Photorefractivity in polymers

Photorefractivity in polymers

George G. Malliaras

Photorefractivity in Polymers George G. Malliaras Ph.D. Thesis University of Groningen, The Netherlands November 1995 ISBN 90-367-0569-x

RIJKSUNIVERSITEIT GRONINGEN

Photorefractivity in polymers Proefschrift

ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus Dr. F. van der Woude in het openbaar te verdedigen op maandag 18 december 1995 des namiddags te 2.45 uur precies

door George Malliaras geboren op 5 juni 1969 te Serres, Griekenland

Promotor: Prof. Dr. G. Hadziioannou

Contents Preface

1

1. Introduction 3 Abstract ..............................................................................................................3 1.1. The photorefractive effect......................................................................4 1.2. Standard model for photorefractivity .....................................................6 1.3. Photorefractive nonlinear optics...........................................................10 1.4. Photorefractivity in polymers...............................................................13 1.5. Aim and outline of this thesis...............................................................17 1.6. References ..........................................................................................18 2. Experimental 21 Abstract ............................................................................................................21 2.1. Introduction ........................................................................................22 2.2. Sample preparation .............................................................................22 2.3. Photoconductivity measurements.........................................................26 2.4. Electrooptic measurements ..................................................................27 2.5. Second harmonic generation measurements..........................................29 2.6. Diffraction efficiency and response time measurements........................31 2.7. Two beam coupling measurements ......................................................36 2.8. Transient holographic and photoconductivity measurements.................39 2.9. References ..........................................................................................42 3. Photorefractivity in poly(N-vinylcarbazole) based composites 43 Abstract ............................................................................................................43 3.1. Introduction ........................................................................................44 3.2. Results and discussion.........................................................................44 3.2.1. Optical absorption ....................................................................45 3.2.2. Photoconductivity .....................................................................47 3.2.3. Orientational mobility of the nonlinear optical molecules and electrooptic response of poly(N-vinylcarbazole) based photorefractive composites........................................................48 3.2.4. Proof for the photorefractive nature of the observed gratings. Properties and comparison with the standard model...................53 3.2.5. Asymmetric energy exchange in poly(N-vinylcarbazole) based photorefractive composites..............................................62 3.2.6. The mechanism of the refractive index change...........................65 3.3. Conclusions and outlook......................................................................67 3.4. References ..........................................................................................68

4. Charge trapping in photorefractive polymers 71 Abstract ........................................................................................................... 71 4.1. Introduction........................................................................................ 72 4.2. (Quasi-) steady state holographic experiments..................................... 73 4.2.1. The response time of the photorefractive grating ....................... 75 4.2.2. The phase shift of the photorefractive grating............................ 77 4.2.3. The amplitude of the photorefractive grating............................. 78 4.3. Transient holographic experiments...................................................... 80 4.3.1. Space charge field formation .................................................... 81 4.3.2. Influence of the trap density on the space charge field formation ......................................................................... 86 4.4. Conclusions and outlook..................................................................... 88 4.5. References.......................................................................................... 88 5. The transient behaviour of the space charge field 91 Abstract ........................................................................................................... 91 5.1. Introduction........................................................................................ 92 5.2. Results and discussion........................................................................ 95 5.2.1. Electric field, temperature and drift length dependence of the hole drift mobility......................................... 95 5.2.2. Comparison with the standard model ........................................ 99 5.2.3. The influence of disorder........................................................ 100 5.3. Conclusions and outlook................................................................... 104 5.4. References........................................................................................ 105 List of abbreviations

106

List of symbols

107

Summary

109

Samenvating

111

List of publications

113

Preface Polymers are not considered as traditional materials for optoelectronics. Although there is by far more plastic than silicon in every computer, isn’t it in the wrong place: around the microchip instead of inside it? In recent years however, more and more devices made almost entirely out of polymers, such as nonlinear optical elements, transistors, light emitting diodes, solar cells, optical fibers, etc. become available. The observation of the photorefractive effect in a polymer in 1991 was yet another manifestation of this “plastic revolution”. The field of polymer photorefractivity is fairly young and most of the research effort has been concentrated on exploring the limits of performance of these materials. A great variety of polymer architectures that show this effect has been synthesized as the race for the best one (in terms of gain coefficient, diffraction efficiency, response time, etc.) still goes on. In this thesis, however, I followed a different line: by focusing on one model polymer composite and systematically studying its properties, I hoped to gain insight into the mechanism of photorefractivity in this class of materials. Although this composite exhibited the highest gain ever in the beginning, it is by now rather moderate in terms of performance compared to newly developed photorefractive polymers. Several more efficient compounds have been synthesized in our laboratory and even the same composite has been improved to show a diffraction efficiency which is more than ten times as high. However, instead of outlining how to optimize a material, I have tried to put together experimental results that show the underlying physics governing the photorefractive effect in polymers. Although it is still too early to tell whether photorefractive polymers will find any practical application, my personal view is optimistic. The tremendous pressure to succeed in efficiently processing and storing the billions of data bytes of information produced every day, combined with the great potential of these materials, may lead to the computer of the next generation.

Acknowledgements I will always recall with fondness my four-year stay in Groningen. It has truly been a privilege and a rewarding experience to work in the creative atmosphere of the group of Prof. Dr. Georges Hadziioannou. First and foremost I would like to thank him for the trust he has shown in me, his continuous guidance, support and encouragement and for being an inexhaustible source of ideas and inspiration. I am grateful to Dr. Victor Krasnikov, who gave me expert guidance and generous professional support. Apart from being my closest colleague he became my best friend. I am also grateful to the chemist of the “photorefractive team” , Henk Bolink, for synthesizing and purifying the compounds used in this thesis, but also for the fun we had together in the lab. My special thanks go to the members of the reading committee, Prof. Dr. Albert Pennings, Prof. Dr. Douwe Wiersma and Prof. Dr. Campbell Scott (IBM Almaden Research Center, USA) for carefully reading the manuscript and for their insightful comments.

2

Preface

I would also like to thank all those who helped me with my graduate studies: Dr. Paul van Hutten for the very interesting scientific and philosophical discussions and for carefully reading and correcting most of my papers; the theoreticians of the group of Polymer Chemistry, Henk Angerman and Prof. Dr. Gerrit ten Brinke for fruitful discussions; Prof. Dr. Albert Pennings and his group for helping me with their expertise in polymer processing; Prof. Dr. Douwe Wiersma, Dr. Koos Duppen, Ben Hesp and generally the group of Chemical Physics for stimulating discussions and for helping with setting up the optoelectronics laboratory; Prof. Dr. Jan Kommandeur for helpful discussions and valuable suggestions on the subject of charge trapping; Dr. Homer Antoniadis (Hewlett-Packard Laboratories, Palo Alto, USA) for suggestions on the subject of charge transport; Prof. Dr. Teun Klapwijk for fruitful discussions; my former supervisors Prof. Dr. Kostas Kambas (Aristotle University, Thessaloniki, Greece) and Dr. Theo Rasing (University of Nijmegen) for their continuous interest and encouragement; finally, my colleagues Jurjen Wildeman, Hendrik-Jan Brouwer, Gerald Belder, Vagelis Manias, Jan Herrema, Richard Gill, Diny Hissink, Vasilis Koutsos, Dominique Morichère, Yiannis Papantoniou, Alain Hilberer, Amar Mavinkurve, Geert Berentschot, Erik Kroeze and the rest of the group for help, stimulating discussions and lots of fun! While setting up the optoelectronics lab, I enjoyed the assistance from my student Roy Gerritsen and the help of Aldert Meulema and Adams Verweij in technical and administrative matters. I am grateful to Nanno Herder, Anne Appeldoorn and Henk Knol, for helping me with the electronics, mechanical constructions and glassware. Thanks are due to Ulco and Sjouke from the library, for assistance with the literature research. I would like to express my special thanks to Hans Beekhuis and his colleagues for checking up the lab every night and to our secretaries, Marjan, Daphne, Ingrid and Betty, for arranging thousand things for me. Last, but not least, my family, though so far away, has always been close to me, making me feel safe. There is no word in the dictionary to fully express my gratefulness. I am also grateful to Stefania, for her unconditional love and support during all this period. The optoelectronics lab was set up with the financial support from the Faculty of Mathematics and Physical Sciences of the University of Groningen, the Dutch Ministry of Economic Affairs, the Stichting Toegepaste Wetenshappen (STW) and the Stichting Scheikundig Onderzoek Nederland (SON). This thesis was shaped on the basis of feedback that I got from presentations at various conferences. This was made possible with the generous financial support from the University of Groningen, the Department of Polymer Chemistry, the Materials Science Centre, the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) and Shell Nederland B.V. All the above are gratefully acknowledged. George G. Malliaras November 1995

Stellingen 1. The existence of photorefractivity in polymers creates the opportunity to study the processes of charge transport and trapping in this class of amorphous materials with optical techniques. 2. Some ideas that are promoted as “new” can be found in older Russian journals. 3. The electrooptic coefficients r33 and r13 do not apply in the waveguide geometry used by Yu at al. Yu et al., Macromolecules 26, 2216 (1993) 4. The zero degrees phase shifted gratings observed by Silence at al. in the polymer PVK:Lophine 1:TNF can also be attributed to a photorefractive response, limited by a large amount of traps. S.M. Silence et al., Appl. Phys. Lett. 64, 712 (1994) 5. The recent development of a holographic lock by Holoplex (briefly described by Psaltis et al.), shows the tremendous potential of optical computing schemes. D. Psaltis and F. Mok, Scientific American, p. 52, November 1995 6. Unnecessary use of complicated terminology and formalism does not imply great science but charlatanism. 7. It is very important for Ph.D. students to present their work at international conferences (not forgetting, it's important for post-docs too!). 8. It takes courage to give up hope, but more courage to keep it. 9. The fact that one can "buy" in advance his own funeral is yet another sign of the degradation of family values. 10. There are two types of optimists: Those who claim things could not be better and those who realize that things could have been much worse. 11. A car is not just a means of transportation from point A to point B: Quality makes the difference. 12. Multitasking in OS/2 can greatly improve someone’s productivity. However, it requires at least 16 MB to run decently. 13. All those who claim to be 100% politically correct should not say "walkman" but "walkperson". George G. Malliaras December 1995

Chapter One Introduction

Abstract In this chapter, a concise introduction to photorefractivity is made. Using the simplest case of the band transport model, the steady state and the dynamics of the space charge field are surveyed. The theory of two beam coupling in photorefractive media is briefly outlined, as it will be useful for the understanding of the experimental results. The main lines behind the engineering of polymers which show the effect follow and the introduction closes with the outline of this thesis. References are given not only to the original work but to several recent reviews, which can serve as a guide to the literature.

4

Chapter One

1.1. The photorefractive effect The photorefractive effect was accidentally discovered in 1966 in LiNbO3 and LiTaO3 as detrimental optically induced refractive index inhomogeneities [1]. It was referred to as "optical damage" because it caused a degradation of the performance of nonlinear optical devices based on these materials. Two years later, holographic optical storage has been demonstrated in LiNbO3 using this newly discovered effect [2]. In 1969, Chen proposed a model based on the migration of photoexcited electrons which explained the main experimental observations and set the basis for future experimental and theoretical work [3]. The term photorefractive, which literally means light induced change of the refractive index, was introduced later on and since then has been reserved for this particular mechanism. In 1976, Kukhtarev et al. derived the dependence of the refractive index change on light intensity and material parameters and described the coupling of beams in thick photorefractive gratings [4]. Today, almost 30 years after its first discovery, photorefractivity is a blooming field of interdisciplinary research. Over the years several materials like BaTiO3, KNbO3, Bi4Ti3O12, Sr1-xBaxNb2O6 (SNB), Ba2-xSrxNayNb5O12 (KNSBN), Bi12SiO20 (BSO), Bi12GeO20 (BGO), GaAs, InP, CdTe, (Pb,La)(Zr,Ti)O3 and many other have been shown to exhibit the photorefractive effect [5,6], which makes it a quite general property of electrooptic crystals. Numerous applications in optical data storage, image processing and amplification, self and mutually pumped phase conjugation, photorefractive resonators, programmable optical interconnects, simulation of neural networks etc. have been proposed and demonstrated on a laboratory scale [6,7]. Apart from potential applications, intensive research has been triggered for the understanding of the microscopic origin of the photorefractive effect, resulting in the discovery of new phenomena, such as the bulk photovoltaic effect [8] and the excited state polarization [9]. Today, the mechanism of photorefractivity, although not fully, is quite well understood. This led to the recent observation of photorefractivity in new classes of materials such as organic crystals [10], polymers [11] and liquid crystals [12]. In figure 1.1, the basic mechanism is explained. The photorefractive effect is observed in materials which are both electrooptic and photoconducting. If such a sample is illuminated with a nonuniform light intensity pattern resulting from the interference of two mutually coherent beams, charge generation will take place at the bright areas of the fringes. These photogenerated charges will migrate and eventually get trapped at the dark areas, a process which can take place through several circles of photogeneration, diffusion and trapping. The resulting charge redistribution creates an internal electric field, the space charge field ESC, which changes the refractive index via the electrooptic effect. The space charge field forces the charges to drift in the opposite direction than diffusion and a dynamic equilibrium is reached when it has grown strong enough to

Introduction

5

cause a drift current which totally compensates the diffusion current. Application of an external electric field assists charge separation through drift and generally a higher space charge field can be produced in this way.

_

_ _

_

_

_

illumination charge generation & migration

+

+

+ +

+ +

x

• _

_

+ + +

_

_

_

+ + +

_

_•

charge redistribution

ϕ space charge field and refractive index grating

Fig. 1.1 : Mechanism of the photorefractive effect. A sinusoidal distribution of light intensity causes spatially modulating charge generation. The mobile charges diffuse and get trapped at the dark areas. A space charge field is established which changes the refractive index via the electrooptic effect.

From the above it is clear that the photorefractive effect provides a way to replicate light intensity patterns into refractive index gratings, with obvious potential applications in optical data storage. Several other mechanisms can do the same thing though: photochemical reactions, thermorefraction, formation of excited states, conventional χ(3) etc. can change the refractive index in the illuminated parts of a sample [13]. The photorefractive effect however processes a combination of

6

Chapter One

characteristics which make it unique: Very high nonlinearities can be achieved even with weak laser beams, as a result of the integrating nature of the effect. The resulting refractive index gratings are reversible, as uniform illumination will erase the space charge field. Another very important characteristic, is the existence of a spatial phase shift between the illumination pattern and the refractive index grating. This is the genuine signature of the photorefractive effect: No other mechanism can produce a phase shifted refractive index grating. As will be discussed below, the existence of this phase shift gives rise to steady state asymmetric energy exchange between two laser beams, which is the basis for several specific applications. Apart from applications, the photorefractive effect provides a means to investigate materials properties such as charge transport and trapping, with "clean" optical techniques. Steady state and transient holographic techniques can be employed to measure small photocurrents optically, expelling the need for sensitive electronic equipment. Moreover, the bulk of the sample is directly probed, eliminating electrode problems. Parameters like charge diffusion lengths, mobilities, trap densities and cross sections etc. are measured in this way [14].

1.2. Standard model for photorefractivity The model of Kukhtarev et al. has been very useful in helping to understand the microscopic origin of photorefractivity in inorganic crystals. To some extent, photorefractivity in polymers can also be understood along the same lines. For this reason a basic description of this model is presented here. In figure 1.2, the basic idea for the space charge field formation is illustrated, for the case of electron transport and a single participating impurity level. Depicted are the valence (EV) and the conduction (EC) band, together with donor (D) and acceptor (A) impurity levels. The only role of the acceptors is to deprive some of the donors from their charge, creating an initial concentration of empty traps. Let ND be the total donor density and ND+ the density of the ionized ones which act as traps. In the dark, electrical neutrality demands ND+=NA, where NA is the density of acceptors. Let the crystal be illuminated with a sinusoidal intensity pattern: I=I0(1+mcos(KGx))

(1.1)

where m is the modulation index and KG is the grating wave vector. According to this model, the space charge field is created through the steps of photoionization of a donor in the bright areas of the fringes (step 1 in figure 1.2), transport of the electron in the conduction band (step 2 in figure 1.2) and subsequent trapping at an ionized donor level (step 3 in figure 1.2).

Introduction

7

The rate of formation of ionized donors has a generation term, proportional to the light intensity and the density of donors that can be ionized, plus an annihilation term proportional to the available density of electrons in the conduction band and the trap density: ∂ND+(x)/∂t=sDI(x)(ND-ND+(x))-γDn(x)ND+(x)

(1.2)

where sD is the photogeneration rate, γD is the trapping rate and n is the electron density in the conduction band. 2 EC

hv

3

1

+

+

-

x

D

A EV

Fig. 1.2 : Band transport model for the photorefractive effect. Electrons are photoexcited (1) from donor states (D) to the conduction band (EC), where they migrate (2), until they get trapped at ionized donor sites (3). Acceptors (A) are present to create a few initially empty traps.

Electrons are mobile once in the conduction band and their density changes not only due to photogeneration and trapping, but also due to transport. The continuity equation is written: ∂n(x)/∂t=∂ND+(x)/∂t+(1/e)∂J(x)/∂x

(1.3)

where e is the electron charge and J the current density, which is a result of drift and diffusion: J(x)=µdren(x)E(x)+kBTµdr∂n(x)/∂t

(1.4)

8

Chapter One

where µdr is the electron drift mobility, E is the total electric field (space charge plus externally applied electric field), kB is the Boltzmann constant and T the absolute temperature. The Einstein equation of diffusion has been used in equation (1.4). The total electric field is calculated from Poisson's law: ∂E(x)/∂x=e(ND+(x)-n(x)-NA)/ε

(1.5)

where ε is the dc dielectric constant. In the limit of small modulation (m<<1), the spatial variation of ND+, n, J and E is small and it can be represented only by the zeroth and the first harmonic in a spatial Fourier expansion. Assuming that ND >> NA >> n and sDI<<γNA, which is true in the majority of photorefractive materials, the steady state and the dynamics of the space charge field can be derived from equations (1.2)-(1.5). In the steady state the complex amplitude of the first Fourier component of E is [15]: E1=ESCexp[-iϕ]=mES(iED-E0)/(ED+ES+iE0)

(1.6)

where ESC is the space charge field, E0 is the externally applied electric field, ED is the diffusion field, equal to: ED=kBTKG/e

(1.7)

and ES is the saturation field, equal to: ES=eNA/εKG

(1.8)

From equation (1.6) it follows that the space charge field cannot exceed mES, which corresponds to the limit where all the traps in the dark areas have been filled. The maximum value of the space charge field thus is set by the experimental geometry, the trap density and the dielectric constant of the material. In the absence of an external electric field, ESC will be limited by the smallest of ED and ES (multiplied by m): Even if there are plenty of traps available, the maximum electric field that can be achieved by diffusion alone cannot exceed mED. The dependence of ESC on the external electric field can be understood from figures 1.3 and 1.4, where the amplitude and the phase shift of E1 are shown as a function of E0 for m=0.01 and for three different values of the saturation field, which correspond to trap densities 3.8⋅1015, 3.8⋅1016 and 3.8⋅1017 cm-3 for ε=3.5ε0. The grating spacing is set to 1.6 µm (actual value for the experiments described in the third

Introduction

9

chapter), which leads to a diffusion field equal to 0.1 V/µm. The space charge field increases linearly for low values of E0. As E0 approaches the saturation field, ESC slowly saturates to a value equal to mES. At the same time, the phase shift, which is 90 degrees for the case of pure diffusion, reaches a minimum and asymptotically tends back to 90 degrees for electric fields higher than the saturation field.

space charge field (V/ µm)

1.0

ES = 5 V/µ m ES = 50 V/µ m ES = 500 V/µ m

0.5

0.0

0

25

50

75

100

electric field (V/µ m) Fig. 1.3 : The space charge field as a function of an externally applied electric field, for m=0.01, ε=3.5ε0 and for three different values of the saturation field, which correspond to trap densities 3.8⋅1015, 3.8⋅1016 and 3.8⋅1017 cm-3. The grating spacing is set to 1.6 µm, which leads to a diffusion field equal to 0.1 V/µm.

The set of equations (1.2)-(1.5) yields also the transient behaviour of the space charge field. During grating growth, the complex amplitude of the first Fourier component of E is [15]: E1(t)=E1(0)(1-exp[-t/τ])

(1.9)

E1(t)=E1(0)exp[-t/τ]

(1.10)

and during erasure:

10

Chapter One

where E1(0) is the steady state value given by equation (1.6) and τ the response time. In the general case, the response time is a complex number, causing oscillatory behaviour of the space charge field during grating growth. However, in the large grating spacing regime, τ is real and is inversely proportional to the photoconductivity σph and the light intensity [15]: τ-1 ∝ σphI

(1.11)

From equations (1.6) and (1.11) it can be seen that although the magnitude of the effect does not depend on light intensity, the response time does.

phase shift (degrees)

90

60

ES = 5 V/µ m ES = 50 V/µ m

30

ES = 500 V/µ m

0

0

25

50

75

100

electric field (V/µ m) Fig. 1.4 : The phase shift of E1 as a function of an externally applied electric field, for the same parameters as the space charge field.

Several extensions of this model with various degrees of complexity have been introduced, including simultaneous electron and hole transport and multiple impurity levels [16]. However, this simple picture is enough to qualitatively understand most of the results described in this thesis.

1.3. Photorefractive nonlinear optics Two waves that interfere inside a photorefractive material create a space charge field, which generates a refractive index grating via the electroooptic effect. In

Introduction

11

the case of a linear (Pockel's) electrooptic response, the amplitude of the first Fourier component of the refractive index grating is given by: n1=-(1/2)n03reffE1

(1.12)

where n0 is the refractive index and reff the effective electrooptic coefficient, which depends on the experimental geometry. The fact that E1 is complex implies the existence of a spatial phase shift ϕ between the refractive index grating and the illumination pattern. As a result of this phase shift, the two waves that interfere to write the grating couple with it, exchanging intensity and phase information. More specifically, the interference of an incident wave with its own diffracted wave (which is phase delayed by π/2), creates a new grating which adds to (or subtracts from) the initial one. Since this new grating is also phase shifted, energy transfer between the incident and the diffracted wave takes place and so on. As a result of this dynamic behaviour, asymmetric energy exchange between the two initial waves takes place and the whole process of grating formation needs to be treated in a self consistent way.

I1 ϑ I2

0

z

d

Fig. 1.5 : Two mutually coherent beams with intensities I1 and I2, incident in a symmetric geometry at an angle ϑ on a photorefractive sample with thickness d.

Consider a photorefractive sample which is illuminated as shown in figure 1.5 with the interference of two coherent beams. The application of the coupled wave theory leads to [15]:

12

Chapter One cosϑ(d/dz)I1=-ΓI1I2/(I1+I2)-αI1

(1.13a)

cosϑ(d/dz)I2=+ΓI1I2/(I1+I2)-αI2

(1.13b)

Γ=(1/m)(π/λ0)n03reffESCsinϕ

(1.14)

where:

with α being the absorption coefficient and λ0 the wavelength of light in vacuum. From the above set of equations it is clear that an asymmetric, steady state intensity exchange will take place between the two beams, which will be maximum for ϕ=π/2. The direction of the energy exchange is determined by the sign of Γ and can be used to identify the type of the mobile carrier if the sign of the effective electrooptic coefficient is known. Thus, one can use a photorefractive material to transfer optical energy from a pump beam (I1) to a probe beam (I2). In the case where I1(0)>>I2(0) and the pump can be considered undepleted, equations (1.13) yield: I1(l)=I1(0)exp[-αl]

(1.15a)

I2(l)=I2(0)exp[(Γ-α)l]

(1.15b)

The definition of Γ as a gain coefficient is clear from the above equations. If Γ>α, the probe beam will experience net gain of energy after a single pass from the sample. Except from the experimental geometry, Γ depends on material parameters and external electric field. In figure 1.6, the dependence of Γ on electric field was calculated for the same parameters as the space charge field and the phase shift in figures 1.3 and 1.4. The refractive index was taken to be 1.7 and the electrooptic coefficient 10 pm/V at 633 nm. A superlinear dependence at small electric fields is followed by an almost linear increase, which becomes sublinear and levels off at fields comparable to the saturation field. For the above plot, material parameters (electrooptic coefficient, dielectric constant, refractive index, electrooptic constant etc.) that are typical for organic compounds have been used. As can be seen, gain coefficients in the order of several tens of cm-1 are expected from theory for these materials. Consider now the case of some inorganic photorefractive crystals. BaTiO3 has a dielectric constant equal to 3600ε0 and the product n03reff is approximately 23000 pm/V [6]. For a geometry that yields ED=0.1 V/µm and a trap density of 1016 cm-3, the saturation field is an order of magnitude lower than the diffusion field and application of an external electric field will not lead to an enhancement of the gain coefficient. For the case of pure diffusion and at 633 nm, a gain coefficient of 114 cm-1 is expected

Introduction

13

according to theory. For LiNbO3 the dielectric constant is equal to 32ε0 and the product n03reff is approximately 330 pm/V [6]. For the same parameters as in the previous example, the saturation field is equal to 1.4⋅106 V/µm and while for the case of pure diffusion Γ=1.4 cm-1, with the application of an external electric field of 50 V/µm, a gain coefficient of 23 cm-1 is predicted. Experimentally, values for the gain coefficient up to a few tens of cm-1 are typically measured in these materials [6]. 100

ES = 5 V/µ m ES = 50 V/µ m ES = 500 V/µ m

gain coefficient (cm-1)

75

50

25

0

0

25

50

75

100

electric field (V/µ m) Fig. 1.6 : The gain coefficient as a function of an externally applied electric field, for m=0.01, ε=3.5ε0 and for three different values of the saturation field, which correspond to trap densities 3.8⋅1015, 3.8⋅1016 and 3.8⋅1017 cm-3. The grating spacing is set to 1.6 µm, which leads to a diffusion field equal to 0.1 V/µm. The refractive index was taken to be 1.7 and the electrooptic coefficient 10 pm/V at 633 nm.

