Handbook of Polymers in Electronics

Handbook of Polymers in Electronics

Bansi D. Malhotra

Handbook of Polymers in Electronics

Bansi D. Malhotra

Rapra Technology Limited Shawbury, Shrewsbury, Shropshire, SY4 4NR, United Kingdom Telephone: +44 (0)1939 250383 Fax: +44 (0)1939 251118 http://www.rapra.net

First Published in 2002 by

Rapra Technology Limited Shawbury, Shrewsbury, Shropshire, SY4 4NR, UK

©2002, Rapra Technology Limited

All rights reserved. Except as permitted under current legislation no part of this publication may be photocopied, reproduced or distributed in any form or by any means or stored in a database or retrieval system, without the prior permission from the copyright holder. A catalogue record for this book is available from the British Library.

ISBN: 1-85957-286-3

Typeset by Rapra Technology Limited Printed and bound by Polestar Scientifica, Exeter, UK

Contents

1

Charge Transport in Conjugated Polymers ...................................................... 3 1.1

Introduction ........................................................................................... 3

1.2

The Electronic Ground State .................................................................. 4

1.3

Charge Transport Carriers ..................................................................... 6 1.3.1

Soliton ....................................................................................... 7

1.3.2

Polaron and Bipolaron ............................................................... 9

1.4

Transport Properties of Polymers ......................................................... 12

1.5

Factors Influencing the Transport Properties of Polymers .................... 14 1.5.1

Disorder ................................................................................... 14

1.5.2

Doping ..................................................................................... 15

1.5.3

Interchain Coupling ................................................................. 17

1.6

Models of Charge Transport in Conducting Polymers ......................... 18

1.7

Conclusions ......................................................................................... 27

Acknowledgements ....................................................................................... 28 References ..................................................................................................... 28 2

Electrical Properties of Doped Conjugated Polymers .................................... 37 2.1

Introduction ......................................................................................... 37

2.2

Metallic State ....................................................................................... 39

2.3

2.2.1

Conductivity ............................................................................ 40

2.2.2

Magnetoconductance ............................................................... 50

2.2.3

Thermoelectric Power .............................................................. 55

2.2.4

Magnetic Susceptibility and Specific Heat................................ 56

Critical and Insulating States ............................................................... 58 i

Polymers in Electronics

2.4

Summary .............................................................................................. 63

References ..................................................................................................... 65 3

Non Linear Optical Properties of Polymers for Electronics ........................... 69 3.1

Introduction ......................................................................................... 69

3.2

NLO Polymer Issues for Device Applications ...................................... 70

3.3

Properties of Third-Order NLO Polymers ........................................... 71 3.3.1

Background of Third-Order NLO Polymer Research .............. 71

3.3.2

Poly(arylenevinylene), PAV ...................................................... 72

3.3.3

n-BCMU-PDA ......................................................................... 75

3.3.4

PT ............................................................................................ 76

3.3.5

Processible π-Conjugated Polymers .......................................... 76

3.3.6

Third-Order NLO Polymer Waveguides .................................. 82

3.4. Properties of Second-Order NLO Polymers ......................................... 84 3.4.1

Azo-Dye-Functionalised, Poled Polymers for Second-Order Non Linear Optics ................................................................... 84

3.4.2

EO Polymers ............................................................................ 87

3.4.3

Serially-Grafted Polymer Waveguides ...................................... 88

3.4.4

Refractive Index Grating Fabrication into Azo-Dye- ................... Functionalised Polymer Waveguides ........................................ 90

3.5

Future Targets of NLO Polymers for Optical Device Applications ...... 93

3.6

Conclusions ......................................................................................... 94

Acknowledgements ....................................................................................... 94 References ..................................................................................................... 94 4

ii

Luminescence Studies of Polymers ................................................................ 99 4.1

Introduction ......................................................................................... 99

4.2

Basic Photophysical Deactivation Processes ....................................... 100 4.2.1

Luminescence ......................................................................... 101

4.2.2

Bimolecular Photophysical Processes ..................................... 103

Contents

4.2.3 4.3

4.4

4.5

Quenching Processes .............................................................. 104

Methods for Fluorescence Studies ...................................................... 105 4.3.1

Time-Correlated Single-Photon Counting Studies .................. 105

4.3.2

Quantum Yields ..................................................................... 105

Fluorescence of Polymers, Excimer Fluorescence ............................... 106 4.4.1

Fluorescence of Polymers in Solution ..................................... 110

4.4.2

Fluorescence of Polymers in Gel State .................................... 122

Conclusions ....................................................................................... 136

Acknowledgements ..................................................................................... 136 References ................................................................................................... 136 5

Polymers for Light Emitting Diodes ............................................................ 141 5.1

Introduction ....................................................................................... 141

5.2

The Physics of Electroluminescent Devices ........................................ 142

5.3

5.4

5.5

5.2.1

The Physics of Conjugated Polymers ..................................... 142

5.2.2

The Physics of the Device....................................................... 144

5.2.3

LED Characterisation ............................................................ 147

Polymeric Structures for LED ............................................................ 148 5.3.1

Polyphenylenes ...................................................................... 148

5.3.2

Polythiophenes ....................................................................... 164

Recent Developments ......................................................................... 168 5.4.1

Polarised Electroluminescence ............................................... 168

5.4.2

Lifetime and Degradation in LEDs ........................................ 170

5.4.3

Microcavities ......................................................................... 170

Concluding Remarks ......................................................................... 171

References ................................................................................................... 172 6

Photopolymers and Photoresists for Electronics .......................................... 185 6.1

Introduction ....................................................................................... 185

iii

Polymers in Electronics

6.2

6.3

6.4

6.5

Microlithography Process .................................................................. 187 6.2.1

Resist Coating ........................................................................ 188

6.2.2

Exposure ................................................................................ 188

6.2.3

Development .......................................................................... 189

6.2.4

Post Baking ............................................................................ 190

6.2.5

Etching .................................................................................. 190

6.2.6

Resist Removal (Stripping) .................................................... 190

6.2.7

Doping ................................................................................... 190

Resist Requirements ........................................................................... 190 6.3.1

Solubility ............................................................................... 191

6.3.2

Adhesion ................................................................................ 191

6.3.3

Etching Resistance ................................................................. 191

6.3.4

Sensitivity and Contrast ......................................................... 191

Resist Materials ................................................................................. 193 6.4.1

Conventional Photoresists ..................................................... 193

6.4.2

Deep-UV Photoresists ............................................................ 197

6.4.3

Electron-Beam Resists ............................................................ 202

6.4.4

X-Ray Resists ........................................................................ 206

6.4.5

Special Resists ........................................................................ 208

Conclusions ....................................................................................... 212

