Enhancement of the Photorefractive Response Time in a Polymeric

Kukhtarev, N. V.; Markov, V. B.; Odulov, S. G.; Soskin, M. S.; Vinetskii, V. L. Ferroelectrics 1979, 22, 949. [Crossref], [CAS]. (27) . Holographic st...
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J. Phys. Chem. C 2007, 111, 1904-1911

Enhancement of the Photorefractive Response Time in a Polymeric Composite Photosensitized with CdTe Nanoparticles Jeffrey G. Winiarz* Nanophotonic Materials Research Group, Department of Chemistry, UniVersity of MissourisRolla, Rolla, Missouri 65409 ReceiVed: September 19, 2006; In Final Form: NoVember 20, 2006

Because of their enhanced spectral response, photorefractive polymeric composites photosensitized with semiconductor nanocrystals are emerging as an important class of materials. Despite their promising characteristics, however, several deficiencies persist. Relatively low diffraction efficiencies and slow response times have prevented these materials from reaching their full potential. In this work we demonstrate the ability to enhance a composite’s response time by nearly 1 order of magnitude without significantly ceding diffraction efficiency through judicious selection of semiconductor material. By replacing the commonly employed cadmium selenide nanocrystals with those of cadmium telluride, the response time was enhanced from 1.05 s to 171 ms. Moreover, through careful control of the photorefractive device’s absorption characteristics, this augmentation in response time is accompanied by a relatively small decrease in internal diffraction efficiency from 24% to 20%.

Introduction In consequence of their large optical nonlinearities, low permittivity, and low cost, polymeric photorefractive (PR) materials are potentially useful in a variety of real-time optical information processing applications including beam cleanup and amplification, dynamic interferometry, phase conjugation, and pattern recognition.1-5 Consequently, much research has been directed toward the advancement of this class of materials, resulting in significant progress including millisecond response times and nearly 100% diffraction efficiencies.3 Despite these important advances, certain problems have plagued all-organic PR polymer composites, perhaps the most critical of which relates to their spectral response. It was envisaged that, by doping these materials with various organic dyes for the purpose of photosensitization, their spectral response could be tuned to suit a specified application. This speculation was met, however, with only limited success. Few dyes are known to exhibit sufficient charge generation quantum efficiency to be viable for practical application. Moreover, none have been reported which can be used to photosensitize PR polymeric composites at the IR wavelengths used for commercial and military applications, specifically 1.3 and 1.5 µm. With the advent of nanotechnology it is now possible to photosensitize PR and photoconductive polymer composites by doping them with semiconductor nanocrystals, also known as quantum dots or Q-dots.6-16 This approach has several advantages, the most attractive is the ease with which the spectral character of Q-dots, and therefore the final PR composite, are modified.8-11 The ability to finely control the optical and electrical properties associated with the nanocrystalline material stems from the inverse relationship between the optical band gap and the physical dimension of the nanocrystal. As a result of the compelling prospects afforded through this innovative approach, several precedents have been established employing semiconductor nanocrystals as the photosensitizer in PR poly* E-mail: [email protected].

meric composites. Most notably, PR behavior has been demonstrated at 1.31 and 1.55 µm for the first time in a polymeric composite using this approach.10,14-16 While this new class of inorganic-organic hybrid polymeric composites shows enormous promise, the technology is still in its infancy, and much work is needed to exploit its full potential. Diffraction efficiencies, operational voltages, and response times associated with PR inorganic-organic composites do not equal that of their all-organic counterparts and must be improved to meet the demands of anticipated applications. In order to address these issues, the fundamental mechanisms involved in photocharge generation and charge transport must be elucidated and creative approaches devised allowing for the PR performance to be optimized for a given application. Such optimization can be accomplished through variation of the constituents’ stoichiometric ratio and prudent choice of the nanocrystalline photosensitizer’s properties. Recently, advances in the syntheses of semiconductor nanocrystals have significantly improved control over nanocrystal morphology, composition, and surface characteristics. However, with few exceptions,17-19 studies involving the photosensitization of PR polymeric composites with Q-dots have employed one of four semiconductor materials: CdSe, CdS, PbSe, and PbS. In this paper we characterize a PR polymeric composite photosensitized with Q-dots composed of CdTe (QCdTe) at strategically selected concentrations and compare its performance to that of a similar composite photosensitized with Q-dots composed of CdSe (QCdSe). The composites also contained poly(N-vinylcarbazole) (PVK) due to its well-characterized hole transporting capability. The glass transition temperature of the composite was lowered to below ambient temperature through the inclusion of N-ethylcarbazole (ECZ), and electrooptic activity was imparted through the addition of 2-[4-bis(2methoxyethyl)amino]benzylidenemalononitrile (AODCST).20 The Q-dots are synthesized through a well-established hightemperature approach utilizing trioctylphosphine oxide (TOPO) and triocylphosphine (TOP) as the reaction solvents and capping