1.4. Photorefractivity in polymers Despite the numerous potential applications that have been proposed for photorefractive materials, none of them has ever been realised on a broad commercial scale. One reason may be that optical processing schemes are highly task specific, meaning that a certain layout of optical components is only used to perform a unique operation. In addition to that, they are bulky and rather complicated, demanding trained personnel for their operation and maintenance. Moreover, existing electronic and

14

Chapter One

hybridic technologies advanced very fast, making possible their application in tasks that were previously feasible only with optical processing schemes. However, the notorious difficulty in the preparation of high quality photorefractive crystals certainly played a major role in that too. The tunability of the properties of these materials is rather limited, and generally not a single crystal exists that combines all the desired characteristics for applications. The observation of photorefractivity in polymers in 1991 [17], created an alternative class of materials which show the effect. Processability is one of their main advantages, while tunability is inherent in the way they are fabricated. Moreover, potentially better performance is foreseen, as a result of the different nature of the electrooptic response [11]. As it will be discussed in the second chapter, the diffraction efficiency depends on the quantity n03reff/ε, which does not vary strongly among inorganic crystals, as a result of the ionic origin of the electrooptic effect [18]: large reff is always associated with large ε [11]. The electronic nature of the electrooptic effect in polymers, plus the newly discovered mechanism of orientational enhancement [19] give a promise for improved performance. As has been mentioned in the previous paragraphs, the necessary properties that a material should have in order to be photorefractive are charge generation, transport and trapping and an electrooptic response. These functionalities are given in a polymer with the addition of specific molecules or monomers which can be placed in three different positions: Incorporated on the polymer backbone, attached as a pendant side group, or simply doped into the polymer (figure 1.7). On the basis of this picture, one can classify the photorefractive polymers into two main groups, fully functionalized, where all the components are attached into the polymer backbone and composites, where low molecular weight dopants are present. The processes of charge generation and transport are rather well studied in polymers, due to their application in xerography [20]. The main requirements for the photorefractive effect are a high quantum yield of photogeneration and a high drift mobility. The most popular approach towards polymers with a high drift mobility has been to disperse donor molecules (from now on referred to as charge transport molecules) like aromatic hydrazones or amines into inert polymers like polycarbonate or polystyrene. Hole drift mobilities as high as 10-3 cm2/Vsec have been observed in these materials [21]. Electron transport can be achieved through doping with acceptors like diphenoquinones, however, the drift mobilities that have been achieved are much lower [22]. Charge transport in these materials takes place via hopping among the dopant molecules [23]. The drift mobility increases exponentially with decreasing distance between hopping sites, thus as high as possible loading is preferred. Phase separation, which (with a few exceptions) typically occurs at dopant concentrations in excess of 30% wt., is the main limiting factor. Poly(N-vinylcarbazole) is one example where this

Introduction

15

problem has been tackled by linking the donor units (carbazoles) on an inert polymer backbone [24]. TPD1 is a second example, where very high concentrations have been achieved due to the inherent difficulty of this molecule to crystallize [25]. The drift mobilities in molecularly doped polymers show (with a few exceptions) a very strong electric field and temperature dependence, which has been a subject of intense experimental and theoretical interest [20].

Fig. 1.7 : The required functionalities for the photorefractive effect are given by specific chemical units, which can be placed in three different positions: Incorporated on the polymer backbone, attached as a pendant side group, or simply doped into the polymer.

Molecularly doped polymers are usually photoconducting in the ultraviolet. In order to extend their photoconductivity in the visible, sensitization is necessary. This is achieved by the addition of small amounts of molecules which either absorb directly in the wavelength of interest (optical sensitization) or do not absorb themselves but form charge transfer complexes which do (chemical sensitization) [26]. The quantum yield of photogeneration in these materials has been shown to be highly electric field dependent, as the separation of the photogenerated electron-hole pairs has to compete with geminate recombination. In most cases, this field dependence is explained within the framework of the Onsager theory of geminate recombination [27]. On the other hand, charge trapping in polymers is not well studied and it remains a vaguely understood process. Intuitively, it is clear that hole trapping should take place at sites with ionization potential lower than that of the hopping sites. However, in almost all the photorefractive polymers that have been reported until today, 1

tetraphenylene diamine

16

Chapter One

no attempt was made to deliberately introduce traps. Trapping is assumed to take place at impurities accidentally present in the material [28], defects of the polymer backbone [11] etc. Identification of the trapping sites is still a subject of investigation even in the case of well studied inorganic photorefractive crystals. The electrooptic effect is a second order (χ(2)) optical nonlinearity which requires the lack of inversion symmetry. In polymers this is achieved by adding dipolar molecules with a large hyperpolarizability (from now on referred to as nonlinear optical (NLO) molecules) and partially aligning them by poling close to the glass transition temperature (Tg) [29]. In the case where the Tg of the polymer is high enough (150 degrees for example) the orientational mobility of the nonlinear optical chromophores at room temperature is rather low and the noncentrosymmetry is maintained for long time. Attaching the chromophores on the polymer backbone and/or crosslinking the polymer matrix further slows down the relaxation of the polar order [30]. On the other hand, if the Tg of the polymer is low enough, poling can be achieved at room temperature, but no orientation is maintained after the electric field is switched off. In figure 1.8 a schematic representation of the space charge field formation process in a photorefractive polymer is shown. Indicated are the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO respectively) of the inert polymer backbone, the sensitizer (charge generating (CG) site) and the nonlinear optical chromophore (EO), together with the HOMO's of the charge transport (CT) and trapping (TS) sites. In this picture, photoionization of the charge transfer complex between the sensitizer and the charge transport species is depicted and a hole is transferred to a charge transport site from where it migrates until it gets trapped at a low ionization potential site. In this picture, the nonlinear optical chromophore does not contribute to the space charge field formation process. Although it can act as a sensitizer at shorter wavelengths, it is preferable to have the functionalities of charge generation and electrooptic effect well separated, for reasons which will be explained in chapter three. Although a polymer which possessed all the necessary functionalities has been described earlier [31], the first unambiguous observation of the photorefractive effect in a polymer was demonstrated in 1991 [17], in an electrooptic epoxy doped with the charge transport molecule DEH2 . The diffraction efficiency was 2⋅10-5 and the typical response time several minutes. A few months later, subsecond response time has been demonstrated in a similar material [32]. Observation of net gain in a PVK based polymer doped with electrooptic molecules followed shortly after that [33]. Recently, a gain coefficient of more than 200 cm-1 and diffraction efficiency of almost 90% has been observed in a PVK based polymer [34], setting photorefractive polymers at new 2

4-(N,N-diethylamino)benzaldehyde diphenylhydrazone

Introduction

17

heights. Today, several different structures have been synthesised that exhibit the photorefractive effect [11,35-36], indicating the versatility of polymeric materials. Benefiting from three decades of work in inorganic crystals, photorefractive polymers have rapidly evolved to fight back for applications.

Backbone LUMO EO CG CT

CT

TS

hv

Backbone HOMO Fig. 1.8 : A schematic representation of the space charge field formation process in a photorefractive polymer. Indicated are the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO respectively) of the inert polymer backbone, the sensitizer (charge generating (CG) site) and the nonlinear optical chromophore (EO), together with the HOMO's of the charge transport (CT) and trapping (TS) sites. LUMO's of the latter are not shown for clarity. A hole which is created by photoionization of the charge transfer complex between the sensitizer and the charge transport species, migrates through hopping among charge transport species, until it gets immobilized at a cite of a trap.

1.5. Aim and outline of this thesis In this thesis the photorefractive effect is studied in a family of model polymer composites based on the well known photoconductor poly(N-vinylcarbazole) (PVK) sensitized with 2,4,7-trinitro-9-fluorenone (TNF). In these materials, holes generated by

18

Chapter One

illumination of the PVK:TNF charge transfer complex are transported by hopping through neighbouring carbazole units. Addition of a NLO molecule like 4(diethylamino)nitrobenzene (EPNA) or 4-(hexyloxy)nitrobenzene (HONB) provides the electrooptic functionality and the composites become photorefractive. In chapter two, the experimental part of the thesis is covered. It begins with a description of the sample preparation procedure and it continues with the measurement techniques which are listed in order of importance for the investigation of the photorefractive effect. For each one of them, the basic theory is outlined, the setup (which is in all cases home-built) is described and the measurement procedure is discussed. The aim of this chapter is to provide a solid background in the preparation and characterization of photorefractive polymers which will be used in the chapters to follow. It contains all the necessary information for the future repetition of this work. In the third chapter, the development and characterization of the photorefractive composites is discussed. Using holographic and other complimentary techniques, the photorefractive nature of the light induced gratings is confirmed and the applicability of the standard model for photorefractivity in the case of polymers is discussed. Net gain is demonstrated in the EPNA composite. Finally, it is shown that the change in the refractive index arises partly due to the reorientation of the NLO molecules under the influence of the space charge field. In the fourth chapter, the problem of charge trapping in photorefractive polymers is tackled. A modification of the trap density of the EPNA containing composite is demonstrated with the addition of 4-(N,N-diethylamino)benzaldehyde diphenylhydrazone (DEH). Measurements of the response time, the amplitude and the phase shift of the photorefractive grating indicate that at low concentrations DEH acts as a trap, while at higher concentrations a new transport pathway is established through hopping among DEH molecules. From the transient behaviour of the photorefractive gratings, the effect of DEH on the hole drift mobility is estimated. The transient behaviour of the space charge field is investigated in chapter five. It is shown that despite the dispersive character of charge transport in polymers, information that allows the estimation of the hole drift mobility can be obtained. The electric field, temperature and drift length dependence of the hole drift mobility in the HONB containing composite is measured with the holographic time-of-flight technique (HTOF) and compared with literature values. The shape of the HTOF signal is found to be consistent with a model for charge transport in disordered materials.

1.6. References [1] [2]

A. Askin, G.D. Boyd, J.M. Dziedzic, R.G. Smith, A.A. Ballman, J.J. Levinstein and K. Nassau, Appl. Phys. Lett. 9, 72 (1966) F.S. Chen, J.T. LaMacchia and D.B. Fraser, Appl. Phys. Lett. 13, 223 (1968)

Introduction [3] [4] [5] [6]

[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

19

F.S. Chen, J. Appl. Phys. 40, 3389 (1969) N.V. Kukhtarev, V.B. Markov, S.G. Odulov, M.S. Soskin and V.L. Vinetskii, Ferroelectrics 22, 949 (1979) and Ferroelectrics 22, 961 (1979) see for example papers in MRS Bulletin, March 1994 P. Günter and J.P. Huignard, eds. "Photorefractive Materials and their Applications I and II", Topics in Applied Physics vol. 61 and 62, SpringerVerlag (1988) M.P. Petrov, S.I. Stepanov and A.V. Khomenko, "Photorefractive Crystals in Coherent Optical Systems", Springer-Verlag (1991) A.M. Glass, D. von der Linde and T.J. Negran, Appl. Phys. Lett. 19, 130 (1971) A.M. Glass and D.H. Auston, Opt. Commun. 5, 45 (1972) K. Sutter, J. Hulliger and P. Günter, Solid State Commun. 74, 867 (1990) W.E. Moerner and S.M. Silence, Chem. Rev. 94, 127 (1994) I.C. Khoo, H. Li and Y. Liang, Opt. Lett. 19, 1723 (1994) H.J. Eichler, P. Günter and D.W. Pohl, "Laser Induced Dynamic Gratings", Springer Series in Optical Sciences vol. 50, Springer (1986) see for example paper of R.A. Mullen in Ref [6]. P. Yeh, "Introduction to Photorefractive Nonlinear Optics", Wiley Interscience (1993) M.C. Bashaw, M.Jeganathan and L. Hesselink, J. Opt. Soc. Am. B 11, 1743 (1994) S. Ducharme, J.C. Scott, R.J. Twieg and W.E. Moerner, Phys. Rev. Lett. 66, 1846 (1991) D.M. Pepper, J. Feinberg and N.V. Kukhtarev, Scientific American, p. 34, October 1990 W.E. Moerner, S.M. Silence, F. Hache and G.C. Bjorklund, J. Opt. Soc. Am. B 11, 320 (1994) P.M. Borsenberger and D.S. Weiss, eds. "Organic Photoreceptors for Imaging Systems", Optical Engineering vol. 39, Marcel Dekker, Inc. (1993) M. Stolka and M.A. Abkowitz, Synth. Metals 54, 417 (1993) P.M. Borsenberger and L.J. Rossi, J. Chem. Phys. 96, 2390 (1992) H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993) W.D. Gill in "Photoconductivity and Related Phenomena", J. Mort and D.M. Pai, eds., Elsevier (1976) M. Stolka, J.F. Janus and D.M. Pai, J. Phys. Chem. 88, 4707 (1984) P.J. Reucroft in "Photoconductivity in Polymers: an Interdisciplinary Approach", A.V. Patsis and D.A. Seanor, eds., Technomic (1976) L. Onsager, Phys. Rev. 54, 554 (1938) J.C. Scott, L.Th. Pautmeier and W.E. Moerner, Synth. Metals 54, 9 (1993)

20 [29] [30] [31] [32] [33] [34] [35] [36]

Chapter One P.N. Prasad and D.J. Williams, "Introduction to Nolinear Optical Effects in Molecules and Polymers", Wiley Interscience (1991) D.M. Burland, R.D. Miller and C.A. Walsh, Chem. Rev. 94, 31 (1994) J.S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991) S.M. Silence, C.A. Walsh, J.C. Scott, T.J. Mattray, R.J. Twieg, F. Hache, G.C. Bjorklund and W.E. Moerner, Opt. Lett. 17, 1107 (1992) M.C.J.M. Donkers, S.M. Silence, C.A. Walsh, F. Hache, D.M. Burland, W.E. Moerner and R.J. Twieg, Opt. Lett. 18, 1044 (1993) K. Meerholz, B.L. Volodin, Sandalphon, B. Kippelen and N. Peyghambarian, Nature 371, 497 (1994) S.M. Silence, D.M. Burland and W.E. Moerner, in "Photorefractive Effects and Materials", D.D. Nolte, ed., Kluwer Academic (1995) Y. Zhang, R. Burzynski, S. Ghosal and M.K. Casstevens, to appear in Adv. Mater.

Chapter Two Experimental

Abstract In this chapter, the experimental part of the thesis is covered. It begins with a description of the sample preparation procedure and it continues with the measurement techniques, which are listed in order of importance for the investigation of the photorefractive effect. For each one of them, the basic theory is outlined, the setup (which is in all cases home-built) is described and the measurement procedure is discussed. Accuracy and sensitivity requirements are addressed. The aim of this chapter is to provide a solid background in the preparation and characterization of photorefractive polymers which will be used in the chapters to follow. It contains all the necessary information for the future repetition of this work.

22

Chapter Two

2.1. Introduction As it was discussed in the previous chapter, photorefractivity requires charge generation, transport and trapping, together with an electrooptic response. This thesis concentrates on the study of photorefractive composites based on the well known photoconductor PVK:TNF. However, the photorefractive properties of a great deal of other compounds that have been synthesised in the chemistry lab had to be evaluated too. In order to respond to this challenge and efficiently characterise newly synthesised materials, a complete laboratory including several experimental setups but also sample preparation procedures had to be established. A major goal of this laboratory was to provide fast feedback to the chemists, leading to the design of better materials. Testing for the existence of photorefractivity in a potential candidate was carried out with a holographic two wave mixing experiment, where the basic properties such as the amplitude, the phase shift and the response time of the photorefractive gratings were measured. Another parameter of interest is the two beam coupling gain coefficient, which was also obtained from the same setup. For a complete understanding of the factors limiting the performance of a material, complementary measurements of photoconductivity and electrooptic effect were carried out in separate setups. Second harmonic generation measurements were used to study the orientation dynamics of the NLO molecules. Finally, a setup for transient photorefractivity experiments was used for the study of the processes of charge transport and trapping in polymers.

2.2. Sample preparation One of the major advantages of polymers as optoelectronic materials lays in the ease of sample preparation. Still, a lot of effort is required until reproducible results are obtained. A main concern is the purity of the chemicals. Impurities can act as charge trapping sites, as charge photogeneration sites (directly or via formation of a charge transfer complex) and more generally as initiators for various photochemical and electrochemical reactions. Typically, polymers are available with purity in the percent range, in contrast with inorganic crystals which can be made pure in a part per billion range. However, purity requirements in polymers are quite different. Consider charge trapping for example: As will be discussed in the third chapter, the effective trap density in the PVK:TNF:EPNA composite is in the order of 10-16 cm-3. The origin of these trapping centers in not yet understood. If they are due to a single impurity with molecular weight equal to 200 g/mol, which is accidentally present in the polymer, concentration as low as 0.0004% wt. relative to PVK can account for that. For a polymer, this is an amazingly low impurity concentration! This contradiction is cleared if we recall that only a very small fraction of all the impurities can act as traps in the case of polymers, as the hole transporting species in these materials are selected to have

Experimental

23

a very low ionization potential. Moreover, even if impurities with lower ionization potential are present, they may not be stable in the cation form, but decompose and become inert [1]. O NO 2

C H 2 CH

NO 2

n

N NO 2

poly(N-vinylcarbazole) (PVK)

2,4,7-trinitro-9-fluorenone (T NF )

C H

N

N

N

4-(N ,N -diethylamino)benzaldehyde diphenylhydrazone (DEH )

N O

NO 2

NO 2

4-(hexyloxy)nitrobenzene (H ON B)

4-(diethylamino)nitrobenzene (EP NA)

Fig. 2.1 : Chemical formulas and full names of the compounds.

Secondary standard PVK was purchased from Aldrich (part. number 36,835-0) and was precipitated three times from chloroform in diethylether [2]. TNF was purchased from Aldrich (part. number T8,080-2) and dried under vacuum over P2O5 for two days. EPNA was synthesized by aromatic substitution of 4-fluoronitrobenzene with di(2-hydroxyethyl)amine and recrystallized from a mixture of dichloromethane and pentane (1:4). HONB was synthesized by a substitution reaction between 4-nitrophenol and 6-bromohexane and recrystallized from a mixture of dichloromethane and pentane (1:4). DEH was prepared by condensation of 4-(diethylamino)benzaldehyde with 1,1diphenylhydrazine and recrystallized twice from a mixture of dichloromethane and pentane (1:1). The chemical formulas and the full names for these compounds are shown in figure 2.1. The concentration of dopants was 0.1% wt. TNF and 40% wt. EPNA or HONB relative to PVK, unless otherwise stated. With respect to the total composition the films contained 71.38% wt. PVK, 0.07% wt. TNF and 28.55% wt. EPNA or HONB. Assuming a (typical) density of 1.2 g/cm3, the number densities were

24

Chapter Two

2673⋅10-18 cm-3 PVK monomer unit, 1.6⋅10-18 cm-3 TNF and 1063⋅10-18 cm-3 EPNA or 925⋅10-18 cm-3 HONB. Indium tin oxide (ITO) covered 2×2 cm2 glass plates were purchased from Balzers (conduction 100A) and used as delivered when patterning was not necessary. The thickness of the plates was 2 mm, which allowed for easy separation of the reflected beams during optical experiments. Two types of samples were prepared: the first one casted on an ITO plate, while the second sandwiched between two ITO plates. The advantages and disadvantages of these two approaches are discussed in the next paragraphs. For the first type of samples, proper amounts of the compounds were dissolved into chlorobenzene. Typical concentrations were 2.2 g solid into 20 ml solvent. Chlorobenzene was chosen due to its high boiling point, which ensures slow evaporation, resulting into clear, bubble-free films. After the solid dissolved, the solution was filtered with a glass syringe through a 0.2 or a 0.45 µm filter (Sartorius Minisart SRP 15) and approximately 0.5 ml were deposited on an ITO covered glass plate. Overnight evaporation of the solvent at room temperature and subsequent drying of the films for several (at least four) hours in a vacuum chamber (pressure lower than 10-2 Torr), resulted in relatively solvent free, good optical quality films of about 60 µm thickness (measured with a dektak 3030ST profilometer). For the application of an external electric field, corona poling with a sharp tungsten needle (made from an scanning tunnelling microscope tip) placed 1.5 cm away from the sample was used. The ITO was grounded and a positive voltage was applied on the needle, through a limiting resistor of 10 MΩ. It is well known that due to the high electric field in the vicinity of the needle, ionization of air occurs and the positive ions are deposited on the surface of the polymer film, creating an electric field across it [3]. A major advantage of this technique is that a higher electric field without total sample breakdown can be applied: In the case of a sandwiched film, a local breakdown at a certain point of the polymer film results into total sample failure, as all the current is drawn through that point. In the case of corona poling, the low conductivity of the interface between the polymer film and air ensures that minimum amount of current flows through that point. Another advantage of this technique is the ease of sample preparation, as sandwiching the polymer between two ITO plates is not necessary. This technique is the most suitable for compounds from which very small quantity is available; the waist of material is minimal. The major drawback of this technique is that the precise value of the electric field applied on the sample is not known. This value may depend on the environment (e.g. humidity of air), thus, for good reproducibility, the experiments should be done within short periods of time. Another disadvantage is that the polymer-air interface is not always entirely flat, causing distortion of the beam and making the absolute

Experimental

25

determination of diffraction efficiency difficult. For this reason, the samples were always illuminated from the ITO side. For the preparation of the sandwiched samples, proper amounts of the compounds were dissolved in spectroscopic grade chloroform. The solution was filtered and the solvent was extracted with a rotary film evaporator, at a water bath temperature of 20 degrees. Subsequently the solid deposit was reduced into powder with the help of liquid nitrogen and stayed overnight into a vacuum chamber (pressure lower than 10-2 Torr) to ensure maximum solvent removal. The resulting powder was put into a 200 µm thick stainless steel mold and it was pressed for 5 minutes at 10 tons at 110 degrees, after 1 minute of heating and thorough degassing. Slow cooling followed and the resulting pellets were sandwiched between two ITO covered glass plates by applying gentle pressure for 10 minutes at 140 degrees. Teflon spacers were used in some samples to fix the film thickness at 100 µm. This sample preparation procedure was designed with the idea in mind to keep both the maximum temperature and the heating time to a minimum. spacer

ITO 2

Fig. 2.2 : The sample configuration. A 1×1.5 cm polymer pellet was placed on one ITO plate and the other one was flipped over it. The two plates were arranged so to permit access to both electrodes. The active electrode area was 1 about cm2.

In order to prevent premature breakdown and edge current leaks in the sandwiched samples, patterning of the ITO was necessary. Part of the ITO plates was covered with Scotch tape (five layers), leaving a few mm off from three edges unprotected. Etching of the unprotected areas was achieved with 5 minutes exposure to HCl vapours, produced from the reaction of ammonium chloride with concentrated sulphuric acid. The Scotch tape was subsequently removed and the plates were thoroughly washed with water, acetone, ethanol, chloroform and spectroscopic grade acetone. The configuration of the sandwiched samples is shown in figure 2.2.

26

Chapter Two

A major issue is to ensure that no damage is done to the polymer as a result of the sample preparation procedure and especially the heat treatment. Although thermal degradation of these compounds takes place at temperatures typically in excess of 180 degrees, possible damage can arise in the form of oxidation, chemical reaction and evaporation/sublimation of the NLO molecule. Oxidation is expected to cause the appearance of a tail in the onset of the optical absorption. The same stands for chemical reactions that increase the conjugation. Loss of the NLO molecule gives rise to a change in the ratio of the spectral peaks (spectra are shown in the next chapter). In order to examine these possibilities, a freshly prepared sample was destroyed and a small piece was dissolved in spectroscopic grade chloroform. Comparison of the absorption spectrum (taken with a SLM Aminco Array Spectrometer) of this solution and that of the starting solution, especially close to the onset of the absorption, showed no difference. Moreover, results from casted and sandwiched films were comparable, indicating that the sample preparation procedure has minimal effect on the sample properties. More on the sample reproducibility is discussed in the third chapter.

