Photoinduced Film Formation of Colloidal CdSe Quantum Dots

Oct 10, 2008 - incubation period. The deposition rate increased linearly with increasing laser intensity and QD concentration. Addition of TOPO molecu...
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J. Phys. Chem. C 2008, 112, 17109–17114

17109

Photoinduced Film Formation of Colloidal CdSe Quantum Dots Kosuke Wada,† Susumu Inasawa,* Atsushi Komoto,‡ Takafumi Uematsu,† and Yukio Yamaguchi Department of Chemical System Engineering, Graduate School of Engineering, The UniVersity of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed: June 19, 2008; ReVised Manuscript ReceiVed: August 18, 2008

Tri-n-octylphosphine oxide (TOPO)-capped colloidal cadmium selenide (CdSe) quantum dots (QDs) in octane formed a QD film under laser irradiation. The film was formed at a constant rate of deposition after an incubation period. The deposition rate increased linearly with increasing laser intensity and QD concentration. Addition of TOPO molecules into the suspension significantly retarded film formation. The TOPO molecules are thought to desorb from the QD surface under laser irradiation because well-capped QDs with TOPO molecules did not form a film. We propose that absorbed photons induce desorption of TOPO molecules from QDs and destabilized QDs are formed in the suspension. The formed unstable QDs attach to the substrate, resulting in the formation of a QD film. A model is proposed to analyze the kinetics of film formation. It consists of three steps: the diffusion of QDs from the bulk suspension, the photoinduced desorption reaction of TOPO molecules, and the mass transport of unstable QDs onto the substrate. Our model describes the experimental results well, and the photoreaction yield to form an unstable QD was on the order of 10-5. 1. Introduction Colloidal quantum dots (QDs) provide a model system in which unique physical/chemical properties under nanoscale confinement can be observed.1 Electron energy levels in cadmium selenide (CdSe),2 relaxation dynamics of excited electrons,3 blinking (photoluminescence intermittency),4,5 and photoinduced electron ejection from QDs (photoionization)6-8 show their unique properties under such confinement. Using these attractive properties, practical applications such as light-emitting diodes,9 photovoltaic cells,10 optical memories,11,12 and sensors13 have been proposed. In most applications, a patterned QD film on a substrate is required to obtain better performance. Droplet vaporization,14 electrophoretic deposition,15 the Langmuir-Blodgett (LB) technique,16 spin coating,17 and layer-by-layer assembly18 are widely used techniques for QD film formation. Using these techniques, one can easily obtain colloidal thin films. However, to obtain a patterned film, an initially patterned substrate is needed. Ink-jet printing,19 poly(dimethylsiloxane) (PDMS) stamping,20 and a conventional lithographic technique are typical approaches used to form patterned structures on a substrate. Although ink-jet printing is a fast and simple method for forming patterns, one of the challenges is the line width, which is generally larger than ca. 10 µm because of limitations on the ink-droplet diameter.21,22 The latter two techniques successfully realize patterned structures with high resolution, but many steps are required to obtain patterned substrates. Thus, establishing a new technique for obtaining a patterned QD film in a simple way is still of fundamental concern. The surface of each CdSe QD is covered with ligands to enable the QDs to be well dispersed in a solvent. Tri-noctylphosphine oxide (TOPO) and thiol ligands are commonly used ligands for organic solvents,23 whereas mercaptoundecanoic * To whom correspondence should be addressed. E-mail: inasawa@ chemsys.t.u-tokyo.ac.jp. † Present address: Kao Corporation, 1334 Minato Wakayama-shi, Wakayama, 640-8580 Japan. ‡ Present address: Canon Inc., 3-30-2 Shimomaruko, Ohta-ku, Tokyo, 146-8501 Japan.

