CRYSTAL GROWTH and CHARGE CARRIER TRANSPORT in LIQUID CRYSTALS and OTHER NOVEL ORGANIC SEMICONDUCTORS a Dissertation Submitted T

Home , Charge carrier

CRYSTAL GROWTH AND CHARGE CARRIER TRANSPORT IN LIQUID CRYSTALS AND OTHER NOVEL ORGANIC SEMICONDUCTORS

A dissertation submitted to Kent State University

in partial fulfillment of the requirements

for the degree of Doctor of Philosophy

by Chandra Prasad Pokhrel

December, 2009

Dissertation written by Chandra Prasad Pokhrel

M.Sc, Tribhuvan University, Nepal, 1991 Ph.D, Kent State University, USA, 2009

Approved by

Dr. Brett Ellman Chair, Doctoral Dissertation Committee

Dr. Elizabeth Mann Member, Doctoral Dissertation Committee

Dr. John Portman Member, Doctoral Dissertation Committee

Dr. Robert Twieg Member, Doctoral Dissertation Committee

Dr. Deng-Ke Yang Member, Doctoral Dissertation Committee

Accepted by

Dr. Bryan Anderson Chair, Department of Physics

Dr. John R. D. Stalvey Dean, College of Arts and Science

ii Table of Contents

List of Figures vi

List of Tables xiv

Acknowledgements xv

Dedication xvii

CHAPTER 1 Organic Semiconductor 1

1.1 Electronic States of Organic Molecules 1

1.2 Basic Properties of Organic Semiconductors 13

1.3 Useful Terms 14

1.4 Charge Carrier Generation 26

1.5 Charge Carrier Transport 32

1.6 Drift Mobility 38

1.7 References 39

CHAPTER 2 Equipment, Setup and Experimental Techniques 42

2.1 A Common Method of Mobility Measurement 42

2.2 The Laser 53

2.3 The Action Spectrum 55

2.4 The Differential Scanning Calorimeter (DSC) 58

2.5 The Cryogenic System 60

2.6 Methods of Making Thin Films 60

iii 2.7 Ionic Zone Refining 63

2.8 References 66

CHAPTER 3 Crystal Growth and Mobility Measurement 67

3.1 Introduction 67

3.2 Purification of the Sample 68

3.3 Bridgman Method of Crystal Growth 74

3.4 Crystal Cutter 81

3.5 Mobility Measurement in 1,4-Diiodonaphthalene Crystal 85

3.6 References 91

CHAPTER 4 Mobility Measurements in Calamitic liquid crystals 93

4.1 Charge Transport in a Terpyridine Liquid Crystal 93

4.2 Charge Transport in Thiophenyl-bipyridinyl Liquid Crystal 107

4.3 References 115

CHAPTER 5 Charge Transport in Disordered Organic Medium 117

5.1 Introduction 117

5.2 Theory 125

5.3 Observations 133

5.4 Analysis and Results 135

5.5 References 142

iv CHAPTER 6 Effects of Mobile Ions on Charge Mobility Measurements 144

6.1 Introduction 144

6.2 Experimental 145

6.3 Observations 154

6.4 Theory 155

6.5 Results and Discussions 167

6.6 References 175

CHAPTER 7 Summary 177

v List of Figures

Figure 1.1: Atomic orbitals. (a) s-orbital (b) px orbital (c) py orbital (d) pz orbital. …..3

Figure 1.2: Electronic configuration. (a) Stable state of carbon. (b) An electron

promoted from 2s orbital to 2p orbital (c) sp3 hybridized model. ….….....4

Figure 1.3: sp hybridization of orbitals. (a) p-orbital and s-orbital (b) interaction of s

and p orbital (c) shape of hybrid orbital, unlike p-orbital, is not

symmetrical. ..……………………………………………………………..4

3 Figure 1.4: sp hybridization of carbon orbitals in CH4. ..…………………………….5

2 Figure 1.5: sp hybridization of carbon orbitals in C2H4. The hybrid orbitals are

shaded and nonhybridized pz-orbitals are not shaded.

..……………………………………………………………………………7

Figure 1.6: sp hybridization of carbon orbitals in C2H2. ..……………………………8

Figure 1.7: Conjugated system. (a) and (b) are two equally possible arrangements of

single and double bonds that makes even distribution of electron density

over entire molecular length as shown in (c)…………………………….10

Figure 1.8: Molecular orbital diagram of an unsaturated carbon-carbon bond. The

HOMO is π orbital and LUMO is π *orbital……………………………11

Figure 1.9: Delocalization of pi-electron system in benzene (top) and the energy

structure…………………………………………………………………..12

Figure 1.10: Energy level scheme of conventional semiconductor (a) intrinsic

semiconductor (b) semiconductor with donor impurity (c) semiconductor

with acceptor impurity…………………………………………………...14

vi Figure 1.11: (a) Small radius Frenkel exciton in which radius a is small in comparison

with a lattice constant aL . (b) The large-radius Wannier-Mott exciton in

which the radius a is large in comparison with a lattice constant. (c) The

intermediate or charge-transfer-exciton………………………………….16

Figure 1.12: Distribution of HOMO and LUMO levels in amorphous organic

semiconductor……………………………………………………………18

Figure 1.13: Trap states and energy transfer states energy level in an organic

semiconductor……………………………………………………………19

Figure 1.14: Energy level diagram of a photoconductor. V is valence band, T is a trap

state and C is a conduction band. Path (1) is a no trap path for electrons,

(2) is the path where electrons encounter shallow traps. (3) Is a path of

electrons encountering a deep trap……………………………………….20

Figure 1.15: (a) Transient SCL current at intense flash illumination under various

applied field. (b) Transient current at strong and weak flash-light intensity.

……………………………………………………………………………24

Figure 1.16: Space charge effect on transient current observed on C10 (pyridine-

thiophene-thiophene-pyridine derivative). Space charge effect is minimum

(red curve) at low intensity and it is prominent at higher intensity (blue

curve) at the same voltage and temperature……………………………...25

Figure 1.17: Singlet-singlet and single-triplet annihilation. S1 and T1 are first excited

* * states of singlet and triplet respectively and S 1 and T 1 are corresponding

higher excited states. The broken line represents the radiationless

transition and solid line is radiative transition…………………………...29

vii Figure 1.18: Temperature dependence of mobility using the Holstein polaron model. At

low temperature, charge transfer mechanism is tunneling and mobility

shows band like transport mechanism and at high temperature charge

transfer mechanism is hopping and mobility shows thermal activated

transport mechanism…………………………………………………..... 36

Figure 1.19: Transport mechanism in solids. (a) Band transport. In a perfect crystal, a

free carrier is delocalized, and it moves as a plane wave without scattering.

In a real crystal, there are always lattice vibrations or phonons that disrupt

the crystal symmetry causing the scattering of the electron and reduce its

mobility. (b) Hopping transport. If the lattice is irregular, the carriers

become localized on a defect site or in a potential well and then lattice

vibration is essential if the carrier is to move from one site to another….37

Figure 2.1: Illustration of principle of TOF method. ………………………………...44

Figure 2.2: (a) Ideal photocurrent trace. (b) A typical photocurrent showing the effect

of deep and shallow trap. Arrow indicates the transit time τ ………..….47

Figure 2.3: Transient photocurrent (a) A typical dispersive transport. Inset is the same

graph in log-log scale. An arrow indicates the transit time. (b) A typical

transport showing the effect of space charge. ...…………………………49

Figure 2.4: Moving charge packet. (a) Normal transport (b) Dispersive transport. ....50

Figure 2.5: Schematics of experimental setup for time of flight measurement. ……..51

Figure 2.6: Picture of optical table fitted with experimental equipment.. ...………...52

Figure 2.7: Block diagram showing the physical layout of the laser assembly. .……54

Figure 2.8: Experimental setup to produce an action spectrum……………………...56

viii Figure 2.9: Action spectrum of glassy material (C54H38N2)………………………….57

Figure 2.10: DSC experimental arrangement………………………………………….59

Figure 2.11: A typical DSC plot for a polymer sample………………………………..59

Figure 2.12: Sketch of the substrate with a hole at the center and a wiper used to make

a suspended thin film by surface wiping of material…………………….62

Figure 2.13: Ionic zone refiner………………………………………………………...65

Figure 3.1: Purification by normal freezing (a) and by zone refining (b)……………71

Figure 3.2: Picture of a zone refiner………………………………………………….73

Figure 3.3: Design of a crystal grower……………………………………………….77

Figure 3.4: Photograph of crystal growth assembly…………………………….……82

Figure 3.5: Above: Picture of beaker containing crystal in crystal growth tube. Below:

Picture of 1,4-diiodobenzene crystal grown in the lab……….. ..….……83

Figure 3.6: The crystal cutter…………………………………………………………84

Figure 3.7: A 1,4-diiodonaphthalene crystal grown in the lab by using the Bridgman

method……………………………………………………………………86

Figure 3.8: Illustration of the experiment to deposit a thin film of C60 on the surface of

1,4-diiodonaphthalene crystal by laser ablation………………………….88

Figure 3.9: A current trace as a function of time in 1,4-diiodonapthalene crystal after

C60 coated on the surface. ……………………………………………90

Figure 4.1: The molecular structure of the calamitic liquid crystal (a terpyridine

derivative). ………………………………………………………………94

Figure 4.2: A representative photocurrent transient in calamitic liquid crystal (a

terpyridine derivative) plotted on a linear /linear scale. ………………...96

ix Figure 4.3: The normalized photocurrent plotted as a function of normalized time for

traces at different voltages to check if they the universality feature……..98

Figure 4.4: Photocurrent transient in double logarithmic scale at voltages of 200, 250,

300, 350, 400 volts for sample thickness of 27 μm . The arrows indicate

the time of flight………………………………………………………....99

Figure 4.5: Time of flight signals parametric in diagonal disorder σˆ at zero off-

diagonal disorder. The signal becomes dispersive when σˆ is greater than

3.5……………………………………………………………………….102

Figure 4.6: Electric field dependence of hole mobility in terpyridine liquid crystal.

Line is a fit to the data (circle)…...………………………………...... 105

Figure 4.7: Photocurrent transient in phenylpyridine based liquid crystal………….106

Figure 4.8: Molecular structure of thiophenyl- bipyridinyl liquid crystal…………..107

Figure 4.9: Photo-generated ion traces at 90 degree celsius (SmF) at various applied

voltages…………………………………………………………………110

Figure 4.10: Photo-generated ionic mobility Vs electric field at different

temperatures…………………………………………………………….111

Figure 4.11: Viscosity as a function of temperature………………………………….113

Figure 4.12: Mobility as a function of temperature in SmF phase…………………...114

Figure 5.1: Molecular structure of 2,4,5-tris(4-(phenylethynyl)phenyl)-1-(3-

phenylpropyl)-1-H-imidazole…………………………………………..118

Figure 5.2: DSC curve of 2,4,5-tris(4-(phenylethynyl)phenyl)-1-(3-phenylpropyl)-1-

H-imidazole (above:1st cycle , below: 2nd cycle). ……………………...119

Figure 5.3: UV absorption spectrum in a sample. ………………………………….121

x Figure 5.4: The charge generation as a function of wavelength. …………………...122

Figure 5.5: A typical current trace on a linear/linear scale. The Inset is the same trace

on a log-log scale. The arrow indicates the time of flight. …………….124

Figure 5.6: Charge-dipole interaction: U (0) is the interaction-energy of charge located

G G at origin with a dipole at r and Ur()0 interaction energy of charge located G at r0 …..………………………………………………………………...128

Figure 5.7: Energy diagram of set of traps in the absence of applied field. Note that

the deep traps are wider. (b) In the presence of electric field, the energy of

the traps is reduced by eEr0 in the forward direction. Wider traps decrease

more than the shallow ones. ……………………………………………131

Figure 5.8: The solid lines are a fit of equation (5.16) to the measured field dependent

mobility represented by circles in experimental material (C54H38N2). Data for the wavelengths of 320 nm and 368 nm lie on the same lines of the corresponding temperatures….…..……………………………………..136 Figure 5.9: Logarithmic zero-field mobility as a function of the inverse-square of

temperature. ……………………………………………………………139

Figure 5.10: Logarithmic zero-field mobility as a function of inverse-temperature. ..140

Figure 6.1: Chemical structure of a HAT5 molecule……………………………….146

Figure 6.2: Above: Schematic representation of phases of the discogens (a)

homeotropically aligned columnar phase, (b) tilted columnar phase and (c)

a disordered non-columnar phase. Below: A DSC curve of HAT5

compound……………………………………………………………….147

Figure 6.3: Polarized optical microscopy texture of HAT5: (a) isotropic phase (b)

columnar phase at 850C, and (c) a crystalline phase……………………149

xi Figure 6.4: Schematics of experimental cell design………………………………...151

Figure 6.5: UV absorption spectrum of HAT5……………………………………...153

Figure 6.6: The timing diagram of photo-generation pulse (indicated by arrow) and

square wave ac voltage applied across the sample……………………..158

Figure 6.7: Schematics of the electric field (left) and ion charge sheet distribution at

t > 0 , before they cross…………………………………………………159

Figure 6.8: Traces of the hole current for delay times of 1, 1.25, 1.75, 6.86 and 11.9

ms (bottom to top) after the square wave field changes sign from negative

to positive on the top electrode. The time of flight increases as the delay

time increases (bottom to top)…………………………………………..161

Figure 6.9: Schematic snapshots of electric fields computed from simulation for

various delay times for equal speed of anions and cations. The charge

carrier TOF is then computed for each snapshot. During the carrier motion

each snapshot is considered to be frozen. Snapshot (d) represents the

situation when two ion sheets cross…………………………………….165

Figure 6.10: Experimental results of the discotic mesophase of HAT5. The x-axis is the

delay time between the potential reversal and photogeneration and the y-

axis is the hole TOF. Dots are experimental results and solid line is the fit.

Inset: Current vs time trace for delay time tms=17 …………………...168

Figure 6.11: Theoretical hole TOF as a function of normalized delay time for various

ionic charge distribution and two choices of mobility asymmetry. The

ρ+ values, in the order from bottom to top for larget , are 0.05, 0.1, 0.25,

0.5 and 1.0………………………………………………………………169

xii Figure 6.12: Theoretical hole time-of-flight as a function of normalized delay time for

fixed ion density and various ionic mobility asymmetries R . Inset: Electric

field as a function of position for t = 0.85for parameters corresponding to

the best fit to the data…………………………………………………...173

xiii List of Tables

Table 2.1: Stokes and anti-Stokes lines. ……………………………………………54

Table 4.1: Mobilityas a function of voltage at 100 degree celsius..…………………95

Table 4.2: Mobility in thiophenyl-bipyridine as a function of applied voltage at

different temperatures...... …………………………………………....109

Table 4.3: Average ion mobility and viscosity as function of temperature for

thiophenyl-bipyridinyl liquid crystal. …………………………….……112

Table 5.1: Mobility values as a function of applied voltage at different temperatures

for the experimental material (C54H38N2)………………………………133

Table 5.2: Fit parameters of equation (5.16). ……………………………………...137

Table 6.1: Mobility Vs delay time at 80 for HAT5………………………………..154

xiv Acknowledgements

I am highly grateful to my research supervisor professor Brett Ellman for his support, and guidance throughout my research. I extend my deepest thanks and great appreciation for his patience in reading my thesis draft and editing mistakes without complaints.

I would like to thank Naresh Man Shakya for his co-operation and discussions in the course of my research and as a co-worker in the lab. Thanks are also due to Dr.

Robert Twieg, Alexander Semyonov and Yulia Getmanenko for their cooperation by letting me use the equipment in the chemistry lab and providing very valuable sample materials used in my research. Thanks also to my friend Adeola Adeluyi with whom I had very useful discussions. I thank Dr. Alan Baldwin for his help in solving electronic problems. I also extend my appreciation to Josh and Wade for their help and cooperation in machine shop work. I am thankful to all the staff of the physics department, including

Greg Putman, Cindy Miller, Loretta Hauser, Chris Kurtz, and Kim Birkner. I would also like to thank my Nepalese colleagues for their comradery. I would like to express my gratitude to the Department of Physics, Kent State University for granting me a scholarship to complete my doctoral research. My gratitude also to all the professors of the physics department, who are responsible for my learning physics at a higher level.

I am grateful to the members of the dissertation committee, Dr. Elizabeth Mann,

Dr. John Portman, Dr. Robert Twieg, and Dr. Deng-Ke Yang for their valuable time and expertise to bring this work into completion.

xv I am indebted forever to my mother, brothers, and sisters for their support, inspiration, and unconditional love. I am also grateful to my brothers-in-law for their motivation and support to me. My special thanks are to my wife Namoona, and sons-

Sudhir and Binil who adhere with me over these many years in my difficulties, always offering love and support.

Chandra Prasad Pokhrel

December, 2009

xvi

Dedication

I dedicate this dissertation to my mother who shows me the path through my difficulties, gives me support and blessing at all times from a small village of Nepal where I was born.

xvii CHAPTER 1

Organic Semiconductors

1.1 Electronic States of Organic Molecules

To understand the electronic properties of organic semiconductors, it is helpful to understand the electronic structure of the carbon atom. The electronic configuration of carbon in the ground state is 1s22s22p2. It contains four electrons in its outer most

electronic level –two s electrons and two p electrons. Therefore carbon has four valence

electrons 2s2 2p2 and it must either gain four electrons or lose four electrons to reach a

rare-gas configuration. Carbon forms covalent bonds (or shares an electron pair) with a

large number of other elements, including hydrogen, nitrogen, oxygen, phosphorous, and

sulfur.

To explain the observed geometry of organic molecules, the concept of orbital

hybridization [1-3] is useful. Hybridization is a linear superposition of orbitals of the

same quantum number n but different l and m . Orbitals (atomic eigenstates) can be

m written as the product of two functions Rnl (r) , the radial part, and Yl ()θ,φ , the angular part:

1 2

m ψ nlm()()rRrY,,θφ= nl l ( θφ ,)

Orbitals with l = 0 are called s -orbitals, and orbitals with l =1 are p -orbitals, and

orbitals with l = 2 are d -orbitals and so on. For a given n , l can have values from 0 to

n −1, and for givenl , m can have (21l + ) values from −l to +l . The radial part of the

orbitals, for a given l , is the same for all(21l + ) values of m . Henceforth, the orbitals

m are often represented by an angular part Yl (θ,φ ) only. The s -orbitals depends only on

r and it’s spherically symmetric. Each p -orbital has two lobes. The expression for s - orbitals ()l = 0 and p -orbitals (l =1) [4, 5] are

1 ns== R() r) Y0 R() r no,04π n ,0

3 np==− R() r Y1 (θ,sinφθ ) R() r eiφ xn,1 18π n ,1

3 np== R() r Y−−1 (θφ,sin ) R() r θ e iφ yn,1 18π n ,1

3 np== R() r Y0 (θ,cosφθ ) R() r zn,1 14π n ,1

In order to form bonds with four hydrogen atoms, the valence-bond theory

requires that carbon atom has to have four half filled orbitals. However, a carbon atom

has only two such half filled orbitals. The px and py orbitals are half filled, while pz is

empty, as shown in Figure 1.2 (a). It seems that carbon permits formation of CH2, but not

CH4. To get rid of this problem, one electron has to be promoted from a filled 2s orbital to a 2p orbital creating four half filled orbitals -one half-filled 2s orbital and three half-

filled 2p orbitals, as shown in Figure 1.2(b). But this configuration is inconsistent with

Figure 1.1: Atomic orbitals. (a) s-orbital (b) px orbital (c) py orbital (d) pz orbital

the fact that all four C-H bond in methane are equivalent. One way to solve this problem is that when a carbon atom has to combine with other atoms, for example with hydrogen, the four atomic orbitals 2s 2px 2py 2pz mix together and rearrange to give four half-filled

bonding orbitals of equal energy, Figure 1.2(c). These new orbitals are called hybrid

orbitals. Each of the four hybrid orbitals are equivalent to each other and contain one

electron. The number of hybrid orbitals is equal to the number of atomic orbitals that take

part in hybridization. A hybrid orbital, like a p-orbital, has two lobes, but unlike a p-

orbital, one lobe is much larger than the other as shown in Figure 1.3(c). The electron

Figure 1.2: Electronic configuration. (a) Stable state of carbon (b) An electron promoted from 2s orbital to 2p orbital (c) sp3 hybridized model.

Figure 1.3: sp hybridization of orbitals. (a) p-orbital and s-orbital (b) interaction of s and p orbital (c) shape of hybrid orbital, unlike p-orbital, is not symmetrical.

spends most of its time in the larger lobe. This is why the smaller lobe is often left out in the drawings.

There are three types of hybridization in carbon.

3 sp : sp3 hybridization occurs when a s-orbital, and three p-orbitals of an atom combine,

to form four hybrid orbitals (as discussed above). Each of these hybrid orbitals will

contain one valance electron of C and overlap with the 1s orbital of H atoms. The angle

between any H-C-H is 109.5 degrees. The geometrical arrangement of these four hybrid

orbitals is tetrahedral, and they point along the four corners of a cube, say (1, 1, 1), (-1,-1,

1), (1,-1,-1), (-1, 1,-1), with the carbon atom at the center. A form for these hybrid

orbitals can be constructed by the linear combination of the 2,s 2,px 2,py and

2 pz orbitals [6]

3 Figure 1.4: sp hybridization of carbon orbitals in CH4.

1 ψ =+++22sp 2 p 2 p 1 2 ()xyz

1 ψ =−−+22sp 2 p 2 p 2 2 ()xyz

1 ψ =+−−22sp 2 p 2 p 3 2 ()xyz

1 ψ =−+−22sp 2 p 2 p 4 2 ()xyz

Each of these hybrid orbitals is normalized and they are orthogonal to each other.

2 2 sp : SP hybridization occurs when an s-orbital and two of the p-orbitals, say, px and

2 py combine. The geometrical arrangement of three sp orbitals lies in a flat plane with a

120 degree angle between them. An atom which undergoes sp2 hybridization has three hybrid orbitals and one unchanged p-orbital. The leftover p-orbital is unaffected and perpendicular to the plane containing the three hybrid orbitals. This p-orbital overlaps with another p-orbital from the neighboring atoms in a sideways manner to form the π -

2 bonds. For example, carbon atoms in C2H4 (ethene) undergo sp hybridization. These hybrid orbitals have the form

⎛⎞12 ψ =+22sp 1 ⎜⎟x ⎝⎠3 3

⎛⎞11 1 ψ 2 =−+⎜⎟22spxy 2 p ⎝⎠36 2

⎛⎞11 1 ψ 3 =−−⎜⎟22spxy 2 p ⎝⎠36 2

2 Figure 1.5: sp hybridization of carbon orbitals in C2H4. The hybrid orbitals are shaded and nonhybridized pz-orbitals are not shaded.

