Field-independent grating formation rate in a photorefractive polymer composite sensitized by CdSe quantum dots

Article abstract of DOI:10.1063/1.1507577

A photorefractive polymer composite sensitized by CdSe quantum dots was described. In contrast to most other photorefractive polymers reported, the hologram formation rate was observed to be independent of applied field. This result was explained by the low saturation field calculated for this material.

Full text of DOI:10.1063/1.1507577

Field-independent grating formation rate in a photorefractive polymer composite
sensitized by CdSe quantum dots
David J. Binks, David P. West, Sebastian Norager, and Paul O’Brien
Citation: The Journal of Chemical Physics 117, 7335 (2002); doi: 10.1063/1.1507577
View online: http://dx.doi.org/10.1063/1.1507577
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/117/15?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 117, NUMBER 15
15 OCTOBER 2002
Field-independent grating formation rate in a photorefractive polymer
composite sensitized by CdSe quantum dots
David J. Binks and David P. West
Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
Sebastian Norager and Paul O’Brien
Department of Chemistry, University of Manchester, Manchester, United Kingdom
͑
Received 27 February 2002; accepted 25 July 2002͒
The rate of grating formation in a photorefractive polymer composite sensitized by CdSe quantum
dots is found to be independent of applied field, in contrast to similar composites sensitized by other
types of nanoparticles. The photorefractive polymer composite under study consists of
poly͑N-vinylcarbazole͒ as the nominal charge transporting matrix, an electro-optic dye, and CdSe
quantum dots passivated by tri-n-octylphosphine oxide. Both the field-independent grating
formation rate and the lower diffraction efficiency compared to other nanoparticle-sensitized
composites are attributed to low initial trap density, i.e., a reduced stability of ionized quantum dots
within the composite in the dark. © 2002 American Institute of Physics.
͓
DOI: 10.1063/1.1507577͔
I. INTRODUCTION
confinement affects the absorption and emission of photons
from the dot. For instance, a reduction in the diameter of a
nanoparticle results in an increase in the band gap; thus the
absorption edge of a material can be tuned by control of the
Photorefractivity in polymers was discovered more than
1
1
0 years ago and since then many advances have been made
both in terms of material performance and in the understand-
ing of the effect as it occurs in polymers. Investigations into
photorefractivity in general are motivated by its many useful
5
particle size. In addition, the small size of the nanoparticle
in relation to the Bohr radius can result in enhanced oscilla-
6
2
tor strength. The surface of a nanoparticle can be altered by
potential applications, such as holographic data storage and
optical information processing,3 and into photorefractive
adding a shell of another material around the dot or by the
selection of a particular passivating molecule ͑i.e., molecules
attached to the surface of the dot that prevent growth beyond
a certain size͒. The nature of the dot surface is likely to
influence the efficiency with which charge is transferred be-
tween the dot and its environment.
͑PR͒ polymers in particular because of the simple and flex-
ible solvent-based chemistry by which they are made. An-
other appealing feature of polymer photorefractivity is that
the materials used can take the form of composites, with
each constituent included to perform a particular role in the
photorefractive effect. One benefit of this approach is that
each of the components can be varied independently to op-
timize a particular physical process. Usually, such a compos-
ite will include a sensitizer species, which photogenerates
charge at visible wavelengths, a charge-transporting host ma-
trix, and electro-optic chromophore molecules. In this study,
a new sensitizing species is introduced and its performance
assessed. Recently, a detailed survey of sensitizers investi-
To date there has been considerable interest in the use of
quantum dots as the charge-photogenerating species in ma-
terials for photovoltaic and solar cells,7 but there have been
only two reports of their use in photorefractive polymers.