acid (MUA) is used for water.24 QDs are unstable in suspension and easily form aggregates without these protective ligands on their surfaces.23,25 In ref 25, it was reported that photoirradiation causes the desorption of TOPO molecules from QDs, suggesting that destabilized QDs are formed only in the irradiated area. If a substrate were inserted into the suspension and the destabilized QDs could attach to the substrate, a QD film on the substrate under photoirradiation could be obtained. If destabilized QDs could be produced in the vicinity of the substrate by selective irradiation, a patterned QD film that reflects the irradiation pattern could be formed. If this expectation is true, then photoirradiation would be a new technique for one-step formation of QD films in a wet process. In this report, using the photoinduced destabilization of TOPO-capped CdSe QDs in suspension,25 we introduce photoinduced film formation of QDs on a glass substrate. Irradiating a continuum Ar+ laser onto the substrate surface in the suspension formed a QD film. The kinetics of film formation are discussed using a model that includes diffusion of QDs and a photoreaction to form destabilized QDs. 2. Experimental Section Synthesis and Characterization of QDs. Cadmium selenide/ zinc sulfide (CdSe/ZnS) core/shell QDs were synthesized with cadmium oxide as the precursor by a previously reported procedure.26 ZnS shells were subsequently grown on the CdSe QDs using diethyldithiocarbamic acid zinc salt.27 The 1 S absorption peak of the obtained QDs was at 547 nm, and the average diameter was estimated to be 4.5 nm, taking into account the bulk lattice parameter of ZnS.28 The average diameter was in good agreement with the direct observation of QDs by transmission electron microscopy (JEM-2010, JEOL, Tokyo, Japan), which showed an average diameter of ca. 5 nm. The molecular weight of the QDs was 4.0 × 105 g mol-1, assuming the number density of TOPO molecules on the QD surface to be 10 nm-2.29 Absorption and fluorescence spectra of the obtained QDs dissolved in octane were recorded on a spectrophotometer (U-

10.1021/jp805397b CCC: $40.75  2008 American Chemical Society Published on Web 10/10/2008

17110 J. Phys. Chem. C, Vol. 112, No. 44, 2008 4100, Hitachi, Tokyo, Japan) and a fluorescence spectrophotometer (FP-6300, JASCO, Tokyo, Japan), respectively. A quartz cell (10 × 10 × 45 mm3) was used for spectrum measurements. The absorbance at 488 nm was 0.29 for a concentration of 0.24 mg mL-1. The absorption cross section of the QDs at 488 nm was calculated as σ ) 8.1 × 10-16 cm2 dot-1. Film Formation Using Confocal Laser Scanning Microscopy. QDs were dissolved in octane (99.5%, Wako, Osaka, Japan). The concentration of QDs was increased from 0.03 to 0.9 mg mL-1. We also changed the concentration of TOPO molecules in the suspension up to 50 µM. To remove initially formed aggregates in suspension, 2.0 mL of the QD suspension was filtered by a syringe filter (0.02-µm pore size, Anotop 25, Whatman, Kent, U.K.) before use. After filtration, the suspension was poured into a glassbottom dish (cover glass thickness ) 0.08-0.12 mm, uncoated, Matsunami, Osaka, Japan). A condensed Ar+ laser (λ ) 488 nm) was applied to the surface of the cover glass from underneath, using a confocal laser scanning microscope (CLMS, TCS-SP2, Leica, Wetzlar, Germany). The objective lens was HCX PL APO [oilimmersion lens, 63× magnification, 1.4 numerical aperture (NA), Leica]. Laser light was scanned as a certain shape (e.g., square, line) or a pattern (“NANO”) for a period of time. Scanning was done at 400 Hz. Laser power (F) was measured with a power meter (PD300-SH, OPHIR Optronics, North Andover, MA), and laser intensity (I) was calculated to be I ) 4F/πd2, where d is the diameter of the laser-beam spot. Considering laser focusing by an objective lens, d can be estimated to be 1.22λ/ΝΑ, where λ is the wavelength of the laser. In our study, d was about 4.3 × 10-7 m. Observation of Formed Films. To confirm formation of a QD film, we irradiated a square region (8 × 8 µm2) on the surface of a glass substrate. After a period of time of scanning, we observed reflection and fluorescence images of the irradiated area by scanning a square of 30 × 30 µm2 around it. The fluorescence spectrum of the square film in the visible light range was measured using the same laser as an excitation source in the confocal system. Images were taken in the wavelength ranges of 483-493 nm for reflection and 535-615 nm for fluorescence. We observed the time course of film deposition to investigate the kinetics of film formation. A linear shape was chosen to study this feature, and the line length was 7.4 µm in all cases. After a period of time of line scanning, planar reflection and fluorescence images were obtained using the same Ar+ laser at low intensity. The laser intensity for observation was 13 kW cm-2, which was about one-third of the lowest laser intensity required to make a film in our study. Cross-sectional images of a linear QD film were obtained using a galvanometer-driven z-specimen stage after a period of time of line scanning. We observed a linear QD film by changing the z position with a height interval of 3 × 10-2 µm. The height and length of cross-sectional images were each 15 µm. Reflection and fluorescence images were taken for cross-sectional observation. Analysis of Film Formation. For quantitative analysis of the film thickness, we defined the reflection reduction ratio as (Iref_sub - Iref_film)/Iref_sub, where Iref_sub and Iref_film are the average reflection intensities from the substrate surface and from the QD film, respectively. The reflection intensities Iref_sub and Iref_film were obtained from planar reflection images of QD films. The effective irradiation time for a laser spot was calculated. Because we made a linear film with a length of 7.4 µm by line scanning and because the laser spot was 0.43 µm, the irradiation time per laser spot was a factor of 0.43/7.4 smaller than the scanning time for one line. Hereafter, we use this irradiation time for a laser spot as the irradiation time to form a QD film.

