Organic Semiconductors for Optoelectronics E-Book

Hiroyoshi Naito

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Series in Materials for Electronic & Optoelectronic Applications
• Sprache: Englisch

Seitenzahl: 703

Veröffentlichungsjahr: 2021

Beschreibung

Comprehensive coverage of organic electronics, including fundamental theory, basic properties, characterization methods, device physics, and future trends

Organic semiconductor materials have vast commercial potential for a wide range of applications, from self-emitting OLED displays and solid-state lighting to plastic electronics and organic solar cells. As research in organic optoelectronic devices continues to expand at an unprecedented rate, organic semiconductors are being applied to flexible displays, biosensors, and other cost-effective green devices in ways not possible with conventional inorganic semiconductors.

Organic Semiconductors for Optoelectronics is an up-to-date review of the both the fundamental theory and latest research and development advances in organic semiconductors. Featuring contributions from an international team of experts, this comprehensive volume covers basic properties of organic semiconductors, characterization techniques, device physics, and future trends in organic device development. Detailed chapters provide key information on the device physics of organic field-effect transistors, organic light-emitting diodes, organic solar cells, organic photosensors, and more. This authoritative resource:

• Provides a clear understanding of the optoelectronic properties of organic semiconductors and their influence to overall device performance
• Explains the theories behind relevant mechanisms in organic semiconducting materials and in organic devices
• Discusses current and future trends and challenges in the development of organic optoelectronic devices
• Reviews electronic properties, device mechanisms, and characterization techniques of organic semiconducting materials
• Covers theoretical concepts of optical properties of organic semiconductors including fluorescent, phosphorescent, and thermally-assisted delayed fluorescent emitters

An important new addition to the Wiley Series in Materials for Electronic & Optoelectronic Applications, Organic Semiconductors for Optoelectronics bridges the gap between advanced books and undergraduate textbooks on semiconductor physics and solid-state physics. It is essential reading for academic researchers, graduate students, and industry professionals involved in organic electronics, materials science, thin film devices, and optoelectronics research and development.

Leseprobe

Table of Contents

Cover

Series Page

Series Editors

Title Page

Copyright

List of Contributors

Series Preface

Wiley Series in Materials for Electronic and Optoelectronic Applications

Preface

1 Electronic Structures of Organic Semiconductors

1.1 Introduction

1.2 Electronic Structures of Organic Crystalline Materials

1.3 Injection of Charge Carriers

1.4 Transition from the Conductive State

1.5 Electronic Structure of Organic Amorphous Solid

1.6 Conclusion

Acknowledgment

References

2 Electronic Transport in Organic Semiconductors

2.1 Introduction

2.2 Amorphous Organic Semiconductors

2.3 Experimental Features of Electronic Transport Properties

2.4 Charge Carrier Transport Models

2.5 Prediction of Transport Properties in Amorphous Organic Semiconductors

2.6 Polycrystalline Organic Semiconductors

2.7 Single‐Crystalline Organic Semiconductors

2.8 Concluding Remarks

2.9 Acknowledgment

References

3 Theory of Optical Properties of Organic Semiconductors

3.1 Introduction

3.2 Photoexcitation and Formation of Excitons

3.3 Exciton up Conversion

3.4 Exciton Dissociation

References

4 Light Absorption and Emission Properties of Organic Semiconductors

4.1 Introduction

4.2 Electronic States in Organic Semiconductors

4.3 Determination of Excited‐state Structure Using Nonlinear Spectroscopy

4.4 Decay Mechanism of Excited States

4.5 Summary

Acknowledgement

References

5 Characterization of Transport Properties of Organic Semiconductors Using Impedance Spectroscopy

5.1 Introduction

5.2 Charge‐Carrier Mobility

5.3 Localized‐State Distributions

5.4 Lifetime

5.5 IS in OLEDs and OPVs

5.6 Conclusions

5.7 Acknowledgments

References

6 Time‐of‐Flight Method for Determining the Drift Mobility in Organic Semiconductors

6.1 Introduction

6.2 Principle of the TOF Method

6.3 Information Obtained From the TOF Experiments

6.4 Techniques Related to the TOF Measurement

6.5 Conclusion

References

7 Microwave and Terahertz Spectroscopy

7.1 Introduction

7.2 Instrumental Setup of Time‐Resolved Gigahertz and Terahertz Spectroscopies

7.3 Theory of Complex Microwave Conductivity in a Resonant Cavity

7.4 Microwave Spectroscopy for Organic Solar Cells

7.5 Frequency‐Modulation: Interplay of Free and Shallowly‐Trapped Electrons

7.6 Organic‐Inorganic Perovskite

7.7 Conclusions

7.8 Acknowledgement

References

8 Intrinsic and Extrinsic Transport in Crystalline Organic Semiconductors: Electron‐Spin‐Resonance Study for Characterization of Localized States

8.1 Intrinsic and Extrinsic Transport in Crystalline Organic Semiconductors

8.2 Electron Spin Resonance Study for Characterization of Localized States

8.3 Conclusion

Acknowledgments

References

9 Second Harmonic Generation Spectroscopy

9.1 Introduction

9.2 Basics of the EFISHG

9.3 Some Application of the TRM‐SHG to the OFET

9.4 Application of the TRM‐SHG to OLED

9.5 Conclusions

Acknowledgement

References

10 Device Physics of Organic Field‐effect Transistors

10.1 Organic Field‐Effect Transistors (OFETs)

References

11 Spontaneous Orientation Polarization in Organic Light‐Emitting Diodes and its Influence on Charge Injection, Accumulation, and Degradation Properties

11.1 Introduction

11.2 Interface Charge Model

11.3 Interface Charge in Bilayer Devices

11.4 Charge Injection Property

11.5 Degradation Property

11.6 Conclusions

Acknowledgement

References

12 Advanced Molecular Design for Organic Light Emitting Diode Emitters Based on Horizontal Molecular Orientation and Thermally Activated Delayed Fluorescence