,8
9
The first study used a composite consisting of ϳ0.2 wt %
CdS dots passivated by p-thiocresol, poly͑N-vinylcarbazole͒
͑PVK͒ as the transport matrix and 4-nitrophenyl-L-prolinol
as the electro-optic chromophore; in this case, tricresyl phos-
phate was also included to plasticize the composite. The sec-
ond example10 of a nanoparticle-sensitized PR polymer com-
posite utilized ϳ0.1 wt % CdSe quantum dots surrounded by
a CdS shell and passivated by tri-n-octylphosphine oxide
͑TOPO͒. In that case, the charge transport matrix was again
PVK and the electro-optic chromophore used was
1-͑2Ј-ethylhexyloxy͒-2,5-dimethyl-4-͑4Љnitrophenylazo͒ ben-
zene ͑EHDNPB͒. The holographic response time of both ma-
terials was highly field dependent.
We report in this paper the photorefractive properties of
a polymer composite consisting of PVK and the electro-optic
chromophore EHDNPB, sensitized by TOPO-passivated
CdSe nanoparticles. A detailed description of this material is
given in the next section, including the method by which the
CdSe dots were synthesized. Transmission spectroscopy and
4
gated thus far has been published. In terms of holographic
response times, the best performances have been observed
from composites sensitized by either C , 2,4,7-trinitro-9-
6
0
fluorenone ͑TNF͒, or trinitrofluorenone dimalenitrile
TNFDM͒.
Quantum dots, or nanoparticles, are promising sensitiz-
͑
ers for PR polymer composites because of their nanoscale
and because they can be engineered to suit particular appli-
cations. The nanoscale of quantum dots ensures that they do
not scatter light at visible or longer wavelengths, which is
important to minimize optical losses in photorefractive appli-
cations. Moreover, at this scale, quantum confinement and
surface effects become very important and therefore manipu-
lation of the dot diameter or modification of its surface al-
lows the properties of the dot to be controlled. Quantum
0021-9606/2002/117(15)/7335/7/$19.00
7335
© 2002 American Institute of Physics
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1

7336
J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Binks et al.
ellipsometry, two-beam coupling, and four-wave mixing
were used to characterize the photorefractive performance of
the composite. These experiments are described and the cor-
responding results presented. The rate of grating formation is
independent of field in this material, in contrast to other pho-
torefractive polymer composites. This observation is attrib-
utable to a very low charged trap density prior to illumina-
tion. This implies that CdSe dots form less stable ions in a
PVK:azo dye matrix than do either CdS dots or CdSe-core/
CdS-shell dots.
II. MATERIALS
FIG. 1. Transmission spectrum for a dilute sample of the CdSe nanopar-
ticles in a toluene solution. Inset: Photoluminescence spectrum for the same
sample.
A. Synthesis of the CdSe-TOPO quantum dots
Synthesis of CSe was carried out using an adaptation of
2
11
the method of Henriksen and Kristiansen. Selenium pow-
B. Preparation of the photorefractive polymer
composite sample
der ͑ca. 30 g͒ was reacted with CH Cl vapor at a high
2
2
temperature ͑575 °C͒ under nitrogen for 6–7 hs. The crude
product was then filtered through activated neutral alumina.
CH Cl was removed at atmospheric pressure and CSe was
Powdered PVK ͑52 mg͒ and EHDNPB ͑47.5 mg͒ were
3
dissolved into 1 cm of the quantum dots in toluene to pro-
2
2
2
obtained after distillation of the crude product under vacuum
Schlenck line͒ into a liquid-nitrogen trap. The product was
stored in a refrigerator at ca. Ϫ20 °C.
duce a solution of PVK:EHDNPB:CdSe in the proportions,
by weight, 52:47.5:0.44. This solution was dripped onto an
indium tin oxide ͑ITO͒–coated glass plate and then the tolu-
ene was driven off by drying in an oven at 135 °C overnight.
A photorefractive device was fabricated by placing a second
ITO-coated plate on top of the first; Kapton spacers were
used to keep the two plates at a fixed separation. The device
was kept under mechanical compression and returned to the
oven for an hour. Finally, the compression was removed and
the plates were secured together by applying epoxy resin
glue. The thickness d of the photorefractive polymer layer
part of this device was measured to be 130Ϯ2 ␮m.
