown in Fig. 127. While the 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 the mixed sample suggests the formation of locally excited bimolecular complex states (see Sec. 2.3.2). In conjunction with absorption spectra presented in Fig. 127c, and lacking the molecular emission of TPD in the Alq3:TPD sample [not shown in Fig. 127b since peaking below 450 nm (see Fig. 6)], they might be 1(Alq3 TPD) trapped states. Under electrical excitation, the large populations of TPD-located holes, and Alq3-located electrons, render the electroplex emission to compete effectively with the emission underlain by molecular Alq3 states including their complexes with TPD. Consequently, the narrower spectrum becomes dominated by less dispersed in energy electroplex states. The field-induced reduction of the exciplex emission (thus, relative increase of the electroplex emission) evident in Fig. 128 is matched by the enhancement in the electron hopping rate. The effect is much better Copyright © 2005 by Marcel Dekker

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Figure 127 (a) PL and EL spectra of a vacuum-evaporated layer of Alq3 in the structure ITO=100% Alq3 (140 nm)=Mg=Ag (see Ref. 57); (b) PL and EL spectra of an Alq3-doped TPD film in the structure ITO=30% Alq3:TPD (150 nm)=Mg=Ag (Cocchi and Kalinowski, unpublished). The front PL spectra are recorded through the ITO-covered glass substrate, and excited with lexc ¼ 420 nm; (c) absorption spectra of Alq3, TPD and Alq3:TPD (3:10) films on quartz. The film thickness d given in the inset (Cocchi and Kalinowski, unpublished).

pronounced in a single layer (SL) mixture (CBP:PC:PBD) than in the bilayer structure (CBP:PC)=PBD. This can be explained by a difference in the average distance (r) between CBP and PBD molecules in these two structures. A lower value of r at the (75% CBP:PC)=100% PBD interface in the DL structure promotes the formation of molecular and exciplex states, the electroplex component constitutes a smaller part of the overall emission spectrum. The field-enhancement of the electron escape from a Coulombically correlated charge Copyright © 2005 by Marcel Dekker

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carrier pair (CBPþCBP), equivalent to its field-assisted dissociation, is not efficient enough to change the dominating exciplex emission. On the other hand, more distant CBPþCBP charge carrier pairs in the bulk of the SL LED (Fig. 128a) are subject to a stronger field effect on their

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dissociation and, consequently, the relative increase in the radiative decay of Coulombically correlated e–h pairs forming electroplex species. At sufficiently high fields, the overall emission spectrum becomes dominated by their emission. The PL spectrum of the (CBP:PC:PBD) sample shows two features corresponding to the two closely spaced maxima of the molecular emission of CBP and a shoulder at ﬃ420 nm which can be assigned to the locally excited exciplex 1(CBP PBD) formed by the exciton resonance between CBP and PBD molecules. This state becomes dominating in the EL emission of the DL structure and the low-field EL spectra of the SL device. A broad band above 500 nm reveals three separable features in the low-field EL spectrum of the SL device. The principal maximum at ﬃ525 nm is assumed to reflect the radiative decay of the unperturbed electroplex composed of an e–h pair located on PBDþ and CBP molecules and separated by a distance r ¼ e2=4pe0eEC ﬃ 0.48 nm, the value obtained with e ¼ 3 and EC ¼ ID IA hn EC ¼ 1.04 eV. The Coulombic e–h attraction energy, EC, has been calculated from Eq. (274) assuming DE ¼ 0, ID ¼ 6.0 eV, AA ¼ 2.6 eV, and using the experimental result for hn EC ﬃ 2.36 eV. By analogy with the lowest-energy band in the electroplex emission in the TPD= PBD system (band A4 in Fig. 124), the features at ﬃ600 nm (EC2) and ﬃ700 nm (EC3) of the electroplex band in Fig. 128a can be assigned to trapped electroplexes. Using Eq. (274) allows the energy level shift, due to local environment

J Figure 128 The PL and EL spectra of combined compositions of (4,40 -N, N0 -dicarbazole-biphenyl) (CBP) and 2-(4-biphenyl)-5-(4tert.-butylphenyl)1,3,4-oxdiazole (PBD) in a form of an SL mixed film (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 comparison. The solid-state energy level scheme of the electronically active materials is shown in the inset of part (a). The differences between PL and EL spectra recorded at different voltages are apparent for both systems. After Cocchi and Kalinowski, unpublished. Copyright © 2005 by Marcel Dekker

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conditions, to be estimated on DE (EC1) ﬃ 0.15 eV, and DE (EC2) ﬃ 0.3 eV. An alternative interpretation of electroplexes 2 and 3 would be the formation of the e–h emitting pairs with different intercarrier separations [120]. Such an approach would give EC leading to r ﬃ 0.3–0.4 nm, the distances characteristic of CT exciplex. The impact of the separation distance on the nature of excited states and corresponding emission spectra has been demonstrated on copolymers containing the electron donor and electron acceptor groups of N-vinylcarbazole (NVK) and PBD [510]. The carbazole and oxadiazolecontaining groups connected to the polymer backbone have been spaced by a distance impeding the formation of exciplexes. The EL spectra of such copolymers have been shown to differ from those of PVK:PBD blends, where the intermolecular NVK–PBD distance is subject to statistical distribution which includes distances below 0.4 nm and molecular orientations suitable for the exciplex formation (cf. Sec. 2.3). While different ratio PV:PBD blended films show the EL maximum near 440 nm characteristic of exciplexes, the EL spectra of SL copolymer-based devices are very broad with well-pronounced three bands peaking in different spectral regions: one at 370– 440 nm, a second at 500 nm, and a third near 610 nm. The shortest wavelength maximum is a superposition of emission from isolated NVK and exadiazole-containing monomer segments and their excimers. The smallest maximum, near 610 nm, has been attributed to PVK electromers. But the emission maximum dominating at comparable contents of NVK and oxadiazole-containing species, and especially at high electric fields, is to be associated with electroplexes since the topological constraints by the polymer prohibit the formation of exciplexes between sequential donor and acceptor units. An interesting case of the electroplex formation may be expected for the low ionization potential of electron donor and high electron affinity of electron acceptor molecules. The electron transition would then occur at large intermolecular distances (EC ! kT) and the optical cross-transition appears at hn cross ﬃ ID – AA [cf. Eq. (274) with DE ¼ 0]. The broad band at ﬃ550 nm in the EL spectrum of a DL LED Copyright © 2005 by Marcel Dekker

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based on the poly(9-tetradecanyl-3,6-(dibutadiynyl)carbazole) (PTD-BC)=hyperbranched polycarbazole (HB PC) seems to be a good illustration of such a situation (Fig. 129). The difference, ID(PTD-BC) ﬃ 5.4 eV and AA(HBPC) ﬃ 3.2 eV, gives hn cross ﬃ (2.2 0.2) eV (520–620 nm) corresponding well to the broad long-wavelength band in the EL, not observed in the PL spectrum. In contrast to this case, EL spectra presented in Fig. 130 demonstrate the importance of local environment for the energy of excited states. They have been obtained for a multi-component molecular structure comprising of a Nd3þ cation surrounded by four negatively charged pyrazolone ligands. The structure has a permanent dipole moment associated with the hemicyanine unit and this is expected to be 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 material PTDBC and electron-transporting material HB PC, see text. The LUMO and HOMO energy interrelations in these materials are given in the right upper corner. Adapted from Ref. 511. Copyright © 2005 by Marcel Dekker

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Figure 130 Absorption (A), photoluminescence (PL) and electroluminescence (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 trivalent rare-earth (Nd3þ) cation surrounded by four organic singly charged anionic ligands (b). The two EL spectra have been taken from a device being run for the first time (EL1), and the emission from a device that has been cycled several times (EL2). Reprinted from Ref. 512. Copyright 1996 with permission from Elsevier.

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molecules formed into an LB film give a centrosymmetric stacking of the monolayers. Application of an external voltage should thus be expected to cause a molecular re-orientation similar to that in conventional second order nonlinear materials. The PL spectrum, partly red shifted from the EL spectra, has a peak at 590 nm (the spectra are normalized at their maximum intensities). The EL spectrum recorded on the first run appears broader than the PL emission with a blue-shifted peak at ﬃ570 nm and a broad shoulder to the red at ﬃ670 nm. Subsequent EL spectra show a further evolution with the redshifted component dominating. The explanation for this behavior is most likely due to unusual nature of the molecular complex used. The EL appears to be characteristic of the hemicyanine counter-ion and not the Nd3þ unlike in lanthanide complexes (cf. Sec. 5.2.3). The blue-shifted peak and red-shifted shoulder could be two dipole-split components reflecting the specific dipole–dipole interactions through orientation of the dipoles of the molecular complex in the external electric field. Cycling of the device promotes in some unknown yet way the second emission component. The external bias field may cause not only rearrangement of the dipoles but could even break up the complex, favoring one of the two types emitting species that is locally modifying the emissive medium. Also, EL emission from triplet bi-molecular states reveals broad band spectra. They are illustrated in Fig. 131 by the emission from the EL device based on the metalorganic complex platinum (II) (2-(40 ,60 -difluorophenyl)pyridinato-N,C2) acetyl acetate (FPt1) doped into the host material 3,5-bis(Ncarbazolyl)benzene(mCP). The vacuum-evaporated layer of 4,40 -bis[N-(1-naphthyl)-N-phenyl-amino]biphenyl (NBP) served as the HTL followed a layer of poly(3,4-ethylenedioxythiophene):poly(styrene sulfonic acid) (PEDOT=PSS) spun onto the ITO injecting holes (hþ) electrode. The 50 nm-thick 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP) layer followed the phosphorescent complex FPt1, and serves as a hole=exciton blocking and electron-transporting layer. The electron (e) injecting electrode consists of LiF and Al. The broad EL spectrum of such a device differs completely from Copyright © 2005 by Marcel Dekker

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Figure 131 The EL device used to probe triplet bi-molecular excited states and molecular structures of FPt1 and mCP (a). Comparison of the room temperature EL (solid line) and PL (dotted line) spectra of the device with a 30 K spectrum of Fpt1 (dashed line) (b). The EL spectrum of the device at different temperatures (c). Reprinted from Ref. 99. Copyright 2003 with permission from Elsevier.

its PL spectra (Fig. 131b), peaking at 1.83 eV (678 nm). The molecular emission spectrum of a neat film of FPt1 with the well-resolved vibronic structure disappears when sandwiched in the organic heterostructure shown in Fig. 131a. The PL of the device contains a large contribution from NPD emission as indicated, and a broad band emission located at 2.07 eV (599 nm). There is an 80 nm red shift in the EL maximum from the broad band maximum location of the PL spectrum of the device at 290 K. Interestingly, two peaks in the low temperature (82 K) EL spectrum can be resolved (Fig. 131c), one Copyright © 2005 by Marcel Dekker

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at 2.07 eV and the second still dominant at 1.83 eV. From their lifetimes of (1.6 0.3) ms and (800 80) ns, respectively, these two broad states have been assigned to the triplet excimer ð3 E0 Þ at 2.07 eV, and to the weakly bound dimer (3D ) at 1.83 eV, resulting from Pt–Pt contacts on adjacent molecules in the neat thin films. The 3D state is present only during electrical excitation [99]. From the above examples, we have seen that the recombination of electrons and holes injected into a single- or multilayer combinations of thin organic films shows a tendency towards the formation of aggregate excited states that underlie complex multi-band emission spectra observed with thin film organic LEDs. The shape and range of these spectra, thus the color of such LEDs, can be controlled by aggregate formation. In particular, the contribution of bi-molecular excited states depends on the composition, morphology, and electric field, and manipulating these factors both the color and EL efficiency could undergo desired measures. However, to tailor these LEDs’ characteristics, the more detailed knowledge on the nature of the aggregate excited states is necessary. A transition from the molecular like behavior of localized excited states to a collective excitation, similar to that of inorganic semiconductors, could be underlain by the formation of bi-excitonic molecules, electron–hole plasma or liquid at high excitation intensities (see e.g., Ref. 513). A red shift, broadening of the PL spectrum and a cubic dependence of the emission intensity on the excitation intensity are then observed [514,515]. These are characteristics also observed with fullerenes—particular allotropes of carbon organized in various closed structures, the most abundant, C60, being a closed cage icosahedron of 60 sp2 hybridized atoms [516]. At room temperature, the C60 crystal structure can be regarded as an excellent example of cubic close packing of isotropic spheres because the molecules have almost total rotational freedom in the fcc lattice [517,518]. The icosahedral ‘‘football’’ like C60 molecules of diameter 0.7 nm are bound by van der Waals interactions with an inter-ball spacing of 0.3 nm. Such a dimension relation poses questions as to the degree of intervs. intra-molecular interactions in solid state fullerenes. Copyright © 2005 by Marcel Dekker

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Therefore, it is not surprising that their electronic properties differ as observed in single crystals, powders, and thin films. For example, a strong dependence of the luminescence on excitation intensity occurring in powders and crystals is not observed in films [519]. Three distinct photoexcited species in C60 films have been identified: a triplet exciton delocalized over the C60 molecules, a localized exciton pinned to a five- or six-membered ring at a local molecular deformation site, and an intermolecular polaron [520]. They are considered to underlie the low excitation intensity PL spectra, but not high excitation intensity PL, and EL spectra (Fig. 132). The evolution from a weak structured PL spectrum at low excitation level, to a broad-band PL spectrum at high excitation intensity, peaking at about 900 nm, with a concomitant and dramatic increase in the luminescence output, has been ascribed to a transition from the linear to non-linear optical response of the C60 crystal, that is from the molecular like behavior of localized states to collective excitation of the interacting molecules. The general correspondence between the high excitation intensity PL and EL spectra in C60 crystals led to a conclusion that both are underlain by the same mechanism based on the Mott description of inter-carrier interactions under high carrier concentration conditions. In this model, as the density of excitons is increased, the electron–hole interaction is screened by a plasma environment h2= until, at a critical density (nC 0.01=a30 , where a0 ¼ 4pe0e 2 mre is the exciton radius, e is the dielectric constant , mr is the reduced mass), they cease to exist. The exchange and correlation energies become of importance and they dominate over the exciton binding energy, resulting in the formation of an electron–hole plasma. Using band calculations to obtain mr ¼ 0.65me [522], a0 ¼ 0.35 nm is obtained with e ¼ 4.3 [523]. This value is consistent with the dimensions of a molecularly localized exciton and leads to the exciton binding energy DEEX ¼ e2=8pe0ea0 ﬃ 0.5 eV being in reasonable agreement with the separation between the exciton energy level and the lower edge of the conduction band [524]. The origin of the broad blue-shifted EL band from a C60 film and an additional maximum just above 400 nm in the single crystal EL Copyright © 2005 by Marcel Dekker

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Figure 132 A comparison of the EL and PL spectra of C60. (1) the EL spectrum of a 100 mm-thick single crystal (see Ref. 520a); (2) the EL spectrum of a vacuum-evaporated film of thickness 10 nm < d < 100 nm (see Ref. 521); (3) the PL spectrum of the crystal at low excitation intensity (<1021 quanta cm2s1); and (4) the PL spectrum of the crystal at high excitation intensity (>1021 quanta cm2 s1) (see Ref. 519). After Ref. 2. Copyright 1999 Institute of Physics (GB).

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spectrum is not clear. One of the possibilities is a combination of the emission from nitrogen ions (300–500 nm) produced by the spurious glow discharge of small amounts of N2 encapsulated on the surface and=or in the bulk of the material during sample preparation, and the PL excited by the ultraviolet radiation emanating from the glow discharge microcavities. The recombination of charge carriers on local fluctuations in crystal packing (structural defects) cannot be excluded (for a more comprehensive discussion, see Ref. 2). Deviations from perfect crystal structure or from perfect randomness of the sample are known to create difficulties in deriving a complete picture of the linear optical and electrical properties of the solid state of fullerene (see e.g., Refs. 525, 526, and references therein). It is, however, apparent from the results presented that the EL emission from single C60 crystal reveals characteristic features of the collective optical response under high excitation conditions, even though the applied fields (102–103 V cm1) and currents flowing through the crystalline samples are rather low as compared with those required for high-intensity EL in other organic LEDs (cf. Secs. 5.3 and 5.4). This observation confirms the complexity of the electronic processes in fullerenes and the ongoing discussion of their theoretical description. The band vs. localized molecular states description of electronic properties of C60 resembles the situation in conjugated polymers [527,528]. Conjugated polymers, such as polythiophene (PDT) or polyphenylenevinylene (PPV), in contrast to conventional low-molecular weight solids, show a close correspondence between the long-wavelength photoconduction threshold and the optical absorption edge [105,529]. This has been considered as an evidence for the equivalence between electrical and optical gap, i.e., that the Coulombic energy of eh pairs is negligible as compared with kT, the situation typical for inorganic semiconductors. However, due to strong coupling to lattice modes, electrons can rapidly be localized and form polaronic states [104]. A correlated on chain pair of negative and positive polarons is then considered as a neutral polaronic exciton, S1 (see Fig. 23). The identical PL and EL spectra in PPV are thought to originate from the radiative decay of singlet polaronic excitons, Copyright © 2005 by Marcel Dekker

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thus, their red shift expected with respect to the absorption spectrum (Fig. 133a). The emission spectra exhibit a wellpronounced vibronic structure which has been attributed to a coupling of phenylene ring stretching modes of the polymer

Figure 133 Optical absorption (optical density, OD), PL and EL spectra for: (a) PPV at room temperature (see Ref. 66); (b) 2,5dihexoxy-PPA at 20 K (see Ref. 530). Copyright 1993 SPIE, with permission. Copyright © 2005 by Marcel Dekker

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chain (ﬃ1600 cm1) to the electronic transitions between p and p states [531]. The much broader and blue-shifted absorption band proves the participation of different excited states which relaxing to the excitonic states produce the observed Stokes shift. The value of the Coulombic energy of the emissive states (the binding energy of a relaxed singlet exciton) has been estimated between 0.2 and 0.5 eV. The nature of the primary excited states is still under debate. The polaronic exciton seems not to be the only relaxed state created upon excitation. The ‘‘spatially indirect’’ singlet excitons have been suggested to occur with a high quantum yield of 0.9 on the basis of picosecond photoinduced absorption and stimulated emission experiments [532]. These are spatially separated bound polaron pairs resembling CT states described in Sec. 2.3.1. While very effective in absorbing light, they were assumed to decay by non-emissive geminate recombination on a 1 ns time scale. In injection electroluminescence polaron pair states can be created by gradual approching of individual polarons undergoing non-geminate polaron– polaron recombination. These would correspond to the notion of electromers defined in Sec. 2.3.1. The electromer-like emission seems to occur in the EL spectrum of the 2,5-dialkoxy derivative of poly(p-phenyleneacetylene)(PPA) as a longwavelength band at about 800 nm (Fig. 133b). It is not observed in its PL spectrum. A strong support for the formation of polaron pairs comes from luminescence-detected magnetic resonance (PLDMR and ELDMR). Figure 134 displays the main narrow PL- and EL-detected resonances of a PPV and a 2,5-dihexoxy-PPA-based SL LEDs at 20 K. The contrast between the enhancing nature of the PL resonance and the quenching nature of the EL resonance is clearly apparent. A consistent explanation of both is based on indirect mechanism invoking the spin-dependent inter- and intra-chain fusion of polarons forming polaron heteropairs (PþP) and likecharged polaron pairs (bipolarons), BPþþ or BP, respectively [533]. Polarons and long-living bipolarons are widely believed to quench emissive singlet excitons, the process corresponding to exciton-charge carrier interaction described in Sec. 2.5.2.1. The enhancing polaron resonance curves reflect Copyright © 2005 by Marcel Dekker

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Figure 134 The main narrow PL- and EL-detected magnetic resonance of a PPV-based LED at 20 K excited at 488 nm and operating at i ¼ 0 and i ¼ 70 mA currents [PL (a), EL (b)], and of a 2,5-dihexoxyPPA-based LED [PL (c), EL (d)]. After Ref. 530. Copyright 1993 SPIE, with permission.

the microwave-induced transitions between Zeeman sublevels of polarons in a way increasing the rate of their non-radiative inter-chain recombination process, the following decrease in the population of polarons reduces the efficiency of the quenching process and results in the increasing population of emissive singlets, thus PL intensity. The quenching polaron resonance, on the other hand, shows the microwaves resonance enhancement of the bipolaron formation process of the intra-chain polaron–polaron fusion. The increased population of bipolarons leads to an increased rate of singlet exciton quenching detected as decreasing emission intensity. The observed decrease, however, may be dominated by a decreasing ratio of the formation of excited singlets, due to decreasing population of free recombining polarons. The question arises why the polaron pair mechanism plays dominating role in the PL, and the formation of bipolarons in the ELDMR, at least at low temperatures (as in Fig. 134). The reason might be associated with the nature and energy of the primary Copyright © 2005 by Marcel Dekker

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excited states. For example, the PL quenching polaron resonance, similar to the ELDMR, can be observed with an aged PPV film excited at 353 nm not observed in pristine highly ordered PPV films. (A. W. Smith quoted in Ref. 533). This would suggest the defect-controlled formation of bipolarons involved in quenching of emissive singlet states. Interestingly, the defect located polaron hetero-pairs (‘‘electromers’’) do not contribute to the main narrow ELDMR (cf. Figs. 133b and 134d). The absence of an observable spin dependence of the electromer-like emission is not clearly understood at present, and speculated as due to rapid spin-lattice relaxation at the trapping site, or to trapping of excitons rather than polarons [530]. The opposite trends in ODMR signals for PL and EL may be considered on the general basis of the difference in the formation of polaron heteropairs and bipolarons. While in the PL the primary excited states are efficiently generated geminate polaron hetero-pairs, in the EL they, by definition, do not exist, the formation of bipolarons as singlet exciton quenching species dominates being promoted by high concentrations of one sign charges injected at electrodes. This difference is demonstrated in Fig. 134a, where the enhancing PL DMR signal decreases as the PPV-based LED becomes an operating device with the driving current i ¼ 70 mA. 5.2.3. Line-like Emission Spectra Narrow-band, often line-like, EL emission spectra from organic LEDs can have different reasons of which the most common will be addressed in the present section. Generally, two their groups are distinguished due to (i) intrinsic optical properties of emissive materials, and (ii) configuration and electrical characteristics of devices. An excellent example of the former are lanthanide metal complexes where metal ions exhibit extremely sharp emission bands differing completely from emission spectra of organic ligands. Recall that, on the contrary, the organic ligand emission is characteristic of such a commonly used complex as Alq3 (Sec. 5.2.1) or some rare-earth complexes as discussed in Sec. 5.2.2. Among the lanthanide metal complexes, europium (Eu) and terbium Copyright © 2005 by Marcel Dekker

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Figure 135 Molecular structures of lanthanide complexes of europium (Eu), tris (thenoyltrifluoroacetonato) Eu3þ (a), tris(thenoyltrifluoroacetonato)(monophenanthroline) Eu3þ (b), and terbium (Tb), tris(acetylacetonato) Tb3þ (c) employed as narrow-band emitters in organic EL devices (see Ref. 19, 425, 534–536 and 539).