12.1 Introduction

12.2 Molecular Orientation in TADF OLEDs

12.3 Molecular Orientation in Solution Processed OLEDs

References

13 Organic Field Effect Transistors Integrated Circuits

13.1 Introduction

13.2 Organic Fundamental Circuits

13.3 High Performance Organic Transistors Applicable to Flexible Logic Circuits

13.4 Integrated Organic Circuits

13.5 Conclusions

References

14 Naphthobisthiadiazole‐Based Semiconducting Polymers for High‐Efficiency Organic Photovoltaics

14.1 Introduction

14.2 Semiconducting Polymers Based on Naphthobisthiadiazole

14.3 Quaterthiophene–NTz Polymer: Comparison with the Benzothiadiazole Analogue

14.4 Naphthodithiophene–NTz Polymer: Importance of the Backbone Orientation

14.5 Optimization of PNTz4T Cells: Distribution of Backbone Orientation vs Cell Structure

14.6 Thiophene, Thiazolothiazole–NTz Polymers: Higly Thermally Stabe Solar Cells

14.7 Summary

References

15 Plasmonics for Light‐Emitting and Photovoltaic Devices

15.1 Optical Properties of the Surface Plasmon Resonance

15.2 High‐Efficiency Light Emissions using Plasmonics

15.3 Mechanism for the SP Coupled Emissions

15.4 Quantum Efficiencies and Spontaneous Emission Rates

15.5 Applications for Organic Materials

15.6 Device Application for Light‐Emitting Devices

15.7 Applications to High‐Efficiency Solar Cells

Acknowledgements

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Typical methods for crystal orbital (CO) calculation

Table 1.2 Electronic properties of polythiophene

a

)

Table 1.3 Calculated diffusion coefficient

D

and mobility

μ

Table 1.4 Miscellaneous dopant species

Table 1.5 Electronic properties and electric conductivities of selected condu...

Table 1.6 Characteristics of Elementary Excitations in Conductive Polymers

Table 1.7 Electronic properties of donor and acceptor molecules

Chapter 3

Table 3.1. Rates of absorption of a photon to form a singlet exciton due to e...

Table 3.2 The calculated intersystem crossing rate

(

k

isc

)

from Eq. (3.49) and ...

Chapter 4

Table 4.1 Measured PLQE (Φ) and PL lifetime (τ) and calculated radiative and ...

Chapter 10

Table 10.1 The mobility calculated by the acoustic deformation potential mode...

List of Illustrations

Chapter 1

Figure 1.1 Logarithmic representation of electric conductivity

σ

(S/cm)...

Figure 1.2 Schematic drawing of 1D crystal.

Figure 1.3 Energy band of a free electron. ɛ

F

and

k

F

signify Fermi energy an...

Figure 1.4 Model potential of 1D crystal.

Figure 1.5 Examples of 1D (a), (b) and 2D (c), (d) crystals and the unit cel...

Figure 1.6 Periodic boundary condition expressed by a ring with an infinitel...

Figure 1.7 Schematic drawing of the valence and the conduction bands.

Figure 1.8 Infinite repetition of atoms A and (b) polyacetylene with the iso...

Figure 1.9 Band structures corresponding to the 1D polymers in (a) Figure 1....

Figure 1.10 Electronic properties derived from the crystal orbital (CO).

Figure 1.11 (a) Band structure and DOS with the unit cell of polythiopehene,...

Figure 1.12 Electronic properties derived from the energy band. Solid and da...

Figure 1.13 (a) Direct band gap and (b) indirect band gap.

Figure 1.14 Selected conductive polymers: (a)

trans

‐polyacetylene (PA), (b) ...

Figure 1.15 (a) A neutral soliton in polyacetylene and (b) its energy level....

Figure 1.16 (a) A positively charged soliton with the energy level, and (b) ...

Figure 1.17 (a) A positively charged polaron with the energy level, and (b) ...

Figure 1.18 (a) Polaron and (b) bipolaron in a polythiophene chain.

Figure 1.19 Energy levels of (a) a positively charged bipolaron and (b) a ne...

Figure 1.20 (a) Growth of bipolaron bands and (b) merging with other bands. ...

Figure 1.21 Selected organic donors: (a) tetracene, (b)pentacene, (c) peryle...

Figure 1.22 Selected organic acceptors: (a) tetracyanoethylene (TCNE), (b) t...

Figure 1.23 Temperature dependence of electric conductivity of TTF‐TCNQ. Ref...

Figure 1.24 Crystalline structure of TTF‐TCNQ. Source: Ref. [16].

Figure 1.25 Energy levels concerning the absorption of CT complex. D

0

and A

0

Figure 1.26 Plot of the CT absorption energy vs. Δ

E

redox

for a number of CT ...

Figure 1.27 Column array of organic CT crystals. (a) Mixed column and (b) se...

Figure 1.28 A simple example of Peierls transition in the 1D metallic chain....

Figure 1.29 Jahn‐Teller distortion in cyclobutadiene with its spin change.

Figure 1.30 Crystalline structure of (TMTSF)

2

PF

6

, where a', b', and c' are t...

Figure 1.31 Temperature dependence of electric resistance of (TMTSF)

2

X.

Sour...

Figure 1.32 Antiferromagnetic alignment of α and β spins.

Figure 1.33 Density of states (DOS) including localized levels.

Figure 1.34 Schematic representations of 1D organic amorphous solids: (a) ir...

Figure 1.35 Concept of effective mean approximation (EMA).

Figure 1.36 (a) DOS of pure (SN)

x

and (SNH)

x

. (b)DOS of random copolymer [SN

Figure 1.37 Hopping of the charge carriers between the metallic islands (dot...

Figure 1.38 (a) Spatial hopping between sites A and B, (b) hopping between t...

Figure 1.39 Concept of the 3D variable range hopping (VRH) in the sphere wit...

Figure 1.40 Interchain hopping utilizing the dopants as “stepping stones”.

Chapter 2

Figure 2.1 Experimental setup of TOF transient photocurrent measurement.

Figure 2.2 Typical time of flight transients for (a) pristine NPB, (b) NPB:t...

Figure 2.3 Electric field dependences of hole drift mobilities in N,N',N″,N″...

Figure 2.4 Plots of hole drift mobilities versus 1/T

2

at different electric ...

Figure 2.5 Photocreated free carriers are trapped in an exponential distribu...

Figure 2.6 Transport energy in a Gaussian distribution of localized states. ...

Figure 2.7 Molecular structures. (a)C6‐2TTN, (b)TTPA, (c)TFIA, (d)p‐TTA, (e)...

Figure 2.8 Comparison of calculated and experimental hole mobilities. Source...

Figure 2.9 Illustration of polycrystal (a) and band diagram along the red li...

Figure 2.10 Schematic illustration showing (top) crystallographic and (botto...

Figure 2.11 Variation of the mobility with grain size in octithiophene (a) a...

Figure 2.12 Schematic of a top‐gate/bottom‐contact C12‐BTBT FET, along with ...

Figure 2.13 Chemical structures of phenyl/alkyl‐substituted benzothieno[3,2‐...

Figure 2.14 Results of Hall measurements for a rubrene single‐crystal transi...

Figure 2.15 Packing structures and transfer integrals for (a) dinaphtho[2,3‐...

Figure 2.16 Bottom‐gate−top‐contact OFET structure and packing structure of ...

Figure 2.17 Bottom‐gate−top‐contact OFET structure of printed Ph‐BTNT‐Cn sin...