͑
3
CSe ͑4.13 g, 24.3 mmol͒ in 1,4-dioxane ͑50 cm ͒ was
2
added slowly with a dropping funnel to a solution of sodium
hydroxide ͑1.0 g, 25 mmol͒ and N-methylphenethylamine
͑3.5 ml, 24.1 mmol͒ at Ϫ10 °C. The resultant orange solution
was filtered and immediately added to a solution of cadmium
chloride ͑2.2 g, 12 mmol͒ to give a yellow precipitate.
The precipitate was then filtered and dried under vacuum.
The crude product, a yellow solid, was recrystallized
from hot dichloromethane to give pale yellow
Cd͑Se CNMeCH CH Ph) melting point 205 °C; yield, 5.20
2
2
2
2
g, 7.2 mmol, 60%͒.
The TOPO capped nanoparticles were synthesized
via the injection of single source precursor,
Cd͑Se CNMeCH CH Ph) dispersed in tri-n-octylphosphine
III. EXPERIMENTS AND RESULTS
A. Transmission and photoluminescence spectra
a
The transmission spectrum of a diluted sample of the
nanoparticles in toluene, contained in a quartz cuvette, was
measured using a Cary 1E spectrophotometer, and is shown
in Fig. 1. A band edge is observed between 500 and 650 nm
that includes an absorption maximum at about 565 nm. This
maximum is attributed to the discretization of absorption
caused by quantum confinement. The inset of Fig. 1 is the
photoluminescence spectrum for the dots, which peaks at
around 580 nm.
The transmission spectrum of the photorefractive device
was also measured and is shown in Fig. 2. A maximum trans-
mission of 78% is observed for wavelengths Ͼ660 nm, and
the transmission at 633 nm is 71%, which corresponds to the
wavelength of the laser used in the photorefractive charac-
terization of the material. Both PVK and EHDNPB exhibit
2
2
2
2
͑TOP͒, into hot TOPO using standard Schlenck techniques.
Typically Cd͑Se CNMeCH CH Ph) ͑0.2 g͒ was dissolved
2
2
2
2
in TOP ͑5 ml͒. This solution was then injected into hot
TOPO ͑30 g, 250 °C͒. A decrease in temperature of approxi-
mately 20 °C was observed. The solution was then allowed
to stabilize at 250 °C and heated for 5 min at this tempera-
ture. The solution was cooled to approximately 70 °C and an
excess of methanol added, a flocculant precipitate formed.
The solid was separated by centrifugation and redispersed in
toluene. The solution was then centrifuged again to remove
any remaining bulk material, resulting in a bright red, clear
dispersion of TOPO-capped CdSe nanoparticles.
Using optical emission spectroscopy, the concentration
of cadmium in the solution was measured to be 260 ͑Ϯ15%͒
3
4
␮
g/cm . Assuming a 1:1 ratio of Cd:Se atoms, then this Cd
negligible absorption for wavelengths Ͼ600 nm. Hence, if it
3
concentration implies a Se concentration of 180 ␮g/cm and
an overall CdSe concentration of 440 ␮g/cm . The particle
is assumed that the transmission losses for wavelengths
greater than 700 nm are largely due to reflections and scat-
tering, then 9% absorption at 633 nm can be attributed to the
3
size is approximately 4.0 nm Ϯ15%, estimated by a combi-
nation of optical absorption spectroscopy and transmission
electron microscopy images.
quantum dots, which corresponds to an absorption coeffi-
Ϫ1
cient of 7.4 cm
.
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J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Grating formation rate in polymer with quantum dots
7337
FIG. 4. Field-induced birefringence transient observed in the transmission
ellipsometer. The fit to Eq. ͑1͒ and the corresponding residuals are also
shown.
FIG. 2. Transmission spectrum of the photorefractive device used in the
experiments.
B. Photorefractive performance
blocking one of the beams. One beam grows in intensity at
the expense of the other, thus confirming the photorefractive
nature of the photograting.
