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Space-charge dynamics in photorefractive polymers

August 2002
Journal of Applied Physics 92(4):1727-1743

August 2002
92(4):1727-1743

DOI:10.1063/1.1491279

Authors:

Oksana Ostroverkhova

Oregon State University

Kenneth D Singer

Case Western Reserve University

The model of space-charge formation in photorefractive polymers due to Schildkraut and Buettner has been modified to include thermally accessible deep traps as well as shallow traps. The dynamic equations have been solved semiempirically using independent measurements of photoconductive properties to predict photorefractive dynamics. Dependencies of the dynamics on charge generation, mobility, trap density, acceptor density, ionized acceptor density, as well as their associated rates are examined. The magnitude of the fast time constant of photorefractive development is successfully predicted. The introduction of deep traps into the model has allowed us to qualitatively predict the reduction in speed due to deep trap filling and ionized acceptor growth. Experimental studies of photoconductivity and photorefraction (PR) in several polyvinyl carbazole photorefractive composites are carried out to demonstrate the applicability of the model. By choosing chromophores with different ionization potentials and by varying the chromophore concentrations, we investigate the influence of the chromophore ionization potential on the photoelectric and PR properties and reveal the nature of deep traps in the composites and their contribution to both photoconductivity and PR dynamics. Effects of plasticizer components are also discussed. © 2002 American Institute of Physics.

Schematic representation of the modified model for photorefractive polymers. Symbols are E : electric field, ␻ : frequency of light, ␳ : free charge density, s : photogeneration cross section, ␥ T : trapping rate, ␥ : recombination rate, and ␤ 1,2 : detrapping rates.

…

Simulated dynamics of dc photocurrent for the case m T 1 ӷ m T 2 ӷ 1

…

Long time scale dynamics of ͑ a ͒ free charge density ͑ dc photocurrent ͒ ͑ b ͒ ionized acceptor number density at B ̃ 2 ϭ 5 ϫ 10 Ϫ 6 at various deep

…

Ionized acceptor number density as a function of photogeneration cross section as simulated using Eq. ͑ 6 ͒ with parameters ␤ ̃ 1 ϭ 5 ϫ 10 Ϫ 4 , ␤ ̃ 2 ϭ 5 ϫ 10 Ϫ 6 , ̃ ϭ 2.5 ϫ 10 2 , m T 1 ϭ 10, and m T 2 ϭ 1 transformed into dimensional form using ␶ 0 ϭ 5 ms and N A ϭ 5 ϫ 10 24 m Ϫ 3 , and fitted with a power law function N i A 0 ϳ s b .

…

Ionized acceptor number density as a function of photogeneration cross section as simulated using Eq. 6 with parameters˜1parameters˜ parameters˜1 510 4 , ˜ 2 510 6 , ˜ 2.510 2 , m T1 10, and m T2 1 transformed into dimensional form using 0 5 ms and N A 510 24 m 3 , and fitted with a power law function N A0 i s b .

…

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Content uploaded by Kenneth D Singer

Content may be subject to copyright.

Space-charge dynamics in photorefractive polymers

Oksana Ostroverkhovaa) and Kenneth D. Singerb)

Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079

共Received 6 May 2002; accepted for publication 9 May 2002兲

The model of space-charge formation in photorefractive polymers due to Schildkraut and Buettner

has been modiﬁed to include thermally accessible deep traps as well as shallow traps. The dynamic

equations have been solved semiempirically using independent measurements of photoconductive

properties to predict photorefractive dynamics. Dependencies of the dynamics on charge generation,

mobility, trap density, acceptor density, ionized acceptor density, as well as their associated rates are

examined. The magnitude of the fast time constant of photorefractive development is successfully

predicted. The introduction of deep traps into the model has allowed us to qualitatively predict the

reduction in speed due to deep trap ﬁlling and ionized acceptor growth. Experimental studies of

photoconductivity and photorefraction 共PR兲in several polyvinyl carbazole photorefractive

composites are carried out to demonstrate the applicability of the model. By choosing chromophores

with different ionization potentials and by varying the chromophore concentrations, we investigate

the inﬂuence of the chromophore ionization potential on the photoelectric and PR properties and

reveal the nature of deep traps in the composites and their contribution to both photoconductivity

of Physics. 关DOI: 10.1063/1.1491279兴

I. INTRODUCTION

The photorefractive 共PR兲effect involves a change in re-

fractive index in an electro-optical material resulting from

the redistribution of charge carriers created under the inﬂu-

ence of optical beams. This mechanism results in a process,

where the phase shift between the incident intensity pattern

and resulting refractive index pattern due to Poisson’s equa-

tion leads to a number of useful nonlinear optical phenomena

of interest for image and data processing and storage. The

speciﬁc processes required for the PR effect include: photo-

generation of charge carriers, transport of mobile carriers,

trapping of these carriers in the regions of destructive inter-

ference and a change of the refractive index in response to

space-charge ﬁeld. Considerable effort has been applied in

order to understand the inﬂuence of each of these processes

on the PR performance in a variety of materials.

Organic and polymeric materials have been the subject

of numerous recent studies. In these materials, several groups

have addressed these photoelectric mechanisms, especially

photogeneration and transport. Photogeneration efﬁciency is

usually probed using the xerographic discharge technique1–3

or is estimated from dc photoconductivity,4while charge car-

rier mobility is measured using the time-of-ﬂight or holo-

graphic time-of-ﬂight techniques.5,6 Charge trapping mecha-

nisms in PR polymers are still not clearly understood,

although several techniques such as two-beam coupling,7ab-

sorption spectroscopy,8and comparison of external photocur-

rent efﬁciency to the photogeneration efﬁciency3have been

used to study the nature of traps. The mechanisms of space-

charge ﬁeld-induced refractive index change has been inves-

tigated by ellipsometric9–12 and electric ﬁeld-induced second

harmonic generation13 experiments.

Since polymeric PR materials are potentially useful for a

number of applications that require fast response times, PR

dynamics is an important subject for investigation. Recently,

a number of studies have been aimed at understanding the

relationship between photoconductivity and PR speed4,14,15

and to develop a theory describing grating formation.16,17

However, a systematic theoretical study of photoconductive

mechanisms in PR speed in polymers has not been carried

out, as has been for steady-state PR.3,18 Even for steady-state

PR, only the limiting cases of deep traps or no traps are

usually considered, although the presence of shallow traps

has been conﬁrmed both by the dispersive nature of charge

transport in these disordered media19,20 and by the sublinear

intensity dependence of the PR grating erasure rate.21

In the theoretical part of this article, we modify Schild-

kraut and Buettner’s16 model to take into account both shal-

low and thermally accessible deep traps. We then use a semi-

empirical technique to solve the dynamical and constitutive

equations of the model to predict the dynamic PR response

from independently measured photoelectric properties. In

particular, we obtain the trapping, detrapping, and recombi-

nation properties of the material from the dynamics of dc

photoconductivity, and use them in combination with mea-

surements of charge generation and mobility to reveal the PR

dynamics. By performing numerical simulations, we explore

the dependence of the PR speed on all of these photoconduc-

tive parameters. The introduction of thermally accessible

deep traps into the model has allowed us to fully characterize

the PR dynamic, and to access their consequences. Thus we

are able to describe the observed growth of radical C60

⫺共ion-

ized acceptors兲in various materials8,22 as well as the PR

response time fatigue due to sample illumination prior to PR

a兲Present address: Department of Chemistry, Stanford University, Stanford,

CA 94305-5080.

b兲Electronic mail: kds4@po.cwru.edu

JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 4 15 AUGUST 2002

measurements.22 Our aim is to provide a useful experimental

and numerical modeling process for predicting PR dynamics

from basic material properties in order to guide the develop-

ment of new materials.

In the experimental part of this article, we assess the

applicability of the modiﬁed model and examine the contri-

bution of chromophores and plasticizers to photoconductive

and photorefractive performance of PR polymers. We ad-

dress how the PR-relevant photoelectric properties such as

mobility, charge generation efﬁciency, trapping, detrapping,

and recombination rates are inﬂuenced by the degree of dis-

order, trap depths, ionization potentials of the constituents,

presence of ionic impurities, etc. We analyze the photocon-

ductive and photorefractive behavior of both plasticized4,11,14

and unplasticized polyvinyl carbazole 共PVK兲composites in-

cluding the sensitizer (C60) and several chromophores. For

composites of both classes, we determine the quantum efﬁ-

ciency, mobility, trapping, detrapping, and recombination

rates from photoelectric measurements. Then using these

rates we 共i兲calculate the PR speed as determined by four-

wave mixing, 共ii兲compare corresponding rates for different

chromophores and relate them to relevant ionization poten-

tials, 共iii兲study the inﬂuence of plasticizer on photoconduc-

tivity and photorefractive performance of the composite, and

ﬁnally, 共iv兲study the nature of shallow and deep traps in

composites and investigate their inﬂuence on photoconduc-

tive and photorefractive properties of the materials.

II. THEORY

The ﬁrst theoretical description of PR in polymers was

adapted from Kukhtarev’s23 theory of inorganic crystals by

Schildkraut and Buettner.16 They included the rate equation

for traps in the system of PR dynamical equations and took

into account the ﬁeld dependence of both photogeneration of

mobile carriers and mobility. The modiﬁed model presented

here differs from Schildkraut and Buettner’s by introducing

two kinds of traps—shallow and deep. Here, by the term

‘‘deep,’’ we mean that the rate of thermal detrapping for

these traps is at least an order of magnitude lower than that

of shallow traps, but still having a nonzero probability for

detrapping. The processes taken into account in here are de-

picted in Fig. 1. A sensitizer 共acceptor兲with density NAis

excited and subsequently ionized by light of frequency

␻

with cross-section s. A free hole is injected into the transport

manifold and hops between transport sites until it either be-

comes trapped or recombines with ionized acceptors with

rate

␥

. Although, generally, the energy spectrum of trapping

sites has a continuous distribution,21 for tractability we con-

sider only two kinds of traps with well-deﬁned energy levels

共ionization potential兲—shallow traps MT1and deep traps

MT2. We assume that the trapping rate does not depend on

the trap depth,24,25 so that shallow and deep traps are ﬁlled

with the same trapping rate

␥

T. Detrapping proceeds with a

thermal excitation rate

␤

1for shallow traps or

␤

2for deep

traps. Optical detrapping is not considered because the depth

of both shallow and deep traps 共⬍0.5 eV兲is much smaller

than the photon energy ប

␻

共⬃1.96 eV for HeNe 633 nm

light兲. Then, the modiﬁed system of nonlinear equations de-

scribing the PR dynamics is given by

⳵␳

⳵

t⫽

⳵

t⫺

⳵

t⫺

⳵

t⫺1

⳵

t⫽

␥

T共MT1⫺M1兲

␳

⫺

␤

1M1,

⳵

t⫽

␥

T共MT2⫺M2兲

␳

⫺

␤

2M2,

共1兲

⳵

t⫽sI共NA⫺NA

i兲⫺

␥

␳

⳵

x⫽e

⑀

共

␳

⫹M1⫹M2⫺NA

i兲,

J⫽e

␮

␳

E⫺e

␮

␰⳵␳

⳵

Here

␳

is the free charge 共hole兲density, NAthe total density

of acceptors 共e.g., C60兲,NA

ithe density of ionized acceptors

共e.g., C60

⫺兲,M1,M2,MT1, and MT2the densities of ﬁlled

shallow traps, ﬁlled deep traps, and total shallow and deep

trapping sites, respectively, Ethe electric ﬁeld, and Ithe

incident light intensity. Jis the current density,

␮

the charge

carrier drift mobility, and

␰

is the diffusion coefﬁcient given

␰

⫽kBT/e. The quantity sis the cross section of photoge-

neration,

␥

␤

2the trapping rate and detrapping rates

for shallow and deep traps, respectively,

␥

the recombination

rate, and

⑀

the dielectric constant. We consider the param-

eters s,

␮

␥

T, and

␥

to be electric ﬁeld dependent assuming

the following dependencies:18

s⫽s共Eref兲共E/Eref兲p,

␮

⫽

␮

共Eref兲e

␤

␮

共E1/2⫺Eref

1/2兲,

共2兲

␥

⫽

␥

共Eref兲e

␤

␮

共E1/2⫺Eref

1/2兲,

␥

T⫽

␥

T共Eref兲e

␤

␥

共E1/2⫺Eref

1/2兲.

Here Eref is the relevant reference electric ﬁeld for each of

the parameters. During photorefractive grating formation, the

reference electric ﬁeld for photogeneration efﬁciency is the

external applied ﬁeld, while for mobility, trapping, and re-

FIG. 1. Schematic representation of the modiﬁed model for photorefractive

polymers. Symbols are E: electric ﬁeld,

␻

: frequency of light,

␳

: free charge

density, s: photogeneration cross section,

␥

T: trapping rate,

␥

: recombina-

tion rate, and

␤

1,2 : detrapping rates.