Chapter 3

Figure 3.1 Schematic diagrams of (a) one spin configuration for the singlet ...

Figure 3.2 Schematic diagram of the effect of exciton‐spin‐orbit‐photon inte...

Figure 3.3 Schematic illustration of a singlet excited state whose molecular...

Figure 3.4 Schematic illustration of thermally activated up conversion from ...

Figure 3.5 Schematic illustration of the formation of CT excitons at the D‐A...

Figure 3.6 Schematic illustration of the formation of CT excitons in a terna...

Chapter 4

Figure 4.1 Chemical structures of some organic semiconductors: (a) anthracen...

Figure 4.2 Absorption and PL spectra of anthracene in methanol.

Figure 4.3 Potential energy curves of a molecule in the electronic ground an...

Figure 4.4 Simplified energy diagram and a main decay channel of excited sta...

Figure 4.5 Absorption and PL (phosphorescence) spectra of Ir(ppy)

3

neat thin...

Figure 4.6 Simplified energy diagram of Ir(ppy)

3

near the HOMO‐LUMO gap. Whe...

Figure 4.7 Absorption and PL spectra of neat thin films of 4CzIPN.

Figure 4.8 Absorption and PL spectra of thin films of α‐ and β‐phase PFO.

Figure 4.9 (a) One‐photon absorption process between the excited state (Ex) ...

Figure 4.10 Two possible situations where a large EA signal is observed. In ...

Figure 4.11 Experimental setup for EA measurements. When the gap between two...

Figure 4.12 (Upper) Experimental setup for TPE measurements. In this example...

Figure 4.13 Absorption spectra of (solid line) vapor‐deposited neat thin fil...

Figure 4.14 (Upper) EA spectrum of DE2‐dispersed PMMA thin films obtained wi...

Figure 4.15 (Upper) EA spectrum of vapor‐deposited DE2 neat thin films obtai...

Figure 4.16 EA spectrum of Ir(ppy)

3

neat thin films. In this figure, the fit...

Figure 4.17 Absorption spectrum of Ir(ppy)

3

neat thin films, and a fit with ...

Figure 4.18 EA spectrum of thin films of α‐phase PFO measured at 100 K.. Sou...

Figure 4.19 (a) EA and (b) TPE spectra of thin films of α‐phase PFO measured...

Figure 4.20 A Jablonski diagram. In this diagram, possible decay channels of...

Figure 4.21 Operational mechanism of a streak tube.

Figure 4.22 Setup for ns time‐resolved PL measurements using a ns laser and ...

Figure 4.23 (Left) Mechanism of photon counting. (Right) Setup for time‐reso...

Figure 4.24 (Left) Experimental setup for PLQE measurements using an integra...

Figure 4.25 PL spectra of α‐phase and β‐phase PFO measured using a He‐Cd las...

Figure 4.26 PL decay curves of (left) α‐phase and (right) β‐phase PFO measur...

Figure 4.27 Fluorescence and phosphorescence spectra of α‐phase PFO measured...

Figure 4.28 PL spectra of Ir(ppy)

3

in THF at various temperatures. Source: R...

Figure 4.29 (Circles) Measured PLQE vs temperature of Ir(ppy)

3

in PMMA (0.01...

Figure 4.30 (Circles) Measured PL decay time vs temperature of Ir(ppy)

3

in d...

Figure 4.31 (Left) Energy diagram for Ir(ppy)

3

. (Right) Magnified diagram fo...

Figure 4.32 A simplified energy diagram of a TADF emitter. After photoexcita...

Figure 4.33 PL spectra of 4CzIPN‐doped m‐CP thin films measured at 6.5 K upo...

Figure 4.34 PL decay curves of 4CzIPN in three different time ranges. The pr...

Figure 4.35 Temperature dependence of PL quantum efficiencies of 5wt% 4CzIPN...

Chapter 5

Figure 5.1 Frequency dependence of normalized capacitance in a trap‐free sin...

Figure 5.2 Electric field dependence of hole mobility as a function of the s...

Figure 5.3 Frequency dependence of capacitance (C) in 2.0 wt.% Ir(ppy)

3

‐dope...

Figure 5.4 Simulated frequency‐dependent capacitance in single injection SCL...

Figure 5.5 Plot of carrier mobility in the presence of exponentially distrib...

Figure 5.6 Frequency dependences of a capacitance measured at 290 K (a) and ...

Figure 5.7 Hole drift mobilities (solid circles) and hole deep trapping life...

Figure 5.8 Frequency dependences of (a) capacitance and (b) conductance of T...

Figure 5.9 Localized‐state distributions from the valence‐band mobility edge...

Figure 5.10 Arrhenius plot of γ

t

(E) vs 1/T. The value of γ

t

(E) is equal to ω...

Figure 5.11 Localized‐state distributions from the valence‐band mobility edg...

Figure 5.12 Simulated frequency‐dependent capacitance in single injection SC...

Figure 5.13 Plot of deep trapping lifetime extracted from IS method vs that ...

Chapter 6

Figure 6.1 Illustrations for the principle of TOF measurement. (a) A schemat...

Figure 6.2 Standard setup of TOF measurement system.

Figure 6.3 (a) Schematic of distribution of an electric field in a TOF sampl...

Figure 6.4 Typical current‐mode transient photocurrent curves for holes in t...

Figure 6.5 (a) Distribution of the electric field and carrier density under ...

Figure 6.6 Schematics of current signals obtained by the TOF measurement. (a...

Figure 6.7 Dispersive transient photocurrent curves for electrons in a disor...

Figure 6.8 Information abstracted from transient photocurrent curves obtaine...

Figure 6.9 Schematic illustration of the xerographic TOF measurement using a...

Figure 6.10 Schematic of the setup of lateral TOF measurement system and ind...

Figure 6.11 Schematic illustration for the screening effect by ionic impurit...

Figure 6.12 Schematic illustrations for the measurement system of the DI‐SCL...

Chapter 7

Figure 7.1 Electromagnetic waves sorted by energy, frequency, and wavelength...

Figure 7.2 Schematic of THz time‐domain spectroscopy system using fs/ps ligh...

Figure 7.3 Schematic of flash‐photolysis time‐resolved microwave conductivit...

Figure 7.4 Illustration of flash‐photolysis TRMC systems with the options of...

Figure 7.5 Illustrations of organic/inorganic electronic materials evaluated...

Figure 7.6 (a) Δσ

max

× τ

1/2

of P3HT:PCBM blend films evaluated using TRMC ex...

Figure 7.7 (a) PCE/

V

oc

vs

. Σ

μ

for the pure polymers. (b) Correlation of...

Figure 7.8 (a) THz spectrum of TiO

2

nanoparticles. The upper and lower panel...