(Tb) complexes (Fig. 135) are well known to be strongly fluorescent at room temperature. Their extremely sharp PL bands [537,538] appear also in the EL spectra of various organic LEDs employing these complexes as emitters (see Fig. 136). While Eu complexes exhibit red emission having a strong peak at ca. 615 nm, Tb complexes such as Tb(acac)3 (phen) exhibit green emission sharp bands with a strongest one located at ca. 545 nm. Despite these differences, the spectra have the same origin, reflecting the fact that the electrons responsible for the properties of lanthanide ions are 4f electrons. Their 4f orbitals are effectively shielded from the influence of the external forces by the overlapping 5s2 and 5p6 shells, which imply the f n configurations to be relatively insensitive to the external fields. Consequently, emission (as well as absorption) bands (f–f transitions) are extremely sharp when electronic transitions occur from one j state of an f n configuration to another j state of this configuration. In Fig. 136c, five different intensity EL line-like bands are attributed to such transitions, the strongest one assigned to the 5D4 ! 7F5 transition. It is important to note a difference in the excitation mechanism of lanthanide metal ions forming Copyright © 2005 by Marcel Dekker

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Figure 136 EL spectra of various organic LEDs employing lanthanide complexes as emitters. (a) ITO=TAD (triphenyldiamine derivative)=Eu(TTA)3(phen)(phen:1,10-phenanthroline þ 4,7-diphenyl-1,10-phenanthroline)=Alq3=MgAg (according to Ref. 425); (b) ITO=Eu (TTA)3:PBD=PBD=LiF=Mg, at the different voltages (after Ref. 539); (c) ITO=TPD=Tb (acac)3=Al, transitions of 4f electrons of the terbium Tb3þ ion are indicated on the sharp peak positions of this spectrum (after Ref. 19).

complexes with organic ligands and organic dyes including other metal complexes [537]. In organic fluorescent dyes, the emission of photons is due to the electronic transitions from the singlet excited states (see Secs. 2.3 and 5.2.1). Organic phosphors like benzophenone [540], but mostly heavy metal organic ligand complexes [541], show molecular phosphorescence underlain by electronic transitions from singlet–triplet mixed molecular excited states or metal-to-ligand charge transfer (MLCT) mixed states. Many luminescence studies have interpreted the results as having competition between MLCT and p–p ligand-centered (LC) states lying very close in energy. For example, the ‘‘metal’’ orbital in Ir– ppy complexes (see the emission spectra in Fig. 120) ranges Copyright © 2005 by Marcel Dekker

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from 45% to 65% Ir (5d) in character, with the remainder of the orbital of ligand p character [542,542a]. In contrast, in lanthanide complexes with p-conjugated ligands such as bdiketonato, the central lanthanide ions are excited via intramolecular energy transfer from the triplet excited states of the ligands [543]. Since the ligand’s triplet states can be efficiently populated by the bimolecular e–h recombination process, the internal efficiencies of devices using these complexes as emitters have been expected to be much higher than the 25% limit for molecular electrofluorescence (cf. Sec. 1.4). An alternative way to use inorganic species to narrowing the emission spectrum from organic containing systems is to fabricate an organic–inorganic layer structure, the inorganic layer being used as a narrow-band emitter and organic serving as carrier transport components. Such a structure based on a layered perovskite compound (C6H5C2H4NH3)2PbI4 (PAPI) (inorganic) combined with an oxadiazole derivative (OXD7) (organic) is shown in Fig. 137. The device driven at liquid-nitrogen temperature shows an intense green emission peaking at 520 nm. The quasi-identical EL and PL spectra of the structure are very narrow (the bandwidth ﬃ 10 nm) and

Figure 137 An organic–inorganic heterostructure EL device using a PAPI spin-coated film (a), molecular structure of an oxadiazole derivative (OXD7) (b), and its emission spectra at 77 K (see Ref. 544). Copyright 1994 American Institute of Physics. Copyright © 2005 by Marcel Dekker

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are attributed to the stable strongly bounded exciton formed in the low-dimensional PAPI semiconductor [544]. The holes injected from ITO are confined in the PAPI side at the PAPI=OXD7 interface, where they recombine with electrons injected from the Mg=Ag cathode and arrived at the interface through the electron transporting organic layer of OXD7. Another property of organic materials that leads to narrowing of the emission bands is their ability to J-aggregation. J-aggregated dyes, in which dye molecules have a headto-tail orientation, reveal relatively narrow-band resonance fluorescence reproduced well in their EL spectra 545–547. Figure 138a 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 and EL spectra with a sharp maximum at ﬃ560 nm and bandwidth ﬃ20 nm indicate the identity of emissive states produced on bi-molecular aggregates of the dye either by optical and electrical excitation. Sharpening of the emission and spectral tunability can be achieved by placing an emitter between reflecting planeparallel mirrors forming an optical microcavity resonator with a mirror spacing comparable to the wavelength dimensions (Fig. 139). The shape of the emission spectra of such microcavity structures depends on the intermirror spacing (d) and emission angle (Y) because of interference effects (Figs. 140 and 141). An enhancement of light occurs from the summation of the amplitudes of direct emission and emission reflected from the 100% mirror for a given wavelength and Y. As a consequence, a narrow wavelength-range part of the emitted light shows up as a relatively strong emission component, sharpening and shifting the overall shape of the spectrum. The enhancement (resonance) condition in the microcavity can be expressed as N X

ni di cos Y ¼ m

i¼1

l 2

ð275Þ

where ni and di represent the refractive index and thickness of the ith of N microcavity layers, respectively, Y represents Copyright © 2005 by Marcel Dekker

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Figure 138 (a) Comparison of EL and PL spectra of a J-aggregated cyanine dye (OCD). The EL spectrum taken from a three-layer LED, ITO=TAD=OCD=PBD=MgAg, as depicted in part (b) including molecular structures of the materials used. Adapted from Ref. 546.

the light propagation angle with respect to the emission surface (cf. Fig. 139), and m ¼ 1,2, . . . is the mode number. The microcavity extending between the metal mirror and the dielectric half mirror in Fig. 140 consists of the two organic layers with thickness d1 ¼ 50 nm (Alq3) and d2 ¼ 50 nm (TAD) and the ITO layer with thickness d3 ¼ 200 nm. The dielectric half-mirror composed of a stack of three pairs of SiO2=TiO2 layers of thickness d4 is equivalent to the optical path length of l=4. An additional optical path length due to Copyright © 2005 by Marcel Dekker

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Figure 139 Comparison of a microcavity structure (a) and a conventional organic LED (b).

the effective penetration depth of the dielectric stack reflector should be taken into account. This term can be described as the effective optical path length n5d5. The shortest value of the optical length of these N ¼ 5 components forming the microcavity predicts reasonably well the short-wavelength peak position at ﬃ480 nm corresponding to m ¼ 2 mode at Y ¼ 0. An optical refractive index n1 ¼ n2 ¼ 1.7 was used for both organic layers. The ITO acts as the electrode and has been treated as a transparent spacer with a refractive index n ¼ 1.72. The additional peak at ﬃ614 nm can be due to the same mode with a cavity extended by the penetration depth into the dielectric mirror. The interference among partial fluxes reflected at the dielectric interfaces can also be of importance. From classical optics, the angular distribution Copyright © 2005 by Marcel Dekker

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Figure 140 The EL spectra for the two types structures depicted in Fig. 139, using the following sequence of layers: ITO=TAD(50 nm)= Alq3(50 nm)=In operating at 100 mA cm2; a sputtered TiO2=SiO2 multilayer film formed a half mirror layer in the microcavity structure (a), and the long-wavelength maximum position as a function of observation angle from the microcavity structure (Fig. 139a) (b). Adapted from Ref. 548.

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Figure 141 EL spectra from the microcavity (a) and conventional LED (b) measured at different fixed detection angles (Y). The microcavity structure comprised a reflective Ag anode (36 nm), a TAD HTL (250 nm), an emission dye layer [15 nm-thick naphthostyrylamine (NSD) film], an ETL [240 nm-thick oxadiazole derivative (OXD) film], and a reflective MgAg cathode. Note that a 10% transmittance Ag layer (36 nm) played here a role of a half mirror component in the microcavity structure (cf. Fig. 139a). A transparent ITO film served as the anode in the conventional LED structure (Fig. 139b). After Ref. 550. Copyright 1993 American Institute of Physics.

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F(Y) of the light intensity emitted from microcavities follows (see e.g. Ref. 548): h i pﬃﬃﬃﬃ ð276Þ F ¼ T= 1 þ a2 R þ 2a R cos d The external observation angle, Y, associated with the internal light incidence angle, Yi, through Snell’s law (n1 sin Yi ¼ sin Y) is contained in the expression for the phase difference d¼

2n1 d 2p cos Yi l

ð277Þ

where d is the microcavity length. T and R in Eq. (276) are the transmittivity and reflectivity of a ‘‘semi’’-transparent mirror, ‘‘a’’ represents the relatively light wave amplitude after each internal reflection. It is clear from Eqs. (275)–(277) that upon increasing the external observation angle, the peak positions of the modes shift to a shorter wavelength, as shown in Fig. 140b, and angular distribution of light intensity depends on microcavity length [549]. (see also Ref. 2). Figure 141 shows the EL spectra from a microcavity (a) and conventional LED (b) based on the emission from an NSD dye forming a thin emitting layer of a three-organic layer device. It is apparent that the half-width of emission spectra from the diode with microcavity is much narrower than those from the diode without cavity. With Y ¼ 00, for example, the half-width of the spectrum of the diode with cavity is 24 nm whereas that of the sample without cavity increases to 65 nm. According to Eq. (275), the resonance wavelength, l, decreases with an increase of Y in agreement with the experimental data of Fig. 141. We note that no unique resonance condition in the planar microcavity is given due to broad-band emission spectrum of the NSD emission layer. Multiple matching of cavity modes with emission wavelengths occurs. Thus, a band emission is observed instead a sharp emission pattern from the microcavity structure as would appear when observed with a monochromator; the total polychromic emission pattern is a superposition of a range of monochromatic emission patterns. The EL spectra Copyright © 2005 by Marcel Dekker

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were also found to evolve with thickness of the organic layers and observation angle for the diode without a half mirror (Fig. 141b), due to constructive interference of direct emission and emission reflected from metal electrode=100% mirror. However, the narrowing and shift effects are much weaker than those for the diode with a half mirror. Nevertheless, they are strong enough to modify the emission spectra of Alq3 from one 515 nm maximum spectrum for d ¼ 76.5 nm to a double band spectrum revealing maxima at 495 and 590 nm for a 127.5 nm-thick Alq3 film [551]. Microcavity effects were demonstrated for polymerbased organic LEDs as well [348,493,552]. Electroluminescent spectra of single PPV layers of different thickness sandwiched between two metal electrodes, detected at selected detection angles, are shown in Fig. 142. A redistribution of the intensity in the EL spectra is clearly observed as thickness of the PPV layer increases (Fig. 142a). The microcavity mode at 560 nm, i.e. the EL emission maximum of PPV, causes substantial narrowing of the emission bandwidth (21 nm) close to the theoretical value of 15.6 nm. With decreasing thickness of the PPV layer, the number of the microcavity modes in the visible spectral region decreases accompanied by an increase in bandwidths of the corresponding emission peaks. On the device with a 265 nm-thick PPV two microcavity modes (m ¼ 2, m ¼ 3) are observed. The assignment of the emission maxima to microcavity modes is verified by the angular dependence of the EL emission (Fig. 142b). The microcavity modes are expected to shift towards shorter wavelengths with increasing detection angle. Indeed, such a shift is apparent for all three peaks in Fig. 142b. The shape of the PL spectrum measured on the device has been shown to be nearly identical to the shape of the EL spectrum [348]. Figure 143 illustrates the high spectral selectivity of the microcavity structure. The EL spectrum of the Eu complexbased conventional LED from Fig. 136a is compared with the EL spectrum of the same organic layers system placed in a microcavity formed by the MgAg metal=100% mirror (150 nm) and a dielectric half mirror (a quarter-wave stack Copyright © 2005 by Marcel Dekker

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Figure 142 Normalized EL spectra recorded normally to the surface of an Au=PPV(d)=Al microcavity structure with different thickness (d) of PPV layer (a). Variation of the EL spectra with detection angle (Y) for an Au=PPV (400 nm)=Al device (b). After Ref. 348. Copyright 1996 American Institute of Physics.

composed of four pairs of SiO2=TiO2 layers). While the EL spectrum of the device without microcavity contains a number of small peaks characteristic for the emission from an Eu3þ ion in free space, the EL spectrum of the device with microcavity consists of a single resonance microcavity line Copyright © 2005 by Marcel Dekker

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Figure 143 Comparison of EL spectra of an Eu complex forming an emitter layer in a conventional organic LED from Fig. 135a (a) with the same system placed in a microcavity (Fig. 139a) with a MgAg electrode=100% mirror and a stack of SiO2=TiO2 layers=half mirror (b). Note the disappearance of the small features of the spectrum in device (a) in the spectrum from the microcavity structure (b). After Ref. 425. Copyright 1998 Taylor & Francis.

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at the main emission maximum, all other features perfectly disappear. The emission from an organic microcavity structure with two metal electrode=100% mirrors can be observed from the LED edge [2]. PL and EL from such edge emitting structures show much sharper spectra and larger emission densities because they are a result of the propagation of a waveguiding mode allowed between two parallel mirrors separated by a distance D (Fig. 144). For a particular structure (Au=Ag)= PDA=Alq3=(Mg=Ag), the bandwidth of the edge emitted spectra is a factor 1.5–3 narrower (dependent on the thickness of the organic layers) as compared to the surface light output spectrum from a conventional organic LED (cf. Fig. 139). The edge emitting LEDs may ultimately enable organic materials to find practical application in electrically pumped lasers [351]. For electrically pumped lasing, much higher injection levels are needed to reach the threshold current density jTH ﬃ 103 A=cm2. Such current densities have been generated using two field-effect transistors as injection contacts to a single tetracene crystal in one of the questioned series of works by Scho¨n et al. [554] (see the Beasley Report in

Figure 144 (a) An edge emitting microcavity structure with two metal electrode=100% mirrors, based on the Alq3 emitter and PDA as HTL and (b) the EL spectra of two such different thickness structures: (1) D ¼ 350 nm and (2) D ¼ 160 nm, detected at Y ¼ 0; the surface light output spectrum is shown for comparison (broken line). After Ref. 553. Copyright 1993 SPIE, with permission. Copyright © 2005 by Marcel Dekker

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News & Events—Lucent Technologies: http: ==www.lucent. com=press=0902=02 0925.blahtml). Narrowing of the 0–1 vibronic transition band at ﬃ575.7 nm from 120 down to 1 meV has been reported and attributed to laser action. Surprisingly, a strong band narrowing has been observed from the Nile Blue (NB)-based edge emitting LED at much lower currents below 1 A cm2 [555]. The LED structure and its EL spectra are shown in Figs. 145 and 146, respectively. Scientific discussion of the above cited results has included significant attention to whether the observations reflect true lasing or only superluminescence and what is the nature of emitting species [2,351]. In the case of singlet excitons in organic crystals, the losses due various excitonic interactions (see Sec. 2.5) at high currents ( >10 A=cm2) seem to eliminate the high values of the optical gain necessary to start the laser action. The formation of an electron–hole plasma, as assumed to underlie the C60 crystal EL spectra (Fig. 132), created by electrical confinement near an interface, can be considered as an alternative. The plasma formation process causes the disappearance of the quasiparticle nature of discrete excitons eliminating many excitonic processes in favor of direct bandto-band recombination at the interface, or other regions (such as that surrounding a defect) where excitons and carriers would localize at high densities. For example, singlet–singlet annihilation will be replaced by non-radiative Auger processes in the plasma, which occur with a lower probability due to phase-space filling. The minimum threshold current density for lasing becomes lower and has been evaluated on 500 A cm2 [351]. The high-density plasma emission may be reinforced by optical confinement introduced by a second non-linear effect: self-focusing due to intensity-dependent saturation of the anomalous dispersion [556]. Its possible role requires further studies in ongoing discussion concerning mechanisms underlying line-like emission spectra from organic LEDs. In any case, lasing has not been convincingly demonstrated in electrically pumped devices, and the main problem to be resolved seems to be associated with reducing losses in the exciton formation zone of high-current operating devices. Copyright © 2005 by Marcel Dekker

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Figure 145 (a) The cross-section of an edge emitting DL LED supposed to act as an electrically pumped organic laser; (b) the molecular structure of Nile Blue (NB); and (c) the energy level diagram for the device. Adapted from Ref. 555.