ψ 4 = 2 pz (unaffected) sp: sp hybridization occurs when an s-orbital and one of the p-orbital combine to give two hybrid orbitals. There is a 180 degree angle between one orbital and another. They are exactly opposite to each other from the center of the carbon atom. Because this type of hybridization uses only one p-orbital, there are still two p-orbitals left which the carbon atom can use. These p-orbitals are at right angles to each other and to the line formed by the hybrid orbital, and are available to form π-bonds. For example, carbon atoms in C2H2 (ethyne or acetylene) undergoes sp hybridization. These sp hybrids have the form

1 ψ1 =+()22spz 2

1 ψ 2 =−()22spz 2

Figure 1.6: sp hybridization of carbon orbitals in C2H2.

ψ 3 = 2 px

ψ 4 = 2 py

Bonding of molecular orbitals

There are two main types of covalent bonds involving carbon. The distinguishing feature of a sigma-bond is that it is formed by head on overlap of orbitals, and the overlap region lies directly between the two nuclei. A pi-bond is formed by a side by overlap between adjacent p-orbitals. The overlap region lies above and below the plane of the carbon atoms. Saturated organic molecules form sigma bonds only while unsaturated organic molecules have both sigma-bond and pi-bond. A double bond is formed by a combination of a sigma-bond and a pi-bond as in C2H4 whereas a triple bond is formed by combination of a sigma bond and two pi-bonds as in C2H2.

Most organic semiconductors have conjugated π -electron system formed by the

2 pz -orbitals of sp -hybridized carbon atoms in the molecules [7]. A conjugated system is formed from series of alternating double bond and single bonds. Consider, for example, an extended hydrocarbon molecule in which carbon atoms are connected by alternate single bonds and double bonds. Each carbon atom which undergoes sp2 hybridization has a half filled p-orbital. These p-orbitals are parallel to each other and combine in alternate pairs to form a system of pi-bonds as in Figure 1.7 (a). Since all p-orbitals are alike, there is an equally likely arrangement in which pi-bonds may shift their position as in Figure

1.7 (b). It can be assumed that electron density in pi-system is extended or shared evenly along the entire length of the molecule as in Figure 1.7(c). This is called delocalization

(“smearing”) of the electron wavefunction. Higher degrees of conjugation and increasing delocalization are found in compounds containing an extended CC= chain. ()n

Therefore, derivatives of such organic compounds work as “organic wires”. A classical example of pi-bond delocalization is found in benzene, a cyclic molecule.

Interacting atomic orbitals (hydridized or unhybridized) themselves mix to form molecular orbitals. Interaction of two atomic orbitals produces two molecular orbitals- one with energy higher than the original one, called the anti-bonding orbital, and another with energy lower than the original orbital, the bonding orbital. Molecular orbitals are also referred to as σ or π-bonds depending on the types of orbitals that mix (overlap). If overlapping hybrid orbitals are in phase with each other, constructive reinforcement of two waves increase the electron probability in the region between two nuclei and serves

Figure 1.7: Conjugated system. (a) and (b) are two equally possible arrangement of single and double bonds that makes even distribution of electron density over entire molecular length as shown in (c) ( Brutting [7] ).

to bind them together. A bonding orbital has lower energy than the initial hybrid orbital.

Conversely, if overlapping orbitals are out of phase they form a node between the two nuclei reducing the electron probability and give an anti-bonding orbital which is represented byσ * or π *. Generally, the energy gap between π * and π -orbitals is smaller than that between σ * andσ bonds. On interaction with a photon, an electron in a bonding σ -orbital may be excited to the anti bonding σ * -orbital. The promotion from the “bonding” to the “anti-bonding” orbitals is referred to as σ → σ * transition. The new state is an excited molecular state. Since the gap between σ -orbital and σ * -orbital is large, it requires a large amount of energy.

Figure 1.8: Molecular orbital diagram of an unsaturated carbon-carbon bond. The HOMO is π orbital and LUMO is π *orbital. (source: orgworld.de)

In another type of transition, the π → π * transition, an electron from a bonding

π -orbital is promoted to an antibonding π *-orbital. Photon excitation of an electron in a

π → π * transition requires less energy than a σ → σ * transition. Therefore π -electrons are easily excited from filled to unfilled levels [8, 9]. Such processes are very important during photogeneration of free charge, such as occurs in our time-of-flight experiments.

Because of their delocalized nature, in studying charge transport one usually focuses on the properties of π -electrons, to the exclusion of the σ -electrons.

Energy levels of semiconductors

A simple way to distinguish between a conductor, insulator and semiconductor is to plot the energy level of the system of electrons. Instead of discrete energy levels of atomic or single-molecule electrons, systems of electrons in macroscopic materials form energy bands. An energy band can be thought of as a collection of many closely spaced

Figure 1.9: Delocalization of pi-electron system in benzene (top) and the energy structure. (source: orgworld.de)

individual energy levels. In insulators, electrons are bound in a valance band and are separated from a conduction band by a large band gap (ΔEkT ) . For example diamond has a band gap of 5.5 eV>>kTroom, which is about 0.025 eV. Metals don’t have a band gap. There is no well defined distinction between insulators and semiconductors, but roughly the size of the band gap in conventional (inorganic) semiconductors is small enough to appreciably thermally populate its conduction band at room temperature. For example Si has a band gap of 1.2 eV and Ge has 0.7 eV. Excitation of atoms in these materials generates free electrons in the conduction band leaving positively charged holes in the valance band.

1.2 Basic Properties of Organic Semiconductors

Organic materials typically have bandgaps of order 0.1-1.0 eV (e.g., 0.2 eV for anthracene)[10]. However, overlap between adjacent molecules is small compared to that between atoms in inorganics, while disorder is typically large. The charge carrier is therefore typically localized (i.e., the wavefunction is exponentially suppressed at long distances). The simple band model is replaced by a hopping model to describe the motion of charge carriers. The basic properties of organic semiconductors are therefore fundamentally different from their inorganic counterparts. Organic molecular crystals are composed of discrete molecules held together by very weak non-covalent interactions

(like van der Waals forces and electrostatic forces) while the molecules themselves consist of atoms held together by strong covalent bonds. Due to the low intermolecular forces, organic molecular crystals have reduced hardness, low melting point, smaller

Figure 1.10: Energy level scheme of conventional semiconductor (a) intrinsic semiconductor (b) semiconductor with donor impurity (c) semiconductor with acceptor impurity.

dielectric constant and much weaker delocalization of electron wave functions between neighboring molecules than in inorganics. The intrinsic conductivity of most organic semiconductors is therefore very low. Organic semiconductors, unlike their inorganic counterpart, also have well-defined spin states (e.g., singlet and triplet) as in isolated molecules, which has important consequences for the photo-physics of these materials.

1.3 Useful Terms

For future reference, some of the terms frequently used while dealing with the transport properties of organic semiconductor are defined below.

Exciton: A molecular exciton may be viewed in two ways. It is a bound state of an electron and a hole in a semiconductor. A mechanism of exciton formation can be described as the follows: when photon energy is absorbed by a semiconductor molecule, it excites an electron from the valance band into the conduction band. The missing electron in the valence band leaves a hole (of the opposite electric charge) behind. The electron-hole pair is attracted to each other by the Coulomb force. This forms a bound hole-electron pair which has definite half-life, migrates through the crystal, and eventually recombines releasing energy as a photon. Another, equivalent, view is that excitons are molecular excitations. The bound electron and hole pairs (excitons) in organic semiconductor provide a means to transport energy without transporting net charge.

There are two types of excitons. If an electron-hole pair is tightly bound and located on the same molecular site, then it is Frenkel exciton. The Frenkel exciton is thus

“neutral’ and has small radius, where the radius of the exciton is defined as the average separation of the electron from its corresponding hole. The dielectric constant of organic material is often low, and so the Coulomb interaction between electron and hole become very strong and the result is a Frenkel exciton. The dielectric constant in an inorganic semiconductor is typically high so charge screening reduces the binding of electron-hole pairs and they can easily become free charges. The result is a Mott-Wannier exciton, which has a radius much larger than the lattice spacing. This is a “loosely bound” or

“ionized” exciton. In an organic system, in addition to the neutral, small radius exciton, there exists the excited state where the promoted electron is transferred to nearest or next-

nearest neighbor molecular site but still remains correlated with its parent hole.

Correlated electron-hole states that have a spatial extent of one or two lattice constants are called charge-transfer (CT) excitons [11].

aL + e +

(a) (b) (c)

Figure 1.11: (a) Small radius Frenkel exciton in which radius a is small in comparison with a lattice constant aL . (b) The large-radius Wannier-Mott exciton in which the radius a is large in comparison with a lattice constant. (c) The intermediate or charge-transfer- exciton ( Pope and Swenberg [11] ).

The motion of Frenkel excitons may be viewed as hopping from one site to another while the Mott-Wannier exciton can move through the solid like a free particle.

The exciton propagating through the molecular crystal can dissipate energy mainly by two mechanisms. The first one is exciton energy dissipated due to interaction with the phonon bath. The other way to destroy the exciton is to have energy carried away by

radiation due to recombination. Excitons may also interact with phonons and lattice distortions to form polarons (defined below).

Traps: Through the use of modern techniques of purification, it is often possible to reduce the level of chemical impurities. However, all organic crystals and liquid crystals contain chemical impurities or physical defects. Both of these may act as traps, or localized states that lower the energy of a charge carrier. For example, absorbed gas such as oxygen may act as an electron trap. Many kinds of crystal defects may act as physical traps. Carriers trapped in a physical trap may be de-trapped either optically, thermally, or by means of an electric field.

In a semiconductor which forms energy bands, each localized state below the conduction band edge, which is able to capture an electron, is an electron trap and each localized state above the valance band edge, which is able to capture a hole, is a hole trap.

If the energy from the bottom of the trap to the bottom of the conduction band is large compared to the thermal energy kT it is a deep trap, otherwise it is a shallow trap. In organic semiconductors the width of the bands can be very narrow and extended states are rarely observed (at least at room temperature). The conduction band and valance band are usually replaced by the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) respectively. Especially in amorphous organic media the density of states (DOS) is quite well represented by Gaussian-like distributions of localized molecular orbitals of individual molecules as shown in Figure 1.12.

Figure 1.12: Distribution of HOMO and LUMO levels in amorphous organic semiconductor ( Brutting [7] ).

The charge transport in such amorphous layers is mainly by hopping processes between strongly localized molecular states. Therefore, it is not obvious how to distinguish between a trap state and a regular transport state. The concept of transport energy first introduced by Monro [12] is useful to distinguish between trap and transport sites. This concept is based on the statistical rule that a carrier in a deep tail state will

most probably escape to a state of energy Et independent of its initial energy. Et is called the transport energy since it describes the level from which a trapped carrier is most probably released to move to a neighboring site. Consequently, each state below the transport energy is a trap while states above the transport energy are regular transport states (note that all states are still localized, i.e., not itinerant). However, the transport

energy is a function of temperature. A state acting as a trap state at room temperature may become a transport state at higher temperature.

Figure 1.13: Trap states and charge transport states energy level in an organic semiconductor (Brutting [7] ).

The presence of the trap alters the mechanism of the charge transport. A deep trap may permanently capture the charge whereas the presence of a shallow trap will increase the time of flight of the charge carrier. A charge carrier trapped in the shallow trap may eventually come out due to thermal activation energy and hop to the next transport site.

The process of multiple trapping/de-trapping continues until the charge carrier reaches to the opposite electrode thereby increasing the total time of flight.

An energy level diagram of a typical organic photoconductor with bands is shown in Figure 1.14. Absorption of light of quanta hν generates an electron-hole pair. If there

Figure 1.14: Energy level diagram of a photoconductor. V is valence band, T is a trap state and C is a conduction band. Path (1) is a no trap path for electrons, (2) is the path where electrons encounter shallow traps. (3) is a path of electrons encountering a deep trap ( Gutmann and Lyons [13] ).

were no traps, the electron would move through the conduction band along the line (1), corresponding to a certain mean free path, until it drops back to the valance band and recombines. The existence of the shallow traps would cause the electrons to spend an appreciable portion of its lifetime within the traps and greatly reduces the mean free path by facilitating its recombination as shown in path (2). Some electrons, however, are caught in deep traps, and are no longer free as shown in path (3).

Origin of traps:

1. Impurities: An impurity molecule in general has different energy levels than the host molecules. In particular, impurity molecules have different ionization energies and electron affinities than the host molecule and this difference forms the basis for a trap. If the ionization energy of the impurity molecule is lower (higher) than the host molecule

then it works as a hole (electron) trap. It is also possible that a chemical impurity is energetically inert as a carrier trap if its ionization energy is greater and electron affinity is less than that of the host. An example of this is molecular anthracene dissolved in crystalline tetracene. Although the impurity does not act as carrier trapping center, it does induce lattice deformation. The presence of such impurities decreases the host molecule density and hence reduces the polarization energy. The impurity site now act as a scattering center to the mobile carrier.

2. Lattice defects: A lattice defect is caused when some of the lattice atoms leave their lattice site and squeeze into positions (interstitial sites) which are not lattice points.

This type of defect is called a Frenkel defect. Lattice defects may also be caused due to an excess or shortage of constituent atoms. For example, in a AgCl crystal, excess Ag atoms may occupy interstitial sites, or some of the Ag atoms may be missing from lattice sites. If a lattice atom is missing then this is called a Schottky defect. Interstitial organic molecules are unlikely in organic crystals because these molecules often have large asymmetric shapes, and thus the most probable defect is a Schottky defect. Even if there are only molecules of the same species, both types of defects change the electronic polarization of the surrounding lattice. The exact energy position of the HOMO/LUMO not only depends on the chemical structure of the molecule itself but also on the electronic polarization of it’s surrounding. A lattice vacancy behaves like a free surface in the sense that a carrier situated next to the vacancy experiences decrease in polarization energy. For this reason, a vacancy tends to act like an antitrap, i.e., it will scatter the carrier without trapping it. This is quite different from the role of vacancies in ionic

crystals, where a vacancy has a net effective charge and tends to trap a carrier of opposite sign. Similarly, presence of atom in interstitial site behaves like a trap in the sense that a carrier situated next to it experiences a increase in polarization energy.

Quantum efficiency: Quantum efficiency of charge-carrier generation is defined as the ratio of the average rate of charge-carrier formation to that of exciton production [14].

Action Spectrum: Simply the photocurrent curve plotted as a function of wavelength or frequency. This shows which wavelength generates most charge.

Polaron: Polarons are formed due to a charge carrier-lattice interaction. An excess charge carrier residing on an organic molecule usually creates a lattice deformation. Such a carrier plus its accompanying polarization field is a quasi-particle called a polaron.

While moving through the crystal, the charge carries the lattice distortion with it. The polarization field resulting from the lattice deformation lowers the energy of the charge carrier, acting as a potential well that hinders the movements of the charge, thus decreasing its mobility.

The polaron motion may be either hopping or tunneling. If the motion is hopping, it has to pass a barrier of height equal to the polaron binding energy in order to move to a neighboring site. The transition of a polaron from a site to a new site results in the destruction of the charge cloud at the old site and the creation of a cloud at the new site.

There is, therefore, a large number of phonon emissions and absorptions accompanying the transition.

Space charge: Space charge effects arise from the presence of large amounts of charge due to injection from the electrode or copious photogeneration. Space charge usually

occurs in dielectric media because in a conductive medium the charge tends to be rapidly neutralized or screened.

In time-of-flight measurements, such as those presented here, deep traps may capture a fraction of the charge in transit. As the accumulation of charge in the traps grows, it distorts the internal electric field. Therefore, the temporal behavior and magnitude of the transient current gets distorted after few passages of charge packets.

This effect is severe as the trapped charge approaches the magnitude of charge in the electrode, CV (which is the basis for a simple check for space charge effects). This problem can be minimized by keeping the magnitude of the charge in transit as small as possible by, e.g., using weak photogenerating light pulses, or by discharging the sample after every reading via the application of a number of excitation pulses at zero applied field. (This technique has proven essential in work on crystals at low temperature.)

Another cause of sample polarization may be the injection of dark-current (current in the absence of the light irradiation) from the electrode in the interval between the application of the field and photoexcitation. In this case, sample polarization can be minimized either by shortening the time interval for which field is applied (pulsed fields) or by using a blocking electrode (this will be discussed below in detail).

Space charge effect is also produced due to the injection of photogenerated charges from the electrodes. An intense flash of radiation not only generates charge carriers in the material but may also generate a large carrier reservoir in the illuminated electrode. Figure 1.15, the work of A. Many et.al, [15], shows the effect of space charge on the transient current in a single crystal of iodine. Initially, (Figure 1.15 (a)), current

(a) (b)

Figure 1.15: (a) Transient SCL current at intense flash illumination under various applied field. (b) Transient current at strong and weak flash-light intensity (Many et.al. [15] ).

rises to a level corresponding to the value given by the charge generation in the material.

This level increases as the voltage increases. Due to space-charge effects only a small

fraction of the charge from the reservoir is allowed to be injected (i.e., the field of the

injected charge prevents further like-sign carriers from entering). As more and more

charges are being injected the initial level gradually increases until the first front of the

carriers reaches the opposite electrode. Then, current gradually decays. The space-charge

effect is more distorting with increasing applied voltage, provided that the reservoir is

large. Light of low intensity can not produce the charge reservoir at the illuminated

electrode and the photocurrent approaches the value corresponding to space-charge free

flow. This effect is shown in Figure 1.15 (b).

Figure 1.16: Space charge effect on transient current observed on C10 (pyridine- thiophene-thiophene-pyridine derivative). Space charge effect is minimum (red curve) at low intensity and it is prominent at higher intensity (blue curve) at the same voltage and temperature.

We frequently observe space charge during our experiments. The space-charge effect observed in C10 is shown in Figure 1.16. Both the curves are for same voltage and temperature but at different light intensity (and therefore charge density). The source of the space charge, however, is not known. From an experimental perspective, space charge, by accelerating the leading edge of a charge packet, leads to artificially high charge velocities and therefore to overly large mobilities. It is therefore of serious concern.

1.4 Charge Carrier Generation

The main mechanisms of charge generation by light in molecular crystal are via the exciton mechanism, injection from electrode, and direct electron-hole pair production

[16]. These mechanisms are discussed below.

Via excitons- In organic semiconductors both photogeneration and radiative recombination of charge carriers may proceed via excitons. Charge carrier generation via excitons involves a number of mechanisms. The most widely held view is that an exciton may interact with a similar exciton, an impurity, a defect or an interface. In each case the result of the interaction is the dissociation of the exciton into a hole and an electron. a) Exciton-surface interaction: Excitons can produce charge carriers by a variety of quenching processes available at the surface. These processes may involve reactions involving defects, impurities and electrodes. For many crystals, the diffusion length of the exciton is too small and photoabsorption coefficient is too large for any exciton to

reach the surface. As a result of exciton annihilation at the surface, a photocurrent is produced that is linear with light intensity.

Sh01+→ν S (1.1)

+− SM1 +→+(surface) he (1.2)

where M is some impurity site, S0 is ground state of the molecule and S1 is the excited singlet state . It is also possible that an impurity site simply quenches (recombines) the exciton without producing any charge. This process requires the transfer of excitation energy to an impurity site.

∗ SM10+→+ SM (1.3)

Excitons can also dissociate at metal electrodes, resulting in carrier injection. At the interface between an organic crystal and a metal contact a ππ ∗ singlet exciton dissociates to yield a free hole within a crystal which can be detected by photocurrent measurements.

The essential process is the transfer of an excited electron through a surface barrier to empty metal states above the Fermi level. b) Exciton-charge interaction: Charges can exist in a free state as current carriers or in a trapped state, where they contribute to the bulk space charge. Excitons can react with trapped charges yielding free carriers and a ground state crystal. Study of charge-exciton interaction in crystalline anthracene was been done by Wakamaya and Williams [17] where injected charges in crystalline anthracene filled up the traps in the crystal. These trapped charges interacted with photons directly or with excitons yielding free carriers

[16]. Excitons are also known to react with free carriers which results in the fluorescence

(radiative) quenching of the exciton and a free charge. c) Exciton-exciton interaction: When two singlet excitons come closer than a critical

radius rc of each other transfer of energy of one singlet exciton to the other becomes highly probable [9]. The final state is a highly excited exciton that possesses sufficient energy to ionize, giving an electron and hole. In the case of anthracene, the singlet exciton has an energy of 3.15 eV, so an exciton-exciton collision produces a state of

6.3eV. This energy is not only greater than the band gap for internal ionization (3.9 eV), but is greater than the ionization energy of the crystal (5.8 eV). The highly excited state either decays to the ground state giving off light, or ionizes to give charge. This process may be written as

∗ SS11+→ Sn ()6.3 eVS + 0 (1.4)

∗ SeVSShn ()6.3 →→+10ν (1.5) or it can ionize

∗−+ SeVehn ()6.3 →+ (1.6)

∗ where S0 represents the ground state and S1 represents the first excited singlet state, Sn represents the higher excited (n ≥ 2) singlet state. Thus in singlet-singlet annihilation one molecule goes to the ground state and the other molecule goes to the higher-excited singlet state which later decays into electron-hole pairs. If the annihilation is singlet- triplet, one molecule goes to the ground state and the other molecule goes to a higher- excited triplet state which decays into the ground state with emission of a photon. This is

Figure 1.17: Singlet-singlet and single-triplet annihilation. S1 and T1 are first excited * * states of singlet and triplet respectively and S 1 and T 1 are corresponding higher excited states. The broken line represents the radiation less transition and solid line is radiative transition ( Pope and Swenberg [9] ).

a bimolecular process. Choi and Rice [18] have given the theoretical basis of charge generation by exciton-exciton interaction.