Figure 7.9 (a) Transient Q curve of TiO

2

nanoparticles under dark (black cir...

Figure 7.10 (a) Schematic drawing of the interplay between real (Δσ') and im...

Figure 7.11 (a) Frequency dispersion of | Δσ”/ Δσ'| observed by TRMC of (a) ...

Figure 7.12 (a) Crystal structure of CH

3

NH

3

PbI

3

perovskite. (b) AFM topograp...

Figure 7.13 TRMC decays of CH

3

NH

3

PbI

3

perovskite with and without doped HTL ...

Chapter 8

Figure 8.1 Upper panel: The temperature dependence of the trasverse Hall “in...

Figure 8.2 (b) Release factor of the trap and release model from Eq. (8.4) f...

Figure 8.3 Simulated ESR spectrum (black solid lines) of 1, 2, and 1.54 pent...

Figure 8.4 Test of SOM procedure to restore distribution of spatial extent o...

Figure 8.5 (a) Dependence of the (a) fit quality

and (b) position of low‐e...

Figure 8.6 Distribution of trap states in pentacene TFT vs spatial extent

...

Figure 8.7 (a) Experimental signal (squares), fit by spectrum in Figure 8.6 ...

Figure 8.8 Dependence of (a) binding energy

in units of bandwidth

and (b...

Figure 8.9 Charge distributions around attractive impurity with potential

...

Figure 8.10 Distribution of trap states in pentacene TFTs as a function of t...

Figure 8.11 Distributions of trap states in pentacene TFTs ((a) is spatial d...

Chapter 9

Figure 9.1 Schematic images of the transition process in the THG and the EFI...

Figure 9.2 (a) Schematic images of the optical setup of the SHG measurement....

Figure 9.3 Schematic images of the SHG setup transition process in the THG a...

Figure 9.4 (a) SHG image obtained from the channel of pentacene FET under th...

Figure 9.5 (a) Fundamental power and (b) External voltage a dependence of th...

Figure 9.6 (a) Output and (b) transfer characteristics of pentacene FET used...

Figure 9.7 Time‐resolved SHG image under (a) positive and (b) negative volta...

Figure 9.8 Time‐evolution of SHG distribution from the pentacene FET channel...

Figure 9.9 (a) Time‐evolution of the electric field at the peak position and...

Figure 9.10 (a) schematic diagram of the prefilling experiment (b) transient...

Figure 9.11 SHG intensity profile with different gate voltages from

V

g

=−10 ...

Figure 9.12 Time evolution of the SHG intensity distribution along the FET c...

Figure 9.13 (a) Polarized microscopic image of the round‐shaped Au electrode...

Figure 9.14 (a) Schematic image of carrier behavior in OLED by applying puls...

Figure 9.15 Typical examples of the transient SHG signal in charging and dis...

Chapter 10

Figure 10.1 Device structure of organic field‐effect transistors. (a) Bottom...

Figure 10.2 (a) Atomic force microscope image and (b) X‐ray diffraction of p...

Figure 10.3 (a) Herringbone‐type crystal structure of pentacene. Source: Bas...

Figure 10.4 Energy band diagram at (a) zero and (b) negative gate voltages....

Figure 10.5 Charge carrier distribution in (a) linear and (b) saturation reg...

Figure 10.6 Comparison of (a) OFETs and (b) silicon MOSFETs.

Figure 10.7 Energy distribution of the density of trap and band states.

Figure 10.8 Origins of traps in OFETs. (a) Chemical impurities. (b) Lattice ...

Figure 10.9 Schematics of five transport models. (a) Band model. (b) Multipl...

Figure 10.10 Temperature dependence of field‐effect mobility in rubrene sing...

Figure 10.11 Hall effect of rubrene single‐crystal OFETs. (a) Magnetic field...

Figure 10.12 (a) Angle‐resolved ultraviolet photoelectron spectroscopy (ARUP...

Figure 10.13 Activation‐type temperature dependence of mobility in pentacene...

Figure 10.14 (a) Density of trap states calculated in the different methods ...

Figure 10.15 (a) Motional narrowing of electron spin resonance (ESR) spectra...

Figure 10.16 Energy diagram of the hopping process, D + A

+

→ D

+

+ A,...

Figure 10.17 Calculation of hopping mobility for (a) pentacene, (b) rubrene ...

Figure 10.18 The fluctuation of transfer integrals between three different p...

Figure 10.19 (a) Schematic picture of the hole transport in pentacene crysta...

Figure 10.20 Domain structure of (a) pentacene and (b) PBTTT thin films obse...

Figure 10.21 (a) Persistent times at each trap site,

τ

intra

, and at eac...

Figure 10.22 Schematics and equivalent circuit model of the charge injection...

Figure 10.23 An example of transmission line method (TLM). Source: Ref [68] ...

Figure 10.24 (a) Image of OFET sample for four‐terminal measurements [69]. (...

Figure 10.25 (a) Transfer characteristics, (b) apparent mobility, and (c) ga...

Chapter 11

Figure 11.1 (a)–(c) Schematic illustrations of the orientation polarization ...

Figure 11.2 (a) Molecular structure of the materials used in this study. (b)...

Figure 11.3 (a) A typical DCM curve of the ITO/

‐NPD/OXD‐7/Al device at a sw...

Figure 11.4 Comparison between the KP and DCM results. Interface charge dens...

Figure 11.5 (a)The surface potential of the Al(7‐Prq)

film on ITO as a func...

Figure 11.6

–

–

characteristics of ITO/

‐NPD/Al(7‐Prq)

/Ca/Al and ITO/

‐NP...

Figure 11.7 (a) DCM curves measured at various sweep rates from 1 to 1000 V/...

Figure 11.8 (a) OLED stack layout under investigation. Strictly speaking, th...

Figure 11.9 (a) Degradation behavior of the OLED under investigation under c...

Figure 11.10 DCM (100 V/s) responses for different degradation steps. (a) an...

Figure 11.11 (a) Dots: Excited states lifetime from TRELS experiments as a f...

Chapter 12

Figure 12.1 Schematic diagram of emission mechanism in OLEDs.

Figure 12.2 Schematic illustration of TADF process.

Figure 12.3 Schematic illustration of OLED showing different optical loss ch...

Figure 12.4 Schematic illustration of OLED showing different optical loss ch...

Figure 12.5 Chemical structures of host molecules and oligofluorenes used in...

Figure 12.6 Optical constants (k and n) of (a) terfluorene, (b) pentafluoren...

Figure 12.7 PL intensity in TM mode as a function of emission angle in 15–20...

Figure 12.8 Orientation order parameter S as a function of the oligomer leng...

Chapter 13

Figure 13.1 Examples of inverter circuits consisted of (a) a p‐type transist...