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Finally, the narrow emission lines can be attributed to excitation of electrode materials. In fact, such emission lines have been observed from Al and Mg:Ag cathodes of the PPVderivatives-based SL LEDs when operated under strong electrical pulse excitation [472]. (see also Sec. 5.3). For example, the reabsorption-shifted characteristic Al emission at 395 nm could explain the relatively narrow line at about 400 nm observed in the Nile Blue (NB)-based edge emitting LED provided with an Al cathode as shown in Figs. 145 and 146. From the above, it is clear that the modification of the shape of the emission spectra from organic emitters containing systems reflects the variation of the position and width of the electronic levels involved in optical transitions. Therefore, the ability of a controllable production of quantized discrete energy levels in organic materials has become of noticeable interest. A way to reach this goal is the confinement of carriers in spatial cages formed by extended defects in the bulk and=or superlattices of ultra-thin organic films [21]. The spatially extended defects can act as multi-charge carrier trapping centers, leading to quantized internal energy levels [247]. The potential energy of a spatially extended domain (macrotrap) described by a spherical symmetry potential of the form (181) is modified by the introduction of N > 1 one-sign elementary charges (e) by an additional term reflecting the Coulombic repulsion of the N charge carriers: EðrÞ ¼ 3l kT lnðr0 =rÞ þ e2 N=4pe0 er ½1 sinðFN =2Þ ð278Þ where FN ¼ arc cos½1 ð2=N Þ

ð279Þ

J Figure 146 (a) The narrow-band spectrum at a voltage of 0.4 V and current of 0.11 mA across the two organic layers; (b) the schematic diagram of the edge emitting device: the thickness of NB layer is 35–50 nm and that of Alq3–NB mixture layer is 45–50 nm; (c) the power edge emission as a function of the driving current, threshold current ith ¼ 88 mA. Adapted from Ref. 555. Copyright © 2005 by Marcel Dekker

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is the energy quantizing factor because N ¼ 1,2,3, . . . are the discrete numbers of trapped elementary carriers. In other words, due to the finite dimensions of the macrotrap and the discrete increment of the charge, the energy corresponding to different carrier populations (N) will form a set of discrete levels with an internal spacing that decreases with the increasing number of captured carriers. A difference between two successive trapping levels, DEt, varies from about 0.2 eV to DEt < kT with N 1, for r0 ¼ 25–100 nm [21]. The recombination of free oppositely charged carriers on the carriers trapped on different (quantized) energy levels would lead to a split set of excited states contributing to either extended emission bands or pronounced features in the long-wavelength wings of the emission spectra. The preference of the quantized energy levels has been demonstrated in triplet exciton quenching experiments [247]. If an ohmic contact is used for charge injection into an organic solid with macrotraps, the position of the quasi-Fermi level (dependent on the stored charge and hence on applied voltage, cf. Sec. 4.3.1) scans sequentially the discrete energy levels, leading to a cascade pattern in various characteristics of the electronic processes determined by the injected charge. For example, a cascade pattern has been observed in the injecting-voltage dependence of the triplet exciton lifetime in anthracene (Fig. 147). The triplet exciton lifetime tT shortens in the presence of charge due to the triplet-charge carrier interaction process (see Sec. 2.5.2). The decay rate constant b ¼ t1 eff increases with charge concentration according to Eq. (114) and the increase is proportional to the ðtÞ concentration of trapped charge (nqt), Db ¼ b bT ﬃ gTq nqt. Since under ohmic injection nqt ﬃ

3 e0 e U 2 ed2

ð280Þ

Db is expected to be proportional to the applied voltage, U (cf. dotted curve in Fig. 147). The sequential filling of discrete traps by injected carriers produces trap-filled segments corresponding to consecutive trapping levels which are Copyright © 2005 by Marcel Dekker

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Figure 147 The relative cascade-like pattern of the increase of triplet exciton monomolecular decay rate constant (b ¼ t1 T ) as a function of charge-injecting voltage in anthracene crystal. Consecutive trap-filled limits are indicated by UTFL (1), UTFL(2) and UTFL (3). Dotted line indicates the averaged (linear) dependence of Db=b0 as resulted from the standard interpretation assuming a continuous increase in the charge density proportional to the injecting voltage [334]. Adapted from Ref. 240.

defined by the position of quasi-Fermi level EF as [334] Et ¼ EF ¼ kT lnðNeff =YntTFL Þ

ð281Þ

where Y is the free-to-trapped charge carrier ratio given by Eq. (186). For two adjacent (i,k) levels ðkÞ

DEtik ¼ Eti Etk ¼ kT ln

Yk DbTFL ðiÞ

Yi DbTFL

ð282Þ

Furthermore, Yk=Yi ¼ (Uk=Ui) [3l] follows from Eq. (186), and " # ð2Þ DU12 3l DbTFL ð283Þ DEt12 ¼ kT ln 1 þ ð1Þ U1 DbTFL Copyright © 2005 by Marcel Dekker

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for the first two trapping levels (1,2) can be obtained from (282). ð2Þ ð1Þ It is thus apparent that both height [DbTFL =DbTFL ] and length (DU12) of the steps in the cascade pattern of the voltage dependence of Db=b are measure of the energy interlevel spacing. To have an idea of the values of DEt12, let us assume typically l ﬃ 3, and use the experimental results of Fig. 147, ð2Þ ð1Þ U1 ¼ 300 V, DU12 ¼ 300 V, and DbTFL ¼ 0.16 bT, and DbTFL ¼ 0.08 bT. Then (283) yields DEt12 ¼ 0.2 eV. This value is close ð12Þ ¼ 0.22 eV—the energy separation between the oneto DEt and two-carrier occupied macrotraps with r0 ¼ 25 nm, rb ¼ 1.5 nm and l ﬃ 3 [r0 and rb are the macrotrap radius and radius of the pinning trap, respectively, see discussion of the macrotrap concept below Eq. (181)]. Another way to produce quantized electronic levels is the confinement of carriers in ultrathin organic films in a manner observed previously with inorganic semiconductors [557]. If a free particle (say electron) is completely confined to a layer of thickness Lz (by an infinite potential well) then the energies of the bound states are En ¼ p2 n2 h2 =2m L2z

ð284Þ

where m is the effective particle mass, and the integer n ¼ 1,2,3, . . . specifying the energy values represents the quantum number. The heterostructures (alternating thin layers of different materials) produce two attractive potential wells of different depths, one for electrons and one for holes. Coulomb attraction correlates the motion of the carriers in the x- and y-directions, forming for each n an exciton state peaking in the optical absorption and emission spectra. As the layer thickness decreases (decreasing Lz), the exciton motion becomes two dimensional. The exciton becomes ‘‘squeezed’’ in the potential well, resulting in an increase in the exciton binding energy. This should produce a blue shift of the absorption and emission maxima of the structure. Such a shift observed in a system of alternating layers of 3,4,9,10pery-lenetetracarboxylic dianhydride (PTCDA) and 3,4,7,8naphthalenetetracarbozylic dianhydride (NTCDA) [558]; and Copyright © 2005 by Marcel Dekker

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TPD and Alq3 (Ref. 149) have been interpreted in terms of multi-quantum-well (MQW) properties. The good agreement between experiment and theory has been obtained, assuming the excitons to be Mott–Wannier in nature. This is, however, a hardly accepted assumption since excitons in organic solids are known to be rather Frenkel-like than Mott–Wannier resembling excited states (see Chapter 2) . Using the Frenkellike exciton energy expression (13), the observed shift could be explained in terms of non-resonance interactions between molecules, D, at the interface between different organic solids [2]. On the boundary (mz ¼ 0) of two molecular layers (A and B), a difference in D appears for molecules in the first layer of the solid A, due to a difference in the interaction strengths between the molecules in the bulk (DAA) and at the surface (DBA S ) [559], X AA AA DD ¼ DBA D ¼ DAB ð285Þ S nm Dnm mz <0

Thus, if the layer is sufficiently thin, the exciton level shift should be seen in the position of the absorption and emission spectra [cf. Eq. (13)]. Since DE can be positive or negative, one would expect a blue (DD > 0) or a red (DD < 0) shift dependent on the relation between the intermolecular interactions A–A and A–B. While the blue shift for the superlattice of PTCDA=NTCDA could be ascribed to stronger interactions between molecules of these two solids, the red shift observed in the emission maximum of tetracene within the superlattice structure of pentacene=tetracene [560] would correspond to stronger interactions between the tetracene molecules in the bulk. This explanation of spectral shifts in absorption and PL spectra observed experimentally only in a small number of organic superlattices seems to be more convincing, although the existence of MQWs for organic solids cannot be completely excluded at present. More experiments on organic materials with a well-defined nature of excitonic states are needed to resolve this ambiguity. The appropriate choice of organic materials forming superlattices allows the fabrication of EL devices with a confinement of charge carriers and Copyright © 2005 by Marcel Dekker

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excitons in thin layers of their emitters [560–565]. EL spectra of 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 structures have been considered to originate from thin (3 nm) Alq3 layers forming quantum wells with finite barrier heights for holes and electrons (Fig. 148b). Narrowing and blue shift of the EL spectra from these structures as compared with these for the conventional DL LED have been taken as a proof for such an assignment. Even more venturous seems an assumption that single molecules can form quantum wells. Such an assumption has been made with rubrene molecules embedded

Figure 148 EL spectra (a) of the PBD and Alq3 (b) based conventional DL LED (c) and MQW structures (d) at room temperature. From Ref. 564. Copyright 1998 Institute of Physics (GB). Copyright © 2005 by Marcel Dekker

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in an Alq3 thin (3 nm) layer by multiple source organic molecular beam deposition method [565]. The nearly identical PL and EL spectra of a four-layer structure seen in Fig. 149 are characteristic of rubrene. The EL spectra have been reported to narrow from 220 to 175 meV, and their maxima to shift up to 55 meV as the thickness of the Rb:Alq3 layer decreased from 60 to 3 nm. The interpretation of these observations in terms of single (molecular) quantum well is highly unjustified for several reasons, to mention only the lacking relation between the thickness of the emitter layer as a whole and extension of the quantum well corresponding to the molecular size of rubrene or thickness effect on the layer morphology. The doping of emitter layers in organic LEDs has been recently shown to affect the type and characteristic parameters 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 shown in the inset. The principal maximum is characteristic of rubrene (Rb) doped in the thin (3 nm) layer of Alq3 [10% Rb:Alq3]. Adapted from Ref. 565. Copyright © 2005 by Marcel Dekker

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and EL spectra and must be taken into account before invoking the MQW interpretation of the experimental data. 5.3. LIGHT OUTPUT The photon flux leaving unit area of a planar electrofluorescent cell of thickness d is ðextÞ FEL

¼x

Zd

YðxÞ dx ¼ xkF

0

Zd

SðxÞ dx

ð286Þ

0

where Y is the EL yield given by number of photons originating in unit volume of the emitter per unit time (photon=cm3 s). It is important to remember that, generally, only a certain fraction of the light generated in the organic emission layer (EML) is available for the face detection from an organic LED. In a planar LED, a large fraction of the emitted light is lost to waveguiding modes in the glass, ITO, and organic layers due to refractive index mismatching (Fig. 150). Thus ðextÞ the external (measured) EL intensity, FEL is largely affected by these modes in addition to natural re-absorption and scattering losses. Its ratio to the internally (within EML) generated light intensity, FEL, reflects the overall losses to the external modes, and defines the so-called ‘‘light output coupling factor’’ ðextÞ

x ¼ FEL =FEL ¼ ð1 RÞð1 cos Yc Þ expðaxÞ

ð287Þ

The absorption loss is described here by the factor exp(ax), where a is the linear absorption coefficient and x is the distance traversed by light on its way from the generation site to the external glass surface. The loss due to the total internal reflection is given by (1 R)(1 cos Yc), where R represents the reflectance coefficient and Yc ¼ arc sin(n1 c ) is the critical angle determined by the appropriate relative refractive index nc of the material. The Y(x) in Eq. (286) is expected to be a function of the distance from the emitting surface due to generally non-uniform distribution of singlet emitting states S(x) Copyright © 2005 by Marcel Dekker

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Figure 150 Different radiative modes in organic LEDs. External ðextÞ modes available for the face detection ½FEL ] constitutes only a fraction of light generated in the EML, the remainder being lost due to various wave guide modes indicated in the figure.

(cm3) throughout all the sample thickness (see Sec. 3.3). The radiative decay of the excited states is characterized by the rate constant kF (s1). 5.3.1. Steady-state EL In a simplified, often used, picture of homogeneously distributed singlets, their concentration, S, under steady-state electron–hole recombination conditions, can be expressed by a simple equation dS ¼ PS gnh ne kS S ¼ 0 dt

ð288Þ

S ¼ ðPS g=kS Þnh ne

ð289Þ

and

where g is the second order recombination rate constant to be identified with geh defined in Sec. 1.3, kS ¼ kF þ kn is the total decay rate constant including all non-radiative decays with Copyright © 2005 by Marcel Dekker

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the overall rate constant kn, and PS is the probability that as result of the e–h recombination event a singlet excited state will be created (see Sec. 1.4). ðextÞ The evaluation of FEL is now straightforward and leads to ðextÞ

FEL ¼ xPS jFL gnh ne d

ð290Þ

where the jFL ¼ kF=kS determines the relative contribution of radiative decay events of excited singlet states, identified often with the fluorescence (FL) efficiency. Equation (290) relates the EL output to the uniform throughout the emitter concentrations of holes (nh) and electrons (ne) . The latter are naturally associated with hole (jhi ) and electron (jei ) currents injected at the electrodes through the following kinetic equations: jhi nh h gne nh ¼ 0 ed tt

ð291aÞ

jei ne gne nh ¼ 0 ed tht

ð291bÞ

Here, tt ¼ d=mF is the carrier transit time dependent on the carrier mobility, m, and electric field, F, operating in the sample. The bimolecular decay of holes and electrons can be expressed by the recombination time 1 e;h ¼ gnh;e ð292Þ trec to be compared with the monomolecular decay time, tt, of carrier discharge at opposite electrodes. Two limiting cases ðextÞ leading to simplified interrelations between FEL and injection currents have been distinguished based on such a comparison [566a]. These are: (i) Injection-Controlled EL (ICEL) for tt trec. Then, according to Eqs. (291), nh ﬃ jhi =emhF, ne ¼ jei =emeF, and ðextÞ

FEL ¼ xjFL PS g

Copyright © 2005 by Marcel Dekker

jei jhi d e 2 me mh F 2

ð293Þ

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The important message that follows from Eq. (293) is that the light output for organic LEDs operating in the ICEL mode cannot be related directly to the driving current ( j) which must not be identified with the recombination current jR ¼ g

jei jhi d e 2 me mh F 2

ð294Þ

and which is not known from electrical measurements. For the ICEL mode, the EL is a ‘‘side’’ effect of the current flow and its intensity is proportional to the product of the electron and hole injection currents. Several subcases of ICEL can be considered dependent on the carrier injection mechanisms from the electrodes [21] (see also Sec. 4.3). (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 recombination process (a weak leakage of carriers to electrodes), jei ¼jhi ¼ j, and j ðextÞ ð295Þ FEL ¼ xPS jFL e Here, the measured current j is simply the recombination curðextÞ rent, jR, and as long as x, PS and jFL do not depend on j, FEL remains directly proportional to the driving current. The slope ðextÞ of the linear plot of FEL with j determines the product xPSjFL. The variety of results on EL intensity vs. current flowing through device has been observed experimentally (see Ref. 21 ðextÞ and references therein). The FEL has been shown to increase both linearly and non-linearly with increasing current. The latter can be either sublinear and supralinear dependent on the applied voltage range. On the analytic side, the interplay between the recombination and leakage current seems to account for the variety of observations. It is useful to distinguish between SL and DL LEDs because interfacial energy and mobility barriers at two component organic layers in the DL devices increase largely the recombination current, leading to the VCEL operation mode or at least to its ðextÞ approximation. One expects the linear increase of FEL with increasing drive current. In SL devices, it is more difficult to avoid the leakage of charge carriers to opposite electrodes, Copyright © 2005 by Marcel Dekker

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unless perfectly Ohmic electrodes are available. They usually ðextÞ operate in the ICEL mode, and FEL becomes a complex function of the drive current. A careful analysis of the experimental data allows then to distinguish three segments of such a dependence. An example is shown in Fig. 151. The non-linear increase of the EL intensity vs. j in the low-current regime ( j < 5 mA=cm2), passes to a linear segment for the intermediate currents regime (5 mA cm2 < j < 15 mA cm2) and tends

Figure 151 EL output as a function of driving current for four different SL LEDs. (1) ITO= (25% TPD:25% Alq3:50% PC)(60 nm)=Mg, (2) ITO=(50% TPD:30% Alq3:20% PC) (60 nm)=Mg, (3) ITO=(70% TPD:10% T5Ohex:20% PC) (70 nm)=Ca, and (4) ITO=(25% TPD:25% Alq3:50% PC) (80 nm)=Mg. For the molecular structures of the materials used, see Fig. 112. After Ref. 389 Copyright 2001 Institute of Physics (GB). Copyright © 2005 by Marcel Dekker

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to saturation at high current densities. This behavior reflects the gradual voltage evolution of the recombination to the leakage current ratio ( jR=jL; j ¼ jR þ jL). Increasing at low voltages and remaining constant at moderate electric fields, it shows remarkable decrease at high voltages (large current densities). Deviations from the linear relationship FEL( j) also occur in DL organic LEDs. This is illustrated in Fig. 152 showing the EL output vs. current density in a doublelogarithmic scale for one of the most studied DL organic LEDs based on the TPD=Alq3 junction. The low-current density supralinear increase followed by a slightly current-increasing EL output at moderate currents rolls off smoothly as the cell current exceeds 100 mA cm2. All three segments of the FEL( j) curve have been approximated by the power-type functions with the powers given by the log FEL log j straight-line plots. This behavior can be explained by the ICEL mode operation conditions predicting FEL( j) to follow

Figure 152 EL intensity vs. current density for DL LEDs based on the TPD=Alq3 junction: (a) ITO=TPD(60 nm)=Alq3(60 nm)=Mg= Ag structure (left hand scale in absolute units) (see Ref. 21); (b) ITO=TPD(20 nm)=Alq3(40 nm)=Mg:Ag (see Ref. 356). Copyright © 2005 by Marcel Dekker

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expression (293). By definition, the measured cell current ðeÞ ðhÞ j ﬃ ji þji . Thus, Eq. (293) provides the EL output variation with the measured current density ( j) in a form j2 ð296Þ m jSCLC 1 1 where m ¼ m1 . Since the current increase is h þ me imposed by the increasing voltage applied to the cell, both j and jSCLC are the voltage-increasing quantities. Moreover, since by definition j < jSCLC, the FEL must be a function of the injection efficiency, jinj, defined by the ratio ðextÞ

FEL

jinj ¼

j jSCLC

1

ð297Þ

The injection efficiency appears to be a crucial factor for the functional shape of FEL( j). Its variation with the applied voltage depends on the type and quality of the injection contact as illustrated in Fig. 153 for the commonly used hole injection contact ITO=TPD. The irreproducible behavior of the ITO=TPD:PC junction is clearly apparent. The contact can range from Ohmic to strongly blocking with the injection efficiency falling or rising with electric field. Moreover, the falling trend can switch to a rising trend for the same sample at a certain electric field strength. The irreproducible behavior of injection contacts enables understanding of the variety of FEL( j) characteristics. The data in Fig. 152 would indicate a strongly increasing jinj at low fields (low current densities) and its much slower increase at high field (high current densities above 1 mA=cm2). In the upper limit of the attainable currents ( > 100 mA=cm2), the FEL( j) approaches linearity and even a sublinear behavior may be seen from its log–log plot (the data with arbitrary units of FEL). The field-induced enhancement of the injection efficiency is difficult to rigorous analytical treatment because different preparation conditions modify the contact in microscopically uncontrollable manner. Therefore, the interpretation of the strong initial gradient @FEL( j)=@j remains an open question, though a more detailed discussion of the processes that underlie the EL efficiency Copyright © 2005 by Marcel Dekker

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Figure 153 The injection efficiency as a function of electric field for three different ITO=50% TPD:50% PC=Au devices all prepared under the same conditions and having similar thickness, d ﬃ 19 mm (see numbers in the inset). Adapted from Ref. 352.

facilitates its understanding (see Sec. 5.4). A relatively simple explanation for the gradient @FEL( j)=@j ¼ n < 2 (but n > 1) can be proposed if a weakly varying jinj( j) and jh ﬃ je obeying the thermionic injection mechanism (203) is assumed in addition to the exponential field increase of the mobility according to Eq. (265). Under these premises, with the accuracy to a h weakly varying function of F, and with bðeÞ m ﬃ bm ¼ bm , FEL ð jÞ j2bm =a

ð298Þ

The experimental value (2 bm=a) ¼ 1.2 requires bm ¼ 0.76 102 (cm=V)1=2 if a ¼ 0.95 102 (cm=V)1=2 is assumed as calculated from Eq. (204) with e ¼ 2.4 for TPD (note that a slightly lower value for a is obtained in Alq3 ðeÞ ðhÞ due to its higher e; but still the equality ji ¼ ji holds due to a little difference in the injection barriers at ITO=TPD and Mg=Alq3 interfaces, cf. Fig. 84). This value of bm is in good Copyright © 2005 by Marcel Dekker

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agreement with the data obtained from the field-dependence of the TOF-measured mobility for holes [336,340] and electrons [336,425] (cf. Fig. 104) in Alq3. A field-decreasing jinj could explain a slightly sublinear plot of FEL( j) at high current densities. Some additional effects such as the current decreasing of the light output coupling factor (x) or the emission efficiency (jFL) can contribute effectively to the saturation tendency at high voltages. Variations in the factor x can occur as a result of the field-evolution of the recombination zone. Its high-field (large current densities) confinement in the near-cathode region (cf. Fig. 150) may change the ratio of EL intensities in the direction normal to the substrate face ðsurfaceÞ = to that emitted from the edge of the substrate (FEL ðedgeÞ FEL ). In the example shown in Fig. 154, the emission into the external modes is roughly 50% larger than the internal modes, decreasing by about 5% as the drive current increases from 0.1 to 10 mA=cm2. Stronger effects on FEL can be expected

Figure 154 The measured surface-to-edge EL intensities as a function of current density in the DL ITO=a-NPD (50 nm)=Alq3 (50 nm)=Mg:Ag LED. Inset: experimental configuration of light detectors used to obtain data in the figure. Adapted from Ref. 494. Copyright © 2005 by Marcel Dekker

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due to a reduction of jFL, caused by singlet exciton quenching on charge carriers, structural defects and metallic contact itself. The quenching of singlet excitons in organic LEDs based on optimal 60 nm-thick Alq3 emitters has been evaluated to create emission losses between 8% and 30% [566]. These are comparable with the losses caused by high-field assisted dissociation of singlet excitons or their electron–hole pair precursors [302,305,306]. Triplet excitonic interactions have been revealed in EL–current relationships for aromatic crystals [2,21]. The total EL flux from these crystals comprises a fast and delayed component attributed to the radiative decay of the Prompt (PEL)- and Delayed (DEL)- formed singlet excitons. If the DEL component originated from singlet excitons created in the process of triplet–triplet annihilation (Sec. 2.5.1), a superlinear increase of FEL with increasing current would appear even for the VCEL-mode operating devices: ðSÞ