10.1021/jp066140y CCC: $37.00 © 2007 American Chemical Society Published on Web 01/12/2007

Polymeric Composite Photosensitized with CdTe

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groups.21,22 In order to improve the solubility of the nanocrystals in the polymeric matrix, the TOPO surface ligands were exchanged for pyridine. These procedures will be detailed in the following section. To characterize the performance of the materials, degenerate four-wave mixing (DFWM), asymmetric two-beam coupling (TBC), visible absorption spectroscopy, and conductivity experiments were employed, the results and implications of which will be presented. In addition to the insights gained into the fundamental mechanisms relevant to this class of materials, an enhancement in the PR response time of nearly 1 order of magnitude is realized. It is anticipated that the enhancement associated with this approach will be applicable to other systems. Experimental Section All chemicals were obtained from Aldrich and used as received unless otherwise noted. The nanocrystals used in this study were synthesized based on a procedure described in the literature.22 Synthesis of QCdSe. Briefly, two solutions were prepared, the first by adding 0.05 g of Se to 2 mL of TOP using standard airless techniques. This solution was degassed under vacuum and mechanically stirred for 1 h and then stored under nitrogen until needed. The second solution was prepared by charging a three-neck round-bottom flask with 3.77 g of TOPO, 0.22 g of tetradecylphosophonic acid (Polycarbon Industries), and 0.05 g of CdO. This mixture was heated to 140 °C and degassed under vacuum for 1 h. After this time, nitrogen was introduced into the reaction flask, and the temperature was raised to 320 °C. When the CdO was fully dissolved, the temperature was lowered to 265 °C, and the Se/TOP solution was injected into the reaction flask, resulting in a temperature drop of ∼15 °C. For the remainder of the reaction the temperature was maintained at 270-280 °C. The progress of the reaction was monitored by taking aliquots of the reaction mixture at various time intervals. After 135 min the absorption associated with the first excitonic peak of the QCdSe was observed to coincide with 633 nm, and the heating mantle was removed. When the reaction temperature reached 60 °C, 10 mL of methanol was injected to prevent solidification of the mixture. The reaction mixture was centrifuged to collect the product, which was then redispersed in methanol, centrifuged, and collected again. This purification procedure was repeated several times to remove any unreacted TOP, TOPO, or TDPA. To remove unreacted CdO and Se, the product was dispersed in toluene and centrifuged, and the supernatant was collected. Synthesis of QCdTe. The procedure was similar to that used in the synthesis of the QCdSe, except 0.08 g of Te was substituted for the Se. Also, after reaching 320 °C, the CdO/ TOPO/TDPA solution was allowed to cool to 240 °C, and the TOP/Te solution was injected. Following the initial drop in temperature, the reaction mixture was subsequently maintained at 240-245 °C. Under these conditions, the first excitonic peak of the QCdTe was observed to coincide with 633 nm after 33 min. At this time the heat was removed, and the QCdTe was purified and isolated using the same manipulations described for QCdSe. Ligand Exchange. The TOPO-capped nanocrystals dispersed in toluene were precipitated through the addition of methanol and centrifuged. The supernatant was discarded, and the wet nanocrystals were dispersed in 5 mL of pyridine. This solution was mechanically stirred until it became optically clear. At this time the nanocrystals were precipitated through the addition of

Figure 1. Visible absorption spectra of QCdSe (dashed line) and QCdTe (solid line) in pyridine.

Figure 2. Visible absorption spectra of the PR devices used in this investigation: CdSe-1% (dotted line), CdTe-1% (solid line), CdTe-A (dashed line), and CdTe-Mol (dash-dotted line).