1728 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

combination rates the reference electric ﬁeld is the projection

of the applied ﬁeld on the grating vector. Parameters p,

␤

␥

and

␤

␮

are determined experimentally.

Since the creation of a photorefractive hologram as-

sumes a nonuniform light intensity pattern created by the

interfering beams, the incident light intensity can be ex-

pressed as a periodic function of x:

I⫽I0⫹I1cos kx,共3兲

where kis the grating vector chosen to be parallel to the x

direction. The general spatial dependence of Eq. 共3兲will also

apply to the response of the polymeric material. The exact

electric ﬁeld and charge density distributions must be deter-

mined by numerically solving Eqs. 共1兲–共3兲. However, as

shown by Schildkraut and Cui18 for the steady state, the nu-

merically determined values for free charge density and the

amplitude and phase of the space-charge ﬁeld were in a good

agreement with the corresponding values obtained from the

Fourier analysis of the equations analogous to our Eq. 共1兲.

Also, the Fourier decomposition approach was used by Cui

et al. for the analysis of dynamics of the PR grating

erasure.21 So, as we proceed, we use a Fourier decomposition

of all the densities, electric ﬁeld, and current and separate the

equations on the basis of the spatial dependence of the terms.

We also consider the case of moderate applied electric ﬁelds

(Ea⬍50 V/

␮

m), where effects of grating bending and

higher spatial harmonics can be neglected,26 and thus limit

our analysis to the zeroth and ﬁrst spatial Fourier compo-

nents. We experimentally investigated the dependence of the

PR dynamics on the intensity modulation depth m⫽I1/I0.

We found that in contrast with a steady-state PR perfor-

mance, the PR dynamics observed under our experimental

conditions of short prior-to-experiment light exposure time

of ⬃10 s and total writing beam intensities below 400

mW/cm2depended only on I0rather than the modulation

depth m, as expected from the theory for the ﬁrst spatial

order Fourier decomposition. Therefore in our range of elec-

tric ﬁelds and incident intensities, the PR dynamics did not

depend on the modulation depth, and thus, the unity modu-

lation depth 共a conventional choice of experimental geom-

etry in PR polymer literature兲, is used in this article. Then,

the solution of Eq. 共1兲can be written in the following form:

␨

⫽

␨

0共t兲⫹

␨

1共t兲共C

␨

1cos kx⫹C

␨

2sin kx兲,共4兲

where

␨

⫽

␳

,M1,M2,NA

i,J. Since the mobility and all of

the relevant charge generation, trapping, and recombination

rates are ﬁeld-dependent, we assume a form similar to Eq.

共4兲for each of these parameters as well as for the electric

ﬁeld Ewith time-independent

␨

0.18 We substitute Eq. 共4兲in

Eq. 共1兲and separate the spatially independent zeroth order

and spatially varying ﬁrst order systems of equations. We

start from the zeroth order equations that describe photocon-

ductivity in PR polymers under homogeneous illumination of

intensity I0. As we proceed, we will use our photoconduc-

tivity experiments and theory 共zeroth order兲to predict the PR

dynamics 共ﬁrst order兲assuming that the inﬂuence of Gauss-

ian rather than uniform incident beams is the same for both

zeroth and ﬁrst order processes.

A. Zeroth order: Photoconductivity in photorefractive

polymers

In this section we explore how the information about

rates relevant for PR grating formation can be extracted from

the photocurrent dynamics. The zeroth order system of equa-

tions derived from Eq. 共1兲is written as follows:

dM10共t兲

dt ⫽

␥

T共E0兲关MT1⫺M10共t兲兴

␳

0共t兲⫺

␤

1M10共t兲,

dM20共t兲

dt ⫽

␥

T共E0兲关MT2⫺M20共t兲兴

␳

0共t兲⫺

␤

2M20共t兲,

共5兲

dNA0

i共t兲

dt ⫽s共E0兲I0关NA⫺NA0

i共t兲兴⫺

␥

共E0兲NA0

i共t兲

␳

0共t兲,

␳

0共t兲⫹M10共t兲⫹M20共t兲⫺NA0

i共t兲⫽0.

One more equation that is not included in Eq. 共5兲but pro-

vides a link to dc photoconductivity experiments is the con-

stitutive equation for the photocurrent J0(t) given by J0(t)

⫽e

␮

(E0)

␳

0(t)E0. Equation 共5兲describes the dynamics of

free charge generation followed by transport, trapping, de-

trapping, and recombination in the photorefractive polymers

under external electric ﬁeld E0. We consider the electric

ﬁeld E0to be constant and given by E0⫽V/d, where Vis the

applied voltage and dis the thickness of the polymeric ﬁlm.

Then, the time evolution of the photocurrent J0(t) probes the

dynamics of free charge density

␳

0(t) that is connected

through Eq. 共5兲to the generation, trapping, detrapping, and

recombination processes in the PR polymers. The rates de-

scribing these processes (s,

␥

␤

1,2 ,

␥

) are intrinsic charac-

teristics of the polymer composites, and our goal is to deter-

mine their inﬂuence on both photoconductivity and

photorefractive speed. It should also be mentioned that since

all the rates are electric-ﬁeld dependent, the photoconductiv-

ity experiments have to be conducted in the range of external

electric ﬁeld E0that covers both applied electric ﬁeld in PR

experiment Eaand its projection on the grating vector E

ain

order to proceed with calculating the space-charge ﬁeld dy-

namics 共ﬁrst order兲on the basis of parameters determined

from the photoconductivity 共zeroth order兲.

To study the temporal behavior of the free charge

␳

trapped charge M1,M2, and ionized acceptor NA

idensities,

it is convenient to transform Eq. 共5兲to a dimensionless form.

The time scale is normalized by the average drift time of the

free carrier before it is trapped by a shallow trap:

␶

⫽t/

␶

where

␶

0⫽1/关

␥

T(E0)MT1兴. The reason for this choice of

time scale will be explained later in the Sec. II A 1. We ex-

press all the densities in terms of total acceptor density NA:

%⫽

␳

/NA,mT1,2⫽MT1,2 /NA,m1,2⫽M1,2 /NA, and nA

⫽NA

i/NA. We also introduce the relative photogeneration,

recombination, and detrapping parameters s

I0⫽sI0

␶

␥

⫽

␥␶

0NA, and

␤

1,2⫽

␶

␤

1,2 , respectively. The dimensionless

analog of Eq. 共5兲is then written as follows:

1729J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

dm10

␶

⫽

冉

1⫺m10

mT1

冊

%0⫺

␤

1m10 ,

dm20

␶

⫽mT2

mT1

冉

1⫺m20

mT2

冊

%0⫺

␤

2m20 ,

共6兲

dnA0

␶

⫽s

I0共1⫺nA0

i兲⫺

␥

nA0

i%0,

%0共

␶

兲⫹m10共

␶

兲⫹m20共

␶

兲⫺nA0

i共

␶

兲⫽0.

This is a nonlinear system that cannot be solved analyti-

cally. However, we can consider different cases depending

on the total trap densities with respect to the acceptor density

in the material, leading to simpliﬁcations of these equations.

Case 1. Both the total shallow and deep trap densities

are smaller or on the order of the acceptor density: mT1,2

ⱗ1.Case 2. The total deep 共shallow兲trap density is smaller

or on the order of the acceptor density, but the total shallow

共deep兲trap density is much larger than the acceptor density:

mT2ⱗ1, mT1Ⰷ1 or vice versa. In this case, the ratio

m10 /mT1Ⰶ1共or m20 /mT2Ⰶ1兲is always valid, and the ﬁrst

共second兲equation in Eq. 共6兲is simpliﬁed.

Case 3. Both deep and shallow total trap densities are

much larger than the acceptor density: mT1,2Ⰷ1. In this case

both ratios m10 /mT1Ⰶ1 and m20 /mT2Ⰶ1 are always valid,

so that both the ﬁrst and second equations in Eq. 共6兲become

linear.

Our simulations show that in the trap-limited regime

共Case 1兲photocurrent dynamics is similar to the short-time

scale regime of Cases 2,3 共Sec. II A 1兲.Case 1 does not

describe long-time scale changes in both photocurrent and

space-charge ﬁeld, and therefore, seems not to be applicable

for most of our materials. Therefore we consider only Case 2

and Case 3, which can be applicable depending on the chro-

mophore ionization potential and concentration.27,28 We start

our analysis from Case 3 and then extend it to Case 2.

1. Trap-unlimited regime

In this section we consider the case when the total den-

sity of both shallow and deep traps is much higher than the

acceptor density mT1,2Ⰷ1共Case 3兲. Then, Eq. 共6兲is simpli-

ﬁed to

dm10

␶

⫽%0⫺

␤

1m10 ,

dm20

␶

⫽mT2

mT1%0⫺

␤

2m20 ,

共7兲

dnA0

␶

⫽s

I0共1⫺nA0

i兲⫺

␥

nA0

i%0,

%0共

␶

兲⫹m10共

␶

兲⫹m20共

␶

兲⫺nA0

i共

␶

兲⫽0.

We also assume that the density of total shallow traps is

much larger than the density of total deep traps mT1ⰇmT2

which seems to be relevant for all the composites we studied

共Sec. III A兲. Then, we can separately consider different time

scales at which either shallow 共‘‘short time scale’’兲or deep

共‘‘long time scale’’兲trap dynamics prevails in order to pro-

vide insight into the experimentally observed trapping, de-

trapping, and recombination rates as deduced from dc pho-

toconductivity.

a. Short time scale. On the short time scale, the dynam-

ics of the system is entirely determined by shallow traps. To

probe the behavior of our system, we ﬁrst consider the initial

rise in photocurrent as the nonlinear term

␥

%0nA0

iin the third

equation of Eq. 共7兲is much smaller than the linear term

I0nA0

iin that same equation. This transforms the nonlinear

system of Eq. 共7兲into a linear one that can be solved ana-

lytically. Then, we seek a solution of the form ␵⫽␵0e⫺␭

␶

where ␵⫽m10 ,m20 ,nA0

i, and then solve for the three char-

acteristic rates ␭

that determine the dynamics of dc photo-

conductivity at this time scale: ␭

1⫽1⫹mT2/mT1⬇1; ␭

⫽s

I0; and ␭

3⬇

␤

2⫹(mT2/mT1)

␤

1. In these equations we

assume that the detrapping parameters

␤

1and

␤

2are much

smaller than 1 and (mT2/mT1), respectively. This assump-

tion holds when the free charge density is much smaller than

the density of ﬁlled traps as observed in a variety of

materials.3,29 We have also conﬁrmed this in our photocon-

ductivity experiment for materials described here. For this

reason and also in keeping with our experimental observa-

tions that the charge generation rate at reasonable experimen-

tal intensities I0⬍1 W/cm2is much smaller than the trapping

parameter 1/

␶

0, i.e., s

I0Ⰶ1共Sec. IV A 1兲, we can assume

that ␭

2Ⰶ␭

1and ␭

3Ⰶ␭

Thus the fastest photoconductivity dynamics is given by

unity ␭

1⬇1 in the dimensionless form. This fact explains our

choice of the time scale being normalized with respect to

␶

0⫽1/(

␥

TMT1). Thus in dc photoconductivity experiments

the fastest photocurrent dynamics 关J0(t)⬃

␳

0(t)兴is deter-

mined by the value for the shallow trapping product

␥

TMT1.

In the next longer time regime 共though still in the shal-

low trapping fast limit兲we need to consider that, as we will

see later, the free charge density has reached a maximum and

starts to decrease. Then, we can replace the free charge den-

sity function %0(

␶

) in the nonlinear term of the third equa-

tion in Eq. 共7兲with a quasi-steady value %0. We again obtain

three time constants out of which ␭

2is of relevance and

given by ␭

2⫽s

I0⫹

␥

%0. In this intermediate time regime, ␭

contains information regarding the recombination parameter

␥

.Summarizing the dynamics of the photoconductivity on

a short time scale 共for PVK-based materials we studied, this

corresponds to

␶

ⱗ50兲, we obtain the following expressions

for dc photoconductivity rates: ␭

1⬇1; ␭

2⫽s

I0⫹

␥

%0.In

keeping with our experiments, in the low intensity regime

共below 1 W/cm2兲, we can simplify these to ␭

1⬇1; ␭

⬇

␥

%0.

Thus in dc photoconductivity experiments, the short time

scale dynamics can be ﬁtted with a biexponential function,

where the faster rate ␭1yields the shallow trapping product

␥

TMT1, and the slower rate ␭2is directly related to the

recombination rate

␥

To test our approximations, we performed numerical

simulations ﬁxing s

I0⫽10⫺2

␶

0,mT2/mT1⫽0.1,

␤

1730 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

⫽0.1

␶

␤

2⫽0.001

␶

0, and varying the average carrier life-

time

␶

0and the recombination parameter

␥

. This choice of

parameters used for the simulation was suggested by the cor-

responding typical values observed experimentally in unplas-

ticized composites 共Sec. IV A 1兲. First, at

␥

⫽5⫻104

␶

0we

substituted different values of the parameter

␶

0into Eq. 共7兲,

and numerically solved this system to ﬁnd the dependence of

%0(

␶

) for

␶

⭐50. At this time scale, the free charge density

grows as the charge is injected into the transport manifold,

reaches the maximum %0,max , and then decreases, due to re-

combination and trapping. We then ﬁt the calculated curve of

the free charge density %0(

␶

) with a biexponential function

%ﬁt⫽A共1⫺Be⫺␭

␶

⫹共B⫺1兲e⫺␭

␶

兲共8兲

to determine ␭

10 共the faster constant兲and compare it to ␭

⫽1. At B⬎1 Eq. 共8兲describes the photocurrent rise with the

rate ␭

10 and then the photocurrent decay with the rate ␭

20 .