FEL ¼ FPEL þ FDEL ¼ jFL PS tS j þ

jFL gTT t2T ð2PS þ PT Þ 2 j e2 d ð299Þ

The effective power of the FEL( j) jn dependence can vary between one and two, depending on the prompt and delayed component contributions which are determined by the effective lifetimes of singlet (tS) and triplet (tT) excitons along with the probabilities of their formation in the e–h recombination process (PS, PT; cf. Sec. 1.4). The DEL component depends ðSÞ in addition on the T–T interaction constant [gTT ] leading to a singlet exciton, and the sample thickness, d. The EL intensity as a function of the measured current for a number of aromatic crystals is shown in Fig. 155. All of the FEL data follow a supra-linear relationship and can be approximated by a power dependence within limited ranges of the current. The explanation is that the total EL output reflects the averaged signals from the PEL and DEL components according to Eq. (299); the increasing DEL increases the power ‘‘n’’. A decrease in the effective power for high currents seen for neat tetracene crystals (marked by the vertical arrows in Fig. 155a) would suggest the triplet–triplet and triplet–charge carrier Copyright © 2005 by Marcel Dekker

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interactions to reduce the effective triplet exciton lifetime according to 1 ðTÞ teff

¼

1 þ gTT T 2 þ gTq nq tT

ð300Þ

In order to explain variations of ‘‘n’’ from crystal to crystal, the PS dependence on the trap depth of one of the recombining carriers may be invoked. The deeper trapped is the carrier, the lower is the probability of the formation of singlet excitons in the electron–hole recombination process [see Eq. (10)]. Thus, the plots with high ‘‘n’’ reflect the presence of deep traps. This is confirmed by the high power of the FEL(l) jn dependence in doped tetracene crystals. A strong support for the triplet–triplet fusion origin of the DEL comes from the magnetic field effect on the EL from tetracene crystals with different ‘‘n’’ (Fig. 156). While the PL evolution with magnetic field in tetracene is a consequence of the magnetic field effect on singlet exciton fission into two triplets only, the modifying action of the magnetic field on triplet–charge carrier interaction can be seen in the magnetic field evolution of the EL intensity (cf. Sec. 2.5.3). The shape of the plots presented in Fig. 156 clearly shows that both singlet exciton fission into two triplets and triplet exciton quenching by charge carriers occur in the EL process. The reduced decrease in EL intensity at low magnetic fields (below 0.5 kG) as compared with that for PL reflects the EL to contain a DEL component

J Figure 155 The EL intensity as a function of the measured current in neat (a) and doped (b) aromatic crystals. The three curves in part (a) are obtained for three different origin tetracene crystals of thickness 16.5 mm (I), 118 mm (II) and 19.5 mm (III). The data for the tetracene-doped anthracene and pentacene-doped tetracene crystals are shown in part (b), where the EL intensity was measured at host and guest emission bands (445 nm for anthracene, 598 and 575 nm for tetracene and 620 nm for pentacene); the near curve numbers denote the slopes of the straight-line log–log plots. Adapted from Ref. 51. Copyright © 2005 by Marcel Dekker

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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 DEL component (crystals II and I, respectively, from Fig. 155a). The change of photoluminescence (PL) as a function of B is shown by the broken line (curves A). The effect was measured in two different wavelength regions: A and B in the red edge and A and C in the short wavelength and emission maximum. No difference in the shape of field evolution of PL was observed. Reprinted from Ref. 287. Copyright 1975 with permission from Elsevier.

quenched by the triplet–charge carrier interaction process. The overall effect is due to the magnetic field increase of the singlet fission g’s [see Scheme (80)], and monotonic decrease in the triplet–doublet interaction rate constant gTq [see Scheme (110)] as discussed in Sec. 2.5.3.1. The magnetic field decrease in gTq makes the low-field minimum of the EL(B) curves shallower (Fig. 156a) and leads to its disappearance in the crystal with a large contribution of DEL (Fig. 156b). At the red edge (B curves), the EL, at least partly, originates from trapped states which can undergo fission into two inequivalent triplet excitons (heterofission [320]), the process less sensitive to the magnetic field than the homofission. An annihilation of inequivalent triplets (see Sec. 2.5.1.2) can lead to the efficient production of trapped singlets resulting in the large DEL component of the red edge EL. Consequently, the low dip in the magnetic field dependence of EL should be markedly reduced or disappear. This is indeed observed for the crystal in Fig. 156b. The striking is the difference between the power ‘‘n’’ for the host and guest electroluminescence from Copyright © 2005 by Marcel Dekker

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an anthracene crystal doped with a small amount of tetracene (Fig. 155b). The treatment of the FEL( j) behavior in terms of two-component emission response according to Eq. (299) clearly proves that while the tetracene guest emission originates from the tetracene singlets produced directly in the electron– hole recombination on guest molecules, the anthracene host emission is dominated by the DEL originating in the course of the bimolecular fusion of host triplets (see Sec. 2.5.1.2). To obtain the EL intensity (either surface or edge) from an EML constituting a part of a microcavity structure, we need to know the intrinsic spectrum of the radiation from the emissive layer along with its angular intensity pattern, FEL(l,Yi). For a given l, FEL ¼ 2p

Z

p=2

FEL ðYi Þ sin Yi dYi

ð301Þ

0

Both, theory [494,567] and experiment [549,550] show FEL(Yi) [thus FEL(Y); cf. Fig. 142] to be a function of device structure parameters and emission wavelength, the intensity angular pattern FEL(Y) has been shown to deviate, in general, from the classical Lambertian angular distribution of radiation [568]. In Fig. 157, the measured angular dependence of monochromatic emission of a cavity and free-cavity devices from Fig. 141 are compared. Emission with a quasiuniform spatial distribution nearly Lambertian can be observed from the leaky ITO=glass anode device (lacking a well-defined microcavity) at wavelength 500 nm close to the emission maximum (see Fig. 141b). The similarity of the far-field intensity profiles has also been reported with (40– 80 nm) Alq3 layers for glass=ITO=PVK=Alq3=Mg:Ag=Ag LEDs [567] and in polymer LEDs [49,569,570]. In contrast, emission from the microcavity structure becomes strongly directed vertically from a diode surface (Fig. 157a); the angle at the peak intensity varies from Y ¼ 0 to Y ﬃ 30 with selected emission at 505 and 480 nm, respectively. Clearly, no unique resonance condition in the planar microcavity exists when the total broad band emission from the emitter is measured. Multiple matching of cavity modes with emission wavelengths occurs. Copyright © 2005 by Marcel Dekker

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Figure 157 Radial plots of outer emission intensity from a microcavity (a) and microcavity-free (b) structures from Fig. 141 at different emission wavelengths as indicated in the figure. After Ref. 550. Copyright 1993 American Institute of Physics.

Thus, no sharp emission pattern can be expected with the overall emission spectrum. Nevertheless, assuming the Lambertian shape of the emission from microcavity structures may lead to an overestimate as large as 30% [571]. An attempt to compare the measured full spectrum external emission as a function of the emitter thickness (Alq3) with theoretical description of microcavity modes has shown substantial disagreement, the theoretical estimates lead to the emission output much below the experimental data, differing by a factor of 2 for a 40 nm-thick emitter [567]. The reason for Copyright © 2005 by Marcel Dekker

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this discrepancy seems to be associated with different quenching efficiency of singlet excitons at the cathode due to a different location and width of the recombination zone. This point is discussed in more detail in Sec. 5.4. According to Eq. (290), high-brightness LEDs can be fabricated using highly fluorescent (high values of jFL) emitters, strongly injecting electrodes (high concentrations of recombining holes, nh, and electrons, ne), and minimizing light losses (high values of x) . Today, outstanding values exceeding 105 Cd=m2 for organic EL devices are reached. For example, luminance 1.4 105 Cd=m2 and a maximum EL efficiency 2.4 d=A were observed at 12 V from one of multilayer yellowlight emitting device structures using a highly fluorescent aluminum complex, tris(4-methyl-8-quinolinato)aluminium (III) Almq3 [572]. These LED structures and their luminance-voltage characteristics are shown in Fig. 158. The highest luminance has been obtained with a multilayer ITO=CuPc=TPD=coumarin 6:Almq3=Almq3=LiF=Al LED with a coumarin 6-doped Almq3 used as the emitter layer. The large improvement in the device is due not only to doping Almq3 with coumarin 6, which is known as a highly fluorescent laser dye being excited mainly by energy transfer from the host material [16], but also balancing the charge carrier injection by using a 15 mm-thick CuPc [573] as a hole-injecting contact and a 0.5 nm-thick LiF as an electron injection electrode [574]. This electrofluorescent LED also shows a high external quantum EL efficiency of 7.1% photon=carrier (for a more detailed discussion of the factors determining the EL quantum efficiency see Sec. 5.4). 5.3.2. Pulsed EL When addressing a LED by rectangular voltage pulse, a gradual rise of EL intensity is observed that reflects the interpenetration of the charge carrier clouds. Figure 159 shows such a voltage pulse and corresponding current and EL response for ITO=MEH-PPV=Al device. The EL response has been observed in selected spectral regions of the overall emission spectra as shown in the same figure for three different Copyright © 2005 by Marcel Dekker

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Figure 158 Brightness vs. voltage applied to four EL devices (a) and molecular structures of organic materials used for their fabrication (b). The curves correspond to the following structures: (1) ITO=TPD(30 nm)=Almq3(70 nm)=Mg:Ag, (2) ITO=CuPc(15 nm)=TPD (30 nm)=Almq3(70 nm)=Mg:Ag, (3) ITO=CuPc(15 nm)=TPD(30 nm) =Almq3(70 nm)=LiF(0.5 nm)=Al(100 nm), (4) ITO=CuPc(15 nm)=TPD (30 nm)=coumarin 6(1%)-doped Almq3(15 nm)=Almq3(55 nm)=LiF (0.5 nm)=Al(100 nm). After Ref. [572]. Copyright 1998 American Institute of Physics.

devices. The short-wavelength narrow bands in the EL spectra have been identified as the atomic emission lines of the cathode metal (Al, Mg or Ag), and the red-shifted broad emission bands as being characteristic of excited states of the polymer [472]. The observation of polymer emission and cathode metal emission from the same devices, showing the same temporal behavior, has been interpreted as due to hole transport properties of the polymeric material. The delay time between the onset of voltage pulse and the EL response has been found to decrease with applied voltage [cf. Fig. 159(5), (6)] in a manner fitting the Poole–Frenkel-type field dependence of mobility (265) with mh (F ¼ 0) ¼ 1 108 m2=V s and bm ¼ 0.44 102 (cm=V)1=2 (cf. Fig. 106b) comparable to those obtained previously for holes in PPV [575] and MEH-PPV devices [356a,576]. This underlies the suggestion that the light generation occurs in the vicinity of the cathode, the Copyright © 2005 by Marcel Dekker

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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 spectra are recorded at different voltage pulse amplitudes. Characteristic cathode metal emission lines are indicated along with the position of broad band-red shifted emission maxima from the polymers. For chemical meaning of MEH-PPV and of M3EH-PPV, see Figs. 106 and 108. The transient current under a 1 ms pulse (4) and transient response of EL polymer and cathode metal emission spectral regions at two different pulse amplitudes, 4.3 MV=cm (5) and 6.6 MV=cm (6) have been measured on ITO=MEH-PPV=Al device. EL transient are normalized to the maximum intensity of the polymer emission. After Ref. [472]. Copyright 2000 American Institute of Physics.

delay between the onset of voltage pulse and the EL response to be identified with the transit time of holes injected at the ITO anode. The decay of the EL signal after the pulse is turned-off must reflect the recombination process inside the Copyright © 2005 by Marcel Dekker

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recombination zone. A somewhat faster decay of the cathode metal emission than that of the polymer results from different mechanisms of their excitation. Since the polymer emission is associated with the electron–hole recombination on polymer molecules, a delay due to the final release time of the carriers from possibly existing near-cathode imperfections (traps) may contribute to the overall decay constant. This is not the case with the cathode metal emission which is featured of the impact EL [2]. At high fields, the carriers (holes) gain an energy exceeding 3 eV sufficient for impact excitation of metal atoms of the cathode [472]. The physical meaning of this process would be the injection of electron from the cathode to the electronic states with energies below the polymer HOMO level. This process ceases immediately at the voltage pulse end, following the decay of the electric field at the cathode. To excite the Mg atom emission (383 nm), a minimum energy gain is 3.2 eV. As demonstrated experimentally, this energy threshold can be obtained for electric fields above 6.4 MV=cm if the electron mean free path ﬃ5 nm is assumed. Such a large electron mean free path in low-molecular weight organic materials seems to be unlikely (cf. Sec. 4.6), but it is conceivable in conjugated polymers for electrons within long polymer chains characterized by the average conjugation length of ca. eight monomeric segments [577,578]. An open question with SL devices is whether and, if so, to what extent the accumulation of space charge near weaker injecting electrodes (i.e., redistribution of the internal electric field) affects the EL delay time. Such an effect could be expected if a thin interfacial layer is built up between an organic EL material and an electrode due to impurities (e.g., oxygen) or its chemical reactions with electrode forming metals. The presence of the space charge would imply the EL delay time dependence on offset voltages applied to the LED before admitting the rectangular voltage pulse. In fact, transient experiments for the SL ITO=Alq3=Mg:Ag LED have shown the EL delay time (td) to be a function of dc bias voltages [341]. A detailed analysis of the experimental data has shown an inverse relationship between td with increasing current (j), the product td j being of the same order of magniCopyright © 2005 by Marcel Dekker

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tude as CAlq3 U (a few nAs), where CAlq3 denotes the electrical capacity of the Alq3 layer. In contrast to the above discussed ITO=MEH-PPV=(Mg=Ag) system, the recombination zone is here located near the ITO anode, the leaking holes form a space charge near the Mg:Ag cathode, which reduce the electric field inside the Alq3 layer. This picture is consistent with the fact that the injection barrier for holes from ITO to Alq3 is higher than that for electrons from (Mg:Ag) (cf. Fig. 84), and the hole mobility being approximately two orders of magnitude lower than that for electrons in Alq3 [336,579]. Also, it is supported by known ability of Alq3 to react with metals such as calcium, magnesium or gold [580–582]. However, the field dependence of me as well as its absolute values obtained from TOF and time-resolved EL measurements are comparable suggesting the internal electric field to be homogeneous and equal to the nominal value of the applied field [341]. More experimental data would help to resolve these inconsistencies. The EL decay signal after the voltage pulse is turned off is in general non-exponential, reflecting either a combination of the RC time of the experiment setup and the time evolution of the recombination process of the charge accumulated in the sample [341], and=or radiative relaxation of the prompt and delayed components of excited singlets [415]. The former has been analyzed in more detail, using DL EL devices, in Sec. 3.3 (Fig. 60), the latter is illustrated by the tetracene single crystal data in Fig. 160. Vapor grown single crystals of tetracene were provided with sodium– potassium alloy cathodes and semitransparent evaporated gold layer anodes. The EL emission was collected from the gold film covered side of the crystals. Concurrently with the voltage pulse (amplitude: U – U0 ¼ 90 V; width 75 ms), the analyzing generator was started producing narrow t0 ¼ 2 ms-duration pulses with varying delay time 0.5 ms < td < 150 ms. This has made possible to count the EL photons at different times of the EL relaxation. Various levels of bias voltage (U0) were applied from a dc regulated voltage supply to get different steady-state current conditions for the pulsed EL. A fast (t < 10 ns) and delayed (t > 1 ms) components can be distinguished in the time-evolving EL signal (Fig. 160a). The first Copyright © 2005 by Marcel Dekker

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Figure 160 Voltage (a) and current (b) dependence of the timeresolved EL in tetracene single crystals. (a) Reading from bottom to top are the bias voltage U0, the rectangular voltage pulses (U– U0), the relaxation curves of electroluminescence (F) referring to the steady-stale EL level F0, the analyzing voltage pulses with varying duration time t0 and delay time td. (b) The EL decay for two different thickness (d) tetracene crystals (crystal I: d ¼ 16.5 mm; mm; crystal II: d ¼ 118 mm) under different steady-state current conditions (1: j ¼ 63 mA=cm2; 2: j ¼ 23 mA=cm2; 3: j ¼ 0.7 mA=cm2; 4: j ¼ 28 mA=cm2; 5: 6.1 mA=cm2). Adapted from Ref. [415].

one has been attributed to the prompt fluorescence of singlet excitons produced directly by the electron–hole recombination process (cf. Fig. 4), and the second to triplet–triplet fusion created singlets emitting with a time characteristic of the triplet exciton lifetime (10 ms) [260]. The decay rate of the delayed component is determined by triplet–triplet and triplet–charge carrier interaction processes (see Sec. 2.5), and by the recombination of detrapped carriers. Thus, it may differ from crystal to crystal and depend on the current flowing through the crystal. The results presented in Fig. 160b support this conjecture. Their detailed analysis has shown that while the delayed EL component in crystal I follows detrapping of charge, the effective relaxation time of the delayed EL in crystal II is largely determined by the triplet exciton lifetime Copyright © 2005 by Marcel Dekker

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reduced by triplet exciton–charge carrier interaction [415]. This is consistent with steady-state EL output characteristics of the same crystals presented in Fig. 155. In DL organic LEDs, the recombination zone is often located at the HTL=ETL interface and the EL delay with respect to the onset of the rectangular pulse can then be ascribed to the time for slower carriers to reach the interface. In Fig. 161, EL evolution in time from a DL LED based on the TPD=Alq3 junction is presented, showing the field-dependent delay between the onset of a rectangular voltage pulse and the EL response. The delay time has been attributed to the electron drift time from the Mg=Ag cathode to the TPD=Alq3 interface over the thickness of the Alq3 layer. A high-field independent mobility of electrons me ﬃ 1.2 105 cm2=V s, results from the linear decrease of the delay time with applied

Figure 161 EL evolution in time (a) and early time regime of the onset of EL (b) from an ITO=TPD(60 nm)=Alq3(60 nm)=Mg=Ag DL LED after application of a rectangular voltage pulses as a function of pulse amplitude (V). The vertical arrows show the EL onset. After Ref. [309]. Copyright 1998 American Institute of Physics. Copyright © 2005 by Marcel Dekker

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field between 1.25 and 3.3 MV=cm (Ref. 309) in good agreement with the data of Barth et al. [341], but being at variance, with much higher and strongly field-dependent electron mobilities obtained on three-layer LEDs of ITO=4,40 ,400 -tris[n-(mtryl)-N-phenyl-amino]-triphenylamine (MTDATA) (60 nm) = TPD(20 nm) =Alq3(60 nm) =Mg:Ag [583]. Upon turning off the external field, injection of carriers and the potential inside the devices change in a way as to force the stored electrons and holes towards each other. The probability of their recombination is close to unity under VCEL conditions and the nonexponential decay of the EL signal of the form FEL(t) tn with n ﬃ 1 is featured of the Langevin-type recombination (see Sec. 1.3), and under ICEL conditions, due to the reduced leakage, currents as compared with the voltage-on stage, a momentary increase of the EL intensity (‘‘the overshoot’’) appears decaying 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 diffusion of holes injected from the ITO anode towards the TPD=Alq3 interface (see Sec. 3.3, Fig. 60). Typical ICEL transients with overshoots for a polymer-based DL LED are shown in Fig. 162. The magnitude of the EL spike evolves with time. Increasing duration of the voltage pulse applied to the device increases the ratio of peak to EL intensity, indicating the time increase of the space charge builtup at the interface. The appearance of the overshoot effect depends on the relation between recombination and leakage currents under steady-state conditions, thus, on the one hand, dependent on the injection efficiency of the electrodes, and, on the other hand, affected by charge transport properties of the materials forming DL LEDs and energy barriers at the organic materials junction. Therefore, replacement of the PVK matrix in the LED in Fig. 162 by polycarbonate, which causes an increase of the hole mobility, increases the relative height of the overshoot spike; the increased leakage current with voltage on makes the charge recombination better pronounced upon turning the voltage off [528]. Selection and combination of the operating current modes of organic LEDs allows to glean important information Copyright © 2005 by Marcel Dekker

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Figure 162 Temporal evolution of the EL intensity from a DL ITO=50% poly[1,4-phenylene-1,2-di(4-phenoxy-phenyl)vinylene] (DPOP-PPV):50% PVK=20% PBD:80% methylpolystyvene(PS)=Al LED upon application of a rectangular voltage pulse of variable duration marked by the spikes of the overshoot EL signals. Adapted from Ref. 528.

on particular electronic processes underlying their light output and=or improve their performance parameters. For example, alternating current (AC) modulation of the EL intensity from LEDs operated in constant (DC) current mode showed why and how triplet-to-singlet exciton concentration ratio varies with injected charge (thus, voltage applied to the device). The AC–DC interaction in EL of anthracene crystals could be observed by the separate light detection channels as shown in Fig. 163. The AC modulation characteristics (Fig. 164) of the DC EL output have been analyzed in terms of different response of two EL components: [584] 2 d 3 Z Zd ðSÞ T 2 ðx; tÞ dx5 ð302Þ FEL ¼ xkF 4 SðxÞdx þ gTT k1 S 0

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Figure 163 Scheme of the experimental arrangement for AC modulation of EL with DC voltage bias of a crystal LED. The photomultiplier (PM) signal produced by the emitted light (hn) is detected either by a DC or an AC selective milivoltmeter, placing the switches K1 and K2 into positions 1 and 2, respectively, which correspond to the DC(F) or AC(F)-excited electroluminescence. The HV supply allows DC bias of the sample under sinusoidal AC excitation. Reprinted from Ref. 584. Copyright 1983 Springer-Verlag, with permission.