25 mL of heptane, collected, and redispersed in pyridine. This solution was filtered to remove any undissolved solids. The QCdSe or QCdTe in pyridine was then diluted with additional pyridine so as to achieve a concentration of 1.07 mg/mL. To realize this concentration, the absorption spectrum of the asprepared solution was ascertained. From the position and intensity of the first exciton peak (λ ) 633 nm) it was possible to determine the diameter of the nanocrystals as well as their concentration in mol/L.23 Then, assuming the density of the nanocrystals to be same as that in bulk, the concentrations in g/L were calculated. From here, the dilution was a trivial exercise. The absorption spectra of the QCdSe and QCdTe in pyridine are presented in Figure 1. PR Composite Samples. AODCST was synthesized in our lab according to a procedure in the literature.20 For the composite samples, 0.25 g of PVK (secondary standard), 0.075 g of ECZ, and 0.175 g of AODCST were dissolved in 14 g of toluene: tetrahydrofuran (13:1 by weight) and filtered to remove any undissolved solids. Subsequently, 3.10 g of this solution (0.107 g of dissolved solids) was introduced into each of four separate vials. DeVice 1 (CdSe-1%). The objective at this point was to fabricate a device containing ∼1 wt % of QCdSe. Thus, 1 mL of the 1.07 mg/mL QCdSe in pyridine was added to the first of the four prepared vials so as to introduce 1.07 mg of QCdSe.

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Winiarz

Once added, this mixture afforded a final composition of PVK: ECZ:AODCST:QCdSe with a mass ratio of 49.5:14.9:34.7:0.99. After thorough mixing, the solvent was removed by storing the composite in a vacuum oven at 50 °C for 24 h. The solid residue was then recovered, placed between two pieces of glass coated with indium tin oxide, and heated above its melting temperature on a hot plate. The sample was then mechanically pressed, forming the familiar “sandwich” geometry using glass spacers to control the thickness of the device at 100 µm. The visible absorption spectrum of the device is depicted in Figure 2, and it was determined that R ) 17.3 cm-1 at λ ) 633 nm. On the basis of this information in conjunction with the literature value for the extinction coefficient, ,23 for QCdSe possessing their first absorption peak at 633 nm, it was possible to determine the concentration of the QCdSe in the composite using the Beer-Lambert law

A ) CL

(1)

where C is the molar concentration (mol/cm3) of the nanocrystals and L is the path length (L ) 0.01 cm). It was determined that the nanocrystal concentration in the final PR composite device was C ) 2.07 × 10-8 mol/cm3. These properties as well as several others are summarized in Table 1. DeVice 2 (CdTe-1%). To produce a composite containing the same weight percentage of sensitizing nanocrystals as that in the CdSe-1% device (but replacing the QCdSe with QCdTe), 1 mL of the 1.07 mg/mL QCdTe in pyridine was added to the second of the four prepared vials consequently introducing 1.07 mg of QCdTe. This produced a device with a mass ratio given as PVK:ECZ:AODCST:QCdTe ) 49.5:14.9:34.7: 0.99. The final device was fabricated and characterized as previously described, and the relevant parameters are given in Table 1. DeVice 3 (CdTe-A). The objective was to produce a PR device photosensitized with QCdTe which would possess a device absorption at λ ) 633 nm equal to that of the CdSe-1% device. Since the ratio of the absorptions of the respective 1.07 mg/mL nanocrystals in pyridine solution is given as

RQCdSe/pyridine 1.83 cm-1 ) ) 1.14 RQCdTe/pyridine 1.60 cm-1 1.14 mL of the 1.07 mg/mL QCdTe/pyridine solution (containing 1.24 mg of QCdTe) was added to the third vial. The device was then prepared as previously described, resulting in a final device absorption of 17.5 cm-1 and a PVK:ECZ:AODCST: QCdTe mass ratio denoted by 49.4:14.8:34.6:1.15. Other relevant parameters are given in Table 1. DeVice 4 (CdTe-Mol). For this sample, the intention was to fabricate a device that possessed the same number of moles of nanocrystals (QCdTe in this device) per unit volume as that of QCdSe-1% device. This was accomplished by ensuring that the ratio of the device absorption at 633 nm was equal to the ratio