2.3. Photoconductivity measurements A basic parameter that governs the photorefractive response is photoconductivity. Observation of photoconductivity implies the presence of charge photogeneration and transport, two of the four requirements for the photorefractive effect. Indication about the presence of traps can also be obtained from photoconductivity measurements, although these traps may be different than the ones that participate in the process of space charge field formation [4]. In the case where holes are mobile, the photoconductivity is written [5]: σph=peµdr=φαIτeffeµdr/hν

(2.1)

where p is the hole density, φ is the quantum yield for free hole generation, α is the absorption coefficient at hν photon energy, τeff is the effective hole lifetime, e is the electron charge and µdr is the hole drift mobility. The material parameter of interest is the photosensitivity Sph=σph/I, which gives the conductivity change per unit light intensity. The photosensitivity is evaluated in a straightforward way, by measuring the change in the conductivity of the sample due to illumination. Usually, measurements are carried out in thinner (spin casted) samples, where almost all photogenerated charges escape from the sample without being trapped. In this way, the quantum yield for free carrier generation can be directly evaluated (photogenerated charges per number of absorbed photons). A superior technique for measuring the photosensitivity, which is more suitable for polymeric materials, is based on the measurement of the light induced

Experimental

27

change in the discharge rate of a leaky capacitor, formed with the sample under investigation [6]. PVK sensitized with TNF is a well known photoconductor and for this reason, a systematic investigation of the photoconductivity of the PVK based composites was not carried out. The existence of photoconductivity was merely demonstrated in one of the sandwiched samples that were used for all the other measurements. One ITO plate of the sample was grounded through a 1 MΩ resistor while the other was connected with a high voltage power supply. Contacts to the ITO plates with external wires were made with silver paste. The voltage drop across the resistor was measured with a high impedance amplifier and a fluke 8842A multimeter interfaced with a computer, as a function of uniform illumination with the expanded beam from a He-Ne laser. As 96% of the incident light at 633 nm was transmitted through the polymer film, no corrections were necessary for nonuniform illumination throughout the sample thickness.

2.4. Electrooptic measurements Another important parameter for the performance of photorefractive materials is the magnitude of their electrooptic response. There are numerous techniques to evaluate the electrooptic coefficients of polymers, using total attenuated reflection, Mach-Zehnder interferometers etc., all measuring the change of the optical path due to an applied ac electric field [7]. The samples are poled by a strong dc electric field, to partially orient the NLO molecules and allow a linear electrooptic response. This reduces the symmetry to C∞m and the only nonzero components of the electrooptic tensor are r33 and r13=r23=r42=r51 [8]. The most popular technique for measuring the electrooptic coefficients of photorefractive polymers is a simple ellipsometric technique, proposed independently by Teng and Man [9] and Schildkraut [10]. It offers two main advantages: First, measurements can be performed on the same sandwiched samples that are prepared for photorefractive characterization, in contrast with most other techniques that require the fabrication of waveguides. Second, the setup is very simple and stable (compared to a Mach-Zehnder interferometer for example). In figure 2.3, the setup is shown. Light from a He-Ne laser is circularly polarized and it is incident on the sample at an external angle of 60 degrees. With an analyzer placed at approximately 45 degrees with the p-polarization direction, the difference δ∆(ωac) in the phase shift between the p- and s-polarized component of light is measured [10]: δ∆(ωac)=(π/λ0)tanϑsinϑn03(r33-r13)δV(ωac)

(2.2)

28

Chapter Two

where ϑ is the angle of propagation of light inside the sample and δV(ωac) is the amplitude of the ac modulation which causes this phase difference. The above equation is valid for mild poling conditions, where the birefringence resulting from the orientation of the NLO molecules can be neglected.

AC Voltage

Lock-In Amplifier

High Voltage

Diaphragm

Oven He-Ne Laser λ/4

Sample

Analyzer

Photodiode

Fig. 2.3 : The setup for the electrooptic measurements. Light from a He-Ne laser was made circularly polarized with a quarter wave plate and it was incident on the sample at an external angle of 60 degrees. The analyzer was rotated approximately 45 degrees with the ppolarization direction and a diaphragm was used to block the reflected beams. A small ac modulation was superimposed on a dc high voltage and the modulation of the transmitted intensity was measured with a lock-in amplifier.

The intensity of light on the photodiode is: I(ωac)=I0(1+sin(δ∆(ωac)))≈I0(1+δ∆(ωac))

(2.3)

where I0 is the dc component of the light on the photodiode. With a lock-in amplifier (Stanford Research Systems SR830), the ac component I(ωac) of the transmitted light was measured and from equations (2.2) and (2.3), the difference r33-r13 was calculated. The amplitude δ∆(ωac) of the ac signal was 10 V and ωac was varied between 50 Hz and

Experimental

29

100 kHz. As will be seen in the next chapter, values in the order of several pm/V were measured for the electrooptic coefficient of the PVK based photorefractive composites. Although the sensitivity of the setup is enough to measure values 100 times lower than that, typical values for almost all photorefractive polymers are in the pm/V range [11]. The major draw back of this technique is that r33 and r13 cannot be measured independently. In several cases however, the assumption r33=3r13, which is based on thermodynamic arguments, is valid and can be used [12]. There are various factors limiting the accuracy of this measurement. For example, in the derivation of equation (2.3), the difference in the reflectivity of the sample for s- and p-polarized light is ignored1 . This gives rise to an error of 30% in the measured value of the electrooptic coefficient. The main requirement from this setup however, is to provide a fast, order of magnitude measurement of the electrooptic coefficient, for comparison of various compounds. For this reason, even an accuracy of 50% is acceptable. When measuring the linear electrooptic coefficient, a contribution from the piezoelectric effect is always present. This contribution however, is insignificant at high modulation frequencies, as mechanical resonances cannot follow. In the presence of a dc field, Kerr effects can mimic a linear electrooptic response. The main contribution from Kerr nonlinearities arises from the reorientation of the NLO molecules, which, depending on the architecture and the glass transition temperature of the polymer, can follow even at high frequencies [14]. Their relative contribution is discussed in the third chapter.

2.5. Second harmonic generation measurements Complimentary information about the orientational dynamics of the NLO molecules was obtainedwith second harmonic generation (SHG) measurements. One major advantage of SHG is that the orientation of the NLO molecules is directly probed, with no interference from piezoelectric and Kerr effects. Moreover, SHG can be used in casted samples, where the electrooptic response cannot be measured (an ac modulating field cannot be applied). In the presence of a dc poling field, the second order macroscopic susceptibility χ(2)zzz for a solid solution of rod like molecules is written [8]: χ(2)zzz∝β333 + γ3333f(0)E0 1

(2.4)

If this is taken into account, a more complex form of I(ωac) is derived and additional measurements, with the analyzer rotated at 0 and 90 degrees are required in order to obtain δ∆(ωac) [13].

30

Chapter Two

where β333 and γ3333 are the dominant components of the first and the second hyperpolarizability tensors of the NLO molecule, θ is the angle between the molecular axis and the applied field, the symbol <> defines average over all possible molecular orientations, f(0) is the dc local field factor and z is parallel to the applied field E0. In most cases, the second term on the right hand side of equation (2.4) is small and it is dropped2 . filters Nd:YAG

M

PC filters

PMT High Voltage

Osc

Boxcar

Fig. 2.4 : The setup for the SHG measurements. The fundamental beam of a Nd:YAG laser was incident on the sample at an external angle of approximately 45 degrees. Colour filters were used before the sample to cut visible radiation form the flash lamps while interference and colour filters were put after the sample to isolate the second harmonic signal. Detection was done with a fast photomultiplier (PMT) and gated electronics (Boxcar) interfaced with a computer (PC). The sample was connected to a high voltage power supply. In the above picture, M is a mirror and Osc is a fast oscilloscope.

2

The contribution from the third order hyperpolarizability can be safely ignored for small molecules like EPNA, with low γ3333 values [15]. Moreover, even in molecules where this contribution is considerable, it is not responsible for more than 20% of the total signal [16].

Experimental

31

From the above equation it can be seen that unless there is a noncentrosymmetric orientation of the NLO molecules, χ(2)zzz is zero. In the case of mild poling conditions, a free gas model is used to describe the average orientation and [17]: =µf(0)E0/(5kBT)

(2.5)

where µ is the dipole moment of the NLO molecules and kBT the thermal energy. The setup for the measurements of the second order macroscopic susceptibility is shown in figure 2.4. Infrared, p-polarized light from a single frequency, Q-switched Nd:YAG laser (Spectra Physics GCR 130-50) was incident on the sample at an angle of approximately 45 degrees. The energy flux was 20 mJ/cm2, with pulses of 10 nsec duration and 50 Hz repetition rate. The frequency doubled output from the sample was separated using colour and interference filters and detected using a photomultiplier and a gated integrator (Stanford Research Systems SR250) interfaced with a computer. The output intensity at 2ω frequency is [18]: I(2ω)∝(χ(2)zzzI(ω))2

(2.6)

Thus, by measuring the intensity of the second harmonic as a function of the electric field, information can be obtained about the orientation of the NLO molecules. The temporal resolution of the measurement is determined by the separation between two subsequent Nd:YAG pulses (20 msec).

2.6. Diffraction efficiency and response time measurements The existence of photoconductivity and electrooptic response in a material does not necessarily lead to photorefractivity. Light induced gratings of photochemical or photochromic origin may overshadow any photorefractive response. Moreover, traps suitable for sustaining a space charge field may not be present. The demonstration of a phase shifted refractive index grating due the existence of a space charge field is the only true evidence for photorefractivity. In order to probe the steady state and the dynamics of this space charge field, the diffraction efficiency η of the photorefractive grating is measured with holographic techniques. In this paragraph, the dependence of η on material parameters is derived and the relevant experimental techniques are discussed. The diffraction efficiency for a volume refractive index hologram has been calculated by Kogelnik [19]. Consider the geometry of figure 2.5, where the sample is illuminated with a sinusoidal intensity pattern, resulting from the interference of two mutually coherent, s-polarized beams, with amplitudes E1 and E2 respectively. If ∆n is the amplitude of the refractive index grating and ϕ its phase shift with respect to the

32

Chapter Two

interference pattern, the coupled wave equations for the amplitudes of the two beams are [20]: (d/dz)E1=-iPexp[+iϕ]E2

(2.7a)

(d/dz)E2=-iPexp[-iϕ]E1

(2.7b)

P=(π/λ0cosϑ)∆n=-(π/2λ0cosϑ)n03reffESC

(2.8)

where :

1 x

ϑ

z

2

d

0

Fig. 2.5 : A photorefractive material is illuminated with a sinusoidal intensity pattern, resulting from the interference of two mutually coherent, s-polarized beams, with amplitudes E1 and E2 respectively. The two beams propagate on the xz plane at an (internal) angle ϑ with the sample normal.

Solution of the above equations for the case where E2(0)=0 gives: E1(d)=E1(0)cos(Pd)

(2.9a)

E2(d)=-iE1(0)exp[-iϕ]sin(Pd)

(2.9b)

The diffraction efficiency η is: η=I2(d)/I1(0)=sin2(Pd)

(2.10)

Experimental

33

and for low values of η, equation (2.10) reduces to: η≈(Pd)2=((πd/2λ0cosϑ)n03reffESC)2

(2.11)

From the above equation it can be seen that the diffraction efficiency depends quadraticaly on the space charge field, which is proportional to the modulation index m. For a better signal to noise ratio, experiments are preferably carried out in the regime of m=1, where the diffraction efficiency is maximum. However, in the derivation of the space charge field from material parameters in chapter one, the assumption is made that m<<1, which allows for neglecting higher spatial frequencies in its Fourier expansion. Including these terms results in a distortion of the sinusoidal shape of ESC, which leads to a smaller refractive index change [21-22]. Thus, equation (2.11) slightly overestimates the magnitude of the space charge field. z

1 2

air E0 KG

ϑG

polymer air

Fig. 2.6 : The tilted geometry used for the study of photorefractive polymers, where ϑG is the angle between the grating wave vector and the external electric field. The two beams were incident on the sample at external angles of 30 and 60 degrees respectively.

For the holographic studies of photorefractivity in polymers, a tilted geometry like in figure 2.6 is used. In this way, the grating wave vector has a component parallel to the applied electric field and reff is nonzero. Moreover, drift of the photogenerated carriers parallel to the grating wave vector is enabled by the component of the applied field along this direction. Two beams from a He-Ne laser (Melles-Griot 15 mW) are incident on the sample at external angles 30 and 60 degrees. Although this is not the most efficient geometry for grating recording and readout, it has been established as the

34

Chapter Two

standard geometry for the study of photorefractivity in polymers. For a refractive index of 1.7, the two beams propagate inside the sample with angles of 17 and 31 degrees respectively. The grating wave vector KG forms an angle ϑG≈66 degrees with the external electric field. The grating spacing is: ΛG=λ0/2n0sin((ϑ2-ϑ1)/2)≈1.6 µm

(2.12)

where λ0=633 nm and ϑj are the internal angles of propagation. For the recording of the photorefractive gratings, two beams with the same power, equal to approximately 600 mW/cm2 outside the sample were used, unless otherwise stated. The setup was build on an optical table (Newport Research Series Plus), to minimize mechanical vibrations. The coherence length of the He-Ne laser was longer than the path difference between the two beams that were used to write the gratings. The diffraction efficiency was measured in a backward degenerate four wave mixing (DFWM) arrangement (figure 2.7). According to this scheme, the grating is written using two s-polarized beams, and the diffraction efficiency is measured using a weaker, p-polarized beam from a separate He-Ne laser, counterpropagating with one of the writing beams. This combination of beam polarizations results in maximum DFWM signal [11]. Using a separate laser for probing the grating ensures the existence of only one interference pattern inside the sample. The Bragg condition for phase matching is automatically satisfied in this beam configuration and for the case of p-polarized readout in a tilted geometry [11]: P=(πcos(ϑ2-ϑ1)/λ0(cosϑ2cosϑ1)1/2)∆n

(2.13)

and the resulting diffraction efficiency is: ηp≈(Pd)2=((πdcos(ϑ2-ϑ1)/2λ0(cosϑ2cosϑ1)1/2)n03reffESC)2

(2.14)

reff=r13(cosϑ2sin(ϑG+ϑ2)+sinϑ1cosϑ2cosϑG)+r33(sinϑ1sinϑ2cosϑG)

(2.15)

where:

In the case of the geometry used here, the effective electrooptic coefficient is mainly determined by r13: reff=0.95r13+0.06r33

(2.16)

Experimental

35

By means of a beamsplitter, the diffracted part of the probe beam was send to a photodiode (Siemens BPX 91B) and the signal was monitored with a HP54502 digitizing oscilloscope and transferred into a computer for further analysis. By monitoring the diffraction efficiency during grating recording or erasure, the response time of the space charge field was obtained. Usually, the erasure behaviour of the gratings under uniform illumination was analysed, as due to the absence of an interference pattern, the signal is insensitive to mechanical vibrations. After the grating has been written, one of the writing beams was blocked and the other is used to erase it, or both writing beams were blocked and erasing was done with the probe beam. The temporal resolution of the setup was better than 10 µsec and the minimum diffraction efficiency that could be measured was around 10-5. BS

M

He-Ne BS PD

High Voltage

He-Ne

Osc M

Fig. 2.7 : The experimental setup for backward degenerate four wave mixing. The grating was written using two s-polarized beams, and the diffraction efficiency was measured using a weaker, p-polarized beam from a separate He-Ne laser, counterpropagating with one of the writing beams. Beam splitters (BS) and mirrors (M) were used to control the direction of the laser beams and a photodiode (PD) connected to an oscilloscope (Osc) was used for the detection of the diffracted beam. High voltage was applied on the sample.

The DFWM arrangement is useful for the measurement of the steady state diffraction efficiency. Care is taken to ensure good spatial overlap of the probe beam and the interference pattern. In order to do this and to avoid edge effects, the probe beam had a smaller diameter than the writing beams. An easier way to measure the response time using only one laser, is to block one of the writing beams after the grating is written and monitor the decay of the

36

Chapter Two

diffracted part of the other beam. For this measurement, p-polarized beams were used in the usual tilted geometry, as the efficiency of p-polarized readout is higher [11]. The diffracted signal was monitored with a photodiode and the digitizing oscilloscope. The temporal resolution was better than 10 µsec.

2.7. Two beam coupling measurements The observation of asymmetric energy exchange during a holographic experiment provides compelling evidence for the existence of a phase shifted refractive index grating, which is the signature of the photorefractive effect. The gain coefficient which is associated with this energy exchange can be measured easily, by measuring the change in the intensity of one of the transmitted beams (probe) a result of the presence of the other beam (pump). Solving equations (1.13) for the undepleted pump regime, the gain coefficient is: Γ=(1/l)[ln(βγ0)-ln((β+1-γ0)]

(2.17)

where β is the ratio of the intensities of the pump and the probe before the sample and γ0 is the ratio of the intensities of the probe beam, with and without the presence of the pump. In the above formula, no corrections are included for the tilted geometry, except that l is the path of the probe beam. With this setup, gain coefficients as low as 10-3 cm-1 could be measured. All the above calculations have been carried out for the case of a purely refractive index grating. In some materials however, photorefractive gratings are accompanied by absorption gratings. For example, if the extinction coefficient of the charge generating species is very different in its ionized state, an absorption grating appears, in phase with the illumination pattern. In order to investigate for the presence of complimentary gratings, the two beam coupling (2BC) method proposed by Sutter et al. [23] was used. This experiment is performed in the usual tilted geometry, with the sample being mounted on a piezotranslator, which can provide rapid (faster than the response time of the gratings) translation of a few micrometers (figure 2.8). After the grating is written, the sample is translated and the modulation is observed on the two beams as they read out the grating. From this modulation information can be extracted concerning the nature (absorption or refractive index), the amplitude and the phase shift of gratings that exist inside the material. The analysis of this experimental results is based on Kogelnik's coupled waves theory, as outlined in the previous paragraph for the case of a refractive index grating. The basic analysis in the simplest geometry is presented here for the sake of clarity. The beam configuration is shown in figure 2.9. The sample is illuminated with a sinusoidal intensity pattern, which results from the interference of two p-polarized beams with

Experimental

37

equal amplitude E0. This produces a refractive index and an absorption grating, with phase shifts ϕP and ϕA respectively. M

BS He-Ne PZT ND PD

PC

ND PD High Voltage Osc

Fig. 2.8 : The two beam coupling experiment. The sample was illuminated in the usual tilted geometry and it was mounted on a piezotranslator (PZT), which could provide fast translation of a few micrometers in the direction indicated be the arrow. The intensity of the two transmitted beams was reduced with neutral density filters (ND) and monitored with photodiodes and an oscilloscope (Osc) interfaced with a computer (PC). The sample was connected to a high voltage power supply. In the above picture, M is a mirror and BS a beam splitter.

The transmitted E1(R) and diffracted E1(S) fields of the wave which propagates along k1 are given by: E1(R)=E0exp[-αd/2cosϑ]exp[i(ωt-k1r)]

(2.18a)

E1(S)=-E0exp[-αd/2cosϑ](iPdexp[-iϕP]+Adexp[-iϕA])exp[i(ωt-k2r)]

(2.18b)

where the approximation is made that the diffraction efficiency is small. In the above equations, P is the diffraction amplitude of the refractive index grating defined in equation (2.8), A is the respective quantity for the absorption grating and d is the thickness of the sample. Similar expressions hold for the second beam.

38

Chapter Two

1 k2 k1

x ϑ

z

2

Fig. 2.9 : A photorefractive material is illuminated with a sinusoidal intensity pattern, which results from the interference of two mutually coherent, p-polarized beams with equal amplitude E0. The two beams propagate on the xz plane at an (internal) angle ϑ with the sample normal, along k1 and k2 respectively.

The power densities of the two beams at the exit side of the sample are: P1=P0exp[-αd/cosϑ](1-2AdcosϕA+2Pdsinϕp)

(2.19a)

P2=P0exp[-αd/cosϑ](1-2AdcosϕA-2Pdsinϕp)

(2.19b)

where P0 is the power density of one of the incoming beams. As can be seen from the above equations, absorption gratings enter with the same sign in both, while refractive index gratings enter with opposite sign, indicating asymmetric energy exchange between the two beams. If the sample is suddenly translated with a constant velocity v, and this translation is done faster than the response time of the gratings, a phase equal to 2πvt/ΛG is added to the phase arguments of the two gratings and equations (2.19) become: P1=P0exp[-αd/cosϑ](1-2Adcos(ϕA+2πvt/ΛG)+2Pdsin(ϕp+2πvt/ΛG))

(2.20a)

P2=P0exp[-αd/cosϑ](1-2Adcos(ϕA+2πvt/ΛG)-2Pdsin(ϕp+2πvt/ΛG))

(2.20b)

From the above equations it can be seen that the modulation of the two beams as a function of the translation time t will show an oscillatory behaviour. In the case of

Experimental

39

pure absorption gratings P1 and P2 modulate in phase, while for a purely refractive index grating, a 180 degrees phase difference will be observed. In intermediate cases, the addition and subtraction of the two power densities can be used to separate the two gratings: P(+)=P1+P2=P0exp[-αd/cosϑ](2-4Adcos(ϕA+2πvt/ΛG))

(2.21a)

P(-)=P1-P2=P0exp[-αd/cosϑ](0+4Pdsin(ϕp+2πvt/ΛG))

(2.21b)

Walsh and Moerner have done the calculation for the tilted geometry used in photorefractive polymers [24]. The two incoming beams have in the general case different amplitudes E01 and E02 (defined inside the sample) and propagate with angles ϑ1 and ϑ2 respectively. Neglecting the exponential absorption terms (which is a good approximation within 3% for PVK:TNF:EPNA and PVK:TNF:HONB), equations (2.21) are written: P(+)=P0'((cosϑ1E012+cosϑ2E022)/(E01E02(cosϑ1cosϑ2)1/2)-4Adcos(ϕA+2πvt/ΛG)) (2.22a) P(-)=P0'((cosϑ1E012-cosϑ2E022)/(E01E02(cosϑ1cosϑ2)1/2)+4Pdsin(ϕp+2πvt/ΛG)) (2.22b) where P0' is a common power density prefactor. In the geometry used here, the power transmission coefficient for propagation out of the sample is close to unity for both beams and the above equations are related to the actual power on the photodiodes. One advantage of this technique is that homodyne detection of the diffracted beam is automatically employed and in this way small variations in the refractive index or the absorption coefficient can be easily measured. A grating with diffraction efficiency of 10-4 for example, will lead according to equations (2.11) and (2.19) to a modulation of the transmitted power in the percent range, which is easily detectable. For an accurate determination of the phase shift however, larger modulations are required. This technique is suitable for the measurement of any refractive index or absorption grating, the only restriction is that their response time should be slow enough to allow for the translation of the sample.

2.8. Transient holographic and photoconductivity measurements The existence of photorefractivity in polymers provides the unique opportunity to investigate the charge transport and trapping processes with purely optical techniques. Transient holographic experiments have been extensively used in the case of inorganic photorefractive crystals to give valuable insight into the dynamics of the

40

Chapter Two

space charge field formation and to measure the drift mobility of the charge carriers [25-27]. In a holographic time-of-flight (HTOF) experiment, an interference pattern from two pico or nanosecond laser pulses creates a sinusoidal distribution of mobile carriers, which drifts under the influence of an external electric field. As charge separation advances, a space charge field builds up that can be probed with a cw laser beam through the electrooptic effect. One measures the diffraction efficiency η(t) [26]: η(t) ∝ ( reff ESC(t) )2

(2.23)

where reff is the effective electrooptic coefficient and ESC(t) is the space charge field. The space charge field reaches a maximum when the mobile carriers have drifted to a position of anticoincidence with the immobile distribution of the countercharges. Further drift causes a decrease of the space charge field until coincidence is reached again and so on. The diffraction efficiency versus time shows oscillatory behaviour and from the time tmax that corresponds to the first maximum the drift mobility µdr can be extracted [26]: µdr = Ldr / ( E0 tmax)

(2.24)

where Ldr is the drift length, equal to ΛG/2cos(ϑG), where ΛG is the grating spacing and ϑG is the angle between the grating wave vector and the external electric field E0. In the case where the mean free path of the mobile charges is smaller than Ldr the diffraction efficiency reaches a steady state value monotonically. The setup for the transient photorefractivity experiments is shown in figure 2.10. Gratings were written using two s-polarized, mutually coherent beams with energy fluxes of 5 mJ/cm2 (the frequency doubled output of the same Nd:YAG laser that was used for the SHG measurements), incident at the sample at an external angle of 30 degrees, in the usual tilted geometry. The sample was mounted on a rotating stage to allow rotation in the direction indicated in figure 2.10. The evolution of the photorefractive grating after a single shot form the Nd:YAG laser was probed with a Bragg matched, p-polarized He-Ne laser beam. The He-Ne intensity was varied between 150 and 1 mW/cm2, maintaining a reasonable signal-to-noise ratio, while keeping the erase time longer than tmax. Under these experimental conditions, the diffraction efficiency did not exceed 5⋅10-4. The diffracted part was separated using colour and interference filters and detected with a photomultiplier connected to the digitizing oscilloscope. The photomultiplier was located at a distance from the sample and two diaphragms were used in order to eliminate pick up of fluorescence from the sample and the surroundings. The response time of the detection system was better than 10 µsec.