The first is a prompt component (PEL) due to the radiative decay of singlet excitons produced directly by electron–hole recombination and the second is a delayed component (DEL) arising from singlets created by triplet–triplet annihilation, triplets being produced in electron–hole recombination (see Secs. 1.4, 2.5.1.2; also above discussion of the results in Fig. 154, 155, and 159). The root-mean-square modulation brightness jFj to the steady-state EL intensity (F) decreases with the modulation frequency (Fig. 164a), increases with the modulation voltage (Fig. 164b), and reveals a maximum at a certain DC bias, except for the lowest frequencies (Fig. 164c). This behavior has been rationalized by a model of sinusoidal current wave [584]. (see also Ref. 2). This model assumes a sinusoidal voltage U ¼ U0 sin 2pnt (if small as compared with a steady-state voltage bias) to produce the current wave of =n, propagating in the crystal of thickness wavelength l ¼ mF d, j~ðx; tÞ ¼ j þ j0 sin 2p½nt ðx=lÞ Copyright © 2005 by Marcel Dekker

ð303Þ

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Figure 164 The AC modulation signal (F) related to the DC-bias signal (F) from a 32 mm-thick single anthracene-crystal LED [CuI anode=anthracene=(Na=K)cathode] as a function of: (a) AC voltage frequency (n) at Urms ¼ 14 V 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 for n ¼ 6 kHz , dashed lines for n ¼ 6 Hz at different bias voltages, U ¼ 200 V (c), U ¼ 500 V ( ), and U ¼ 700 V ( ). (c) DC bias voltage at the modulation voltage Urms ¼ 14 V with different frequencies, n ¼ 6 Hz ( ), n ¼ 60 Hz ( ), and n ¼ 6 kHz (`). Reprinted from Ref. 584. Copyright 1983 Springer-Verlag, with permission.

where j is the steady-state current flowing through the crystal ¼ U=d is the average field through the sample. The and F current wave represents a carrier flux moving along the field lines. The concentrations of singlet S(x) and triplet T(x,t) excitons can be expressed by ~j solving the rate equations: dS ðSÞ þ kS S ¼ aj~þ gTT T 2 dt Copyright © 2005 by Marcel Dekker

ð304aÞ

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dT þ kT T ¼ bj~ gTT T 2 dt

ð304bÞ

where a ¼ PS=ew and b ¼ PT=ew are generation terms of singlet and triplet excitons within the recombination zone of width w. Note that kT (the effective mono-molecular triplet exciton decay rate constant) and ~j are functions of steadystate voltage U which leads to important consequences in the interpretation of the DC voltage dependence of the AC modulation depth jF=Fj. Solving Eqs. (304) and inserting S(j~) and T(j~) to Eq. (302) yield analytical expressions for both F and F as functions of U, U and n [584]. They predict the general behavior of the jF=Fj ratio as a function of these variables, and allow a quantitative fit to the experimental data. The experimental jF=Fj ¼ f(n) curves in Fig. 164a have been fitted with optimized triplet exciton lifetimes tT ¼ 5.7, 4 and 0.8 ms going from U ¼ 150 V, through 300 up to 700 V. The triplet exciton lifetime decreases with DC bias voltage because of the voltage increasing concentration of charge carriers which act as effective triplet exciton quenching centers. The shortened triplet exciton lifetime results in a reduction of the DEL (but not PEL) intensity [the second term in the square brackets of Eq. (302)], and the voltage varying triplet exciton lifetime can account for this behavior. We note that increasing U translates into increasing j and current wavelength l in Eq. (303) defining the current wave. Three major ranges in the frequency decrease of the jF=Fj can be distinguished: the low-frequency range (<100 Hz), where a nearly constant high value of MD is observed, the high-frequency range ( >10 Hz) with a nearly constant but much lower MD, and the intermediate frequency range (100 Hz–1 kHz), where the relative modulation signal decreases markedly. The reason for such a cascade-like behavior is the changing relation between the modulation period (n 1) and the effective triplet exciton lifetime. In the low-frequency range [n < kT(U)], the charge concentration changes are slow enough for triplet excitons to follow them during the triplet lifetime, both PEL and DEL intensities are subject to the AC modulation. For n comparable with kT, the quenching of triplet excitons and followCopyright © 2005 by Marcel Dekker

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ing modulation of the DEL component become less efficient, the MD decreases within the intermediate frequency range. As the frequency continues to rise ( > 1 kHz) only the PEL component can be modulated, MD saturates with increasing frequency. Naturally, the range of both low- and high-frequency plateau increases with increasing DC bias voltage because the accompanying increase of the concentration of the injected charge reduces the lower and upper limits of the effective triplet lifetime [cf. Eq. (300)]. Further, one would expect n lim ﬃ kS ﬃ 108 Hz to be a limiting frequency of the modulation since for n > n lim the period of U becomes shorter than the singlet exciton lifetime tS ﬃ 10 ns [333]. This relatively high value of n can, however, be effective only in thin crystals or films for which d=mF < 10 ns. This means that with F ¼ 104 V=cm, dlim ¼ 1 mm. For any d=F < 104 (cm=V) dlim(cm), n max < n lim and should increase, as the DC voltage increases. These predictions are confirmed by the experimental results of Fig. 164a. Some differences between the experimental values of the effective n max and those calculated as mF=d come from the assumption F ¼ U=d, which, for space charge limited current conditions holding in this experiment, is only a rough approximation. As intuitively understood, the modulation depth increases with U, a linear increase being observed at the highest DC voltages (Fig. 164b). The periodic carrier injection used above for explaining the U frequency and strength modulation of a DC-biased EL signal from an anthracene crystal-based LED is insufficient to understand the non-monotonic variation of the MD with DC bias voltage apparent at higher frequencies (Fig. 164c). Redistribution of singlet to triplet concentration ratio with DC is required to attain this goal. Due to a relatively low concentration of the charge stored in the crystal, positions of quasi-Fermi levels are far from suitable free carrier bands (taken to be positive with the gap-sided edge of the bands) at low voltages and the probability PS of creation of excited singlets can be very low because it is to a large extent controlled by the deeply trapped free charge carrier recombination process described by Eq. (10). The trapping levels are filled sequentially as U increases and the shallow-trapped-free carrier recombination Copyright © 2005 by Marcel Dekker

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dominates the recombination process. Since PT is practically independent of U (can change between 3=4 and 1; see Sec. 1.4), the total voltage dependence of PS=PT proceeds through PS(U). Thus, modulating AC voltage changes the concentration of emitting singlets by directly varying the concentration of charge and indirectly by periodic shifting the position of quasi-Fermi levels among a manifold of deep traps. If at low voltages PS is very low, the EL output is dominated by the delayed EL component proportional to the concentration of triplets T jtT. Modulating DEL at low frequency (e.g., 6 Hz in Fig. 164c), the MD jF=Fj follows roughly the voltage decreasing triplet exciton lifetime, the effect compensated partly by increasing ratio FPEL=FDEL. As a consequence, a slightly decreasing modulation effect is observed. At higher voltages, when FPEL=FDEL ratio becomes established at a constant level, reflecting spin statistics in the formation of singlet and triplet excitons, the MD follows roughly a decreasing value of the triplet exciton lifetime. The same situation occurs at higher modulation frequencies in the high-field region. However, a remarkable difference can be seen in the low-voltage region. Here, the increasing MD is explained by the decreasing role of triplet–charge carrier interactions the MD increase being assigned to the increasing PS=PT ratio. Charge trapping modifies the overall performance of organic LEDs significantly [585,586]. The EL output from a DL=LED based on vacuum evaporated blue emitting film of para-hexaphenyl has been shown to increase by more than one order of magnitude as the period of duty cycle of the pulse operated devices increased from t ﬃ 10 ms (determined by the RC time constant of the experimental setup) to 500 ms (Fig. 165). It has been rationalized in terms of electron injection enhancement at the Al cathode due to the enhanced field imposed by the space charge of holes blocked at the PHP=DOB interface. The magnitude of the enhancement is determined by the accumulation build-up time on a millisecond time scale [585]. Figure 166 compares the luminance stability of organic EL devices driven by different current modes. The device driven by the PC mode shows better stability compared with the devices operated in the DC and AC modes. Copyright © 2005 by Marcel Dekker

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Figure 165 Chemical structures of hexaparaphenyl (PHP) and 4,40 -diamino-octofluorobiphenyl (DOB) and the device structure based on these materials (a). The EL output vs. period of applied voltage rectangular pulses (Uappl ¼ 14 V; F ¼ 0.7 MV=cm; j ¼ 11 mA= cm2); duty cycle 50% (the dashed line is a guide to the eye) (b). After Ref. 585. Copyright 1998 Wiley-VCH, with permission.

While the light output decreases to 70% of its initial value after 250 hr for the DC driven device, this period increases through 500 hr for the PC up to 1000 hr for AC operated devices. The origin of these differences is, as yet, not quite clear although some possibilities, including trapping effects, can be speculated. In general, they must be associated with chemical and morphological changes in the bulk as well as at electrodes during continuous device operation. Chemical reactions lead to degradation of the emitting layer, producing effective quenchers of the emitting states. The degree of the degradation proceeds with the number of charges passed through the device (thus, operation time). A likely cause for the most rapid degradation mechanism (100 hr time scale) of organic device layers is a morphological change of the material. It is likely that the initial disorder ‘‘frozen’’ in metastable molecular orientations, relax to a more crystalline state affecting carrier transport and shape of the emission spectrum. This relaxation would occur more rapidly at higher temperatures and high applied fields. The microscopic origin of the luminescence loss may be related to a change in the carrier mobility or carrier injection, which, for example, would Copyright © 2005 by Marcel Dekker

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Figure 166 The time dependence of device luminance (a) for a three layer LED (b) operated at a field ca. 1 MV=cm as driven by the direct current (DC), alternating current (AC) and pulsed current (PC) modes. The frequency of the pulsed excitation was 1 kHz for both the AC and DC modes. After Ref. 586. Copyright 2000 Jpn. JAP, with permission.

worsen the carrier balance. In contrast to the LEDs based on low-molecular weight organic materials (cf. Fig. 166), the longest term degradation mechanism in polymer LEDs seems to be independent of the current operation mode. Time for the device luminance to drop to half of its value is roughly the same for the DC and PC driven devices, but decreases largely with temperature as shown in Fig. 167. These results suggest that ultimate degradation of these polymeric devices comes mainly from a bulk degradation of the polymer film, resulting Copyright © 2005 by Marcel Dekker

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Figure 167 Time for the derivative of PPV (OC1C10)-based device, ITO=polyaniline(50 nm)=OC1C10(100 nm)=Ca=Al, to drop to halfluminescence of its initial value plotted as a function of temperature. 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, 200 Hz, same average luminance as DC devices). Current density for DC driven devices is 8.3 mA=cm2. After Ref. 587. Copyright 1999 American Institute of Physics, with permission.

in a loss of luminance, whereas, low-molecular weight material-based devices seem to include more markedly interfacial deterioration mechanism such as oxidation and oxides decompositions at electrodes, diffusion of metals and their reactions with organic molecules (for a more systematic description of degradation mechanisms in organic LEDs the reader is referred to Nguyen et al. [3]). Copyright © 2005 by Marcel Dekker

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5.4. QUANTUM EL EFFICIENCY The quantum EL efficiency is one of the most important critical figures of merit for organic LEDs and by definition relates the photon [hn(J)] flux per unit area [FEL ¼ IEL=hn (photon=cm2 s), where IEL is the light energy (radiant) flux per 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 of the current into light. The quantum efficiency (QE) defined by Eq. (305) can be associated with other performance parameters such as the dimensionless energy conversion efficiency Z¼

EEL Ui

ð306Þ

where EEL is the light-energy (radiant) flux (Watt) and Ui is the electrical power (Watt) supplied to the device jEL ¼

eU Z hn

ð307Þ

It follows from Eq. (307) that for the applied voltages U > 3 V, jEL > Z whenever emission occurs within the visible light range. We note that the definition equation (305) assumes monochromatic emission at a constant photon energy, hn. Commonly, the radiant flux IEL is measured over the total emission band f(hn), and the averaged photon energy hhni must be used to obtain FEL, R1 hnf ðhnÞ dðhnÞ hhni ¼ 0R 1 ð308Þ 0 f ðhnÞ dðhnÞ Furthermore, for the face detected emission (as usually is the case), the light output coupling factor (287) reduces the meaðextÞ sured FEL to FEL , so that we deal with the external quantum EL efficiency ðextÞ

ðextÞ

jEL ¼ xjEL ¼ eFEL =j Copyright © 2005 by Marcel Dekker

ð309Þ

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which can be a small fraction of the internal EL quantum efficiency, jEL (cf. discussion in Sec. 5.3). Also, the angular intensity pattern of the emitted light must be taken into account [cf. Eq. (301)]. So that, the precise estimation of the EL QE requires experimentally measured angular distribution of the EL intensities at all wavelengths within the emission spectrum (note that emission spectra differ in general when measured at different observation angles) (see Figs. 140–142); IEL(hn,Y), and then their summation ðextÞ jEL

R1 2pxe 0 IEL ðhn; YÞ sin YdðhnÞdY .R ¼R 1 1 hnf ðhnÞdðhnÞ 0 0 f ðhnÞdðhnÞ

ð310Þ

Commonly, the Lambertian emission pattern is assumed, and Eq. (310) often approximated by Z 1 pex ðextÞ IEL ðhnÞ dðhnÞ ð311Þ jEL ﬃ jhhni 0 For the integral in Eq. (311), the total energy flux per unit area as measured by a radiometer at the normal direction to the emissive surface is substituted. This approximation can lead to substantial (up to 30%) deviations from the external value of the EL efficiency expressed and measured according to Eq. (310) [571]. In optoelectronic applications, photometric quantities are often used to express the degree of the current conversion into light. The luminous efficiency with the Lambertian emission pattern is pL0 Cd ðextÞ ð312Þ jEL ðLÞ ¼ A j where L0 is the luminance L (Cd=m2) at normal incidence. The luminous efficiency of 1 Cd=A corresponds to 4p lm=A. The photopic vision function V(l) must be invoked to translate luminous to physical quantities [588]. Z 1 pexL0 ðextÞ f ðhnÞVðhnÞ dðhnÞ ð313Þ jEL ¼ hKm jhhni 0 Copyright © 2005 by Marcel Dekker

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The constant Km ¼ 673 lm=W is here the luminous efficiency at l ¼ 555 nm, where the function V(l) reaches its maximum. For example, a very high luminous efficiency 28 Cd=A 350 lm=A for an electrophosphorescent LED based on the Ir(ppy)3:CBP emitter translates into the power conversion efficiency Z ﬃ 30 lm=W( 0.056) and the quantum efficiency ðextÞ jEL ﬃ 10% photon=carrier at L ﬃ 100 Cd=m2 [589]. By comparing Eq. (309) with Eq. (295), the external EL quantum efficiency ðextÞ

jEL ¼ xPjr

ð314Þ

can be simply expressed by the probability of creation of a singlet (P ¼ PS) or triplet (P ¼ PT) exciton and the efficiency of their radiative decay (jr). It is important to note that Eq. (295), thus (314), assumes the recombination probability PR ¼ 1. This is indeed the case when the driving current coincides with the recombination current, or in other words, for the upper limit of the VCEL operating LEDs. Whenever, the LED function obeys the ICEL operation mode, Eq. (295) is no longer valid, and ðextÞ

jEL ¼ xPPR jr

ð315Þ

where PR ¼

krec <1 krec þ kt

ð316Þ

is the recombination probability defined by the bimolecular recombination (krec) and monomolecular (kt) decay first order rate constants. To get a better physical picture of the phenomena underlying PR, it is convenient to replace the rate constants by their 1 inverses trec ¼ k1 rec and tt ¼ kt which have been defined as the recombination time (292) and carrier transit time (248), respectively. Then, PR ¼

1 1 þ trec =tt

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ð317Þ

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From Eq. (317), it is clear that maximizing PR (thus jEL ) requires minimizing the ratio trec=tt, PR ! 1 as trec=tt ! 0. For trec ¼ tt, PR ¼ 1=2, and for trec=tt 1, PR ﬃ tt=trec. The ICEL and VCEL modes can be redefined on the basis of PR. The ICEL mode, when the major carrier decay is due to the electrode capture, assumes PR < 1=2, i.e., trec=tt > 1; the VCEL mode under the carrier decay dominated by the recombination applies for PR > 1=2 , i.e., trec=tt < 1. The PR and thus trec=tt ratio can be determined from the absolute value of ðextÞ jEL if x, P and jr are provided independently [see Eq. ðextÞ (315)]. Since, typically, jEL shows a non-monotonic dependence on driving voltage (field applied to a device), the field dependence of trec=tt has been extracted from such experimental data. In Fig. 168, several examples of electrofluorescence and electrophosphorescence quantum efficiency along with the luminescence efficiency are presented, and the field dependence of trec=tt given in addition in Figs. 169 and 170. Independent of the LED structure, the initial field (or current) increase in ELQE is followed by the roll off preceded by more or less broad maximum dependent on the carrier injection efficiency from the electrodes and transport properties of the materials forming the EL device. Caution is appropriate concerning the generalization of some literature results showing the high-field saturated (see e.g., Ref. 474) or increasing (see e.g., Ref. 397) EL efficiencies, since they can be simply due to the limited range of the applied field or to modified external interactions of excitons with metal electrodes (see discussion below). Figure 170c,d shows the variations of trec=tt with applied field. As expected, the minima occur at the field strengths corresponding to those for the maxima of the ELQE (Fig. 170a,b). The ratio trec=tt exceeds unity within the entire range of electric fields attained, though for the highest concentrations of TPD in the HTL, it approaches unity. This indicates that all these LEDs operate in the ICEL regime approaching the demarcation value of trec=tt ¼ 1 (PR ¼ 1=2) below which the VCEL mode sets in. The absolute values of the trec=tt ratio as well as their electric field gradient may be a subject to some uncertainties associated with the assumption of the field independence of x, P, Copyright © 2005 by Marcel Dekker

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and jr. However, the apparent trend of the ratio to decrease with concentration of TPD in HTL suggests its values (thus, ðextÞ jEL ) to be associated with the injection efficiency of holes. In fact, using the definition equations for trec (292) and tt (248), we find me;h F trec ¼ gnh;e d tt

ð318Þ

which for comparable concentrations of holes and electrons (nh ﬃ ne) translates into trec eme;h ðme þ mh ÞF 2 8 e me;h ðme þ mh Þ jSCL ¼ ¼ 9 e0 e meff g tt gjd j

ð319Þ

where jSCL=j is the inverse of the injection efficiency defined by Eq. (297) and meff is the effective mobility of the carriers (237) under double injection current ( j). Assuming me,h and g J Figure 168 The EL external quantum efficiency as a function of applied field (a) and luminance efficiency as a function of applied voltage (b) for various organic LEDs. 1:ITO=[6% wt Ir( ppy)3:74 wt% TPD:20 wt% PC](50 nm)=100% PBD(50 nm)=Ca=Ag; 2: ITO=TPD(60 nm)=[0.5 wt% quinacridone(QAC):Alq3](50 nm)=Mg; 3: ITO=TPD(60 nm)=Alq3 (60 nm)=Al-CsF; 4: ITO=TPD(60 nm)= Al-LiF; 5: ITO=TPD(60 nm)=Alq3(60 nm)=Mg; 6: ITO=(75 wt% TPD : PC) (60 nm)=Alq3(60 nm)=Mg; 7: ITO=(75 wt% TPD:PC) (60 nm)=Alq3(55 nm)=Mg; 8: ITO=TPD(60 nm)=(0.5% QAC:Alq3) (50 nm)=Al; 9: ITO=polyethylenedioxythiophene(PEDOT)(20 nm)= terphenyl-PPV(80 nm)=low-work function cathode; 10: ITO=PEDOT (20 nm)=polyspiro[2,20 ,7,70 -tetrakis (2,2-diphenylamino)spiro-9,90 bifluorene (Spiro-TAD); 2,20 ,7,70 -tetrakis (2,2-diphenylvinyl) spiro-9,90 bifluuorene (Spiro-DPVBi)] (80 nm)=low-work function cathode; 11: ITO=PEDOT(20 nm)=Spiro-TAD(20 nm)=[Alq3:DCM](10 nm)=Alq3(30 nm)=cathode (not speci-fied); 12: ITO=polystyrene sulphonate (PSS):PEDOT=polyfluorenes or PPV=low-work function metal cathode (ink-inject printed organic layers); 13: as in item 12 with the spin coating prepared organic layers; 14: ITO=PEDOT(20 nm)=[4 wt% PtOEP: (PMMA:Alq3(1:1)) (100 nm)]=Ca=Al; 15: ITO=PEDOT(20 nm)=[4 wt% PtOEP:(PMMA:PBD)(1:1)(100 nm)]=Ca=Al.