We found that the faster constant in the biexponential ﬁt

yields values equal to unity within 10%, as anticipated. To

extract the slower rate, we used a ﬁxed

␶

0⫽5ms 共typical

value for an unplasticized sample observed in dc photocon-

ductivity experiment at E0⬃30 V/

␮

m and I0⬃50 mW/cm2兲

for different recombination parameters

␥

, found %0(

␶

), and

ﬁt it using Eq. 共8兲to determine ␭

20 . We found that ␭

20 agrees

with ␭2⫽

␥

%0(%0⫽%0,max) within a factor of 3. As we show

in Ref. 28 and mention later in Sec. II B 1, an error of this

magnitude in the recombination rate actually has a negligible

effect on the PR speed. This agreement is remarkable since

we dealt so crudely with the nonlinear term containing the

charge density.

As an example, consider the dynamics of the dc photo-

current simulated using the parameters s

I0⫽5⫻10⫺5,

mT2/mT1⫽0.1,

␤

1⫽5⫻10⫺4,

␤

2⫽5⫻10⫺6, and

␥

⫽2.5

⫻102共solid line in Fig. 2兲. The dashed line in the ﬁgure is a

biexponential ﬁt of the short time behavior using Eq. 共8兲. The

faster inverse time constant of this ﬁt ␭

10⫽1.1 reﬂects the

expected value of 1⫹mT2/mT1⫽1.1. The slower speed ␭

⫽1.9⫻10⫺2divided by the dimensionless free charge den-

sity in its maximum %0,max⬇4.4⫻10⫺5yields, according to

␭

20⫽

␥

%0,max , the recombination parameter

␥

⬇4.3⫻102,

which is within the expected range of values given the input

value

␥

⫽2.5⫻102. The biexponential of Eq. 共8兲ﬁts the

%0(

␶

) dependence perfectly at

␶

⬍50 共inset of Fig. 2兲, but as

the processes which are not taken into account at short time

scale take over at

␶

Ⰷ50, the short time scale ﬁt does not

follow the photocurrent dynamics correctly 共dashed line in

Fig. 2兲, and thus long time scale analysis should be applied.

We now use a procedure to produce a better time evolu-

tion for %0that will also yield the detrapping parameter for

shallow traps. Although it is not obvious how to analytically

extract the detrapping parameter for shallow traps

␤

1,%0(

␶

)

at short time scales is rather sensitive to changes in

␤

1.28 To

ﬁnd the detrapping parameter

␤

1and to ﬁne-tune the recom-

bination parameter

␥

, we used the

␥

estimated above as the

initial value in Eq. 共7兲and varied both

␤

1and

␥

. At every

step we calculated the dimensionless free charge density

%0(

␶

) and ﬁt to Eq. 共8兲. Then we transformed the dimension-

less ﬁt parameter ␭

20 to the dimensional form ␭20⫽␭

20 /

␶

and compared them to the analogous parameters of a biex-

ponential ﬁt of dc photoconductivity data. The comparison

was executed by searching for a minimum of the function

f⫽

冉

␭20,exp⫺␭20

␭20,exp

冊

⫹

冉

Bexp⫺B

Bexp

冊

2,共9兲

where ␭20,exp ,Bexp are the experimental parameters analo-

gous to corresponding parameters ␭20 ,Bintroduced in Eq.

共8兲.Summarizing the short time scale dc photoconductivity

dynamics for the case mT1ⰇmT2Ⰷ1, we are able to deter-

mine the shallow trapping parameter

␥

TMT1, recombination

rate

␥

, and shallow detrapping rate

␤

b. Long time scale. On the long time scale (

␶

⬎103),

shallow traps have reached quasiequilibrium, and deep traps

determine the dynamics of the dc photoconductivity. The di-

mensionless parameters to be determined here are the ratio of

total deep traps with respect to shallow traps mT2/mT1and

the thermal detrapping parameter of deep traps

␤

2. We per-

formed a numerical simulation ﬁxing the parameters s

⫽5⫻10⫺5,

␤

1⫽5⫻10⫺4,

␥

⫽2.5⫻102, and varying

mT2/mT1共while maintaining the ratio mT2/mT1Ⰶ1兲and

␤

Similar to the short time scale approach, we ﬁt the free

charge density %0(

␶

) with a biexponential similar to Eq. 共8兲

共dotted line in Fig. 2兲. The faster speed ␭

10 was kept ﬁxed

equal to unity. Then, our ﬁt yielded two coefﬁcients—the

slower speed ␭

20,long and the exponential prefactor Blong . Al-

though at this time scale, it is not straightforward to relate

the constants of the ﬁt to the parameters of the material di-

rectly, our simulations show that the deep to shallow trap

density ratio mT2/mT1and deep detrapping parameter

␤

can be found from the ﬁt constants in a manner similar to the

short time scale analysis. When dealing with the experimen-

tal data, we constructed the function

FIG. 2. Simulated dynamics of dc photocurrent for the case mT1ⰇmT2Ⰷ1

using Eq. 共7兲and parameters s

I0⫽5⫻10⫺5,mT2/mT1⫽0.1,

␤

1⫽5

⫻10⫺4,

␤

2⫽5⫻10⫺6, and

␥

⫽2.5⫻102. The inset shows the short time

scale part of the photocurrent transient 共data and ﬁt兲.

1731J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

f1⫽

冉

␭20,exp,long⫺␭20,long

␭20,exp,long

冊

⫹

冉

Bexp,long⫺Blong

Bexp,long

冊

where ␭20,exp,long and Bexp,long are the experimental constants

analogous to ␭20,long⫽␭

20,long /

␶

0and Blong . Similar to the

short time scale approach, we sought values for mT2/mT1

and

␤

2that would minimize the function f1.

Summarizing the long time scale dc photoconductivity

dynamics for the case mT1ⰇmT2Ⰷ1, we are able to experi-

mentally determine the product

␥

TMT2and the detrapping

rate

␤

2. Trap-limited regime

In this section, we consider the dc photoconductivity dy-

namics when the total density of traps is on the order or less

than the acceptor density. We will limit our discussion to the

case when the regime is ‘‘trap-limited’’ only with respect to

deep traps 共Case 2兲that appears to be relevant for the mate-

rials we studied.28 So, further in this section we assume that

mT1Ⰷ1 and mT2⭐1. In this case, the condition mT1ⰇmT2is

satisﬁed automatically and thus the time scale division onto

‘‘short’’ and ‘‘long’’ is still appropriate. Also, since for shal-

low traps the condition mT1Ⰷ1 is the same as in the previous

Sec. II A 1, all the short time scale considerations are valid.

However, long time scale behavior is no longer the same as

in the trap-unlimited regime, mainly because in this case the

condition m20 /mT2Ⰶ1 is no longer valid, so Eq. 共6兲with the

ﬁrst equation replaced with the ﬁrst equation of Eq. 共7兲has

to be solved. Modiﬁed in this way, the system of Eq. 共6兲

contains one more parameter than Eq. 共7兲, so that it is not

enough to determine the ratio mT2/mT1because of mT2in

the term m20 /mT2. Our simulations show that if mT2⬃1

then the use of simpliﬁed Eq. 共7兲instead of Eq. 共6兲is still

possible which allows us to determine the ratio mT2/mT1

within 10% error. However, if mT2⬍1, then the modiﬁed Eq.

共6兲must be solved since the error becomes ⬎100%. This

complicates the analysis of the long time scale behavior.

Also, when the density of total deep traps becomes of the

order of 1% or less of the acceptor density (mT2⭐0.01), it

appears to be impossible to detect deep traps in the material

using dc photoconductivity. We simulated the long time scale

evolution of the dimensionless free charge density %0(

␶

)

with the ﬁxed parameters s

I0⫽5⫻10⫺5,

␤

1⫽5⫻10⫺4,

␤

⫽5⫻10⫺6,

␥

⫽2.5⫻102,mT1⫽10, and varying mT2from

0.01 to 1. Figure 3共a兲shows the deep-trap limited behavior

of the photoconductivity for various total deep trap densities.

As seen from Fig. 3共a兲, when mT2⫽0.01, the decay of %0(

␶

)

is less than 3% over the time scale corresponding to the

experimental run of duration ⭓103s for the PVK-based

composites we studied 共Sec. III兲, so that it would be hard to

obtain a reliable ﬁt to such data and thus the trap densities

below 0.01 cannot be detected by this method. As mentioned

before, in the case when mT2⫽0共no deep traps兲, the photo-

conductivity degradation during continuous illumination is

not observed.

3. Time evolution of ionized acceptor density n

According to the last equation in Eq. 共5兲, the free charge,

ﬁlled traps, and ionized acceptor densities are constrained by

the charge neutrality equation, thus the photoconductivity de-

cay, trap ﬁlling, and the growth of the density of ionized

acceptors are directly connected to each other. Figure 3共b兲

shows the simulated time growth of the ionized acceptor

density nA0

␶

) using the ﬁxed parameters listed in the pre-

vious Sec. II A 2 and varying the total deep trap density mT2

from 0.01 共deep trap-limited regime兲to 10 共deep trap-

unlimited regime兲. As seen in Fig. 3共b兲, the more deep traps

are available in the material, the more pronounced is the

ionized acceptor density growth. Also, the trap depth is the

factor that affects the time evolution of nA0

i. Figure 3共c兲

shows how the depth of the traps 共thermal detrapping rate兲

affects the formation of ionized acceptors. For this simula-

tion we used the same parameters as for the simulation

shown in Fig. 3共b兲, but with ﬁxed mT2⫽1 and varied

␤

from 5⫻10⫺7to 5⫻10⫺5.

Our simulations show that the steady-state number den-

sity of ionized acceptors (NA0

i) in the material depends on all

FIG. 3. Long time scale dynamics of 共a兲free charge density 共dc photocur-

rent兲共b兲ionized acceptor number density at B

2⫽5⫻10⫺6at various deep

trap number densities; and 共c兲ionized acceptor number density at mT2⫽1at

various deep trap detrapping rates, as calculated from Eq. 共6兲using param-

eters s

I0⫽5⫻10⫺5,

␤

1⫽5⫻10⫺4,

␥

⫽2.5⫻102, and mT1⫽10.

1732 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

the rates participating in the photoconductivity–

photogeneration cross-section s, trapping rate

␥

T, recombi-

nation rate

␥

, and detrapping rates

␤

1,2 . In particular, Fig. 4

shows the simulated ionized acceptor density achieved in a

typical unplasticized material as a function of photogenera-

tion cross section 共simulated dependence is ﬁtted with power

law NA0

i⬃sb, where bwas determined to be ⬇0.5兲. This

dependence explains differences in the steady-state PR per-

formance, which depends on the density of ﬁlled traps re-

lated to ionized acceptor density by the electric neutrality

equation 关the last equation of Eq. 共5兲兴, observed in the same

material sensitized with different sensitizers.30

In summary, the density and depth of available traps as

well as other photoconductivity parameters are directly re-

sponsible for the variations in the growth of ionized accep-

tors nA0

i共e.g., C60

⫺兲experimentally observed by several

groups.8,22

We have determined many of the parameters of Fig. 1,

and, in the next section, will show how these may be used to

predict the PR dynamics. Here we provide a numerical simu-

lation of the dynamics of the free charge and ionized accep-

tors for materials with deep traps, and in Sec. III we consider

experimental data for different PVK-based composites and

discuss the nature of traps in these materials.