Figure 13.2 Circuit diagrams with truth tables for (a) NOR and (b) NAND logi...

Figure 13.3 Circuit diagrams for (a) 1T1C and (b) 2T1C pixel elements. Sourc...

Figure 13.4 (a) An example of a pixel structure of the top‐emission OTFT‐dri...

Figure 13.5 Temperature sensor arrays and an active matrix to read their sig...

Figure 13.6 (a) Schematic of a cross‐sectional view of an example of a verti...

Figure 13.7 An example of integrated organic circuits for RFID tag applicati...

Figure 13.8 D‐flip flop circuits integrated on a plastic substrate with high...

Chapter 14

Figure 14.1 Chemical structures of benzo[

c

][1,2,5]thiadiazole (BTz) and naph...

Figure 14.2 NTz‐based D–A polymers.

Figure 14.3 (a) Chemical structures of quaterthiophene–NTz polymer with 2‐de...

Figure 14.4 (a) Schematic illustration of the solar cell with the convention...

Figure 14.5 2D GIXD images of the PNTz4T thin film (a), PBTz4T thin film (b)...

Figure 14.6 Schematic illustration of typical orientation motifs of the poly...

Figure 14.7 (a) Molecular structures of the model compound using NTz (NTz2T)...

Figure 14.8 (a) Chemical structures of naphthodithiophene–NTz polymers. (b) ...

Figure 14.9 (a)

J−V

curves of the polymer/PC

61

BM‐based cells using PNN...

Figure 14.10 2D GIXD images of the polymer‐only film for PNNT‐DT (a), PNNT‐1...

Figure 14.11 Schematic illustration of the polymer structure predicted by th...

Figure 14.12 Photovoltaic characteristics of PNTz4T‐based cells with convent...

Figure 14.13 GIXD data for PNTz4T/PC

61

BM blend films. (a) 2D GIXD image of t...

Figure 14.14 Schematic illustrations of PNTz4T/PC

61

BM blend films in the cel...

Figure 14.15 (a) Chemical structures of the polymers based on thiophene, TzT...

Figure 14.16 2D GIXD images of PTzNTz/PC

71

BM blend films (c), and DIO (1%)‐a...

Figure 14.17

J

–

V

curves of the solar cells based on PTzNTzs. (a) The active ...

Figure 14.18 Change of PCE for the cells using PTzNTz‐EHBO fabricated withou...

Chapter 15

Figure 15.1 (a) Electric field distribution of the SPP propagating mode calc...

Figure 15.2 (a) Electric field distribution of the localized SP mode around ...

Figure 15.3 Sample structure and experimental configuration of previous stud...

Figure 15.4 Schematic diagram of the enhanced light emission efficiency by t...

Figure 15.5 Generation and propagation of SPP modes from the point light sou...

Figure 15.6 The spontaneous emission rates of InGaN/GaN with/without silver ...

Figure 15.7 (a) Sample structure of dye doped polymer with both pump light a...

Figure 15.8 Energy conversion schemes of the SP enhanced LEDs and solar cell...

Figure 15.9 Possible device structures for the plasmonic LED with electric p...

Figure 15.10 Reported plasmonic organic LEDs driven by electrical pumping.

Figure 15.11 Several types of the device structures of reported photovoltaic...

Figure 15.12 Energy conversion schemes of the SP enhanced LEDs and solar cel...

Guide

Cover

Table of Contents

Title Page

Copyright

List of Contributors

Series Preface

Preface

Begin Reading

Index

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Wiley Series in Materials for Electronic and Optoelectronic Applications

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Organic Semiconductors for Optoelectronics

Edited by

Hiroyoshi Naito

Osaka Prefecture UniversityOsaka, Japan

This edition first published 2021

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Name: Naito, Hiroyoshi, editor.Title: Organic semiconductors for optoelectronics / edited by Hiroyoshi  Naito.Description: First edition. | Hoboken, NJ : Wiley, 2021. | Series: Wiley  series in materials for electronic and optoelectronic applications |  Includes bibliographical references and index.Identifiers: LCCN 2020051135 (print) | LCCN 2020051136 (ebook) | ISBN  9781119146100 (hardback) | ISBN 9781119146117 (adobe pdf) | ISBN  9781119146124 (epub)Subjects: LCSH: Organic semiconductors. | Optoelectronics.Classification: LCC QC611.8.O7 O6967 2021 (print) | LCC QC611.8.O7  (ebook) | DDC 537.6/223–dc23LC record available at https://lccn.loc.gov/2020051135LC ebook record available at https://lccn.loc.gov/2020051136

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List of Contributors

Kazuyoshi Tanaka

Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan

Jai Singh

School of Engineering and Information Technology, Charles Darwin University, Australia

Monishka Rita Narayan

School of Engineering and Information Technology, Charles Darwin University, Australia

David Ompong

School of Engineering and Information Technology, Charles Darwin University, Australia

Takashi Kobayashi

Department of Physics and Electronics, The Research Institute of Molecular Electronic Devices, Osaka Prefecture University, Sakai, Japan

Takashi Nagase

Department of Physics and Electronics, The Research Institute of Molecular Electronic Devices, Osaka Prefecture University, Sakai, Japan

Hiroyoshi Naito

Department of Physics and Electronics, The Research Institute of Molecular Electronic Devices, Osaka Prefecture University, Sakai, Japan

Kenichiro Takagi

Department of Physics and Electronics, Osaka Prefecture University, Sakai, Japan

Masahiro Funahashi

Department of Advanced Materials Science, Faculty of Engineering, Kagawa University, Takamatsu, Kagawa, Japan

Akinori Saeki

Department of Applied Chemistry, Graduate School of Engineering, Osaka University, Suita, Osaka, Japan

Andrey S. Mishchenko

RIKEN Center for emergent Matter Science (CEMS), Wako, Japan

Takaaki Manaka

Tokyo Institute of Technology, O‐okayama, Meguro‐Ku, Tokyo, Japan

Mitsumasa Iwamoto

Tokyo Institute of Technology, O‐okayama, Meguro‐ku, Tokyo, Japan

Hiroyuki Matsui

Graduate School of Organic Materials Science, Yamagata University, Yamagata, Japan

Yutaka Noguchi

Department of Electronics and Bioinformatics, Meiji University, Tokyo, Japan

Hisao Ishii

Center for Frontier Science, Chiba University, Chiba, Japan

Lars Jäger

Institute of Physics, University of Augsburg, Augsburg, Germany

Tobias D. Schmidt

Institute of Physics, University of Augsburg, Augsburg, Germany

Wolfgang Brutting

Institute of Physics, University of Augsburg, Augsburg, Germany

Li Zhao

Center for Organic Photonics and Electronics Research, Kyushu University, Fukuoka, Japan