Figure 3. Electric field dependence of the photoconductivities, σp (solid symbols), and dark conductivities, σd (open symbols), of CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

of the respective photosensitizer extinction coefficients. That is to say

QCdTe 1.92 × 10-5 L/(cm mol) RCdTe-Mol ) ≈ ) QCdSe 8.36 × 10-5 L/(cm mol) RCdSe-1% 0.0404 cm-1 ) 0.234 0.173 cm-1 Hence, 0.234 mL of the 1.07 mg/mL QCdTe/pyridine solution (containing 0.250 mg of QCdTe) was added to the final vial. The device was then prepared as previously described resulting in a PVK:ECZ:AODCST:QCdTe mass ratio designated as 49.9: 15.0:34.9:0.233. See Table 1 for additional parameters. All the devices used in this investigation have not shown any signs of phase separation over the course of 7 months. In addition to these devices, a device was fabricated that did not contain any photosensitizer, with a composition represented as PVK:ECZ:AODCST and possessing a mass ratio designated as 50.0:15.0:35.0, herein referred to as the control device. Photorefractive Characterizations. The photorefractive properties of the composite devices were studied via TBC and DFWM techniques using a standard tilted geometry. Holographic gratings were written through the intersection of two coherent beams generated by a helium-neon (HeNe) laser operating at 633 nm with incident angles of θ1 ) 45° and θ2 ) 75° (in air) relative to the sample normal. In the TBC experiments, both writing beams were p-polarized with intensities of I1 ≈ 0.05 mW and I2 ≈ 8 mW. The external bias was applied such that I1 would experience gain at the expense of I2. Asymmetric energy transfer was observed by monitoring the intensities of the writing beams after the PR device with a photodiode. In the DFWM experiment the writing beams were s-polarized with intensities of I1 ≈ 3 mW and I2 ≈ 9 mW. In addition, a p-polarized probe beam propagated in a direction opposite to I1 with an intensity of Ip ≈ 2 × 10-3 mW. Through the use of a polarizing beam splitter placed in the path of I2 in conjunction with a photodiode, the diffracted portion of Ip, also referred to as the signal beam, Is, could be quantified. All beams had diameters of 0.98 mm.

TABLE 1: Relevant Properties of the Devices Used in This Study device

device abs at λ ) 633 nm (cm-1)

device transmission at λ ) 633 nm (%)

particle diameter, d (nm)23

particle concn (mol/cm3)

particle concn (mg/cm3)

particle extinction coeff,  (L/(cm mol))23

CdSe-1% CdTe-1%t CdT-A CdTe-#

17.3 15.2 17.5 4.04

67.1 70.5 66.8 91.1

6.44 4.04 4.04 4.04

2.07 × 10-8 7.93 × 10-8 9.01 × 10-8 2.10 × 10-8

10.1 10.2 11.7 2.70

8.36 × 105 1.92 × 105 1.92 × 105 1.92 × 105

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Photoconductivity, σp, characterizations were made using a dc-photocurrent technique with a Keithley electrometer used to measure the current passing through the sample as a function of applied bias. The beam intensity for all σp characterizations was ∼10 mW. The UV-vis absorption spectra were recorded on a Beckman DU 640B spectrophotometer. Results and Discussion The goal of this study was to improve the PR characteristics of a polymeric composite photosensitized with semiconductor nanocrystals by replacing QCdSe with QCdTe. Until now, QCdSe and QCdS were most commonly used for investigations at visible wavelengths with the performance of QCdSe exceeding that of QCdS. Even so, care must be exercised when attempting to draw a direct comparison because the studies were conducted at different wavelengths with QCdSe being used at 633 nm and QCdS being used at shorter wavelengths such as 488 and 514 nm.8,9,13 QCdSe and QCdS were used in these preliminary investigations because methods for their syntheses were most advanced; however, recent progress in synthetic techniques has allowed for the fabrication of nanocrystals composed of other materials such as QCdTe,22 greatly expanding the types of nanocrystals available for photosensitizing PR polymeric composites. In view of results reported in previous studies, we speculated that replacing QCdSe with QCdTe in a PR polymeric composite would improve its overall PR performance.24,25 In these earlier investigations, it was revealed that the presence of semiconductor nanocrystals in a photoconductive composite (PVK:QCdS in this case) improved the mobility, µ, of charge carriers relative to that associated with the pristine polymer. The enhancement of the charge-transport process then results in an increase in the σp as dictated by the equation