Experimental

41

Transient photoconductivity was measured under uniform illumination of the samples with a pulse from the same laser. The fast component of the current was measured directly with the oscilloscope (at 50 Ω), while for timescales longer than 100 µs, a high impedance amplifier, connected to the oscilloscope was used. BS

filters Nd:YAG

M ND

telescope

M

He-Ne

PC diaphragm filters

High Voltage

Osc PMT Fig. 2.10 : The setup for the study of the transient behaviour of the photorefractive gratings. Gratings were written using two s-polarized, mutually coherent beams from a frequency doubled Nd:YAG laser, overlapping in the sample at an external angle of 30 degrees, in the usual tilted geometry. The sample was mounted on a rotating stage to allow rotation in the direction of the arrow. The evolution of the photorefractive grating after a single shot form the Nd:YAG laser was probed with a Bragg matched, p-polarized He-Ne laser beam. A 2× telescope was used to expend the He-Ne beam and neutral density filters (ND) to attenuate it. The diffracted part was separated using colour and interference filters and detected with a photomultiplier (PMT) connected to an oscilloscope (Osc) and interfaced with a computer (PC). The photomultiplier was located at a distance from the sample and two diaphragms were used in order to eliminate pick up of fluorescence from the sample and the surroundings. The sample was connected to a high voltage power supply. In the above picture, M stands for mirror and BS for beam splitter.

42

Chapter Two

2.9. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

J.C. Scott, L.T. Pautmeier and W.E. Moerner, Synth. Metals 54, 9 (1993) Purification and synthesis of the compounds described in this thesis has been carried out by H. J. Bolink, in the laboratory of Polymer Chemistry. H. Hampsch, J. Tolkerson, S. Bethke and S. Grubb, J. Appl. Phys. 67, 1037 (1990) B.E. Jones, S. Ducharme, M. Liphardt, A. Goonesekera, J.M. Takacs, L. Zhang and R. Athalye, J. Opt. Soc. Am. B 11, 1064 (1994) D.M. Pai in "Photoconductivity and Related Phenomena", J. Mort and D.M. Pai, eds., Elsevier (1976) J.C. Scott, L.T. Pautmeier and W.E. Moerner, J. Opt. Soc. Am. B 9, 2059 (1992) D.M. Burland, R.D. Miller and C.A. Walsh, Chem. Rev. 94, 31 (1994) P.N. Prasad and D.J. Williams, "Introduction to Nonlinear Optical Effects in Molecules and Polymers", Wiley Interscience (1991) C.C. Teng and H.T. Man, Appl. Phys. Lett. 56, 1734 (1990) J.S. Schildkraut, Appl. Opt. 29, 2839 (1990) W.E. Moerner and S.M. Silence, Chem. Rev. 94, 127 (1994) D.J. Williams in "Nonlinear Optical Properties of Organic Molecules and Crystals", D.S. Chemla and J. Zyss, eds., Academic Press (1987) P. Röhl, B. Andress and J. Nordmann, Appl. Phys. Lett. 59, 2793 (1991) M.G. Kuzyk, J.E. Sohn and C.W. Dirk, J. Opt. Soc. Am. B 7, 842 (1990) L.T. Cheng, W. Tam, S.H. Stevenson, G.R. Meredith, G. Rikken and S.R. Marder, J. Phys. Chem. 95, 10631 (1991) A. Dhinojwala, G.K. Wong and J.M. Torkelson, J. Opt. Soc. Am. B 11, 1549 (1994) C.P.J.M. van der Vorst and S.J. Picken, J. Opt. Soc. Am. B 7, 320 (1990) K.D. Singer, J.E. Sohn and S.J. Lalama, Appl. Phys. Lett. 49, 248 (1986) H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969) P. Yeh, "Introduction to Photorefractive Nonlinear Optics", Wiley Interscience (1993) P. Refregier, L. Solymar, H. Rajbenbach and J.P. Huignard, Elect. Lett. 20 656 (1984) E. Ochoa, F. Vachss and L. Hesselink, J. Opt. Soc. Am. A 3, 181 (1986) K. Sutter and P. Günter, J. Opt. Soc. Am. B 7, 2274 (1990) C.A. Walsh and W.E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992) J.M.C. Jonathan, Ph. Roussignol and G. Roosen, Opt. Lett. 13, 224 (1988) J.P. Partanen, J.M.C. Jonathan and R.W. Hellwarth, Appl. Phys. Lett. 57, 2404 (1990) P. Nouchi, J.P. Partanen and R.W. Hellwarth, Phys. Rev. B 47, 15581 (1993)

Chapter Three Photorefractivity in poly(N-vinylcarbazole) based Composites Abstract Two novel photorefractive polymer composites have been developed, based on the well known photoconductor poly(N-vinylcarbazole) (PVK) sensitized with 2,4,7trinitro-9-fluorenone (TNF) and the nonlinear optical (NLO) molecules 4(diethylamino)nitrobenzene (EPNA) or 4-(hexyloxy)nitrobenzene (HONB). Using holographic and other complimentary techniques, the photorefractive nature of the light induced gratings in these materials is confirmed and net gain is demonstrated in the EPNA composite. The applicability of the standard theory of photorefractivity in the case of polymers is discussed. Finally, it is shown that the change in the refractive index arises partly due to the reorientation of the NLO molecules under the influence of the space charge field.

44

Chapter Three

3.1. Introduction In the last few years an increasing interest has been observed in the development of photorefractive polymer materials with possible applications in image processing and reversible dynamic holographic storage [1]. The first photorefractive polymer was an electrooptic polymer which was made photoconducting after doping with a hole transport agent [2]. Several other similar materials [3-5] as well as fully functionalized polymers [6,7] have been reported, all showing moderate performance. Subsecond grating response was demonstrated in one of them [3]. The various polymeric architectures, together with their advantages and drawbacks will not be outlined here, as they can be found in review articles [1,8,9]. Recently, net gain, high diffraction efficiency and a fast response time were observed in a PVK based photoconducting polymer, doped with the NLO molecule FDEANST1 [10]. In this material, PVK plays a dual role, providing both the functionality of charge transport and the required mechanical stability. This approach has proven to be the most fruitful in terms of performance and several PVK based photorefractive polymers have been reported until today, doped with a variety of NLO molecules [11-16]. In order to explore the mechanism of photorefractivity in this class of materials, two novel composites were developed by doping PVK with the NLO molecules EPNA or HONB and small amounts of TNF, which functions as a sensitizer. Their properties were studied using holographic and other complimentary techniques and the results where discussed in view of the standard model for photorefractivity. Finally, the mechanism of the refractive index change in these materials was investigated. The theory, the sample preparation procedures and the measuring techniques, together with sensitivity and accuracy considerations, have been discussed in the previous chapters. Here, only the most important experimental conditions are stated and some equations are repeated for the sake of completeness.

3.2. Results and discussion The preparation of samples has been described in the previous chapter. Early results were obtained from casted films containing 39% wt. EPNA and 0.1% wt. TNF relative to PVK, with thicknesses around 65 µm. 100 µm thick sandwiched samples with 40% wt. EPNA or HONB and 0.1% wt. TNF relative to PVK were also studied. As the concentration of the NLO molecules was well below the limit where phase separation becomes visible (approximately 50% wt.), the optical quality of the samples 1

3-fluoro-4-(N,N-dithylamino)-β-nitrostyrene.

Photorefractivity in PVK based Composites

45

was good and did not degrade in time. The main reason for sample degradation was the tendency of the polymer film to stick off the ITO plate after a few days. The glass transition temperature (Tg) of pure PVK is around 200 degrees. With the introduction of large quantities of a NLO molecule, plasticization is expected to take place [17]. The composite films would soften at a temperature around 100 degrees. Electrooptic measurements also indicate that the Tg is in this range (see below). Accurate measurements with differential scanning calorimetry (DSC) however were inconclusive, mainly due to the fact that the NLO molecules were subliming at elevated temperatures [18]. This sublimation problem was apparent in early attempts to expel residual solvent from the sample with prolonged heating. Since then, the sample preparation procedure (as described in the previous chapter), was designed to minimize the loss of the NLO molecules during heat treatment.

3.2.1. Optical absorption In order to be advantageous for applications, a photorefractive material should have a large range of wavelengths where it can be used. Especially in the high density information storage devices, response in the blue side of the visible is preferable. From this point of view, PVK is a promising material for photorefractive applications. It can be processed into good optical quality films, which absorb in the ultraviolet region of the spectrum and with the addition of small amounts of a sensitizer like TNF, it exhibits photoconductivity throughout the visible. The wavelength range of PVK based photorefractive polymers is ultimately limited by the NLO molecules. In all photorefractive polymers so far, π conjugated donor-acceptor molecules, are used to provide the electrooptic functionality. Their hyperpolarizability increases strongly with the length of the conjugated block [19] and for this reason, stilbenes or larger blocks are preferred. However, a trade-off is known to exist between the nonlinearity and the transparency of these molecules, meaning that the ones with the highest hyperpolarizability, show strong absorption in the visible. Although in some cases they act as sensitizers [20], illumination at, or near their absorption tail is not desirable: Permanent gratings with long response times observed in several photorefractive polymers have been attributed to photochemical reactions involving these molecules [10,21-23]. Moreover, for the achievement of net gain, the absorption should be kept at a minimum. For these reasons, the range of wavelengths used to study photorefractive polymers has been limited to the red-near infrared part of the spectrum. In DEANST2 containing polymers for example, the onset of absorption is around 600 nm and permanent gratings have been observed at 633 nm [23]. 2

4-N,N-(diethylamino)-β-nitrostyrene

46

Chapter Three

From a transparency point of view, benzene derivatives seem attractive candidates as NLO molecules in photorefractive polymers. As can be seen in figure 3.1, the onset of absorption of EPNA (in CHCl3 solution) is below 475 nm. In the same figure, the optical density of the PVK:TNF:EPNA starting solution used for the preparation of the sandwiched samples is plotted. This spectrum is the superposition of the spectra of PVK and EPNA solutions with the proper concentration (the absorption of TNF is too weak to be seen on this scale), indicating the absence of any reaction between these two compounds. However, a large wavelength range is still wasted, as the absorption of EPNA extends about 100 nm more than that of PVK. This waste is minimized when HONB is used as the NLO molecule (inset of figure 3.2), due to the fact that the alkoxy group is a weaker donor than the dialkylamino one.

composite

0.3

PVK

optical density

EPNA 0.2

0.1

0.0

300

350

400

450

500

wavelength (nm) Fig. 3.1 : Optical density of the PVK:TNF:EPNA starting solution compared with PVK and EPNA solutions of proper concentration, all in CHCl3.

The optical density of the sandwiched samples is shown in figure 3.2. Strong absorption for the EPNA composite begins about 500 nm, while the HONB composite offers 50 nm broader window towards the blue and it operates even at 488 nm [24]. The tail of the absorption is due to the PVK:TNF charge transfer complex and as expected, it is the same for both samples. Absorption at 633 nm is solely due to the PVK:TNF charge transfer complex. A formation of a charge transfer complex between PVK and

Photorefractivity in PVK based Composites

47

EPNA for example, can be ruled out, as samples that contain no TNF show no photorefractive response at 633 nm. 1.00 0.4

optical density

0.50

optical density

0.3

0.75

0.2

0.1

0.0 250

300

0.25

0.00 400

350

400

450

500

wavelength (nm)

500

600

700

800

wavelength (nm) Fig. 3.2 : Optical density of the sandwiched samples (solid line is for the EPNA composite and dotted line for the HONB composite). The two spectra are not corrected for reflections. The arrows indicate 488 and 633 nm. Inset : Optical densities of the PVK:TNF:EPNA (solid line) and PVK:TNF:HONB (dotted line) starting solutions in CHCl3.

3.2.2. Photoconductivity The photoconductivity of PVK:TNF composites has been extensively studied in the past [25]. Absorption at wavelengths longer than 450 nm is attributed to the charge transfer complex which is formed between these two compounds [26]. For small amounts of TNF, the absorption of the composite increases linearly with TNF concentration [27]. The efficiency of charge generation is strongly electric field dependent and has been described on the basis of the Onsager theory of geminate recombination [26]. Both holes and electrons can be mobile in PVK:TNF composites, depending upon the composition. For low TNF concentration however, like in the composites that are discussed here, the electron mobility is practically zero [28]. Hole transport takes place via hopping, which is an activated process and the resulting

48

Chapter Three

mobility is strongly electric field and temperature dependent [28]. More on the transport properties of PVK will be discussed in the next chapters.

conductivity (10-12 (Ωcm)-1)

20

15

10

5

0

0

20

40

60

time (sec) Fig. 3.3 : Photocurrent response of the HONB composite. A He-Ne light beam with intensity of 40 mW/cm2 was switched on for 40 seconds, at time equal ~6 sec. The electric field was 55 V/µm.

The photocurrent response of the HONB composite is shown in figure 3.3. At time equal ~6 sec, a He-Ne light beam with intensity of 40 mW/cm2 is switched on for 40 seconds, causing a reversible increase in conductivity, with the rise time of the photocurrent being in the subsecond range. Heating due to the laser beam can be safely ruled out, as the light intensity is very weak and the absorption of the sample very low. The corresponding sensitivity is in the order of 3⋅10-10 (Ωcm)-1/(W/cm2), which is typical for photorefractive polymers [1].

3.2.3. Orientational mobility of the nonlinear optical molecules and electrooptic response of poly(N-vinylcarbazole) based photorefractive composites The electrooptic properties of host-guest polymers are a subject of continuous research interest [29]. For a solution of NLO molecules in a polymer matrix, the electrooptic coefficient can be described as [30]:

Photorefractivity in PVK based Composites r33 ∝ χ(2)zzz ∝ N β333

49 (3.1)

where N is number density of the NLO molecules, β333 is the dominant component of their first hyperpolarizability tensor, θ is the angle between the molecular axis and the applied field and the symbol <> defines an average over all possible molecular orientations. A similar expression holds for r13. Poling, which is necessary to remove the inversion symmetry and allow an electrooptic response, is usually carried out at temperatures close to the Tg, where the orientational mobility of the NLO molecules is relatively high. The poled structure is inherently unstable and the orientation of the NLO molecules tends to relax back to its random state, with a time constant that depends on the Tg, the architecture of the polymer and the poling procedure. Various approaches have been described in the literature, aiming at the maximization of the loading with NLO molecules, or the improvement of their orientational stability [29]. In host-guest polymers like the composites discussed here, the stability of the polar order at room temperature is rather poor [31]. As no physical linkage exists between the NLO molecules and the polymer backbone, relatively little constrain is present to prohibit their orientational relaxation. At the same time, in the case of photorefractive polymers, a high electric field is applied anyhow, in order to enhance charge generation and transport. The question arises, whether the same electric field can be used for efficient in situ poling of the NLO molecules at room temperature. To check that, second harmonic generation (SHG) experiments were performed on casted samples, in the geometry described in the previous chapter. At the absence of an electric field, no signal could be measured, as a result of the centrosymmetric random arrangement of the NLO molecules. When the voltage on the needle exceeded 2 kV (the value above which corona discharge took place), SHG was immediately observed, indicating the ability of the NLO molecules to (partly) orient at room temperature. In figure 3.4, the square root of the SHG signal from a PVK:TNF:EPNA sample is plotted, exhibiting the expected quadratic behaviour with electric field3 . SHG would essentially vanish as soon as the voltage was switched off. From the above it is clear that it is possible to induce a certain degree of molecular orientation at room temperature. As with SHG, no electrooptic response could be measured on the sandwiched samples at the absence of an electric field. As the electric field was switched on, the electrooptic coefficient would reach a constant value and decay back to almost zero after the field was removed, within the temporal resolution of the measurement (a few seconds). A small magnitude tail, indicating some amount of residual orientation, would persist for a few minutes after prolonged poling. In figure 3.5, the electrooptic 3

see equation (2.6).

50

Chapter Three

coefficient r33-r13 versus the electric field across the sample is shown for PVK:TNF:EPNA and PVK:TNF:HONB, measured at a modulation frequency of 1 kHz. A linear increase with the electric field is observed, in agreement with equation (3.1)4 . The electrooptic effect in the EPNA composite is larger, which is expected due to the larger hyperpolarizability and dipole moment of this molecule [32]. Values in the pm/V range are typical for photorefractive polymers [1]. 2.0

(SHG signal) 1/2 (a.u.)

1.5

1.0

0.5

0.0 0

2

4

6

8

10

needle voltage (kV) Fig. 3.4 : Square root of the SHG signal from a PVK:TNF:EPNA casted sample as a function of the voltage on the needle. The offset on the horizontal axis is due to the existence of a threshold value for the establishment of the corona discharge. The line is a guide to the eye.

The orientational mobility of the NLO molecules is expected to increase as the temperature is raised close to the Tg. This is shown in figure 3.6, where the electrooptic coefficient of the two composites increases in a linear-like fashion, reaching at 110 degrees a value that is about three times larger than that at room temperature. This behaviour is governed by the polymer matrix and as expected it is the same for both composites. Above 110 degrees, saturation and a slight decrease is observed. This effect has also been measured in other host-guest polymers at temperatures close or 4

=µf(0)E0/(5kBT) (see equation (2.5)).

Photorefractivity in PVK based Composites

51

equal to Tg [33]. From the above it is clear that by lowering the Tg of the composites with the use of proper plasticizer, an increase of the electrooptic coefficient up to three times can be achieved. 4

PVK:TNF:EPNA PVK:TNF:HONB

(r33 - r13) (pm/V)

3

2

1

0 0

10

20

30

electric field (V/µ m) Fig. 3.5 : The electrooptic coefficient r33-r13 versus the electric field across the sample for the EPNA and the HONB composites, measured at a modulation frequency of 1 kHz and at room temperature. The lines are fits with slopes 0.127 and 0.045 (pm/V)/(V/µm) respectively. The actual value of the electrooptic coefficient showed a variation in the order of 10% from point to point on the same sample and 20% from sample to sample.

In the presence of a dc electric field, Kerr effects can mimic a linear electrooptic response: The measured refractive index change, when Kerr effects are included, is given by [30]: ∆n ∝ rET + sET2

(3.2)

where r and s are the linear (Pockels) and quadratic (Kerr) electrooptic coefficients and ET is the total electric field which is applied on the sample. Their main contribution is expected to arise due to birefringence which is induced from the reorientation of the NLO molecules in the ac field. Contrary to the linear electrooptic response, which is

52

Chapter Three

electronic in origin (thus inherently fast), molecular reorientation is less likely to follow the ac field at high frequencies. This provides a means of separating the two effects.

PVK:TNF:EPNA

3

(r33 - r13) (pm/V)

PVK:TNF:HONB

2

1

0

30

60

90

120

temperature (degrees) Fig. 3.6 : The temperature dependence of the electrooptic coefficient for the two composites. The samples were heated up stepwise, with the electric field (9 V/µm) switched off during heating-up in order to avoid permanent poling at high temperatures.

In figure 3.7, the frequency dependence of the electrooptic coefficient is shown for the two composites. A pronounced decrease of the electrooptic coefficient is noticed for both of them, indicating that molecular orientation is mainly responsible for the observed refractive index change. According to this, the electrooptic coefficients that are measured here are not the true ones in the standard sense, but correspond to: r* = r+2sEdc

(3.3)

where Edc is the dc electric field. The exact magnitudes of r and s cannot be estimated as long as no plateau is observed in the frequency dependence, even up to 100 kHz. However, as it will be shown below, it is r* that is important for the photorefractive effect. From now on, r* will be referred to as the electrooptic coefficient, unless otherwise stated.

Photorefractivity in PVK based Composites

PVK:TNF:EPNA PVK:TNF:HONB

1.5

(r33 - r13) (pm/V)

53

1.0

0.5

0.0

100

1000

10000

100000

frequency (Hz) Fig. 3.7 : The frequency dependence of the electrooptic coefficient r33-r13 at room temperature. The electric field was 9 V/µm.

3.2.4. Proof for the photorefractive nature of the observed gratings. Properties and comparison with the standard model The coexistence of photoconductivity and electrooptic effect does not necessarily lead to photorefractivity. Traps suitable for sustaining a space charge field may not be present, or other types of light induced absorption or refractive index changes may dominate. Study with holographic techniques is necessary to identify the nature of the light induced gratings. Photochromic effects have usually long time constants, are non-reversible and show no electric field dependence. Thermal effects show no electric field dependence either. The gratings that were observed in PVK:TNF:EPNA and PVK:TNF:HONB had typical response time in the order of a second, were erasable and could only be written and read-out when an electric field was applied across the sample. Moreover, no gratings could be written when the two beams where incident in a symmetric geometry with respect to the sample normal, indicating that the electrooptic effect is responsible for the refractive index change5 . Although the 5

in a symmetric geometry reff=0.

54

Chapter Three

combination of these characteristics provides strong evidence for the existence of photorefractivity, it is not a definite proof. In the PVK:TNF:Lophine 1 composite6 , reversible, electric field dependent, light induced refractive index gratings were attributed to a non-photorefractive mechanism, involving local photochemistry [34].

intensity (a.u.)

1.05

1.00

0.95 0

2

4

6

8

time (sec) Fig. 3.8 : Asymmetric energy exchange is observed in a PVK:TNF:EPNA sample when an electric field of 50 V/µm is switched on at time equal zero. The field is removed at approximately 5.6 sec.

Unambiguous proof for the existence of photorefractivity is provided with the demonstration of a phase shifted refractive index grating. As it was discussed in the first chapter, the nonlocal character of photorefractive gratings results in a steady state asymmetric energy exchange between the two beams that write it. In figure 3.8, this is shown to be the case in PVK:TNF:EPNA. At time equal zero the electric field is switched on instantly, causing energy to be transferred from one beam to the other. This is the signature of the photorefractive effect in polymers. Under the influence of the electric field, the EPNA molecules adopt a non centrosymmetric arrangement and the sample becomes electrooptic. At the same time, charge generation and transport are enhanced and the space charge field begins to grow, giving rise to the photorefractive 6

Lophine 1 is 2-(4-nitrophenyl)-4,5-bis(4-methoxyphenyl)imidazole

Photorefractivity in PVK based Composites

55

grating. When the electric field is switched off, the EPNA molecules relax back to their random arrangement and the intensity of both beams returns back to its original value (the observed time scale during removal of the electric field is artificial, caused by the slow discharge of the power supply). The space charge field may still exist inside the sample for quite some time, but in the absence of electrooptic effects there is no refractive index change. Reversing the polarity of the applied field causes energy exchange in the opposite direction, due to the fact that the electrooptic coefficient changes sign.

beam 1

1.00

0.95

0.90

beam 2

1.05

1.00

0.95 -0.04

0.00

0.04

0.08

0.12

time (sec) Fig. 3.9 : The modulation of the transmitted power of the two beams in a PVK:TNF:EPNA sample, due to translation at t=0.0 sec. The electric field was 55 V/µm and translation begun at time equal zero.

After the presence of a photorefractive grating is established with this simple experiment, quantitative information about its basic properties, the amplitude and phase shift, as well as about the presence of complimentary absorption gratings is acquired with the two beam coupling (2BC) technique. In figure 3.9, a typical trace from a PVK:TNF:EPNA sample is shown. At time equal to 0.0 sec sample translation begins and the signals on the two photodiodes are modulated as the two beams read out the

56

Chapter Three

grating. The two signals are 180 degrees out of phase, indicating the dominance of the refractive index grating7 . Slight erasure during sample translation is observed. 0.1

P(-)

0.0

-0.1

P(+)

1.975

1.970

1.965 -0.04

0.00

0.04

0.08

0.12

time (sec) Fig. 3.10 : The sum P(+) and the difference P(-) of the powers of the two beams plotted in figure 3.9.

The analysis of the 2BC data is carried out on the basis of the sum P(+) and the difference P(-) of the two signals, which are plotted in figure 3.10. A small modulation in P(+) reveals the presence of a weak local absorption grating8 , with an amplitude that is around 35 times smaller than that of the refractive index one (shown in P(-)). Local absorption gratings (which may arise due to the difference in the absorption of the neutral and the ionized charge generating site), often accompany photorefractive ones in inorganic crystals. Their presence has also been reported in a photorefractive polymer and photochromism was suggested as a possible source [35]. The origin of the absorption grating in PVK:TNF:EPNA is not clear at present, however, its amplitude is very small and its contribution to the diffraction efficiency is negligible.