References ................................................................................................... 212 7

Polymer Batteries for Electronics ................................................................. 217 7.1

Introduction ....................................................................................... 217

7.2

Ionically Conducting Polymers .......................................................... 218

7.3

7.2.1

Lithium Polymer Electrolytes and Lithium Batteries .............. 218

7.2.2

Proton Polymer Electrolytes ................................................... 239

Electronically Conducting Polymers .................................................. 242 7.3.1

iv

Lithium-Doped Conducting Polymer and LithiumPolymer Batteries ................................................................... 243

Contents

Acknowledgements ..................................................................................... 245 References ................................................................................................... 245 8

Polymer Microactuators .............................................................................. 255 8.1

Introduction ....................................................................................... 255

8.2

Sample Preparation and Measurements of Electrolytic Deformation . 257

8.3

Electrochemistry and Expansion Behaviour in Polyaniline Film ......... 259

8.4

Dependencies of the Expansion Ratio on the Degree of Oxidation and Dopant Ions ................................................................................ 260

8.5

pH Dependence of Electrolytic Expansion ......................................... 262

8.6

Time Response of the Electrolytic Expansion..................................... 265

8.7

Anisotropy of Electrolytic Expansion in Polyaniline Films ................. 266

8.8

Contraction Under Strain in Stretched Polyaniline Films ................... 267

8.9

Electrolytic Expansion in Other Conducting Polymers ...................... 267

8.10 Applications of Electrolytic Expansion .............................................. 268 8.11 Conclusions ....................................................................................... 269 References ................................................................................................... 269 9

Membranes for Electronics ......................................................................... 271 9.1

Introduction ....................................................................................... 271

9.2

Plasma Polymerisation ....................................................................... 276

9.3

9.4

9.2.1

History .................................................................................. 277

9.2.2

General Characteristics .......................................................... 277

9.2.3

Synthesis of Plasma Polymers ................................................ 278

Characterisation of Plasma Polymers ................................................. 282 9.3.1

IR Spectroscopy ..................................................................... 283

9.3.2

XPS ........................................................................................ 283

Applications of Plasma Polymers ....................................................... 283

v

Polymers in Electronics

9.4.1

Packaging .............................................................................. 284

9.4.2

Insulator ................................................................................ 284

9.4.3

Semiconductive Films ............................................................. 285

9.4.4

Conductive Films ................................................................... 286

9.4.5

Resist Films ............................................................................ 286

9.4.6

Ultrathin Polymer Films ......................................................... 286

9.4.7

Chemical Sensors ................................................................... 287

9.4.8

Biosensors .............................................................................. 287

Acknowledgements ..................................................................................... 290 References ................................................................................................... 291 10 Conducting Polymer-Based Biosensors ........................................................ 297 10.1 Introduction ....................................................................................... 297 10.1.1 Biosensors .............................................................................. 298 10.1.2 Construction of Biosensors .................................................... 299 10.1.3 Transducers ........................................................................... 301 10.1.4 Biological Component ........................................................... 301 10.1.5 Importance of Conducting Polymers to Biosensors ................ 302 10.2 Preparation of Electrodes ................................................................... 304 10.2.1 Synthesis of Conducting Polymers ......................................... 304 10.2.2 Conduction Mechanism in Conducting Polymers .................. 305 10.3 Immobilisation of Biomolecules/Enzymes .......................................... 305 10.3.1 Methods of Immobilisation.................................................... 305 10.3.2 Advantages of Immobilisation ............................................... 309 10.4 Characterisation of Enzyme Electrodes .............................................. 309 10.4.1 Determination of Enzyme Activity ......................................... 309 10.4.2 Effect of pH ........................................................................... 310 10.4.3 Effect of Temperature ............................................................ 311 10.4.4 Effect of Storage Time ........................................................... 312 10.4.5 Response Measurements ........................................................ 313

vi

Contents

10.5 Types of Biosensors ............................................................................ 313 10.5.1 Optical Biosensors ................................................................. 314 10.5.2 Electrochemical Biosensors .................................................... 315 10.6 Biosensors for Healthcare .................................................................. 318 10.6.1 Glucose Biosensor .................................................................. 318 10.6.2 Urea Biosensor ....................................................................... 320 10.6.3 Lactate Biosensor ................................................................... 321 10.6.4 Cholesterol Biosensor ............................................................ 323 10.6.5 DNA Biosensor ...................................................................... 324 10.7 Immunosensor ................................................................................... 326 10.8 Biosensors for Environmental Monitoring ......................................... 326 10.9 Conclusions ....................................................................................... 326 Acknowledgements ..................................................................................... 327 References ................................................................................................... 327 11 Nanoparticle-Dispersed Semiconducting Polymers for Electronics .............. 341 11.1 Introduction ....................................................................................... 341 11.2 Material Preparation Methods ........................................................... 344 11.3 Photophysics of Charge Separation Nanoparticle-Polymer Systems ... 346 11.3.1 TiO2-Conjugated Polymer Composites .................................. 348 11.3.2 Nanoparticle Semiconductors-Polymer Systems ..................... 353 11.3.3 Gold-Polythiophene Blends .................................................... 357 11.4 Summary ............................................................................................ 360 Acknowledgements ..................................................................................... 361 References ................................................................................................... 361 12 Polymers for Electronics .............................................................................. 367 12.1 Introduction ....................................................................................... 367 12.2 Polymer Electroluminescence ............................................................. 368 12.3 Conduction in Polymers ..................................................................... 375

vii

Polymers in Electronics

12.4 Molecular Electronics ........................................................................ 379 12.5 Polymer Deposition Technologies ...................................................... 379 12.6 Summary ............................................................................................ 388 Acknowledgements ..................................................................................... 388 References ................................................................................................... 388 13 Conducting Polymers in Molecular Electronics ........................................... 393 13.1 Introduction ....................................................................................... 393 13.2 Synthesis of Conducting Polymers ..................................................... 397 13.3 Preparation of Ultrathin Conducting Polymer Films .......................... 399 13.3.1 Langmuir-Blodgett Films ........................................................ 399 13.3.2 Self-Assembly Monolayers ..................................................... 404 13.4 Characterisation of Conducting Polymers .......................................... 404 13.5 Molecular Devices Based on Conducting Polymers ............................ 406 13.5.1 13.5.2 13.5.3 13.5.4 13.5.5 13.5.6 13.5.7 13.5.8

Diodes ................................................................................... 406 Field-Effect Transistor ............................................................ 409 Biosensors .............................................................................. 411 Electronic Tongue .................................................................. 414 Electronic Nose ...................................................................... 415 Nanowires ............................................................................. 418 Electroluminescent Displays .................................................. 419 Microactuators ...................................................................... 423