The region of exciton formation is close to the surface because light is absorbed within a small distance in the experiments. Therefore, for observation of bulk-generated carriers by singlet exciton fusion in organic crystals, it is essential that the surface of the crystal be rigorously clean and free of oxygen. If the surface of the crystal is contaminated, then exciton dissociation at an impurity or defect will dominate the carrier generation exciton-exciton interaction.

Direct production of electron-hole pair: A ground state molecule can be excited by choosing the appropriate frequency and polarization for the incident light. An important characteristic feature of producing charge by this process is that it is a direct process, which proceeds without interaction with impurities, charges or excitons. The excited molecule relaxes by auto-ionization. This can be a single-photon process or multi-photon process. If the light is strongly absorbed (high absorption coefficient) a ground state molecule absorbs a single photon (6.3 eV for anthracene) to go to a higher-excited state and then auto-ionizes to give charge pair. Two photon absorption is also possible when the light is intense:

∗+− Sh0 +→→+ν Sn he (Single-photon process) (1.7)

∗−+ Sh012++νν h →→+ Sn eh (Double-photon process) (1.8)

In this process a ground state molecule absorbs two photons and undergoes a transition to a higher-excited singlet state. This state can subsequently either relax to the ground state with emission of photon or it can auto-ionize. These processes are known as intrinsic generation processes [19] .

The observable photocurrents, neglecting diffusion, are related to the concentration of the carriers by

j+++= neμ E (1.17)

j−−−= neμ E (1.18)

where μ± are the effective carrier motilities for the positive and negative charge carriers,

E is the local electric field, and e is the electronic charge. The total current is the sum of

j+ and j− , but with a sandwich-cell sample arrangement where the excitation light is strongly absorbed and one sign of potential is applied, only carriers of one sign migrate through the crystal bulk. In practice this is accomplished by irradiating either the positive electrode (leading to hole current) or the negative electrode (leading to electron current).

Here, one has to bear in mind that in contrast to metals there is not usually a linear relationship between j and E since both carrier density (photo generation efficiency) and mobility can depend on the applied field.

The distinction between single-photon intrinsic carrier generation (i.e direct- ionization, equation (1.5) and the extrinsic mechanism, (equation 1.2) is given in several papers [9, 14, 20, 21]. The extrinsic generation, which is generally caused by the reaction of singlet excitons at the crystal surface, may be distinguished from single-photon intrinsic generation as follows:

1. The action spectrum of extrinsic generation resembles the absorption spectrum of

the crystal whereas the action spectrum of single-photon generation does not.

2. The photocurrent in extrinsic generation depends on the nature of the electrode

and crystal surface, whereas in intrinsic single-photon it does not.

3. The photocurrent in extrinsic generation decreases if fluorescence quenchers are

introduced between the electrode and crystal, whereas intrinsic generation of

photocurrent is independent of the quenchers.

Photoinjection from electrode- There also exists the possibility for electron or hole injection from an optically excited electrode into a crystal. This process of charge generation was reported by Takai [22] who used optically excited gold electrodes (Au) to

inject charge into the polymer poly(2-chloro-p-xylyene). They observed the photocurrent as a function of the wavelength of incident light. A large photocurrent was observed in the wavelength range over which the absorption coefficient of the polymer was negligibly small. This photocurrent was considered to be induced by injection from the electrodes, not by the excitonic process. Enhanced charge injection into the photoactive layer was reported by Yilmaz at el [23] by using hybrid organic-inorganic electrode.

1.5 Charge Carrier Transport

There are two main pictures of carrier transport in solids: the band model and the hopping model. In a band model, the carrier moves in a broad band as a highly delocalized plane wave. The scattering of the charge carrier is very small so it has a relatively large mean free path. An example of such motion is the motion of holes in Ge, where the valance bandwidth is 3eV, the scattering time is 10-3 s, and the mean free path

0 at room temperature is 1000 A , a value pretty large compared to lattice constant of 2.45

0 A [9]. The band theory describes the charge carrier transport well in highly conductive metals, semiconductors and insulating crystals such as diamond.

In a hopping model, the carrier is highly localized and moves by hopping from site to site. If two molecules are separated by a potential barrier, a carrier on one can move to another by moving over the barrier via an activated state. The activation energy may be supplied by either thermal or electrical sources. This mechanism is often important when an intermolecular potential barrier is too thick for tunneling [24].

The band model is valid when mobility and the mean free path are sufficiently large. For the very low mobilities found in most organic semiconductors, the mean free path is smaller than the lattice spacing. Scattering then removes the possibility of using the band theory. For example, the band width in anthracene is about 0.6 eV [10, 25]. The narrowness of the band width favors the model of a localized charge carrier rather than a delocalized one in a band. The mean free path of the electron in polyacene-type crystals

0 calculated, by Katz et al. and Silby is 3-4 A [10], which is smaller than the lattice parameter. These results say that charge carriers are scattered at every site of a lattice.

They are really strongly localized. Such localization excludes the applicability of traditional band scheme and favors the hopping model.

The band and hopping motion is also distinguished by the magnitude and temperature dependence of the mobility. In wide bands the mobility μ >1cm2 Vs and temperature dependence goes as μ ∝ Tn−n ,> 1(for anthracene n =1.7 ) [9, 20]. As the temperature increases, the scattering cross-section presented to the electron by phonons increases so that mobility decreases. If the carrier is strongly localized, μ <<1 and

μ ∝−exp(E /kT ) , where E is activation energy (this is only a rough description – details are found below). Roughly speaking, the high value of mobility and decreasing mobility with rising temperature indicates that carriers are free and limited in their path by lattice collisions. A low value of mobility, less than1cm2 Vs , and increasing mobility with temperature indicates the localization of the charge carriers and activated mode of charge transfer across potential barriers.

In the absence of chemical or physical defects, the nature of the charge transport depends on both electronic interaction and on the electronic-phonon interaction. In covalent bonded semiconductors, the electron-phonon interaction is much smaller compared to the electronic interaction and simply scatters the delocalized carrier. In organic molecular crystals, where molecules are bonded by Van der Walls and other comparatively weak forces, the electron-phonon interaction is typically larger than the electronic interaction.

The electron-phonon system then forms a polaron. Several theories have been reported to describe the charge carrier transport mechanism by polarons in organic crystal. One of the first, and still a very useful model is the Holstein polaron. In this case, transport sites are modeled as an ordered 1-dimensional array of deformable molecules and charge carriers as small (molecule size) polarons. Polarons may form either bands or may hop.

The total mobility of the carriers is the sum of contributions from the two modes of charge transfer,

μ =+μμtun hop (1.19)

The first term is due to the contribution from tunneling and second term is from hopping.

The relative contribution of each term depends on the strength of electron-phonon coupling ()g . An illustrative example of the temperature dependence of the mobility over various coupling strength is given in reference [26]. At weak electron-phonon coupling()g 2 1 , the mobility is dominated by tunneling and shows the band like temperature dependence (μ ∼ T −n where n >0) . For strong coupling()g 2 1 , there are three distinct temperature regimes. At low temperature, the mobility is band-like. As the

temperature increases, the hopping term starts to dominate and mobility shows temperature activated transport behavior. At very high temperature, the polaron dissociates and the carriers get scattered by thermal phonon, and the mobility decreases with temperature. Further study of the phonon-assisted hopping using Holstein model

[27] can be found in [28] and in [29].

Other popular classes of models are based on extensive disorder, and are commonly applied charge transport models in non-crystalline organic solids such as those we have studied. The motivation here comes from the “dispersive,” or broadened current transients observed in some inorganic and organic systems. The pure polaron model outlined above has every carrier moving at the same average speed, resulting in non- dispersive transport. However, the Holstein pure polaron model is less applicable in disordered systems because the magnitudes of the polaron binding energy and/or the variation in transfer integral in disordered system can be larger than the band widths for ordered organic crystals [30, 31].

Disorder models were used to study transport properties by several authors such as Scher & Montroll [32], and Bassler [33]. The origin of the disorder is believed to be the variation in the site energies (diagonal disorder) and variation in the relative position of the transport sites and transfer integrals (off-diagonal disorder). These transport models are expected to be operative in organic materials which present an amorphous character such as molecularly doped polymer, glasses, and possibly some liquid crystals.

The often quoted charge transport model for these materials is the Gaussian Disorder

Figure 1.18: Temperature dependence of mobility using the Holstein polaron model. At low temperature, charge transfer mechanism is tunneling and mobility shows band like transport mechanism and at high temperature charge transfer mechanism is hopping and mobility shows thermal activated transport mechanism ( Coropceanu et al. [26] ).

Figure 1.19: Transport mechanism in solids. (a) Band transport. In a perfect crystal, a free carrier is delocalized, and it moves as a plane wave without scattering. In a real crystal, there are always lattice vibrations or phonons that disrupt the crystal symmetry causing the scattering of the electron and reduce its mobility. (b) Hopping transport. If the lattice is irregular, the carriers become localized on a defect site or in a potential well and then lattice vibration is essential if the carrier is to move from one site to another ( Pope and Swenberg [9] ).

Model (GMD) as formulated by Bassler. In this model, the electron wave function is assumed to be localized on one molecule, and hopping occurs to neighboring molecules which have their energies distributed independently and within Gaussian density of states. One expression for mobility, obtained by simulation, is [34]

μμ=−exp⎡⎤⎡⎤ 2 σ / 3kT22 exp CE12 σ kT −∑ 2 0 ⎣⎦⎣⎦(){ () }

where μ0 is the mobility extrapolated to zero electric field, σ is the Gaussian width which gives measure of energetic disorder, and ∑ is a measure of positional disorder. We will discuss these and other models in detail below.

1.6 Drift Mobility

Drift mobility is an intrinsic property of organic material to characterize it in terms of its conductivity of charge. It is defined as the net distance moved in the field direction by a carrier in unit time in a unit electric field.

μ = vE (1.20) where μ is mobility, v is velocity of the charge carrier, and E is applied electric field.

1.7 References

[1] D. Nasipuri, Stereochemistry of Organic Compounds (John willey & Sons, 1991).

[2] F. A. Carey, Organic Chemistry (The McGraw-Hill Companies Inc., 1996).

[3] R. T. Morrison, and R. N. Boyd, Organic Chemistry (New York University,

1983).

[4] C. Cohen-Tannnoudi, B. Diu, and F.Laloe, Quantum Mechanics (Wiley-

Interscience Publication, 1991), Vol. I.

[5] G. Aruldhas, Quantum Mechanics (Prentice-Hall of India, 2002).

[6] B. K. Agarwal, and H. Prakash, Quantum Mechanica (Prentice-Hall of India,

2002).

[7] W. Brutting, Physics of Organic Semiconductors (Wiley-VCH Verlag GmbH &

Co. KGaA, 2005).

[8] R. V. Hoffman, Organic Chemistry (Wiley-Interscience, 2004).

[9] M. Pope, and C. E. Swenberg, Electronic Processes in Organic Crystals (Oxford

University Press, 1982), p. 70.

[10] E. A. Silinsh, and V. Capek, Organic Molecular Crystal: Interaction,

Localization, and Transport Phenimena (AIP, 1994).

[11] M. Pope, and C. E. Swenberg, Electronic Processes in Organic Crystals (Oxford

University Press, 1982).

[12] D. Monro, Phys. Rev. Lett. 54, 146 (1985).

[13] F. Gutmann, and L. E. Lyons, Organic Semiconductor Part A (Robert E. Krieger,

1981).

[14] R. F. Chaiken, and D. R. Kearns, J. Chem. Phys 45, 3966 (1966).

[15] A. Many, S. Z. Weisz, and M. Simhony, Phys. Rev. 126, 1989 (1962).

[16] J. Mort, and D. M. Pai, Photoconductivity and Related Phenomena (Elsevier

Scientific, 1976).

[17] N. Wakayama, and D. F. Williams, J. Chem. Phys 57, 1770 (1972).

[18] S. Choi, and S. A. Rice, J. Chem. Phys 38, 366 (1963).

[19] R. F. Chaiken, and D. R. Kearns, J. Chem. Phys 45, 3966 (1966).

[20] F. Gutmann, H. Keyzer, and L. E. Lyons, Organic Semiconductor Part B (Robert

E. Krieger Publishing Co., 1983).

[21] G. Castro, and J. F. Horing, J. Chem. Phys 42, 1459 (1965).

[22] Y. Takai, J. Phys. D: Appl. Phys. 11, L139 (1978).

[23] O. F. Yilmaz, S. Chaudhary, and M. Ozkan, Nanotechnology 17, 3662 (2006).

[24] R. M. Glaeser, and R. S. Berry, J. Chem. Phys 44, 3797 (1966).

[25] Y. C. Cheng, and R. J. Silby, J. Chem. Phys 118, 3764 (2003).

[26] V. Coropceanu, J. Cornil, and et.al., Chem. Rev. 107, 926 (2007).

[27] T. Holstein, Ann. Phys. 8, 325 (1959).

[28] D. Emin, Adv. Phys. 24, 305 (1975).

[29] R. Silby, and R. W. Munn, J. Chem. Phys 72, 2763 (1980).

[30] I. I. Fishchuk, A. Kadashchuk, and et. al, Phys. Rev. B 67, 224303 (2003).

[31] P. E. Perris, V. M. Kenkre, and D. H. Dunlap, Phys. Rev. Lett. 87, 126601 (2001).

[32] H. Scher, and E. W. Montroll, Phys. Rev. B 12, 2455 (1975).

[33] H. Bassler, Phys. Stat. Sol. (b) 175, 15 (1993).

[34] L. B. Schein, and A. Tyutnev, J. Phys. Chem. C 112, 7295 (2008).

CHAPTER 2

Equipment, Setup and Experimental Techniques

2.1 A Common Method of Mobility Measurement

The electrical properties of organic semiconductors can be analyzed by measuring the motion of charge carriers flowing through them. To measure the mobility we use the time-of-flight (TOF) method in which we measure the transit-time of a charge sheet produced by a light of suitable wavelength incident on the material under influence of external field. The general principle of this technique is shown in Figure 2.1. The material is sandwiched between two electrodes. Electrodes are glass plates coated with, e.g., indium tin oxide (ITO) or nm-thick Al, and are semitransparent to transmit the photogenerating light (only one plate actually needs to be transparent). The top electrode is connected to a voltage source (Stanford DS345/PS325) and the bottom electrode is connected to an oscilloscope (LeCroy LT364L) through a transimpedance (current to voltage) amplifier. The sample sandwiched between electrodes is mounted on a hot stage

(Instec HCS402/HCS202) whose temperature is controlled by a temperature controller

(LakeShore331). The top electrode is either raised to a positive or negative voltage depending on whether we want to study the mobility of holes or electrons, respectively.

42 43

When a light of suitable wavelength hits the sample (thickness L ) it is absorbed in a very

small thickness of materialδ x producing pairs of electrons and holes. If the top electrode

is given a positive voltage, electrons will collide quickly with the top electrode whereas

holes will drift towards the bottom electrode taking a finite time. The time taken by the

charge carriers to go across the sample to reach the bottom electrode is called the transit

time and denoted byτ .

The duration of time te that the light pulse hits the sample should be very small

compared to the transit time, (i.e te 〈〈τ ). te is about 10 ns in our case. Before the light

pulse, the charge density on each electrode is the same in magnitude (say σ 0 ) and

opposite in sign. The electric field inside the material is uniform and is given by VLo

where V0 is the applied voltage. After the light pulse, the amount of charge on the top

electrode is no longer equal to the bottom electrode and the electric field inside the

material is not uniform. Let σ1 be the density of charge on the top electrode and σ 2 be

the density of charge on the bottom electrode. The electric field between the charge sheet

and the top electrode is

σ E = 1 (2.1) 1 ε

Similarly electric field between the charge sheet and bottom electrode is

σ E =− 2 (2.2) 2 ε

Let x be the distance of the charge sheet from the top electrode at time t . Then

VxELxE01=+−() 2 (2.3)

Figure 2.1: Illustration of principle of TOF method

σ σ VxLx=+12() − 0 εε

Since the total charge is constantσ12+σσ=− and σ12= σσ+ (in magnitude)

()σ +σσ VxLx=+−22() 0 εε

1 σ =−()εσVx 20L

i i σ x σ = 2 L

i i where x is the drift velocity of the charge sheet. Since x = μEeff , we can write

i σμE σ = eff 2 L

where μ is the mobility and Eeff is the effective electric field. If E0 is the electric field in the absence of the charge sheet, the effective electric field is approximately

()/2/EE12+== EVL 00 and the current is

i σμV σ = 0 (2.4) 2 L2

Since this current lasts only for a finite time we can write above equation (2.4) in terms of step function of time as

i σμV σθ=−0 ()tt 20L2

This is the expression for the current pulse generated due to the drift motion of the charge sheet. An ideal trace of current is shown in Figure 2.2a. This is a well defined square pulse of current, which is characteristic of a narrow sheet of charge going across the

sample at constant mean velocity. The real trace may be different from the ideal trace because of various effects discussed below. The transit time τ is given by the time corresponding to the knee of the trace. This is indicated by an arrow in Figure 2.2b. By knowing the transit time, the mobility can be calculated from the equation

L2 μ = V0τ

The TOF method provides information on trapping and the underlying transport mechanism in addition to accurate mobility measurements. For example, deviations from the ideal current shape are expected if carriers in transit are trapped. Figure 2.2b is a typical trace of photocurrent in the presence of trapping. It has an initial short spike, a plateau, and a long tail. This is a typical photocurrent shape when there is multiple trapping and de-trapping. The initial spike may be due to surface trapping of the charge or the contribution to the current of the opposite sign charge carriers moving towards the nearest electrode. If the carries are deep-trapped before they transverse the sample the number of free carriers (and thus the current) will decrease exponentially. The slight rounding of the signal around τ is due to dispersion in carrier arrival times. The reason is that the width of the charge sheet can broaden during its transit due to statistical variation of the drift velocity or space charge effects causing mutual repulsion of the carriers within the generation volume. The long tail is due to the traps whose lifetime is comparable to the transit time. Such traps are called shallow traps. During the transit, charge carriers get trapped and de-trapped in the shallow traps and ultimately reach the

Figure 2.2: (a) Ideal photocurrent trace. (b) A typical photocurrent showing the effect of deep and shallow trap. Arrow indicates the transit time τ .

other electrode. A large density of shallow traps cause two noticeable effects [1]. One is that they increase the measured time-of-flight, while the second is that the slope of the curve during the recovery time (i.e. t >τ ) decreases. If there is a single set of shallow discrete traps, the Gaussian character of the drift is not disturbed because the equilibrium that is set up between the trap and charge transfer state is fast enough so that the net effect is merely a decrease in the mobility (multiple-trapping transport) [2]. When there are different sets of such traps with distinct activation energies, the velocity of the carriers gets much more dispersed, which results in a curve with a long tail and a broad

“knee,” making the extraction of the transit time somewhat ambiguous. Such transport is called non-Gaussian or dispersive [3] and is shown in Figure 2.3a. In this situation the current signal can be plotted on a log-log scale for analysis. Then the current may form two a nearly straight lines of different negative slopes. The intersection of the tangents to these lines clearly defines the transit time as indicated by arrow in the graph shown inset.

Such a process would, for instance, occur in a disordered medium [3].

In normal transport, the peak of the packet and the mean distance d are located at the same position and move with some constant velocity as shown in Figure 2.4a [4].

In this case the charge distribution is roughly Gaussian in shape. In dispersive transport

(discussed in detail in chapter 5), the peak of the packet remains fixed at the point of origin of the carriers, while the mean position d separates from the peak and moves away from the peak with decreasing velocity in time as shown in Figure 2.4b. The additional effects of space charge are shown in Figure 2.3b. As mentioned earlier the

Figure 2.3: Transient photocurrent (a) A typical dispersive transport. Inset is the same graph in log-log scale. An arrow indicates the transit time. (b) A typical transport showing the effect of space charge.

Figure 2.4: Moving charge packet. (a) Normal transport (b) Dispersive transport ( Scher et al. [5] ).

presence of the space charge causes the time of flight to decrease. The reason is that if there are a large number of charge carriers in the sample, mutual repulsion causes some of them move faster. As discussed above, space charge effects are prominent when light intensity and/or applied electric field is high. The presence of space charge makes the situation of measuring time of flight much more complicated because it creates regions of non-uniform field inside the sample. We therefore have to avoid the situation of space

charge as much as possible. The space charge effect is not prominent when QCV 0 where Q is the amount of charge in the sample and C is the capacitance of the sample cell.

Figure 2.5: Schematics of experimental setup for time of flight measurement.

Figure 2.6: Picture of optical table fitted with experimental equipment.

2.2 The Laser

Our Nd:YAG laser (Neodymium-doped Yttrium Aluminum Garnet) is a solid state laser in which triply ionized neodium (Nd+3) replaces yttrium in the crystal structure of the yttrium aluminum garnet. Nd+3 is about 1% by weight. Pulsed mode Nd-YAG lasers are typically operated in the Q-switching mode or in mode-locking. Q-switching is a technique to produce a high power short pulsed laser output, much more powerful than the beam of the same laser in continuous mode. Fig. 2.7 is a physical layout of the

Nd:YAG laser and Raman shifter. The laser (Continuum Electro-Optics Inc.) emits a fundamental wavelength (1064 nm) and second, third or fourth harmonics (532, 355, 266 nm). The harmonics are obtained by passing the fundamental through the harmonic generator and separated using dichoric mirrors. Two right angle deflections are used to direct the laser beam into the Raman shifter.

A Raman Shifter is used to produce beams of different energies (frequencies).

The Raman shifter is filled with pure hydrogen gas at pressure of ~120 psi. When

monochromatic radiation of frequency ω1 is incident, most of it is transmitted without change but, in addition, some scattering of radiation occurs. The scattered radiation

contains not only the frequency ω1 associated with the incident radiation but also pairs of

frequencies of the type ω1 ±ωm , where ωm is the frequency associated with the transitions between rotational, vibrational or electronic levels of the molecular (H2) system (in our case only vibrational modes enter). The scattering without change of frequency is called Rayleigh scattering, and that with change of frequency is called

Figure 2.7: Block diagram showing the physical layout of the laser assembly.