σp ) peµ

(2)

where p is the density of mobile charge carriers (holes) and e is the fundamental electric charge. Moreover, it was demonstrated that this enhancement in µ scaled with the nanocrystal concentration. Thus, all other things being equal, the inclusion of an additional mass of nanocrystals results in an increase in σp and, because σp is an integral component of the PR effect, an enhanced PR performance. On the basis of this conjecture, it was anticipated that the use of QCdTe as an alternative to QCdSe would improve the performance of the PR composite. This is so because a larger mass of QCdTe would be required to achieve the same absorption in a given PR composite due to the lower extinction coefficient possessed by a single QCdTe nanocrystal relative to that of a single QCdSe nanocrystal (both with their first excitonic peak at λ ) 633 nm; see Table 1).23 This advantage is offset, however, by the smaller size of the nanocrystal. In order to quantify the increase in loading mass associated with this approach, the ratio of the extinction coefficients must by multiplied by the ratio of the mass of an individual nanocrystal. This can be expressed as

QCdSe mQCdTe ) QCdTe mQCdSe 8.36 × 105 L/(cm mol) 2.13 × 10-19 g/particle 1.92 × 105 L/(cm mol) 8.12 × 10-19 g/particle

) 1.14

indicating that in order to achieve the same absorption in a device photosensitized with QCdTe instead of QCdSe, one would need to use a factor of 1.14 more mass of QCdTe to

impart the same level of absorption. Thus, by replacing QCdSe with QCdTe, it is possible to increase the overall nanocrystal content without realizing the negative affects associated with increasing the absorption of the device. A second anticipated advantage associated with replacing QCdSe with QCdTe comes directly from the smaller size associated with a QCdTe nanocrystal, which implies that a given mass of QCdTe has a higher surface area than an identical mass of QCdSe (assuming both have their first absorption peak at λ ) 633 nm and taking into consideration their respective densities). Using the method presented in the literature to determine the size of each respective nanocrystal,23 and assuming bulk densities, the ratio of surface areas per gram, m2/g, can be calculated as

(m2/g)QCdTe (m2/g)QCdSe

)

2.4 × 1020 m2/g ) 1.5 1.6 × 1020 m2/g

This increase in surface area translates into a greater probability of a hole encountering the surface of a nanocrystal as it moves through the composite material. This in turn may increase the probability of a hole undergoing the process of tunneling into the volume of a nanocrystal, thus enhancing its macroscopic mobility. Ideally, one would like to directly characterize the µ associated with each PR composite. Charge carrier mobilities in polymeric thin films are typically determined using the “timeof-flight” (TOF) technique. TOF measurements are conducted by injecting a thin sheet of charge carriers into the material and monitoring with an oscilloscope the current flow in the external circuit as the sheet of charge carrier transports across the material under the influence of an applied electric field. Because of the high concentration of dipolar electrooptic chromophores in PR composites, however, the thin sheet of charge carriers becomes too dispersive as it traverses the material, and therefore it has not been possible to directly measure the charge-carrier mobility in most PR polymeric composites using this technique. This problem is also often encountered in polymer/nanocrystal composites. In this study, an attempt was made to measure the charge-carrier mobility in QCdSe:PVK and QCdTe:PVK thin films; however, under the current experimental conditions the oscilloscope traces revealed that the charge transport was too dispersive to obtain meaningful data. In order to characterize the actual advantage associated with substituting QCdTe for QCdSe in a PR composite, it is necessary to fabricate a set of devices possessing equal concentrations of the photosensitizer. In general, however, there are three parameters which describe the concentration of nanocrystalline photosensitizer in a PR composite: weight percent, magnitude of absorption imparted to a device as a result of photosensitization, and moles of particles per unit volume. It was therefore decided that three devices photosensitized with QCdTe would be fabricated and compared to a single device photosensitized with QCdSe. For each of these QCdTe-containing devices, one of the aforementioned parameters was held constant relative to the QCdSe-photosensitized device. The first device was photosensitized with ∼1 wt % QCdSe and referred to as CdSe-1%. This concentration was chosen because it is representative of the concentrations most commonly used in similar studies cited in the literature. The weight was calculated using a method based on the absorption associated with the nanocrystals as described in the Experimental Section and detailed in the literature.23 The second device contained the same weight percentage of photosensitizer; however, in this

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Figure 4. Electric field dependence of the ratio of photoconductivity to dark conductivity, σp/σd, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

Winiarz

Figure 6. Electric field dependence of the internal diffraction efficiencies, ηint, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are the best fit to the theory (see text).