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Figure 1. Typical example of (a) reflection and (b) fluorescence images of a glass substrate surface in a QD suspension after square scanning. The black square corresponds to the irradiated area in a, and the green square area shows fluorescence in b. (c) Fluorescence spectra of the obtained square film (solid line) and a QD suspension (dashed line). The full width at half-maximum (fwhm) of each spectrum was 43 nm for the QD film and 38 nm for the suspension. C0 ) 0.2 mg mL-1, and I ) 2.0 × 102 kW cm-2. The total irradiation time for the square was 300 s. The scale bar is 2 µm.

3. Results Figure 1a,b shows reflection and fluorescence images, respectively, of a glass substrate after square irradiation for 300 s. The black square in Figure 1a corresponds to the irradiated area. In the fluorescence image in Figure 1b, only the square area shows fluorescence. The fluorescence spectrum of the square film is shown in Figure 1c. The fluorescence spectrum of a QD suspension is also shown. The spectrum of the square film is slightly wider but almost identical to that of the QD suspension, indicating that the square film consists of QDs. It is considered that spectrum broadening was caused by the difference in the wavelength resolution in the fluorescence spectra (1 nm for a suspension and 3 nm for the QD film). The fluorescence quantum yield of QDs in the formed film is one of the scientifically interesting topics, but it is beyond the scope of this work. Because of the absorption and scattering of Ar+ laser light by the QD film, the QD film is black in the reflection image. The formed film remained attached to the substrate after the laser was turned off. We tried to observe the surface structure of the formed film by scanning electron microscopy (SEM). However, we could not obtain useful information from surface observation because the formed film shrank and became deformed as a result of the evaporation of solvent. Judging from the confocal images shown in Figure 1, the surface of the film has micron-scale roughness. Planar reflection images of a linear QD film during film formation are shown in Figure 2a-c. Before irradiation, only the reflection from the glass substrate surface (blue) was seen. After irradiation, black and white lines were observed, and these lines became clear (Figure 2b,c). Because the QD film appears black in the reflection image in Figure 1a, the black lines in Figure 2b,c correspond to a linear QD film. The reflection intensity of the QD film became lower with increasing irradiation time, indicating that the film was getting thicker. It is considered that the white lines beneath the QD lines were caused by a strong reflection from the formed interface between the glass substrate and the QD film because of the large difference in refractive indices: n ) 1.5 for glass30 and n ) 2.7 for CdSe.31 Corresponding cross-sectional images of a linear QD film during laser irradiation are shown in Figure 2d-f. The fluorescence image (green) is overlaid on the reflection image (blue). Before irradiation, no fluorescence but the reflection from

Photoinduced Film Formation of Colloidal CdSe QDs

Figure 2. (a-c) Planar reflection images of a linear QD film. The surface of the glass substrate (blue) and the formed linear QD film (black) are shown. (d-f) Corresponding cross-sectional images of the linear QD film. In the cross-sectional images, reflection (blue) and fluorescence (green) images are overlaid. The irradiation times were (a,d) 0, (b,e) 3.5, and (c,f) 5.9 s. The concentration of QDs was 0.03 mg mL-1, and I ) 1.4 × 102 kW cm-2. The bars are 2 µm.

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Figure 4. Time course of thickness of a QD film. The concentration of QDs was 0.09 mg mL-1. The laser intensity was (b) 1.4 × 102, (9) 88, and (2) 45 kW cm-2. The deposition rate, k, and incubation time, τ, are also shown.