7

see equations (2.20).

8

see equations (2.21).

Photorefractivity in PVK based Composites

57

From the 2BC experiment, the diffractive amplitude P of the refractive index grating is revealed to be around 3 cm-1 at 55 V/µm applied across the sample. This value was reproducible from spot to spot on the same sample within 10%. The corresponding refractive index is given by9 : ∆n = P/(πcos(ϑ2-ϑ1)/λ0(cosϑ1cosϑ2)1/2)

(3.4)

and it is found to be in the order of 4⋅10-4. Another important parameter that can be estimated from the 2BC experiment is the diffraction efficiency10 : η ≈ (Pd)2

(3.5)

which reaches a value in the order of 0.1%, at 55 V/µm. The same value was measured with DFWM. This diffraction efficiency may seem low, compared to almost 100% which has been demonstrated in inorganic photorefractives [36]. However, the thickness of the polymer is only 100 µm and its properties are far from optimized. With efficient plasticization, a diffraction efficiency of almost 100% has also been observed recently in a PVK based photorefractive polymer [16]. A very important quantity that is revealed with the 2BC experiment is the phase shift of the refractive index grating. According to the standard model for photorefractivity, ϕ tends towards π/2 in the region of high applied electric fields. The data of figure 3.10, reveal a value for ϕ which is around 40 degrees. Before considering an explanation on the basis of the standard model, let us examine an alternative scenario: In the case where a local, unknown origin refractive index grating coexists with a π/2 phase shifted photorefractive one with approximately the same amplitude, the 2BC experiment (which would measure the first Fourier component of the sum of these two gratings) would yield a phase shift around 45 degrees. This local grating has to be electric field dependent and reversible, otherwise it would be detected during write and read-out experiments, but it should have a different time constant11 . According to this scenario, the decay of the diffraction efficiency should consist of two components, with approximately equal amplitude and different response time. 9

see equation (2.13).

10

11

see equation (2.14).

It is very hard to imagine a complimentary refractive index grating other than photorefractive, which is electric field dependent and has the same response time as the photorefractive one.

58

Chapter Three

This is clearly not the case in figure 3.11, where the diffraction efficiency in PVK:TNF:EPNA is shown to decay in a single exponential fashion. The line is a fit according to the standard model for photorefractivity12 : η(t) ∝ (ESC(0)exp(-t/τ))2

(3.6)

where ESC(0) is the steady state value of the space charge field. Form the above picture it is clear that only one grating exists inside the sample. Its response time constant τ was found to decrease with increasing TNF concentration, applied electric field and light intensity.

10

inverese erase time (sec-1)

diffraction efficiency (a.u.)

1

0.1

1

100

1000

intensity (mW/cm 2 )

0.01 0.0

0.5

1.0

1.5

2.0

time (sec) Fig. 3.11 : Erasure of the photorefractive grating in a PVK:TNF:EPNA sample. The voltage on the needle was 10 kV and the sample was 65 µm thick. The beam intensity was 600 mW/cm2 outside the sample. The line is a fit to equation (3.6), with τ=183 msec. Inset : The dependence of inverse response time constant τ-1 on the erasing beam intensity for the EPNA composite. The electric field was 55 V/µm.

12

see equations (2.11) and (1.10).

Photorefractivity in PVK based Composites

59

In the inset of figure 3.11, the inverse response time constant τ-1 is shown for various intensities of the erasing beam. Although a linear dependence would fit the data rather good, a power law is commonly used in literature. The reason for this is that shallow traps, which are expected to occur naturally in polymers13 , cause a sublinear dependence of τ-1 on intensity. This has been firstly demonstrated in BaTiO3 [37] and has been also observed in several photorefractive polymers [3,10,13]. Accordingly, the line in figure 3.11 is a fit to a power law, yielding an exponent of 0.7±0.3. The large error is due to the limited range of the measurement, which is set by the maximum intensity which is available from the laser and the dark erase time. Although no definite conclusion can be drawn from this fit concerning the presence of shallow traps, their density should not be very high, otherwise it would cause a derivation from the exponential decay of diffraction efficiency versus time [38]. Let us consider the electric field dependence of the amplitude and the phase shift of the photorefractive grating and discuss it within the standard model for photorefractivity. This model was developed to describe the space charge field formation in inorganic photorefractive materials and subsequently, when it comes to polymers, several distinct characteristics are ignored: The mobility and the efficiency of charge generation for example are highly electric field dependent in polymers. Moreover, the nature of trapping sites is not known and their density may as well be field dependent. Despite these deficiencies, the physical picture of the space charge field formation in polymers is very similar with that in inorganic materials. Since the equations on which the model is based are very general, it should still be able to predict trends and give reasonable order-of-magnitude estimates in the steady state regime. According to this model, the space charge field, in the case where the diffusion field is ignored14 , is given by15 : ESC=mEK[1+(EK/ES)2]-0.5

(3.7)

where EK is the projection of the external field along the grating wave vector and ES is the saturation field. The space charge field increases in a linear-like fashion for small 13

this point will be further discussed in chapter four.

14

In this geometry ED=0.1 V/µm. However, the Einstein relation between the diffusion coefficient and the drift mobility is believed not to hold in disordered materials [39]. Moreover, from time-of-flight experiments it was shown that charge transport in PVK cannot be described with the introduction of a diffusion coefficient [40]. For this reason, in a first approximation, the diffusion field is ignored. 15

see equation (1.6).

60

Chapter Three

applied electric fields and reaches saturation when EK approaches ES (figure 1.3). The diffractive amplitude of the photorefractive grating depends on the electrooptic coefficient, which increases linearly with electric field and the space charge field16 : P ∝ reff ESC

(3.8)

90 3

P (cm-1)

2

30

1

0 0

20

40

phase shift (degrees)

60

0 60

electric field (V/µ m) Fig. 3.12 : The diffractive amplitude P and the phase shift ϕ of the refractive index grating for PVK:TNF:EPNA, measured with the 2BC experiment on the same spot of the sample. The lines are fits to the standard model for photorefractivity. At 55 V/µm, the value of P showed a variation in the order of 20% from sample to sample, while the variation in ϕ was up to 40%.

Thus, a superlinear dependence is expected in the region of small electric fields, followed by a linear increase after the saturation field has been reached. The electric field dependence of P for PVK:TNF:EPNA is shown in figure 3.12. A superlinear dependence indicates that the space charge field is below or close to its saturation value. The line is a fit to equation (3.8), yielding excellent agreement between the standard model and the experimental data for a value of the saturation field equal to 21.5±9 16

see equation (2.8).

Photorefractivity in PVK based Composites

61

V/µm. This value of ES, which is comparable to EK (EK is equal to 22 V/µm when 55 V/µm are applied across the sample), is rather reasonable. It corresponds to a trap density of (1.7±0.7)⋅1016 cm-3 (for ε=3.5ε0)17 , which is typical for inorganic photorefractive materials. A similar trap density has been recently measured in an other PVK based photorefractive polymer [41]. The origin of these trapping centers is not clear at present; a discussion on this subject can be found in the next chapter. The space charge field reaches a value in the order of 15 V/µm for 55 V/µm applied across the sample (EK=21.5 V/µm and m=1). Values in this range, which are typical for photorefractive polymers [2], are rather larger compared with what is usually observed in inorganic photorefractive materials. This comes as a result of the lower dielectric constant of polymers, which allows a higher electric field for the same amount of trapped charge. With this value of the space charge field, an electrooptic coefficient in the order of a few pm/V is needed in order to explain the observed diffraction efficiency. Since the saturation field is comparable to EK, intermediate values between 0 and π/2 are expected for the phase shift of the photorefractive grating. According to the standard model, in the case where the diffusion field is ignored, ϕ is given by18 : ϕ=arctan(EK/ES)

(3.9)

In figure 3.12, the calculated dependence of ϕ is shown for EK=21.5 V/µm, together with measured values. Considering the simplicity of the model, the agreement is rather satisfactory. The intermediate values of the phase shift can be understood within the standard model as a result of a high trap density, in the order of 1016 cm-3. However, this value should be regarded as highly approximate. Substantial scatter is observed in the data, especially among samples from different bunches. The phase shift for example can show variations up to 40%, presumably due to impurities that enter accidentally in the polymer during sample preparation. These variations translate to larger ones for the trap density. In the above, the discussion was limited to the EPNA composite, as the diffraction efficiency is higher, allowing a better signal-to-noise ratio. The same observations however apply also to the HONB composite. In this case, the diffractive amplitude of the photorefractive grating was roughly four times lower, a value that corresponds to the ratio of the electrooptic coefficients at low frequencies, indicating a comparable magnitude of the space charge field in both composites. The diffraction 17

see equation (1.8).

18

see equation (1.6).

62

Chapter Three

efficiency was around 0.006% at 55 V/µm. The phase shift of the HONB samples was slightly higher, indicating that the trap density exhibits a weak dependence on the NLO chromophore. This point will be further discussed in chapter five.

3.2.5. Asymmetric energy exchange in poly(N-vinylcarbazole) based photorefractive composites The gain coefficient Γ is among the most important characteristics of a photorefractive material. Most of the proposed applications rely on the existence of large gain, which surpasses the absorption losses, giving rise to net gain, or amplification of a laser beam propagating through the material. This is shown in figure 3.13 to be the case for the EPNA composite, at electric fields higher than 40 V/µm. The absorption coefficient is plotted on the same graph, indicating the level above which net gain occurs. The HONB composite on the other hand shows no net gain below 80 V/µm due to the lower electrooptic coefficient. 15

PVK:TNF:EPNA gain coefficient (cm-1)

PVK:TNF:HONB 10

5

0 0

20

40

60

80

electric field (V/µ m) Fig. 3.13 : The gain coefficient for PVK:TNF:EPNA and PVK:TNF:HONB as a function of electric field. The error bars, which are not shown for clarity, are within 10%. The lines are fits to the standard model. For this experiment β=1. The reproducibility of Γ from sample to sample was within 20%.

Photorefractivity in PVK based Composites

63

This superlinear dependence is in agreement with a space charge field below or close to its saturation value and has been observed in other PVK based photorefractive polymers [10,13,16]. According to the standard model, the enhancement of Γ with an applied electric field is through the electrooptic coefficient, the space charge field and the phase shift19 : Γ ∝ reff ESC sinϕ

(3.10)

1.06

intensity (a.u.)

1.04

1.02

1.00

0.0

0.5

1.0

1.5

2.0

time (sec) Fig. 3.14 : The intensity of the probe beam in a PVK:TNF:EPNA sample as the pump is switched on at t=0.3 sec. The pump is blocked at approximately 1.8 sec. The electric field was 65 V/µm.

The lines in figure 3.13 are fits to equation (3.10), yielding a saturation field equal to 19±1 V/µm for PVK:TNF:EPNA and 16±1 V/µm for PVK:TNF:HONB. The agreement with theory is stunning. The saturation field for the EPNA composite is in agreement with the previously estimated trap density, while for the HONB composite, the latter quantity is around 20% lower. This point will be further discussed in chapter five. 19

see equation (1.14).

64

Chapter Three

In the casted samples a gain coefficient up to 26 cm-1 was achieved for 10 kV on the needle, due to the higher electric field that could be applied before breakdown. Unfortunately, the exact value of the applied electric field during corona poling is not known. Using data from the sandwiched samples however, this value is estimated to be around 155 V/µm, meaning that approximately 80% of the voltage on the needle was applied across the sample during corona poling.

gain coefficient (cm-1)

12

8

4

0 1

10

100

β

Fig. 3.15 : The dependence of the gain coefficient of PVK:TNF:EPNA (squares) and PVK:TNF:HONB (circles) on the ratio β between the intensity of the pump and the probe beam.

The temporal behaviour of the energy exchange is shown in figure 3.14, where the intensity of one of the writing beams (probe) is monitored as a function of the presence of the second beam (pump), in a PVK:TNF:EPNA sample. At time ~0.3 sec, the pump beam is instantly switched on and gain is observed in the intensity of the probe. This energy exchange does not take place instantly, but has a finite rise time, associated with the growth of the space charge field. At time ~1.8 sec, the pump beam is switched off and the intensity of the probe beam returns to its initial value. The photorefractive grating persist inside the sample for some time before it is erased and some part of the probe beam is diffracted, but energy transfer seizes instantly, as it requires the presence of both beams.

Photorefractivity in PVK based Composites

65

Finally, the dependence Γ on the ratio β between the intensity of the pump and the probe was investigated. According to theory, the gain coefficient is independent of the modulation index of the photorefractive grating, thus it should be independent of β. This is shown to be true in the case of PVK:TNF:EPNA and PVK:TNF:HONB (figure 3.15), for almost two decades of β. This independence of gain on the modulation index has been also observed in photorefractive inorganic crystals [42] and polymers [10].

3.2.6. The mechanism of the refractive index change In the standard photorefractive model, the space charge field changes the refractive index via the linear electrooptic effect: ∆n=-(1/2)n03reffESC

(3.11)

where reff is the true linear electrooptic coefficient. However, according to SHG and electrooptic measurements, the NLO molecules in PVK:TNF:EPNA and PVK:TNF:HONB have a substantial degree of orientational mobility at room temperature, giving rise to Kerr effects. During photorefractive grating growth, the NLO molecules are under the influence not only of the external field, but also of the space charge field, which has only a few times smaller magnitude. It is thus tempting to assume that their orientation will be modulated by the space charge field, causing a spatial variation of the birefringence and the electrooptic coefficient. Both these effects can contribute to the refractive index change, leading to an increase of the diffraction efficiency. This mechanism is known as the orientational enhancement of photorefractivity [43]. In order to check whether the mechanism of orientational enhancement is operational in PVK:TNF:EPNA and PVK:TNF:HONB, polarization anisotropy (the ratio between the change in refractive index for p- and for s-polarized light, ∆np and ∆ns respectively) measurements can be used. In the case of a pure linear electrooptic effect, the ratio ∆np/∆ns is solely determined by the ratio r33/r13 (which is equal to 3 for poled polymers [30]) and it is always positive, even in the tilted geometry used here [43]. This is not true in the case of orientational enhancement: Wu has calculated the change in the refractive index due to an applied electric field, in the simplest case of an ensemble of dipolar, rodlike molecules [44]. The change due to birefringence is: ∆n||(BR)=CBRET2

(3.12a)

∆n⊥(BR)=-(1/2)CBRET2

(3.12b)

and due to the modulation of the electrooptic coefficient is:

66

Chapter Three ∆n||(EO)=(1/2)CEOET2

(3.13a)

∆n⊥(EO)=(1/6)CEOET2

(3.13b)

where ∆n|| and ∆n⊥ are the changes in the refractive index parallel and perpendicular to the electric field and the constants C depend on the temperature, density and molecular parameters of the NLO molecules. ET is the total electric field, which in the case of photorefractive polymers is the sum of the external and the space charge field. From equations (3.12) it can be seen that the change of the refractive index due to birefringence reverses sign when measured parallel and perpendicular to the applied electric field. This means that the ratio ∆np/∆ns for a refractive index grating that arises from a spatial variation of the birefringence, will be negative.

beam 2

1.1

1.0

p-polarized 0.9 1.05

beam 2

s-polarized 1.00

0.95 -0.04

0.00

0.04

0.08

0.12

time (sec) Fig. 3.16 : Two beam coupling traces from the EPNA composite, for pand for s-polarized light. Only the second beam is shown in both cases.

In figure 3.16, the modulation of the intensity of one of the beams during a two beam coupling experiment in the EPNA composite is shown for p- and s-polarized light. According to theory20 : 20

equation (2.20b), with A set to zero.

Photorefractivity in PVK based Composites P2 ∝ 2Pdsin(ϕP+2πvt/ΛG)

67 (3.14)

which means that P and consequently the change in the refractive index ∆n reverses sign with polarization, indicating a substantial contribution from the spatial modulation of birefringence. The traces in figure 3.16 clearly demonstrate that the mechanism of orientational enhancement is operational in PVK:TNF:EPNA and PVK:TNF:HONB. The exact magnitude of the contribution due the modulation of the birefringence and the electrooptic coefficient cannot be estimated without separate measurements. These contributions however are also present in the electrooptic experiments and in this way, the electrooptic coefficient that is measured can be used for order-of-magnitude estimates and comparison of various compounds.

3.3. Conclusions and outlook In conclusion, by combining the well known photoconductor PVK sensitized with TNF and the NLO molecules EPNA and HONB, two novel polymer composites that exhibit photorefractivity at 633 nm were developed and net gain was measured in one of them. The electrooptic effect in these materials was shown to contain a major contribution from Kerr effects, arising from the substantial orientational mobility of the NLO molecules at room temperature. The standard theory of photorefractivity could describe the electric field dependence of the amplitude and the phase shift of the photorefractive grating and give reasonable order-of-magnitude estimates of important parameters. A trap density in the order of 1016 cm-3 was estimated for both composites. Finally, the refractive index change in these materials was found to contain a contribution from the spatial modulation of the birefringence due to the reorientation of the NLO molecules in the space charge field. PVK based composites seem to be promising candidates for efficient photorefractive materials. However, still a lot of things remain to be understood. The nature of the trapping centers in one of them. An approach towards the study of charge trapping in photorefractive polymers is presented in the next chapter. The mechanical properties of the composites discussed here are clearly not at the optimum and there is substantial room for improvement. The temperature dependence of the electrooptic coefficient for example, suggest that almost a ten fold increase of the diffraction efficiency may take place, if the Tg is lowered close to room temperature with the addition of a proper plasticiser. The existence of the orientational enhancement mechanism hints that the NLO molecule should not be attached to a polymer chain, as this would lead to a decrease of its orientational mobility. The exact magnitude of the contribution due to the modulation of the birefringence and the electrooptic coefficient should be estimated and the NLO molecules designed accordingly.

68

Chapter Three

3.4. References [1] [2] [3] [4] [5] [6]

[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

W.E. Moerner and S.M. Silence, Chem. Rev. 94, 127 (1994) S. Ducharme, J.C. Scott, R.J. Twieg and W.E. Moerner, Phys. Rev. Lett. 66, 1846 (1991) S.M. Silence, C.A. Walsh, J.C. Scott, T.J. Mattray, R.J. Twieg, F. Hache, G.C. Bjorklund and W.E. Moerner, Opt. Lett. 17, 1107 (1992) J.S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991) M. Liphardt, A. Goonesekera, B.E. Jones, S. Ducharme, J.M. Takacs and L. Zhang, Science 263, 367 (1994) H.J. Bolink, V.V. Krasnikov, G.G. Malliaras and G. Hadziioannou, in Nonlinear Optical Properties of Organic Materials VI, SPIE proc. 2025, ed. G.R. Möhlmann, San Diego (1993) L. Yu, W. Chan, Z. Bao and S.X.F. Cao, Macromolecules 26, 2216 (1993) S.M. Silence, D.M. Burland and W.E. Moerner, in "Photorefractive Effects and Materials", D.D. Nolte, ed., Kluwer Academic (1995) Y. Zhang, R. Burzynski, S. Ghosal and M.K. Casstevens, to appear in Adv. Mater. M.C.J.M. Donkers, S.M. Silence, C.A. Walsh, F. Hache, D.M. Burland, W.E. Moerner and R.J. Twieg, Opt. Lett. 18, 1044 (1993) Y. Zhang, Y. Cui and P.N. Prasad, Phys. Rev. B. 46, 9900 (1992) B. Kippelen, Sandalphon, N. Peyghmbarian, S.R. Lyon, A.B. Padias and H.K. Hall Jr., Elect. Lett. 29, 1873 (1993) M.E. Orczyk, B. Swedek, J. Zieba and P.N. Prasad, J. Appl. Phys. 76, 4995 (1994) S.M. Silence, M.C.J.M. Donkers, C.A. Walsh, D.M. Burland, R.J. Twieg and W.E. Moerner, Appl. Opt. 33, 2218 (1994) M.E. Orczyk, J. Zieba and P.N. Prasad, J. Phys. Chem. 98, 8699 (1994) K. Meerholz, B.L. Volodin, Sandalphon, B. Kippelen and N. Peyghambarian, Nature 371, 497 (1994) Du Lei, J. Runt, A. Safari and R.E. Newnham, Macromolecules 20, 1797 (1987) Thanks are due to H.J. Bolink and G.O.R. Alberda van Ekenstein for carrying out the DSC measurements. A. Dulcic, C. Flytzanis, C.L. Tang, D. Pepin, M. Fitzon and Y. Hoppiliard, J. Chem. Phys. 74, 1559 (1981) J.C. Scott, L. Pautmeier and W.E. Moerner, Synth. Metals 54, 9 (1993) T. Kawakami and N. Sonoda, Appl. Phys. Lett. 62, 2167 (1993) B. Kippelen, K. Tamura, N. Peyghambarian, A.B. Padias and H.K. Hall Jr., Phys. Rev. B 48, 10710 (1993)

Photorefractivity in PVK based Composites [23] [24] [25]

[26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

[37] [38] [39] [40] [41] [42] [43] [44]

69

H.J. Bolink, V.V. Krasnikov, G.G. Malliaras and G. Hadziioannou, Adv. Mater. 6, 574 (1994) G.G. Malliaras, V.V. Krasnikov, H.J. Bolink and G. Hadziioannou, manuscript in preparation. for a recent review see P.M. Borsenberger and D.S. Weiss, eds. "Organic Photoreceptors for Imaging Systems", Optical Engineering vol. 39, Marcel Dekker, Inc. (1993) and references therein. P.J. Reucroft in "Photoconductivity in Polymers: an Interdisciplinary Approach", A.V. Patsis and D.A. Seanor, eds., Technomic (1976) G. Weiser, J. Appl. Phys. 43, 5028 (1972) W.D. Gill, J. Appl. Phys. 43, 5033 (1972) D.M. Burland, R.D. Miller and C.A. Walsh, Chem. Rev. 94, 31 (1994) P.N. Prasad and D.J. Williams, "Introduction to Nolinear Optical Effects in Molecules and Polymers", Wiley Interscience (1991) and references therein. H.T. Man and H.N. Yoon, Adv. Mater. 4, 159 (1992) A. Dulcic and C. Sauteret, J. Chem. Phys. 69, 3453 (1978) P.K. Wu, G.R. Yang, X.F. Ma, A. Cococziela and T.M. Lu, J. Appl. Phys. 77, 2258 (1995) S.M. Silence, M.C.J.M. Donkers, C.A. Walsh, D.M. Burland, W.E. Moerner and R.J. Twieg, Appl. Phys. Lett. 64, 712 (1994) C.A. Walsh and W.E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992) see for example P. Günter and J.P. Huignard in "Photorefractive Materials and their Applications I and II", P. Günter and J.P. Huignard eds., Topics in Applied Physics vol. 61 and 62, Springer-Verlag (1988) D. Mahgerefteh and J. Feinberg, Phys. Rev. Lett. 64, 2195 (1990) P. Tayebati and D. Mahgerefteh, J. Opt. Soc. Am. B 8, 1053 (1991) L. Pautmeier, R. Richert and H. B@ssler, Phil. Mag. B 3, 587 (1991) H. Scher and E.W. Montroll, Phys. Rev. B 12, 2455 (1975) M.E. Orczyk, J. Zieba and P.N. Prasad, Appl. Phys. Lett. 67, 311 (1995) N.V. Kukhtarev, V.B. Markov, S.G. Odulov, M.S. Soskin and V.L. Vinetskii, Ferroelectrics 22, 961 (1979) W.E. Moerner, S.M. Silence, F. Hache and G.C. Bjorklund, J. Opt. Soc. Am. B 11, 320 (1994) J.W. Wu, J. Opt. Soc. Am. B 8, 142 (1991)

70

Chapter Three

Chapter Four Charge Trapping in Photorefractive Polymers

Abstract The process of charge trapping is of vital importance for the photorefractive effect, yet no systematic attempt has been made to understand and control it in photorefractive polymers. In this chapter, a modification of the trap density of a poly(Nvinylcarbazole) based polymer composite is demonstrated with the addition of 4-(N,Ndiethylamino)benzaldehyde diphenylhydrazone (DEH). Measurements of the response time, the phase shift and the amplitude of the photorefractive grating indicate that at low concentrations DEH acts as a trap, while at higher concentrations a new charge transport channel is established through hopping between DEH molecules. Using transient photorefractivity measurements the effect of the change in the trap density on the hole drift mobility is estimated.