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Figure 169 External quantum efficiency of molecularly dopedpolymer-based SL LEDs from Fig. 151 as a function of electric field (a), and recombination-to-transit time ratio for three of them, obtained from Eqs. (315) and (317) with P ¼ PS ¼ 0.25, x ¼ 0.6 and jr ¼ 11% for LEDs 1,2 and 3, respectively (b). After Ref. 389. Copyright 2001 Institute of Physics (GB), with permission.

to be field-independent parameters, the ratio trec=tt is inversely proportional to the injection efficiency jinj ¼ j=jSCL. The decreasing tendency in the trec=tt ratio with increasing concentration of TPD in HTL is compatible with this prediction since the injection efficiency increases as the concentration of the electron donor centers (TPD) at the contact with ITO increases [see discussion of Eq. (271)]. Equation (319) expresses that the field dependence of the ratio trec=tt is governed by the field dependence of the mobilities, me, mh, recombination coefficient, g, and injection efficiency, j=jSCL. For the Langevin recombination mechanism, the g is governed by the carrier motion [see Eq. (4)] so that Eq. (319) can be simplified to trec 8 me;h jSCL ¼ ð320Þ 9 meff j tt Two different expressions have been presented for meff in Sec. 4.5, for the weak recombination case (240) and for the strong Copyright © 2005 by Marcel Dekker

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Figure 170 External EL quantum efficiency plotted against current density (a) and against applied field (b) driving ITO=(% TPD:PC)(70 nm)=Alq3(60 nm)=Mg=Ag DL LEDs with different concentrations of TPD in the HTL (given in the figure). Corresponding recombination-to-transit time ratio calculated from Eqs. (315) and (316) using the data for jEL and x ¼ 0.6, jr ¼ 25% and P ¼ PS ¼ 0.25, and plotted against the current (c) and applied field (d). After Ref. 303. Copyright 2001 Institute of Physics (GB), with permission.

recombination case (241). They would correspond to the ICEL operating LED’s ratio

trec tt

2 me;h jSCL ﬃ pﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 p me mh j ICEL

Copyright © 2005 by Marcel Dekker

ð321Þ

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and to the VCEL operating LED’s ratio trec 8 me;h jSCL ﬃ tt VCEL 9 me þ mh j

ð322Þ

The experimental values of trec=tt if Figs. 169 and 170, all exceeding unity, and of jinj ¼ j=jSCL 1 as shown in Fig. 171 indicate that the ICEL operation mode occurs typically for TPD=Alq3 junction-based LEDs, and trec=tt should obey Eq. ðextÞ (321). A higher value of jEL for the (75% TPD:PC) HTL as compared with the 100% TPD HTL LED can be explained by different morphology of recrystallizing pure TPD and TPD mixed with PC binder layers. Due to the mass transport for crystallization of initially amorphous pure TPD films, bare ITO glass islands are formed [596] reducing the effective area for hole injection. The polymer (PC) suppresses the crystallization process in the (TPD:PC) layers, making them less rough [597] and covering uniformly accessible area of the substrate. Thus the injection current from ITO is a result of trade off between the effective injection area and concentration of electron donor centers (TPD) in the HTL [303]. Taking I Figure 171 Comparison of the electric field dependence of injection efficiency for the TPD=Alq3 junction-based DL LEDs using the experimental data for j published in the literature and jSCLC calculated from (236) and (241) assuming meff ¼ me þ mh with mh ¼ mh(TPD) þ me(Alq3) ﬃ mh(TPD) ﬃ 5.2 104(cm2=V s) exp(0.0187 F1=2), and e ¼ 3. (a) The data obtained for the following structures: (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%TPD:PC (60 nm)= Alq3(120 nm), (4) ITO=75% TPD:PC(60 nm)=Alq3(60 nm)=Mg=Ag (See Ref. 303), (5) ITO=100%TPD(60 nm)=Alq3(60 nm)=Mg (see Ref. 590), (6) ITO= 100% TPD(47 nm)=Alq3(62 nm)=Mg:Ag (see Ref. 303), (7) ITO=100% TPD (60 nm)=Alq3(60 nm)=Al-CsF=Al, (8) ITO=100% TPD(60 nm)=Alq3(60 nm)=Al-LiF AC (see Ref. 590). (b) Theoretical fit (solid lines) according to the diffusion-controlled injection current DCC (231), j ¼ 5 106 exp(0.017 F1=2) and Schottky-type injection current (203), j ¼ 5 106 exp(0.0095F1=2). Circles and up triangles are the data 4 and 6 from part (a). Copyright © 2005 by Marcel Dekker

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(trec=tt) ﬃ 5 at 106 V=cm (100% TPD=Alq3 in Fig. 170d) me,h= pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ me mh ﬃ 102 follows from Eq. (321) using jSCL=j ¼ 1.4 103 from Fig. 171a (curve 4). This implies the me mh choice for pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the me,h in the numerator of the ratio me;h = me mh ¼ me =mh , and me=mh ﬃ 104. This is not the case neither for me and mh in Alq3 (me=mh ﬃ 102; see Ref. 336) nor me in Alq3 and mh in TPD (me=mh ﬃ 102; Refs. 336 and 338). Thus, the only possibility to rationalize this ratio is attributing mh ﬃ 107 cm2=V s to holes in Alq3 and me ﬃ 1011 cm2=V s to electrons in TPD (at F ¼ 106 V=cm). The latter is a very low value, difficult to measure under usual TOF conditions as reported in the literature [338]. We note that applying Eq. (322) to the same data gives me ﬃ 102mh which could relate the electron mobility in Alq3 ( ﬃ 105 cm2=V s; see Ref. 341) to the hole mobility in TPD ( ﬃ 103 cm2=V s; Ref. 338). The latter can be easier acceptable for the lowest trec=tt ! 1 obtained with the (75% TPD:PC) =Alq3 structure at F ﬃ 1.4 106 V=cm (Fig. 170d) and with jinj ﬃ 102 (Fig. 171a). An important message follows from Fig. 171b. The figure reveals a distinct difference between the field dependence of the injection efficiency for the currents controlled by diffusion (see Sec. 4.4) and those limited by the field-assisted thermionic injection (see Sec. 4.3.2). Both jDCC and jILC are proportional to the product F3=4 exp(beffF1=2), ILC but bDCC eff ¼ a þ bm as compared with beff ¼ a. Clearly, ILC bDCC eff > beff because the former contains a term bm characteristic of the Poole–Frenkel-type electric field increase of the carrier mobility [cf. Eq. (265)]. The field dependence of the jDCC=jSCL ratio agrees very well with the experimental data ðDCCÞ following the DCC behavior of j with beff ¼ 0.017 (cm=V)1=2 [68]. This does not exclude the occurrence of the ILCs in other EL structures. It is worthy to note here that the (trec=tt) ratio differs from zero (PR < 1) even for j ¼ jSCL. Yet

trec tt

ﬃ SCLC

1 1 þ mh;e =me;h

ð323Þ

according to Eq. (322), and trec=tt ! 0 (PR ﬃ 1) only if mh,e me,h. For mh,e ¼ me,h, trec=tt ﬃ 1=2 (PR ﬃ 2=3), and for mh,e me,h, Copyright © 2005 by Marcel Dekker

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trec=tt ﬃ 1 (PR ¼ 1=2). Let us consider the case of an SL LED based on TPD, where mh me. Surprisingly, the PR for holes and electrons is different. Equations (323) and (317) yield trec=tt ﬃ 1 and PR ¼ 1=2 for holes, and trec=tt ! 0 and PR ﬃ 1 for electrons. However, it can be understood if the spatial distribution of the injected charge will be taken into account. The formal condition for the SCL current is the concentration of the injected charge at the injecting contact to attain infinity (cf. Sec. 4.3.1), so that trec ¼ (gn)1 ! 0 only at the contacts. Since fast holes reach the opposite contact (cathode) after a short time (tt ! 0 for mh ! 1), and slower electrons reach the anode after a much longer time (tt ! 1 for me ! 0), the ratio trec=tt for holes equals 1, and tends to 0 for electrons. This reflects in the position and width of the recombination zone as discussed already in Sec. 3.3 and addressed in more experimental context later on in this section. It follows from experiment that the injection efficiency and carrier mobilities increase or at least not diminish at high electric fields (F > 105 V=cm) in amorphous or polycrystalline organic layers forming thin film LEDs (see e.g., Figs. 104, 109, 153, 171a). This should give a monotonic decrease in trec=tt (320), unless me,h is a much stronger field increasing function than meff. As a conðextÞ sequence PR and jEL are expected to be monotonically increasing functions of applied field. Indeed, such a behavior can ðextÞ be observed in the lower-field segment of the jEL (F) curves. The question arises what is the reason for the high field decðextÞ rease of jEL (F). One of them could be a transition from the Langevin to Thomson description of the volume recombination process (see Sec. 1.3). The recombination coefficient g in Eq. (319) cannot be longer expressed by the mobility of charge carriers [see Eq. (4)] and trec=tt follows a field increasing function of the mobility in the numerator of Eq. (319) or=and field-decreasing g. The Thomson-like recombination occurs whenever the capture time (tc) in the ultimate step of the recombination process becomes comparable with the dissociation time (td) of an initial (Coulombically correlated) charge pair (CP). Such a recombination scheme, depicted in Fig. 172, allows PR to be expressed by Eq. (3). However, to complete this picture, the overall recombination probability should also Copyright © 2005 by Marcel Dekker

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Figure 172 Two-step kinetic scheme of the volume-controlled recombination (VR), taking into account the motion (tm) of oppositely charged carriers forming a correlated eh pair (CP) and its decay by either the back dissociation (td), direct transition (tCP) to the molecular ground state or the ultimate capture (tc) of each other leading to an excited singlet state (S1) which produces electrofluorescence (hn EL). Note that the capture can create other excited states as indicated in Fig. 11. After Ref. 598. Copyright 2001 Jpn. JAP, with permission. ð3Þ

include exciton–charge carrier interaction [PR ]. Then ð1Þ

ð2Þ

ð3Þ

PR ¼ PR PR PR ¼ð1 þ tm tt Þ1 ð1 þ tc =td Þ1 ð1 þ tS =tSq Þ1 ð3Þ

ð324Þ

where PR ¼ (1 þ tS=tSq)1 for excited molecular singlets is determined by the ratio of the singlet exciton lifetime tS to their quenching time (tSq) due to the interaction with charge carriers (q) (the direct relaxation of the CP states has been assumed to be very slow as compared with td and tc). Singlet exciton–charge carrier interaction has been considered as the process contributing to the electrofluorescence roll off at high electric fields [566], and has been shown to modify the electric field-induced PL quenching rate [233]. A comparison of the electric field dependence of the PL quenching rate in Alq3 when using non-injecting Al electrodes [233,302,305,306] and electron injecting Mg:Ag cathode [233] allows to evaluate the singlet exciton–charge carrier interaction rate constant, gSq. In Fig. 173, a higher quenching rate of PL is observed when the Mg:Ag cathode device is used in the PL quenching Copyright © 2005 by Marcel Dekker

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Figure 173 Electric field dependence of the PL quenching rates of two different devices: ITO=Alq3(200 nm)=Mg:Ag ( ) and ITO= Alq3(100 nm)=Al ( ) (with a solid line as a guide to eyes). The negative values of the electric field indicate the negative bias of the ITO electrode. After Ref. 233. Copyright 2001 Jpn. JAP, with permission.

experiment. The difference in the quenching rate Dkq ﬃ 9 106 s1 at F ¼ 1.4 106 V=cm can be ascribed to the quenching rate of singlet excitons by injected electrons. Thus gSq ¼ gSe ¼ Dkq=ne ﬃ 109 cm3 s1 is obtained for ne ﬃ j=e meF ﬃ 1016 cm3, identifying the current as the electron injection current from the Mg:Ag cathode. This yields tSq ﬃ 107 s. The fluorescence quenching by injected holes has been suggested to occur in thin (15 nm) layers of donor-type materials of tetra(N,Ndiphenyl-4-aminophenyl) ethylene (TTPAE) [599]. However, a more exact analysis of the data leads to a conclusion that the effect is due to the field-induced dissociation of singlet excited states rather than to their hole quenching. The fieldinduced dissociation of singlet excitons in Alq3 also seems to be responsible for the quenching effects in the devices with Copyright © 2005 by Marcel Dekker

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the Al cathode and negatively biased ITO electrode (Fig. 173). This point has been discussed and the effect supported by the charge photogeneration measurements in Sec. 2.6. The fieldassisted dissociation seems to commonly appear whenever the excited states are produced in the presence of high electric fields regardless of their spin multiplicity (singlets or triplets), type of excitation (optical or electrical) (cf. Sec. 2.6) and electronic properties of the material (evidence for electric field-assisted dissociation of excited singlets in conjugated polymers has been reported in several works, see e.g., Refs. 600–602. Various dissociation models have been discussed to explain the experimental results, but excellent agreement with experiment is provided by the 3D-Onsager theory of geminate recombination as demonstrated in Fig. 47 for high ð2Þ electric fields. Employing this model to PR and substituting ð1Þ ð2Þ ð3Þ PR ﬃ PR PR (that is assuming PR ¼ 1) to (315), the field dependence of the EL quantum efficiency (QE) can be calculated for different current conditions. The results are presented in Fig. 174. The role of the field-assisted dissociation upon Ohmic injection (SCLC in the figure) is to reduce the low-field constant value of the QE starting from ca. 10% at 105 V=cm up to an order of magnitude at 5 106 V=cm for r0=rc ¼ 0.15 that is for the initial inter-carrier separation of eh pairs r0 ﬃ 2.3 nm (rc ﬃ 15 nm with e ¼ 3.8). In the case of either diffusion-limited current (DCC) or Schottky-type injection current, the low-field decrease in QE is observed, then QE passes through a series of minima and maxima whose positions are sensitive to the average initial intercarrier separation, r0. For the DCC case, one well-pronounced maximum occurs around 0.8 MV=cm, the field evolution above 105 V=cm resembles typical experimental results presented in Fig. 168. In contrast, only weak features on the QE(F) curves for the Schottky-type injection underlain device currents can be distinguished with a general decreasing trend in QE. This prediction is in reasonable agreement with variation of the relative EL efficiency as a function of applied bias at room temperature for a 90 nm-thick film of TPD provided with a weakly injecting Al cathode (Fig. 175). Quantitative comparison between theory and experiment for DL TPD=Alq3 Copyright © 2005 by Marcel Dekker

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Figure 174 The field dependence of the EL quantum efficiency (QE) in TPD=Alq3 junction-based LEDs working in the VCEL mode as calculated from Eqs. (315), (322), and (324) with x ¼ 0.2, P ¼ PS ¼ 0.25, jr ¼ 0.25 and e ¼ 3.8 at T ¼ 298 K. The following ð1Þ assumptions have been made in the calculation: PR ¼ (1 þ tm=tt)1 with tm=tt ﬃ 2 mh(Alq3)=mh(TPD)(jSCL=j) and field-dependent mobilities mh(Alq3) and mh(TPD) in Alq3 and TPD, respectively, and (jSCL=j) ð2Þ taken from Fig. 171b; PR ¼ (1 þ tc=td)1 with tc=td ¼ tcn 0 OOns(F), OOns(F) given by (137) at different ratios of r0=rc (cf. Sec. 2.6) and tcn 0 ¼ 10. The small circles marked curves are due to the QE deterð1Þ mined solely by the PR . Note the difference in the curve shapes for three different injection mechanisms (SCLC, DCC, and Schottkytype injection). After Kalinowski and Stampor, unpublished.

junction-based LEDs indicates that the dissociation quenching only is unable to reproduce the functional dependence of the QE on applied field (Fig. 176a), but completed with quenching due to singlet exciton–charge carrier interaction yields good agreement (Fig. 176b). The latter can be reached at tcn 0 ¼ 15, where n 0 is the usual frequency factor equal to 1012–1013 s1. This allows to evaluate the capture time tc on 1.5 (1012–1011) s scale. The rate constant assumed in this way, gSq ﬃ 109 s, agrees as to the order of magnitude Copyright © 2005 by Marcel Dekker

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Figure 175 Variation of the relative EL efficiency with applied bias for the device ITO=TPD(90 nm)=Al at different temperatures (the attainable voltage range 5–25 V corresponds to the field range 0.5–3 MV=cm. Adapted from Ref. 397.

with that deduced from the data of Fig. 173 for singlet exciton–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) ðextÞ

jEL ¼

xPjr 1 þ w=d

ð325Þ

Recall that, according to the definition equation (152), w may exceed largely the device thickness, d, leading to a very low ðextÞ value of jEL ¼ (d=w) xPjr whenever w d. On the other ðextÞ hand, the upper limit of jEL ¼ (1 þ 2=d)1 xPjr (nm) is smaller than xPjr since due to the discrete structure of materials w must be limited to ca. 2 nm corresponding to an average dimension of the molecules forming low-molecular weight organic layers of EL device. The often employed expression ðextÞ for jEL ¼ xPjr assuming PR ¼ 1, is unjustified since it would require w ! 0, thus, an unphysical assumption of a continuous homogeneous medium with the recombination time for Copyright © 2005 by Marcel Dekker

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Figure 176 The field dependence of the EL quantum efficiency (QE) for a diffusion-limited current driven ITO=TPD=Alq3=Mg:Ag LED. The lines represent theoretical predictions of QE(F) according to Eqs. (315), (322), and (324) with different model parameters ð1Þ (r0=rc; tcn 0). The small circle curves show the case with PR ¼ PR only (no quenching). The shaded circles stand for the experimental data of Ref. 68. Copyright © 2005 by Marcel Dekker

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carriers trec ! 0. It is necessary to point out that the ðextÞ w=d ¼ trec=tt ratio, affecting jEL through Eqs. (315), (317) and (325), may differ if different assumptions are made as to the relative contributions of the electron and hole currents flowing in the device. For example, a difference in the mobility relations for the w=d ratio in Eq. (155) and those in Eq. (322) results from the assumption of equal contributions of both electron and hole flows (mene ﬃ mhnh) for the former, and equal carrier concentrations (ne ﬃ nh) for the latter. The qualitative difference disappears in the case of the above discussed TPD=Alq3-based LEDs, where me(Alq3) mh(TPD). The ratio w=d ﬃ 2me(Alq3)=mh(TPD) which follows directly from Eq. (155) is within a factor of 2 identical with the (trec=tt)VCEL when j ¼ jSCL according to Eq. (322). Table 7 demonstrates how the EL quantum efficiency changes with varying ratio (w=d) of the width of the recombination zone w to an electrofluorescent (P ¼ PS ¼ 0.25) device thickness d. Limiting the ratio w=d to the range 0 (w ¼ 0)–1000 (w d) implies variaðextÞ tion of jEL between 1.25% and 103% photon=carrier for typically x ¼ 0.2 and jr ¼ 0.25. The above described lower limit for w ¼ 2 nm reduces the former value to 1.22% photon=carrier for common organic layer thickness d ¼ 100 nm, but to about 1% photon=carrier for d ¼ 10 nm. The extension of the recombination zone over all the device thickness d ðextÞ (w ¼ d) reduces this value by a factor of 2 (jEL ﬃ 0.63% photon=carrier). These data indicate that in order to optimize the EL quantum efficiency from a light emitting diode, one has to minimize the recombination zone width as related to the device thickness. Furthermore, if one assumes the recombination zone width to be independent of thickness, d, Eq. (325) provides a simple method to determine w by means of experiðextÞ ðextÞ mentally measured jEL as a function of d. A plot of 1=jEL 1 vs. d 1 ðextÞ jEL

¼Aþ

B d

ð326Þ

where A ¼ (xPjr)1 and B ¼ Aw is then expected to be a straight line with the slope to intercept ratio yielding directly Copyright © 2005 by Marcel Dekker

ðintÞ

jEL x ¼ 1, jPL ¼ 1 25% ðextÞ

ðextÞ

x ¼ 1, jPL ¼ 1 25% ðextÞ

x ¼ 1, jPL ¼ 0.25 6.25% ðextÞ

jEL (%) x ¼ 0.2, jPL ¼ 1, I

jEL (%) x ¼ 0.2, jPL ¼ 0.25, II

jEL (%) x ¼ 0.35, jPL ¼ 1, III

jEL (%) x ¼ 0.35, jPL ¼ 0.25, IV

5.00a 4.55 4.30 4.17 4.00 3.85 3.70 3.57 3.33 3.13 2.94 2.78 2.63 2.50b 2.38 2.27

1.25a 1.14 1.09. 1.04 1.00 0.96 0.93 0.89 0.83 0.78 0.74 0.69 0.66 0.63b 0.60 0.57

8.75a 8.00 7.60 7.29 7.00 6.73 6.48 6.25 5.83 5.47 5.15 4.86 4.60 4.38b 4.17 3.97

2.20a 2.00 1.91 1.83 1.76 1.69 1.63 1.57 1.47 1.38 1.29 1.22 1.16 1.10b 1.05 1.00

0a 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.00b 1.10 1.20

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(Continued)

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w=d PS ¼ 0.25

x ¼ 1, jPL ¼ 0.25 6.25%

Chapter 5. Optical Characteristics of Organic LEDs

Table 7 EL Quantum Efficiencies Calculated According to Eq. (325) as a Function of the Recombination Zone Width to the Sample Thickness Ratio (w=d) at Different Values of x and jr (jPL).