1. Two-beam coupling
There are various mechanisms other than photorefractiv-
ity, such as photoisomerism, that can form photoinduced in-
dex gratings in polymer materials. However, only the grating
due to photorefractivity will exhibit asymmetric two-beam
coupling ͑TBC͒, i.e., net energy transfer from one beam to
the other ͑the direction of transfer being determined by the
applied field direction͒. This net energy transfer is a result of
the unique nonlocal nature of the photorefractive index grat-
ing, and hence it is used as a test of photorefractivity.12 Thus,
to confirm that presence of the photorefractive effect in a
PVK:EHDNPB composite sensitized by CdSe-TOPO quan-
tum dots, a TBC experiment was performed. In our TBC
experiment, the two beams were separated by 50° outside the
sample and their bisector formed an external angle of 45°
with the sample normal. The two beams, produced by a
2. Transmission ellipsometry
The holographic contrast in high-performance photore-
fractive polymers is chiefly determined by the rotational re-
sponse of the dipolar chromophores to the space-charge field
formed by the photorefractive effect. This rotational response
can be studied independently of the photorefractive effect
using a transmission ellipsometer ͑TE͒. The TE experiment
and the analysis of the subsequent results have been de-
13
scribed in detail previously. A field is applied across the
photorefractive polymer sample whilst it is positioned be-
tween two crossed polarizers. The birefringence induced in
the material by the field rotates the polarization of a laser
beam passing through the sample that is thus partially trans-
mitted at the analyzer. The results of the TE experiment can
be used to both predict the steady-state holographic contrast
of the photorefractive composite and quantify the rotational
freedom of the chromophores within the sample. Figure 4
shows the TE transient for the CdSe-sensitized PR sample
helium-neon laser, were both s-polarized, had an intensity of
Ϫ2
0
5
.08 W cm each and had a wavelength of 633 nm; a
Ϫ1
0-V ␮m field was applied across the sample. Figure 3
shows the transient change in intensity for both beams that
results when the photorefractive effect is initiated by un-
Ϫ1
for a 30-V ␮m applied field as a step function. Since the
chromophores are rotating within an amorphous medium,
they typically exhibit nonexponential dynamic behavior. It
has been shown previously14 that this nonexponential dy-
namic response to a constant applied field E results in bire-
fringence transient, ⌬nBR(t), that is well described by the
following bipower-law function:
SE2
␶1
␶2
2
s
s
2
1
⌬
nBR͑t͒ϭcos ͑␸͒
1ϩ
t Ϫ
t
,
ͭ
ͮ
2
␶2Ϫ␶1
␶2Ϫ␶1
͑
1͒
where
1
2
s1,2ϭϪ
ϭϪ2D ͑2ϯ
ͱ
1Ϫu /5͒,
͑2͒
0
␶1,2
and ␸ represents the internal angle between the beam direc-
tion and the sample normal. S is a material constant, which
depends on the nature and concentration of the chro-
mophores and determines the magnitude of the birefringence
FIG. 3. Two-beam coupling transient showing the asymmetric beam cou-
pling that is characteristic of the photorefractive effect.
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1

7338
J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Binks et al.
sensitized by CdSe/CdSe-TOPO core/shell quantum dots ex-
Ϫ1
hibited, at a field of 70 V ␮m , a diffraction efficiency of
1
.3%,10 whilst sensitization by 2,4,7-trinitro-9-fluorenone
has resulted in a maximum diffraction efficiency of 60%
from a similar composite.19 A value of ␩ϭ0.035% was mea-
sured with no field applied. First-order diffraction from a
photorefractive grating does not occur in the absence of an
applied field and so a finite zero-field diffraction efficiency
indicates that one or more other forms of photoinduced grat-
ing are also present in the sample.
Since similar geometries and identical chromophores at
similar concentrations were used in these other cases, the low
diffraction efficiency observed for this sample can be attrib-
uted to the formation of only a small space-charge field, E1 ,
by the photorefractive effect. The magnitude of the space-
charge field, for equal intensity writing beams and in the
limit of negligible charge diffusion, depends on the angle ␪
FIG. 5. First-order diffraction efficiency as a function of applied field mea-
sured in the four-wave mixing experiment.