72

Chapter Four

4.1. Introduction The field of polymer photorefractivity has greatly benefited from knowledge gathered during previous studies of the optoelectronic properties of polymers. The processes of charge generation and transport are quite well studied, due to the application of these materials in xerography [1]. The electrooptic effect has also been a subject of intense research interest, due to their potential exploitation in light modulators and switches [2]. On the other hand, the process of charge trapping in polymers is less well studied. This is reflected in all photorefractive polymers that have been reported until today, where no attempt was made to introduce trapping species. Holes are assumed to become trapped at impurities accidentally present in the polymer [3], defects of the polymer backbone (such as chain ends) [4], sensitizer [5] and chromophore [6] molecules etc. As it was indicated in the first chapter, the space charge field strongly depends on the saturation field, which is proportional to the trap density. The response time of the photorefractive effect is also dependent on the presence of traps. It is thus very important for the optimisation of the performance of photorefractive polymers to understand and control charge trapping. This may be the route towards long storage time and high diffraction efficiency, which is required for optical data storage applications. By definition, trapping takes place at hopping sites that require an energy substantially higher than the average energy to release the charge carriers. Hole transport in photorefractive polymers takes place via hopping in a manifold of localized states, provided by the addition of donor-like species (the charge transport species). Due to positional and energetic disorder, these localized states have an energy distribution, with a width that depends on the degree of disorder [7]. Typical values for this width are of the order of 0.1 eV [8]. According to this picture, holes that are localized at the tail of this distribution require more thermal energy than the average, in order to hop to a neighbouring site. For this reason, shallow trapping is expected to occur naturally in photorefractive polymers. Shallow traps however cannot sustain a space charge field, as they will empty thermally as soon as illumination is discontinued. Addition of sites with ionization potential substantially lower than that of the transport species is required. The effect of addition of low ionization potential molecules in a polymer that exhibits hole transport was studied in the past, long before photorefractivity in polymers was discovered. The time-of-flight (TOF) technique1 was used to measure the hole drift 1

According to this experiment, a polymer film is sandwiched between two blocking electrodes, one of them which is transparent. A strongly absorbing pulse of light excites a thin sheet of carriers inside the film, that drift towards the opposite electrode under the application of an electric field. The current versus time plot shows a shoulder that indicates

Charge Trapping in Photorefractive Polymers

73

mobility in a solid solution of NIPC2 in polycarbonate as a function of doping with small concentrations of TPA3 . As TPA has a lower ionization potential than NIPC (about 0.47 eV lower), it was found to strongly affect charge transport: Holes, that are normally transported through NIPC, became temporarily immobilized at TPA sites, which caused a decrease of their drift mobility [9]. The same behaviour has been observed later, in other molecularly doped polymers [10-12] and the reduction of mobility for a certain dopant concentration was found to increase with the difference in the ionization potentials [13]. Although information about charge trapping can be obtained from time-offlight measurements, the presence of photorefractivity in polymers creates the opportunity to study the process of charge trapping in a more straightforward way, and with the use of "clean" optical techniques. As it was indicated in the first chapter, the saturation field, which can be assessed with holographic measurements, is directly proportional to the trap density. The hole drift mobility can also be measured, with transient holographic techniques. Apart from being more versatile, optical techniques are more natural to use in photorefractive polymers, as they directly measure the parameters that determine the photorefractive response, on the same sample that will be used for further characterization. For example, the trap density that is measured with holographic techniques is the trap density that controls the space charge field formation process. In an effort to study charge trapping in photorefractive polymers, the PVK:TNF:EPNA composite was doped with various amounts of DEH, which has a lower ionization potential than PVK [14]. The influence of the DEH concentration on charge transport in PVK was investigated using (quasi-) steady state and transient holographic techniques.

4.2. (Quasi-) steady state holographic experiments This part of the investigation was carried out with casted samples. All of them were prepared by adding different amounts of DEH to a portion of the same master solution, in order to ensure that the relative concentration of EPNA and TNF in PVK was exactly the same. The master solution contained 39% wt. EPNA and 0.1% wt. the arrival of the carriers at the opposite electrode. Knowing the thickness of the sample and the applied field, the drift mobility is estimated from the time that corresponds to that shoulder (see chapter five for details). 2

N-isopropylcarbazole.

3

triphenylamine.

74

Chapter Four

TNF relative to PVK. Five samples where prepared, with DEH concentrations equal to 0, 0.18, 1.78, 8.89 and 19.74% wt. relative to PVK. The DEH/PVK monomer unit molar ratios were 0, 1/1000, 1/100, 1/20 and 1/9 respectively. In table 1, the composition of the various samples is shown. Their average thickness was 57±7 µm.

Table I Composition of films. The first row shows the percentage in the total film weight, while the second shows the number density in 1018 cm-3, assuming a density for the films equal to 1.2 g/cm3. Sample

PVK

TNF

EPNA

DEH

0

71,89% 2692

0.07% 1.6

28.04% 1045

0

1/1000

71.80% 2689

0.07% 1.6

28.00% 1043

0.13% 2.7

1/100

70.99% 2658

0.07% 1.6

27.68% 1031

1.26% 27

1/20

67.57% 2531

0.07% 1.5

26.35% 982

6.01% 127

1/9

62.96% 2358

0.06% 1.4

24.55% 915

12.43% 262

For the measurements of the amplitude P and the phase shift ϕ of the photorefractive gratings, the two beam coupling (2BC) method was used, in the geometry described in chapter two. In all samples, purely refractive index gratings were observed and equations (2.20) were used to fit the data and extract P and ϕ. For the measurements of the response time, one of the writing beams was blocked and decay of the diffracted part of the other beam was monitored. While writing the gratings, the asymmetric energy exchange between the two beams was observed and allowed to reach saturation, before carrying out a measurement. Generally, the gratings were written for a time that was equal or larger than the response time.

Charge Trapping in Photorefractive Polymers

75

4.2.1. The response time of the photorefractive grating In figure 4.1 the inverse response time τ-1 under uniform illumination (600 mW/cm ) is plotted versus the DEH concentration. A sharp decrease of τ-1 is observed as one DEH molecule is introduced every 1000 carbazole units in the photorefractive composite. After reaching a minimum value of 0.41±0.04 sec-1 for the sample with 1/100 DEH to carbazole ratio, τ-1 increases, reaching a value of 16.0±1.3 sec-1 for the sample with the highest DEH concentration. 2

inverse response time constant (sec -1)

100

10

1

0.1 0.00

0.03

0.06

0.09

0.12

DEH/Carbazole molar ratio Fig. 4.1 : Inverse response time of the photorefractive grating as a function of the DEH/carbazole molar ratio. The voltage on the needle was 10 kV and the intensity of the erasing beam, incident at 60o with the sample normal, amounted to 600 mW/cm2. The line is a guide to the eye.

The behaviour of τ-1 with DEH concentration can be understood from the simple scheme of figure 4.2. Transport of holes in the PVK:TNF:EPNA composite takes place via hopping between localized energy levels, provided by the carbazole units (step 1). Addition of very small amounts of DEH gives rise to hole trapping (step 2): The holes will reside at the site of DEH, until an electron from a neighbouring carbazole unit gains statistically enough thermal energy to move "uphill" to the site of

76

Chapter Four

the trap (step 3). Thus, at low concentrations of DEH, trapping is expected to decrease the drift mobility and subsequently τ-1, which is proportional to the former4 .

4 1

2

DEH

PVK

3

Fig. 4.2 : Hopping transport: (1) via the high ionization potential (Ip) compound; (2) trapping at sites of low Ip; (3) detrapping; (4) hopping via the low Ip compound.

DEH however is a donor-like, low ionization potential molecule, which allows hole transport as much as a carbazole unit. Further increase of its concentration creates a new transport channel for holes, as the distance between two neighbouring DEH molecules becomes small enough and direct hopping is possible (step 4). In this way, the effective trap density decreases and this is reflected in τ-1, which increases for DEH concentrations higher than 1 per 100 carbazole units. More over the transport properties of DEH is discussed below. It should be mentioned that the decay of the gratings in the samples containing DEH shows complicated dynamics. In most cases a biexponential decay for the space charge field would fit the data rather good, with a few exceptions. This behaviour, which cannot be explained within the standard theory of photorefractivity, has been observed in inorganic photorefractive crystals and it is attributed to the presence of a substantial amount of shallow traps, from which charge can be thermally excited [15]. The limited dynamic range of the setup in the region of low diffraction efficiency (not better than two orders of magnitude) prohibited a systematic study of the slow component of space charge field decay. In contrast with the fast component, whose amplitude and time constant did not change with the writing time, the amplitude and time constant of the slow component was dependent on the writing time. However, the decay of the diffraction efficiency down to 10% of its initial value could always be fitted with a single exponential, from which τ-1 was calculated ( τ is equal to twice the time constant of the diffraction efficiency decay).

4

see equation (1.11).

Charge Trapping in Photorefractive Polymers

77

Recently, Zhang et al. [16] also studied the effect of addition of a low ionization potential molecule in a PVK based photorefractive polymer. The authors have used TPM5 as an additive and measured the response time and the dark decay of the photorefractive gratings as a function of the TPM concentration. Both quantities showed the same trend as in figure 4.1, exhibiting a fast initial increase and slowly recovering for TPM concentrations larger than 1019 cm-3 (roughly the same concentration in which the maximum τ is observed in figure 4.1). The explanation for this behaviour was the same as the one outlined above.

4.2.2. The phase shift of the photorefractive grating In order to get more insight into the influence of DEH on the charge trapping process, the phase shift of the photorefractive grating was measured as a function of the DEH concentration. As can be seen in figure 4.3, it shows similar behaviour with τ-1. The phase shift for the PVK:TNF:EPNA composite was measured to be 32±9 degrees. The large error bars are due to the scatter in ϕ from sample to sample, presumably due to the accidental presence of impurities which act as traps. As can be seen in figure 4.3, ϕ is very sensitive to certain additives: addition of as little as 1 DEH molecule every 1000 carbazole units causes a steep decrease of ϕ. The dependence of the phase shift on DEH concentration can be understood according to the standard model for photorefractivity. In the steady state regime, ϕ is given by6 : ϕ=arctan(EK/ES)

(4.1)

where EK is the projection of the external field along the grating wave vector and ES is the saturation field, which is proportional to the trap density. In the case of PVK:TNF:EPNA, the value of the phase shift implies that the saturation field is comparable to the external field, indicating the presence of substantial amount of traps to begin with. With the addition of DEH, the trap density is changed in a controlled way and this change can be directly probed with a measurement of the phase shift. As can be estimated from figure 4.3, the trap density increases initially, as DEH is added at small amounts. When the concentration of DEH exceeds 1 per 100 carbazole units, the trap density decreases, as the DEH molecules begin to act as hole transport species instead of trapping centers. Furthermore, due to the lower ionization 5

bis[2-methyl-(4-N,N-diethylaminophenyl)]phenylmethane

6

see equation (3.9).

78

Chapter Four

potential of DEH compared to PVK, hopping through DEH is expected to be less affected from trapping at accidentally present impurities than hopping through PVK.

phase shift (degrees)

60

40

20

0

0.00

0.04

0.08

0.12

DEH/Carbazole molar ratio Fig. 4.3 : Phase shift of the photorefractive grating as a function of the DEH/carbazole molar ratio. The voltage on the needle was 10 kV. The line is a guide to the eye.

Consider an order-of-magnitude estimate of the trap density induced by DEH. The phase shift of the undoped sample is around 32 degrees. Assuming that 80% of the voltage on the needle drops across the film (as it was estimated in the previous chapter), the trap density is in the order of 7⋅1016 cm-3. In the same way, in the sample with 1/1000 DEH to carbazole ratio, it is in the order of 35⋅1017 cm-3, which is about ten times lower than the DEH concentration. However, the standard model for photorefractivity does not allow thermal excitation of trapped carriers, and the calculated trap density should be regarded as an effective one. If thermal excitation is possible, the effective trap density depends not only on the concentration of the trapping species, but also on parameters such as the trapping and detrapping rates [17-18].

4.2.3. The amplitude of the photorefractive grating The diffractive amplitude P of the photorefractive grating as measured with the two beam coupling technique is plotted in figure 4.4 (open circles), in units of percent

Charge Trapping in Photorefractive Polymers

79

modulation of the transmitted beams during sample translation (thus, what is plotted on the y axis is the quantity P*=2Pd, where d is the sample thickness). In the sample which contains no DEH, P* is equal to 5.8±1.2 and reaches a maximum value of 9.3±1.4 for the sample with 1/20 DEH to carbazole ratio. This corresponds to an increase in the diffraction efficiency (which depends quadratically on P*) of about 3 times. Further addition of DEH leads to a decrease in P*.

amplitude of modulation (%)

12

8

4

0 0.00

0.04

0.08

0.12

DEH/Carbazole molar ratio Fig. 4.4 : Amplitude P* of the modulation as a function of the DEH/carbazole molar ratio. Open circles: Experimental points, from the two beam coupling experiment. The voltage on the needle was 10 kV. The line is a guide to the eye. Filled triangles: Theoretical points, according to equation (4.2).

The dependence of the amplitude of the photorefractive grating on the DEH concentration is rather complicated. According to theory7 : P∝reffESC The space charge field is given by8 : 7

see equation (2.8).

(4.2)

80

Chapter Four ESC=mEK[1+(EK/ES)2]-0.5

(4.3)

In figure 4.4, the filled triangles (which are shifted 0.004 units on the horizontal axis for clarity), are calculated values according to equation (4.2). From the phase shift data of figure 4.3, the ratio EK/ES is calculated for each sample using equation (4.1) and subsequently the space charge field and P are deduced. The proportionality factor of equation (4.2) was evaluated from the measured value of P* for the sample containing no DEH, and subsequently P* was calculated for the other samples. The large error bars are due to the experimental error in the determination of the phase shift and the distribution in the sample thickness (which influences the measured values of P*). However, P depends also on reff, which makes the analysis more complicated. The effective electrooptic coefficient is proportional to the number density of the EPNA molecules, which varies 12.5% between the samples with no DEH and maximum DEH. Moreover, plasticization, which increases the electrooptic coefficient, is expected to take place at the samples with the highest DEH concentration. These effects need to be accounted for properly by a separate measurement of the electrooptic coefficient, in order to interpret the behaviour of the diffraction efficiency on DEH concentration. The main conclusion from figure 4.4 however, is that the increase in the diffraction efficiency with addition of DEH is not spectacular, due to the existence of an already substantial amount of traps in the PVK:TNF:EPNA polymer.

4.3. Transient holographic experiments Transient photorefractivity experiments have been used in the case of inorganic photorefractive crystals to study the dynamics of the space charge field formation [19-21]. In a particular variation, the drift mobility is measured with a holographic time-of-flight (HTOF) technique [20], as it was outlined in chapter two. The application of HTOF technique in photorefractive polymers seems very interesting: although the physical picture of the space charge field formation is similar to that in inorganic crystals, the nature of charge transport in disordered materials is very distinct. Investigation with the conventional time-of-flight technique has shown that charge transport in polymers exhibits anomalously broad TOF signals and that it is characterized by an electric field and temperature dependent mobility [22]. For this reason, it is not clear a priori if any feature that allows the determination of mobility will be observed in the temporal behaviour of the diffraction efficiency. An extensive discussion on the applicability of the HTOF technique on the measurement of the drift mobility in photorefractive polymers is presented in the next 8

see equation (3.7).

Charge Trapping in Photorefractive Polymers

81

chapter. In this section, results from PVK:TNF:EPNA samples with various amounts of DEH are presented and the origin of the transient signal is investigated. The influence on the hole drift mobility due to the change in the trap density induced by DEH is directly measured. HTOF experiments were conducted in three of the samples described in Table I: The one with no DEH, the one with 1/1000 DEH to carbazole ratio, which has an increased trap density compared to the former and the one with 1/9 DEH to carbazole ratio, where DEH contributes to hole transport. Both sandwiched and casted samples where examined and similar features have been observed. However, for the determination of the drift mobility, knowledge of the exact value of the applied electric field is required and for this reason, the behaviour in the former type of samples is discussed here. These were assembled by pressing 200 µm thick pellets between two ITO plates. Spacers were not used at that time and although mild pressing was applied and the polymer film did not flow extensively, a thickness decrease has taken place. By breaking some of the samples and measuring the thickness of the polymer layer, a variation of 30% was measured. The response time, the phase shift and the amplitude of the photorefractive gratings in these samples yielded the same overall behaviour as in the casted ones discussed above. HTOF experiments were carried out with the setup which was described in the second chapter, with a drift length of 1.7 µm.

4.3.1. Space charge field formation In figure 4.5 the transient behaviour of the diffraction efficiency in PVK:TNF:EPNA is shown for different electric fields: A dramatic change is apparent: at low electric fields (15 V/µm), it merely reaches saturation, which is followed by slow erasure from the probe He-Ne beam (not shown in this plot). However, as the applied field increases, a clear maximum appears gradually. According to the picture for the space charge field formation (outlined in the second chapter), this maximum corresponds to the position of anticoincidence between the hole distribution and the immobile countercharges. In the trace that corresponds to 35 V/µm, the diffraction efficiency reaches a maximum at tmax=32 msec, from which a hole drift mobility of 1.5⋅10-8 cm2/(Vsec) is estimated. The influence of the space charge field was ignored in this calculation, because during transient experiments it is small compared to the external electric field. The accuracy of the estimated mobility is within 30%, mainly due to thickness variations. The value of tmax was reproducible on the same sample with accuracy better than 10%. The measured value for the hole drift mobility is one to two orders of magnitude lower than values reported for pure PVK at the same range of electric fields [23]. This is expected due to the presence of large amount of EPNA in the composite, which reduces the effective concentration of the carbazole units. Moreover, the presence

82

Chapter Four

of polar molecules is believed to have a negative effect on the drift mobility [24-26]. This point will be further discussed in the next chapter.

diffraction efficiency (a.u.)

1.0

0.5

15 V/µ m 20 V/µ m 35 V/µ m

0.0 0.0

0.2

0.4

time (sec)

Fig. 4.5 : Normalized diffraction efficiency versus time for various electric fields applied across the PVK:TNF:EPNA sample.

A potential danger during HTOF experiments in polymers arises from the existence of the orientational enhancement of photorefractivity. As it was shown in the previous chapter, the EPNA molecules reorient under the influence of the space charge field, leading to an enhancement of the electrooptic coefficient and subsequently the diffraction efficiency. In calculating the mobility from the trace of figure 4.5, the assumption was made that the change in the diffraction efficiency was solely due to the space charge field formation process. In order to prove this, it must be demonstrated that no substantial change in the orientation of the EPNA chromophores takes place at this time scale. Otherwise, the convolution of the EPNA reorientation time and the growth of the space charge field is measured and the extraction of the mobility is not trivial. Form the frequency dependence of the electrooptic coefficient (figure 3.7), the orientation time of EPNA seems to be rather fast. A response time of 1 msec for example, corresponds to approximately 200 Hz (=1/2πτ), at which the electrooptic coefficient has reached 80% of its maximum value. However, the orientational

Charge Trapping in Photorefractive Polymers

83

dynamics of EPNA can be directly estimate using electrooptic measurements in the time domain. For this reason, the setup for the electrooptic coefficient measurements was used (figure 2.3), as described in the second chapter. The sample was kept under a dc bias and the transmitted intensity was measured as a voltage pulse was suddenly applied across it. Under the influence of this pulse the EPNA molecules reorient, causing a phase shift between the p- and s-polarized component of light propagating in the sample, that leads to an increase of the transmitted intensity after the analyzer (figure 4.6).

pulse ON

intensity (a.u.)

1.10

1.05

1.00

pulse OFF 0.0

0.2

0.4

time (sec) Fig. 4.6 : Transmitted intensity versus time for the electrooptic experiment. The arrows indicate the voltage pulse.

Two components are clearly visible, with different time scales: A fast one which follows instantly the risetime of the voltage front (which was better than 100 µsec) and could not be time resolved and a slow one, which is responsible for approximately half of the measured signal and has an approximate response time in the 100 msec range. The origin of this slow component cannot be clarified from this experiment alone and it is impossible to conclude if EPNA reorientation happens at this time scale. Usually however, low frequency contributions during electrooptic measurements arise from effects other than electrooptic [27]. Indeed, measurements with a fiber optic interferometer from an atomic force microscope [28] have shown that the sample thickness decreases as much as a few nm when 1 kV is applied across the

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sample. This thickness variation took place at the same time scale as the slow component of the electrooptic response. Electrode attraction causing a sample compression, accompanied by a change in the refractive index due to elastooptic effects is a possible reason for the slow time scale.

pulse ON

pulse OFF

SHG signal (a.u.)

10

5

0

-0.1

0.0

0.1

0.2

time (sec) Fig. 4.7 : Second harmonic generation signal and applied voltage versus time. The line is a guide to the eye. The arrows indicate the voltage pulse.

In order to get more insight into the dynamics of the EPNA orientation, SHG experiments were performed on the same time scale. The experimental geometry was described in chapter two. In this case however, the response time of the detection system was brought to the msec range with the addition of a proper RC circuit, to allow observation of the individual pulses in the desired time scale. The results are shown in figure 4.7, where it can be seen that the slow component is absent in the SHG signal: In contrast with the signal in figure 4.6, which almost doubled its initial value in the first 200 msec, the SHG response remains constant. In contrast with electrooptic experiments, SHG issensitive only to dipolar orientation. This means that only the fast time scale in figure 4.6 is associated with EPNA orientation, which reaches a constant value in a time less than 100 µsec. This conclusion is in agreement with dielectric relaxation studies of host-guest polymers, which show that upon the application of an

Charge Trapping in Photorefractive Polymers

85

electric field, the NLO molecules react with a jump-like motion [29]. Thus, what is observed in figure 4.5 is indeed the formation of the space charge field. Further evidence for the photorefractive nature of the gratings observed in figure 4.5 is provided by transient photocurrent measurements. According to the physical picture for the space charge field formation, the change in the diffraction efficiency originates from the motion of carriers which gives rise to macroscopic current flow. The transient photocurrent, shown in figure 4.8, has a very fast component that follows the Nd:YAG pulse and cannot be time resolved (inset of figure 4.8), followed by a small magnitude tail. This tail still exists at time scales that correspond to grating growth time. The tail of the transient photocurrent follows an inverse power law dependence with time, which is typical for amorphous materials [22], in contrast with exponential decays observed in the case of inorganic photorefractive crystals [20]. 0.4

Current (µA)

0.3

Current (µA)

300

200

100

0.2 0 -20

0

0.1

0.0 0.0

20

40

time (nsec)

0.1

0.2

0.3

0.4

time (msec) Fig. 4.8 : Tail of the transient photocurrent for the PVK:TNF:EPNA sample. The voltage across the sample was 7 kV. Inset : The fast component of the transient photocurrent follows the shape of the nanosecond Nd:YAG laser pulse.

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Chapter Four

4.3.2. Influence of the trap density on the space charge field formation According to the (quasi-) steady state measurements, the presence of 1 DEH molecule every 1000 carbazole units should reduce the drift mobility of holes and thus affect the rise time of the space charge field formation. This is apparent in figure 4.9, where the transient behaviour of the diffraction efficiency in the sample with 1/1000 DEH is shown. It should be stressed that in this case, the decrease of the diffraction efficiency after 10 sec is due to erasure of the grating by the He-Ne probe beam and the dark conductivity. An upper limit of 5⋅10-11 cm2/(Vsec) can be calculated for the drift mobility from this plot, which is more than three orders of magnitude lower, compared to the mobility in undoped PVK:TNF:EPNA.

diffraction efficiency (a.u.)

1.0

0.5

35 V/µ m

0.0 0

10

20

30

time (sec) Fig. 4.9 : Normalized diffraction efficiency versus time for the sample with 1/1000 DEH to carbazole unit molar ratio.

The transient behaviour of the diffraction efficiency in the sample with 1/9 DEH to carbazole ratio is shown in figure 4.10. The maximum returns back to the msec time scale, which corresponds to a drift mobility of 10-8 cm2/(Vsec) for 35 V/µm applied across the sample. This increase of the mobility comes as a result of the contribution of DEH to charge transport. DEH dissolved in polycarbonate is known to exhibit hole transport at this concentration [30]. However, the determination of its exact

Charge Trapping in Photorefractive Polymers

87

contribution is difficult, as the mobility of DEH solid solutions is strongly dependent on the polarity of the polymer matrix [31]. The observed dependence of the hole drift mobility on the DEH concentration is in agreement with earlier work of Pai et al. [10]. The authors measured (with the conventional TOF technique) the hole drift mobility of PVK, doped with various amounts of TPD (which has a lower ionization potential). A steep decrease of three orders of magnitude was observed for low TPD concentrations. However, as the TPD concentration exceeded 2% wt. relative to PVK, the hole drift mobility slowly recovered. It is worth pointing out that according to the phase shift measurements of figure 4.3, the maximum trap density in PVK:TNF:EPNA is observed for the same DEH concentration. This is not a coincidence, as both molecules have comparable molecular weight and size.

diffraction efficiency (a.u.)