Table 2.1: Stokes and anti-Stokes lines

266 nm 355 nm 532 nm

S3 398.1 673.3 1582.3

S2 341.6 503.7 954.3

S1 299.1 416.5 683.2

AS1 239.5 309.3 435.6

AS2 217.8 274.1 368.8

AS3 200 246 319.8

AS4 223.2 282.2

AS5 204.2 252.6

Raman scattering. Raman bands at frequencies less than the incident frequency (i.e. of the

type ω1 −ωm ) are called Stokes bands, and those at frequencies greater than the incident

frequency (i.e. of the type ω1 +ωm ) are called anti-Stokes bands [6]. Note that, for anti-

Stokes bands, the molecule must be excited before the scattering event. Selection of the desired frequency of the stimulated Raman shifts is selected by using a simple fused- silica prism mounted on a rotary stage. The table 2.1 shows the Stokes and anti-Stokes lines of the hydrogen-gas filled Raman shifter for different laser harmonics.

2.3 The Action Spectrum

An action spectrum is the amount of charge-generation plotted against the wavelength of the photogenerating light. It shows which wavelength of light is most effectively used in producing charge. Figure 2.8 shows the experimental setup. A monochromator (Spectral produce CM110) produces monochromatic light from a wide range of wavelengths (from 200 nm to the IR) available from a xenon lamp. A small fraction (~ 5%) of the light is reflected into a sensor to monitor the incident power. A rotating disc chopper (Stanford research system SR540) has multiple slits in an opaque blade which intersects the light path. It is mounted on a motor head and can be set to a variety of rotation frequencies. When the optical beam from the monochromator is chopped, the light intensity vs. time is a square wave. This oscillating beam hits the sample, which is contained in a cell with transparent electrodes held under a potential.

The charge generation (current) as function of wavelength is recorded by a lock-in

Figure 2.8: Experimental setup to produce an action spectrum.

Figure 2.9: Action spectrum of glassy material (C54H38N2).

amplifier (Stanford research system SR830). A typical action spectrum for a glassy material is shown in Figure 2.9.

2.4 The Differential Scanning Calorimeter (DSC)

Differential scanning calorimetry (DSC) is a technique to study the thermal behavior of a material such as phase change temperatures and enthalpies to high accuracy. In this technique the difference in the amount of heat required to increase the temperature of the sample and a reference pan is measured as a function of temperature. The temperature is controlled by computer and programmed such that both the sample holder and the reference pan are kept at the same, linearly increasing temperature throughout the experiment. The basic principle underlying this technique is that when a sample undergoes a physical transformation such as phase change (particularly a first order transition), more or less heat will be needed to flow to the sample than the reference pan to maintain the same temperature. Whether more or less heat must flow to the sample depends on whether the process is exothermic (downwards “peak” in our convention) or endothermic (upwards peak). For example, as a solid sample melts to liquid, it will require more heat flowing to the sample to increase its temperature at the same rate as the reference pan (due to latent heat). Figure 2.11 is a typical DSC plot. Note that at a glass

transition (Tg ) there is no clear dip or peak. These do appear in DSC traces usually as a weak step in power. However, they are more difficult to characterize due to the magnitude of the signal and the dynamic nature of the transition (i.e., the signal size

Figure 2.10: DSC experimental arrangement

Figure 2.11: A typical DSC plot for a polymer sample [7]

depends on the rate of temperature change).

2.5 The Cryogenic System

This system is used for doing experiments at low temperatures and in vacuum.

The cryogenic system (Janis Research Co., Inc) consists of an inner and outer compartment (insulating). Both are evacuated with a turbo-pump (Turbo-V70, Varian).

Creating a low temperature is a bit tricky. First, the inner compartment has to be thermally isolated from the ambient temperature by creating vacuum in the outer jacket.

This is necessary to reduce the conductive heat load due to any gas present inside this jacket. When the outer jacket is evacuated, the valve of the outer jacket is closed and the vacuum pump is now connected to the inner jacket to create a pressure as low as 10-6 torr.

The vacuum pump is now disconnected and small amount of helium gas is inserted into the inner jacket. The System is now ready to cool by turning on the helium compressor

(Sumitomo, Heavy Industries Companies Ltd.) along with the water supply system

(M150, Thermo Neslab). When the system reaches the desired low temperature, the helium is pumped out. This system is able to cool as low as 4 K, monitored using a Si diode thermometer. Both optical and electrical access is available to the sample.

2.6 Methods of Making Thin Films

The thickness of thin film ranges from a few nanometer to several micrometers.

Some of the techniques we employed to make thin films are discussed below.

Physical Vapor Deposition (PVD): Physical vapor deposition is a process to deposit a film of material on the surface of the substrate by vaporizing a material under vacuum.

We used three techniques:

1. Sputtering: This method was used to deposit thin films of gold on the surface of glass. In sputtering, ionized gas molecules bombard a target’s surface to dislodge atoms, which deposit on the surface of a substrate to form a thin film. We used a

Hummer 6.2 (Anatech Ltd) machine to coat gold on the surface of glass substrates to use as electrodes. This machine contains a vacuum chamber in which a specimen and a sputter source can be fitted. A pressure of about 40 millitorr of argon gas is maintained and a high voltage is applied to ionize the Ar. The ions accelerate toward the negatively charged sputter source and dislodge metal atoms. These metal atoms eventually adhere to the specimen forming a thin film. The thickness of the film depends on the deposition time, the type of material to be deposited, the pressure and the applied field. While ions move toward the sputter source, energetic electrons move in the opposite direction. These electrons are deflected away from the specimen using magnetic fields to avoid thermal heating. Sputtering is a cold process which avoids thermal damage to the specimen.

2. Thermal Evaporation: This method was employed to coat aluminum on the surface of glass for electrodes. In this method a source material is kept in an electrical resistance heater known as boat. The material is heated until it melts and vaporizes. This is done in vacuum so that vapor reaches the substrate without scattering and contamination with other gases. Film thickness was measured in situ using a quartz crystal monitor.

3. Pulse laser deposition: This method was used to coat thin films of C60 onto the surface of a 1,4-diiodonaphthalene crystal. Here, 266 nm ultraviolet light from our Nd-

YAG laser was focused on the target material in high vacuum. The material gets ablated by the absorbed laser, and deposits on the surface of the crystal. The beauty of this method is twofold: The fullerene target need not conduct (as in dc sputtering) and there is no heating whatsoever of the temperature-sensitive sample.

Figure 2.12: Sketch of the substrate with a hole at the center and a wiper used to make a suspended thin film by surface wiping of material.

4. Surface wiping of material: This is a technique to make thin films of liquids and liquid crystals. In this technique, a material in the isotropic phase is wiped on the surface of a substrate by a fine blade to form a thin layer of material. We used this technique to form suspended thin films of liquid crystal materials to study mobility properties. A circular beveled hole of 2-3 mm in diameter was made at the center of the substrate

(laminated Kapton). A reservoir of material was kept on the side of the hole, heated to its

isotropic temperature, and wiped across the hole, forming a thin, freely suspended layer.

We note that some liquid crystals can form thin films below the isotropic phase. The thickness of the film was measured by an optical interference method.

2.7 Ionic Zone Refining

In many situations, organic compounds contain significant amount of ionic impurities. Despite extensive effort, synthesis and purification may leave residual ions of unknown nature. The presence of an ionic impurity hinders the intrinsic measurement of the properties of the compound under study. Especially for the measurement of charge carrier mobility measurement, the presence of ions (a) adds a large signal to the small desired current transient, and (b) acts as space charge, distorting the internal field in a time-dependent manner. In liquid crystal displays, ionic impurities alter the internal electric field and reduce the picture qualities causing flickering, non-uniform contrast and persistent image. Therefore it is necessary to lower the ion concentration and maintain high resistivity. We have begun developing a new technique to separate ionic impurities from organic compounds using an ionic zone refiner. Note that this is work in progress.

The working principle and design of an ionic zone refiner is discussed below. The sample contained in a glass tube is clamped firmly in the vertical motion stage controller.

The glass tube is made to move through a pair of electrodes, which are made of two halves of a metal tube of suitable size. The electrodes are supported by fitting them into a hole made at the center of a copper disk, with intervening electrical insulation. A rod type heater is fitted into the copper disk so that it works as a heater to melt the sample. The

temperature is measured with a thermocouple. The heater and electrode assembly is supported by a hollow aluminum tube which is attached on a base plate. The heater is also thermally insulated from the supporting aluminum tube to prevent heat loss by using a Teflon disk. The temperature of the copper disk is set above the melting point of the sample and a very high voltage (10,000 V) is applied across the electrode. The sample tube then very slowly raised or lowered (~2 cm/hr). When the sample moves slowly, ions are pulled towards and accumulate at the electrodes, in principle leaving the sample purer in each cycle. When the sample tube completes moving in one direction it is pulled back very fast to make another cycle. The rate of motion and distance is controlled by a computer. A labeled diagram of an ionic zone refiner is shown in Figure 2.13.

Figure 2.13: Ionic zone refiner. Labels: Sample tube (1), Teflon disk (2), Circular copper plate (3), Power supply wires (4), Electrodes (5), Thermocouples (6), Rod type heaters inserted into the copper disk (7), Vertical motion stage controller (8), Supporting aluminum tube (9), Base plate (10).

2.8 References:

[1] K. Hudson, and B. Ellman, Appl. Phys. Lett. 87, 152103 (2005).

[2] M. Pope, and C. E. Swenberg, Electronic Processes in Organic Crystals (Oxford

University Press, 1982), p. 70.

[3] J. C. Scott, L. T. Pautmeier, and L. B. Schein, Phys. Rev. B 46, 8603 (1992).

[4] H. Scher, M. F. Shlesinger, and J. T. Bendler, Physics Today 44, 26 (1991).

[5] H. Scher, M. F. Shlesinger, and J. T. Bendler, Physics Today 44, 26 (January,

1991).

[6] D. A. Long, The Raman Effect (John Wiley & Sons, 2002), p. 7.

[7] http://pslc.ws/macrog/dsc.htm.

CHAPTER 3

Crystal Growth and Mobility Measurement

3.1 Introduction

A crystal is a solid in which constituent atoms, molecules or ions are packed in a regularly ordered repeating pattern. A unit cell [1, 2] is the smallest repeating unit that, when stacked together without any gaps, can produce an entire crystal lattice. It has the same symmetry as the entire crystal. In non-crystalline or amorphous solids, particles are arranged in a more random manner.

The crystallization process consists of two major events, nucleation and crystal growth. Nucleation [3-5] is the process in which the solute (or liquid, in the case of a pure melt rather than a solution) molecules start to gather in a small region to form the stable cluster. These stable clusters constitute the nucleus. If the clusters are not sufficiently stable or large, they redissolve. Therefore a cluster needs to reach a critical size in order to form a stable nucleus. Nucleation occurs slowly as initial crystal components bump into each other in a correct orientation and placement in order to form a small crystal.

Nucleation can be either homogenous i.e. without the influence of an externally supplied cluster of ordered molecules or heterogeneous i.e. with the influence of an external

67 68

cluster. Heterogeneous nucleation is faster than homogeneous nucleation as the external seed acts as a seed for crystal growth. Artificial crystallization is mainly done using the following techniques: crystallization from vapor, crystallization from solution, and crystallization from melt. In this thesis, we have used the latter technique, growing crystals from ultra-pure melts of the organic semiconductor. Note that I primarily worked on sample preparation and crystal growth. Some limited characterization results are also presented.

3.2 Purification of the Sample

The samples were purified by two different methods before use in crystal growth: first by re-crystallization and then by zone refining.

Recrystallization

The impure material is dissolved in a minimum amount of a mixture of suitable solvents and heated until all the material is dissolved to form a saturated solution. The solution is then allowed to cool. As the temperature decreases, the solubility of the compound in the solution drops, resulting in re-crystallization of the compound,

(hopefully) leaving the impurity in the solution. Crystals are then isolated from the solution by vacuum filtration. When choosing a solvent for re-crystallization, the impure compound should have poor solubility at low temperature but be completely dissolved at higher temperature. As an example, the re-crystallization of 1,4-diiodobenzene is described here. 1,4-diiodobenzene is dissolved in a solution of CHCl3 and 1-PrOH mixed

in the ratio of 1:1 and brought to boiling to make the solution saturated. A no.4 pleated filter paper is flushed with boiling 1-PrOH, then with chloroform; the washing is discarded. The solution is filtered through the filter paper into a chloroform washed flask, which is set in a Dewar overnight for crystallization. The re-crystallized material is

filtered from the remaining solution with the help of a Buchner flask and vacuum. This

process is repeated two times. The compound is then completely dissolved in CHCl3 and slightly heated to make an unsaturated solution. This solution is then syringe-filtered through an 0.45 micron filter. Half of the chloroform is removed under vacuum. 1-PrOH is then added and the purified substance is re-crystallized again.

Zone Refining

Zone refining is a method of separating impurities from an element or compound by slowly passing a number of molten zones through a long impure ingot of solid in one direction. As the molten zone travels, it redistributes the impurities carrying some fraction of the impurity to the end or to the beginning of the solid charge, thereby making the remainder purer and segregating impurities at one or both ends. By passing the molten zone through the ingot repeatedly, the material in the center of the ingot is highly purified. The final distribution of the impurity depends on its distribution before the start, its relative distribution in the solid and liquid phase (known as the distribution coefficient

K), the size, and the number of passes of the molten zone.

Zone refining was first developed at Bell Labs to refine germanium to make transistors. The purity attained was one atom of impurity in 10 billion atoms of

germanium [6]. Many of the elements and organic and inorganic compounds are made pure by zone refining allowing the determination of their intrinsic properties.

Principle

To understand the principle of zone refining in a simple way, let us consider a

tube of material A containing another material B as an impurity. When this tube is heated

until the material melts and allowed to cool slowly from one end to the other as shown in

Figure (2.1a), the impurity concentrates in the last-to-freeze zone of the tube. During this

process, component B is redistributed in the sample because the advancing solid-liquid

interface prefers to reject the impurity. This process is called normal freezing. The

redistribution, measured by distribution coefficient K [6], is defined as

concentration of impurity B in the just forming solid A K = concentration of impurity B in the liquid

The value of K is less than unity because the rejected impurity accumulates in the liquid just ahead of the advancing solid so that the advancing solid sees the liquid more impure than itself. In zone refining, a series of molten zones travel the ingot in the same direction through a series of heaters as shown in Figure (2.1b). Each zone takes the impurity at its melting interface and leaves the purer solid at its freezing interface as it moves in each cycle. With successive zone passes, the concentration of the impurity at the beginning of the ingot drops lower and lower until it eventually reaches a limit called the ultimate distribution.

Figure 3.1: Purification by normal freezing (a) and by zone refining (b)

Let us suppose a single molten zone is passed through an ingot that has a uniform

concentration C0 of solute B in solvent A. As the molten zone moves, the first solid to freeze behind it has a concentration of solute B equal to KC0. Since K is less than one, the

newly formed solid contains less of solute B than the original ingot does. This means that some of B is rejected into the molten zone, raising its concentration. Simultaneously the solid of concentration C0 is being melted into the zone at its leading interface. These

concurrent processes increase the solute concentration in the molten zone until it reaches

the value C0/K. At that point, the concentration of solid the entering and leaving the zone

are equal. There is no more zone refining afterwards.

To appreciate the effect of zone refining, let us suppose that the impurity

concentration C0 in the original ingot is one percent and the distribution coefficient K is

0.5. The first solid to freeze behind the first pass of molten zone will contain

C1=K*C0=0.5*1=0.5 percent of the solute

If K remains 0.5,

The first solid to freeze behind the second pass will contain

C2=K*C1=0.5*0.5=0.25 percent of solute and so on.

After ten passes the purity of the central region will improve to from 95% to 99.9 percent

(assuming the no sample degradation takes place under melting).

Procedure

The sample in powder form is filled into a Teflon tube with the help of a specially

designed funnel. A Teflon tube was chosen as a container because it does not

contaminate the material and it is semi-transparent. The tip of the funnel is inserted into

the vertically fixed Teflon tube whose lower end is closed by a stopper. The sample

material in the funnel is melted with the help of a hot air gun and runs into the tube. Once

the tube is filled completely by the liquid, the open end is also closed with a stopper. The

tube is then fitted into the Zone Refiner (Design Scientific), which has four alternate hot

and cold zones. Each zone is 1 cm long. The total distance that a molten zone moves per

cycle is 2 cm. A typical zone rate-of-motion is (0.5- 2) cm/hr for organic compounds.

There are two temperatures to be adjusted. The melt temperature is set about 5 degrees

Figure 3.2: Picture of a zone refiner

above the melting point of the sample while the freeze temperature is set about 5 degrees below the melting point. A picture of the zone refiner is shown in Figure 3.2.

3.3 Bridgman Method of Crystal Growth

In this method [7-11], crystallization is done by directional cooling of the liquid phase. The system consists of two separate temperature zones, the melt zone and the growth zone, which are formed by two immiscible liquids. The molten compound in the melt zone is slowly lowered into the growth zone in a controlled fashion. In a typical arrangement, a melt is contained in a crucible with a conical bottom which is lowered through the temperature gradient so that freezing first takes place at the tip, forming a seed crystal. In some cases, a small amount of material is saved from melting by carefully adjusting the position of the crucible so that the tip containing the seed is at a lower temperature while the entire volume is above the melting temperature. When the crucible is slowly lowered, crystal growth starts in the conical tip and proceeds through the crucible. The detailed description of the instrument and working procedure is discussed below.

Description of the instrument

In our experimental setup which I designed and built with N. Shakya, the two temperature zones were formed in a large beaker by filling it with two immiscible liquids silicon oil and glycerin, both of which have boiling points higher than most of the organic compounds used for growing crystals. The melt zone is a silicon oil of density 0.963

g/cm3 and the growth zone is glycerin of density 1.262 g/cm3. The temperature of each

zone is controlled by a temperature controller and measured by thermocouples fitted in

each zone near the interface of the zones where crystal growth occurs. The lower liquid

layer is heated by the commercially made hot plate (Corning Hot Plate) and the upper liquid layer is heated by a locally-designed circular heater made of a hollow aluminum cylinder fitted with six cartridge heaters (100-120V, 146 Ω) connected in series or parallel combinations depending on the power desired. The upper liquid layer is maintained at a temperature higher than the melting point of the sample and the lower liquid layer is maintained at a temperature lower than the melting point of the sample with the help of temperature controllers (Omega Company). The beaker was wrapped

with ceramic insulation to limit heat loss. The wrapper had two small windows on the

opposite sides for illumination and viewing of the interface. Three propellers (each

formed from three copper “blades”) rotated by d.c. motors (12 -24 V) are used to make

very gently stir each liquid, creating uniform temperature zones without appreciable

disturbance of the liquid/liquid interface. Each propeller consists of three copper wings

fixed at three different parts of the supporting rods.

A long glass tube was used as a growth crucible. The upper part of the tube was

made of Pyrex glass and has a diameter of 1 cm while the lower part of the tube was made of an extremely thin walled (to assist heat transfer) NMR tube of very uniform

thickness. If the wall is not smooth, it may result in having many lines of small crystals

because the texture on the wall of the glass may act as nucleation centers. The shape of

the lower part was highly pointed. This helped nucleate a seed and prevent the formation

of multiple nucleation sites. The upper part of the tube was fixed to a linear-motion stage

(Sigma Koki Co. Ltd) and the lower part of the tube containing the sample was immersed in the melt (upper) zone of the liquid. The sample tube may also be rotated via a motorized rotary stage to eliminate azimuthal temperature gradients (this was rarely necessary in actual use). Both the linear and rotary stages may be controlled manually or by computer automation. The open end of the tube can be flushed with inert gas or held under vacuum during growth to avoid impurities, including the electron trap oxygen.

The temperature of the upper liquid is set above the melting point of the sample and lower liquid is set below the freezing point. Now the tube is filled with a purified sample to a suitable amount. The tube is then fixed to the linear and rotary stages and connected to vacuum or inert gas systems. With the help of the stage controller, the tube is then dipped into the upper liquid so that its tip just touches the interface of the two liquids. The sample is then allowed to melt. At this point, one has to be careful to save a very tiny amount of the solid sample for a seed to grow the crystal. The smaller the seed, the better. The tube is then allowed to go down very slowly through the lower liquid layer

(glycerin). The typical speed of the vertical motion and the circular motion for our experiment are respectively 1mm / hr and 180 degree / min.

In some crystals, cracks may form due to the phase changes when it is allowed to cool to room temperature. In that case, the tube is allowed to cool slowly inside the beaker by turning off the heater. The tube is first washed with alcohol and acetone and then is broken carefully to pull the crystal out of the tube. The design of our crystal growth instrument is shown in Figure (3.3) with the labels.

Figure 3.3: Design of a crystal grower

1. Sample tube (22” length, 0.39” external diameter, 0.32” internal diameter)

2. Growing crystal inside the tube

3. Silicon Oil (d 0.963)

4. Glycerin (d 1.262)

5. Circular heaters (Aluminum, outer diameter 5.5 “, thickness 0.5”, 61.5 ohm, 160 watt)

6. Heater plate

7. Thermocouples (Precision Fine Wire Thermocouples)

8. Power supply wires for heaters

9. Propellers (rod diameter 0.25’’ and fan’s length 0.5”)

10. AC motors (12 / 24 V DC)

11. Aluminum stands for stage controller

12. Vertical motion stage controller

13. Circular motion stage controller (diameter 2.3’’)

14. Adaptor for Vacuum system fitting

15. Pyrex beaker (4 lit, height 10’’ and diameter 6.5’’)

16. Circular heater and thermocouples supporting plate (8.5’’x 8.5’’x 0.4’’)

17. AC motor supporting plate (11.9’’x 8.1” x 0.2’’)

18. Supporting aluminum rods (height 25’’and diameter 1’’)

19. Base plate (12’’x 12’’ x 0.25’’)

20. Vertically moving plate (3” x 3” x 0.25’’)

Crystals of 1,4-diiodobenzene, diiododurene, 1,4-diiodotetraflurobenzene, 1,4-

dioidonaphthalene and naphthalene were grown in our laboratory. The growth conditions

used to grow crystals of these compounds are given below in brief.

1,4-Diiodobenzene (C6H4I2)

Melting point: (128-130) 0C

Melt zone temperature: 135 0C

Growth zone temperature: 115 0C

Purification-two times zone refined, three times re-crystallized and one time micron filtered. Cooling- tube was taken immediately outside the beaker and let it cool down at room temperature. Crystal grow- grown under vacuum. Cutting- crystal was cut using string saw soaked in toluene. Polishing- polishing by rubbing crystal in toluene-wet Kim- wipes. Nucleation- tiny material was left at the tip of tube to help nucleation. Crystal color is white.