between E and the grating vector K; the component of the
a
induced by a field. The rotational freedom of the chro-
applied field along the grating vector, E ϭE cos(␪); and the
0
a
mophores is characterized by D , the diffusion constant,
saturation field Eq :
0
which is dimensionless but has a magnitude that is deter-
mined by the time scale of the experiment. The ‘‘balance
ϪE Eq
1
0
parameter,’’ uϭ␮ E/kT, is determined by the applied field,
E ϭ
ͯ
ϫ
ͯ
d
1
2
E ϩiE0 1ϩp͑E ͒cos ␪
q
a
the dipole moment ␮ , Boltzmann’s constant k, and the ab-
d
solute temperature T ͑ϭ293 K here͒. For typical field values
E E
1
0
q
2
15
u /5Ӷ1 and estimating the value of u/Eϭ0.0087 is suffi-
cient to obtain a good fit between theory and measurement.
Figure 4 shows the field-induced birefringence transient ob-
served in the TE and includes the fit of Eq. ͑1͒ to the data
and the corresponding residuals. The fit resulted in values of
ϭ
2ϫ
,
͑3͒
2
2
0
ͱ
E ϩE 1ϩp͑Ea͒cos ␪
q
where p(E ) is a parameter that results from incorporating
a
the effect of field-dependent photogeneration into the stan-
dard theory of photorefractivity.
Ϫ7
2
Ϫ2
17,20,21
Sϭ6.81(1)ϫ10 ␮m V
and D ϭ0.103(1) ͑ms time
Hence, a small space-
0
scale͒. These values of S and D are very similar to those
charge field can be the result of a low value of E . The
0
q
found for similar materials sensitized with other photogener-
saturation field itself is given by
1
6,17
ating species;
hence, as expected for a subpercent con-
centration component the CdSe quantum dots have little ef-
fect on the static or dynamic electro-optic response of the
chromophores.
Ϫ
Ϫ
eN
N
E ϭ
q
ͩ
1Ϫ
ͪ
,
͑4͒
⑀
K
N
Ϫ
where N represents the ionized sensitizer population den-
sity and N is the total ͑ionized plus un-ionized͒ sensitizer
population density; E also depends on the electronic charge
e and the dielectric constant ⑀. For most polymer composites,
it is reasonably assumed that the value of N is sufficiently
3. Four-wave mixing
The holographic performance of photorefractivity can be
characterized by degenerate four-wave mixing ͑DFWM͒, an
q
experiment that has been described a number of times
Ϫ
1
6,18
previously.
The same geometry was used as that for the
great such that E ӷE , and therefore the dependence of E
q
0
1
TBC described above but with the addition of a weak,
p-polarized, probe beam of the same wavelength, which was
aligned to counterpropagate with one of the writing beams.
The formation of a photorefractive or other grating within
the sample causes some fraction of the probe beam to be
diffracted so that it counterpropagates with the second writ-
ing beam. Measurement of the efficiency of this first-order
diffraction allows the holographic index contrast to be calcu-
lated.
on E is effectively eliminated; the low diffraction observed
in the present sample, however, means that it is not possible
q
to neglect E in this case.
q
The first-order index contrast ⌬n produced by the pho-
1
16,18
torefractive effect in the polymer is given by
⌬
n ͑E ͒ϭSk
E E ,
͑5͒
1
a
geom
0
1
a. Steady-state results. The diffraction efficiency ␩ as a
where kgeom is a factor that depends on the geometry chosen
for the DFWM experiment. For equal intensity writing
beams, the first-order diffraction efficiency from the sample
is determined by the total index contrast ⌬ntot , which in
general is due to the combination of the index contrasts pro-
duced by the photorefractive and other effects. Explicitly, the
first-order diffraction efficiency ␩ is given by22
function applied field E to the sample is shown in Fig. 5. A
a
maximum diffraction efficiency of 0.15% was observed for
an applied field of 75 V ␮mϪ1, which is relatively small
compared to the diffraction efficiencies observed from
samples that are otherwise similar except for the type of
sensitizer employed. For instance, an identical PR composite
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J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Grating formation rate in polymer with quantum dots
7339
FIG. 6. Holographic index contrast as a function of applied field. The fit to
Eq. ͑7͒ is also shown.