633 nm and are presented in Figure 3. These data were calculated using the equation

σ)

Figure 5. Electric field dependence of the quantum efficiencies, Φ, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

case the QCdSe was replaced with QCdTe. This device is designated as CdTe-1%. The concentration was determined in a manner identical to that used for the CdSe-1% device. The degree of error associated with this approach can be significant; however, measuring the absorption of various solutions and subsequently evaporating the solvent and weighing the solid residue, it was determined that the QCdTe in this device was within ∼10 wt % of that in the CdSe-1% device. The third device, photosensitized with QCdTe, was fabricated such that its absorption was equal to that of the CdSe-1% device at λ ) 633 nm. On the basis of the respective absorption coefficients, and assuming bulk densities, the third device contained 1.14 times as much photosensitizer by mass. Herein, this device is referred to as CdTe-A. The fourth and final device, also photosensitized with QCdTe nanocrystals, contained the same number of nanocrystals per unit volume as the QCdSe1% device. This device is referred to as CdTe-Mol. The absorption spectra of the four devices are presented in Figure 2. In order to determine whether the anticipated enhancement in the QCdTe-photosensitized devices was realized, σp and the dark conductivities, σd, of the devices were measured at λ )

J E

(3)

where J is the current density which is determined experimentally and E is the magnitude of the externally applied electric field. Evident in the figure, the σp of the CdTe-1% and the CdTe-A devices exceed that of the CdSe-1% device. Unfortunately, the QCdTe-photosensitized devices also exhibited a sharp increase in σd at relatively higher E. The origin of this behavior is not currently known; however, this trend was not as significant for the QCdSe-photosensitized device. As depicted in Figure 4, this undesirable operation resulted in a maximum in the σp/ σd ratio for the QCdTe-photosensitized devices at E ) 30-40 V/µm, with a subsequent decrease in this figure-of-merit above these voltages. The implications of this functioning with regard to the overall PR properties will be discussed as the relevant data are presented. It is also noted that, for the sensitivity associated with our experiment, the control device did not show any photoconductivity at 633 nm. From the σp data it is possible to determine the chargegeneration quantum efficiencies, Φ, using the equation

Φ)

Ncc hc ) Jp Nph λeRd

( )

(4)

where Ncc is the number of charge carriers generated per unit volume, Nph is the number of photons absorbed per unit volume, h is Planck’s constant, c is the speed of light, λ is the wavelength of the incident radiation, e is the fundamental unit charge, R is the absorption coefficient of the device, and d is the device thickness. These data are presented as a function of E in Figure 5. As one might anticipate, the Φ associated with the QCdTephotosensitized devices were very similar and indicate the absence of nanocrystal-nanocrystal interaction for the concentrations studied. Also apparent in the figure is that the Φ of the QCdSe-photosensitized device is slightly reduced relative to the QCdTe-photosensitized devices. These data reveal an unanticipated advantage associated with substituting QCdTe for QCdSe in a PR device. Specifically, the number of free charge carriers created within a QCdTe-photosensitized composite exceeds that of a QCdSe-photosensitized composite. This implies that for each exciton created within a QCdTe nanocrystal, as compared

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Figure 7. Electric field dependence of the external diffraction efficiencies, ηext, for CdSe-1% (squares), CdTe-A (triangles), CdTe1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are the best fit to the theory (see text).