I 1,4-Diiodonaphthalene (C10H6I2)

Melting Point: 113 0C

Melt zone temperature: 118 0C

Growth zone temperature: 103 0C

Crystal grown: Under vacuum I Zone refined: Under nitrogen gas.

Polishing: By rubbing in toluene-wet paper. Cooling- heaters were turned off and let it cool down to room temperature and taken out. No phase change occurred when cooled to

room temp.

Naphthalene (C10H8):

Melting point: 80 0C

Melt zone temperature: 90 0C

Growth zone temperature: 70 0C

Nucleation: Tiny material left to help nucleation. Purification: First by sublimation and

then zone refined under nitrogen. To prevent the evaporation of material during crystal

grow, the material is filled in a tube and fitted to the vacuum system. It is then heated

until all of the material melts. Then the mouth of the tube is sealed. This leads to an an

atmosphere of the compound at its vapor pressure when the material evaporates and

prevents further evaporation of the material during crystal growth. If the mouth is kept

open, pressure will be low due to the continuous vacuum process so that more material

will be lost.

Diiodotetrafluorobenzene:

Melting point: 109 0C

Melt zone temperature: 115 0C

Growth zone temperature: 103 0C

Nucleation- tiny material left at the bottom of the

tube helps for nucleation. Crystal needs to be kept at or above 80 0C otherwise phase

changes occur if kept at lower temperature.

I Diiododurene (C10H12I2)

CH CH3 Melting point: 140 0C 3

Melt zone temperature: 145 0C

Growth zone temperature: 125 0C CH3 CH3 Cooling: Since a structural phase change of I diiododurene occurs at 55 0C, the crystal can not be

taken out at room temperature. Therefore first the temperature of the growth zone is

lowered to 70 0C and the tube is quickly taken outside and dipped in soap water which is

maintained at 70 0C to wash off the oil on the outside of the tube. The crystal is taken out of the tube by gently baking it in a hot air stream and kept in a tube dipped in silicon oil at 70 0C. The crystal was growth under a nitrogen gas supply. To cut the crystal, a string

soaked in hot toluene was used (see below). Sides of the piece of a crystal is polished by

rubbing it over a Kimwipe soaked in hot toluene and placed on a hot stage No external

material is required for nucleation. The color of the crystal is yellow.

3.4 Crystal Cutter

A crystal can be cut into small slices with the help of a crystal cutter. A crystal

cutter is a string saw which consists of a running string passing through the crystal and

over pulleys which are driven by an electrical motor. Droplets of suitable solvent are

Figure 3.4: Photograph of a crystal growth assembly

Figure 3.5: Above- Picture of a beaker containing crystal in a crystal growth tube. Below- Picture of a 1,4-diiodobenzene crystal grown in the lab.

Figure 3.6: The crystal cutter.

dropped onto the string before it passes over the crystal. When the string soaked in the solvent passes over the crystal held by the holder, it slowly cuts the crystal. The crystal

cutter designed in our lab is shown in Figure 3.6.

3.5 Mobility Measurement in a 1,4-Diiodonaphthalene Crystal

One of the primary determinants of the compound’s utility in the electronic

devices is the charge carrier mobility. The charge carrier mobility in a small molecule

crystalline system have sometimes been reported to be high. For example, the hole

mobility in a 1,4-diiodobenzene crystal is 13 cm2V-1s-1 [12]. Crystals display the intrinsic

properties of the semiconductor without disorder. Another advantage of molecular

crystals is that they are often stable under standard environmental conditions, in contrast

to the liquid crystalline semiconductor which often exhibit instabilities under the influence of water and oxygen [13]. Therefore, a search for a better semiconducting molecular crystal is always desirable. Little study on charge transport properties in a 1,4- diiodonapthalene crystal has been done in the past. The study of charge transport

properties in this compound is interesting also due to the presence of iodine atoms (I)

which may have a significant role in the charge transport as they lead to the increase of

the transfer integral. A theoretical study study on diiodobenzene [12] shows that the

majority of the wave function overlap between the nearby molecules arises from the

iodine atoms.

In this work, 1,4-diiodonaphthalene (DIN) was purified first by sublimation. The

resulting material was then zone refined for several times. Crystals were grown

Figure 3.7: A 1,4-diiodonaphthalene crystal grown in the lab by using the Bridgeman method.

successfully by the Bridgeman technique described above. The surface of the diiodonaphthalene crystal was rubbed on the surface of Kimwipe, which was wet with toluene, in order to smooth out the surface, and reduce its thickness to about 1.5 mm. The sample was sandwiched between two electrodes, one of which was a semitransparent indium-tin-oxide (ITO) coated glass plate and other was a stainless steel plate. It is then placed inside a cryostat so that the experiment can be done at low pressure

( ∼ 2.0× 10−5 torr) in order to apply high voltage as demanded by a relatively large thickness of the sample. The basic measurement technique (TOF) explained in chapter two was employed to attempt to measure the mobility of charge carriers. Several attempts with different wavelengths were made to generate the charge on the surface of the sample. But there was no signal to indicate charge generation with any wavelength. In order to generate the charge, a thin layer of C60 was coated on the surface of the crystal

-6 by pulsed laser (266 nm) ablation in vacuum ( ∼ 10 torr). C60 is a commonly used semiconductor with high photogeneration efficiency. An illustration of the experimental setup to deposit C60 by laser ablation is given in Figure 3.8. A small amount of C60 was placed inside a glass tube (SiO2). A piece of diiodonaphthalene crystal was held a few centimeters above the C60 target by mounting it on the substrate holder. The glass tube was fitted to the vacuum pump (Turbo V70). Laser pulses were directed to C60, roughly at an angle of 45 degrees. A lens was used to adjust the irradiating spot and to produce high intensity laser focused in a small area. Irradiation of laser on the target for several minutes left a thin layer of C60 coated on the surface of the substrate by ablation. The physics of laser ablation involves a sequence of steps, initiated by laser radiation

Figure 3.8: Illustration of the experiment to deposit a thin film of C60 on the surface of 1,4-diiodonaphthalene crystal by laser ablation.

interacting with the target material, absorption of energy, localized heating of the surface, and subsequent material evaporation. The resulting ablation plume impinges on the substrate to be coated.

With C60 coated on the surface of the sample, a short pulse of laser light (266 nm) produced a large current signal which was a clear sign of charge generation on the surface of the sample held at a constant voltage. A representative current trace at room temperature is shown in Figure 3.9. Although there is no plateau to indicate the clear time of flight, the trace is an unambiguous signature of charge carrier flow. The trace has a long tail with a large recovery time of about 0.15 ms. The tail is a signature of a large number of traps with different energetic depths. Such a situation may arise because of impurities, or material inhomogeneities such as grains, grain boundaries and nonuniform thickness. The result is a large spreading in the transit time of the carrier and decreasing current level. The long tail represents the slow dribble of the carriers. In order to be able to accurately measure the mobility in a single crystal, further research is needed, particularly in sample purification. The tools I have developed are in regular use for studies on this and various other organic crystalline semiconductors.

Figure 3.9: A current trace as a function of time in 1,4-diiodonaphthalene crystal after C60 coated on the surface.

3.6 References

[1] J. J. Rousseau, Basic Crystallography, p. 9 (John Willey and Sons, 1998).

[2] C. Kittle, Introduction to Solid State Physics, p.6 (John Wiley and Sons, 1988).

[3] R. A. Laudise, The Growth of Single Crystal, p. 55 (Prentice-Hall Inc., 1970).

[4] W. Bardsley, and D. T. J. Hurle, Crystal Growth: A Tutorial Approach (North

Holland Publishing Company, 1979).

[5] I. Tarjan, and M. Matrai, Laboratory Mannual on Crystal Growth, p. 19

(Akademiai Kiado, 1972).

[6] W. G. Pfann, Scientific American 217, 63 (1967).

[7] H. Zhang, J. Chen, G. Ren, and D. Shen, Journal of Crystal Growth 267, 588

(2004).

[8] J. C. Brice, Crystal Growth Process, p.104 (Thomson Science and Professional,

1978).

[9] G. A. Karas, Trends in Crystal Growth Research, p. 101 (Nova Science Publisher

Inc., 2005).

[10] D. S. Robortson, J. Phys. D: Appl. Phys. 5, 604 (1971).

[11] C. H. L. Goodman, Crystal Growth: Theory and Technique, p. 238 (Plenum

Press, 1978).

[12] B. Ellman, S. Nene, A. Semyonov, and R. Twieg, Adv. Mater. 18, 2284 (2006).

[13] A. Breemen, P. Herwig, and et.al., J. Am. Chem. Soc. 128, 2336 (2006).

CHAPTER 4

Mobility Measurements in Calamitic Liquid Crystals

4.1 Charge Transport in a Terpyridine Liquid Crystal

Calimitic liquid crystals may exhibit greatly varying degrees of order, ranging

from the largely disordered nematic to essentially crystalline high-order smectic phases.

We concentrate here on smectic mesogens, since their greater positional and orientational

order are expected to be quite beneficial to electronic transport[1]. Pyridine compounds

are, naively at least, a promising field of investigation. The presence of the nitrogen atom

in the aromatic core of a liquid crystal molecule often results in the formation of higher

order smectic phases[2], which may have implications in device development. Hence the

mobility studies of phenyl-pyridine liquid crystal molecules presented below are of

particular interest.

The chemical structure of one material studied is shown in Figure (4.1). The

phase sequence with temperature (0C) during heating is as Cr 60.51 SmF 123.31 SmI

142.64 SmC 184.42 SmA 205.9 Iso. The measurements reported here were made at 100

0C (SmF) by cooling the sample from above the isotropic temperature of 206 0C at the rate of 0.02 degree per sec. The experimental cell was prepared using two indium-tin-

93 94

Figure 4.1: The molecular structure of the calamitic liquid crystal (a terpyridine derivative) oxide (ITO) coated glass substrates with no alignment layer. The ITO electrodes were separated by SiO2 spacers. The spacer was spread on the lower plate and then the top

plate was gently placed over it leaving some space for sample. The cell was filled with

the liquid crystal in the isotropic phase using capillary action. The filled cell was placed

in a spring loaded mount in order to keep the electrodes together at fixed spacing. The

thickness ()27μm of the cell was ascertained by measuring the capacitance,

()CkAd= ε 0 where ε 0 is permittivity of free space and k is dielectric constant of the

material, using a high precision LCR meter and a commercial 10 micron thick cell as a

reference. The time-of-flight technique described in chapter two was employed to

measure the transient photocurrent. A 10 ns pulse of 368 nm light was used for photo-

generation with a positive voltage applied on the illuminated electrode to measure the

hole mobility. The displacement current signal was amplified and acquired with a LeCroy

LT364L digital oscilloscope. The data were taken over a small range of electric field due

to the experimental limitation that trapping is an issue at low field and cell electrical

breakdown occurs at high field. This material shows hole mobility in the SmF phase (100

0C) from 3.5× 10−42cm / Vs to 6.4× 10−42cm / Vs for fields of 0.74× 105 to

1.48× 105Vcm / . A representative hole current transient is shown in Figure 4.2. No electron current was detected, which suggests the presence of deep traps for the electrons

Table 4.1: Mobility as a function of voltage at 100 0C. Voltage (V) 200 250 300 350 400

Mobility μ ()×10−4 3.50 4.26 4.90 5.70 6.40 ()cm2 / Vs

(possibly oxygen). The photocurrent exhibits an initial short spike (~6 microseconds), and a long tail. The initial spike may be due to trapping by sites with a lifetime exceeding the transit time in the sample, while the long tail is presumably due to the dispersion of the trap release time [3]. A dispersion in transit time arises if there is dispersion in the distance between nearest-neighbor transport site available for hopping and/or dispersion in potential barrier between these sites. Both of these variables strongly affect the hopping time. Hence, the distribution of the hopping times could have a long tail. The analysis of the anomalous broadening of the tail in time-of flight (TOF) signal is a part of the discussion in this chapter. Qualitatively, the shape of the photo-current transient allows us to conclude that the compound contains either multiple impurities and/or structural defects.

An analysis of certain dispersive photocurrent transients is given in a classic paper of Scher and Montroll [4] (SM). The theory assumes that each charge carrier independently undergoes a random walk biased in a preferred direction by the applied

Figure 4.2: A representative photocurrent transient in calamitic liquid crystal (a terpyridine derivative) plotted on a linear /linear scale.

field. The random walk is a succession of carrier hop from one localized site to another.

The distance between various neighboring sites have some variation from the mean value. The effective intersite transition rates, which depends on these distances, suffers a wide statistical dispersion. This in turn yields a broad distribution of hoping times. The analysis is based in terms of the hopping time distribution functionψ ()t . The hopping time is defined as the time interval between the moment of arrival of a carrier into one site and the moment of arrival into the next site. In their picture, the distribution of the hopping-time will have a long tail of the form

ψ ()tt∼ −+α(1 ) , 01<α< (4.1)

The propagating charge packet associated with equation (4.1) is a non-Gaussian. When the inverse power tail of the form exists, a considerable fraction of the carriers remains fixed at the point of origin of the carriers. As the charge packet propagates with a decreasing velocity, the peak of the packet lags behind the mean position of the packet.

This causes the propagating charge packet to be more and more asymmetric as it propagates. However, the packet spreads in the same manner as the moving mean so that ratio of the mean position 〈〉l of the propagating packet of carriers to the rms spread σ is independent of time, i.e., σ / l =constant. The current traces associated with such charge packets are universal. Here, universality of the current traces means that different traces corresponding to a wide range of transit time (obtained either by changing electric field or by changing sample thickness) all collapse into one curve if the current I ()t for each

trace is normalized to its transit time current Iτ , and time is normalized to corresponding

Figure 4.3: The normalized current plotted as a function of normalized time for different traces to check if they have the universality feature.

Figure 4.4: Photcurrent transient in double logarithmic scale at voltages of 200,250,300,350,400 volts for sample thickness of 27 μm . The arrows indicate the time of flight.

100

transit timeτ .We have analyzed our experimental current traces to check if they are universal in nature. The transit time was calculated from the intersection of the tangents to the plateau and to the tail plotted in double logarithmic scale. The traces used have different transit time obtained by changing electric field. The result is shown in Figure

4.3. Since all the traces do not collapse into one curve, universality- a unique signature of the SM dispersive transport - is not compatible with our data. Another prediction of the

SM theory is that for current variation with time will have the form [4] of

I() t∼ const× t −−α(1 ) for t <τ

I() t∼ const× t −+α(1 ) for t >>τ

In a plot of log I as a function of logt , the sum of the slopes at times t /1τ < and t /1τ >> would be ⎣⎦⎡⎤()11−α +( +α) = 2. In the experimental traces (see Figure 4.4), the slope ()10−α = for all lines at t /1τ < supporting non-dispersive transport [5]. The slope ()1+α is less than one for all lines att /1τ >> . The sum of slopes deviates from 2.

These analyses of the current traces lead to the conclusion that our data do not support

Scher-Montroll charge (non-Gaussian packet) transport formalism.

Another often-used model to describe dispersive charge transport is the Gaussian disorder model (GDM) formulated by Bassler [6, 7] and coworkers. This model assumes the transport of charge by hopping among random localized sites whose energies are

Gaussian distributed. The transport sites are subject to diagonal disorder (σ ) and off-

101

diagonal disorder ( ∑ ). The origin of diagonal disorder is the fluctuation of the lattice polarization energies. However, the self energies of the adjacent sites are uncorrelated.

The electron-phonon coupling is assumed, however, to be too weak to bound produce polarons. The off-diagonal disorder comes from the local variation in the inter site distances and mutual orientations of the molecules (since molecules are usually non- spherical). The jump rate among sites i and j is assumed to be of the Miller-Abraham type, i.e,

⎛⎞⎛Δ−−Rijεε j i eEr ⎞ ν ij=Γν 0 exp⎜⎟⎜ ij exp − ⎟ for ε ji> ε (4.2) ⎝⎠⎝akT ⎠

⎛⎞ΔRij =Γν 0 exp⎜⎟ij for ε ji< ε ⎝⎠a where a is lattice parameter, ν 0 is a prefactor, Γij is the wave function overlap

parameter, εi and ε j are site energies, and eEr is the electrostatic energy in the presence of an electric field. The probability of an upward jump is an exponential function of energy, while a downward jump does not need any activation energy (100% probability), and also is not accelerated by the electric field.

The fundamental parameters of this model are diagonal disorder σ and ∑ .

Bassler et al.’s simulation results show that, in general, mobility increases with increasing

∑ at constant electric field. The superimposing of off-diagonal disorder on the array of energetically ordered hopping sites (σ=0) increases the carrier diffusivity, and hence the mobility. The reason for this is that, though Σ is assumed to be symmetrically (indeed,

Gaussian) distributed about a mean Σ0, the hopping probability Γij is asymmetrically

102

Figure 4.5: Time of flight signals parametric in diagonal disorder σˆ at zero off-diagonal disorder. The signal becomes dispersive when σˆ is greater than 3.5 (Bassler [6]).

103

distributed about mean Γ0 due to the exponential in Equation (4.2): Prob. ~ exp( Γij ).

Although some routes will be blocked due to unfavorable intersite coupling, the asymmetry causes enhanced diffusion by opening some easy channels allowing a charge carrier to arrive faster at an accepter site earlier than it would without off-diagonal disorder. The role of the diagonal disorder is just opposite to that of the off-diagonal disorder. The increase of the energetic disorder not only causes a decreases of mobility but also makes the TOF signal dispersive due to dispersion in hopping times. The degree of dispersion depends on the degree of disorder. At low levels of disorder the TOF signal may be non-dispersive. Bassler’s paper, ref [6], shows a series of TOF signals parametric in σˆ (=σ / kT ) at vanishing off-diagonal disorder (Figure 4.5). The TOF signal is non- dispersive until energetic disorder σˆ (=σ / kT ) >3.5. The presence of the long tail of the non-dispersive TOF signal is the result of the non-thermal field assisted spreading of the drifting carrier packet due to disorder. We try to analyze our data in this context. We note, without a satisfactory explanation, that it is puzzling that diagonal disorder and off- diagonal disorder have such disparate effects on mobility when both enter the Miller-

Abraham expression in similar fashions. This point is not explained in the publications cited (e.g., [6]) and requires clarification.

The GDM predicts that the hopping mobility in a disordered medium is a function of electric field. Application of the electric field reduces the hopping barriers by tilting the barrier height in the field direction. The mobility, therefore, increases with increasing electric field and follows the Poole-Frenkel law, [8-12],

12 μμ= ′exp ⎣⎦⎡⎤ βE (4.3)

104

in a limited field range, where μ′ is the zero field mobility, and βσ=−∑C ()ˆ 22 is a disorder parameter such that σˆ = σ kT , k is Boltzman’s constant, and C is a constant

(not a priori predicted from the theory) [8, 12]. The mobility is calculated by defining the transit time at the intercept of the pre-transit and post-transit straight lines drawn on the photocurrent plotted on a double logarithmic scale (Figure 4.4). The transit times are indicated by arrows. The plot of the logarithm of mobility versus the square root of the field, shown in Figure 4.6, is a straight line for this sample over our field range. The positive field dependence of the mobility (Figure 4.6) with large slope is indicative of a system in which energetic disorder makes a greater contribution than the positional disorder (in other words, β>0). A fit of equation (4.3) to the experimental date allows us to extract β =×5.5 10−3 ()cm V 1/2 and zero field mobility μ′ =×7.9 10−52cm / Vs . From the results shown in Figure 4.6 it can be concluded that field dependence of the mobility is in good agreement with the prediction of the Gaussian disorder model.

Despite the high degree of ordering (SmF) of the molecules, the mobility in this material is small. Here, it is worth mentioning our mobility study on a phenylpyridine liquid crystal [13], which shows that mobility increases with a decreasing degree of ordering: μ~1x10-6 cm2/Vs in the crystalline phase, rising to 3x10-6 cm2/Vs in the

(almost crystalline) SmH and further increasing to ~4x10-6 cm2/Vs in the isotropic state.

Most importantly, these mobilities are much smaller than those of the corresponding hydrocarbon-based liquid crystal [3] even though the pyridine-based sample is in a higher-ordered phase. One may argue that such a low mobility is due to ions. To check

105

Figure 4.6: Electric field dependence of the hole mobility terpyridine liquid crystal. The line is a fit to the data (circle) (see text).

106

this, we added 1 molar percent of an impurity (the calamitic liquid crystal 8PNPO12).

Even the addition of such a small amount of an impurity makes the photocurrent transient featureless (i.e., completely dispersive - see Figure 4.7). We would expect essentially no change if the current transient was due to ions, since only 1% addition of impurity would not have significant effect on the viscosity. Hence, the combination of these results with the study on the terpyridine compound raises an important question: does the presence of the pyridine rings play a role in decreasing the mobility? A further study is needed to investigate why pyridine based compounds exhibit such low a mobility despite it often results in the formation of higher order smectic phases.

Figure 4.7: Photocurrent transient in phenylpyridine based liquid crystal.

107

4.2 Charge Transport in Thiophenyl-bipyridinyl Liquid Crystal

The following results in some sense constitute a failure in that we did not succeed in measuring carrier mobilities. However, they do demonstrate two important points.

Firstly, ionic mobilities, which as noted above are potential confounders in carrier transport measurements, are generally (though, as noted above, not always) easily detected. Secondly, even ionic transport has lessons to teach us.

Figure 4.8: Molecular structure of thiophenyl-bipyridinyl liquid crystal.

The molecular structure of the thiophenyl-bipyridinyl liquid crystal studied is shown in Figure 4.8. In addition to the pyridine rings it also contains a thiophene ring. A literature review shows that liquid crystal molecules that have higher mobility often contain thiophene moieties [14-16]. The relatively large sulfur atom plays an important role in close molecular packing and enhances the intermolecular overlap of the molecular orbitals and therefore increases the hopping conduction of charge carriers [17]. The phase sequence as a function of temperature (0C) is Cr 62.89 SmF 122.91 SmC 147.74 Iso. The observation were taken in a sample of thickness 10 microns for temperatures from 80 0C

(SmF) to 124 0C (SmC) using a 320 nm laser pulse. The illuminated electrode was given

108

a positive voltage for hole transport study. The current traces show that carrier transport is non-dispersive (Figure 4.9). These transit times are in the order of milliseconds resulting in very low, temperature-dependent mobilities in the range of 610× −62cm V . s .