DaeHyeon Kim

Center for Organic Photonics and Electronics Research, Kyushu University, Fukuoka, Japan

Jean‐Charles Ribierre

Center for Organic Photonics and Electronics Research, Kyushu University, Fukuoka, Japan

Takeshi Komino

Center for Organic Photonics and Electronics Research, Kyushu University, Fukuoka, Japan

Chihaya Adachi

Center for Organic Photonics and Electronics Research, Kyushu University, Fukuoka, Japan

Mayumi Uno

Osaka Research Institue of Industrial Science and Technology (ORIST), Osaka, Japan

Itaru Osaka

Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan

Kazuo Takimiya

RIKEN, Center for Emergent Matter Science, Saitama, Japan, and Graduate School of Science, Tohoku University, Sendai, Japan

Koichi Okamoto

Department of Physics and Electronics, Osaka Prefecture University, Sakai, Japan

Series Preface

Wiley Series in Materials for Electronic and Optoelectronic Applications

This book series is devoted to the rapidly developing class of materials used for electronic and optoelectronic applications. It is designed to provide much‐needed information on the fundamental scientific principles of these materials, together with how these are employed in technological applications. These books are aimed at (postgraduate) students, researchers, and technologists engaged in research, development, and the study of materials in electronics and photonics, and at industrial scientists developing new materials, devices, and circuits for the electronic, optoelectronic, and communications industries.

The development of new electronic and optoelectronic materials depends not only on materials engineering at a practical level, but also on a clear understanding of the properties of materials and the fundamental science behind these properties. It is the properties of a material that eventually determine its usefulness in an application. The series therefore also includes such titles as electrical conduction in solids, optical properties, thermal properties, and so on, all with applications and examples of materials in electronics and optoelectronics. The characterization of materials is also covered within the series as much as it is impossible to develop new materials without the proper characterization of their structure and properties. Structure–property relationships have always been fundamentally and intrinsically important to materials science and engineering.

Materials science is well known for being one of the most interdisciplinary sciences. It is the interdisciplinary aspect of materials science that has led to many exciting discoveries, new materials, and new applications. It is not unusual to find scientists with a chemical engineering background working on materials projects with applications in electronics. In selecting titles for the series, we have tried to maintain the interdisciplinary aspect of the field, and hence its excitement to researchers in this field.

Arthur Willoughby

Peter Capper

Safa Kasap

Preface

The photoconductive and semiconducting properties of organic semiconductors were reported in 1906 and 1950, respectively, and since then, basic research has steadily continued. In 1980, molecularly dispersed polymers in which hole transport molecules were dispersed in insulating polymers were commercialized as photoreceptors for electrophotography. The manufacturing process for this organic photoreceptor was a coating process, which contributed to the low cost of the photoreceptor. Organic light‐emitting diode (OLED) and organic solar cells were reported in 1987 and 1989, respectively. These devices were highly efficient at that time and showed the potential of the organic devices. OLEDs were commercialized as an automotive display in 1997, and are currently being used in high‐definition OLED TVs and OLED lighting. In the future, it is expected that organic semiconductors will be successfully applied to flexible displays, biosensors, and other devices that could not be realized with conventional inorganic semiconductors. The development of future organic devices cannot be achieved without a proper understanding of the optoelectronic properties of organic semiconductors and how these properties influence the overall device performance. Therefore, it is intended here to have one single volume that covers fundamentals through to applications, with up‐to‐date advances in the field.

This book summarizes the basic concepts and also reviews some recent developments in the study of optoelectronic properties of organic semiconductors. It covers examples and applications in the field of electronic and optoelectronic organic materials. An attempt is made to cover both experimental and theoretical developments in each field presented in this book, which consists of 15 chapters contributed by experienced and well‐known scientists on different aspects of optoelectronic properties of organic semiconducting materials. Most chapters are presented to be relatively independent with minimal cross‐referencing, but chapters with complementary contents are arranged together to facilitate the reader with cross‐referencing.

In Chapter 1 by Tanaka, the fundamental electronic properties of organic semiconducting materials are concisely reviewed and the chapter to provides basic concepts for understanding the electronic properties. In Chapter 2, Naito presents a review of electronic transport properties of organic semiconductors, and Chapter 3 by Singh et al. covers the theoretical concepts of optical properties of organic semiconductors. In Chapter 4, Kobayashi et al. have presented a comprehensive review of advanced, as well as standard experimental techniques, for the characterization of optical properties of organic semiconducting materials including fluorescent, phosphorescent and thermally assisted delayed fluorescent emitters. In Chapters 5 to 7, a comprehensive review of advanced and standard experimental techniques for the characterization of transport properties of organic semiconducting materials are presented. Naito reviews impedance spectroscopy, which is applicable to the measurement of drift mobility of thin organic semiconducting films in Chapter 5. Funahashi reviews standard time‐of‐flight measurements with different measurement configurations for drift mobility in organic liquid‐crystalline semiconductors in Chapter 6, and Saeki reviews microwave and terahertz spectroscopy, which is a unique electrodeless technique, in organic and organic‐inorganic perovskite solar cells in Chapter 7. Chapter 8, by Mishchenko, covers electron spin resonance study for the characterization of localized states. In Chapter 9, Manaka and Iwamoto present recent advances in second harmonic generation spectroscopy. In Chapters 10 to 12, reviews of device physics of key organic devices are presented. Matsui presents a comprehensive review of the device physics of organic field‐effect transistors in Chapter 10 and, in Chapter 11 by Noguchi et al., basic processes in OLEDs are reviewed. Zhao et al. discuss the relationship between out‐coupling efficiency and molecular orientation in OLEDs in Chapter 12. Uno reviews the application of organic field‐effect transistors to integrated circuits in Chapter 13 with Osaka and Takimiya reviewing high performance polymeric semiconductors for organic solar cells in Chapter 14. Finally, in Chapter 15, Okamoto covers plasmonics for the improvement of efficiencies of light‐emitting and photovoltaic devices.

The aim of the book is to present its readers with recent developments in theoretical and experimental aspects of optoelectronic properties of organic semiconductors. Accomplishments and technical challenges in device applications are also discussed. The readership of the book is expected to be graduate students, as well as teaching and research professionals.

Finally, the Editor wishes to thank Jenny Cossham and Katrina Maceda for their help and encouragement in the editing and production processes.