B. First order: Photorefraction

In this section, we consider the formation of the ﬁrst

spatial Fourier component of the free charge, ﬁlled traps, and

ionized acceptors densities as well as space charge ﬁeld and

hence PR dynamics. Here it appears more convenient to use

dimensional equations rather than dimensionless for easier

comparison of the simulated PR dynamics with the experi-

ment. After substitution of Eq. 共4兲into Eq. 共1兲, and sepa-

rately collecting terms with sin kx and cos kx, we obtain a

system of ten equations—eight differential equations 共with

respect to time兲and two equations relating the space-charge

ﬁeld to free charge, ﬁlled traps, and ionized acceptor densi-

ties. We consider that the photogeneration cross section, mo-

bility, recombination, and trapping rates are electric ﬁeld de-

pendent and assume the dependencies given in Eq. 共2兲.As

mentioned before, due to these ﬁeld dependencies all the

parameters acquire a spatially varying part upon formation of

the space-charge ﬁeld. Using Eq. 共2兲and the approach sug-

gested by Schildkraut and Cui,18 we can express all the rates

in terms of space-charge ﬁeld as follows:

s⫽s共Ea兲关1⫹p共E1/Ea兲兴,

␮

⫽

␮

共E

a兲关1⫹共1/2兲

␤

␮

⫺1/2E1兴,

共10兲

␥

⫽

␥

共E

a兲关1⫹共1/2兲

␤

␮

⫺1/2E1兴,

␥

T⫽

␥

T共E

a兲关1⫹共1/2兲

␤

␥

⫺1/2E1兴,

where Eais the applied electric ﬁeld, E

ais the projection of

the applied ﬁeld on the grating vector, and E1is the space-

charge ﬁeld given in accordance with Eq. 共4兲by the relation

E1⫽E11(t)cos kx⫹E12(t)sin kx. Then, the ﬁrst order system

of equations describing PR dynamics is

dE11,12

dt ⫽⫺

␮

⑀

冋

冉

1⫹

␤

␮

1/2

冊

␳

0共t兲E11,12共t兲

⫺E

␳

11,12共t兲⫿k

␰␳

11,12共t兲

册

dM11,12

dt ⫽

␥

TMT1

冉

␳

11,12共t兲⫺

␤

␥

⫺1/2

2E11,12共t兲

␳

0共t兲

冊

⫺

␤

1M11,12共t兲,

dM21,22

dt ⫽

␥

TMT2

冉

␳

11,12共t兲⫺

␤

␥

⫺1/2

2E11,12共t兲

␳

0共t兲

冊

⫺

␤

2M21,22共t兲,

dNA11

dt ⫽sNAI1⫺关sI0⫹

␥

␳

0共t兲兴NA11

i共t兲⫺

␥

NA0

i共t兲

␳

11共t兲

⫺

冉

sNAI0

⫺

␥␤

␮

⫺1/2

␳

0共t兲NA0

i共t兲

冊

E11共t兲,

共11兲

dNA12

dt ⫽⫺关sI0⫹

␥

␳

0共t兲兴NA12

i共t兲⫺

␥

NA0

i共t兲

␳

12共t兲

⫺

冉

sNAI0

⫺

␥␤

␮

⫺1/2

␳

0共t兲NA0

i共t兲

冊

E12共t兲,

E11共t兲⫽e

⑀

k关

␳

12共t兲⫹M12共t兲⫹M22共t兲⫺NA12

i共t兲兴,

E12共t兲⫽⫺ e

⑀

k关

␳

11共t兲⫹M11共t兲⫹M21共t兲⫺NA11

i共t兲兴.

Here E11 ,M11 ,M21 , and NA11

iare the time-dependent am-

plitudes of space-charge ﬁeld, ﬁlled shallow traps, ﬁlled deep

traps, and ionized acceptors, respectively. These have a spa-

tial dependence cos kx 共in-phase with the incident light illu-

mination兲. The quantities E12 ,M12 ,M22 , and NA12

iare the

corresponding amplitudes of functions with a spatial depen-

dence sin kx 共90° out-of-phase with the intensity of incident

light兲.

It is conventional16,21,29 to assume that the PR dynamics

is much slower than the photoconductive dynamics, which is

FIG. 4. Ionized acceptor number density as a function of photogeneration

cross section as simulated using Eq. 共6兲with parameters

␤

1⫽5⫻10⫺4,

␤

⫽5⫻10⫺6,

␥

⫽2.5⫻102,mT1⫽10, and mT2⫽1 transformed into dimen-

sional form using

␶

0⫽5msandNA⫽5⫻1024 m⫺3, and ﬁtted with a power

law function NA0

i⬃sb.

1733J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

analogous to setting the zeroth order 关

␳

0(t),NA0

i(t)兴func-

tions to be constant in time in Eq. 共11兲. In this case, Eq. 共11兲

can be solved analytically as linear equations with constant

coefﬁcients. This approach can be applied on the short time

scale. However, longer times require accounting for deep

traps, which result in slowly changing components of both

␳

0(t) and NA0

i(t), requiring Eq. 共11兲to be solved numeri-

cally. In the next section we will concentrate on obtaining the

four wave mixing 共FWM兲dynamics from the theory and

photoconductivity parameters.

1. Photorefractive rise

In this section we examine the factors that affect the PR

rise time. First of all, it is important to perform a simulation

using conditions as close as possible to a real experiment. In

our case, a real experiment 共FWM兲is performed as follows:

we turn on the electric ﬁeld with one writing beam on, then

in 10 s we turn on the other writing beam of the same inten-

sity and monitor the space-charge ﬁeld formation with a

probe beam. In Eq. 共11兲that describes the PR dynamics, we

need to deﬁne the behavior of zeroth order functions

␳

0(t)

and NA0

i(t), so ﬁrst we simulate the time evolution of these

functions under the experimental conditions described in

Sec. III. The dependence of these zeroth order functions on

the experimental conditions is responsible for the history de-

pendence of the PR performance, as we will explore later in

this section. So, as we determined

␳

0(t) and NA0

i(t) for the

time span of our PR experiment, we use them in Eq. 共11兲to

simulate the evolution of the space charge ﬁeld. We then

calculate the diffraction efﬁciency,

␩

共t兲⬃E11

2共t兲⫹E12

2共t兲共12兲

and ﬁt it to a single exponential,

␩

⫽

␩

0共1⫺e⫺

␯

t兲2共13兲

where the parameter

␯

is PR speed. Usually in the literature,

the experimentally measured diffraction efﬁciency is ﬁt with

a biexponential function. In this case, the initial rise is attrib-

uted to photoconductivity, and the slower one to chro-

mophore reorientation. Thus a single exponential ﬁt 关Eq.

共13兲兴 to describe the initial space-charge ﬁeld formation is

adequate. This case corresponds to PR dynamics observed in

our unplasticized composites. When both faster and slower

experimental time constants are due to photoconductivity,

which is the case for our plasticized composites, the simu-

lated data should be ﬁt with a biexponential function. Here,

for simplicity, we consider the former case and use single

exponential ﬁts 关Eq. 共13兲兴 to describe the diffraction efﬁ-

ciency rise due to space-charge ﬁeld formation.

To explore the factors that affect the speed of space-

charge ﬁeld formation, we modeled the PR experiment by

varying the photogeneration rate s, thermal detrapping rate

␤

1, recombination rate

␥

, total density of shallow trapping

sites MT1, and mobility

␮

. For each set of parameters we

calculated PR speed

␯

from Eqs. 共11兲–共13兲. Although some

of these parameters depend on each other and, strictly speak-

ing, cannot be varied independently, this simulation still can

provide some insight into factors determining the PR speed.

Our simulation shows that the PR speed is nearly insensitive

to the shallow traps release rate: the change in parameter

␤

over four orders of magnitude barely changed the PR speed

by a factor of 2.28 Larger effects were observed when chang-

ing other parameters: a decrease in the total density of shal-

low trapping sites of a factor of 500 led to a sixfold increase

in PR speed, and a four order of magnitude decrease in the

recombination rate yielded a 30-fold increase in PR speed.28

It should be noted that a decrease in total trap density may

decrease the diffraction efﬁciency. Thus in this case there is a

trade-off between PR speed and steady-state diffraction efﬁ-

ciency. As shown in Fig. 5共a兲, the changes in mobility and

photogeneration cross section had the largest impact on a PR

speed. However, it should be mentioned that an independent

variation of the photogeneration cross section is more justi-

ﬁed than an independent variation of mobility, because the

recombination rate is mobility-dependent and affects the PR

speed the opposite way to the mobility itself. Thus, in a real

system, the mobility dependence will be smaller than that

shown in Fig. 5共a兲.

We now explore the history dependence of the PR speed.

As an example, we consider a composite with deep traps that

led to decay of the dc photoconductivity and the slow growth

of the ionized acceptor density. The parameters used in this

simulation were experimentally observed typical values for

the unplasticized composite PVK/AODCST/C60 共Sec. IV兲at

an electric ﬁeld of 40 V/

␮

m and total light intensity of 1

W/cm2.

We simulated a FWM experiment using a fresh sample

and both beams being turned on simultaneously, then the

same experiment after illuminating the sample with one

beam for 10 s and then turning on another one and so on up

to homogeneous illumination with one beam for 5000 s prior

to the PR experiment. The results of the simulation are pre-

sented in Fig. 5共b兲and show that there is a substantial history

FIG. 5. Dependence of PR speed on 共a兲photogeneration cross section and

charge carrier mobility and 共b兲the time of the homogeneous illumination

prior to PR experiment, as calculated from Eqs. 共11兲–共13兲.

1734 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

dependence of the PR speed, in particular the response time

degradation in materials with deep traps, as reported in pre-

vious measurements.31,32 The material will relax back to its

initial 共‘‘fresh’’兲state in the dark when the traps empty, and

the released charge recombines with ionized acceptors. The

relaxation time is mostly determined by the trap depth.

III. EXPERIMENT

A. Materials

For our experiments we chose PVK as a photoconduc-

tive polymer, C60 as a sensitizer, BBP as a plasticizer, and

the chromophores AODCST, PDCST, and 5CB.33 One class

of composites under investigation included the molar con-

centrations of the following: PVK(99%)/C60(1%) 共compos-

ite 1, Tg⬃230 °C兲and PVK(89%)/C60(1%)/NLO(10%)

where NLO is a nonlinear chromophore which in our case

was represented by AODCST 共composite 2, Tg⬃133 °C兲,

PDCST 共composite 3, Tg⬃137 °C兲,or5CB共composite 4,

Tg⬃130 °C兲. Another class had the plasticizer at a loading

complementary to the chromophore molar concentrations:

PVK(49%)/C60(1%)/BBP(50%– x%)/AODCST(x%) and

PVK(49%)/C60(1%)/BBP(50%– x%)/5CB(x%), where x

was varied from 0% to 40%. Studying the chromophore con-

centration dependence of such composites where the chro-

mophore is substituted with the plasticizer rather than just

being added provides for consistent orientational effects

since the glass transition temperature (Tg) was near room

temperature of ⬃21 °C for all the concentrations. In particu-

lar, Tgof AODCST-containing plasticized composites re-

mained constant within 1 °C as xchanged from 2% to 40%

(Tg⬃20 to 21 °C兲, and glass transition temperature of 5CB-

containing plasticized composites increased from ⬃21 °C at

x⫽5% to ⬃24°C at x⫽40%. Thus orientational effects are

similar for all the composites, as we proved by an orienta-

tional dynamics study using electric ﬁeld induced second

harmonic generation 共EFISHG兲.13 Also, the photoelectric

properties of the materials connected to charge transport

共mobility, trapping, and recombination rates兲change with

temperature relative to Tg,⌬T⫽Texp⫺Tg, where Texp is the

temperature at which the experiment is conducted.3,34,35

Therefore we ensured that ⌬Tis almost the same for all our

composites. We used puriﬁed materials and freshly made

samples for all our experiments since we found that both

chemical impurities and sample aging over a period of sev-

eral months led to deep trap formation, which would con-

found the data.

Sample preparation included the following steps. First,

PVK was dissolved in a mixture of toluene and cyclohex-

anone wt. 4:1. Then, C60 was dissolved in toluene and added

to a solution of PVK. Finally, the dye and the plasticizer

were added to a solution of PVK and C60 . The volume con-

centration of C60 was calculated to be NA⬇3.8⫻1024 m⫺3.

For mobility and photogeneration efﬁciency measurements,

we prepared spin-coated samples on an Al substrate, while

another Al electrode was deposited directly on top of the

ﬁlms. For photorefractive measurements we ﬁrst prepared

the ﬁlms on the indium tin oxide 共ITO兲slides and then sand-

wiched them together and baked them in a vacuum oven at

120 °C for 1 h.

The thickness of the samples for mobility and photoge-

neration efﬁciency measurements 共Al electrodes兲was

⬃5–10

␮

m, and ⬃30–70

␮

m for the photorefractive

samples 共ITO electrodes兲. We used both types of electrodes

for dc photoconductivity measurements to ensure that the

parameters calculated from the photocurrent transients are

not inﬂuenced by the type of the electrode or sample thick-

ness. The dielectric constant was measured at a frequency of

1 Hz using a capacitance bridge.

B. Photoconductive measurements

Equation 共1兲introduced in Sec. II is valid for the bulk

material of inﬁnite extent. In real experiments, the external

circuit and electrodes may inﬂuence the observed

behavior.19,36,37 Because of the high degree of disorder and

ﬁeld dependence of all of the photoelectric parameters in

polymers, a systematic analysis of current–voltage character-

istics for different electrodes and their combinations is nec-

essary to fully elucidate the electrical characteristics.38–41

Schildkraut and Cui18 found good agreement between

the steady state values for free carrier density, amplitude, and

phase of space-charge ﬁeld calculated from the bulk dynamic

equations 关e.g., Eq. 共1兲兴 for no boundary conditions 共inﬁnite

bulk兲, ohmic boundary conditions 共‘‘inﬁnite’’ supply of

charge from the electrodes兲, and blocking boundary condi-

tions 共Schottky barrier兲. We performed the dc photoconduc-

tivity experiments with two types of electrodes, Al and ITO,

and for our experimental conditions 共range of electric ﬁelds

and intensities兲did not ﬁnd differences between the param-

eters calculated from the photocurrent transients. Thus we

assume Eq. 共1兲approximates our samples well.