FIG. 7. First-order diffraction efficiency transients observed for a range of
applied fields.
⌫
l
␩
ϭexp
ͩ
Ϫ
sin ⌽
ͪ
used to find a theoretical fit to the experimental data, and this
is shown in Fig. 6. The geometry factor kgeom was calculated
using the method described in Ref. 16 and the value of S
2
⌫
l
⌫l
ͫ
cosh
ͩ
Ϫ
sin ⌽
ͪ
Ϫcos
ͩ
cos ⌽
ͪ
ͬ
2 2
Ϫ7
2
Ϫ2
2
2
⌫ l
ϭ6.8ϫ10 ␮m V determined from TE was used in the
fit, as was a value of refractive index for the polymer of n
ϭ1.7, determined by a total internal reflection measurement.
Hence, the value of the saturation field was the only free
parameter in the fit and it was thus determined to be Eq
ϫ
Ϸ
,
͑6͒
1
ϩexp͑Ϫ⌫l sin ⌽͒
16
where l is the effective interaction length and ⌽ is the phase
difference between the index grating and intensity modula-
tion pattern; the effective interaction length l incorporates the
effect of the obliquity of the writing beams to the sample
Ϫ1
ϭ4.6 V ␮m . This value is small compared to those found
for similar materials sensitized by other photogenerating spe-
2
2
normal and is given by l ϭt /(cos ␪ cos ␪ ), where ␪ and
1
2
1
cies under similar experimental conditions, for instance, es-
␪2
are the internal angles between the two beams and the
normal and t is the sample thickness. The gain coefficient,
ϭ2k⌬ntot cos(␪ Ϫ␪ ), depends on the wave number k for
Ϫ1
timates of E ϳ70–80 V ␮m have been reported for TNF-
sensitized composites.
q
1
2
1
9,24
A small saturation field is
⌫
2
1
consistent with the low diffraction efficiencies observed.
This reduced saturation field can be attributed to a small
the probe beam and the internal angle between the beams as
well as the total index contrast.12 The approximate form of
Ϫ
population density of ionized sensitizers, N ͓see Eq. ͑4͔͒.
x
Eq. ͑6͒ is valid for small index modulations such that e
The total sensitizer concentration N used in this material is
2
2
Ϸ1, cos(x)Ϸ1Ϫx /2 and cosh(x)Ϸ1ϩx /2, and is applicable
in the present case.
comparable to that used in other composites and so the frac-
Ϫ
tional ionization of the sensitizers, N /N must be relatively
Using the approximate form of Eq. ͑6͒, the total index
modulation as a function of field was calculated from the
measured diffraction efficiencies and is shown in Fig. 6.
Since in the low space-charge field regime Eq affects the
Ϫ
small for N to be reduced. „Mathematically, almost com-
Ϫ
plete dot ionization, i.e., N ϷN, would also result in a small
E value ͓see Eq. ͑4͔͒ but such a situation is unlikely in a
q
nonpolar polymer environment.…
magnitude of E and therefore ⌬n and ⌬n , the data pre-
1
1
tot
b. Dynamic results. The growth in diffraction efficiency
initiated by unblocking of one of the two writing beams, thus
forming patterned illumination, was recorded for a range of
applied fields. Some examples of these transients are shown
in Fig. 7. As can be seen from Fig. 7, although the magnitude
of the diffraction efficiency increases with field, the rate of
growth of ␩ is broadly unaffected by the field applied to the
sample. This is in contrast to most other polymer composites
reported thus far, which typically exhibit increases in the
diffraction efficiency growth rate of several hundred percent
over similar field ranges.
sented in Fig. 6 can be used to calculate the value of the
saturation field for this material. The total index contrast de-
pends on E not only via Eqs. ͑3͒ and ͑5͒ but also because
the phase difference ⌽ between the photorefractive grating
and the grating due to other effects requires that their respec-
q
2
3
tive index contrasts ⌬n and ⌬n be combined vectorially
1
0
as
2
1
2
0
⌬
n ϭ
tot
ͱ
⌬n ϩ⌬n ϩ2⌬n ⌬n cos͑␲Ϫ⌽͒,
͑7͒
͑8͒
1
0
where
One method of quantifying the rate of formation of a
photorefractive grating is to extract the space-charge field
rise time ␶sc from the index contrast transient, calculated
from the diffraction efficiency dynamic via Eq. ͑6͒. The
growing space-charge field, which according to the standard
ϪE0
⌽
ϭtanϪ1
ͫ
ͬ
.