13.6 Conclusions ....................................................................................... 424 Acknowledgements ..................................................................................... 425 References ................................................................................................... 425 Abbreviations and Acronyms............................................................................. 441 Contributors ...................................................................................................... 449 Index ................................................................................................................. 453

viii

Preface

There is a global effort towards the applications of polymers in electronics. The demand for new polymeric materials that can replace the widely used semi-conductor silicon in microelectronics has recently intensified. This has essentially been due to the continuing drive towards higher circuit density of the micro-electronic components and the muchneeded very high speed processing of the data being continuously generated in various research, manufacturing and commercial establishments located worldwide. It is anticipated that polymers may perhaps offer viable solutions to the problems presently being confronted by the modern electronics industry. Among the various polymeric materials, conjugated polymers have been projected to have innumerable applications in electronics and are thus presently at the centre-stage of research and development. Conducting polymers have been found to have applications in a wide range of emerging areas such as light-emitting diodes, photonics, micro-actuators, light-weight batteries, biosensors and molecular electronics. However, it may be noted that development of polymers for electronics is still an open field wherein polymers are used not only as insulators but can also be tailored for the desired electronic properties for specific applications. It was thus thought that a Handbook dedicated entirely to the preparation, characterisation and potential applications of polymers coupled with the fundamentals of the electrical, optical and photo-physical properties will go a long way in bridging a long-felt industrial need and motivate the dedicated and younger researchers to venture into new experiments. ‘Handbook of Polymers in Electronics’ has been designed to discuss novel ways polymers can be used in the rapidly growing electronics industry. Recent developments in microelectronics have prompted enhanced interest towards the search for new molecular materials that can be utilised for increased density of packaging. Vibha Saxena and cowriters (Chapter 1) discuss the phenomenon of charge transport in electrically conducting polymers, considered to be a direct consequence of conjugation, i.e., chemical un-saturation of the carbon atoms in the polymer chain. It is indicated that an improved understanding of the mechanism of charge transport in these materials is likely to unravel new hidden phenomena having implications in polymer electronics. Reghu Menon (Chapter 2) discusses the role of easily polarisable delocalised p-electrons in determining the electrical properties of conducting polymers. Toshikuni Kaino (Chapter 3) focuses on the transmission and processing of digital information using conjugated non-linear optical devices based on polymers. Barbara Wandelt (Chapter 4) in her extensive coverage of the luminescence properties of polymers reveals how fluorescence probes can provide an insight into the nature of intermolecular interactions in these systems. Alberto Bolognesi and cowriters (Chapter 5) reveal that polymers offer a 1

Handbook of Polymers in Electronics unique possibility of working with cheaper technology giving flexible films that can be used to emit light. Jean-Claude Dubois (Chapter 6) discusses the technological developments of photopolymers and photo-resists presently being used in microelectronics industry. Bruno Scrosati (Chapter 7) has provided an interesting insight into the potential of polymeric electrodes for lightweight batteries for applications in electronics. Keiichi Kaneto and cowriters, in their outstanding appraisal (Chapter 8), have shown that the changes in molecular conformations arising due to the localisation of p-electrons and electronic repulsion between the polycations influence the operation of a conducting polymer micro-actuator. Isao Karube and cowriters (Chapter 9) have given an excellent review of the preparation, characterisation of the plasma-polymerised membranes for application in electronics. Conducting polymers have been predicted to play decisive role towards the fabrication of third generation biosensors. Keeping this in view, Asha Chaubey and cowriters (Chapter 10) have shown that redox polymers can be advantageously used to combine both the role of protein immobilisation matrices and the physical transducer resulting in improved response characteristics and miniaturisation. K.S.Narayan (Chapter 11) reveals a synergistic approach towards the nanoparticle dispersed particles semi-conducting polymers for application in miniaturised electronic devices. Tim Richardson (Chapter 12) deals with the various options available to a device engineer associated with the technological development of polymer based electronic devices. Chapter 13 contains a comprehensive review on molecular electronic applications of conducting polymers. ‘Polymers in Electronics’ is the result of the invaluable contributions of many celebrated researchers who have been active in their respective fields for many decades. I am grateful to all of them for their active participation in this important project. Special thanks are due to Ms Frances Powers of Rapra for her timely suggestion that this project should be undertaken. Ms Claire Griffiths, Dr Arshad Makhdum and Dr Sarah Ward of the editorial staff at Rapra have worked extremely hard to check that everything in the Handbook is correct and that the project is completed in time. Mr Steve Barnfield is thanked for the typesetting and the excellent cover design of the Handbook. I would also like to extend my thanks to Geoffrey Jones of Information Index who so skilfully produced the index. I am thankful to all the members of my research group (Biomolecular Electronics & Conducting Polymers) of the National Physical Laboratory (NPL), New Delhi for the many discussions and suggestions during the operation of the project. The Handbook would not have been possible without the invaluable advice received on many occasions from a number of eminent scientists including Professor S.K. Joshi, Dr R.A. Mashelkar, FRS, Dr W. Hayes, Professor A.P.F. Turner, Professor E.S.R. Gopal, Professor S. Slomkowskii, Dr A.K. Raychaudhri, Dr Krishan Lal and Dr Howard H. Weetall. I am thankful to all my colleagues especially Dr K.K. Saini, Dr. S.S. Bawa and Dr Subhas Chandra of NPL, New Delhi for many discussions held during the implementation of the project. Finally, it would have been difficult to complete the project without the emotional support I received from Shashi (wife), Aditi (daughter) and Rajat (son). Bansi D.Malhotra

2

1

Charge Transport in Conjugated Polymers V. Saxena and B.D. Malhotra

1.1 Introduction Since the early 1950s, polymers have been used extensively as passive components in electronic devices because of their light weight, flexibility, corrosion resistance, high chemical inertness, electrical insulation and ease of processing. In 1975, an inorganic conjugated polymer, polythiazyl, (SN)x, was discovered, which possesses metallic conductivity and becomes a superconductor at 0.29 K [1]. However, the idea of using polymers for their electrical conducting properties actually emerged in 1977 with the findings of Shirakawa and co-workers [2], that the iodine-doped transpolyacetylene, (CH)x, exhibits conductivity of 103 S cm-1. Since then, an active interest in synthesising other organic polymers possessing this property has been initiated. As a result, other polymers having a π-electron conjugated structure, such as polyaniline (PANI), polypyrrole (PPy), polythiophene (PT), polyfuran (PFu), poly(pphenylene) (PPP) and polycarbazole (PCz) [3-6] have been synthesised and studied. Some important conducting polymers and their energy gaps are shown in Table 1.1. Since the beginning of the last decade, these polymers (hereafter called conducting or conjugated polymers) have been extensively investigated for an understanding of their physical and chemical properties.