1. dc photoconductivity (short time scale)

For the short time scale measurements 共t⬍50

␶

0, where

␶

0is the average lifetime of a free carrier兲, we applied an

electric ﬁeld to the sample and waited until all the transient

processes disappeared, then opened a shutter 共switching time

below 40

␮

s兲and recorded the sample current under 633 nm

illumination with an oscilloscope. For unplasticized compos-

ites the time span of this short time scale experiment was ⱗ4

s, while for the composites with plasticizer it was ⱗ40 s

depending on the applied electric ﬁeld. We performed this

experiment for various electric ﬁelds and incident intensities.

The photocurrent transients were then ﬁt to a biexponential

function

␳

ﬁt⫽A关1⫺Be⫺␭10t⫹共B⫺1兲e⫺␭20t兴共14兲

and the product of trapping rate and density of available

shallow traps

␥

TMT1, the recombination rate

␥

, and the shal-

low trap detrapping rate

␤

1were determined as functions of

intensity and electric ﬁeld in accordance with the procedure

described in Sec. II A 1 a. From the electric ﬁeld dependence

of the trapping rate, we calculated the parameter

␤

␥

关deﬁned

in Eq. 共2兲兴.

1735J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

2. Dark conductivity and dc photoconductivity (long

time scale)

For dark conductivity and the long time scale (t

⬎103

␶

0) photoconductivity measurements, we monitored

the current through the sample for ⬃20 min using a Keithley

6517 electrometer. A typical experimental run for plasticized

samples included the following: the electric ﬁeld was turned

on, and the dark current (jdark) was recorded for ⬃20 min.

Then, the electric ﬁeld was turned off and then in 2 min

turned on again, and dark current was monitored again for

⬃20 min. If the ﬁrst two dark current runs reproduced, then

the light was turned on, and the current under illumination

(jlight) was monitored for another ⬃20 min. Then, the pho-

tocurrent jphoto was calculated using jphoto⫽jlight⫺jdark .If

the ﬁrst two dark current runs did not reproduce, a third dark

current run was executed, and for all the samples under study

the third run reproduced the second.

In unplasticized composites the dark current is due to

injection from the electrodes. It reaches steady state in sev-

eral seconds and is at least an order of magnitude smaller

than the photocurrent at the incident intensity 20 mW/cm2at

an applied ﬁeld of E0⬃40 V/

␮

m. In plasticized samples the

dark current is due to both injection from the electrodes and

to impurity ions moving towards opposite electrodes. It

reaches a steady state only after 20–30 min and at low elec-

tric ﬁelds (E0⬃10 V/

␮

m) is ⬃30% of the photocurrent at

the incident intensity I0⬃40 mW/cm2, so it is important to

take careful measurements of dark current to reliably deter-

mine the photocurrent.28

The long time scale photoconductivity measurement was

performed as a function of applied ﬁeld and incident inten-

sity. The photocurrent transients were ﬁt to Eq. 共14兲, and the

product of trapping rate and density of available deep traps

␥

TMT2and the detrapping rate

␤

2for deep traps were deter-

mined as described in Sec. II A 1 b.

3. Mobility

Mobility was measured using the time-of-ﬂight 共TOF兲

technique. We used a wavelength of 320 nm that is the third

anti-Stokes of H2—stimulated Raman-shifted 532 nm of a

Nd:YAG laser with a 3.5 ns pulse of ⬃5

␮

J/pulse. The

sample current was transformed to a voltage, ampliﬁed, and

monitored with an oscilloscope. Then, mobility was calcu-

lated using a log-log plot for determining a transient time tT

and the relation

␮

⫽d2/(tTV), where dis the thickness of the

sample and Vis the voltage applied. We measured mobility

as a function of electric ﬁeld to determine the parameter

␤

␮

deﬁned in Eq. 共2兲that describes the mobility ﬁeld depen-

dence. For unplasticized samples and plasticized samples

with low chromophore content 共⬍10% concentration兲the

TOF transients could be easily resolved at electric ﬁelds E

⬎20 V/

␮

m. The transients for high chromophore content

plasticized samples 共⬎10% chromophore concentration兲at

all electric ﬁelds and low chromophore content plasticized

samples at electric ﬁelds E⬍10 V/

␮

m yielded TOF tran-

sients that were too dispersive for reliable determination of

the mobility from TOF experiment. In this case we estimated

the mobility from the dc photoconductivity measurements

using the formula4

␮

⫽d2(

␥

TMT1)/(2 V). This estimate

showed reasonable agreement with TOF results for unplasti-

cized and low chromophore content plasticized samples at

higher electric ﬁelds (E⬎20 V/

␮

m), thus we used it to cal-

culate the mobility for the samples which could not be accu-

rately measured by the TOF technique.

4. Photogeneration efﬁciency

The xerographic discharge technique was used for this

measurement for unplasticized samples and plasticized

samples at higher electric ﬁelds (E⬎20 V/

␮

m). The sample

was charged to an initial voltage and then disconnected from

the power supply. The decay under HeNe illumination of 633

nm was monitored using a static voltmeter and an oscillo-

scope. The cross section of photogeneration swas calculated

from the slope of the discharge rate versus illumination in-

tensity:

兩

(dV/dt)

兩

light⫽关sd2eNA/(

⑀

)兴I0, where I0is the

intensity of light, dis a thickness of the sample,

⑀

is a di-

electric constant, and NAis a number density of C60 .We

also estimated the photogeneration cross section from the dc

photoconductivity as described in Ref. 4 using the formula

s⫽(

␳

␥

TMT1)/(I0NA) where

␳

0is the maximum free

charge density. We ensured consistency of this method by

comparing the photogeneration cross sections determined

from dc photoconductivity and xerographic discharge for un-

plasticized and plasticized samples at higher ﬁelds where the

xerographic discharge technique provided reliable data. For

plasticized samples at low electric ﬁelds (E⬍10 V/

␮

m) re-

liable measurements of xerographic discharge could not be

obtained because of relatively large dark current. In this case,

we calculated the photogeneration cross section sfrom the dc

photoconductivity.Analyzing the electric ﬁeld dependence of

s, we obtained the photogeneration ﬁeld-dependence param-

eter pof Eq. 共2兲for each composite.

C. Photorefractive measurements

The diffraction efﬁciency was measured in a degenerate

four-wave mixing geometry. The grating was written with

two s-polarized HeNe 633 nm beams of the same internal

intensity with a total intensity varying from 25 to 400

mW/cm2. The probe beam was p-polarized with intensity 5

mW/cm2. The external angle between the crossing beams

was 28°, and the external angle between the sample normal

and the bisector of two writing beams was 50°. This experi-

mental geometry along with the index of refraction n⫽1.637

yielded a diffraction grating of period ⌳⬇1.8

␮

m. A typical

experiment for unplasticized samples included the following

steps: ﬁrst, we applied the electric ﬁeld 共⬃30 V/

␮

m兲with

one writing beam and the probe beam on, then in 10 s when

all the transients disappear, we opened the other writing

beam with a shutter and recorded the diffracted signal with a

photodetector, lock-in ampliﬁer, and computer. After the dif-

fracted signal reached the quasi-steady state 共⬃20 s兲, the

light was blocked and the ﬁeld was turned off. The samples

were kept in the dark for ⬃30 min before the next measure-

ment to assure complete decay of the space charge ﬁeld and

the absence of ionized acceptors and ﬁlled traps. For plasti-

cized samples, the experimental run was similar, with the

1736 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

difference being that we used a lower electric ﬁeld 共⬃10

␮

m兲and waited for at least 60 s after turning the electric

ﬁeld on to ensure that most of the impurity ions have accu-

mulated at the electrodes.42 Also, for plasticized samples, we

monitored the diffracted signal following homogeneous illu-

mination of various durations 共up to 1 h兲to study the inﬂu-

ence of deep traps on the photorefractive signal for different

chromophores and chromophore concentrations.

We ﬁt the PR grating formation dynamics with a biex-

ponential

␩

⫽

␩

0关1⫺ae⫺

␯

1t⫺共1⫺a兲e⫺

␯

2t兴2.共15兲

In unplasticized composites the faster speed

␯

1was attrib-

uted to photoconductivity and dominated with weight a

⬇0.7 to 0.8 共inset of Fig. 7兲. The slower speed

␯

2in these

composites is due to orientational enhancement which was

veriﬁed experimentally by comparing the ratio of p-polarized

and s-polarized diffraction efﬁciencies

␩

sto this ratio

calculated from geometry of the experiment and the electro-

optic effect.43 The slower speed was intensity independent

and on the order of 0.5–1 s⫺1, which is consistent with our

EFISHG measurements of the dynamics of chromophore re-

orientation in these unplasticized materials.13

In plasticized composites, both the faster (

␯

1) and

slower (

␯

2) speeds were attributed to photoconductivity and

varied from 0.1 to 10 s⫺1and from 0.01 to 1 s⫺1, respec-

tively, depending on the chromophore concentration, applied

electric ﬁeld, and incident light intensity. Thus the chro-

mophore reorientation time constant of about 50 ms 共as de-

termined by EFISHG兲which is faster than both

␯

1and

␯

does not contribute.

IV. RESULTS

A. Unplasticized composites

In this section we determine the photoconductivity pa-

rameters for composites 1– 4 and discuss the differences in

the parameters depending on the chromophores. Then based

on these parameters we model the dynamics of photorefrac-

tive grating formation and compare it to experiment.

1. Photoelectric properties

The photoconductivity parameters and rates introduced

in Sec. II and calculated from the TOF, xerographic dis-

charge, and dc photoconductivity 共at incident intensity I0

⫽100 mW/cm2兲experiments described in Sec. III at the

electric ﬁeld E0⫽40 V/

␮

m are summarized in Table I. All

the trends we describe in this section are applicable for com-

posites 1– 4 in the studied electric ﬁeld range of E

⬇20– 80 V/

␮

m. Diagrams describing charge generation,

transport, and trapping for different composites are shown in

Fig. 6. Here we used the relative highest occupied molecular

orbital 共HOMO兲level energies for PVK 共0eV兲,C60 共⫺0.17

eV兲, AODCST 共0.03 eV兲, PDCST 共0.1 eV兲, and 5CB

共⬍⫺0.4 eV兲provided in Ref. 8.

Photogeneration cross-section sis a measure of quantum

efﬁciency and for low absorption is given by the relation s

⫽

␣␾

/(ប

␻

NA) where

␣

is the absorption coefﬁcient,

␾

quantum efﬁciency, and

␻

is the light frequency. Photoge-

neration cross section microscopically depends on the

donor–acceptor charge transfer and electron–hole dissocia-

tion rates.44 According to their HOMO levels, chromophores

AODCST and PDCST as well as PVK are donors with re-

spect to C60 , and thus could participate in photogeneration.

If we take into account the dependence of the charge transfer

rate kCT on the energy difference ⌬EDA between HOMO

levels of donor and acceptor44,45 kCT⬃exp关⫺(⌬EDA

⫺␭)2/(4␭kBT)兴where ␭is the reorganization energy, then

in the noninverted regime, the photogeneration efﬁciency

would be highest for composite 3, followed by composites 2,

1, and 4. The noninverted regime refers to the case ⌬EDA

⬍␭, which seems to describe our composites.44 However,

the donor–acceptor charge transfer is not the only factor that

contributes to charge generation. The other factor is the

electron–hole dissociation,44 which proceeds more strongly

as the mobility increases. Based on our results for photoge-

neration cross sections and mobilities for composites 1– 4

共Table I兲, we conclude that the mobility differences that af-

fect dissociation in addition to the charge transfer rate kCT

could account for the differences in quantum efﬁciencies for

the composites 1– 4.

The hole mobility of all of the composites 2– 4 is smaller

than that for the PVK/C60 共composite 1兲. This is expected

when adding polar chromophores to the system due to the

FIG. 6. Schematic representation of the intrinsic states and processes of a

PR composite with various chromophores.

TABLE I. Photoelectric parameters relevant for photorefraction for composites 1–4. No plasticizers were added.