2
E ͑1ϩp cos ␪͒
q
The above expression for ⌽ results from modifying the stan-
dard theory of photorefractivity to include field-dependent
photorefractivity. Therefore, Eqs. ͑3͒, ͑5͒, ͑7͒, and ͑8͒ were
2
4
25
theory of photorefractivity is exponential in form ͑with
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7340
J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Binks et al.
FIG. 8. An example of the fit to a holographic index contrast transient. In
Ϫ1
this case, the applied field was 50 V ␮m
.
Ϫ1
FIG. 9. Space-charge field rise time ␶sc as a function of applied field.
characteristic time ␶ ), drives the rotation of the chro-
2
sc
ne␮
EM
͑1ϩp cos ␪͒E ϩE ϩiE
q
D
0
Ϫ1
mophores and therefore the change in index. Due to the
amorphous nature of the polymer composite, the chro-
mophore rotational response is dispersive in character, which
results in a non-exponential form for the index contrast tran-
␶
ϭ
,
sc
ͫ
ͬ
⑀
E ϩE ϩiE
0
Eq
M
D
͑
10͒
where n is the mobile hole population density and ␮ is the
hole mobility. E ϭN ␥/K␮ and E ϭkTK/e are the mo-
2
6
sient. Recently, the space-charge field dynamic has been
convolved with the dispersive response of the chromophores
leading to an analytical form for the index contrast growth:
Ϫ
M
D
bility and diffusion fields, respectively, where ␥ is the recom-
bination rate constant. The diffusion field, however, is negli-
gible in most polymer materials; hence EDӶEq , EM , E0 .
␶1
␶2
ss
1
s
s
2
1
17
⌬
n1͑t͒ϭ⌬n
ͫ
1ϩ
ͩ
ͪ
t Ϫ
ͩ
ͪ
t
ͬ
ͭ
Furthermore, it has recently been shown that the assump-
␶2
Ϫ␶1
␶2Ϫ␶1
tion of Langevin recombination explains the field depen-
dence of ␶sc in high-Eq photorefractive polymers. For
Langevin recombination ␥ϭ␮e/⑀ and one of the conse-
quences for the photorefractive effect is that, in the limit of
N ӶN, the mobility and saturation fields are equivalent,
i.e., E ϭE . Since a low saturation field has been measured
Ϫ1
t
␥͑s ϩ1,Ϫt/␶ ͒
1
sc
s
1
Ϫexp
ͩ
Ϫ
ͪͩ1ϩ
͑Ϫ␶ ͒
sc
␶sc
͑␶ Ϫ␶ ͒
1
2
␥
͑s ϩ1,Ϫt/␶ ͒
Ϫ
2
sc
s
Ϫ
͑Ϫ␶sc͒ 2
ͪ
,
͑9͒
ͮ
͑
␶ Ϫ␶ ͒
1
2
q
M
for this material, the approximation E ӷEq can also be
0
where ␥(s ϩ1,Ϫt/␶) is the incomplete gamma function
limits 0 to Ϫt/␶ ) and ⌬n1 represents the steady-state
n
ss
made. Therefore, for this material, Eq. ͑10͒ can be reduced to
ϭn␥. Alternatively, this relation can be rewritten by sub-
stituting for n with the expression given by the standard
͑
sc
Ϫ1
sc
␶
value of the index contrast and is given by Eq. ͑5͒. Combin-
ing Eq. ͑9͒ with the index contrast transient recorded at zero
theory of photorefractivity
applied field, ⌬n (t), via Eq. ͑7͒ provides a complete de-
0
scription of the transients observed. This model was fitted to
each of the measured dynamics and the corresponding value
sI N
nϭ
,
͑11͒
Ϫ
␥
N
of ␶sc thus extracted. The fit utilized the values of D , and S
0
where I is the average light intensity and s is the photoion-
ization coefficient. Hence, the rate of space-charge field for-
mation becomes
found from the TE experiment and the value of E found
q
from the steady-state FWM results. Thus only one free pa-
rameter, ␶ , was involved in the fitting process. An example
sc
N
of the fit to the data obtained by this technique is shown in
Fig. 8. Figure 9 shows the values of the space-charge field
rise time found in this way as a function of applied field.