Table 1.1 Important conducting polymers Polymer

Optical absorption edge (eV)

Trans-polyacetylene

1.4

Cis-polyacetylene

2.0

Polypyrrole

2.5

Polythiophene

2.0

Poly(p-phenylene)

3.0

Poly(p-phenylenevinylene)

2.4

Polyaniline

1.6

3

Handbook of Polymers in Electronics The charge transfer process is one of the most intriguing properties of conducting polymers because the electrical conductivities of this class of polymers vary over many orders of magnitude due to chemical or electrochemical doping. It is understood that a wide variety of phenomena are involved in charge transport in this group of materials. A major source of this phenomenon originates from the quasi-one-dimensional (q-1D) nature of the materials. A polyconjugated chain can be considered as a q-1D metal, having one charge carrier per carbon atom. It is a well-established fact that such a half-filled system gives rise to Peierls instability by opening up an insulating gap at the Fermi level. This leads to a band structure responsible for the important electronic properties in polymers and thereby results in the existence of a non linear excitation called a soliton. This excitation and other excitations, such as polarons and bipolarons found in non degenerate groundstate systems, are produced due to the chain relaxation or deformation that results from adding/removing an electron from the polymeric chain. Under the influence of an applied electric field these non linear defects become mobile, resulting in an increased electrical conductivity. Each of these particles possesses its own characteristic transport properties. A clear understanding of the intrinsic excitations in doped and undoped conjugated polymers is still lacking [7-8]. A considerable amount of work has been carried out by several researchers focusing on this fundamental problem. The charge transfer properties as a function of temperature, pressure, magnetic fields, etc., for various polymeric samples have also been reported in the literature. The collective contributions from various parameters, such as electron-phonon interaction, electron-electron interaction, quantum lattice fluctuations, interchain interactions, etc., make it difficult to estimate the contribution from individual parameters quantitatively. Moreover, the contributions from disorder and doping, etc., make it rather difficult to envisage a microscopic mechanism for charge transport in doped conducting polymers. Therefore, the theoretical modelling of transport properties in conducting polymers is still a challenging problem due to the extreme complexity of the system. However, recent developments in reducing the extent of disorder have explained many phenomena regarding charge transport in doped conducting polymers. In this chapter, an overview of the past few years, a study of charge transport in conducting polymers is presented.

1.2 The Electronic Ground State It is well known that the accessible energy levels of an electron in a crystal are grouped into bands, which may be visualised as originating from the electronic levels of the atom. The bands form by the splitting of the atomic levels when the atoms approach one another and obtain their equilibrium positions in the crystal. The bands are separated by forbidden energy ranges called the energy gap. In a semiconductor, this gap separates the band which is completely filled (valence band) from the lowest energy band which is completely empty at absolute zero (conduction band) and accounts for the conduction processes in

4

Charge Transport in Conjugated Polymers this class of materials. In metals, the conduction band is partially filled, implying that a finite density of states exists at the Fermi level. Conjugated polymers differ from crystalline semiconductors and metals in several aspects and are often treated theoretically as a one-dimensional system. The formation of the band gap is explained taking into account either electron-phonon interactions or electronelectron interactions among π-electrons. If electron-phonon interaction dominates in real π-conjugated polymers, these systems could be treated using Peierls theory. In contrast, when electron-electron interactions dominate, the Hubbard model could be used to explain the physical properties of polymers. The Peierls model explains why a chain of unsaturated carbon atoms with one conduction electron per atom does not exhibit metallic properties. If all the atoms are spaced at equal distance, a, the basic cell in reciprocal space is the Brillouin zone in the interval –π/a> kBT. At room temperature this analysis gives high intrinsic conductivity, σ = 1.4 x 107 S cm-1. Kivelson and Heeger carried out a detailed study on the intrinsic conductivity of conducting polymers [77]. They described the expression for the conductivity as: 2πnν0e 2a 2t0

2

2 2

α h

⎛ hν ⎞ exp⎜ ⎟ ⎝ kBT ⎠

(1.3)

where α (~4.1 eV/Å) is the electron-phonon coupling constant, ν0 is the phonon frequency, t0 is the electron hopping matrix element [107], h is Planck’s constant, n is the conduction electron density and a is the C-C distance in the chain direction. A large t0, and a small number of phonons gives the conductivity at room temperature as 107 S cm-1. This value increases exponentially at low temperatures. Since the charged ions are spatially removed from the q-1D conduction path, the usual scattering of phonons is reduced. This is because phonons of wave vector 2kF are required to backscatter electrons. Since these phonons are thermally excited only at higher temperatures, the resistivity is very small at low temperatures, with a rapid rise when the thermal energy kBT approaches the energy of the 2kF phonons. At 0.12 eV, the rapid increase in resistivity can account for the change to metallic temperature dependence, which is a prominent feature of the conductivity in conducting polymers. As discussed earlier, the interchain couplings are necessary to prevent 1D localisation. Even a small interchain coupling, t⊥ ~0.1 eV, may give rise to the suppression of the Peierls distortion. The condition necessary for the system to remain three-dimensional is L/a >> 2t0/t⊥

(1.4)

where L characterises the distance between the chain interruptions or sp3 defects or crosslinks. When the concentration of chain interruptions is sufficiently high such that the left hand side of equation 1.3 is small, then the wave function will be localised. The possible limits for the conductivity arise from the chain interruptions and/or phonon scattering. All the above factors suggest that in high-quality conducting polymers the electronic mean free path could be much larger than the structural coherence length and real metallic features could be observed.