These mobilities values are much smaller than the hole mobilities in many other clamitic liquid crystals [1, 17, 18]. It is reasonable to hypothesize that the transient photocurrents

(Figure 4.9) represent the transport of photo-generated ions rather than discrete holes.

The ionic mobility in calamitic liquid crystals reported in the literature [1, 18, 19] is of the order of 10-6 cm2/Vs for positive ions and 10-5 cm2/Vs for negative ions. The origin of the ionic species responsible for slow transient photo-currents could be the photo-ionized chemical impurities, which are originally neutral molecules contaminating the liquid crystal [18]. Another possibility is the contamination of the sample by ionic compounds, such as NaCl, due to improper handling of the cell. The chemical structure of such impurities is not known. For the carrier transport of ionic nature, Walden’s rule

[19] (Eq. 4.4) or its modification (Eq. 4.5) should be valid:

μηπ= er6 (4.4)

μηα = constant (4.5)

where η is the viscosity of mesophase, r the ionic radius, and α is a constant.

0 Assuming the radius of Na+ in the order of 2 A , the viscosity is calculated using equation

(4.4). Another source may be ionized molecules of the sample material itself or perhaps some other unknown degradation product. From table 4.3, the viscosity of the liquid crystal sharply decreases with increasing temperature [20] (see Figure 4.11). The

109

Table 4.2: Mobility in thiophenyl-bipyridine as a function of applied voltage at different temperature. Voltage 100 125 150 175 200 225 125 0 C μ ()×10−5 1.09 1.09 1.10 1.09 1.11 1.11

()cm2 / Vs

Voltage 150 175 200 225 250 275 300 115 0 C μ ()×10−6 9.19 9.21 9.25 9.25 9.30 9.32 9.38

()cm2 / Vs

Voltage 150 175 200 225 250 275 300 325 350 105 0 C μ ()×10−6 5.97 5.95 5.95 6.00 5.97 5.96 5.95 6.03 6.08

()cm2 / Vs

Voltage 175 200 225 250 275 300 323 350 375 90 0 C μ ()×10−6 3.66 3.67 3.76 3.84 3.82 3.78 3.89 3.91 4.01

()cm2 / Vs

Voltage 250 275 300 325 350 375 400 425 450 80 0 C μ ()×10−6 2.63 2.76 2.62 2.67 2.69 2.77 2.77 2.70 2.81

()cm2 / Vs

110

Figure 4.9: Photo-generated ion traces at 90 0C (SmF) at various applied voltages.

111

Figure 4.10: Photo-generated ionic mobility Vs electric field at different temperatures.

112

Table 4.3: Average mobility and viscosity as a function of temperature for thiophenyl- bipyridinyl liquid crystal. Temperature 80 90 105 115 124 (0C) Average mobility 2.7× 10−6 3.82× 10−6 5.98× 10−6 9.27× 10−6 1.1× 10−5 2 (cm /V.s)

Viscosity (Ns/m2) 0.157 0.111 0.071 0.046 0.040

diffusion of the ionic charge is easier at low viscosity, and mobility increases with increasing temperature, Figure 4.12. A particularly telling feature is that the mobility increases with decreased ordering (SmF to SmC), which is consistent with ionic conduction but not with that of holes. (As noted in the previous section, however, this fact alone is not sufficient to identify ionic transport).

The resistance of the experimental cell is estimated from the off-set dc-current

(the current flowing into the cell when no light is applied). For the applied voltage of 500 volts in the cell of thickness 42 μm at temperature 105 0C, the off-set current was

1.5× 10−7 A . This gives a resistance R = 3.3×Ω 109 . We know that R = ρ ()LA or

σ ==1 ρ L RA where σ is conductivity, ρ is resistivity, L is sample thickness, and A is the area of the electrode. We also know that σ = nμ where n is charge density and μ is the mobility. From these two expressions of conductivity, we can write

nLRA= μ

113

For our ITO electrodes, Am=10−42, and the average mobility at 105 0C is

μ =×5.98 10−10mVs 2 . . Putting all corresponding values in the expression of n , we get n = 0.2 Cm/ 3 . Assuming singly-charged ions (i.e. Ne= n ), the estimated number density ( N ) of ionic charge is 13× 1017 per cubic meter. For a liquid crystal density of

1gm/cm3, ionic concentration is roughly one part per 109.

Figure 4.11: Viscosity as a function of temperature.

114

Figure 4.12: Mobility as a function of temperature in SmF phase.

115

4.3 References

[1] M. Funahashi, and J. Hanna, Phys. Rev. Lett. 78, 2184 (1997).

[2] G. Yulia, Ph.D Thesis (Kent State University, 2007).

[3] I. Shiyanovskaya, K. Singer, R. Twieg, L. Sukhomlinova, and V. Gettwert, Phys.

Rev. E 65, 041715 (2002).

[4] H. Scher, and E. W. Montroll, Phys. Rev. B 12, 2455 (1975).

[5] A. Mozer, and et.al., Phys. Rev. B 71, 035214 (2005).

[6] H. Bassler, Phys. Stat. Sol. (b) 175, 15 (1993).

[7] G. Schonherr, H. Bassler, and M. Silver, Phil. Mag. B 44, 47 (1981).

[8] Y. Zhang, K. Jespersen, and et.al., Langmuir 19, 6534 (2003).

[9] V. Duzhko, E. Aqad, and et.al., Appl. Phys. Lett. 92, 113312 (2008).

[10] M. Kastler, F. Laquai, K. Mullen, and G. Wegner, Appl. Phys. Lett. 89, 252103

(2006).

[11] L. Chen, T. Ke, and C. Wu, Appl. Phys. Lett. 91, 163509 (2007).

[12] M. Redecker, D. Bradley, M. Inbasekaran, and E. Woo, Appl. Phys. Lett. 74,

1400 (1999).

[13] Y. A. Getmanenko, R. Twieg, and B. Ellman, Liquid Crystals 33, 267 (2006).

[14] N. Shakya, and C. Pokhrel, To be published (2007).

[15] H. Iino, and J. Hanna, Jpn. J. Appl. Phys. 45, L867 (2006).

[16] M. Funahashi, and J. Hanna, Appl. Phys. Lett. 76, 2574 (2000).

[17] K. Oikawa, H. Monobe, and et.al., Chem. Commun., 5337 (2005).

[18] H. Iino, and J. Hanna, Opto-Electron. Rev. 13, 295 (2005).

116

[19] K. Okamoto, S. Nakajima, A. Itaya, and S. Kusabayashi, Bull. Chem. Soc. Jpn.

56, 3545 (1983).

[20] M. J. F. Contreras, A. R. Dieguez, and M. M. J. Soriano, Il Farmaco 56, 443

(2001).

CHAPTER 5

Charge Transport in A Disordered Organic Medium

5.1 Introduction

This chapter covers the discussion of charge transport properties in an organic glass, a very strongly disordered medium. A glass is an amorphous material usually formed when a molten material cools very rapidly without enough time for regular crystal lattice formation. It can be also said that it is a super cooled liquid because there is no first order phase transition on cooling. Material in a glassy state has no long-range molecular order.

The motivation of the research of the transport properties of amorphous materials like glasses is their potential uses in electronic devices such as photocopying machines.

In particular, they are, in principle, very easy to deposit as films (e.g., no care need be given to forming large crystalline domains). The charge carrier transport in disordered organic materials has been discussed in many papers [1-4].

The molecular structure of the experimental material (chemical formula:

C54H38N2) is shown in Figure 5.1. The thermodynamic behavior is shown by the DSC curve in Figure 5.2. When a crystalline solid gets heated, crystal symmetry eventually

117 118

Figure 5.1: Molecular structure of 2,4,5-tris(4-(phenylethynyl)phenyl)-1-(3- phenylpropyl)-1-H-imidazole.

119

Figure 5.2: DSC curve of 2,4,5-tris(4-(phenylethynyl)phenyl)-1-(3-phenylpropyl)-1- H-imidazole (above:1st cycle , below: 2nd cycle).

120

breaks down and the material turns into a liquid. This is indicated by the sharp peak at

164.73 0C in the heating curve. This is a first order transition. But during cooling there is

no sharp peak indicating any thermodynamic phase change. Instead, the liquid super-

cools, turning into a glass phase, as indicated by the change in slope of the cooling curve

(this is clearer in the second thermal cycle).

The synthesis [5] and purification was done by Yulia Getmanenko as described

below (this information is here for reference – I took no part in these procedures). The

material was synthesized from N-H imidazole by a two step sequence from carbonyl

containing precursors. The parent N-H imidazole were constructed by the condensation

of aryl aldehydes with 1,2-dicarbonyl compounds in the presence of a large excess of

ammonium acetate. Deprotonation of the imidazole N-H with NaH followed by the

reaction of the anion with alkyl halides produced the N-alkylated imidazole. Aryl

aldehydes used for the preparation of imidazole and their precursors were synthesized

from commercially available 4-bromobenzaldehyde or 2-bromo-5-thienylcarboxaldehyde

by Sonogashira coupling with the corresponding acetylene derivatives. High performance

liquid chromatography (HPLC) was done to check the purity of the material. If there were multiple components in HPLC, the material was Biotage (medium pressure liquid chromatography) purified and re-crystallized twice.

Experiments were carried out in lab-made cells. The cell was prepared by using two ITO coated glass plates [6] as electrodes and 20 μm silica spheres as spacers. The material was heated to its isotropic point and then allowed to fill the cell by capillary

121

Figure 5.3: UV absorption spectrum in a sample.

122

Figure 5.4: The charge generation as a function of wavelength.

123

action. Since the material was very viscous, it entered the cell very slowly. When the cell was filled, it was taken out of the hot stage for cleaning and electrical wiring. The cell

was again placed on the hot stage and heated to the liquid state. It was allowed to cool

fast (without control) to the experimental temperature of 76 0C. A graph of charge

generation as a function of wavelength (an “action spectrum") is shown in Figure 5.4. By comparing the two results we find the wavelength that is most absorbed and generates maximal charge. The action spectrum shows that a wavelength of 400 nm photo- generates charge most efficiently. But looking at the UV absorption spectra 400 nm easily passes through the material with very little absorption. Study of the photo-

generation graph and UV absorption graph indicates that 320 nm is the suitable

wavelength that is absorbed in the material and also produces charge. 368 nm is also a

possible wavelength.

In practice, both 320 nm (fourth anti-stoke line of 532 nm) and 368 nm (third anti-

stoke) light from the 10 ns pulsed Raman shifted doubled Nd-YAG laser were used as sources for optical excitation. A photocurrent pulse (converted into a voltage pulse) is shown in Figure 4.5 below. The shape of the trace departs far from the ideal trace shown in Figure 2.2a, Chapter 2. The trace has sharp peak at the beginning and then it decays

without a clear plateau and the sharp “kink” required for unambiguous TOF

measurement. But the TOF is clear when analyzed in log-log plot as shown in inset.

124

Figure 5.5: A typical current trace on a linear/linear scale. The Inset is the same trace on a log-log scale. The arrow indicates the time of flight.

125

5.2 Theory

The experimental results (see Figure 5.8) show that mobility depends on the exponential of the square root of electric field. Such a “Poole-Frenkel” field dependence of mobility,()μ

μγ∝ exp(E ) (5.1) where γ is a material-dependent parameter that typically decreases with increasing temperature, has long been a subject of interest for people working in the area of disordered semiconductors[7-12]. It is found that this field dependence of mobility arises when charge carriers hop among localized sites distributed in a random potential energy landscape. Many theoretical attempts to explain the observed exponential dependence of mobility on E are based on the various roles of disorder. For example, the Gaussian disorder model (GDM) proposed by Bassler (discussed in chapter 4) assumes Gaussian distributions of site energies with root mean square width σ . The site energies are distributed independently, with no correlations occurring over any length scale. The

Monte Carlo simulation indicates that mobility can be expressed as an exponential function of E only in relatively large fields ( E >105-6 V/cm). This is contrary to the linear dependence of ln μ on E down to EVcm=×810/3 observed in many molecularly doped polymers [13] and pure molecular glasses like our experimental material. Also, Bassler model assumes the periodic array of transport sites, which is not applicable to glassy material. Dipole is most likely substantially smaller for the liquid

126

crystal than for the glassy material making the dipolar disorder theory less applicable to the material in chapter 4.

Dunlap and co-workers [7] have proposed a correlated disorder model (CDM) in which charge carriers move in a spatially correlated random potential. The source of disorder in this model is the interaction of the charge carrier with the permanent dipoles of neighboring molecules giving rise to a Gaussian-like density of states. The charge- dipole interactions are of sufficient range to lead to significant positive correlations among the energies of the hopping sites. (In this model, unlike the Gaussian disorder model (GDM) of Bassler, there is no off-diagonal disorder ( Σ=0).) Gartstein and

Conwell [10] showed that finite-range correlations imposed on the GDM can push the regime over which the field dependence described by equation 5.1 to lower fields. A

strong field dependence should occur when the potential drop eEr0 , and say that

U= eEr0 over some length scale r0 is comparable to kT . With uncorrelated energies the only length scale in the problem is the mean intersite spacing. Correlation introduces a new, longer length scale, namely, the correlation length associated with the energetic disorder, thereby reducing the electric field required for a sizable U[7]. As our experimental material is constituted of polar molecules, CDM may well be applicable to describe the charge transport in this material.

Since the charge-dipole interaction is long range, each charge interacts with many G surrounding dipoles. To put a carrier at the site r0 requires an energy [8, 14]

GGG G G G −∑ p .ErG equal to its interaction energy with each dipole p , where ErG () is the mmr0 () m m rm0

127

G electric field due to charge carrier at r0 evaluated at the site of dipole. For random dipole orientation, the interaction energy distribution tends to be a Gaussian with zero mean [8].

The temperature and electric field dependence of the mobility are determined by the escape rates of the charge carriers from these traps. These traps are thermally activated with activation energy Δ . In the presence of an electric field, each trap is tilted along the field direction [15] and the activation energy is reduced by eEr , i.e. Δ→Δ−eEr where r is the radius of the Coulombic well. The traps in the reverse direction have their energy raised by the same amount. Under the action of the electric field the trap escape time from the given site is proportional to the Boltzman factor

⎛⎞Δ−eEr ττ= 0 exp⎜⎟ (5.2) ⎝⎠kT

where k is Boltzman factor, τ 0 is characteristic time of flight and T is the temperature. To discuss the theory in more detail let us consider a Gaussian probability distribution function [8] of potential energy of depth Δ with zero mean and variance 〈Δ2 ()r 〉 :

1 ⎛⎞Δ2 fr(,)Δ= exp⎜⎟ − 2 (5.3) 2π 〈Δ2 〉 ⎝⎠2()〈Δ〉r

Since the trap depth changes the trap escape time also changes. The average trap escape time is ∞ 〈〉=ττ∫ f () Δ,rd Δ (5.3) 0 ∞ 2 τ0 ⎛⎞ΔΔ−⎛⎞eEr =−exp⎜⎟2 exp⎜⎟d Δ 2 ∫ 2〈Δ 〉 kT 2π 〈Δ 〉 0 ⎝⎠⎝⎠

128

⎛⎞−〈Δ〉eEr2 () r (5.4) =+τ0 exp⎜⎟2 ⎝⎠kT2( kT )

As stated above the fluctuation in the site energy arises from the fluctuation in the interaction energy of charge carrier with fixed permanent dipole. Since the charge dipole interaction is long range each charge interacts with many surrounding dipoles. Therefore the potential energy [7] GGGG Ur()=− p . EG ( r ) (5.5) 0 ∑m mrm0 G is the potential energy of a charge e located at point r0 and surrounded by randomly G G GGGG oriented identical dipoles p . In terms of dipole density, p (rprr )=−δ ( ) , the m ∑ m mm above equation can be written as

Figure 5.6: Charge-dipole interaction: U (0) is the interaction-energy of charge located at G G G origin with a dipole at r and Ur()0 interaction energy of charge located at r0 .

129

G GGGG3 Ur()=− pr () ⋅ EG () rdr (5.6) 0 ∫ r0 GG G G er()− r0 where ErG ()= r0 GG3 4π ε−rr0 G G is the electric field at r due to a charge at r0 . The energy difference between two sites G separated by arbitrary distance r0 is

Δ=Ur()0 − U (0) (5.7)

G GG =−p.()()⎡⎤Er E rdr3 ∫ ⎣⎦0 r0 G G = ∫ p.()Erdr3 GGGGG G where Er()=− E () r E () r can be interpreted as the field due to a positive charge sphere 0 r0 of radius a located at the origin and a negative charge sphere located at r . We exclude the interaction energy of the molecule on which the charge is sitting by excluding a volume of radius a comparable to the size of molecule. We can also view the field as arising from a uniformly charged sphere of radius a , inside of which the field vanishes.

The average of the square of the energy difference or the variance 〈Δ2 〉 can be written as[7]

2 pn2 r0 ε G 〈Δ223 〉 =0 ∫ | Er()| dr 3∈2a

r 2 2 pn2 0 ε ⎛⎞e 1 = 0 .4π rdr2 ∫ ⎜⎟2 324εεa ⎝⎠π r

130

a =−σ 2 (1 ) (5.8) r0

22 21/2 where σπ=ε()epn0 /6 a . (5.9)

and n0 is dipole number density. Equation (5.8) shows the relation between the width of

the potential well r0 and its depth Δ . This shows that wider valleys tend to be deeper and deeper valley tends to be wider. The deepest traps are the ones that limit the rate of charge release. However, the concentration of deep traps is very small, decreasing exponentially with depth of the trap (see equation 5.3). Also the energy of the deep traps

(i.e. they have large r0 ) decrease more in the presence of field than the shallower ones

because potential depth changes by eEr0 . Therefore the most effective traps for a given field are neither the widest (deepest) ones nor the narrowest (shallowest) ones but those

of intermediate critical dimension rc . This critical dimension can be calculated by

maximizing 〈〉τ ()r0 with respect to r0 . Substituting equation (5.8) in equation (4.5), the average trap escape time becomes

⎡⎤2 −eEr0 σ ⎛⎞a 〈〉=ττ()r 0 exp⎢⎥ +⎜⎟ 1 − (5.10) kT2 r ⎣⎦⎢⎥2()kT ⎝⎠0

⎡⎤⎡⎤22 ∂τσσeEr0 ⎛⎞aeEa |exprr= =τ 0 ⎢⎥⎢⎥−+ 1 − −+ = 0 0 c 22⎜⎟ 2 ∂rkTrkTr000⎢⎥⎢⎥22()kT⎝⎠ () kT ⎣⎦⎣⎦rr0 = c

eEσ 2 a ⇒ = 2 2 kT2()kT rc

131

Figure 5.7: (a) Energy diagram of set of traps in the absence of applied field. Note that the deep traps are wider. (b) In the presence of electric field, the energy of the traps is reduced by eEr0 in the forward direction. Wider traps decrease more than the shallow ones [8] .

132

σ 2a ⇒ r 2 = c 2kTeE

⎛⎞σ 2 ⇒ ra= ⎜⎟ (5.11) c ⎜⎟ ⎝⎠2eEakT

These traps are the most important ones in determining the mobility. At low fields the widest traps are important, consistent with the idea that they are also the deepest. At high fields the widest traps flatten thereby strongly reducing the release time and therefore shallow traps become important. The average release time of the critical traps is obtained

by replacing r in equation (5.10) by rc in equation (5.11).

⎡⎤eEσσσ222 a a2 kTeE 〈〉=ττexp ⎢⎥ − + − 0 kT2 eEkT22σ 2 a ⎣⎦⎢⎥22()kT() kT

⎡⎤σσσeEa2 eEa =−τ exp ⎢⎥ + − 0 kT22 kT2 kT kT ⎣⎦⎢⎥2()kT

⎡⎤σσ2eEa 2 =−τ exp ⎢⎥ + (5.12) 0 kT kT 2 ⎣⎦⎢⎥2()kT

The mobility of the material with the energy topology discussed above will depend on the ratio of the mean distance 〈〉d between the traps to the average escape time of the critical traps that most limit the transport.

〈〉d μ = (5.13) E〈〉τ d ⎡⎤σσ2 2eEa =−+exp ⎢⎥ EkTkTτ 2 0 ⎣⎦⎢⎥2()kT

133

⎡⎤σ 2 =−+μγ0 exp ⎢⎥2 E ⎣⎦⎢⎥2()kT

σ 2ea where γ = (5.14) kT kT

σ 2 So, logμμ=− log 0 + γE (5.15) 2()kT 2

5.3 Observations

Table 5.1: Mobility values as a function of applied voltage at different temperatures

for the experimental material (C54H38N2). Sample thickness 20.5 μm λ = 320 nm

40 0C Voltage(V) 1200 1250 1300 1350 1400 1450 Mobility μ 3.72 4.10 4.52 4.99 5.39 5.97 (10× −52cm / Vs )

50 0C Voltage(V) 1000 1050 1100 1050 1200 1250 1300 Mobility μ 3.81 4.35 4.66 5.23 5.61 6.18 6.68 (10× −52cm / Vs )

60 0C Voltage(V) 850 900 950 1000 1050 1100 Mobility μ 4.41 4.83 5.27 5.86 6.41 7.02 (10× −52cm / Vs )

70 0C Voltage(V) 750 800 850 900 950 1000 Mobility μ 4.87 5.36 5.92 6.32 6.78 7.41 (10× −52cm / Vs )

134

75 0C Voltage(V) 1000 1050 1100 1050 1200 Mobility μ 8.54 9.09 9.70 10.30 10.90 (10× −52cm / Vs )

76 0C Voltage(V) 1100 1150 1200 1250 1300 Mobility μ 10.64 11.26 11.92 12.64 13.28 (10× −52cm / Vs )

Sample thickness 20.5 μm λ = 368 nm

40 0C Voltage(V) 1250 1300 1350 1400 1450 1500 Mobility μ 4.29 4.81 5.29 5.82 6.3 7.07 (10× −52cm / Vs )

50 0C Voltage(V) 1150 1200 1250 1300 1350 Mobility μ 5.4 5.80 6.37 6.96 7.83 (10× −52cm / Vs )

60 0C Voltage(V) 1050 1100 1150 1200 1250 Mobility μ 6.46 7.10 7.81 8.35 9.23 (10× −52cm / Vs )

70 0C Voltage(V) 900 950 1000 1050 1100 Mobility μ 6.46 7.01 7.58 8.34 8.91 (10× −52cm / Vs )

75 0C Voltage(V) 950 1000 1050 1100 1150 1200 Mobility μ 8.7 9.19 10.0 10.8 11.0 11.9 (10× −52cm / Vs )

135

5.4 Analysis and Results

The above equation (5.15) can be rewritten as

logμμ=+ log() 0,TE γ (5.16) where

σ 2 logμμ (0,T )=− log 0 (5.17) 2()kT 2 is the zero-field mobility which is given by the intercept of the fit line whose slope is γ .