Figure 3. Linear relationship between the reflection reduction ratio and the film thickness.

the glass surface was observed (Figure 2d). After irradiation, fluorescence was clearly observed, and the thickness of the fluorescent line increased with increasing irradiation time (Figure 2e,f). We concluded that the fluorescence was from the formed linear QD film because the formed QD film showed fluorescence in Figure 1b and because the length of the fluorescent line was almost the same as the line length of 7.4 µm in Figure 2e,f. These images suggest that the thickness of the QD film increased with increasing irradiation time. In Figure 2d, the surface of the cover glass appears as a line with a thickness of ca. 0.6 µm, although the glass surface does not have a thickness. This image indicates the resolution limit of our confocal laser scanning microscopy system. Because of this limitation, we determined the thickness of a QD film by subtracting the “surface thickness” of 0.6 µm from the thickness observed in the overlaid cross-sectional images. The reflection reduction ratio of the QD film (see Analysis of Film Formation for definition) in planar images shows a linear relationship to film thickness (Figure 3). Hereafter, the film thickness was determined on the basis of the reflection reduction ratio because planar observation is more convenient than crosssectional observation because of rapid scanning and lower sensitivity to the fluctuation of the sample stage. The time course of the film thickness during laser irradiation under various intensities is shown in Figure 4. In all cases, film formation occurred at a constant rate of deposition after an incubation period, where both the rate of film formation and the induction period clearly depend on laser light intensity. Intense laser light brings a short incubation period and a high rate of deposition. Film thickening stopped when the thickness reached ca. 0.8 µm, which is almost the same as the focus depth of the lens (about 0.5 µm). This indicates that photoinduced film formation occurs only in the light-condensed field. The second film layer was obtained when the focus point was changed to an upper position after the formation of the first film. However, if we try to increase the thickness of the film

Figure 5. Effect of laser light intensity on (a) deposition rate and (b) incubation time. Solid and dashed lines in a are guides for the eye. In region 1, k increases in a linear manner. In region 2, k is almost constant. For both cases, C0 ) 0.2 mg mL.

further by executing the same procedure in a repetitive manner, film thickening would stop at a few microns because of the absorption of laser light by the formed film. As the film thickness increases, the laser light transmitted by the formed film would decrease, resulting in insufficient laser intensity for film formation in the vicinity of the film surface. In Figure 4, we define the rate of film deposition, k, as the slope, and the incubation time, τ, as the period before the onset of film formation. k and τ are characteristic values for film formation. The effect of laser intensity on the deposition rate is summarized in Figure 5a. In the low-intensity region, k depends on laser intensity in a linear manner (region 1), but k is constant in the high-intensity region above ca. I ) 2.0 × 102 kW cm-2 (region 2). From Figure 5a, light relates to the rate-limiting step in the film formation in region 1. The independent nature of k in region 2 means that the photorelated path is not the ratelimiting step in the high-intensity region. In Figure 5b, the decrease of τ with increasing laser intensity is shown. τ stays almost constant under intense irradiation. The dependence of the deposition rate on the initial concentration of QDs, C0, is shown in Figure 6. In this C0-control experiment, k increased with increasing C0 in a linear manner. We did not observe a clear incubation period above C0 ) 0.3 mg mL-1 because of the fast formation of the film. The obtained values of τ were 1.6 s for 0.03 mg mL-1 and 1.0 s for 0.09 mg

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Figure 6. Dependence of k on C0 obtained in the C0 control experiment. I ) 1.4 × 102 kW cm-2. The solid straight line is the best-fitting result for all data.

Figure 7. (a) Retardation effect of TOPO addition on deposition rate. C0 ) 0.2 mg mL-1, and I ) 1.5 × 102 kW cm-2. In the inset, the inverse of k is plotted in terms of CTOPO, showing a linear relationship. The solid line is the best-fitting result for these data as k-1 ) 2.7CTOPO + 3.0. All data except for CTOPO ) 50 µM are plotted in the inset. (b) Effect of TOPO addition on incubation time.