21

Handbook of Polymers in Electronics Similar charge transport models have been proposed by Prigodin and Firsov [108, 109]. According to their model, an abrupt transmission from extended to localised states is expected at the critical interchain exchange integral t⊥c~(3h/2πτ), τ being the scattering time. Therefore, the delocalisation in a q-1D metallic chain appears only if t⊥ is larger than the threshold value, t⊥~0.3/τ. Later, Nakhmdeov and co-workers carried out a study of hopping transport in q-1D systems near the M-I transition with weak disorder [98]. They set the cut-off temperature regimes in which band transport crosses over to hopping transport. In a high temperature regime, the band transport is governed by phonon scattering and disorder while at low temperatures, the hopping has been ascribed to Mott’s VRH. In the intermediate temperature region, the temperature dependence of conductivity shows a power law behaviour. However, these temperature regions are different in a q-1D system when there is a weak intrachain coupling. In these cases, the temperature dependence of conductivity gradually varies from 1D behaviour at high temperatures to that of an isotropic 3D behaviour at low temperatures. In the intermediate range, the conductivity follows exp(-T0/2T)exp[-(T0/2T)]1/2 dependence. Joo and coworkers extended this model, suggesting that the effect of finite temperature emerges through phonon scattering, which is expected to be highly anisotropic [110-112]. The role of phonon forward scattering is to break the phase coherence of the impurity scattering and thereby destroy the weak localisation. Moreover, the conductivity versus temperature curve exhibits a characteristic maximum at temperatures where the phonon backward scattering time becomes comparable with the impurity scattering time. Epstein and co-workers have widely used q-1D models to interpret transport properties in both metallic and insulating polymer systems [113, 115]. Conducting polymers were considered as an inhomogeneous system, which consists of partially crystalline and amorphous regions. The overlap of π-orbitals gives rise to crystalline regions whereas amorphous regions emerge from weak chain interactions. When the size and volume fraction of the crystalline region increases with respect to the amorphous region, the system is expected to undergo a transition from insulator to metal. The charge carriers are subjected to 1D localisation while passing through the amorphous region in between the crystalline region and thereby the movement of charge carriers occurs through the 1D localised regions and often dominates throughout the 3D extended states in crystalline regions. When the volume fraction of 3D extended states increases, the probability of movement of charge carriers is through the path of least resistance and therefore, a percolative metallic transport is expected. Microscopic properties in crystalline and amorphous regions are different and hence the usual Anderson localisation in the homogeneous disorder limit is not appropriate for conducting polymers. More recently, Samukhin and co-workers proposed [99] a q-1D fractals model in order to explain the experimental data obtained for poorly conducting polymers. It is found that at low temperatures, the VRH conductivity obeys a q-1D Mott’s law, σdc ∝ exp-(T1/T)1/2, but

22

Charge Transport in Conjugated Polymers the characteristic temperature T1 is greater than T0 for a 1D chain by a factor 1/D-1, D being the dimensionality of the system. Similar temperature dependence was obtained for dc conductivity. Low frequency conductivity is entirely controlled by the weak charge transfer between clusters, each cluster being very dense and well isolated. In contrast to q-1D models, Qiming and co-workers proposed a granular-rod model for the metallic state of the conducting polymer [116]. In this model, the metallic islands correspond to single strands of polymer. The macroscopic conductivity results from anisotropic threedimensional VRH in the network of metallic rods. This model explains very well the temperature dependence of the conductivity, σ = σ0exp(-T0/T1/2), the doping dependence of T0, the anomalous 1/T dependence of the thermoelectric power as well as the linear increase of Pauli susceptibility with dopant concentration. A temperature range, where the variable range hopping is valid, is decreased below the experimentally observed temperature range (over which the above equation holds) if the metallic islands correspond to 3D bundles of the polymer strands. Sheng’s fluctuation induced tunnelling (FIT) model was used extensively to interpret transport properties in metallic polymers. This model was originally developed for granular metal [117, 118] and polymers filled with carbon black or alumina flakes. The polymer system is described in terms of highly conducting regions separated by much less conducting or insulating areas. The electrical conduction is dominated by electron transfer between large conducting segments. Since the electrons tend to tunnel between conducting regions at points of their closest approach, the relevant tunnel junctions are usually small in size and are therefore subject to large, thermally activated voltage fluctuations across the junction. By modulating the potential barrier, the voltage fluctuations directly influence the tunneling probability and introduce a characteristic temperature variation to the normally temperature independent tunnelling conductivity. A non metallic feature of doped polyacetylene was explained in the framework of this model [119]. A similar model was used to interpret the transport properties of emeraldine polymer as a function of the protonation level, x [120]. At no composition level does the conductivity appear truly metallic. For all compositions, the conductivity behaviour is similar to that of a granular metal and this data fits transport via charging energy limited tunnelling between conductivity islands. The data were found to be consistent with percolation among these islands for x ≥ 0.3 with the presence of an insulating layer surrounding each island above the percolation threshold. The size of these islands is estimated to be 200-300 Å. Lux and co-workers reported scanning electron microscopy (SEM) and transmission electron microscopy (TEM) pictures of highly conducting polyaniline in support of the conducting island concepts [121]. Experimental measurements of TEM, X-ray diffraction (XRD), temperature dependence of dc conductivity and magnetic susceptibility indicate the applicability of this model. However, electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility studies also suggest that pristine and doped polyaniline contain at least two types of spin carriers. It was suggested by Conwell and Mizes that the

23

Handbook of Polymers in Electronics conduction mechanism is not due to FIT dependence in conducting polymers since the metallic regions in the FIT model have negligible temperature dependence of conductivity. Also, the phonon scattering, scattering due to imperfections, and defects in the metallic regions are not considered in the FIT model. They determined the band motion versus diffusive hopping transport in oriented metallic conducting polymers to understand the effective dimensionality of the system. They showed that for band motion t⊥τ// is much greater than h/2π, while for diffusive motion t⊥τ// is much less than h/2π, τ// being the average time for the electron scattering along the chains (τ//~10-14 s from σ// = ne2τ//m*, if σ~105 S cm-1, n = 1022 cm-3, m* = free electron mass = 9.1 x 10-28 g, e = 1.6 x 10-19 C). If the system consists of high conducting regions mixed with low conducting regions, then σ⊥ is the mixture of band motion and hopping. However, the measurements σ// /σ⊥ as a function of temperature in oriented metallic trans-polyacetylene shows that σ// /σ⊥ is nearly temperature independent and hence it is impossible that σ⊥ is due to diffusive hopping in both cases [122, 123]. In contrast, experimental results demonstrated by Park and coworkers [124] indicate that σ// /σ⊥ increases with σ// and therefore, the issue of transport in highly oriented metallic conducting polymers is still debatable. Voit and Buttner examined the FIT model critically and it was concluded that physical parameters obtained from this model do not allow consistent description of highly doped polyacetylene [125]. Kaiser and Graham extended the FIT model for heterogeneous systems by introducing geometric factors to the insulating barriers. Such barriers could be due to material imperfections that dominate the total resistance of the sample [48]. If the intrinsic conductivity is very large and barriers form only short segments in the conduction path, the temperature dependence of the measured conductivity reflects that of the barriers, but the magnitude is very much larger than the barrier conductivity due to geometrical factors. Furthermore, if the barriers are reasonably good heat conductors, the temperature differences across them (and therefore, their contribution to thermoelectric power) will be small [126]. In contrast to conductivity, the thermoelectric power could then follow the intrinsic metallic behaviour. In addition to the tunnelling transport across the insulating barrier, a parallel phonon assisted hopping transport was included in the Kaiser and Graham model. The bulk conductivity is the combination of Kivelson and Heeger q-1D transport, hopping/ tunnelling transport and 3D disordered metallic transport (Figure 1.9). This heterogeneous model was reviewed by Kaiser for understanding the experimental data obtained on Naarman-polyacetylene. Localisation effects can appear at low temperatures despite the high conductivity. These could be due to charging energy effects in interchain transfer at low temperatures or to quantum corrections. The linear thermoelectric power behaviour observed indicates a smaller interaction between electrons and phonons than in normal metals, which is consistent with the remarkably high conductivities observed [127]. Paasch was of the opinion that this model contains seven independent data and so may describe