Osaka, Japan

Hiroyoshi Naito

1Electronic Structures of Organic Semiconductors

Kazuyoshi Tanaka

Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan

CHAPTER MENU

Introduction

Electronic Structures of Organic Crystalline Materials

Injection of Charge Carriers

Transition from the Conductive State

Electronic Structure of Organic Amorphous Solid

Conclusion

1.1 Introduction

Electric conductivities of organic materials are normally low and they are classified as insulators or semiconductors. In general, electric conductivity of the semiconductor is broadly considered to be in the range from 10−10 to 102 Scm−1 (Figure 1.1). Electric conductivity σ is expressed by

(1.1)

where n is the number of charge carriers for electric transport, e the elementary charge ( C), and μ the mobility of the carriers. Appearance of high conductivity in organic material per se is quite rare or completely absent. This is because organic materials do not have enough number of n though they might have large μ in a potential sense embodied by, e. g., extended π‐conjugation appropriate to the electric conduction throughout the material.

The above description means that organic materials can change into semiconductive or even metallic state in terms of appropriate injection of carriers if they are guaranteed to show appropriate μ values. From the latter half of the previous century, a great deal of attempts toward this direction have been piled up and nowadays organic semiconductors or organic metals have become quite common members in electronics materials such as organic field‐effect transistor (OFET), organic light‐emitting diode (OLED), organic photovoltaic (OPV) device, and so on. It is noted here that characteristic features of organic semiconductors or organic metals come from their structural low dimensionality. This is simultaneously accompanied with the fact that the direction of electric transport is remarkably developed toward one or two directions in the material and, in this sense, these are called one‐dimensional (1D) or two‐dimensional (2D) materials. For example, polymer with rather rigid spine can be regarded as 1D material and graphene a complete 2D material. These low‐dimensional materials often show peculiar behavior in relation to electronic properties when they are in the semiconductive or metallic state.

Figure 1.1 Logarithmic representation of electric conductivity σ (S/cm) of miscellaneous materials at room temperature.

Analysis of the electronic structure is of primary importance in consideration of the semiconductive or metallic properties of organic materials. In this Chapter, we are to study (i) the ways of carrier injections and (ii) transition from the conductive state inherent in low‐dimensional materials, with respect to organic semiconductors. Emphasis will also be put on understanding of the electronic properties of these materials based on their electronic structures. We first start from the electronic structures of organic materials with regular repetition of molecular unit, that is, crystalline structure, and then elucidate the electronic properties derived from the electronic structures. The prospects for typical conductive polymers and charge‐transfer organic crystals are also to be afforded. In the last part, the electronic properties of organic amorphous material will also be dealt with.

1.2 Electronic Structures of Organic Crystalline Materials

In this Section, electronic structure and its related quantities of organic materials with crystalline structures are described with respect to the 1D system not only for the sake of simplicity but also due to being realistic in most of the organic semiconductors. Note that the 1D organic crystal has regular repetition of the unit cells as illustrated in Figure 1.2 being somewhat similar to the primary structure of ideal polymers. Extension to 2D or 3D crystal is quite straightforward. In order to describe the electronic structure of organic crystal, the orbital approximation occurring from one‐electron picture is to be employed throughout this Section unless specially noted, since it allows us to have a simple but clear idea in the same spirit as the molecular orbital (MO) scheme for the ordinary organic molecules. In organic crystals, the wavefunction based on the one‐electron picture is often mentioned as crystal orbital (CO) as is described later. We will try to figure out the electronic properties of organic crystals mainly derived from the COs.

Figure 1.2 Schematic drawing of 1D crystal.

1.2.1 Free‐Electron Picture

First, we start from the simplest wavefunction of a free electron in 1D space, using the Schrödinger equation which is expressed as

(1.2)

without any potentials for a free electron. The wavefunction of a free electron at a point x is accompanied with a variable k as

(1.3)

where i stands for the imaginary unit and k is called wavevector (or wave number) being proportional to momentum p of the electron, that is,

(1.4)

with , h being the Planck's constant. As a matter of course, k becomes vector k for 2D and 3D cases. Furthermore, A and B in Eq. (1.3) are the formal normalization constants. Each of the two terms in the right‐hand side of Eq. (1.3) signifies the motion of a free electron to the x and –x directions.

The free‐electron wavefunction basically describes the electron motion in a free space without any potentials as is mentioned above and, in this sense, is considered to describe the electrons inside the space of crystal as ideal gas. Note this wavefunction takes a complex value, which is natural in the picture of quantum mechanics. The energy of a free electron is a function of k and is given by

(1.5)

which has a continuous parabolic shape with a variable k as shown in Figure 1.3. The plot of the energy value depending on k is generally called energy band or band structure. According to the number of electrons, there appears the upper limit of energy levels filled with electrons called Fermi energy (ɛF) dividing both the valence and conduction bands. The wavevector at the position of ɛF is called Fermi wavevector kF. Note that ±k gives the same energy signifying the degeneracy according to inversion of the momentum, which is also mentioned as time‐reversal symmetry due to the change of momentum direction.

Figure 1.3 Energy band of a free electron. ɛF and kF signify Fermi energy and Fermi wave vector, respectively.

1.2.2 Tight‐Binding Framework

1.2.2.1 Formalism

The next step is to introduce an infinite array of the unit cells in the concerning organic 1D crystal structure already shown in Figure 1.2. This concept simultaneously brings about the spatial regular array of potentials V(x) in Figure 1.4 into the Schrödinger equation as

(1.6)

Figure 1.4 Model potential of 1D crystal.

where

(1.7)

with a being the translation length. Several examples of unit cells in the organic 1D and 2D crystals are given in Figure 1.5.

Figure 1.5 Examples of 1D (a), (b) and 2D (c), (d) crystals and the unit cells (shown in parentheses, oval, or square). The arrows indicate the direction(s) of the translation.

In order to obtain the plausible wavefunction for general 1D crystal with infinite repetition of the unit cells shown in Figure 1.2, periodic boundary condition (or Born‐von Karman boundary condition) is introduced toward simple mathematical treatment as in the ordinary solid‐state physics. This condition is embodied by considering a huge “ring” with an infinite diameter consisting of an infinite array of the unit cells as shown in Figure 1.6. This makes the 1D free‐electron wavefunction in Eq. (1.3) change into the 1D Bloch function which satisfies the relationship

(1.8)

Figure 1.6 Periodic boundary condition expressed by a ring with an infinitely large diameter. The first unit cell (black circle) becomes overlapped with the last unit cell after the infinite translation.

where, again, k signifies the wavevector and a the translation length. The Bloch function is considered as deformation of the free‐electron wavefunction into that modulated by the array of the unit cells containing the atoms or molecules. Also note that Eq. (1.8) signifies that the translated wavefunction ψ(x + a) is represented by multiplication of the phase factor exp[ika] to the original function ψ(x). The value of k ranges from –π/a to π/a, which is called the first Brillouin zone or simply Brillouin zone.