1.0

0.5

25 V/µ m 35 V/µ m 0.0 0.0

0.2

0.4

time (sec) Fig. 4.10 : Normalized diffraction efficiency versus time for various electric fields for the sample with 1/9 DEH to carbazole unit molar ratio.

One final point before closing this chapter: Although the hole drift mobility in the undoped sample and the one with 1/9 DEH to carbazole ratio is almost the same, the shape of the diffraction efficiency transient is very different: The decrease of the signal after the maximum is reached is much higher in the latter sample (figures 4.5 and 4.10). It is reasonable to assume that such a feature is associated with the degree of dispersion of charge transport, which seems to be different for these two samples. However, due to

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lack of theory which takes into account the dispersive nature of charge transport in amorphous materials, extraction of such information is not possible. More on this issue will be discussed in the next chapter.

4.4. Conclusions and outlook In conclusion, a change in the trap density of the PVK:TNF:EPNA polymer composite was achieved in a controlled way with the addition DEH. This change affected the response time, the phase shift, the amplitude and the dynamics of the space charge field formation of the photorefractive gratings. Despite the dispersive character of charge transport in polymers, a well-defined maximum was observed in the transient behaviour of the diffraction efficiency in PVK:TNF:EPNA, which allowed an estimation of the hole drift mobility. From this study it is clear that there is an optimum concentration of the trapping species, for which the photorefractive grating will exhibit the slowest erasure. By introducing extra trapping centers in PVK:TNF:EPNA with the addition of DEH, the response time decreased slightly more than an order of magnitude. In order to make a material suitable for optical data storage applications, a deeper trap is needed. Moreover, the addition of DEH did not lead to a significant increase in the diffraction efficiency, due to the presence of an already substantial amount of traps. It seems very interesting to continue the investigation of charge trapping in photorefractive polymers. The low diffraction efficiency regime during the erasure of gratings in DEH doped PVK:TNF:EPNA has not been studied at present and little is known about the photosensitivity of the DEH traps. Investigation in this direction seems particularly interesting in the light of the newly discovered quasinondestructive readout of holograms in photorefractive polymers [32]. Finally, theoretical modelling of the HTOF signal, taking into account the anomalous character of charge transport in polymers, is needed to support this powerful technique.

4.5. References [1] [2] [3] [4] [5]

see for example P.M. Borsenberger and D.S. Weis, "Organic Photoreceptors for Imaging Systems", Marcel Dekker, Inc., New York (1993) see for example P.N. Prasad and D.J. Williams, "Introduction to Nonlinear Optical Effects in Molecules and Polymers", Wiley Interscience (1991) J.C. Scott, L.Th. Pautmeier and W.E. Moerner, Synth. Metals 54, 9 (1993) W.E. Moerner and S.M. Silence, Chem. Rev. 94, 127 (1994) S.M. Silence, C.A. Walsh, J.C. Scott and W.E. Moerner, Appl. Phys. Lett. 61, 2967 (1992)

Charge Trapping in Photorefractive Polymers [6] [7] [8] [9] [10] [11] [12] [13] [14]

[15] [16] [17] [18]

[19]

[20] [21] [22] [23] [24] [25] [26] [27] [28]

89

B.E. Jones, S. Ducharme, M. Liphardt, A. Goonesekera, J.M. Takacs, L. Zhang and R. Athalye, J. Opt. Soc. Am. B 11, 1064 (1994) H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993) H. Bässler, Adv. Mater. 5, 662 (1993) G. Pfister, S. Grammatica and J. Mort, Phys. Rev. Lett. 37, 1360 (1976) D.M. Pai, J.F. Janus and M. Stolka, J. Phys. Chem. 88, 4714 (1984) H.J. Yuh, D. Abramsohn and M. Stolka, Phil. Mag. Lett. 55, 277 (1987) M.A. Abkowitz, M.J. Rice and M. Stolka, Phil. Mag. B 61, 25 (1990) M.A. Abkowitz, M. Stolka, R.J. Weagley, K. McGrain and F.E. Knier, Synth. Metals 28, C553 (1989) TPD is estimated to have 0.5-0.6 eV lower ionization potential than PVK [10] and DEH is believed to have 0.26 eV lower ionization potential than TPD [12-13]. This gives a difference of 0.76-0.77 eV between PVK and DEH. Although these estimates are highly approximate, the difference is rather high compared with the width of the energy distribution of localized states in PVK. D. Mahgerefteh and J. Feinberg, Phys. Rev. Lett. 64, 2195 (1990) Y. Zhang, R. Burzynski, S. Ghosal and M.K. Casstevens, to appear in Adv. Mater. P. Tayebati and D. Mahgerefteh, J. Opt. Soc. Am. B 8, 1053 (1991) M.H. Garrett, G.D. Fogarty, G.D. Bacher, R.N. Schwartz and B.A. Wechsler, in "Photorefractive Effects and Materials", D.D. Nolte, ed., Kluwer Academic (1995) see for example J.C.M. Jonathan, Ph. Roussignol and G. Roosen, Opt. Lett. 13, 224 (1988), P. Nouchi, J.P. Partanen and R.W. Hellwarth, Phys. Rev. B 47, 15581 (1993), G. Pauliat and G. Roosen, J. Opt. Soc. Am. B 7, 2259 (1990) J.P. Partanen, P. Nouchi, J.C.M. Jonathan and R.W. Hellwarth, Phys. Rev. B 44, 1487 (1991) J.P. Partanen, J.M.C. Jonathan and R.W. Hellwarth, Appl. Phys. Lett. 57, 2404 (1990) H. Scher and E.W. Montroll, Phys. Rev. B 12, 2455 (1975) M.D. Tabak, D.M. Pai and M.E. Scharfe, J. Non-Cryst. Solids 6, 357 (1971) S.V. Novikov and A.V. Vanikov, Chem. Phys. 169, 21 (1993) A. Dieckmann, H. Bässler and P.M. Borsenberger, J. Chem. Phys. 99, 8136 (1993) P.M. Borsenberger and J.J. Fitzgerald, J. Phys. Chem. 97, 4815 (1993) M.G. Kuzyk, J.E. Sohn and C.W. Dirk, J. Opt. Soc. Am. B 7, 842 (1990) This device is described in: Kees Grim, "Direct View of Thin Polymer Films with Scanning Probe Microscopes", Ph.D. Thesis, University of Groningen (1995). Thanks are due to Gerald Belder for helping with the measurements of sample thickness with the interferometer.

90 [29] [30] [31] [32]

Chapter Four W. Köhler, D.R. Robello, C.S. Willand and D.J. Williams, Macromolecules 24, 4589 (1991) J.X. Mack, L.B. Schein and A. Peled, Phys. Rev. B 39, 7500 (1989) L.B. Schein and P.M. Borsenberger, Chem. Phys. 177, 773 (1993) S.M. Silence, R.J. Twieg, G.C. Bjorklund and W.E. Moerner, Phys. Rev. Lett. 73, 2047 (1994)

Chapter Five The Transient Behaviour of the Space Charge Field

Abstract The transient behaviour of the space charge field is studied in a poly(Nvinylcarbazole) based composite using the holographic time-of-flight (HTOF) technique. The electric field, temperature and drift length dependencies of the hole drift mobility are shown to be consistent with previously published data. The shape of the HTOF signal reflects the degree of charge transport disorder in this class of amorphous materials.

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5.1. Introduction Charge transport in polymers has been a subject of intense research effort, partly due to their application in xerography and partly due to the fundamental interest in the theoretical description of transport phenomena in amorphous systems [1]. The main parameter that characterizes charge transport is the drift mobility of the charge carriers, which is a measure of their average drift velocity under the influence of an applied electric field.

current

2

1

time Fig. 5.1 : Curve 1 is a typical TOF trace from a material with a well-defined mobility. Curve 2 is what is usually observed in polymers.

In amorphous materials, the tool of choice for the study of charge transport is the conventional time-of-flight (TOF) technique [2]. For this experiment, a thin layer of the material (typically a few tens of microns thick) is sandwiched between two blocking contacts, one of them being transparent. A strongly absorbing pulse of light excites a thin sheet of carriers inside the sample, just underneath the transparent electrode. Under the influence of an applied electric field, this sheet of carriers drifts towards the opposite side and the so produced current is measured as a function of time. Curve 1 in figure 5.1 shows its expected behaviour in a material with a well-defined mobility: Initially, a constant value is measured as a result of the constant velocity of the carriers in the bulk of the sample. Upon their arrival and annihilation at the opposite electrode,

Transient Behaviour of the Space Charge Field

93

the current drops to zero, within a transition region that measures the spreading of the packet due to normal diffusion. The mobility is calculated from: µdr = Ldr/(E0⋅tarr)

(5.1)

where Ldr is the thickness of the sample, E0 the applied field and tarr the arrival time, defined as the time at which the current reaches half of its plateau value. In several polymers [3-5] and amorphous semiconductors [6-7] however, profiles like curve 2 in figure 5.1, with an ill-defined plateau and an exceptionally long tail are observed, indicating that a great variation exists in the velocity of the charge carriers traversing the sample. A great deal of theoretical work has been focused on the description of this dispersive transport as a result of disorder, which is inherent in amorphous materials [1]. The observation of photorefractivity in polymers creates the opportunity to study the process of charge transport with optical means: A charge redistribution inside a photorefractive material creates a space charge field ESC, which is replicated via the electrooptic effect to a refractive index change. One measures the diffraction efficiency1 : η(t) ∝ (reff ESC(t))2

(5.2)

where reff is the effective electrooptic coefficient. In a holographic time-of-flight (HTOF) experiment2 , a sinusoidal distribution of mobile carriers is created throughout the bulk of the sample and it is forced to drift on top of the immobile distribution of countercharges. When anticoincidence is reached, a maximum appears in the temporal behaviour of the diffraction efficiency and the drift mobility can be calculated from equation (5.1), where tarr=tmax (the time that corresponds to this maximum) and: Ldr=ΛG/2cos(ϑG)

(5.3)

where ΛG is the grating spacing and ϑG the angle between the grating wave vector and the external electric field. When the mean free path of the mobile carriers is larger than the drift length, the diffraction efficiency shows oscillatory behaviour in time, as the alternation between coincidence and anticoincidence occurs repeatedly. This has been experimentally verified in BaTiO3 [8]. One advantage of the HTOF technique over the conventional time-of-flight technique is that the mobility can be easily measured for different values of the drift 1 2

see equation (2.23). the HTOF experiment has been described in chapter two.

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length on the same sample. This is particularly useful in the case of polymers, as in some cases a length dependent mobility, which is not a material parameter, can be measured due to dispersive transport [9]. Furthermore, the HTOF technique does not suffer from the restrictions concerning the sample thickness and the absorption depth of the light used for charge generation.

diffraction efficiency (a.u.)

1.0

0.8

0.6

0.4

0.2

0.0 0

2

4

6

8

10

t/tm a x Fig. 5.2 : Typical HTOF signal for the PVK:TNF:HONB composite at room temperature. E0=55 V/µm, tmax=2.7 msec and Ldr=1.7 µm.

The application of HTOF experiments in polymers seems very interesting: On one hand, knowledge of the drift mobility of the charge carriers is very important for the optimization of photorefractivity: The response time of the space charge field, is set either by this quantity or the photogeneration efficiency. With the HTOF technique, the drift mobility can be easily measured on the same sample that will be used for other photorefractive measurements. On the other hand, the study of charge transport in polymers doped with polar molecules is by itself a very interesting problem. The HTOF technique can be combined with other photorefractive measurements to provide valuable information and check theories that describe the influence of dipole molecules on charge transport [10-11]. In the previous chapter, the HTOF technique was used to estimate the hole drift mobility in EPNA containing composites. In order to further explore its applicability in the study of charge transport in polymers, the electric field, temperature and drift length

Transient Behaviour of the Space Charge Field

95

dependence of the hole drift mobility was measured in the HONB composite and the results were compared with previously published data. The transient behaviour of the diffraction efficiency was analyzed in view of both the standard model for photorefractivity and a model of charge transport in disordered media.

5.2. Results and discussion The HONB composite was used for this study, as its absorption lays far from 532 nm. HTOF experiments were carried out in the geometry described in the second chapter, on 100 µm thick sandwiched samples. The concentrations of the dopants were 0.1% wt. TNF and 40% wt. HONB relative to PVK. In figure 5.2 a typical HTOF trace is shown. After a fast initial rise, the diffraction efficiency reaches a well-defined maximum at time tmax and then decreases to a plateau value. Slow erasure by the He-Ne beam follows at longer times (not shown in this plot). Remarkable is the absence of any further oscillations after the maximum has been reached. A broad, dispersive decay follows instead. The difference between the maximum and the plateau value of the diffraction efficiency increased with voltage, as in the case of the EPNA composite (figure 4.5). Before discussing the shape of the HTOF signal any further, let us focus on the dependencies of the mobility on the electric field, temperature and drift length.

5.2.1. Electric field, temperature and drift length dependence of the hole drift mobility Charge transport in PVK based polymers is believed to be a thermally activated hopping process [1]. Gill [12] has measured the electric field and temperature dependence of the mobility in PVK and its charge transfer complexes with TNF and found that it can be described with the empirical equation: µdr = µo exp (- (ε0-βE00.5)/kTeff)

(5.4)

where µo is a prefactor mobility, ε0 is the zero field activation energy, β is a constant coefficient which represents the lowering of the activation energy due to the electric field and Teff follows the relationship: 1/Teff = 1/T - 1/To

(5.5)

where T is the absolute temperature and To is a characteristic temperature. Although the absolute magnitude of the hole mobility was found to be very sensitive to the amount of TNF, changing more than two orders of magnitude from pure PVK to pure

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mobility (cm2/Vsec)

TNF, equation (5.4) could describe all the data with a single value of the coefficient β equal to 2.7⋅10-5 eV(m/V)0.5 [12]. In figure 5.3, the logarithm of the hole drift mobility in PVK:TNF:HONB, as calculated from equation (5.1), is plotted as a function of the square root of the external electric field. The solid line is the best fit using equation (5.4) and has a slope of 0.55 (µm/V)0.5, which is the same as in PVK:TNF charge transfer complexes at room temperature [12]. The fact that the same value for the lowering of the activation energy due to the electric field is measured as in PVK, strongly suggests that with the HTOF technique one measures the same activated process as with the conventional TOF experiment. For β equal to 2.7⋅10-5 eV(m/V)0.5, To is equal to 611 K, which is within the range from 520 to 660 K, reported for the PVK:TNF composites [12].

10-7

10-8

4

5

6

7

8

9

E0 0 . 5 (V/µ m)0 . 5 Fig. 5.3 : The electric field dependence of the hole drift mobility at room temperature. The line is a fit using equation (5.4).

The absolute magnitude of the mobility for the PVK:TNF:HONB composite corresponds to that of a composite with 0.4:1 TNF:PVK monomer unit molar ratio [12]. Weiser has shown that in the latter, 61% of TNF is complexed with PVK [13]. From this, it can be calculated that the actual molar ratio of non transporting (free TNF, complexed TNF and PVK) to hole transporting species (free PVK) is 0.85:1 [12]. In our case, this ratio is equal to the molar ratio of HONB to PVK monomer unit, which is equal to 0.35:1. This means that HONB causes a larger decrease in the hole

Transient Behaviour of the Space Charge Field

97

drift mobility compared to TNF, which is not surprising, as the presence of polar molecules in a polymer matrix is well known to decrease the hole drift mobility [14]. This decrease is even more pronounced in the EPNA composite, where µdr is around 1.5⋅10-8 cm2/(Vsec) at 35 V/µm, compared to the value of 5.1⋅10-8 cm2/(Vsec) measured for the HONB composite at the same electric field. Moreover, as it was discussed in the third chapter, the trap density in the latter is slightly lower, indicating that the NLO molecules have a measurable influence in charge transport in PVK. This is believed to arise from the broadening of the energy distribution of the hopping sites which is caused by the random internal fields that are associated with dipolar molecules, a situation which is analogous with an increase of the density of shallow traps [10,15].

mobility (cm2/Vsec)

10-6

10-7 3.0

3.1

3.2

3.3

3.4

-1

1000/T (K ) Fig. 5.4 : The temperature dependence of the hole drift mobility for an electric field of 55 V/µm. The line is a fit using equation (5.4).

For the measurements of the hole drift mobility as a function of temperature, the sample was put into a small oven and a thermocouple was brought into contact with it to measure the temperature. In figure 5.4 the temperature dependence of mobility is shown, together with the best fit of equation (5.4). Although the temperature range is rather limited, the mobility changes almost an order of magnitude, following the same dependence as in the PVK:TNF composites. Using a β coefficient equal to 2.7⋅10-5 eV(m/V)0.5, a zero field activation energy ε0 equal to 0.64 eV is calculated from the slope of this line. Within the accuracy of this measurement, which is limited due to the

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small temperature range, this value is close to values in the range of 0.65-0.68 eV reported for the PVK:TNF composites [12]. The value of µo in equation (5.4) can be calculated independently from the measured electric field and temperature dependencies of the mobility. The values that were obtained are 7.8⋅10-4 and 8.2⋅10-4 cm2/(V⋅sec), respectively, in fair agreement with each other.

0.75 10-6

mobility (cm2/Vsec)

diffraction efficiency (a.u.)

1.00

0.50

0.25

10-7

1

2

3

4

5

drift length (µ m)

0.00 0

2

4

6

t/tm a x Fig. 5.5 : HTOF traces that correspond to drift length equal to 1.7 µm (open circles, tmax=1 msec) and 5 µm (open triangles, tmax=3 msec), respectively. Inset : The hole drift mobility for different values of the drift length, at room temperature and for an electric field of 75 V/µm. The line is a guide to the eye.

By changing the tilt angle of the sample, the angle between the grating wave vector and the external electric field was varied and the mobility was measured as a function of the drift length Ldr (equation (5.3)). As can be seen in the inset of figure 5.5, the mobility is independent of Ldr, in agreement with earlier measurements on PVK [16]. This indicates that a bulk material property is measured [17]. The HTOF technique can be used to measure the mean free path lfree of holes: If the drift length is made larger than the mean free path, the well defined maximum in the temporal behaviour of the diffraction efficiency will disappear. This effect was observable at low voltages, where the drift mobility is small.

Transient Behaviour of the Space Charge Field

99

5.2.2. Comparison with the standard model Let us now discuss the shape of the HTOF signal in the framework of the standard model for photorefractivity. Solution of equations (1.2) to (1.5) in the regime of illumination with a short pulse, yields a diffraction efficiency that grows as a function of time according to [18]: η = η∞  1-exp(-Γt)  2

(5.6)

Γ = (τD-1 + KG2D) - iKGµdrE0

(5.7)

with:

where τD is the deep trap lifetime3 , KG the grating wave vector and D the diffusion coefficient4 . A more sophisticated model that includes shallow traps predicts essentially the same dependence [8]. The imaginary part of Γ is responsible for the oscillations, while the real part defines the speed of grating growth and the damping of the oscillations. Using equation (5.6) it was not possible to fit the shape of the HTOF signal (figure 5.2), which indicates the inapplicability of this simple model in the case of photorefractive polymers. One possible reason for the absence of oscillations could be that holes suffer extensive recombination when they arrive at coincidence with the distribution of the countercharges (former bright fringe area). In this case, the shape of the transient would have strongly depended on the contrast of the interference pattern. To verify that, the intensity of one of the beams was decreased 10 times but no change was observed in the shape of the HTOF trace (except of a change in the amplitude). The absence of oscillations is not due to a small mean free path: in figure 5.5, the HTOF traces corresponding to Ldr equal to 1.7 and 5 µm are shown, as a function of t/tmax. Although the width of the latter is broader, a well-defined maximum is also observed, indicating that the mean free path of the holes at 75 kV/µm is larger than 5 µm. This means that lfree is sufficiently larger than the drift length for the curve that corresponds to Ldr equal to 1.7 µm. The departure of the shape of the HTOF signal from the theoretically predicted one could be explained if electrons were also mobile in the polymer composite. From all of its components however, only TNF is known to support electron transport and only

τD-1=γDND+(x)≈γDNA, in agreement with equation (1.2). 4 No assumption is made here about the validity of the Einstein relation between the diffusion coefficient and the drift mobility. 3

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at high concentrations. At a concentration of 0.1% wt. the electron drift mobility is practically zero [12]. Finally, care was taken to ensure that the shape of the HTOF trace is not influenced by space charge from previous experiments. Sufficient time was allowed after each measurement for the produced charge to recombine and as a result, the HTOF trace remain unaltered during all consecutive measurements. Prolonged application of voltage across the sample was avoided and its polarity was frequently reversed, in order to minimize the effects of charge storage after injection. Thus, the shape of the HTOF trace is an inherent property of the investigated samples, which cannot be explained within the framework of the standard model.

5.2.3. The influence of disorder Inherent within the standard model for photorefractivity, is the assumption of a well-defined mobility. In the steady state regime, this assumption is not very crucial and the model works rather well. During HTOF experiments however, where the charge separation that leads to the space charge field formation is observed, the dispersive character of charge transport has to be taken into account. In this section the shape of the HTOF trace is discussed in view of the Scher and Montroll theory of charge transport in disorder media [9]. The aim is not to provide a full theoretical framework for the analysis of the experimental results, but rather to demonstrate how certain features of the HTOF trace, like the absence of oscillatory behaviour, arise naturally due to the presence of disorder. Charge transport can be viewed as an accumulated sequence of charge transfer steps from one localized site to another. According to this picture, each carrier independently undergoes a random walk, biased into one direction by an applied electric field. The entire character of a propagating packet of carriers depends on a key feature, the hopping time probability distribution ψ(t). In an ordered single crystal, where the hopping rate W is constant, ψ(t) is given by [19]: ψ(t) ∝ exp[-Wt]

(5.8)

and the charge packet exhibits normal Gaussian transport. In disordered systems however, there is a wide distribution of hopping rates, leading to a large range of hopping times that extend well into the experimental time scale. In this case, probability distributions of the form: ψ(t) ∝ t-(1+a) , 0
(5.9)

Transient Behaviour of the Space Charge Field

101

proposed by Scher and Montroll [9], have been very successful in describing TOF experiments in polymers and amorphous semiconductors. Such probability distributions imply an extremely large hopping time dispersion which can arise from relatively small variations between the distance and the mutual orientation of the hopping sites. The mean position of a spatially biased, time-evolving packet of charge carriers that undergoes a random walk with a probability distribution like in equation (5.9) varies as [9]: l(t) ∝ ta

(5.10)

and it is a sublinear function of time, giving rise to the peculiar character of charge transport in disorder media. Such a sublinear temporal dependence is a direct result of the presence of disorder: As time progresses, more and more charge carriers will encounter one site that corresponds to a long hopping time and get temporarily immobilized, a situation which is analogous to deep trapping. The parameter a measures the degree of disorder [20]: When a→1, the mean position l(t) increases linearly with time, as in the case of Gaussian transport. Smaller a's are associated with higher a degree of disorder. In a conventional TOF experiment, the current that is measured before the packet reaches the opposite electrode is [9]: I(t) ∝ dl(t)/dt ∝ t-(1-a)

(5.11)

and it is no longer constant, but it is decreasing with time! When carriers begin to reached the opposite electrode and become annihilated, a faster drop in current is observed [9]: I(t) ∝ t-(1+a)

(5.12)

According to equations (5.11) and (5.12), the shape of the TOF trace is described by only one parameter. When plotted in a double logarithmic scale, it consists of two lines with slopes -(1-a) and -(1+a), crossing at a time that corresponds to tarr. Moreover, if the current and time are normalized with respect to tarr, a universal plot is obtained, describing all the curves for various electric fields. Despite its simplicity, the theory of Scher and Montroll was found to provide an excellent description of the shape of the TOF transients in PVK for a=0.66 [21]. In order to examine the predictions of the Scher and Montroll theory for the case of the HTOF experiment, a computer simulation was carried out [22]. A charge was allowed to undergo a random walk (in one dimension) with a probability distribution like in equation (5.9), biased by an external electric field. The bias factor

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was selected to be equal to one, meaning than only steps towards one direction where allowed. Recombination and space charge field effects due to the immobile distribution of countercharges were not taken into account, which is justified by the fact that when changing the contrast of the interference pattern in the experiment, no change was observable in the HTOF shape. One million of charges were used in order to construct a distribution G(y,t) of carrier density versus distance from the origin at a given time t. The convolution H(x,t) of this distribution with a sinus function gives the spatial density of the mobile carriers in a HTOF experiment: H(x,t) = ∫ dyG(y,t)sin[2π(x-y)/ΛG]

(5.13)

diffraction efficiency (a.u.)

1.6

1.2

0.8

0.5 0.6 0.7 0.8

0.4

0.0 0

5000

10000

15000

20000

time (a.u.) Fig. 5.6 : Simulated HTOF traces for various values of the disorder parameter a and ΛG=200.