24

Charge Transport in Conjugated Polymers

Figure 1.9 Schematic representation of the conduction processes in (a) microscopic or (b) macroscopic pictures that are in agreement with transport data in Naarman-polyacetylene

the smooth temperature dependence. He argued that multiparameter fits of simple dependencies sometimes make the picture seem unambiguous whether the relative influences of the different contributions are reliable or not [128]. He modified the FIT model, arguing that one of the main barriers for the tunneling process is the chain segments with residual dimerisation. These segments exhibit a dimerisation gap which acts as a tunnelling barrier for the charge carriers. In general, however, the multiple parameter fitting procedure in FIT model has not been found satisfactory to explain the physical properties of conducting polymers. The exponential dependence of conductivity in the insulating regime of conducting polymers has been usually attributed to VRH. However, a wide range of exponent (d = 0.25-1) has been observed [49, 129, 130]. Moreover, T–1/2 behaviour of conductivity is often observed in granular metallic systems. Schreiber and Grussbach [131] suggested that the fluctuations in mesoscopic systems could give a wide range of values of the exponent due to the fractal nature of wavefunctions near the mobility edge. The transition of polymer system from q-1D to 3D was studied as a function of doping level [132].

25

Handbook of Polymers in Electronics Stafstrom [133, 134] reported that the enhancement in interchain interaction with increased dopant concentration can induce 3D localisation of the electronic states. He used the many-channel Buttiker-Landaur conductance formula [135] to study the conductance as a function of length of the system. Each channel contains several polymer segments represented by chain interruptions. The chain interruptions along the channels can be caused by sp3 defects, crosslinking between chains, etc. The hopping across such a chain interruption should, therefore, be reduced considerably compared to the interchain hopping. He showed that the most relevant parameter for causing localisation in the number of chain interruptions is the number of chain interruptions and not the channel length. The conductance of the system is unaffected by the presence of chain interruptions up to a critical value and, therefore, the critical chain length for which the conductance begins to drop should be used to characterise the transition between diffusive and non diffusive conductance. Moreover, if the interchain hopping term is equal to the interchain hopping strength (3D case) or if the number of channels is very small (1D case), the usual type of disorder-induced exponentially localised wave functions appear. Therefore, the q-1D nature of conjugated polymeric systems provides an example of a class of materials that differ from previously studied materials in the way the conductance responds to disorder in the form of chain interruptions. Recently, Schon and co-workers suggested the possibility of band-like transport in oligothiophene as a result of strong observed dispersion of the valence band based on band structure calculations [136]. Phillips and co-workers proposed a random dimmer model (RDM) [137-139] which has a set of delocalised conducting states, even in 1D, that initially allow a localised particle to move through the lattice almost ballistically. They showed that any disordered bipolaron lattice can be mapped onto a RDM. The model is found to be applicable to the M-I transition in a wide class of conducting polymers, such as polyaniline and heavily doped polyacetylene. Calculations performed on polyaniline demonstrate explicitly that the conducting state of the RDM is coincident with a recent calculation of the location of the Fermi level in the metallic region [140, 141]. A RDM analysis on poly(p-phenylene) also indicates the presence of a set of conducting states in the vicinity of the band edge. In highly disordered conducting polymers, the usual exponential dependence of temperature is explained by phonon assisted hopping or tunnelling or both. Zuppiroli and co-workers have proposed a model which describes adiabatically, the dimensionality, homogeneity, coulomb interactions and multi-phonon character in the framework of hopping conduction [142, 143]. It was shown that the electron transport in these materials is due to correlated hopping between polaronic clusters. They showed, both theoretically and experimentally, that the charging energy is the principal barrier to hopping. Polaronic clusters which originate from fluctuations in the dopant concentration function as metallic grains in the granular metal hopping model. The final temperature dependence is the same as in the case of models of Sheng,

26

Charge Transport in Conjugated Polymers Abeles, Arie or Efros and Shklovskii [144, 145]. Nagashima and co-workers recently described ac transport studies in polymers by using a statistical model of resistor network [146]. The model takes into account the polydispersiveness of the material as well as intrachain and interchain charge transport processes. The real and imaginary part of the resistivity was determined using a transfer-matrix technique. At low frequencies, interchain processes are more important and determine the transport mechanism. On the other hand, at high frequencies charge transport should be restricted along the polymer chains, as interchain processes should be dominant. Both regimes described by the model reproduce the experimental results in a remarkable way. Among various models proposed by several researchers for conducting polymers in the insulating side, the theoretical work by Ovchinnikov and Pronin [147] and Lewis [148] are slightly different from other models. In the former model, a q-1D percolation model was proposed for explaining the conductivity. According to this model, an impurity captures an electron from one of the adjacent chains and forms a charged impurity centre. Such a carrier can detrap by an activated process and diffuse along the chain. This polaron can recombine with another impurity centre near the chain and then escape to an arbitrary chain adjacent to the second impurity centre. Thus, conduction by percolation is possible in such a system if an infinite cluster of chains can be connected by impurity centres. Lewis and co-workers suggested that the charge transport occurs by tunnel transitions between localised states and lattice fluctuations, and electronlattice coupling tends to broaden and reorganise the energy levels at each site. They estimated the electric field, frequency and temperature dependences of charge transport in both conducting and non conducting polymers. Moreover, in this model the localised states correspond to the Urbach states in amorphous systems since the optical absorption from a distribution of states extend out from the fundamental absorption band edge.

1.7 Conclusions It can be concluded that interchain interaction and disorder play a leading role in governing the transport properties of polymers. Nevertheless, the theoretical understanding of charge transport phenomenon is not yet completely developed in these polymers. None of the models for charge transport in these polymers is able to explain all the features of the conducting polymers. The major hurdle is in quantifying the intrinsic and extrinsic parameters, for example, interchain and intrachain interaction, coulomb interaction, electron-phonon interaction, charge delocalisation, extent of conjugation length and disorder, etc., whose contributions to charge transport are greatly intermixed. Therefore, better understanding of the charge transport in these materials is essential to determine the various physical phenomena operating in the polymerbased electronic devices.