ðextÞ

396

Table 7 (Continued ) ðextÞ

ðextÞ

ðextÞ

jEL (%) x ¼ 0.2, jPL ¼ 0.25, II

jEL (%) x ¼ 0.35, jPL ¼ 1, III

jEL (%) x ¼ 0.35, jPL ¼ 0.25, IV

1.50 1.80 2.00 3.00 5.00 6.00 7.00 8.00 9.00 10.00 15.00 20.00 30.00 50.00 100.00 1000.00

2.00 1.79 1.67 1.25 0.83 0.71 0.63 0.55 0.50 0.45 0.31 0.24 0.16 0.10 0.05 0.005

0.50 0.45 0.42 0.31 0.21 0.18 0.16 0.14 0.13 0.11 0.08 0.06 0.04 0.03 0.01 0.001

3.50 3.13 2.92 2.19 1.46 1.25 1.09 0.97 0.88 0.80 0.54 0.42 0.28 0.17 0.09 0.008

0.88 0.79 0.73 0.55 0.37 0.31 0.28 0.24 0.22 0.20 0.14 0.10 0.07 0.04 0.02 0.002

a b

Maximum, w ¼ 0. w ¼ d.

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w=d PS ¼ 0.25

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the width of the recombination zone, w. In addition, the light output coupling factor x can be determined from the intercept at d1 ! 0, if P and jr are known independently. This approach has been successfully applied to the ITO=TPD(dh)= Alq3(de) =Mg:Ag structures [603]. Figure 177 shows external quantum efficiency as a function of electric field measured at various Alq3 thickness. For thin emitting layers ðextÞ (de < 20 nm) jEL appears to be field-independent, whereas for thick Alq3 films (de > 25 nm), a non-monotonic evolution ðextÞ of jEL with electric field is observed and is consistent with ðextÞ previous results illustrated in Fig. 168. The inverse of jEL can be fitted to a straight line plot vs. d1 e (Fig. 177b) giving

Figure 177 The external EL quantum efficiency as a function of electric field (a) of the bilayer devices ITO=TPD(dh)=Alq3(de)=Mg:Ag of the total thickness d ¼ dh þ de ¼ 120 nm with varying Alq3 thickðextÞ ness (de). (b) The inverse jEL as a function of the inverse of the emitter thickness (de) at three different electric fields (uptriangles, downtriangles, diamonds). The data fit to Eq. (326) are given by straight solid lines. (c) The carrier injection efficiency as a function of applied field for the devices with three different emitter thickness. Adapted from Ref. 603. Copyright © 2005 by Marcel Dekker

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the field-dependent w, 70 nm at 0.75 MV=cm and 40 nm at 1 MV=cm. The value x ﬃ 0.43 of the light-output coupling factor follows from the intercept A ¼ (xPjr)1 with P ¼ PS ¼ 0.25 and jr ¼ jPL ¼ 25% at F ¼ 0.75 MV=cm and jr ¼ 17% at 1.0 MV=cm. The reduced value of jr has been used at high fields because of exciton quenching by electric field and interaction with charge carriers. This value of x is twice as large as that estimated from classical ray optics to be 1=2n2 [2,569,604], using the refractive index for Alq3, n ¼ 1.7. An alternative would be jr ¼ jPL ¼ 25% kept constant, and x varying with electric field. The physical picture of the carrier recombination is that it proceeds along the path of holes migrating through the emitter layer of Alq3 towards the Mg:Ag cathode. However, due to the accumulation of both holes and electrons at the TPD=Alq3 interface, the most efficient recombination occurs in the Alq3 region adjacent to the interface and, whenever w < de forming a sufficiently narrow zone far from the cathode, the singlet exciton quenching by this metallic electrode can be ignored. When Alq3 thickness becomes small enough (<25 nm), the EL quantum efficiency becomes dominated by the excitonic quenching at the cathode and it practically does not depend on electric field ðextÞ (Fig. 177a). Another reason for decreasing jEL with decreasing de is a drop in the injection efficiency for thin emitter devices (see Fig. 177c). The drop comes simply from the assumption meff ¼ me þ mn when using Eq. (236) for the calculation of jSCL, which is valid only for the strong recombination case and should not be applied for thin Alq3 layers when increasing leakage of holes towards the cathode renders the flow to be described by the weak-recombination limit rather as discussed in Sec. 4.5. From the above, it is seen that the EL efficiency is a complex function of thickness interrelations in double- and multi-layer Alq3-based LEDs (cf. Sec. 4.3.2). The observed dependence of jEL on the emitter-to-device thickness ratio [303,605] is difficult to a quantitative interpretation and needs further efforts in order to improve its theoretical description. Furthermore, in more exact considerations, a temperature effect on the EL quantum yield must be taken into account since the PL quantum efficiency of Alq3 appears Copyright © 2005 by Marcel Dekker

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to be reduced at a gradient djPL=dT ﬃ 3.9 103 K1 (Ref. 50), not mentioning the temperature dependence of electrical characteristics, and the LEDs warm up substantially at larger current densities [606]. A similar analysis can be performed for polymer-based LEDs, where EL output has been shown to be a function of thickness ratio of two component layers of bi-layer device structures [607]. Obviously, the recombination zone width can be obtained ðextÞ directly from the experimental value of jEL 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 dissociation of excited states and their interaction with charge carð2Þ ð3Þ riers can be neglected [PR ¼ PR ¼ 1 in Eq. (324) ]. Under such ðextÞ conditions, the field dependence of jEL (F) is an increasing function of F following the field decreasing width of the recombination zone. This approach has been employed to study the effect of electric field on the recombination zone width with doped and undoped emitter layers [68,566]. Figure 178 shows that the well-resolved maxima of the QE plots vs. applied field for neat and lightly doped Alq3 emitters shift strongly toward high fields and disappear at high dopant concentrations. Applying Eq. (325) to the increasing segments of ðextÞ the jEL (F) curves enables to find the field dependence of recombination zone width, showing the effect of a dye doping. The DPP:Alq3 emitter doped devices show generally the recombination width to be less sensitive to the applied field, but its absolute value reveals a minimum (w ﬃ 2 nm) at 0.25 mol% of DPP in Alq3 (Fig. 178). On the other hand, it can be as large as 65 nm that is covering the total thickness of the 0.8%TPP:Alq3 emitter and Alq3 ETL in the case of the ITO=TPD(60 nm)=0.8% DPP:Alq3(35 nm)=Alq3(30 nm)= Mg:Ag device. The recombination zone width for the neat Alq3 emitter-based LED decreases from about 50 nm at low fields down to 12 nm at a high field (ﬃ0.7 MV=cm). The latter is in good agreement with the same value calculated on the basis of electron and hole mobilities assuming space-chargelimited injection to the TPD=Alq3 bilayer structure [309]. Since all PR values calculated from Eq. (315) on the basis of ðextÞ the experimental data for jEL and the field independent Copyright © 2005 by Marcel Dekker

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Figure 178 The EL QE and overall recombination probability (PR) (a), and the recombination zone width (b) vs. electric field applied to the EL devices ITO=TPD=% DPP:Alq3=Alq3=Mg:Ag with different mol% concentration of 6,13-diphenlyl pentacene (DPP) in Alq3 as emitter. After Ref. 68. Copyright 2001 American Institute of Physics, with permission. Copyright © 2005 by Marcel Dekker

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x ¼ 0.2, P ¼ PS ¼ 0.25 and jr ﬃ 25%, exceeds 0.5 (Fig. 178a), we deal with the VCC mode operating devices and Eq. (322) applies which for jSCL=j ﬃ 103 (see Fig. 171) implies me,h=(me þ mh) 1. This means that the hole motion toward the cathode determines the recombination path (mh=me 1 in Alq3 and DPP-doped Alq3 layers). mh=me ﬃ 0.4 103 follows from Eqs. (317) and (322) with PR ¼ 0.7 from Fig. 178a, which is at least one order of magnitude lower than the hole-to-electron mobility ratio in neat Alq3 measured by means of TOF technique [336]. The underestimated light output coupling factor (x ¼ 0.2) and=or chemical hole traps seem to be responsible for this difference. Intentional doping of Alq3 with DPP reduces the hole mobility since the HOMO level of DPP is located by about 0.5 eV above that of Alq3 [608]. Moreover, the carrier mobility changes because the presence of dopants modifies disorder parameters s and S (cf. Sec. 4.6). Taking into account the disorder effect on carrier mobility (265), where Y ¼ (2s=3)2=kT and bm ¼ C[(2s=3kT)2 S2], Eq. (155), approximated by me;h d ð327Þ wﬃ me þ mh for me,h mh,e (cf. discussion above), predicts that w is, in general, a non-monotonic function of diagonal (s) and nondiagonal (S) disorder parameters. In the above example with the DPP-doped Alq3 emitters (mh me), w ﬃ (mh=me)de, where de is the thickness of emitting layers including both thickness of the emitter layer (EML) and electron transporting layer (ETL). This simple expression allows to explain the variation of the recombination zone width with concentration of the dopant presented in Fig. 179. The concentration evolution of w reflects variations in mh imposed by doping. Since by definition low doping imposes stronger off-diagonal than diagonal disorder [29], the field-dependent hole mobility, mh ¼ meh exp(2s=3kT)2 expfC[(2s=3kT)2 S2]F1=2g, will enhance decreasing tendency of mh due to hole trapping. This leads to narrowing of the recombination zone. At higher concentrations of the dopant, the hole mobility increases because the hole transport becomes dominated by the hopping between Copyright © 2005 by Marcel Dekker

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Figure 179 Variation of the recombination zone width as a function of DPP concentration in the Alq3 emitter for selected electric field strengths as taken from Fig. 178

guest molecules (not via the Alq3 matrix) and by strongly increasing diagonal disorder for both electrons and holes with se > sh. The recombination zone is subject to the spatial extension, as observed. Values for the recombination zone width for the devices with the highest concentrations of dopant are a factor of 1.5–2 larger than the thickness of their EMLs. This should not be surprising since by definition (152) the recombination zone is the path on which all the carriers recombine under conditions characteristic of EML. The (Alq3 þ DPP)=Alq3 interface breaks the continuity of the EML medium, holes trapped on DPP dopant molecules increase the concentration of recombination centers in the EML, and strongly reduce the hole penetration into the pure Alq3 ETL. This is why one does not see characteristic emission of Alq3 from the ETL and why the recombination zone physically becomes limited to the geometrical thickness of the EML. The residual Copyright © 2005 by Marcel Dekker

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green emission comes from the EML as a result of the competition between Alq 3 ! DPP energy transfer and radiative decay of Alq 3 to the ground state [68]. The role of the penetration depth of electrons (le) into a double-emitter-based polymeric LED has been reported [344]. It has been identified with the spatial extent of the recombination zone to be compared with w. Like in the (DPP þ Alq3)=Alq3 junction-based LED, the w appeared to decrease with applied voltage. This is illustrated in Fig. 180 by the current (i) decreasing function of the electron penetration depth (le). The lowest value of le ¼ 55 10 nm at F ¼ 2 106 V=cm corresponds well to the values of w for the heavily DPP-doped Alq3 emitter system in Fig. 178. The electron range le has been extracted from the experimental ratio of TPS to PPV emission (R), assuming the recombination probability to be expressed by ðeÞ

PR ¼

Z

d

expðx=le Þ dx

ð328Þ

0

Hence, ðTSAÞ

R¼

jPL

R d1 d0

ðPPVÞ R d

jPL

expðx=le Þ dx

d1 expðx=le Þ dx

ðTSAÞ

ðPPVÞ

ð329Þ

where jPL and jPL are the PL efficiencies of TSA and PPV, respectively. The results are in good agreement with theoretical predictions based on Eq. (153), assuming a uniform distribution of recombination centers (holes) and ðeÞ mh me. The latter, according to Eq. (154), makes w ﬃ [ jSCL = ðeÞ ðeÞ j]d and PR ﬃ [ jSCL =j]1, where jSCL ﬃ e0emeF2=d is the electron injection SCL current, j is the measured device current domiðeÞ nated by holes [ j ﬃ emhnhF > jSCL ], and d ¼ d0 þ d1 þ d2 (see Fig. 180b). Based on the experimental i(F) curve, the electron ðeÞ injection efficiency [ j=jSCL ] and PR have been calculated parametric in the electron mobility. A good fit to the experimental data is provided with me ¼ 3.3 108 cm2=Vs. Also, it is apparent that while in the high-field regime (large current values > 5 mA), the electron range le < d corresponding to the VCEL Copyright © 2005 by Marcel Dekker

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Figure 180 The range (le) of electrons (right ordinate) and the ðeÞ recombination probability [PR ] for electrons (left ordinate). A comparison between the theoretical predictions according to Eqs. (153) and (328) (lines) and experiment (data points) shows good agreement for the electron mobility me ¼ 3.3 108 cm2=V s (a). Schematic cross-section of the EL device and monitoring of emission from two different emitters: (PSu þ TSA)—a blend of polysulfone (PSu) and tris(stilbene)amine(TSA), and PPV-poly(phenylenevinylene). Their thicknesses (d1, d2) are subject to variation, d0 is the quenching zone of excitations by the Ca cathode (b). Adapted from Ref. 344.

operation mode, low-current values of le > d correspond to ðeÞ PR < 0.5 and indicate the ICEL operation conditions. Like electrofluorescence, electrophosphorescence quantum efficiency (EPH QE) depends on the device structure Copyright © 2005 by Marcel Dekker

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and shows, in general, non-monotonic dependence on the device current. Some examples are shown in Fig. 181. A two orders of magnitude increase in the EPH QE can be seen when passing from an inefficient device ITO=(TPD:PC)= Ir(ppy)3=Ca=Ag (QE ﬃ 0.1% photon=carrier) to an efficient one with a hole-blocking layer of PBD, ITO=6%Ir(ppy)3: 74%TPD:20%PC=100%PBD=Ca=Ag (QE ﬃ 10% photon= carrier). Although no correlation between the QE and its j behavior 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 driving current. The data for 6% [Ir(ppy)3]:CPB (circles) are taken from Ref. 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 the second run, the down triangles are the data for the (TPD:PC)=[Ir(ppy)3]=PBD system, and the up triangles are the data for the (TPD:PC)=[Ir(ppy)3] system. The intersection between the ðextÞ current-independent segment of the jEL (j) plot and its falling part is indicated as PC. After Ref. 304. Copyright 2002 American Physical Society, with permission. Copyright © 2005 by Marcel Dekker

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play between processes increasing and decreasing the overall recombination probability (324) which are not directly associated with the device structure. In the case of electrophosphorescence exciton–exciton interaction (see Sec. 2.5.1) can largely contribute to the reduction of the QE because of the long lifetime of emitting triplet excitons. The EPH quantum efficiency is proportional to the concentration (T) of triplet excitons ðextÞ

jEPH ¼ xjPH

ewe T j tPH

ð330Þ

where tPH represents the intrinsic triplet exciton lifetime, the excitons being homogeneously distributed throughout the emission zone of width we. The current dependence of the EPH QE is determined by the current variation of T. The latter comes from the kinetic equations describing formation and decay of excited states (Fig. 182). Under steady-state electrical excitation conditions, the concentrations of singlet (S) and triplet (T) excitons may be described by the equations: ðSÞ

ðSÞ

dS j kr þ kISC þ kn ðSÞ ¼ a1 ð 1 ZÞ þ gTT T 2 S¼0 ðSÞ dt ew 1 Zex ð331aÞ ðTÞ

ðTÞ

dT j kr þ kn T ¼ a2 ð1 ZÞ þ kISC S ðTÞ dt ew 1 Zex h i ðSÞ ðTÞ 2gTT þ gTT T 2 ¼ 0

ð331bÞ

where j is the recombination current density flowing within the recombination zone of width w, and the symbol k (s1) ðSÞ ðTÞ denotes unimolecular rate constants for radiative [kr ,kr ] ðSÞ ðTÞ and radiationless [kn ,kn ] singlet and triplet exciton transitions, respectively, and for intersystem crossing singlet– triplet conversion (kISC). It must be pointed out that, unlike earlier kinetics assuming all the encounter charge pairs (CP) to form molecular excitons [167], Eqs. (331) include their spin weights (a1, a2; cf. Sec. 1.4) and the reduction factors due Copyright © 2005 by Marcel Dekker

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Figure 182 Formation of molecular excited states (S1, T1) and charge pair states [(CP) and (CT)] in the course of bimolecular recombination (a) and under optical excitation (b). After Ref. 304. Copyright 2002 American Physical Society, with permission. ðSÞ

to dissociation processes of CPS (Z ¼ Z0O), singlet [Zex ] and triðTÞ plet [Zex ] molecular excitons (cf. Sec. 2.6). Major simplifications are achieved for their solutions if we consider two limits of low (case I) and high (case II) current level at room temperature. Case I: The triplet exciton concentration is too low to give rise to triplet–triplet fusion and the T2 terms in Eqs. (331) can be dropped. Then, h i ðSÞ ðSÞ a þ a k = k þ k þ k 2 2 r n ISC ISC ð1 ZÞj Tﬃ ð332Þ ðTÞ ðTÞ ew kr þ kn ðSÞ

ðTÞ

if Zex ﬃ Zex ﬃ Zex is assumed. Copyright © 2005 by Marcel Dekker

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The triplet exciton concentration increases linearly with the recombination current density, j. Case II: The triplet exciton lifetime is dominated by the 2 T term in this regime, and Tﬃ

8 <ð1 ZÞj :

ew

h i h i 91=2 ðSÞ ðSÞ ðSÞ = a2 þ kISC a1 1 Zex = kr þ kISC þ kn h i h i h i ðSÞ ðTÞ ðSÞ ðSÞ ðSÞ ðSÞ 2gTT þ gTT kISC gTT 1 Zex = kr þ kISC þ kn ; ð333Þ

pﬃﬃ is proportional to j. A j-independent and inversely proportional to the root ðextÞ square of j, jEPH is expected from Eq. (330) for these two limðextÞ iting cases, the slope of a semilogarithmic plot of jEPH vs. j should give 0 and 0.5, respectively. While, roughly, the first limit can be recognized in the experimental data of Fig. 181 for low- (or moderate-) field regions, a higher slope than 0.5 is typically observed at large current densities (except for one case for not too high currents). This strongly suggests the existence of other mechanisms of quenching triplet excitons or their precursors. A similar conclusion can be drawn from comparison of the current dependence of the EPH QE and EPH lifetime as shown in Fig. 183 for the phosphorescent platinum complex PtOEP (cf. Fig. 31). Such a comparison is straightforward for Eq. (330) replaced by ttot ðextÞ ð334Þ jEPH ¼ xa2 ð1 ZÞjPH tPH where i h i 1 h ðSÞ ðTÞ ðTÞ ¼ t þ g n 1 Z þ g þ 2g t1 Tq tot PH ex TT TT T

ð335Þ

represents the effective (total) triplet exciton rate constant including all monomolecular and bimolecular quenching processes such as triplet–charge carrier (gTqn) or triplet–triplet ðSÞ ðSÞ ðTÞ ðTÞ ðTÞ f[2gTT þgTT ]Tg annihilation, and jPH ¼[kr =][kr þkn ]. AssuðTÞ

ming that the dissociation efficiencies [Z, Zex ] are independent of current density, the current dependence of the EPH QE ðextÞ [jEPH =( j)] should be projection on that for the effective lifeCopyright © 2005 by Marcel Dekker