Composite s,10

⫺5

m2/J

␮

,10

⫺11

m2/共Vs兲

␥

TMT1,

s⫺1

␥

TMT2,

s⫺1

␤

s⫺1

␤

s⫺1

␥

,10

⫺19

m3/s

␤

␮

,10

⫺4

共m/V兲1/2

␤

␥

,10

⫺4

共m/V兲1/2 p

⑀

1 Neat 1.7 5.3 850 2.7 2.5 4.9⫾0.2 8.3⫾0.5 2.04⫾0.06 3.1

2 AODCST 1.6 3.9 300 3 0.75 8.5⫻10⫺40.09 5.8⫾0.5 3.3⫾0.4 2.04⫾0.04 4.3

3 PDCST 0.84 2.5 770 23 0.3 1.5⫻10⫺40.08 4.9⫾0.2 6.5⫾0.3 2.04⫾0.04 3.8

4 5CB 0.83 1.7 550 1.5 0.09 6.0⫾0.3 4.6⫾2.0 2.1⫾0.2 4.5

1737J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

increase in energetic disorder.20,46 Based only on the dipole

moment of the chromophore, composites 2 and 3 would be

expected to yield similar mobilities due to almost equal di-

pole moments 共6.9 D for AODCST and 6.6 D for PDCST兲,

and composite 4 would yield the higher mobility than the

composites 2 or 3 since the dipole moment of 5CB 共4.1 D兲is

lower than that of both AODCST and PDCST. Our results

show that the composite 2 possesses the largest value for

mobility out of three composites with chromophores 共2–4兲.

We attribute this to the fact that the HOMO level of

AODCST is situated inside the transport manifold of PVK,

so that AODCST molecules participate in transport by in-

creasing the density of transport states.

All three chromophores inﬂuence the PVK/C60 system

modifying the position and depth of shallow traps that are

intrinsic to PVK.3Here we need to make a distinction be-

tween shallow traps whose release 共detrapping兲time is much

smaller than the transit time, in other words shallow traps

that broaden the tail of the current transients observed in our

TOF experiment, and traps whose release time is much larger

than the transit time. The latter traps are relevant for photo-

refractive performance of the polymer composites considered

here.

The parameters describing shallow traps are the trapping

rate

␥

T, the total number density of available shallow traps

MT1, and the detrapping 共releasing兲rate

␤

1. Comparing de-

trapping rates

␤

1for composites 1– 4 共Table I兲, we observe

that the addition of all chromophores leads to a decrease in

detrapping rate

␤

1that may arise from a decrease in the

overlap integral 共intersite distance兲, an increase in the trap

energy depth ⌬ET共Fig. 6兲,24,47 or both. Both AODCST and

PDCST have a larger impact on

␤

1than 5CB since they can

provide sites that can serve as deeper traps. Since in our

experiments we cannot measure the trapping rate

␥

Tand

total trap density MT1, but only the product

␥

TMT1, we can

only speculate about possible contributions of each. The

trapping rate

␥

Tat a given electric ﬁeld is expected to de-

pend on the free hole mobility and the neutral trap capture

cross section.24 In this case we should expect a smaller trap-

ping rate

␥

Tvalue for the composites 2– 4 in comparison to

composite 1 due to decreased mobility. In composite 3 the

product

␥

TMT1is larger than that of composites 2 and 4

which could indicate that PDCST actually adds shallow traps

to the system in addition to just changing the average depth

of existing shallow traps in pure PVK. On the contrary, com-

posite 2 has the smallest product

␥

TMT1which could mean

that AODCST reduces the relative density of relevant shal-

low traps intrinsic to PVK by providing extra transport sites.

Similar to shallow traps, we characterize deep traps by their

number density MT2and detrapping rate

␤

2. We could not

detect deep traps in the PVK/C60 system and in composite 4

共with 5CB as chromophore兲which means that the density of

available deep traps (MT2) in these composites is on the

order of 1% or less of the acceptor density NA. Both

AODCST 共composite 2兲and PDCST 共composite 3兲create

deep traps, with the trap depth larger for PDCST than for

AODCST which is consistent with experimental studies per-

formed with these chromophores in Ref. 8 and with our nu-

merical simulations. From the comparison between

␥

TMT2

values for composites 2 and 3 we conclude that PDCST cre-

ates more deep traps than AODCST as would be expected by

their HOMO levels.

The recombination rate

␥

describes interaction of the

free hole with the ionized acceptor (C60

⫺) and usually is

treated as Langevin bimolecular recombination

␥

⫽e

␮

⑀⑀

0).24 According to this relation, the ratio

␥

␮

de-

pends only on dielectric constant

⑀

of the material. In poly-

mers, due to disorder, deviations from the Langevin form are

observed.24 Our measured recombination rate for PVK/C60

shows good agreement with the value obtained using the

Langevin form. However, the measured values for compos-

ites 2– 4 are considerably lower than the corresponding val-

ues calculated from the Langevin form.

2. Photorefractive properties

In this section we applied all the photoelectric param-

eters we determined above to Eq. 共11兲. When considering the

space-charge ﬁeld formation, we used the values for mobil-

ity, trapping, and recombination rates calculated using the

value of the projection of the electric ﬁeld on grating vector

while the photogeneration cross section was calculated using

the applied electric ﬁeld. We solved Eq. 共11兲to determine the

dynamics of photorefractive grating formation 关E1(t)兴for

the composites 2– 4. Then, we calculated the diffraction ef-

ﬁciency signal time evolution as it appears in the four wave

mixing 共FWM兲experiment48

␩

⬃E1(t)2and ﬁt with the

function of Eq. 共13兲to predict the photoconductive part of

photorefractive speed

␯

. The calculated speed

␯

is to be com-

pared with the measured

␯

1introduced in Sec. III C. The

anticipated speed

␯

as a function of total internal intensity of

two beams for the composites 2– 4 is shown in Fig. 7 共lines

with symbols兲. The measured 共as described in Sec. III C兲

faster component of the photorefractive speed

␯

1for com-

posites 2– 4 is also shown in Fig. 7 共symbols兲and is in a

reasonable agreement with the speed

␯

predicted using ex-

FIG. 7. Photorefractive speed as a function of intensity for composites 2–4:

line with symbols represents a theoretically predicted speed for this com-

posite 共no adjustable parameters兲using Eqs. 共11兲–共13兲; symbols represent

actual PR speed determined from the FWM experiment. The inset shows a

typical transient measured in composite 2 at a total intensity of 125

mW/cm2.

1738 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

perimentally determined photoelectric parameters for these

composites. Both calculated and experimentally measured

PR speed are sublinear functions of light intensity 共

␯

⬃Ia, where a⫽0.6 to 0.7 depending on a composite兲, simi-

lar to intensity dependencies of simulated and measured pho-

toconductivity 共taken at maximal photocurrent value, see

Fig. 2兲in these composites.

B. Plasticized composites

In this section we consider the dependence of the PR

properties of composites on the chromophore and plasticizer

concentration. First, we consider how substitution of the

chromophore molecule by the plasticizer 关increase in param-

eter x(%) introduced in Sec. III A兴affects the photoelectric

parameters such as mobility, photogeneration efﬁciency, re-

combination, trapping, and detrapping rates. We studied this

for two chromophores, 5CB and AODCST, to determine the

inﬂuence of the chromophore ionization potential on these

characteristics. Second, we used the parameters determined

from photoconductivity to model the time evolution of a

photorefractive grating 共diffracted signal observed in FWM

experiment兲and compare it with experimental data for dif-

ferent concentrations. Finally, we discuss the dependence of

the diffracted signal on the illumination history for different

concentrations of AODCST and 5CB.

1. Photoelectric properties

The most distinct feature of the plasticized composites in

comparison to unplasticized ones is the presence of large

dark current observed in ‘‘fresh’’ samples that were not ex-

posed to either electric ﬁeld or illumination. In this case the

dark current is caused by both charge injection from the elec-

trodes and native ionic impurities49 that become mobile un-

der the electric ﬁeld due to the conformational freedom of

the plasticized polymer chains.24 As the sample is kept under

electric ﬁeld, the mobile ions move towards the oppositely

charged electrodes and either neutralize42 or build up, reduc-

ing the electric ﬁeld inside the polymeric ﬁlm. The samples

of all concentrations xfor both 5CB and AODCST showed

similar behavior. After the transient, the current gradually

decreases until it reaches a quasi-steady level, which in our

materials occurs at time ⬃20–30 min after the electric ﬁeld

is turned on.28 We performed all the measurements after the

samples were electrically cleansed to avoid dynamic effects

directly induced by moving impurity ions. Although we tried

to maintain exactly the same experimental conditions for the

samples at all concentrations, our measurements of both pho-

toconductivity and diffraction efﬁciency at different times

after turning on the electric ﬁeld without any prior illumina-

tion show that internal electric ﬁelds are different for differ-

ent concentrations of the chromophore. However, these ef-

fects were minor in comparison with the direct concentration

effects that we investigated. The energy diagram illustrating

different composites studied is shown in Fig. 8. Based on the

ionization potentials of the plasticizer and chromophores, we

expect that an increase in concentration of 5CB 共relative to

the concentration of plasticizer BBP兲should not change the

mobility, photogeneration efﬁciency, trapping, and other

photoelectric parameters for reasons other than an increase in

energetic disorder due to the difference in dipole moments of

5CB (4.1D) and BBP (1.1D). In the case of AODCST, how-

ever, in addition to the change in energetic disorder, we also

expect changes due to the contribution of AODCST sites in

charge photogeneration and transport. Indeed, our results

show that both mobility and photogeneration cross section

increase with concentration of AODCST and stay almost

constant for all concentrations of 5CB. Although these trends

were observed for the whole range of electric ﬁelds studied

共1–50 V/

␮

m兲, the most pronounced concentration depen-

dence was found at low electric ﬁelds 共⬍15 V/

␮

m兲. This

could be due to the smaller inﬂuence of energetic disorder at

low ﬁelds, so that the largest impact on concentration depen-

dence is attributed to the effects only due to ionization po-

tential of the chromophores relative to transport states. The

concentration dependence of mobility and photogeneration

cross section for 5CB and AODCST at electric ﬁeld E0

⫽10 V/

␮

m is shown in Fig. 9. As determined from dc pho-

toconductivity at electric ﬁeld E0⫽10 V/

␮

m and intensity

I0⫽40 mW/cm2, the product

␥

TMT1increased monotoni-

cally in a similar to sand

␮

manner from 3.5 s⫺1for x

⫽0% 关PVK(49%)/BBP(50%)/C60(1%)兴to 20 s⫺1for x

⫽40% in the case of AODCST and did not change in the

case of 5CB. This change reﬂects the increase in mobility

and intersite distance that affect the trapping rate for

AODCST and no changes in these for 5CB.28 The detrapping

rate

␤

1increased from ⬃0.05 to ⬃0.1 s⫺1for AODCST,

reﬂecting increase in the overlap integral 共decrease in inter-

site distance兲. The recombination rate was ⬃2⫻10⫺21 m3/s

and did not change appreciably with concentration, probably

because the increase in mobility in the case of AODCST was

partially compensated by an increase in dielectric constant as

the concentration of AODCST increased.

The presence of deep traps in the composites was stud-

ied by monitoring dc photoconductivity on a long time scale

共Sec. II A 1 b兲.28 The composites with x⫽0 and with any

FIG. 8. Illustration of chromophore and plasticizer roles in charge genera-

tion, transport, and trapping: 共a兲high x%, AODCST; 共b兲low x%,

AODCST; and 共c兲any x%, 5CB.

1739J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

concentration of 5CB showed no photodegradation and thus

the deep trap density in these composites was below our

detection limit of MT2⭐0.01NA. Our numerical simulations

of PR dynamics show that when the available density of

deep traps is on the level MT2⬃0.01NAor less 共provided

shallow trap-unlimited regime MT1ⰇNA兲, the PR grating

time evolution is not inﬂuenced by deep traps. In the

AODCST-containing composites, the degradation of the pho-

tocurrent increased as the concentration of AODCST in-

creased, so that the product

␥

TMT2describing deep trapping

increased from ⬃0.02 s⫺1for x⫽2% to ⬃1.6 s⫺1for x

⫽40%, and the detrapping rate

␤

2correspondingly changed

from 1.1⫻10⫺5to 8.2⫻10⫺4s⫺1, although the values for

low concentrations of the chromophore may contain a large

error due to the small concentration of deep traps MT2in

these composites. Similar to the method described in Sec.

IV A 2, we substitute all the calculated values into the equa-

tions describing photorefractive grating formation 关Eq. 共11兲兴

and model the PR performance of the composites. We ﬁt the

calculated diffraction efﬁciency

␩

(t) with a biexponential

function 关Eq. 共15兲兴 since, as we mentioned above for these

samples, both the slow and fast components of the photore-

fractive speed are due to photoconductivity. The calculated

faster and slower PR speed 共

␯

1and

␯

2, respectively兲as a

function of concentration of the chromophore with no adjust-

able parameters is presented in Fig. 10共a兲共line with symbols

corresponding to concentrations for which we determined

photoelectric parameters on whose basis the PR speed was

calculated兲.