Equation (4.16) shows that log μ is a linear function of E [16]. When we plot our data for log μ as a function of E we get set of straight lines with slope γ ()T for different temperatures as shown below in Figure 5.9 where circles are data and lines are the fit of equation (5.16). The fit values are presented in Table 5.2. The field dependence of the mobility becomes stronger at lower temperature, i.e. the slope of the logarithmic mobility vs square root of the field becomes steeper at lower temperature. When the temperature increases, carriers gain thermal energy and so the effect of disorder decreases, resulting in the decrease of the slope of ln μ Vs E1/2 . It is interesting to note that all the curves could merge at a point, which corresponds to mobility at zero-hopping barrier, at very high fields. Electrical breakdown prevented us from experimentally accessing this field.

However, this can be predicted from the Poole-Frenkel model theoretically.

Equation (5.17) shows that the plot of logμ ( 0,T ) as function of inverse-square of the temperature is a straight line whose slope allows us to extract the Gaussian width

136

Figure 5.8: The solid lines are a fit of equation (5.16) to the measured field dependent mobility represented by circles in experimental material (C54H38N2). Data for the wavelengths of 320 nm and 368 nm lie on the same lines of the corresponding temperatures.

137

Table 5.2: Fit parameters of equation (5.16). TK() Slope γ (/)mV1/2 Intercept Voltage (V) logμ ( 0,T )

313 6.48× 10−4 -24.47 1150:1550:50

323 5.75× 10-4 -23.40 950:1400:50

333 5.13× 10-4 -22.56 800:1300:50

343 4.52× 10-4 -21.78 700:1150:50

348 4.13× 10-4 -21.39 900:1250:50

349 4.02× 10-4 -21.29 1000:1250:50

σ of the density of states. The Gaussian width, which one recalls is a measure of energetic disorder, is found to be 0.15 eV. The value of σ could be expected to be temperature dependent due to changes in rotational freedom of the molecule. But the straight line nature of the graph shows (Figure 5.19) that σ is a constant. Presumably due to regard to the large size of the molecule and the small range of the experimental temperature, the rotational freedom does not contribute significantly to this value.

Similarly, from the y-intercept of the same graph we can extract the zero-barrier hopping

−5 2 mobility μ0 =×5.6 10 cm/ Vs . From equation (5.9), the dipole moment of the molecule can be expressed as

2 2 6εεπ a()r 0 σ p = 2 ne0

138

The dielectric constant of the material calculated by measuring the capacitance of the experimental cell is εr = 3 . A characteristic size of the molecule calculated using ab-

0 0 initio theory is about 25 A . For the sphere of radius a =12.5 A ( half the size of the molecule in order to avoid the contribution to the interaction energy by the molecule on

27− 3 which the charge is sitting) and a dipole density of nm0 =10 (a typical values taken from ref. [7], the dipole moment is p = 1.2 Debye.

At any given temperature, the size of the critical trap ( rc ) decreases with increasing field. Combining equations (5.11) and (5.14), the size of the critical trap can be expressed as

γ kT 1 r = (5.18) c 2e E

This value of rc and hence the trap release time changes as the value of the applied field changes. Thus the field dependence of mobility comes from the field dependence of the

size of the critical trap rc .

The temperature dependence also can be described by an Arrhenius-like law [10,

17], μμ()0,TkT=−Δ0 exp(), where Δ is the activation energy. The corresponding fit is presented in Figure 5.10. For our limited range of temperature, it is difficult to distinguish whether log μ ()T Vs 1/T or log μ (T ) Vs 1/T 2 best represents the data. The

1/T expression is commonly used in the field to describe data (see, e.g., [17]) even though, from a theoretical standpoint, it is difficult to motivate. For completeness, we note that the resulting activation energy, Δ is 1.63 eV.

139

Figure 5.9: Logarithmic zero-field mobility as a function of the inverse-square of temperature.

140

Figure 5.10: Logarithmic zero-field mobility as a function of inverse-temperature.

141

In this chapter, the transport properties in organic glass, a disordered medium, were analyzed. The dipole moment plays an important role in controlling [18] the disorder and hence the mobility. Although we have not measured the effect of the dipoles by changing their value, theoretically it can be said that higher dipole moments creates larger disorder and hence lowers mobility. The theoretical model discussed above works well as the expression for mobility fits the experimental results and enables us to extract

parameters such as σ , μ0 , p and Δ . Further work can be done to analyze the effect of the dipole on charge transport experimentally by doping dipolar molecules at different concentrations.

142

5.5 References

[1] S. V. Niviko, Russian Journal of Electrochemistry 38, 165 (2002).

[2] H. Bassler, Phys. Stat. Sol. (b) 175, 15 (1993).

[3] A. P. Tyutnev, Y. F. Kundina, and E. D. Pozhidaev, High Perfomance Polymers

15, 77 (2003).

[4] S. V. Niviko, Journal of Polymer Sciences Part B: Polymer Physics 41, 2584

(2003).

[5] Y. Getmanenko, Ph.D Thesis (Kent State University, 2007).

[6] EHC Inc.

[7] D. H. Dunlap, P. E. Parris, and V. M. Kenkre, Phys. Rev. Lett. 77, 542 (1996).

[8] P. E. Parris, D. H. Dunlap, and V. M. Kenkre, Phys. Stat. Sol. (b) 218, 47 (2000).

[9] R. M. Hill, Phil. Mag. 24, 1307 (1971).

[10] Y. N. Gartstein, and E. M. Conwell, Chem. Phys. Lett. 245, 351 (1995).

[11] D. H. Dunlap, Phys. Rev. B 52, 939 (1995).

[12] S. V. Niviko, and e. al., Phys. Rev. Lett. 81, 4472 (1998).

[13] L. B. Schein, A. Peled, and D. Glatz, J. Appl. Phys. 66, 686 (1989).

[14] H. B. Dieckmann, H. Bassler, and P. M. Borsenberger, J. Chem. Phys. 99, 8136

(1993).

[15] J. G. Simmons, Phys. Rev. 155, 657 (1967).

[16] R. H. Young, and J. J. Fitzgerald, J. Chem. Phys. 102, 2209 (1995).

[17] I. Shiyanovskaya, K. Singer, R. Twieg, L. Sukhomlinova, and V. Gettwert, Phys.

Rev. E 65, 041715 (2002).

143

[18] A. Dieckmann, H. Bassler, and P. M. Borsenberger, J. Chem. Phys. 99, 8136

(1993).

CHAPTER 6

Effect of Mobile Ions on Charge Mobility Measurement

6.1 Introduction

In this chapter we change our emphasis. Previously, we have studied a variety of new materials and tried to understand the roles of disorder and molecular structure in determining charge transport. Here, we use a much-studied liquid crystal as a “guinea pig” and develop and analyze a new technique for use with impure samples. As previously stated, liquid crystalline semiconductors are technologically promising, largely because of the possibility of low-cost, large area fabrication. On the other hand, due to low viscosity as compared to solids, they often allow ions (as opposed to free holes/electrons) to move with relative ease, i.e., their ionic mobilities are often large. This presents a number of problems. First of all, from the experimental point of view, the ion current can interfere with the sensitive charge carrier (e.g. time-of-flight) measurements needed to characterize the material (indeed, this problem has limited the range of materials we can practically study). This can be circumvented by using blocking electrodes – one or more electrodes that do not physically contact the sample. Referring to the description of TOF in chapter 2, one notice that all that is required is an electric

144 145

field in the sample – no charge injection from the electrodes is needed. Preventing

contact between electrodes and the sample also prevents electrochemical reactions

involving the sample. However, the presence of ionic space charge screens the internal

electric field in the sample, changing the environment in which carriers move.

Furthermore the ions themselves move in the field, introducing non-linearities in the

problem and making the determination of the intrinsic (ion-free) electronic properties

difficult. We study these ionic effects experimentally and theoretically in a model liquid

crystal using a simple but complete model of ionic motion in the mesophase. We note

that, while we specialize here to a particular discotic system, the results generalize to any

system, liquid, liquid crystalline, or glassy, that contains mobile ions.

6.2 Experimental

The sample, hexapentyloxytriphenylene (HAT5) [1, 2], was synthesized and

purified by Alex Semyonov, as described in the literature [3]. The molecular structure[4] is shown in Figure 6.1. The shape of the molecule is relatively two dimensional since the central triphenylene core is flat and rigid[4-6] . The attached pentyl groups are highly flexible [7], and lead to the liquid crystallinity of the compound. Specifically, since the overall shape of the molecule is disk-like, HAT5 is called a discotic mesogen (as distinguished from, e.g., the rod-like calimitics previously discussed).

HAT5 exhibits a discotic hexagonal columnar mesophase[2, 8] due to its ability to

self organize into columns [9, 10]. To form the columns, molecules on average stack one

over the other. The stacking may be perpendicular so that the stack axis is perpendicular

146

Figure 6.1: Chemical structure of a HAT5 molecule.

to the plane of the conjugated core or non-perpendicular in which case the stack axis is

tilted with respect to the cores (see Fig. 6.2b) [11-13]. In an isotropic phase, molecules exist in the state of disorder and the column stacking does not exist. The transition from

the crystalline phase to the mesophase, studied with DSC and polarized light microscopy

(Figure. 6.2), was observed at 68.21 0C and from the mesophase to the isotropic phase at

123.0 0C during heating (these temperatures are in agreement with the literature). On

slow cooling from the isotropic liquid to the mesophase, the molecules orient themselves

homeotropically to yield relatively large uniform domains in which all the column axes

are perpendicular to the electrodes [2, 14]. However on rapid cooling, the liquid crystal

shows highly birefringent mosaic textures[9] and corresponds to a state in which there are

147

Figure 6.2: Above: Schematic representation of phases of the discogens (a) homeotropically aligned columnar phase, (b) tilted columnar phase and (c) a disordered non-columnar phase. Below: A DSC curve of HAT5 compound.

148

many domains, each with different relative orientations of the columns.

Optical microscopic views of liquid crystal sample taken under cross polarizer are

shown in Figure 6.3. Since the presence of isotropic material does not change the

polarization of the incident light, the field of view is dark in the isotropic phase, Figure

(6.3a). Upon cooling the material we observed the mesophase with bright and dark

regions, Figure (6.3b). The black domain is the homeotropic hexagonal mesophase [14]

whereas the bright brush-like area is formed due to a defect. Molecular columns inside

the brushes lie parallel to the glass substrate and bend into circles around the brush

centers. The black brushes indicated by arrows are formed where the director coincides

with the direction of polarizer or analyzer. The observed brushes are 900 apart and are

parallel to the crossed polarizer. This indicates that columns are formed by moieties

whose planes are normal to the column axis. If the molecules are tilted with respect to the

column axis, the black brushes would appear at an angle with respect to the polarizer and

analyzer direction [13, 15]. The solid phase obtained by cooling the liquid crystal does

not retain the stacked structure of the columnar discotic mesophase, Figure (6.3c).

As mentioned above, the interface between the electrodes and the sample in a

TOF cell is often problematic. Firstly, it is often the site of destructive electrochemical

reactions, which introduce impurities (traps) to our ultra-pure samples. Secondly, it is potentially a source of current injection (with a time dependence that does not reflect the intrinsic properties of the sample) [16]. Therefore, we are interested in avoiding contact between the sample and electrode by using blocking electrodes. We have prepared simple cells of this type in our laboratory. The schematic of the cell is shown in the Figure 6.4.

149

Figure 6.3: Polarized optical microscopy texture of HAT5: (a) isotropic phase (b) columnar phase at 850C, and (c) a crystalline phase.

150

In the diagram, the top indium tin oxide (ITO) [17] electrode is isolated from the sample

of thickness L2 by glass of thickness L1. The bottom ITO electrode contacts the sample.

The upper electrode works as the blocking electrode to eliminate the dc ionic current and

reduces the electrochemical degradation of the sample. Silica spheres of diameter 20

micron were used as spacers. First, the silica balls were spread around the sides of the

ITO-coated glass placed in the hot stage, after which the cover slip was carefully placed

over it. It was then filled by capillary action with liquid crystal in the isotropic phase.

After cooling to room temperature, the top ITO-coated plate was placed over it. The

assembly was then placed in a spring loaded mount to hold the electrodes firmly together

at fixed spacing.

The cell is effectively two capacitors in series, one filled with glass and the other

with sample. Therefore, the thickness of the sample was determined using the cell

capacitance and the simple formula.

111 =+ CCCngm

where Cn is the net capacitance of the cell, Cg is the capacitance of the capacitor with

glass sandwiched between electrode, and Cm is the capacitance of the capacitor filled with

material. Defining LL121,, A and A2 as the thickness of the glass spacer, thickness of the material, area of the glass and area of the material inside the electrode respectively, and

noting that Since AAA12== is the effective overlap area of the electrode, we can write

above equations as

151

Figure 6.4: Schematics of experimental cell design

ε A LL 0 =+12 Cn ε12ε

⎛⎞ε 0 A L1 L22=−⎜⎟ε (6.1) ⎝⎠Cn ε1

The dielectric constant of the material, is determined by comparing the capacitance of a

Cd10 10 10 micron cell filled with the same material: ε 2 = . We have measured the ∈010A dielectric constant of the material to be 2.8. Similarly the dielectric constant of the blocking electrode glass (cover slip) was measured to be 8.8 (which is a typical value for glass). We now calculate the uncertainties in the thickness of the material. Substituting

ε 2 in equation (6.1), we get the expression for the thickness of material as

152

AC d ⎛⎞11 L =−10 10 (6.2) 2 ⎜⎟ ACC10 ⎝⎠ng

In terms of the uncertainties of the known quantities A,,,,CdCC10 10 g , the uncertainties in

L2 is calculated from the variance using

2 2 222⎛⎞ 22⎛⎞∂∂∂∂∂LLLLL22 2⎛⎞ 2 ⎛⎞ 222 2 ⎛⎞ 2 σσLA=+ σ c⎜⎟ + σ d ⎜⎟ ++ σ c ⎜⎟ σ c⎜⎟ (6.3) 210⎜⎟ 10 ng⎜⎟ ⎝⎠∂∂Ac⎝⎠10 ⎝⎠ ∂ d 10 ⎝⎠ ∂∂ cng⎝⎠ c

where

2 2 1 2 1 2 2 1 2 σ A =∑−AA, σ C =∑()CC10 − 10 , σ Cgg=∑()CC − N ()10 N g N

AC,,,10 Cg Cn were measured a number of times and their averages were calculated.

σ =±0.5μm as given by the manufacturer[2]. Using the above equation (6.3), the error d10 in the thickness of the cell was calculated to be 1.64 μm , which is about 7.7% of 21.2

μm , the calculated thickness of the material using equation (6.1).

A 10 ns Raman-shifted laser pulse of wavelength 320, was used to photogenerate charge. The pulse entering through the top electrode and cover slip was absorbed within a

very thin depth of sample (penetration depth « L2 ). Once again, a suitable wavelength was chosen by combining UV-Vis spectroscopy and measurement of the action spectrum.

Although the UV spectrum, Figure 6.5, shows that maximum absorption occurs for wavelengths close to 300 nm, we have used λ=320 nm because light of wavelength less than 320 is almost completely blocked by the glass. All measurements were taken at 80

0C (discotic mesophase).

153

Figure 6.5: UV absorption spectrum of HAT5

154

6.3 Observations

Table 6.1: Mobility Vs delay time at 80 0C for HAT5

Laser delay TOF μ (×10−32cm / Vs) time (ms) (x 10-5sec)

0.74 6.28 1.81

1.0 6.94 1.64

1.25 7.14 1.60

1.75 7.84 1.45

6.86 8.28 1.37

11.9 8.55 1.33

17.03 8.96 1.27

22.0 9.38 1.21

32.07 9.55 1.19

42.23 9.50 1.20

155

6.4 Theory

We now calculate the electric field within the material of thickness L2 covered by

glass of thickness L1 and the time of flight of the charge carriers. (We will refer to holes

or electrons as charge carriers to distinguish them from ions.) Let ε1 and ε2 be the dielectric constants of the glass and sample material, respectively. The electric field

inside the glass is E01 , while that inside the material is E02 , as shown in Figure 6.4. If V0

is the applied voltage, and V01 and V02 are the voltages across the glass and the sample,

now we can write VV00102=+ V or

VELEL0011022=+ (6.4)

In the absence of ions, there are no free charges at the boundary of the glass and material.

Now we have to use the boundary condition [18] for the electric field ε101EE= ε 202 to get

ε 2021EL VEL0022=+ ε1

V01ε E02 = ()LL12ε + 21ε

ε L VV ==12 00β εε12LLLL+ 21 2 2 where

ε L β = 12 (6.5) ε12LL+ ε 21

156

is a dimensionless quantity. From Gauss’s law [18], E01= σ 0/εε 0 1 and E02= σ 0/εε 0 2

where σ 0 is the surface charge density on the top electrode in the absence of ions and

charge carriers. The surface charge density σ 0 can be obtained as

VELEL0011022=+

σ LLσ =+01 02 ε 01εεε 02 which implies

ε 0120εεV σ 0 = ε 21LL+ ε 12

βεεV = 020 (6.6) L2

The intrinsic time of flight of charge carrier is given by

2 LL22 τ 0 == (6.7) μEV02βμ 0

This is in the absence of ions; the time of flight will be different when ions are present in the sample. Before considering ionic charge density, we note that the best cell would be one in which the blocking electrode is very thin as compared to the sample thickness

2 ( β =1). In that case, the time of flight in the absence of ions will simply be τ 020= LVμ .

Therefore we made many unsuccessful attempts to fabricate very thin layers on ITO electrodes by spin-coating a polymeric insulating layer. We failed in that the layers were never sufficiently resistive. One possibility is that, since the layer was very thin and delicate, it was easily broken by the silica balls used as spacers when pressed by the two

157

electrodes in a spring loaded mount. Another possibility is that dust disrupted the layers over the fairly large areas we were coating (no clean room was readily available).

Therefore it was decided to use a standard glass cover slip as the blocking electrode, which makes the cell extremely simple and inexpensive to construct (albeit complex to analyze).

To probe the effects of ions on charge carrier transport, we invented a technique relying on oscillating electric fields. A square wave ac field of frequency 11 Hz was applied across the cell by using a signal source (Stanford DS345/PS325) and amplifier.

We chose 11 Hz as being long enough so that positive and negative ions (which have much lower mobility than charge carriers) can completely segregate at opposite sides of the sample during one cycle of the field. The photogenerating laser pulse was then fired after a precisely known variable time interval t after the square wave potential changed sign from negative to positive on the top electrode. The timing diagram is shown in

Figure 6.6. We consider the following situation that occurs inside the cell. Assume that, for t < 0 , the upper electrode is negative and bottom electrode is positive. Nearing the end of the 11 Hz cycle, there are two oppositely charged ionic sheets, with the positive ion sheet adjacent to the glass blocking the top electrode and the negative ion sheet adjacent to the bottom electrode.

In a simplified situation assuming infinitesimal thickness of the blocking dielectric and equal charge of the ionic sheets, we may get the following distribution of ionic sheet as a function of time and the corresponding electric field. At t = 0 , the field in the sample is identical to the field of V0. As the potential reverses direction, the positive

158

Figure 6.6: The timing diagram of photo-generation pulse (indicated by arrow) and square wave ac voltage applied across the sample.

ion sheet moves towards the bottom electrode while the negative charge sheet moves toward the top electrode. This creates three regions inside the sample (see Fig. 6.7): (a) the space between the upper electrode and the positive charge sheet, (b) the space between the positive sheet and the negative sheet, (c) the space between the negative sheet and the lower (grounded) electrode. The electric fields in region (a) and (b) are

equal and smaller than E0 , respectively, while the field in region (b) is larger than E0 . The motion of the charge carrier will therefore be slower in region (a) and (c) than in region

(b). At some time determined by the relative motion of the positive and negative ions, the charge sheets will cross. If the mobilities of the ions are equal, the charge sheets cross at the center of the cell. Momentarily they cancel, and the field throughout the cell

becomes E0 . If the laser is fired at this moment, the time of flight of the charge carrier

will be the ion-free time of flight τ 0 (the intrinsic value). After crossing, the field in

159

region (a) and (c) will be equal and larger than E0 , while in (b) will be smaller. As time increases, the ion sheets get more separated and finally reach to the opposite electrodes.

The cell once again will have a field of V0 . Therefore, if fast moving carriers are generated at different times during ionic motion, they move at varying velocities as a function of position in the cell and so TOF is function of ion concentration and mobilities. This effect reduces the effective electric field and therefore the carrier time of flight increases. The effect of the ions on the charge carrier mobility is clearly seen in traces taken at increasing time interval after the potential change signs from negative to positive (Fig. 6.8). This is a simplified situation ignoring nonzero spacer thickness, thermal diffusion and self-repulsion of the ionic clouds.

Figure 6.7: Schematics of the electric field (left) and ion charge sheet distribution at t > 0 , before they cross.

160

We now consider a 1-dimensional theory [19] to describe the ionic motion and carrier transport in an ionically impure sample. We assume that there are an equal number of cations and anions in the sample (actually, we need only assume that the charge densities are equal – the ionic charges may differ). We also assume that we can treat the ions as independent charges, i.e., that ionic space charge effects (which would broaden the ionic sheets) are small. Let the position of the ions and charge carriers be

measured by x with x = 0 at the side of the top glass plate facing the sample, ρ+ (x ) be

the cation density, ρ− (x ) be the anion density, and the total ion density

ρt ()x =+ρρ+− ()xx (). If ρ0 represents the homogeneous (no field) density of cations present in the sample, then the ion layer position at t = 0 can be written as

ρρδρδt ()()x,0txxL==002 −( −)

In the presence of ions, the surface charge density on the top electrode changes with time as the ions move and is represented by σ ()t . The electric fields inside the blocking

electrode ()E1 and inside the material (E2 ) are also a function of time and are given via

Gauss’ law by the following equations:

σ ()t E1 = ε 01ε

σ ()txdxρ ( ) Ex()=+ 2 ∫ ε 02εεε 02

L2 VELExdx=+() 0112∫ 0

161

Figure 6.8: Traces of the hole current for delay times of 1, 1.25, 1.75, 6.86 and 11.9 ms (bottom to top) after the square wave field changes sign from negative to positive on the top electrode. The time of flight increases as the delay time increases (bottom to top).