27

Handbook of Polymers in Electronics

Acknowledgements The authors are grateful to Dr. K. Lal, Director, NPL, New Delhi, India, for his interest in this work. Viba Saxena thanks CSIR, India, for the award of a Research Associateship.

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36

2

Electrical Properties of Doped Conjugated Polymers R. Menon

2.1 Introduction In the past three decades, several types of π-electron systems have shown very interesting features in electrical transport properties [1-4]. Charge-transfer complexes, intercalated graphite, conjugated polymers, carbon-60, carbon nanotubes, etc., are some of the wellknown π-electron systems. Polymeric materials were considered as insulators before the discovery of metallic poly(sulfur nitride), [SN]x, and the enhancement of conductivity in doped polyacetylene, (CH)x, by several orders of magnitude [4, 5]. The polyconjugated chains -(C=C-C=C-C=C)n- consist of alternating single (σ-bonds) and double bonds (π-bonds). The π-electrons are highly delocalised and easily polarisable, and these features play important roles in the electrical and optical properties of polyconjugated systems. It also makes the latter rather different from conventional electronic systems [6-8]. Moreover, the intrinsic q-1D nature and the extent of both intra- and interchain delocalisation of π-electrons play significant roles in the structural, electrical and optical properties of polyconjugated systems. Nevertheless, the complex morphology of polymeric systems, which are partially crystalline and partially amorphous in nature, plays a crucial role in the physical properties. In general, the conjugation length, the strength of the interchain interaction and the extent of disorder are some of the significant parameters that govern the physical properties of polyconjugated systems. The electrical and optical properties of (CH)x, PANI, PPy, PT, poly(p-phenylenevinylene) (PPV), PPP and polythienylene vinylene (PTV) are some of the extensively studied conjugated polymers [7, 9]. In first-generation conducting polymers (1976-1986), the maximum possible values of electrical conductivity were limited due to the presence of structural and morphological disorder, disorder-induced localisation, etc. The metallic features were rather weak. This was mainly due to the presence of strong structural and morphological disorder, as a result the π-electrons were not very well delocalised to facilitate intra- and interchain charge transport [10]. In the past decade, significant improvement in reducing the structural and morphological disorder has helped to create the new generation of conducting polymers in which the metallic features are predominantly observed in transport measurements. For example, in iodine-doped Tsukomoto (CH)x, the conductivity was around 105 S cm-1 [11].

37

Handbook of Polymers in Electronics By the early 1990s, several groups had started making high quality materials of PPV, PPy, PANI and polyalkylthiophene (PAT) [9]. In doped, oriented PPV samples the conductivity is of the order of 104 S cm-1 [12]. In high quality, PF6-doped PPy and PT samples (prepared by low temperature electrochemical polymerisation), the conductivity is nearly 500 S cm-1 [13]. With the development of counterion-induced processibility of PANI by dodecylbenzoyl sulfonic acid (DBSA) and camphor sulfonic acid (CSA) dopants, the conductivity was enhanced to nearly 500 S cm-1, and its temperature dependence showed a significant metallic positive TCR in the range 150-350 K [14-16]. The conductivity was enhanced to 103 S cm-1 in the case of regioregular PAT [9, 17]. The conductivity of undoped polyconjugated systems is 10-6-10-10 S cm-1, hence it can be considered at the semiconductor-insulator boundary [18]. The band gaps of known polyconjugated systems vary from 0.8 to 4 eV [9]. The charge carrier density in conducting polymers can be varied by several orders of magnitude (nearly 8 orders) by doping. In fully doped systems, the carrier density could be as high as 1022/cm3. The carrier mobility in doped conducting polymers is much lower with respect to that in inorganic semiconductors, and this is largely due to the presence of strong disorder in polymeric systems. Transient charge carriers can be generated by photoexcitation in conjugated polymers [7, 8, 19]. The maximum level of doping in conjugated polymers could be as high as 50%, and that corresponds to one dopant per two monomers. In conducting polymers the doping process can generate various types of charge carriers like polarons, bipolarons, solitons, free carriers, etc., and this to a large extent depends on the doping level, the structure of the polyconjugated chain, interchain interactions, disorder, etc., [7, 8, 19]. In degenerate systems like (CH)x, solitons are formed, especially at doping levels below 6%. However, in non degenerate systems like PPy, PT, etc., both polarons and bipolarons are formed depending upon the energetics. However, as the interchain interactions and the carrier density increases and the extent of disorder decreases, these excitations could behave more like free carriers. The M-I transition in doped conducting polymers is mainly governed by the extent of disorder, interchain interaction and doping level [18, 20]. The main source of disorder in conducting polymers are the sp3 defects in the chain, chain ends, chain entanglements, voids, morphological and doping induced defects, etc., [9]. In fibrillar morphology, the chains are extended, hence it is possible to have delocalised states along the chain length direction. In globular morphology, the chains are coiled up, and this tends to localise the electronic states. In unoriented conducting polymer systems, the chains are randomly dispersed and the physical properties are isotropic. However, by orienting the polymer chains by mechanical stretching it is possible to enhance the conductivity along the orienting axis, and an anisotropy of conductivity of the order of 100 can be

38

Electrical Properties of Doped Conjugated Polymers easily achieved. Since conducting polymers are partially crystalline and partially amorphous, the volume fraction of crystalline regions and the size of the crystalline coherence length play dominant roles in the charge transport. In general, the disorderinduced localisation plays a dominant role in the M-I transition and in the transport properties of conducting polymers.

2.2 Metallic State The metallic state in doped conducting polymers is inferred from the following: a large finite dc conductivity as the temperature (T) goes to 0 K, temperature independent Pauli spin susceptibility down to 10 K, linear temperature dependence of the thermoelectric power down to 10 K, linear term in the specific heat at low temperatures, free carrier absorption and large metallic reflectance in the infrared, etc., [20]. This evidence indicates the presence of a continuous density of states with a well-defined Fermi energy. In some conducting polymers, the typical metallic positive TCR was observed from 300 to 150 K, and in some others it was only below 20 K. However, recently Park and co-workers reported a metallic positive TCR in doped (CH)x, from 300 to 1.5 K, which is quite exceptional [21]. Although the typical negative TCR in high quality conducting polymers is indicative of non metallic behaviour, its temperature dependence was rather weak so that the logarithmic derivative of conductivity, σ, (W = dlnσ/dlnT) has a positive temperature coefficient. This implies a finite value of conductivity and a finite density of states at the Fermi level at very low temperatures, as expected in the case of disordered metallic systems. This evidence indicates that in spite of the disordered q-1D nature of polymer chains, it is possible to have a metallic state in these systems [22]. In the metallic state, the average size of the delocalised states is considerably larger than that of the structural coherence length, hence the carrier transport is slightly hindered by the presence of disorder potentials in the amorphous region. Although conducting polymers are intrinsically q-1D electronic systems, the interchain coupling can be sufficiently large to enable the formation of three-dimensional metals. The critical parameter in the M-I transition is the statistical average of a wide range of values of the correlation/localisation length, Lc. If Lc is greater than the average structural coherence length (which characterises the size of the crystalline regions), then the disorder can be considered as within the weak limit, which means the system sees only an average of the random fluctuations of the disorder potentials. Conversely, if Lc is less than the average structural coherence length, then the extent of disorder is considerably higher. The values of Lc and structural coherence length can be determined by transport property measurements and X-ray diffraction, respectively [9, 20].