2. Photorefractive properties

The faster and slower PR speed 共

␯

1and

␯

2兲obtained

from the biexponential ﬁt of Eq. 共15兲to the experimentally

measured diffraction efﬁciency for different concentrations is

plotted in Fig. 10共a兲共symbols兲along with a characteristic ﬁt

关Fig. 10共b兲兴. Faster PR speed in both 5CB and AODCST-

containing composites shows reasonable agreement with the

values of

␯

1calculated from photoconductivity 共line with

symbols兲. The experimentally measured slower speed

␯

shows good agreement with calculated values for 5CB-

containing composites. Although we could not ﬁnd mono-

tonic dependence of slower PR speed on various parameters,

our simulations show that at low photogeneration efﬁciencies

and charge carrier mobilities electric ﬁeld dependence of

photoelectric rates 共i.e., nonzero parameters p,

␤

␮

␤

␥

兲leads

to nonsingle exponential behavior of space-charge ﬁeld in

materials without deep traps, such as our 5CB-containing

composites.

In materials with deep traps, the slower component is

inﬂuenced by trapping rate

␥

T, deep trap density MT2, and

detrapping rate

␤

2. The slower PR speed in AODCST-

containing composites shown in Fig. 10共a兲is calculated us-

ing shallow and deep trap unlimited approximation 共Case 3兲.

As seen from Fig. 10共a兲,Case 3 describes well composites

with high chromophore content. However, at low chro-

mophore concentrations, it seems that the deep trap limited

Case 2 needs to be considered.27,28 In these materials, it is

not enough to know the trapping parameter

␥

TMT2that we

are able to determine from the photoconductivity, but knowl-

edge of the trapping rate

␥

Tand trap density MT2separately

is required to predict the slower PR speed.

According to our simulations, the materials with deep

traps are expected to show a change in both rise and decay

FIG. 9. Concentration dependence of 共a兲photogeneration cross section and

共b兲mobility. The lines provide visual guidance.

FIG. 10. 共a兲Concentration dependence of faster and slower PR speed for

5CB- and AODCST-containing composites. Lines with symbols correspond

to the photoelectric parameter values for PR speed calculated using Eqs.

共11兲,共12兲, and 共15兲; symbols correspond to FWM experimental data at ap-

plied ﬁeld Ea⫽10 V/

␮

m and total internal intensity I⫽300 mW/cm2.共b兲

Data and ﬁt with Eq. 共15兲to two composites.

1740 J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

transients due to the duration of uniform illumination prior to

the experiment, which is supported by our experimental data.

Figure 11 illustrates the diffraction efﬁciency time evolution

in ‘‘fresh’’ samples and preilluminated samples of the com-

posites containing x⫽40% of 5CB 关Fig. 11共a兲兴 and x

⫽40% of AODCST 关Fig. 11共b兲兴. The experimental run con-

sisted of the following steps. First, the electric ﬁeld of 10

␮

m was turned on and kept on for 60 min without any

illumination. Then, one of the writing beams of intensity 150

mW/cm2was turned on, and then after ⬃20 s the second

writing beam of the same intensity was turned on, and the

diffraction grating formation was monitored for 60 s. Then,

one writing beam was turned off, and the grating decay was

monitored. The second writing beam 共with the applied ﬁeld

on兲was illuminating the sample for 5–15 min, and then

again the second beam was turned on and grating formation

monitored. To ensure that the effects we observe in this ex-

periment are due to illumination and not due to internal ﬁelds

formed by uncompensated traps and impurity ions, we per-

formed a similar experiment but without any illumination

between the grating decay and formation measurements. Our

results show that all the dependencies described here and

shown in Fig. 11 are due to illumination only. The 5CB-

containing composite showed no substantial history depen-

dence because the dynamics involves only shallow traps, and

the equilibrium between photogeneration, trapping, detrap-

ping, and recombination processes in the system is reached

within several seconds and then does not change over a long

time scale. In such systems, the long time scale illumination

does not change the density of ionized acceptors and ﬁlled

traps, and so the initial conditions for the onset of diffraction

are the same at any time. Thus there is no illumination his-

tory dependence 共Fig. 11兲. The behavior is different for the

composites with high AODCST concentration. After the

sample illuminated for 5 min, the grating formation and de-

cay are substantially different in comparison with those ob-

served in the fresh sample. This is because after illumination

the initial conditions for the grating formation change dra-

matically due to deep trap ﬁlling and ionized acceptor

growth, so that deep traps noticeably contribute to the grat-

ing dynamics, as predicted by numerical simulations.27,28

The illumination history dependence can be undesirable

for applications requiring a long time period grating

formation/decay repetition in the presence of illumination

and, thus materials containing deep traps are not suitable for

these applications.

V. CONCLUDING REMARKS

We have carried out a detailed investigation of the pro-

cesses that affect the PR speed. Although it has been previ-

ously experimentally demonstrated that photogeneration

cross section and mobility have a large impact on PR speed,

our calculations conﬁrm this. However, we also demonstrate

the role of other parameters such as recombination rate, trap-

ping rate, and density of traps. We have shown the subtle role

that traps play in photorefractive dynamics. We have also

shown how the PR dynamics have a rather complicated

form, but have nonetheless demonstrated how biexponential

ﬁts to the data can be useful when carried out over the ap-

propriate time scales.

We considered two kinds of thermally accessible traps,

shallow and deep. We attribute the shallow traps to structural

defects and conformational traps of the carbazole units50 in

the photoconductor itself 共PVK兲, which can be affected by

the presence of chromophores. Although there could be some

deep traps in PVK itself, the essential contribution in the

density of deep traps that may affect the space-charge ﬁeld

formation is determined by the chromophores. Deep traps

lead to slow growth of ionized acceptor density, as previ-

ously observed,8which leads to complicated long time scale

PR dynamics and illumination history dependence of both

photoconductive and photorefractive properties.

Ionized acceptor density (NA0

i) was identiﬁed earlier in

the literature8,22 as ‘‘deep photoexcitable photorefractive trap

density,’’ since it turned out to be approximately equal to

ﬁlled trap density (M10⫹M20) measured in the two-beam

coupling experiment.8We believe that photorefractive traps

in polymer composites are not photoexcitable and are the

ones we discussed above, which are due to structural defects

in PVK and to the position of the ionization potential of a

chromophore with respect to the photoconductor. The density

of such traps in the material and their depth, together with

other photoelectric rates intrinsic to the material, determines

the dynamics of growth of the ionized acceptors. However,

ionized acceptor density is indeed a good measure for ﬁlled

trap density, since the relation NAO

i⬇M10⫹M20 is always

true according to the charge neutrality equation 关last equation

in Eq. 共5兲兴 under the condition of free charge density (

␳

much smaller than ﬁlled trap densities (M10,20), which seems

to be the case in most PR polymer composites. For example,

if the same material is sensitized with different sensitizers

共meaning that the photogeneration cross section sis the only

parameter that changes in the system兲, the different ﬁlled trap

densities 共as manifested through different gain coefﬁcients兲

FIG. 11. Inﬂuence of homogeneous illumination prior to FWM experiment

on diffracted signals for 共a兲x⫽40%, 5CB and 共b兲x⫽40% , AODCST at

applied electric ﬁeld Ea⫽10 V/

␮

m and total incident intensity I0

⫽300 mW/cm2.

1741J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

observed in the two-beam coupling experiment30 are due to

the difference in charge photogeneration efﬁciency, which

leads to the difference in ionized acceptor density and, there-

fore, ﬁlled trap density.

Experimentally, we studied a set of unplasticized com-

posites with 5CB, AODCST, and PDCST as chromophores

and chromophore concentration dependence of plasticized

composites with 5CB and AODCST as chromophores. We

applied the modiﬁed Schildkraut and Buettner’s model to

compare both photoconductive and photorefractive proper-

ties of the composites under investigation. We were able to

predict with no adjustable parameters the faster photorefrac-

tive speed for a variety of composites from the experimen-

tally measured values of the relevant photoelectric rates. The

slower PR dynamics was predicted with no adjustable pa-

rameters for composites with no deep traps 共composites with

5CB as a chromophore兲and with a high concentration of

deep traps 共high AODCST content composites兲. We also

studied the inﬂuence of deep traps on the illumination history

dependence of the photorefractive performance. The modi-

ﬁed model seems to describe qualitatively the experimentally

observed trends.

Figure 10 points out the complexities of assessing pho-

torefractive speed and designing high speed materials. As

can be seen in that ﬁgure, the slow time constant in

AODCST composites is always slower than that for 5CB

composites due to more deep trapping, while the fast time

constant for AODCST composites can be faster than 5CB

composites due to a higher density of states created by

AODCST states within the transport manifold. The complete

ﬁt in Fig. 10共b兲indicates the difﬁculties in assessing the PR

speed. Diffraction builds more quickly in AODCST compos-

ites, but stabilizes more slowly compared with 5CB compos-

ites. An optimum chromophore would possess a fast compo-

nent like the AODCST composite, but suppress a slow

component like the 5CB composite. Such a chromophore

would possess an ionization potential high enough and/or a

density of states narrow enough so that deep traps are not

formed even at high concentration to suppress the long time

constant, but an ionization potential low enough so that its

density of states overlaps with the transport manifold in-

creasing the initial speed of grating formation. The ionization

potential of 5CB is too high for this, while that of AODCST

may be too low to avoid deep trapping. We are not aware of

an optimized composite that exhibits both a fast short time

constant and a short or suppressed long time constant. As is

well-known, the presence of deeper traps slows the dynam-

ics, but increases the diffraction efﬁciency. This trade-off

must also be addressed depending on the requirements of the

application. We believe that this study provides a method to

assess the impact of trapping on dynamics in a quantitative

manner.

Despite some successful predictions we were able to

make using the modiﬁed model, there are some outstanding

issues. First of all, the composites with trap densities on the

level of MT⬃0.01⫺1NAcannot be treated the way elabo-

rated for the case MT1,2ⰇNA, and thus in many composites

the longer scale behavior of space-charge ﬁeld cannot be

predicted as well as the shorter time scale behavior. Second,

the trapping, detrapping, and recombination rates (

␥

␤

␥

)

were found to depend sublinearly on light intensity28 which

is not explicitly included or predicted by the model, thus it

seems that some process has not been taken into account.

Third, it might be helpful to include the effect of the forma-

tion of the internal electric ﬁeld inside the sample due to the

ﬁlling of uncompensated traps as well as non-neutralized im-

purity ions. Also, both photoconductivity and photorefractive

signals are sensitive to the presence of deep traps in the

composite, so that impurities that could serve as deep traps

can obscure the performance of a purer system. A ﬁnal re-

mark is that Eq. 共1兲is written for an inﬁnite bulk material

and does not take into account the possible effects of elec-

trodes. These issues require further study.

ACKNOWLEDGMENTS

The authors thank Professor R. Twieg for AODCST. Dr.

V. Ostroverkhov is acknowledged for assistance in the nu-

merical simulations. Dr. I. Shiyanovskaya and Dr. J. An-

drews are acknowledged for helpful discussions. The re-

search described in this article was made possible by the

support of the National Science Foundation through the AL-

COM Science and Technology Center 共DMR 89-20147兲, and

by the Air Force Ofﬁce of Scientiﬁc Research, Air Force

Material Command, USAF 共F49620-99-1-0018兲.

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1743J. Appl. Phys., Vol. 92, No. 4, 15 August 2002 O. Ostroverkhova and K. D. Singer

Photorefractivity and photocurrent dynamics of triphenylamine-based polymer composites

Article

Full-text available

May 2024

The photorefractive properties of triphenylamine polymer-based composites with various composition ratios were investigated via optical diffraction, response time, asymmetric energy transfer, and transient photocurrent. The composite consisted of a photoconductive polymer of poly((4-diphenylamino)benzyl acrylate), a photoconductive plasticizer of (4-diphenylamino)phenyl)methanol, a sensitizer of [6,6]-phenyl-C61-butyric acid methyl ester, and a nonlinear optical dye of (4-(azepan-1-yl)-benzylidene)malononitrile. The photorefractive properties and related quantities were dependent on the composition, which was related to the glass transition temperature of the photorefractive polymers. The quantum efficiency (QE) of photocarrier generation was evaluated from the initial slope of the transient photocurrent. Transient photocurrents were measured and showed two unique peaks: one in the range of 10⁻⁴ to 10⁻³ s and the other in the range of 10⁻¹ to 1 s. The transient photocurrents was well simulated (or reproduced) by the expanded two-trapping site model with two kinds of photocarrier generation and recombination processes and two different trapping sites. The obtained photorefractive quantity of trap density was significantly related to the photoconductive parameters of QE.

Photoelectron Yield Spectroscopy and Transient Photocurrent Analysis for Triphenylamine-Based Photorefractive Polymer Composites

Article

Full-text available

Dec 2022

The photocurrent for poly(4-(dimethylamino)benzyl acrylate) (PDAA) photorefractive composites with (4-(diphenylamino)phenyl)methanol (TPAOH) photoconductive plasticizers was measured to be two orders of magnitude higher than that obtained with (2,4,6-trimethylphenyl)diphenylamine (TAA) photoconductive plasticizers. In this study, to determine the reason for the large difference in the photocurrent measured for PDAA photorefractive composites containing two different photoconductive plasticizers of TPAOH and TAA, the highest occupied molecular orbital (HOMO) level identical to the ionization potential (Ip) and the width of the density of states (DOS) were evaluated using photoelectron yield spectroscopy, and the transient photocurrent was analyzed using a two-trap model. The estimated hole mobility was also rationalized using a Bässler formalism together with the energetic disorder of the width of the DOS and the positional disorder of the scattering situation for carrier hopping.

Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration

Article

Full-text available

Jul 2016

The development of a single mode fiber-based pulsed laser with variable pulse duration, energy, and repetition rate has enabled the characterization of photorefractive polymer (PRP) in a previously inaccessible regime located between millisecond and microsecond single pulse illumination. With the addition of CW and nanosecond pulse lasers, four wave mixing measurements covering 9 orders of magnitudes in pulse duration are reported. Reciprocity failure of the diffraction efficiency according to the pulse duration for a constant energy density is observed and attributed to multiple excitation, transport and trapping events of the charge carriers. However, for pulses shorter than 30 μs, the efficiency reaches a plateau where an increase in energy density no longer affects the efficiency. This plateau is due to the saturation of the charge generation at high peak power given the limited number of sensitizer sites. The same behavior is observed in two different types of devices composed of the same material but with or without a buffer layer covering one electrode, which confirm the origin of these mechanisms. This new type of measurement is especially important to optimize PRP for applications using short pulse duration.

Simulation of space charge transport in solid dielectric materials using transmission lines modeling method

Article

Full-text available

Jan 2020

In this paper, a lumped RC circuit model, which is based on the Transmission Line Modeling (TLM) method, is used to describe the space charge production and displacement mechanisms in three different solid dielectric materials (LDPE, PTFE and FR4). Each dielectric material is considered as a transmission line with the capacitive and resistance elements. The obtained circuit equations are solved along with the continuity equations for the various charged species in the bulk of solid dielectric material. The electric potential and field, density of different charged species and their recombination rates, resistive and capacitive properties of the solid dielectric material are calculated. In addition, the effects of the variations in the applied voltage, dielectric permittivity and temperature on these physical parameters are examined. Besides, compared with LDPE and PTFE, the net charge density increment rate in FR4 is much higher. Moreover, the influences of temperature on the net charge density in LDPE are not significant. Furthermore, at the higher applied voltages, the current density is increased. Interestingly, the effects of temperature variations on the recombination rates, net charge and current density in LDPE are much lower. Hence, the suitability of LDPE as solid dielectric material is proved.

Determination of optical parameters of zinc oxide nanofibre deposited by electrospinning technique

Article

Full-text available

Jan 2017

Electrospun ZnO was deposited on a glass substrate from zinc acetate dihydrate (Zn(CH3COO)2.2H2O) with polyvinyl acetate (PVAc) polymer dissolved in N, N, dimethyl formamide (DMF) and annealed in the presence of oxygen until organic molecules were decomposed. The resultant fibre was characterized Scanning Electron Microscope attached with Energy dispersive spectrophotometry (SEMEDS), Fourier transform infra-red (FTIR), Rutherford backscattering spectroscopy (RBS). SEMEDS and FTIR showed total decomposition of the organic precursor. The mean fibre width was found to be 260nm while fibre thickness was 460nm. XRD patterns show ZnO was corundum with the hexagonal wurtzite structure. The crystallite size obtained from the Debye formula was 54nm. The optical analysis showed that the percentage transmittance increased after calcination. The material band gap for this electrospun ZnO fibre was found to be 3.28eV. The material optical parameter such as dispersion energy, average oscillator strength, single oscillator strength were also calculated. The optical conductivity and dielectric plot showed that the material conductivity and dielectric properties increase with increasing photon energy and increases sharply around the material energy bandgap. The Urbach tail analysis of the materials shows that the materials obey the Urbach rule. Therefore, n-type electrospun ZnO fibre high refractive index could be attributed to excess oxygen.

Triphenylamine-Based Plasticizer in Controlling Traps and Photorefractivity Enhancement

Article

May 2021

Synthesis of Photoconducting Non-linear Optical Co-Polymer of 2-Methacryloyl-1-(4’-nitro-4-azo-1’Phenyl) Salicylic acid With Methylacrylate

Article

Jul 2017
IOSR-JAC

Dipak Kumar Mukhopadhyay

Synthesis of Electro-optic Copolymer of 3,3’, 5,5’-tetra methyl- 4,4’-dimethacryloyloxy stilbene With Methyl methacrylate.

Article

May 2017
IOSR-JAC

Dipak Kumar Mukhopadhyay

Recent Progress in Organic Photorefractive Materials

Article

Apr 2017

Photorefractive holograms have received great attention for decades due to their transmissive geometries and dynamic nature. The PR mechanism involves charge generation, charge transport, charge trapping, and modulation of the refractive index. So far, photorefractive hologram is regarded as one of the most important holographic materials with dynamic features. Since the first PR mechanism was described about 50 years ago, extensive investigations have been undertaken by many researchers and it is anticipated that PR materials will be the center of optoelectronic material research in the near future. This article reviews the current understanding of the mechanism responsible for the PR effect and current research trends, and briefly introduces recent progress in applications and material design.

Organic Optoelectronic Materials: Mechanisms and Applications

Article

Full-text available

Oct 2016
CHEM REV

Oksana Ostroverkhova

Organic (opto)electronic materials have received considerable attention due to their applications in thin-film-transistors, light-emitting diodes, solar cells, sensors, photorefractive devices, and many others. The technological promises include low cost of these materials and the possibility of their room-temperature deposition from solution on large-area and/or flexible substrates. The article reviews the current understanding of the physical mechanisms that determine the (opto)electronic properties of high-performance organic materials. The focus of the review is on photoinduced processes and on electronic properties important for optoelectronic applications relying on charge carrier photogeneration. Additionally, it highlights the capabilities of various experimental techniques for characterization of these materials, summarizes top-of-the-line device performance, and outlines recent trends in the further development of the field. The properties of materials based both on small molecules and on conjugated polymers are considered, and their applications in organic solar cells, photodetectors, and photorefractive devices are discussed.

Orientationally enhanced photorefractive effect in polymers

Article

Full-text available

Feb 1994
J OPT SOC AM B

We present experimental data that show that the greatly improved performance of a new class of photorefractive polymers [see Donckers et al., Opt. Lett. 18, 1044 (1993)] is too large to be explained by the simple electro-optic photorefractive effect alone. In these materials a photoconducting polymer host is doped with a small concentration of a sensitizer and a large concentration of a nonlinear optical chromophore that has orientational mobility at ambient temperatures. We present a theoretical model for a new orientational enhancement mechanism in which both the birefringence of the sample and the electro-optic coefficient are periodically modulated by the space-charge field itself. The predictions of this model for the size of the enhancement (which is greater than an order of magnitude in diffraction efficiency), the polarization anisotropy between p-polarized and s-polarized readout, and the presence of index modulation at twice the grating wave vector are in good agreement with the measured properties. This orientational enhancement mechanism should be important in any system in which the nonlinear optical chromophores have sufficient orientational mobility and dipole moment so as to be oriented by the space-charge field itself.

Organic Photoreceptors for Imaging Systems

Book

Oct 2018

Borsenberger

The Electrical Properties of Polymers

Article

Improved photogeneration efficiency of charge-transfer complexes between C60 and low ionization potential arylamines

Article

Jun 2000

Photogeneration of carriers was measured at 633 nm in a series of polymer composites based on polystyrene, doped with a triphenyldiamine derivative as hole transport molecule and C60 as sensitizer. Light absorption and generation of mobile carriers was achieved through the charge-transfer (CT) complex formed between the hole transport molecule and the sensitizer. We discuss the influence of the ionization potential of the hole-transport molecule on the photogeneration efficiency of the CT complex it forms with the sensitizer C60. Photogeneration efficiency of unity at an applied electric field of 55 V/μm is found in one composite.

Influence of composition on the photoconductive and photorefractive properties of PVK composites

Article

Jan 2002
Proceedings of SPIE

We present a theoretical and experimental study of both photoconductivity and photorefraction (PR) in several PVK- based photorefractive composites. We used the modified Schildkraut and Buettner's model of space-charge formation in photorefractive polymers that includes both deep and shallow traps. The dynamic equations have been solved semi- empirically using independent measurements of photoconductive properties to predict photorefractive dynamics. Dependence of the dynamics on charge generation, mobility, trap density, acceptor density, ionized acceptor density, as well as their associated rates is examined. The magnitude of the fast time constant of photorefractive development is successfully predicted. The model has also been found to qualitatively predict the reduction in speed due to deep trap filling and ionized acceptor growth. By choosing chromophores with different ionization potentials and by varying the chromophore concentrations, we study the influence of the chromophore ionization potential on the photoelectric and PR properties and reveal the nature of deep traps in the composites and their contribution to both photoconductivity and PR dynamics. Effects of plasticizer components were also investigated.

Systematics of two-wave mixing in a photorefractive polymer

Article

Feb 1998
J OPT SOC AM B

The high-performance photorefractive polymer composite PVK:PDCST:BBP:C60 is investigated in detail by use of optical two-wave mixing characterization measurements in conjunction with the grating translation technique for determination of the photorefractive phase shift. A large effective trap density of Neff = 1.5 × 1017 cm−3 is estimated from the dependence of the phase shift on the grating spacing and the applied electric field. The theory of orientational enhancement is successfully used to explain the observed photorefractive response, and in this low-glass-transition temperature system the modulation of the refractive index is shown to stem primarily from the spatial modulation of the birefringence.

Common features in the transport behaviour of diverse glassy solids: Exploring the role of disorder

Article

Jan 1991

Key results of time-of-flight drift mobility measurements on silicon and germanium backbone polymers are reviewed. Transport in these polymers displays a convoluted and yet familiar pattern of electric field and temperature dependences similar in remarkable detail to behaviour already reported for a very diverse collection of disordered molecular solids. The latter, while varied in composition and morphology, all share at least two common features, namely firstly transport controlled by interaction with localized states which are either hopping sites or shallow traps in communication with a band and secondly disorder. We explore in this paper the application of what is arguably the simplest model (derived from Monte Carlo simulation) of transport incorporating these characteristics. Consideration will be restricted to hopping among a spatially regular array of sites made energetically inequivalent by disorder. Thus, neither positional disorder nor site relaxation is explicitly considered. Some reformulation of experimental data is carried out to facilitate critical comparison with predictions of the model. It is demonstrated that both the commonly observed Poole-Frenkel-like field dependence of drift mobility and the transit pulse widths (always well in excess of that predicted by simple diffusion) can be simultaneously accounted for in terms of a single disorder parameter. The disorder parameter can in turn be directly related to the distribution of transport interactive states.

Spectroscopic determination of trap density in C60-sensitized photorefractive polymers

Article

Jul 1998
CHEM PHYS LETT

A new and simple method for the determination of the trap density in C60-sensitized photorefractive polymers is presented. We show that the radical anion of C60 acts as the primary photorefractive hole trap, using the strong near-infrared absorption of C60− to quantify the anion concentration in situ. The spectroscopically determined concentration correlates well with the photorefractive trap density obtained from analysis of the photorefractive performance. In our model, optical irradiation is needed to activate the trapping sites, and the nonlinear optical chromophore acts as a temporary reservoir for the photogenerated holes (compensator). This model is further clarified using cyclic voltammetry.

High-electric-field poling of nonlinear optical polymers

Article

Jan 1998
J OPT SOC AM B

We have investigated electrical conduction phenomena during high-electric-field poling of a standard covalently functionalized DR-1 side-chain polymer. We performed electric current and second-harmonic measurements simultaneously to derive the effective internal field strength. Various metals and transparent indium tin oxide were used as electrodes. Current densities appeared to be interface (electrode) limited, with little dependence on the work function of the metal for the top electrode (Bardeen barrier at the electrode–dielectric interface), whereas for the bottom electrode–dielectric interface a dependence on the work function of the metal was observed. The field dependence of the current density was found to be Schottky charge emission for medium field strengths (EPOL≤100 V/μm), whereas it was dominated by Fowler–Nordheim tunneling at higher poling fields. In the presence of an additional inorganic barrier layer, significant suppression of tunneling was observed, which led to a reduced probability of singular breakdown events and shifted the limit of avalanche breakdown to higher internal effective poling field strengths.

Competing photorefractive gratings in organic thin-film devices

Article

Jul 1998
J OPT SOC AM B

Recently, amorphous organic photorefractive materials have generated great excitement because of their excellent performance, which permits applications in high-density holographic storage, real-time image processing, and phase conjugation. However, the heterostructure of the devices (consisting of glass cover slides, transparent electrodes, and the photorefractive material) and the tilted recording and readout geometry commonly used result in multiple reflected beams in addition to the normal object and reference beams. This result leads to several photorefractive gratings competing inside the photorefractive polymer device. We prove the coexistence of these gratings by two-beam coupling and four-wave mixing experiments and demonstrate how to distinguish between them. 1998 Optical Society of America S0740-3224(98)04207-6

Space-charge dynamics in photorefractive polymers

Abstract and Figures

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