Figure 8. Temporal evolution of the diffracted probe beam, Is, in the DFWM experiment for the CdTe-A device at E ) 50 V/µm. Only every tenth datum is shown for clarity. The solid line is a fit to a weighted biexponential function (see text).

to that of a QCdSe nanocrystal, there exists a greater probability of the hole eventually migrating to the PVK matrix and ultimately contributing to the overall charge-carrier density. This phenomenon may be explained by the larger surface to volume ratio of the relatively smaller QCdTe nanocrystals, which may in turn result in a greater probability of the photogenerated hole being found near the nanocrystal surface and consequently its subsequent oxidation of a nearby PVK molecule. The internal diffraction efficiencies, ηint, were measured experimentally and determined according to the equation

ηint )

Is Ip′

(5)

where Ip′ is the intensity of the probe beam after the device with no bias applied and Is is the intensity of the diffracted portion of Ip. These data are presented in Figure 6. The lines in the figure represent the best fit to the equation

η ) sin2(C∆n)

(6)

where ∆n is the change in refractive index and C is a constant dependent on the experimental geometry.26 Apparent in the figure, the QCdSe-1% device shows the highest ηint with a maximum of 24.0%. The superior performance exhibited by the QCdSe-photosensitized device can qualitatively be attributed to the higher σp/σd ratio associated with this device. This is so because the magnitude of the space-charge field, |ESC|, is correlated with the ratio σp/σd as dictated by the equation

[

|ESC| ) mEq

]

E02 + Ed2

E0 + (Ed + Eq) 2

1/2

2

1 1 + σd/σp

(7)

where m is the depth of modulation, E0 is the is the component of the electric field which coincides with the grating vector, Eq is the trap-density-limited space-charge field, and Ed is the diffusion field.27 It is also noted that while the σp/σd achieves a maximum for all devices, the ∆n does not. This is attributed the dependence of ESC upon the externally applied electric field in addition to σp/σd as well as the fact that the effective trap density, included in Eq, may too depend upon the externally applied electric field. This hypothesis is the subject of future study.

Figure 9. Electric field dependence of the fast time constants, τ1, of the grating growth for CdSe-1% (squares), CdTe-A (triangles), CdTe1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

Despite the superior performance exhibited by the QCdSephotosensitized device, it is not significantly higher than the ηint of the CdTe-A device, which demonstrated an internal diffraction efficiency of 19.8% and was the highest diffraction efficiency exhibited by any of the QCdTe-photosensitized devices. Also apparent in the figure is that the CdSe-1% device displayed overmodulation at ∼60 V/µm. For this reason this was the maximum voltage used in subsequent characterizations. While the internal diffraction efficiencies are of significant fundamental importance, it is the external diffraction efficiencies, ηext, which are of practical significance. The ηext associated with the devices are shown as a function of E in Figure 7. Here ηext, accounting for reflections, was determined according to the equation

ηext )

Is Ip

(8)

where Ip is the intensity of the probe beam before the device and Is is the intensity of the diffracted portion of the probe beam after the device. The lines in the figure represent the best fit of the data to eq 6. As depicted in Figure 7, the CdSe-1% device exhibited the highest figure-of-merit with a maximum ηext of 15.3%; however, the CdTe-A device showed a maximum ηext

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Figure 10. Electric field dependence of the TBC gain coefficient, Γ, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

Figure 11. Electric field dependence of the change in refractive index, ∆np, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

of 12.5%, implying that for most practical applications there does not exist a significant difference between devices photosensitized by QCdTe and similar devices photosensitized with a QCdSe device. Time-resolved DFWM techniques were used in the quantification of the holographic grating growth rates, τ. For this experiment, an external electric field was applied to the device while blocking one of the writing beams. The device was permitted to settle for ∼30 s, and the writing beam was unblocked. The diffracted portion of the probe beam was then recorded as a function of time. An example of the data obtained in this experiment is presented in Figure 8. The solid line in the figure represents the best fit to a biexponential equation of the form

η(t) ) sin2{A[1 - m exp(-t/τ1) - (1 - m) exp(-t/τ2)]} (9) where A is a fitting constant, m is a weighting ratio, t is time, τ1 is the fast time constant, and τ2 is the slow time constant. The fast time constants, τ1, are presented as a function of E in Figure 9. Evident in the figure, the response times associated with CdTe-A and the CdTe-1% devices appreciably exceed that of the CdSe-1% device. In the case of the CdTe-A device this enhancement is nearly 1 order of magnitude, decreasing from 1.05 s for the CdSe-1% device to 171 ms for the CdTe-A device. This enhancement in response time is supported by the σp data.