39

Handbook of Polymers in Electronics

2.2.1 Conductivity The electrical conductivity is mainly determined by the carrier density, n, relaxation time, τ, and effective mass, m, of the carrier (electrical conductivity, σ = ne2τ/m, where e is the electron charge). According to the Ioffe-Regel criterion, the interatomic distance is considered as the lower limit for the mean free path, λ, in a metallic system. Hence, for a metallic system kFλ is greater than 1, where kFλ = [h(3π2)2/3] / (e2ρn1/3), kF is the Fermi wavevector and ρ is the electrical resistivity [23-25]. In highly doped conducting polymers, n ≈1021 per cm3, λ is around 10 Å, and kFλ ≈1-10, at room temperature. The details about metallic conducting polymers are shown in Table 2.1 [26].

Table 2.1 The details of various doped conducting polymers in the metallic state Abbreviation

Repeat Unit

Orientability

Crystallinitya

Conductivityb

(CH)x

C2H2

High

80%

104-105

PPV

(C6H4)C2H2

High

80%

104

Polyaniline

PANI

(C6H4)NH

Low

50%

400

Polypyrrole

PPy

C5H2N

Low

50%

400

PEDOT

C7H4O2S

Low

40%

300

PMeT

(C5H2S)CH3

Low

40%

400

Polymer Polyacetylene Poly(p-phenylene vinylene)

Poly(3,4-ethylene dioxythiophene Poly(3-methyl thiophene) a

Approximate values for high-quality samples.

b

In S cm-1. The values give approximately the highest observed values. In the cases of (CH)x and PPV, the conductivity in the highly oriented state along the direction of the chain alignment is given. Reproduced by permission from M. Ahlskog, R. Menon, Journal of Physics: Condensed Matter, IOP Publishing, 1998, 10, 32, 31-33, 7171.

Pietronero suggested that in a one-dimensional chain the only possible source of scattering for charge carriers is from +kF to –kF, involving the high-energy 2kF phonons [27]. Moreover, due to phonon freezing effects, possible even at room temperature, the first-order scattering should induce a strong enhancement in conductivity in one-dimensional chains. The conductivity in the chain direction, σ⎜⎜, in a one-dimensional chain is given by:

σ⎜⎜ = (ne2a/πh)vFτ = (ne2a2/πh) / (λ/a)

40

(2.1)

Electrical Properties of Doped Conjugated Polymers where a is the carbon-carbon distance, vF (=2t0a/h) is the Fermi velocity, t0 (= 2-3 eV) is the π-electron hopping matrix element and τ is the backscattering lifetime. In the limit of elastic scattering for a half-filled band system, σ⎜⎜(300 K)≈105 S cm-1. However, since the main scattering involved in a conducting polymer chain is only due to the 2kF phonons, and by including the inelastic scattering process below the characteristic temperature (kBT∼hω0/4 and T∼600 K), another two orders of magnitude of enhancement in conductivity should be possible, i.e., ≈ 107 S cm-1. Similar estimates of conductivity have also been obtained by the Kivelson and Heeger model [28]. In later models, the conductivity is expected to increase exponentially at low temperatures. Hence, the theoretical studies suggest that the intrinsic conductivity in one-dimensional models of conjugated polymers is expected to be even larger than that of conventional metals. The low temperature conductivity measurement is a simple and sensitive method to get a qualitative level of understanding about the extent of disorder present in the system. Since conductivity is directly related to the mean free path (which is rather sensitive to the presence of any disorder) the variation in low temperature conductivity is quite dramatic as disorder varies. The characteristic behaviour of the temperature dependence of conductivity can be understood in detail by defining the reduced activation energy, W, as the logarithmic derivative of the temperature dependence of conductivity, i.e., W = d(lnσ)/d(lnT) [29, 20]. If the system has a finite value of conductivity with a negative TCR, then W shows a positive temperature coefficient at low temperatures. Moreover, this ensures that there is a finite conductivity as T→0. In general, as the resistivity ratio, ρr [(= ρ(1.4 K)/ρ(300 K)], increases the temperature dependence of W gradually moves from a positive (metallic) to a negative (insulating) temperature coefficient at low temperatures. The approximate values of ρr for various conducting polymers in the metallic (M), critical (C) and insulating (I) regimes are shown in Table 2.2 [30]. The conductivity in the disordered metallic regime is expressed by [25, 31]

σ(T) = σ (0) + m´T1/2 + BTp/2

(2.2)

where m´ = α[4/3 – γ Fσ/2], α is a parameter depending on the diffusion coefficient, γFσ is the interaction parameter, p is determined by the scattering rate (for electron-phonon scattering, p = 3; for inelastic electron-electron (e-e) scattering, p = 2 in the clean (weakly disordered) limit or 3/2 in the dirty (strongly disordered) limit). The second term in Equation 2.2 results from the e-e interactions and the third term is the correction to σ(0) due to the localisation effects. In disordered metals, e-e interactions play an important role in the low temperature transport. Usually, the sign of m is negative when γFσ > 8/9, and this results in the change of sign (from negative to positive) in the TCR at low temperatures.

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Handbook of Polymers in Electronics

Table 2.2 The σ(300 K) and ρr ≈ [ρ ρ(1.3 K)/ρ(300 K)] of various conducting polymers in the metallic (M), critical (C), and insulating regime (I) M

(CH)x-I2

C σ(300 K)

ρr

σ(300 K)

ρr

σ(300 K)

5,000

10-20

3-5 x 104

>20

400

27

50

0.7

g-line

436

2.8

Steppers

Limited resolution

>0.35

i-line

365

4

Steppers

Deep-UV

248

(6.2-4.8)

No vacuum necessary

Limited resolution

>0.24

Deep-UV

193

No vacuum necessary

Resist to be optimised

>0.12

Technique Contact (vis.UV)

X-ray E-beam

Ion-beam

186

>0.30

0.5-5

2500-250

Global exposure

Resist sensitivity

>0.1

0.01-0.02 (corresponding to an associated wavelength λ)

0.5-2 x 103

Direct writing

Vacuum necessary