The amplitude A*(t) of H(x,t) (which is also a sinus function) and its phase shift ϕ (t) with respect to the distribution of the immobile countercharges were used to calculate the diffraction efficiency: *

η(t) ∝ 1+(A*(t))2-2A*(t)cos[2πϕ*(t)]

(5.14)

In figure 5.6, simulated HTOF traces for various values of a are shown. For a=0.5 the diffraction efficiency merely reaches saturation, but as a increases, the

Transient Behaviour of the Space Charge Field

103

tendency towards oscillatory behaviour is apparent. The simulation resembles the experimental data of figure 5.2 for a in the range of 0.6-0.7, which corresponds to the value measured in PVK with the conventional TOF experiment [21]. No further oscillations in this range of a's was observed, even if the grating spacing ΛG (which, in figure 5.6 is equal to 200 times the distance between two hopping sites) was changed several times.

180

135

0.8 90

0.4 45

0.0

0

5000

10000

15000

phase shift (degrees)

diffraction efficiency (a.u.)

1.2

0 20000

time (a.u.) Fig. 5.7 : Simulated HTOF trace and the phase shift of H(x,t) with respect to the immobile distribution of the countercharges for a=0.6 and

ΛG=200. The absence of oscillations can be understood by examining the phase of H(x,t) (figure 5.7), which stays in the neighbourhood of 90 degrees, instead of increasing continuously, as in the case of Gaussian transport. This comes as a result of the propagation characteristics of a charge packet, undergoing random walk with a long tailed probability distribution like in equation (5.9): The position of the maximum of the distribution does not coincide with the position of the mean, but stays almost invariable with time [9]. When calculating the hole drift mobility from the HTOF data, the assumption was made that the maximum in the diffraction efficiency corresponds to the situation where the mobile carriers have drifted to a position of anticoincidence (thus 180 degrees) with the immobile distribution of countercharges. This assumption, which is

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intuitive for normal Gaussian transport, is no longer correct for the case of dispersive transport: The maximum of the diffraction efficiency in figure 5.7 occurs when the spatial density of the mobile carriers is shifted approximately 90 degrees with respect to the immobile distribution of the countercharges. This means that the drift length has been overestimated by a factor of two and the actual value of the hole drift mobility is twice less. The Scher and Montroll theory was chosen here for the discussion of the HTOF traces due to its simplicity. It has however several shortcomings: For example, it fails to predict the correct electric field dependence of the hole drift mobility (equation (5.4)) while it anticipates a dependence of µdr on the drift length, in disagreement with the experiment. These discrepancies may arise partly from the fact that the presence of disorder is implemented only as fluctuations in the distance and the mutual orientation of the hopping sites (off-diagonal disorder), while fluctuations in the energy of the hopping sites (diagonal disorder) are ignored. Diagonal disorder, which is important in materials with a high concentration of polar molecules [10,15], may have a dominant role in photorefractive polymers. Despite these discrepancies however, (which have been partly corrected in recent, more sophisticated computer simulations [17] and analytical theories [23] based on disorder arguments), a correct description of the shape of the HTOF trace arises naturally, meaning that disorder is important and it should be the starting point for any further theoretical description.

5.3. Conclusions and outlook In conclusion, the applicability of the HTOF technique in the measurement of the drift mobility in photorefractive polymers has been demonstrated. The measured electric field, temperature and drift length dependencies of the hole drift mobility in the PVK:TNF:HONB composite were found to be in agreement with literature data for PVK. The influence of the dispersive character of charge transport in amorphous materials on the transient behaviour of the space charge field was observed. A simulation based on the theory of Scher and Montroll reproduced the shape of the HTOF traces. The application of the HTOF technique to study the effect of the NLO molecules in the space charge field formation process seems a very attractive idea. In this way, one could probably check the validity of recent theories for charge transport in polymeric materials, such as the dipole trap model [11]. Another interesting direction is to apply the HTOF technique in photorefractive polymers based on DEH or TPD like molecules. Charge transport in solid solutions of these molecules is believed to be non-dispersive [24-25] and in this case the HTOF signal should show oscillatory behaviour.

Transient Behaviour of the Space Charge Field

105

5.4 References [1]

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

[23] [24] [25]

see for example chapter 8 in P.M. Borsenberger and D.S. Weiss eds., Organic Photoreceptors for Imaging Systems, Optical Engineering vol. 39, Marcel Dekker, Inc. (1993) J.R. Haynes and W. Shokley, Phys. Rev. 81, 835 (1951) J. Mort and A.I. Lakatos, J. Non-Cryst. Solids 4, 117 (1970) J. Lange and H. Bässler, Phys. Stat. Sol. (b) 114, 561 (1982) E. Muller-Horsche, D. Haarer and H. Scher, Phys. Rev. B 35, 1273 (1987) G. Pfister, Phys. Rev. Lett. 36, 271 (1976) G. Pfister and H. Scher, Adv. Phys. 27, 747 (1978) P. Nouchi, J.P. Partanen and R.W. Hellwarth, Phys. Rev. B 47, 15581 (1993) H. Scher and E.W. Montroll, Phys. Rev. B 12, 2455 (1975) A. Dieckmann, H. Bässler and P.M. Borsenberger, J. Chem. Phys. 99, 8136 (1993) S.V. Novikov and A.V. Vannikov, Chem. Phys. 169, 21 (1993) W.D. Gill, J. Appl. Phys. 43, 5033 (1972) G. Weiser, J. Appl. Phys. 43, 5028 (1972) A.V. Vannikov, A.Y. Kryukov, A.G. Tyurin and T.S. Zhuravleva, Phys. Stat. Sol. (a) 115, K47 (1989) P.M. Borsenberger and J.J. Fitzgerald, J. Phys. Chem. 97, 4815 (1993) A.R. Tahmasbi and J. Hirsch, Solid State Commun. 34, 75 (1980) H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993) J.P. Partanen, J.M.C. Jonathan and R.W. Hellwarth, Appl. Phys. Lett. 57, 2404 (1990) H. Scher, M. Shlesinger and J.T. Bendler, Physics Today, p. 26, January 1991 M. van der Auweraer, F.C. De Schryver, P.M. Borsenberger and H. Bässler, Adv. Mater. 6, 199 (1994) F.C. Bos and D.M. Burland, Phys. Rev. Lett. 58, 152 (1987) Thanks are due to Henk Angerman for working out the analytical solution to the Scher and Montroll theory and the algorithm of the random walk and to Rudolf Niemeyer for parallelizing the program for the CRAY. D.H. Dunlap, Phys. Rev. B 52, 939 (1995) M. Stolka and M.A. Abkowitz, Synth. Metals 54, 417 (1993) A. Hirao, H. Nishizawa and M. Sugiuchi, Phys. Rev. Lett. 75, 1787 (1995)

List of Abbreviations ac 2BC CG CT dc DEANST DEH DFWM EO EPNA HOMO HONB HTOF ITO LUMO NLO PVK TNF TOF TS

1 2

alternating current two beam coupling charge generation species charge transport species direct current 4-(N,N-diethylamino)-β-nitrostyrene 4-(N,N-diethylamino)benzaldehyde diphenylhydrazone degenerate four wave mixing electrooptic species 4-(diethylamino)nitrobenzene1 highest occupied molecular orbital 4-(hexyloxy)nitrobenzene holographic time-of-flight indium tin oxide lowest unoccupied molecular orbital nonlinear optical poly(N-vinylcarbazole)2 2,4,7-trinitro-9-fluorenone time-of-flight trapping sites

the abbreviation stems from the alternative name N,N-diethyl-para-nitroaniline the abreviation is with a K to avoid confusion with poly(vinyl chloride) (PVC)

List of Symbols α a αij A A*(t) β βijk γ0 γD γijkl Γ ∆n d D ε ε0 e E E0 ED EK ES ESC ET η θ ϑ ϑG ϕ ϕ*(t) φ f G(y,t) h H(x,t) I J

absorption coefficient disorder parameter polarizability of a molecule diffractive amplitude of absorption gratings amplitude of H(x,t) ratio of intensity of the pump and the probe beam or mobility coefficient first hyperpolarizability tensor of a molecule ratio of intensities of the probe with and without the presence of the pump trapping rate for electrons second hyperpolarizability tensor of a molecule two beam coupling gain coefficient or inverse growth time constant change in the refractive index thickness of sample diffusion coefficient dielectric constant zero field activation energy electron charge amplitude of a light wave externally applied electric field diffusion field projection of E0 along the grating wave vector saturation field space charge field total electric field diffraction efficiency angle between the molecular axis and the applied electric field angle of incidence or propagation angle between the grating wave vector and the applied electric field phase shift of the photorefractive grating phase shift of H(x,t) quantum yield for free hole generation local field correction factor carrier density at a distance y from the origin, at time t Planck's constant carrier density in a HTOF experiment optical intensity or current current density

108 kB KG ki λ0 ΛG l l(t) lfree Ldr µ µdr µ0 m ν n n0 NA ND NT π p P P* reff r* σph s sD Sph τ τD τeff t T v V W χ(n) ψ(t) ωac

List of Symbols Boltzmann's constant grating wave vector wave vector of a light beam wavelength of light (in vacuum) grating spacing length mean position of a packet of carriers mean free path drift length dipole moment drift mobility prefactor mobility modulation index of the interference pattern optical frequency density of electrons in the conduction band refractive index acceptor density donor density trap density 3.141592654...... hole density power density of a beam or diffractive amplitude of refractive index gratings the quantity 2Pd, which is measured with the 2BC experiment effective electrooptic coefficient effective electrooptic coefficient including Kerr effects photoconductivity quadratic (Kerr) electrooptic coefficient photogeneration rate for electrons photosensitivity response time of the photorefractive grating deep trap lifetime effective lifetime of a free carrier time absolute temperature velocity of sample translation during two beam coupling measurement voltage hopping rate nth order susceptibility hopping time probability distribution frequency of ac voltage

Summary The photorefractive effect is observed in materials which are both electrooptic and photoconducting. When a light pattern is incident on such a material, charges that are photogenerated in the illuminated regions, migrate and eventually get trapped at the dark regions of the sample. The resulting charge redistribution creates an internal electric field, the space charge field, which changes the refractive index via the electrooptic effect. In this way, a refractive index hologram which is a replica of the illumination pattern is created. Although there are several other mechanism that allow storage of optical information in solid state materials, the photorefractive effect processes a combination of characteristics which make it very attractive from application point of view: Very high nonlinearities can be achieved even with weak laser beams, due to its integrating nature. The resulting refractive index gratings are reversible, as uniform illumination will erase the space charge field. Another very important characteristic, is the existence of a spatial phase shift between the illumination pattern and the refractive index grating, which gives rise to steady state asymmetric energy exchange between two laser beams. Until recently, photorefractivity was exhibited only in certain inorganic crystals that are very difficult to grow. Over the last five years however, alternative material classes which show the effect appeared: organic crystals, polymers and liquid crystals. Polymers attracted immediately great interest and tremendous progress has been achieved, mainly due to the tunability that they offer, concerning their optoelectronic and mechanical properties: The necessary functionalities of charge generation, transport, trapping and electrooptic response are given in the polymer with the addition of specific molecules or monomers, whose concentration can be easily varied. In this thesis, the photorefractive effect is investigated in polymer composites based on the well known photoconductor poly(N-vinylcarbazole) (PVK) sensitized with 2,4,7trinitro-9-fluorenone (TNF). In this material, holes generated by illumination of the PVK:TNF charge transfer complex are transported by hopping among neighbouring carbazole units. Addition of a nonlinear optical (NLO) molecule like 4(diethylamino)nitrobenzene (EPNA) or 4-(hexyloxy)nitrobenzene (HONB) provides the electrooptic functionality and the composite becomes photorefractive. As this thesis is a result of experimental work, a variety of experimental techniques is outlined, with emphasis in holographic recording and read-out, both in the steady state and in the transient regime. The underlying theory, together with accuracy-sensitivity considerations are described for each one of them. The behaviour of the space charge field in these materials is found to be in reasonable agreement with the predictions of the standard model, which has been developed to describe photorefractivity in inorganic materials. However, the question arises about the nature of the charge trapping centers. In an attempt to understand and control the process of charge trapping, the molecule 4-(N,N-diethylamino)benzaldehyde diphenylhydrazone (DEH)

110

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is added in various amounts into the EPNA containing composite. Measurements of the properties of the photorefractive grating indicate that at low concentrations DEH acts as a trap, while at higher concentrations a new transport pathway is established through hopping among DEH molecules. This is understood by a simple hopping picture based on the difference between the ionization potential of DEH and PVK. From this investigation it becomes clear that the existence of photorefractivity in polymers provides the opportunity to study the processes of charge transport and trapping in these materials with purely optical techniques. This is further demonstrated with the measurement of the hole drift mobility in the HONB composite, using a holographic version of a time-of-flight experiment. The temporal behaviour of the space charge field formation is shown to reflect the degree of charge transport disorder in these materials.

Samenvatting Het fotorefractieve effect kan optreden in materialen die zowel fotogeleidend als electro-optisch actief zijn. Wanneer zo'n materiaal wordt belicht zullen de gecreëerde ladingsdragers vanuit de belichte gebieden migreren naar de onbelichte gebieden, en daar gevangen worden ('trapping'). Deze ladingsverdeling veroorzaakt een intern electrisch veld, het ruimteladingsveld, dat de brekingsindex van het materiaal verandert d.m.v. het electrooptisch effect. Op deze manier wordt een brekingsindexhologram gecreëerd dat een exacte kopie is van het belichtingspatroon. Hoewel er naast het fotorefractieve effect nog andere mechanismen bestaan waarmee optische informatie opgeslagen kan worden in vaste stoffen, heeft het fotorefractieve effect een aantal kenmerken die het erg interessant maken voor toepassingen. Dit zijn met name de hoge nonlineariteit die door het integrerende karakter van het effect bereikt kan worden met zwakke laserbundels, en ook de omkeerbaarheid van de brekingsindextralies; immers, uniforme belichting zal het ruimteladingsveld doen verdwijnen. Een andere zeer belangrijke eigenschap is dat er een ruimtelijk faseverschil bestaat tussen het belichtingspatroon en de brekingsindextralie. Dit faseverschil geeft in de stationaire toestand aanleiding tot asymmetrische uitwisseling van energie tussen twee laserbundels. Fotorefractiviteit werd tot voor kort alleen waargenomen in anorganische kristallen die zeer moeilijk te groeien zijn. De laatste vijf jaar zijn er andere materialen ontwikkeld waarin het fotorefractieve effect kan optreden, zoals organische kristallen, polymeren en vloeibare kristallen. Met name polymeren trokken vanaf het begin veel aandacht en er is dan ook een enorme vooruitgang geboekt met deze materialen. Dit komt voornamelijk doordat de optoelectronische en mechanische eigenschappen ervan naar wens ingesteld kunnen worden. De noodzakelijke eigenschappen zoals de opwekking, het transport en het vangen van ladingsdragers, alsmede het electro-optisch effect worden in polymeren verkregen door de toevoeging van specifieke molekulen of monomeren, waarvan de concentratie gemakkelijk gevarieerd kan worden. Dit proefschrift beschrijft de bestudering van het fotorefractieve effect in polymeercomposieten gebaseerd op de bekende fotogeleider poly(N-vinylcarbazole) (PVK), geactiveerd met 2,4,7-trinitro-9-fluorenon (TNF). In dit materiaal worden de gaten die gecreëerd zijn door het belichten van het ladingsoverdrachtscomplex PVK:TNF getransporteerd via naburige carbazole groepen, d.m.v. het hopping proces. Door toevoeging van niet-linear optische (NLO) molekulen zoals 4-(diethylamino)nitrobenzeen (EPNA) of 4(hexyloxy)nitrobenzeen (HONB) verkrijgt het materiaal electro-optische eigenschappen, waardoor het composiet fotorefractief wordt. Omdat dit proefschrift het resultaat is van experimenteel onderzoek worden een aantal experimentele technieken beschreven, waarbij de nadruk ligt op het holografisch schrijven en lezen in zowel de stationaire als de nietstationaire toestand. De achterliggende theorie, vergezeld van een beschouwing van nauwkeurigheid en gevoeligheid, wordt voor iedere techniek afzonderlijk beschreven.

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Het gedrag van het ruimteladingsveld in deze materialen blijkt in redelijke overeenstemming te zijn met de voorspellingen van het standaardmodel dat ontwikkeld is om fotorefractiviteit in anorganische materialen te beschrijven. De aard van de ladingsvallen ('traps') is echter minder goed begrepen. In een poging om het proces van het vangen van ladingen te begrijpen en te beheersen worden er variërende hoeveelheden van het molekuul 4(N,N-diethylamino)benzaldehyde diphenylhydrazone (DEH) aan het EPNA bevattende composiet toegevoegd. Metingen van de eigenschappen van de fotorefractieve tralie geven aan dat DEH bij lage concentraties fungeert als een ladingsval, terwijl bij hogere concentraties een nieuwe transportroute ontstaat via hopping van ladingsdragers tussen de DEH moleculen. Dit kan begrepen worden vanuit een simpel beeld van hopping gebaseerd op het verschil in ionisatiepotentiaal tussen DEH en PVK. Uit deze studie blijkt duidelijk dat het bestaan van fotorefractiviteit in polymeren het mogelijk maakt om het transport en het vangen van lading in deze materialen te bestuderen met puur optische technieken. Dit wordt nog eens gedemonstreerd met metingen van de driftmobiliteit van gaten in het composiet dat HONB bevat, gebruikmakend van een holografische variant van de klassieke time-of-flight meting. De wijze waarop het ruimteladingsveld zich opbouwt in de tijd blijkt een afspiegeling te zijn van de wanorde waarmee ladingstransport in deze materialen plaatsvindt.

List of Publications - G.G. Malliaras, H.A. Wierenga, Th.H.M. Rasing, “Optical second harmonic generation study of vicinal Si(110) surfaces”, Proc. of the 12th Greek- Bulgarian Conference on Semiconductor Physics, eds. K. Kambas, D. Papadopoulos, p.131, Thessaloniki, Greece (1991) - G.G. Malliaras, H.A. Wierenga, Th.H.M. Rasing, “Study of the step structure of vicinal Si(110) surfaces using optical second harmonic generation”, Surf. Sci. 287/288, 703 (1993) - J.K. Herrema, J. Wildeman, R.H. Wieringa, G.G. Malliaras, S.S. Lampoura, G. Hadziioannou, “Light emitting devices from poly[(silanylene)thiophene]s”, Polym. Prepr. 34, 282 (1993) - D.H. Hissink, H.J. Bolink, J.W. Eshuis, G.G. Malliaras, G. Hadziioannou, “Silicon based donor-acceptor compounds in a polymer matrix”, Polym. Prepr. 34, 721 (1993) - P.F. van Hutten, G.G. Malliaras, D.H. Hissink, G. Hadziioannou, “Calculations of nonlinear optical properties of donor-acceptor diphenylsilanes”, Polym. Prepr. 34, 715 (1993) - G.G. Malliaras, J.K. Herrema, J. Wildeman, R.E. Gill, S.S. Lampoura, G. Hadziioannou, “Colour tuning of poly[(silanylene)thiophene] block copolymers”, in Nonlinear Optical Properties of Organic Materials VI, SPIE proc. 2025, p. 441, ed. G.R. Möhlmann, San Diego (1993) - H.J. Bolink, V.V. Krasnikov, G.G. Malliaras, G. Hadziioannou, Invited Paper “Photorefractive polymer materials”, in Nonlinear Optical Properties of Organic Materials VI, SPIE proc. 2025, p. 292, ed. G.R. Möhlmann, San Diego (1993) - D.H. Hissink, H.J. Bolink, P.F. van Hutten, G.G. Malliaras, G. Hadziioannou, “Silicon based donor-acceptor compounds in a polymer matrix”, in Nonlinear Optical Properties of Organic Materials VI, SPIE proc. 2025, p. 37, ed. G.R. Möhlmann, San Diego (1993) - G.G. Malliaras, J.K. Herrema, J. Wildeman, R.H. Wieringa, R.E. Gill, S.S. Lampoura, G. Hadziioannou, “Tuning of photo- and electroluminescence in multi-block copolymers of poly[(silanylene)thiophene]s via exciton confinement”, Adv. Mater. 5, 721 (1993) - G. Hadziioannou, J. Wildeman, G.G. Malliaras, J.K. Herrema, R. Wieringa, “Tunable-multi-block copolymers for light emitting diodes”, European Patent 1993

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- R.E. Gill, G.G. Malliaras, J. Wildeman, G. Hadziioannou, “Tuning of photo- and electroluminescence in alkylated polythiophenes with well-defined regioregularity”, Adv. Mater. 6, 132 (1994) - R.E. Gill, J. Wildeman, G.G. Malliaras, G. Hadziioannou, “Regioregular polymer based tunable light emitting diodes”, European Patent 1993 - G.G. Malliaras, R.E. Gill, J.K. Herrema, S.S. Lampoura, J. Wildeman, H.J. Bolink, V.V. Krasnikov, G. Hadziioannou, “Polymers for optoelectronics”, Proc. of the 14th Greek-Bulgarian Conference on Semiconductor Physics, ed. K. Kambas, p.64, Thessaloniki, Greece (1993) - S.S. Lampoura, G.G. Malliaras, J.K. Herrema, R.E. Gill, J. Wildeman, G. Hadziioannou, “Light emitting diodes from poly[(silanylene)thiophene] block copolymers”, Proc. of the 14th Greek-Bulgarian Conference on Semiconductor Physics, ed. K. Kambas, p.79, Thessaloniki, Greece (1993) - R.E. Gill, J.K. Herrema, P.F. van Hutten, J. Wildeman, G.G. Malliaras, G. Hadziioannou, “Chemical tuning of photoluminescence and electroluminescence in block copolymers and regiospecific polymers”, to appear in Organic Electroluminescence, eds. D.D.C. Bradley, T. Tsutsui, Cambridge University Press - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Photorefractive polymer composite with net gain and subsecond response at 633 nm”, Appl. Phys. Lett. 65, 262 (1994) - H.J. Bolink, V.V. Krasnikov, G.G. Malliaras, G. Hadziioannou, “The role of absorbing nonlinear optical chromophores in photorefractive polymers”, Adv. Mater. 6, 574 (1994) - G. Hadziioannou, H.J. Bolink, G.G. Malliaras, V.V. Krasnikov, “Photorefractive polymers”, Programme et Communications, Journeèes Polymeères Conducteurs, Strasbourg, France (1994) (in French) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, Invited Paper “Engineering of photorefractive polymers”, Technical Digest of Conference on Lasers and Electro-Optics Europe, p.361, Amsterdam, the Netherlands (1994) - A. Hilberer, R.E. Gill, J.K. Herrema, J. Wildeman, G.G. Malliaras, G. Hadziioannou, “Conjugated copolymers for light emitting diodes”, J. Chim. Phys. 92, 931 (1995) (in French)

List of Publications

115

- D. Morichère, G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Photorefractive polymers”, J. Chim. Phys. 92, 927 (1995) (in French) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Control of charge trapping in photorefractive polymers”, Appl. Phys. Lett. 66, 1038 (1995) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Transient behaviour of photorefractive gratings in a polymer”, Appl. Phys. Lett. 67, 455 (1995) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Holographic time-offlight measurement of the hole drift mobility in a photorefractive polymer”, Phys. Rev. B 52, R* (1995) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, “Charge trapping in photorefractive polymers”, to appear in Xerographic Photoreceptors and Photorefractive Polymers, proc. SPIE 2526, eds. S. Ducharme, P.M. Borsenberger, San Diego (1995) - H.J. Bolink, I. van der Weide, G.G. Malliaras, V.V. Krasnikov, G. Hadziioannou, “Photorefractive host-guest systems and fully functionalized polymers”, to appear in Xerographic Photoreceptors and Photorefractive Polymers, proc. SPIE 2526, eds. S. Ducharme, P.M. Borsenberger, San Diego (1995) - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, Invited Paper “Transient photorefractive gratings in polymers”, to appear in Nonlinear Optical Properties of Organic Materials VIII, proc. SPIE 2527, ed. G. Möhlmann, San Diego (1995) - H.J. Bolink, I. van der Weide, V.V. Krasnikov, G.G. Malliaras, G. Hadziioannou, “A photorefractive polyurethane with extended transparency in the visible”, submitted to Macromol. Chem. Phys. - G.G. Malliaras, V.V. Krasnikov, H.J. Bolink, G. Hadziioannou, Invited Paper “Photorefractivity in poly(N-vinylcarbazole) based polymer composites”, to appear in Pure and Applied Optics - H.J. Bolink, C. Arts, G.G. Malliaras, V.V. Krasnikov, G. Hadziioannou, “A novel bifunctional chromophore for photorefractive applications”, submitted to Adv. Mater.