162

σσ()tL () tL L2 x ρ()x′ dx′ dx V =++12 0 ∫∫ εε01 εε 0200 εε 02

L2 x dx′ dx σσβρ()txL=− (′ ) 02∫∫ 00 LL22

We now pass to a normalized system of units where the equations of motion for the ions are normalized using values for the situation of vanishing ion density i.e.

ρ+−()xx==ρ () 0. For example, all times referring to ionic motion are normalized to the

intrinsic ionic time-of-flight t0 , which is the time of flight of a single ion moving in the

field present in the absence of ions (E02 ) . All charge densities are normalized by σ 0 , the charge on the top electrode in the absence of ions. The carrier time-of-flight, τ , is

normalized to the intrinsic carrier time-of-flightτ 0 , while lengths are normalized to the sample thickness, L2. We will represent normalized quantities by adding a tilde (~). So, for example,

1 x σβρ()t=− 1∫∫ ( x′′ ) dx dx (6.8) 00

where xxL==/,(,)220ρ xtLρσ (,)/ xt . Ionic space charge plays an important role in the internal field in the sample. The field changes with the position of the ion sheet as well as with its concentration. The limiting value of ion concentration is given by ρ ∼ 1 at which ion field equals the applied field. Rewriting the field inside the sample, we find

σ ()txdxρ ( ) E =+ 2 ∫ ε 02εεε 02

163

In the absence of ions, the surface charge density on the top electrode is σ 0 , and the

σ 0 electric field inside the sample is E02 = . The normalized electric field inside the ε 02ε sample is therefore

ExLσ ()tdxx ρ() 22=+∫ EL02σσ 00 0 2

x Ext (,)=+σρ () t (,) xtdx (6.9) 2 ∫ t 0

The change in position of the cations and anions ions in a short time time δt is therefore

given by δ x++= μδExt2 () and δ x−−= −μδExt2 () . These equations can be normalized

by dividing by x0020= μ+ Et.

δ x+ = Et2δ (6.10)

δ x− =−RE2δ t (6.11)

where R is the ratio of anionic to cationic mobility, R = μ− / μ+ .

The motion of ions in the sample was simulated using equations (6.8) to (6.11) for various initial conditions and ionic charge densities. The total charge present of each sign was discretized into 2000 units of equal charge i.e a total of 4000 units of ionic charge.

The position of the charge sheets and the corresponding field was simulated using equations (6.10), (6.11) and (6.9) respectively for the time step of δtx =110−4 sec. Larger numbers of charge bins and a smaller time step did not affect the results. Each “charge” was tracked individually, so that the assumption in the simplified discussion above of sharp ionic charge sheets is relaxed. In other words, ionic space charge may be

164

substantial. Periodically during the ionic simulation, the charge carrier TOF was computed. A charge carrier with mobility μ takes a time ddxExtτ = /μ ( , ) to move a distance dx . Therefore, the time-of-flight for hole or electrons at a time t is

1 dx τ = (6.12) ∫ 0 Ext2 (,)

In using equation (6.12) to calculate the time-of-flight for the charge carrier, we have assumed the following conditions:

a) Carrier time-of-flight is much shorter than ion time-of-flight. This means ions are

frozen during the charge carrier transient and thus the carriers provide a snapshot

of temporal evolution of the electric field in the sample.

b) There are no charge carrier space charge effects, i.e. the total hole or electron

charge per unit area is much less than σ 0 .

The temporal evolution of the electric field obtained from the simulation is qualitatively as shown in the Figure 6.9. There are three different regions of electric field in each snapshot. The motion of the carrier is different in different regions. The carrier time of flight is the sum of the time carriers spent in each region:ττ=+(123)()() τ + τ . If the

laser is fired at a delay time tt= 0′ at which the ion sheets cross (snapshot (d)), the carrier

TOF is an ion-free carrier TOF. As the delay time becomes longer (snapshot (g)), the

carrier TOF is much longer than the ion-free carrier TOF (τ τ 0 ) .

The experiment described here measures the current flowing to the bottom electrode as a function of time after the charge is photogenerated. The theory discussed

165

Figure 6.9: Schematic snapshots of electric fields computed from simulation for various delay times for equal speed of anions and cations. The charge carrier TOF is then computed for each snapshot. During the carrier motion each snapshot is considered to be frozen. Snapshot (d) represents the situation when two ion sheets cross.

above gives the current in terms of the electric field at a given snapshot of time. Consider

a situation where a thin sheet of charge carriers ρσδccc( x,txvt) =−( ) travels across the sample, beginning a time t′ after voltage reversal. If E (txt′;,) represents the snapshot of

the electric field at delay timett= ′ , the carrier velocity is vEtxtcc= μ ()′;, , where μc is the carrier velocity. The current flowing to/from the bottom electrode is

∂∂σ ′ ∂σ ()t Lx =− =βρx′,tdxdx′ ∫∫ c () ∂∂∂ttt00

==βσccvEtxt βσ c μ c ( ′;,) (6.13)

166

The equation (6.13) shows that the experimental traces not only give the carrier TOF, but also give information about the internal electric field in the sample as a function of time, i.e. the details of the ionic distribution as a function of t .

The thermal diffusion of ions, which could change the effective electric field, is taken into consideration in the simulation by adding a zero-mean Gaussian deviate δ x ,

of width σ t to the updated position of the ionic charge density at each time step. Here

σ t = 2Dtδ where D is the diffusion constant which satisfies the Einstein relation

DkTe= μion B / . We normalize δx and δt as previously described and find that the

normalized width σt as

σμtionB2Dtδ 2 kTδ t ==22 LL22 eL 2 or 2kTB δ t σt = eVβ 0

The mean distance the ions will diffuse in time t is 〈〉=x2 2Dt . Normalizing 〈x2 〉

2 by L2 , we get

2kT 〈〉=x2 B t (6.14) eVβ 0

2 where ttt= 0 . If we set t = 1, 〈x 〉 gives the mean ion diffusion length in the same

time cations would take to cross the ion-free cell under influence of the field VL02 2 . For

167

typical experimental parameters ε1 = 9.3, ε 2 = 2.8 , Lm1 =160μ , Lm2 = 21.2μ ,

0 −23 T = 80 C , V = 136 volts, and kB =×1.38 10 J/ sec, we get

ε L β ==12 0.304 εε21LL+ 12 and 〈〉=x2 0.038

Thus the thermal diffusion at the experimental temperature is negligible, unless the space

charge causes the ionic drift to last much longer than t0 , which only occurs for large

values of ρ+−, .

6.5 Results and Discussions

So far we have described the experimental details and the simulation of the experiment. We now analyze the experimental data and compare it to the theory. Figure

6.10 shows the experimental results on HAT5. Points are the actual data whereas the solid line is the fit of the equation (6.12) from the simulation. The x-axis is the delay time t after the potential switches from “-“ to “+” polarity on the top plate, while the y-axis shows the hole time-of- flight, τ . The overall shape of the curve is concaved downward with increasing τ , possibly saturating as t →∞. The best fit of the equation (6.12) to the

experimental data was obtained from the simulation by varying R , ρ+ , t0 andτ 0 .

Theoretical values of normalized TOF are plotted as a function of normalized delay time in Figure 6.11 and Figure 6.12. Figure 6.11 shows the values drawn from the simulation

168

Figure 6.10: Experimental results of the discotic mesophase of HAT5. The x-axis is the delay time between the potential reversal and photogeneration and the y-axis is the hole TOF. Dots are experimental results and solid line is the fit. Inset: Current vs time trace for delay time tms= 17 .

169

Figure 6.11: Theoretical hole TOF as a function of normalized delay time for various ionic charge distribution and two choices of mobility asymmetry. The ρ+ values, in the order from bottom to top for larget , are 0.05, 0.1, 0.25, 0.5 and 1.0.

for two values of R at different values of ρ+ . The nature of the curve is similar to the

experimental curve for small value of ρ+ and it is more complicated (even non-

monotonic) for the large ρ+ for both values of R . The best fit to the experimental result

isρ+ =± 0.39 0.014 . Recall that this is normalized by ion-free surface charge density

ε 0120εεV −52 σ 0 ==×4.8 10Cm / . LL12εε+ 21

σ ρ Therefore, ρ =≈0 + 0.89Cm3 . If the ions are singly charged, this corresponds to a L2 volume density of about 510× 12cm− 3 . Since HAT5 contains 48 carbon atoms, 6 oxygen

170

atoms and 72 hydrogen atoms, its molar mass M is 744 gms. If density D of HAT5 is 1 gm/cm3 (roughly correct), the number of moles in a unit volume is

()nV== DM()1 744 cm−3 . The number of HAT5 molecules in a unit volume

22− 3 is NN==×()1 744A 3.6 10 cm, where N A is Avogadro number. Hence the ion concentration in HAT5 is roughly seven parts per 109 , a very small concentration: this technique is very sensitive indeed to ionic impurities.

The shape of the experimental curve also gives a clue to the relative magnitude of the anionic and cationic mobilities, i.e. of R . In Figure 6.12, the theoretical hole TOF is plotted as a function of normalized delay time for the various R and the fixed charge

density ρ+ . For a small R , τ is quasilinear for a small t and then suddenly increases in slope, a behavior not evident in the data. For a large R , the overall shape of the curves are closer to the experiment. The best fit value is R = 9.5± 1. This indicates that anions move roughly ten times faster than cation ions. Finally the fit also provides an estimation of the

ion TOF, tm0 =±20.4 1.3 sec and the intrinsic carrier TOF τ 0 =±71 .1μ sec . Using

2 equation tLE020220==μ LVβμ, we may estimate the intrinsic ionic mobility:

−62 −52 μ+ =×5.3 10cm / Vs and μμ−+==×R 510cm / Vs . Similarly we can estimate the carrier mobility μ =×1.5 10−32cm / Vs , in reasonable agreement with the literature [20].

The calculations do not appear to be in perfect agreement with the data at large t (see Figure 6.10), especially in regard to the rate at which the data saturate. A major factor neglected in the theory is charge carrier trapping, either by ionic or neutral impurities. Trapping has two effects: it changes the overall shape of the current transient

171

and through multiple trapping it increases the time-of-flight of the carriers. We expect the

latter effect to be relatively small since the measured τ 0 is fairly close to the literature values. The former effect, however, smooths outs the carrier transient making the carrier time-of-flight measurements more ambiguous. Whether this can account for the difference between theory and experiment is unclear.

The analysis of Figure 6.11 gives further insight into the ionic motion in the sample. It helps to address an important question, namely whether it is possible to extract intrinsic charge carrier mobilities from samples containing ions without doing simulations as described above. The answer is yes. For a thin blocking electrode, i.e.

β =1, one simply has to wait a time much longer than the ion drift time. In that case, all ions would be collected adjacent to the opposite electrode and the effective electric field

in the sample would be simply VL02. The corresponding carrier time-of-flight would be

the intrinsic time-of-flight. However, for a larger thickness L1 the situation becomes

complicated. The effective electric field would be βVL02 minus the field of the ions if the ions are completely segregated at the cell walls. The problem is that we do not a priori know the ion density. However, an interesting feature of Figure 6.11 gives a clue as to how to measure the intrinsic mobility in the samples containing ions. In this figure, all of the curves for a wide range of ionic densities cross near t = 1, the intrinsic value.

Thus it appears that by measuring a sample with two or more ionic concentrations, one may extract a carrier mobility close to that of an ion-free sample. This can be done just by plotting time-of-flights as a function of delay time. The point where two (or more) curves

172

intersect gives the intrinsic carrier time-of-flight. The reason for all curves meeting at a point is simple: the sheet of oppositely charged ions present at t = 0 eventually cross in the sample at a point determined by R . At this moment, there is no net ionic charge in the sample and the charge carrier conduction will be unaffected by the ions.

The ionic space charge effects are nonlinear since the field the ions move in depends on their configuration. At extreme large ionic density and a long delay time, ions are collected on the opposite electrodes making the electric field zero. This may lead to the “stagnation” of the carrier movement, i.e. τ →∞. This effect can be seen in Figure

6.11 for large ionic density and long delay time. The upper bound to the ionic charge density can be derived by inserting equation (6.9) to equation (6.8).

1 σβ()tExtdx=−1 ∫ ⎣⎦⎡⎤() − σ() 0

1 11−−=σββ()tExdx ()∫ () (6.15) 0

For a simple case of two ionic charge sheets of densityσs , one located at x = 0 and other of opposite sign at x =1, equation (6.15) implies that E = 0 when the charge density of

the sheet is σβs =−11(). For our cell, β = 0.304 , which gives σs = 1.44. This represents the upper bound to the ionic charge for mobility measurements with a nonzero thickness blocking layer electrode in an ionically impure sample. As the spacer

thickness goes to zero, σs →∞.

The inset in the Figure 6.12 shows E as a function of x for the best fit parameters and delay time corresponding to that of experimental TOF trace shown in the

173

Figure 6.12: Theoretical hole time-of-flight as a function of normalized delay time for fixed ion density and various ionic mobility asymmetries R . Inset: Electric field as a function of position for t = 0.85for parameters corresponding to the best fit to the data.

inset to Figure 6.10. The delay time for this trace is tms= 17 and, from the simulation,

tms0 = 20.4 . That is, the electric field shown in the inset is for t ==()17 20.4 0.83 . The effect of the ionic space charge is evident if we compare the electric field in Figure 6.7, where it is a sharp step function, to that of the field from the simulation shown in the inset of Figure 6.12, where it is smoothed and broadened by the repulsive-driven growth of the ion charge clouds. The simulation shows that the electric field in the sample

Ex()varies by about 35% as a function of x .

In summary, an ionic space charge can significantly affect the time-of-flight measurement when using a blocking electrode. We have developed a theory and obtained

174

a carrier mobility that is quantitatively in agreement with the literature. One may utilize this simple model of ionic and a carrier charge motion in two ways. On the one hand, the

TOF data offers insights into the ionic motion in a liquid crystal itself. On the other hand, by measuring the carrier time-of-flight for various ionic concentrations (or by modeling the data as we have done above), one can extract the intrinsic (ion free) carrier mobility.

175

6.6 References

[1] R. Bushby, and O. Lozman, Curr. Opin. Solid State Mater. Sci. 6, 569 (2002).

[2] D. Adam, F. Closs, and e. al., Phys. Rev. Lett. 70, 457 (1993).

[3] A. N. Semyonov, Ph.D Thesis (Kent State University, 2007).

[4] V. Duzhko, H. Shi, K. Singer, A. Simyonov, and R. Twieg, Langmuir 22(19),

7947 (2006).

[5] R. Bushby, and O. Lozman, Current Opinion in Colloid & Interface Science 7,

343 (2002).

[6] R. J. Bushby, and et.al., J. Mater. Chem. 13, 470 (2003).

[7] K. J. Donovan, and et.al., Mol. Cryst. Liq. Cryst. 396, 91 (2003).

[8] H. Lino, J. I. Hanna, and at.el, App. Phys.Lett. 87, 192105 (2005).

[9] H. Lino, J. I. Hanna, and et.al., J. Appl. Phys. 100, 043716 (2006).

[10] I. Shiyanovskaya, K. Singer, V. Percec, T. K. Bera, and M. Glodde, Proc. SPIE

4491, 242 (2003).

[11] S. Chandrasekhar, and V. Balagurusamy, Proc. R. Soc. Lond. A 458, 1783 (2002).

[12] H. Fujikake, T. Murashige, M. Sugibayashi, and K. Ohta, Appl. Phys. Lett. 85,

3474 (2004).

[13] M. O'Neill, and M. K. Kelly, Adv. Mater. 15, 1135 (2003).

[14] K. Yoshino, H. Nakayama, M. Ozaki, M. Onoda, and M. Hamaguchi, Jpn. J.

Appl. Phys. 36, 5183 (1997).

[15] I. Shiyanovskaya, K. Singer, V. Percec, T. K. Bera, Y. Miura, and M. Glodde,

Phys. Rev. B 67, 035204 (2003).

176

[16] H. Zang, and J. Hanna, J. Appl. Phys. 88, 270 (2000).

[17] EHC Inc.

[18] D. J. Griffith, Introduction to Electrodynamics (Prentice-Hall, 2002).

[19] C. Pokhrel, N. Shakya, S. Purtee, B. Ellman, A. Semyonov, and R. Twieg, J.

Appl. Phys. 101, 103706 (2007).

[20] V. Duzhko, A. Semyonov, R. Twieg, and K. Singer, Phys. Rev. B 73, 064201

(2006).

Chapter 7

Summary

In this dissertation, we have studied the entire gamut of organic semiconductors, including crystals, liquid crystals, and amorphous glasses.

Research interest in organic semiconductors is growing due to their potential use in many electronic devices including light emitting diodes, transistors, photovoltaic cells, and printing and copying technology. To reiterate some of the potential advantages of these materials, organic semiconductors:

1. are often easier to purify

2. are highly compatible with flexible substrates

3. are suitable for uniform large-area thin film devices (e.g. organic LED displays)

4. exhibit tunable electronic and opto-electronic qualities

In this dissertation, we studied transport in various regimes of disorder, the understanding of which might help further development of this promising technology.

For example, chapter four reviewed hole conduction in certain pyridine/thiophene- containing calamitic liquid crystals, which are an interesting class of organic semiconductor because of their variable degree of molecular ordering, e.g., poorly ordered nematic phase to highly ordered smectic phases. Compounds based on pyridine and thiophene are particularly interesting because they often have more ordered (and therefore potentially higher mobility) mesophases. Photocurrent traces in terpyridine

177 178 based liquid crystals were analyzed with reference to the two most-cited models- the

Scher-Montroll model of non-Gaussian disorder and Bassler’s Gaussian disordered model. Our data do not support the former: two important characteristics of the Scher-

Montroll model - universality of current traces and the sum of the post-transit and pre- transit straight line slopes being a fixed constant - are not displayed by the data. This lead us to conclude that our data do not follow the Scher-Montroll model. However, the mobility variation as a function of electric field is in good agreement with the prediction of the Gaussian disorder model. The mobility in this compound is relatively low ( ∼ 10−4 cm2/Vs) compared to the high degree of ordering (SmF). In combination with work we have done on another pyridine-containing compound, these results call for a careful assessment of the possible role of pyridine rings in lowering the mobility of liquid crystalline organic semiconductors. In another sample, a thiophenyl-bipyridine based liquid crystal, the mobility values were extremely low ( ∼ 10−6 cm2/Vs), independent of the electric field, supporting the argument that charge transport exhibited in this material is ionic in nature. An analysis of the properties of this transport was carried out.

Chapter five reviews our study of the charge transport mechanism and mobility measurements in an extremely disordered glassy medium. In such a system, the potential energy landscape over which the charge moves is not periodic and uniform but completely random. In our system, we believe that the disorder in energy arises due to variations in charge-dipole interaction energies. Since the charge-dipole interaction is long range, the energy of the charge transport sites is spatially correlated. A theory, the correlated disorder model (CDM) of Kenkre, Dunlap, and others, is used to describe the charge transport phenomena. The mobility in this material is relatively low, of the order 179 of 10-5 cm2/Vs. The electric field dependence of hole mobility is Poole-Fremkel type, i.e. log μ ∝ E . The theory was quite successful in quantitatively describing the data, and allowed for the extraction of several important parameters, including the width of the energy distribution, activation energy, and dipole moment of the molecule.

The effect of ions on the transport of charge carriers and measurements of mobility in a typical discotic liquid crystal (HAT5, a relatively ordered system) was studied and discussed in chapter six. The presence of free ions not only may overwhelm the sensitive transient current from holes and electrons, but also changes the internal field making the intrinsic carrier mobility difficult to measure. Here we develop and test a simple theory that completely describes and allows the modeling of these effects. Hole time-of-flight data on a sample of the discotic liquid crystal hexapentyloxytriphenylene containing ionic impurities were obtained. By photogenerating holes at various times after reversing the potential across the cell, we have studied the effect of ions on the measured TOF for various ionic spatial configurations. Comparing the results with the simulations of the coupled ionic/hole transport, we address the question of whether reliable charge transport data can be extracted from impure samples. Alternatively, we show how TOF experiments provide a useful probe of the spatiotemporal evolution of ionic charge densities under an applied potential.

There are numerous opportunities raised by this work for future exploration. For example, as noted above, we believe that fluctuations in the charge-dipole interaction energies are responsible for the Poole-Frenkel-like conduction in the glass. This hypothesis can be tested by measuring the effect of dipole concentration experimentally on charge transport by doping the dipolar molecules at different concentration into the 180 transport medium. Another difficult, but exciting idea, is to dope a glass or liquid crystal

(or even a crystal) with azobenzene impurities. This class of compounds has the property of changing from trans to cis configurations on irradiation with specific wavelengths of light. In other words, we can change the dipole moment of these impurities externally and, in principle reversibly.

Obviously, further work is needed on pyridine-containing calimitics with high- order smectic phases. A set of such compounds is in hand (courtesy of R. Twieg and Y.

Getmanenko) and studies on them are continuing. At the same time, ab-initio calculations of the electronic properties of the cores of such semiconductors are also needed.

The coupled ion/carrier transport theory here developed is a tool which should increase the range of materials we can study. It may prove particularly valuable in, e.g., research on the effects of irradiation on transport in liquid crystalline semiconductors

(e.g., for radiation-hard materials [1] or photovoltaic under solar irradiation). The technique of using square-wave potential with precisely timed photoexcitation pulses also offers the possibility of measuring ionic motion in a liquid crystal on short length- and time-scales using the charge carriers as probes. Effectively, this offers another method of characterizing the local (microscopic) viscosity of the mesophase.

[1] K. Hudson, and B. Ellman, Appl. Phys. Lett. 87, 152103 (2005).