There is no clear trend with field. In comparison, similar
composites sensitized by C60 ͑Ref. 17͒ and CdSe/CdS-TOPO
Ϫ1
␶
ϭsI
.
͑12͒
sc
Ϫ
N
Most photorefractive polymer composites have been suc-
cessfully analyzed using the assumption that an ionized sen-
sitizer ͑or trap͒ density preexists inside the material and that
͑Ref. 10͒ exhibited fivefold and fourfold reductions in ␶sc ,
Ϫ
the effect of photogeneration on N is negligible. Therefore,
respectively, over comparable field ranges.
even though the photoionization coefficient in polymers is
field-dependent,1 a relatively large pre-existing concentra-
tion of ionized sensitizers, corresponding to a large satura-
tion field, ensures that N will be nearly constant with field.
Under these conditions, ␶sc will have the same field depen-
dence as s. However, for a much lower saturation field, those
ionized sensitizers produced by photogeneration will make a
significant contribution to the total and therefore N will
7,20
IV. DISCUSSION
Ϫ
Ϫ1
The observed field independence of the space-charge
Ϫ1
field formation rate ␶sc may be explained by the low satu-
ration field value for this material. The formation rate in
polymers is given by17
Ϫ
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J. Chem. Phys., Vol. 117, No. 15, 15 October 2002
Grating formation rate in polymer with quantum dots
7341
vary with field through the field dependence of s. The ob-
served field independence of the space-charge formation rate
plausibly indicates that there is, at least over the field range
studied and to the experimental accuracy, a linear relation-
a potential barrier in the dark to the recombination of a hole
trapped in a compensator site and an ionized dot.
1
Ϫ
S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett.
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6
6, 1846 ͑1990͒.
Why should the ionized fraction of sensitizers be re-
duced in this case, as compared to the fraction for other
sensitizers placed in similar composites and examined under
the same experimental conditions? More particularly, why
should the quantum dots described in Ref. 10, which differ
only in that they are surrounded by a CdS shell, exhibit a
much higher ionized fraction in an identical environment and
under the same conditions? In a photorefractive polymer in
the dark, the sensitizer anions are stabilized by compensator
sites that immobilize the corresponding holes. These com-
pensator sites are a feature of an amorphous polymer mate-
rial such as PVK and constitute a set of traps with a range of
depths. It seems that the CdS shell is acting to reduce the
likelihood of the sensitizer anion recombining with the
trapped hole. The bulk band gap of CdS ͑2.42 eV͒ is greater
than that of CdSe ͑1.73 eV͒ and so the CdS shell can plau-
sibly act as potential barrier to recombination for a greater
number of the holes in compensator sites. A shell material of
higher conduction band energy when in thermal equilibrium
with the core of the dot may lead to an increase in the ion-
ized sensitizer concentration. The consequent increase in the
saturation field can be expected to result in enhanced photo-
refractive performance.
2
3
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1
1
1
6
7
8
V. SUMMARY AND CONCLUSIONS
19
20
A photorefractive polymer composite sensitized by CdSe
quantum dots has been fully characterized for the first time.
In contrast to most other photorefractive polymers reported,
the hologram formation rate is observed to be independent of
applied field. This result is explained by the low saturation
field calculated for this material.
This low value of saturation field is attributed to a re-
duced concentration of negatively ionized nanoparticles.
Comparison with a similar material sensitized with CdSe/
CdS core/shell quantum dots suggests that the CdS shell acts
2
1
2
2
2
2
3
4
2
2
5
6
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1