Winiarz

Figure 12. Electric field dependence of the phase shift between the illumination pattern and the modulation of the refractive index, φ, for CdSe-1% (squares), CdTe-A (triangles), CdTe-1% (diamonds), and CdTe-Mol (circles) at λ ) 633 nm. The lines are guides for the eye.

Figure 13. Γ - R for CdSe-1% (E ) 60 V/µm), CdTe-A (E ) 30 V/µm), CdTe-1% (E ) 30 V/µm), and CdTe-Mol (E ) 40 V/µm) at λ ) 633 nm.

Unlike the DFWM efficiency, η, which is dependent upon the ratio σp/σd, the response time, τ, is inversely proportional to σp, as given by the equation

τ)

 σp

(10)

where  is the dielectric constant of the material.28 Therefore, despite a slightly diminished performance with regard to diffraction efficiency, the QCdTe-photosensitized devices, CdTe-A and the CdTe-1%, nevertheless exhibit an enhanced response time relative to the QCdSe-photosensitized device. A distinct characteristic feature of the PR effect is that the refractive index grating created in the medium is spatially shifted with respect to the light intensity pattern of the writing beams.26 As a result, an asymmetric exchange of energy occurs between beams interfering in a PR medium. The PR nature of the gratings created within the composites used in this study was confirmed using conventional TBC experiments. The TBC gain coefficient, Γ, is given in terms of the experimentally measured quantities γ0 and β as

1 Γ ) [ln(γ0β) - ln(β + 1 - γ0)] L

(11)

Polymeric Composite Photosensitized with CdTe

J. Phys. Chem. C, Vol. 111, No. 5, 2007 1911

where L is the path length of the beam experiencing gain inside the sample, β is the ratio of the writing beam intensities before the sample, and γ0 is the ratio of the intensity of the beam experiencing gain with and without the pump beam. The TBC gain coefficients, Γ, as a function of E are presented in Figure 10. Inspection of the data reveals that the usual dependency upon E2 is not observed. It was initially believed that this atypical performance was due to beam-fanning; however, further experimentation confirmed that this was not the case. The similarities among the trends observed in the TBC gain coefficients, Γ, and that of the σp/σd ratio is palpable and may provide insight into the source of this occurrence. Confirmation of a correlation between these trends is outside the scope of this study but is the subject of future research. It is also noted that this anomalous trend is not apparent in the DFWM data; however, it is speculated that the trend associated with the σp/ σd ratio may manifest itself more strongly in the TBC phenomenon because TBC is dependent not only upon ∆n but also upon the magnitude of the phase shift between the illumination pattern and the modulation of the refractive index, φ. The change in refractive index with respect to p-polarized probe beam, ∆np, can be calculated using the equation29

[

ηint ) sin2

2πd∆np

λ(cos θ1 + cos θ2)

]

(12)

The results of this manipulation are presented in Figure 11. Using these data, it is possible to estimate the phase shifts, φ, according to the equation29

φ ) sin-1

Γλ (2π∆n )

(13)

which are plotted as a function of E in Figure 12. As shown, the φ associated with the CdSe-1% device remains relatively constant at all applied voltages; however, φ for the QCdTephotosensitized devices is relatively large at low applied voltages and decreases as higher voltages are attained. Therefore, while the DFWM may be adversely affected by the eventual decrease in the σp/σd ratio and its influence over ∆n, it is not sensitive to the φ and so is not unfavorably affected at higher voltages by the decrease in φ. TBC, on the other hand, is sensitive to ∆n as well as to φ and therefore is more severely affected at higher voltages where the diminution in both of these parameters is most exaggerated. For practical applications, the optical amplification, Γ, should exceed the absorption, R, for a given device. For all devices involved in this study Γ does exceed R. This is depicted graphically in Figure 13 where the maximum Γ measured for each device and their respective absorptions are shown. In this instance the CdTe-Mol device exhibits the highest figure-ofmerit, with Γ - R ) 23 cm-1 at 40 V/µm. This is due in large part to the relatively small absorption of the device. Of almost equal performance in this regard is that of the CdSe-1% device with a figure-of-merit of Γ - R ) 22 cm-1 at 60 V/µm. Conclusion. In this study it has been established that by replacing QCdSe with QCdTe as the photosensitizer in a polymeric PR composite it is possible to improve several

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