Quantum chemical treatment of organic molecules are generally based on the linear combination of atomic orbitals (LCAO) framework, which can also be brought about into the Bloch function for organic crystal. [1] This is called CO after the conventional MO as has been already mentioned above. The CO is expressed by

(1.9)

where N formally stands for the total number of the unit cell numbered by j, χμ (x – ja) for the μ‐th atomic orbital (AO) involved in the j‐th unit cell, s the energy level of ψs(k, x), and Cμ,s(k) the coefficient. Among these variables, the coefficients Cμ,s(k) are initially unknown and their values are to be variationally determined by solving the corresponding Schrödinger equation in terms of the secular equation. Note that N is infinite in actuality, since there are an infinite number of the unit cells in Figure 1.6.

The concept employed above is often mentioned as the tight‐binding method, since the wavefunction, based on the free‐electron, is now modulated by AOs near the atomic region involved in each unit cell. In this sense, the COs still remain complex functions. It is straightforward to show that the tight‐binding wavefunction in Eq. (1.9) satisfies the relationship in the 1D Bloch function of Eq. (1.8). There are several approximation methods for the actual calculation of COs, which are basically similar to those for the conventional MO calculations. Typical calculation methods are listed in Table 1.1. A few software packages are commercially available for the CO calculations.

Table 1.1 Typical methods for crystal orbital (CO) calculation

Method of calculation

Features

Hückel

for only π electrons total energy unhandled spins unhandled

Extended Hückel

for all the valence electrons band gap unreliable total energy unhandled spins unhandled

VEH (Valence‐effective Hamiltonian)

for all the valence electrons seldom used recently employs adjustable parameters

Semiempirical Hartree‐Fock (CNDO, INDO, MINDO, MNDO, AM1, etc.)

for all the valence electrons seldom used recently employs adjustable parameters total energy less reliable band gap overestimated

Hartree‐Fock

for all the electrons total energy plausible structural optimization possible band gap overestimated

DFT (Density functional theory)

for all the electrons total energy plausible structural optimization possible band gap plausible

The procedure to obtain the CO also gives the energy level ɛs(k) of each ψs(k, x). Since ɛs(k) is obtained at each k continuously existing in the Brillouin zone in the range [–π/a, π/a] mentioned above, it constructs an energy‐band structure for each s at the same time, similar to that of a free electron in Figure 1.3. A simple image of two energy bands obtained by the tight‐binding scheme is illustrated in Figure 1.7, where two electrons are supplied per unit cell. Note that two electrons per unit cell occupy one band in total. In this case, the energetically lower part of the energy band is occupied by the electron and the upper part is unoccupied. The occupied branch is called the valence band and the unoccupied is called the conduction band.

Figure 1.7 Schematic drawing of the valence and the conduction bands.

1.2.2.2 Simple Example

In order to understand the electronic structure of the organic 1D crystal, it will be appropriate to start from an explanation of the band‐structure analysis of the simplest infinite 1D chain with iso‐distant array of lattice; the unit cell of which consists of single atom A, the translation length being a as in Figure 1.8a. This atom A can also be substituted by atomic group or so. For instance, when A is changed into a CH group, this chain can be considered as non‐bond alternant polyacetylene in Figure 1.8b. Let us examine the electronic structure of this system within the framework of the simple Hückel approximation. The secular equation in this case is expressed by

(1.10)

Figure 1.8 Infinite repetition of atoms A and (b) polyacetylene with the iso‐distant translation length. (c) and (d) represent the bond‐alternant cases.

where α denotes the Coulomb integral of the AO on A, β the resonance integral between the adjacent AOs, and a the translation length as denoted in Figure 1.8b. Note that both α and β are of negative values. The resonance integral β is also called the transfer integral t (t = −β) in solid‐state physics. The variable k signifies the wavevector in the Brillouin zone [−π/a, π/a] and the eigenvalue ɛs is the function of k.

The band structure of the 1D iso‐distant chain is then obtained as shown in Figure 1.9a from the eigenvalues ɛ1(k) and ɛ2(k) by solving Eq. (1.10)

(1.11)

Figure 1.9 Band structures corresponding to the 1D polymers in (a) Figure 1. 8(a), (b), and (b) Figure 1.8 (c), (d). Note that the translation length a in (b) is twice as long as that in (a) due to the dimerization in Figure 1.8.

It is seen that at , the highest occupied (HO) band ɛ1(k), and the lowest unoccupied (LU) band ɛ2(k) stick together to give the zero‐band gap. Hence, the 1D iso‐distant chain should have the metallic property.

Next, let us consider the case in which the above 1D chain is not iso‐distant but with alternant distance (say, 1D alternant chain) as in Figure 1.8c. In this case, two kinds of resonance integrals β and β′ exist corresponding to, e.g., A=A and A‐A, bonds, respectively (). This chain can also be considered similar to the bond‐alternant polyacetylene in Figure 1.8d. The secular equation for the 1D alternant chain is then given by

(1.12)

where the corresponding eigenvalues are obtained as

(1.13)

The band structure of the 1D alternant chain is illustrated in Figure 1.9b, where the band gap ΔEg appears with the value

(1.14)

This signifies that the 1D alternant chain should show semiconductive or insulating property depending on the value of ΔEg, which is also true for the bond‐alternant polyacetylene.

It is an interesting problem to predict which system is the more energetically stable, the 1D iso‐distant or the 1D alternant chain in the above. The answer to this question will be discussed in Section. 1.4.1.

1.2.3 Electronic Properties Based on the Electronic Structure

Several pieces of useful information on the electronic properties of organic 1D crystal can be obtained from the Bloch‐type CO ψs(k, x) and its energy level ɛs(k), the diagram of which is shown in Figure 1.10. In the following, these will be described item by item.

Figure 1.10 Electronic properties derived from the crystal orbital (CO).

1.2.3.1 Characteristics of the Energy Band

The energy‐band structure of organic crystals affords much information such as band gap, band width, ionization potential, electron affinity, and so on as seen in what follows. In particular, the highest occupied (HO) and the lowest unoccupied (LU) bands often play crucial roles not only in electronic property but also chemical reactivity. Though it is rather tiresome to examine all the energy bands of the organic 1D crystal, the analyses of the HO and the LU bands and their neighboring bands often give us sufficient information to consider the essential electronic properties.

It is of note that the classification of COs based on the symmetry such as, σ or π character, for example, reflects the corresponding energy band. The symmetry for the 1D crystal stems from the linear group in the space symmetry being a bit different from the point group to which the ordinary molecules belong. For instance, the energy‐band structure of polythiophene with infinite chain length, as an example of organic 1D crystal, is shown in Figure 1.11a. Here, crossing of σ and π bands are seen. The fact that these crossings can take place comes from the symmetry rule of the linear group, which has been discussed elsewhere. [2