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time of triplets [ttot( j)]. The experimental data for the EPH lifetime and quantum efficiency show a remarkable discrepancy (Fig. 183). The QE drops down by about 90% at j ﬃ 150 mA=cm2, whereas the effective lifetime decreases by less than 40% only at the same current density. A decreasing tendency in the phosphorescent lifetime as the photoexciting energy pulse increases suggests the EPH quenching to be underlain by triplet–triplet annihilation process at lower curðextÞ rent densities. The stronger drop for jEPH above 10 mA=cm2 requires additional quenching channels. An exception is observed for the first lower-current range run in Fig. 181, 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-octaethyl21H, 23H-porphine platinum (II) (PtOEP) embedded in an Alq3 matrix as a function of current density. Two filled circles are the lifetimes of the phosphorescence taken at increasing photoexcitation pulse (left: 160 nJ=cm2; right: 16 mJ=cm2). The data adapted from Ref. 493a by Kalinowski et al. [304] Copyright 2002 American Physical Society, with permission. Copyright © 2005 by Marcel Dekker

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(PC) with the horizontal line representing jEPH ¼ const ¼ 11% photon=carrier, one can evaluate the T–T annihilation rate ðextÞ constant gTT. At the intersection point jEPH ( j ¼ jcrit) ¼ 0.11. ðextÞ

The jEPH (case II) can be approximated by ðextÞ jEPH ðIIÞ

1=2 xjPH ew ¼ 2tPH jcrit gTT ðSÞ

ð336Þ

if Z 1, a2 ¼ 3=4 and gTT ﬃ gTT is assumed and contribution of the intersystem crossing transitions is neglected as compared to the direct e–h recombination forming triplet excitons (cf. Fig. 182). The triplet–triplet annihilation rate constant could be estimated from Eq. (336) on the basis of the experimental value of jcrit (a value of abscissa at PC) if the recombination zone width, w, were known. The recombination zone, though difficult to evaluate exactly, can be assumed to be very narrow because of the confinement of charge carriers at the [TPD:Ir(ppy)3:PC]=PBD interface, imposed by the relatively high-energy barriers for both holes and electrons. This is confirmed by the volume-controlled current flow in the device (see Fig. 67). Therefore, a lower limit for w can be compared with the dimension of the two nearest-neighbor molecules (ﬃ2 nm). Thus, gTT ﬃ 1014 cm3=s follows from Eq. (336) using x ﬃ 0.2, jPH ¼ 40% (Ref. 609), tPH ¼ 15 ms (Ref. 610), and jcrit ¼ 2 103 A=cm2 from Fig. 181. This value agrees reasonably with that for another organic phosphorescent system, PtOEP:CBP, gTT ﬃ 3 1014 cm3=s obtained from the fitting of ðextÞ the experimental data of jEPH ( j) to the triplet–triplet quenching mechanism [610]. The physical meaning of these numbers has been discussed in Sec. 2.5.1.2. Let us, now, assume that the greater than 0.5 slope of ðextÞ the log jEPH vs. j plots in Fig. 181 belongs to the dominating triplet–charge carrier interaction, that is t1 tot (335) approxiﬃ g n, where n is the concentration of charge mated by t1 Tq tot which in the high-field region (SCLC conditions; cf. Fig. 67) can be expressed by n ﬃ (3=2)e0eF=ed. With these assumptions, Eq. (330) for the external EPH quantum efficiency leads Copyright © 2005 by Marcel Dekker

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to ðextÞ

jEPH ¼

2 a2 xð1 ZÞjPH ed we 3 e0 egTq tPH F w

ð337Þ

where the emission zone width, we, is distinguished from the recombination zone width, w. If the latter is very narrow, as in the present case, the emission zone is larger than w, being limited on the large values side by the thickness of the emitting layer d=2 ¼ 50 nm. On the basis of Eq. (337), a plot of ðextÞ jEPH vs. F1 is expected to give a straight line with the slope dependent on three material (e, gTqtPH) and device (d) parameter of the system. Such straight-line plots poorly approximate experimental data (Fig. 184) and their slopes yield gTq ﬃ 1012 cm3=s for the first run and gTq ﬃ 7.5 1012 cm3=s for the second run at e ¼ 3, tPH ¼ 15 ms, d ¼ 100 nm, and w ¼ wmin=we ¼ 2 nm=50 nm ¼ 0.04. If one assumes that both gTT and gTq are governed by the triplet exciton motion, then the diffusion coefficient of triplet excitons (DT) can be calculated from their values, gTq ﬃ gTT ﬃ 8pRDT [by analogy to Eq. (71) derived for singlet excitons]: 4 109 cm2=s DT 3 106 cm2=s. The capture distance has arbitrarily been taken as R ﬃ 1 nm in the calculation. These values of the triplet exciton diffusion coefficient are much lower as compared with those for molecular singlet excitons (DS) (see Sec. 2.5.1.1). It is not surprising, the diffusion coefficients of triplets are expected to be lower than of singlets since both energy donor and acceptor transitions are disallowed [26] (also see Sec. 2.4). However, the poor fit between theory and experiment (Fig. 184), required additional experimental checks concerning quenching mechanisms at high current densities. The field-increasing dissociation efficiency (Z) of charge pairs (Fig. 182) appears to be a straightforward candidate reducing significantly the EPH quantum efficiency as the applied voltage increases [see Eq. (334)]. In the high-field limit, it can be considered as a dominating quenching factor. This means that the ttot(F)=ttot(F0) ratio is a weakly varying function of electric field, close to unity. Since the CP dissociation process is enhanced by the applied field only indirectly by Copyright © 2005 by Marcel Dekker

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Figure 184 External quantum EPH efficiency data taken from ðextÞ Fig. 181 and represented by a jEPH F1 plot in order to fit with the triplet–charge-carrier interaction limit for triplet exciton decay according to Eq. (337) (solid lines). After Ref. 304. Copyright 2002 American Physical Society, with permission.

the device current, we translate selected curves from Fig. 181 into the field dependence of the EPH quantum efficiency in order to compare with the electric field effect on phosphorescence (Fig. 185). The phosphorescence output from the sandwich structure Al=100% [Ir(ppyP3]=Al, which does not show any emission (EPH) under action of an electric field only (without photoexcitation), decreases gradually as the applied field increases and drops down by as much as 30% at a field about 2 106 V=cm. A decrease of twice as much is observed ðextÞ in the jEPH (second run) at the same electric field. This sugðextÞ gests at least a large part of the reduction in jEPH to have the same origin as the electric field-induced quenching of phosphorescence, and this has been shown to be the electric-field-assisted dissociation of Coulombically correlated electron–hole pairs as governed by the 3D Onsager theory Copyright © 2005 by Marcel Dekker

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Figure 185 Phosphorescence (PH) and electrophosphorescence (EPH) efficiency response to the dc applied electric field. The relative PH efficiency at lPH ¼ (526 6) nm was measured with an excitation wavelength of 436 nm and an exciting light intensity of I0 ﬃ 1014 quanta=cm2 s. For the PL and EL spectra of [Ir(ppy)3], see Fig. 120. After Ref. 304. Copyright 2002 American Physical Society, with permission.

of geminate recombination (Sec. 2.6; Fig. 50). Measurements on some other electrophosphorescent LEDs show the low-field external efficiency as high as 20%, but like those in Fig. 181, it decreases at high current densities (Figs. 186 and 187). The high EPH quantum efficiency has been achieved from a triple-layer LED using bis(2-phenylpyridine) iridium(III)acetylacetonate [(ppy)2Ir(acac)] phosphor molecule doped into a wide energy gap host of 3-phenyl-4-(10 -naphthyl)-5-phenyl1,2,4-triazole (TAZ) as the emitter, 4,40 -bis[N,N0 -(3-tolyl)amino]-3,30 -dimethyl biphenyl (HMTPD) [611] as a HTL and ðextÞ Alq3 as an ETL (Fig. 186). A maximum jEPH was observed at (ppy) 2Ir(acac) concentrations from 5% to 12%, while a sigðextÞ nificant decrease in jEPH was observed at both higher and lower concentrations. In addition, a gradual decrease in the Copyright © 2005 by Marcel Dekker

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ðextÞ

Figure 186 (a) The external EL QE [jEL ] and power efficiency of a highly efficient EPH LED:ITO=HMTPD(60 nm)=12%(ppy)3 Ir(acac):TAZ(25 nm)=Alq3(50 nm)=Mg:Ag. Inset: molecular structure of the organic phosphor (ppy)2Ir(acac). (b) Energy diagrams of the device with low- and high-concentration of the phosphor in the emitting layer (EML). For chemical names of the materials forming organic layers, see text. After Ref. 495. Copyright 2001 American Institute of Physics, with permission. Copyright © 2005 by Marcel Dekker

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Figure 187 (a) The external quantum efficiency of organic LEDs using 6.2 mol% [Ir(ppy)3]:TCTA as an emitter and three different hole-blocking materials, vs. device current density. (b) The EPH device 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.

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blue emission band from HMTPD was observed with an increase in (ppy)2Ir(acac) concentration. The energy level scheme inferred from absorption and PL spectra of (ppy)2Ir(acac) (cf. 186b) in connection with the concentration evolution of the EL spectra of the device allowed to distinguish two different ways of the formation of emitting states. At low concentrations of the phosphor [ < 2% in Fig. 186b (I)], hole injection from the HMTPD into the TAC HOMO is energetically unfavorable and carrier recombination partly occurs within HMTPD leading to the blue HMTPD emission in addition to exciton formation at (ppy)2Ir(acac). At (ppy)2Ir(acac) concentrations higher than 6% [Fig. 186b(II)], the hole injection from the HMTPD into the much higher-located LUMO of the phosphor molecules embedded in TAZ, the triplet and singlet MLCT states are predominantly created via the electron–hole recombination among (ppy)2Ir(acac) molecules. Thus, the blue HMTPD emission practically disappears, and the EL spectrum reflects an efficient emission from (3MLCT) triplet states, formed either by on molecule e–h recombination process or via intersystem crossing from the singlet charge transfer state (1MLCT) [495]. A 20% photon=electron external EPH efficiency can also be achieved with [Ir(ppy)3] if ‘‘starburst’’ perfluorinated phenylenes layers are used and a holetransporting material 4,40 ,400 -tri(N-carbazolyl)triphenylamine (TCTA) employed as a matrix for the emitting phosphor molecules in multi-layer organic LEDs [612]. The current density dependence of the external quantum efficiency in such EL structures is shown in Fig. 187a. The efficiency improving role of X- and Y-shaped C60F42 blocking layers (Fig. 187b,c) ðextÞ is obvious by comparison with the jEPH ( j) dependence for the LEDs devoided such layers (Fig. 187a). The high EL quantum efficiency of all types of electrophosphorescent LEDs is underlain by the efficient production of emitting triplet (mixed) states, the singlet-to-triplet exciton ratio 1:3 being governed by simple spin statistics. This ðextÞ assumption implies P ¼ PT ¼ 3=4 in expression (315) for jEPH while PS ¼ 1=4 only. It is, therefore, obvious that an increase in the electrofluorescence efficiency would be achieved if an increase in the PS were possible. Such a possibility appears Copyright © 2005 by Marcel Dekker

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as a result of a quantum mechanical mixing of the electronic wave functions of the initial reactant species (e,h) and those of the final products of the eh pair capture due to a stronger ionic character of singlet than triplet excitons formed in conjugated polymers (see Sec. 1.4). At low temperatures, as much as 83 7% of excitons can have singlet character as inferred from the infrared absorption study in working conjugated polymer light-emitting diodes [613]. The stringent test for the singlet-to-triplet ratio would be a comparison of the fluorescence and phosphorescence output from the same EL structure. The triplet and singlet state emission have been observed from a platinum-containing conjugated polymer [614]. The spin–orbit coupling introduced by the platinum atom allows triplet-state emission in addition to the singlet exciton emission originating from the molecular skeleton of monomer or conjugated polymer structure. The PL and EL spectra (Fig. 188) of the monomer and polymer structure show two characteristic emission bands and different relative contributions of each band to the total emission output (indicated as a percentage in the figure). The low-energy band is assigned to the emission of triplets (T1) and the high-energy band to the emission of singlets (S1) . A greater percentage of the photons from triplet states is observed for the EL spectrum of monomer, whereas their percentage for both PL and EL spectra is clearly much lower for the polymer. In photoluminescence, a number of excitons are originally all created in the singlet S1 state, and from there they can decay radiatively or non-radiatively to the singlet ground state S0, or undergo intersystem crossing to the triplet manifold. Both radiative and non-radiative decay occur from the triplet state T1 to the ground state S0 (cf. Fig. 10). For electroluminescence, a certain fraction of triplet excitons can be created directly by the e–h recombination (cf. Fig. 4). This explains why singlet-to-triplet emission ratio is high for the PL spectra with either monomer and polymer samples. In contrast, the singlet-to-triplet generation ratio in electroluminescence, extracted from the experimental percentage contributions of singlet and triplet light outputs accounted for the quantum yields for their radiative decays, amounts to 0.15 0.01 and Copyright © 2005 by Marcel Dekker

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0.40 0.03 for monomer and polymer, respectively, at room temperature [614]. There is another approach to explain the increase in the singlet-to-triplet output ratio under electrical excitation, namely, the singlet fraction is increased by ISC from the triplet manifold after formation at bound neutral excitons. S1 and S2 excited bound states are formed with the ratio 1:3, the energy exchange between these states competes with triplet exciton cooling, the number of excited S1 states increases [615]. At present, no experimental data exist allowing the distinction between these mechanisms. The EL quantum efficiency from organic LEDs based on the emission of bi-molecular excited states (see Sec. 2.3) is expected to be low due to increasing rate of their radiationless relaxation arising from increased intermolecular phonon interactions, and an overall reduction in the oscillator strength of the dimer (see e.g. Ref 26). Indeed, apart from the well-known singlet excimer of pyrene molecules, where the emission efficiency as high as 75% has been reported [616], the PL quantum efficiency of the emission underlain by bi-molecular excited states falls usually much below this value as for example that of ca. 20% observed with exciplexes formed by the molecules of hole-transporting and electrontransporting materials used in the fabrication of organic LEDs [507,508]. The triplet bi-molecular excited states, expected to show even less efficient emission, have recently been reported to reach 15% for the triplet excimer of a Pt organometallic phosphor molecule [99]. The radiative decay efficiency (jr) is not, however, the only factor affecting the EL quantum efficiency [see Eq. (315)]. With given jr and x, ðextÞ jEL can be increased by improving the probability of charge J Figure 188 PL and EL spectra of light-emitting diodes of the platinum-containing monomer and polymer at 290 K. The triplet emission is denoted by T1 and the singlet emission by S1 . The percentual numbers provide the fraction of the numbers of singlet and triplet emitted photons with respect to the totally emitted photons (the larger numbers of S1 and smaller numbers for T1 characterize the PL spectra). Reprinted by permission from Ref. 614. Copyright 2001 Macmillan Publishers, Ltd. [http:==www.nature.com=].

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carrier recombination (PR) and formation of desired excited state (P). An efficient exciplex emitting LED has been fabricated improving the recombination efficiency at the m-MTDATA=PBD interface where charge carriers become strongly confined due to the high energy barriers for the electron and hole transfer toward electrodes. The EL spectrum of ITO=m-MTDATA:PC=PBD=Ca devices is entirely due to exciplex emission with external quantum efficiencies exceeding 1% photon=carrier at a luminance 1000 Cd=m2 [508]. This value as compared to SL devices ITO=m-MTDATA:PBD:PC=Ca increases by a factor of 3 and over two orders of magnitude as compared with TPD-based DL devices (cf. Figs. 124–126). These relations can be seen in Fig. 189a, where the external EL quantum efficiency as a function of applied field for various EL devices is displayed. Another way to improve the EL QE is to increase the probability (P) of the formation of the emissive states. Since the exciton formation is, in general, spin dependent (see Sec. 1.4), an increase in the singlet exciton formation rate would increase the electrofluorescence efficiency, and utilizing the dominating channel of the triplet formation (that is the replacement of PS ¼ 1=4 with PT ¼ 3=4) leads to increasing electrophosphorescence efficiency. The latter applies also to bi-molecular triplet states, which, being more efficiently created than their singlet counterparts, should lead to an increased EL J Figure 189 (a) External EL quantum efficiency as a function of applied field for the SL (1) and DL (2) exciplex emitting organic LEDs. SL LED: ITO=(50%) m-MTDATA: 40% PBD:20% PC)(60 nm)=Ca; DL LED: ITO=(75% m-MTDATA:25% PC)(60 nm)= 100% PBD(60 nm)Ca (for chemical names and molecular structures of m-MTDATA, see Fig. 126, and of PBD and PC, Fig. 26). The data for the SL and DL LEDs with m-MTDATA replaced by TPD (3,4) are given for comparison (see Fig. 125). After Ref. 508. Copyright American Institute of Physics, with permission. (b) Luminescence efficiency and quantum efficiency vs. current density of the molecular aggregates emitting device shown in Fig. 131a. Inset: Current density (squares) and luminance (line) vs. voltage characteristics of device in Fig. 131a. Adapted from Ref. 99. Copyright © 2005 by Marcel Dekker

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quantum efficiency of EPH devices. In fact, a roughly threeðextÞ fold increase in the jEL can be observed with a triplet excimer emitting LED (Fig. 189b) as compared with that of the above mentioned singlet exciplex emitting LEDs (cf. Fig. 189a). From this section, we have seen that the EL quantum efficiency is a function of material parameters and structure of EL systems. Various physical mechanisms must be taken ðextÞ into account to determine jEL and its evolution with the voltage driving organic LEDs.

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6 Summary and Final Remarks

Organic electroluminescence (EL) is a broad field with great technological implication. However, the current understanding of the elementary processes underlying the functioning of organic light-emitting devices (LEDs) is still unsatisfactory. We have attempted to present the physical mechanisms of the functioning of organic LEDs in a way that reveals the limitations as well as the strengths of the theoretical models. Because of the complexity of EL phenomena and because of the diversity of types of organic compounds that exhibit luminescence, it is clear that there is no single, simple theory of EL of organic solids. The understanding of EL phenomena and their appearance in organic LEDs are interwoven with the theoretical bases of other related branches of physics and chemistry. Although the general characteristics of organic LEDs can be derived from theoretical description of energy supply modes, excitation mechanisms, and nature of excited states, quantitative properties of specific materials and EL structures can rarely be obtained from one theory alone. For example, the concept of molecular excitons for excited states is well 423

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founded in theory of molecular aggregates and approximate values of their energies can be obtained from elaborate calculations of electron orbital theory, but specific intermolecular interactions and disorder must be invoked to determine exact values for particular materials. Let us recall a large group of luminescent conjugated polymers, where, due to a p-bond network, the excited state wave function becomes delocalized over at least 50 unit cells (ﬃ40 nm) which led to treating the excitation p–p as the transition across a free carrier band gap. However, because of the high degree of intrinsic anisotropy in conjugated polymers, disorder-induced localization of excited electronic states is of major importance. Therefore, dependent on the degree of disorder, either band-based models and localized exciton-based models have been used to explain optical properties of conjugated polymers. Furthermore, specific local intermolecular interactions may cause the formation of bi-molecular and multi-molecular units in the ground and excited states (dimers or multi-molecular aggregates, excimers, electromers). Their counterparts in two- and multi-component materials take on the form of hetero-dimers (hetero-aggregates), exciples, and electroplexes. Obviously, their contribution to the optical emission renders the EL to reveal multi-band complex spectra difficult to a simple description impeded in addition by electrical field and surface optical modes effects on their shape. Disorder, structural, and chemical defects of materials determine to a large extent transport and trapping of charge carriers. The recombination process proceeding on trapped carriers may lead to emission spectra from organic LEDs which differ completely not only from those of molecularly dispersed materials but also of their ordered or a least partly ordered aggregates. The diversity of the emission spectra from organic LEDs is demonstrated by the numerous examples in the section devoted to optical characteristic of organic LEDs. The main difficulty encountered in attempting to rationalize the LED performance is in quantifying the effect of injection and transport of charge carriers within the device structure. In the application of theoretical models, the choice of appropriate quantities is of great importance. For the EL quantum efficiency, an association of the Copyright © 2005 by Marcel Dekker

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Chapter 6. Summary and Final Remarks

425

recombination probability with the charge injection efficiency and carrier mobility is essential and has been described in the last section. This has been done in a unified manner by introducing characteristic times for the carrier recombination, transition across the device structure, and excitonic interactions. The predictive power of such an approach has been demonstrated by its qualitative application to different organic LEDs and a quantitative analysis for the model organic LED based on the TPD=Alq3 junction. The important role of excitonic interactions and electric field assisted dissociation of excited states emerges in the explanation of the electric field evolution of the EL quantum efficiency. These effects should be of particular care in attempts to fabricate electrically pumped organic laser, though the essential condition of high injection currents must be first fulfilled and external coupling of the emission of light taken into account. The predictive content of theoretical models of organic EL is increasing, particularly in the conversion of electrical current into light and light emission mechanisms themselves. We may yet attain the long-sought goal of the design of new luminescent materials and the prediction of described characteristics of organic EL devices from theoretical considerations concerning electronic processes that underlie their functioning.

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