Wada et al. addition of TOPO molecules significantly retarded film formation. Because TOPO molecules have coordination bonds with QDs, they are in an adsorption/desorption equilibrium under dark conditions. When TOPO molecules are added, the equilibrium shifts to adsorption, and well-capped QDs are stably dispersed in suspension even under laser irradiation. The retardation effect of TOPO molecules on film formation is explained by the increase in the colloidal stability of QDs; i.e., QDs that are well-capped with TOPO molecules do not form a film. To form a film, it is thought that the TOPO molecules on the QD surface should be removed to decrease the colloidal stability in the suspension. In our previous article, we reported that irradiation of a CdSe QDs dispersion produces dispersion instability, followed by the formation of QD aggregates.25 In that system, the photons act as an accelerator for TOPO desorption from QDs.25 We propose that destabilization of colloidal QDs is caused by photoinduced desorption of TOPO molecules, and these unstable QDs form a film. Because a QD film is formed only in the light-condensed field, we hypothesize that photoinduced destabilized (unstable) QDs are predominantly formed in that restricted region. The laser intensity at a point 1 µm above the light-condensed field is estimated to be a maximum of 3% of that in the light-condensed field;32 therefore, formation of unstable QDs outside the light-condensed field is negligible. Understanding Photoinduced Film Formation Based on a Simple Model. Based on the photoreaction step noted above, we propose that film formation consists of three processes (Figure 9): (i) diffusion of QDs from the bulk suspension to the light-condensed field, (ii) photoreaction of stable QDs to form unstable QDs, and (iii) mass transfer of unstable QDs followed by film formation. The third process includes adherence of unstable QDs to the substrate surface. The first process is independent of laser intensity, but the others are affected by the irradiation conditions. The rate-limiting step in region 2 in Figure 5a, where k is constant in terms of laser intensity, is ascribed to diffusion of stable QDs from the bulk suspension. For simplicity, we consider the light-condensed field as a cylinder (Figure 9b). The diameter is 4.3 × 10-1 µm, and the height is 0.8 µm. In that system, the deposition rate is described in terms of the diffusion constant of QDs, D, as

k) Figure 8. Reflection image of a NANO-patterned QD film obtained by photoinduced film formation. Only the NANO pattern was irradiated throughout scanning. The scale bar is 1 µm.

mL-1. In Figure 7, the retardation effect of CTOPO on film formation is shown. (CTOPO is the concentration of TOPO molecules in the suspension after the addition of TOPO molecules.) The addition of TOPO molecules significantly retarded film formation. When CTOPO was 50 µ M, the deposition rate was almost zero. We demonstrated that the photoinduced film formation of QDs is a viable patterning technique in a wet process. By irradiating only the pattern NANO throughout laser scanning, a NANO-patterned QD film with a line width on the order of submicrons was obtained (Figure 8). This could be a potential application for the patterning of QD films. 4. Discussion Role of Photons in Formation of QD Film. The deposition rate increased with increasing intensity of laser light. The

2h0 R2R

DC0

(1)

where h0 is the height of the cylindrical field, R is the radius of the spot, and R is the molar density of QDs in the QD film. (See Appendix A for the derivation of eq 1.) D was estimated using the Stokes-Einstein equation,33 with the viscosity of octane being 5 × 10-4 Pa s,30 the diameter of QDs being 4.5 nm, and the length of the TOPO molecules being 0.7 nm.34 To estimate R, we assumed the packing fraction in a QD film to be 0.55, which corresponds to the random loose packing of spheres.35,36 (See Appendix B for details.) Using the values of R ) 1.9 × 10 mol m-3, D ) 1.5 × 10-10 m2 s-1, and C0 ) 5.0 × 10-4 mol m-3 (for 0.2 mg mL-1), we obtained k ≈ 0.1 µm s-1, which approximately agrees with the observed value of 0.5 µm s-1 in Figure 5a, differing by a factor of 5. This estimation supports our interpretation. In region 1 in Figure 5a, light relates to the rate-limiting step. Here, we consider the mass balance equations on the basis of the proposed model. Suppose that destabilized QDs (QDs*, with a concentration of C*) are formed by the photoreaction of stable QDs (QDs, with a concentration of C). This reaction is described as

Photoinduced Film Formation of Colloidal CdSe QDs

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Figure 9. Photoinduced formation of QD film (schematic). (a) Our experimental system around an objective lens. (b) Enlarged figure of the dotted area in a. The cylindrical volume between the dotted and solid circles in b is the light-condensed field. The numbers 1-3 in b correspond to the three steps in our model (see text).

QDs + photons T QDs* + TOPO molecules

(2)

Considering all three steps, the mass balance equations are given by

dC ) -kdIC + kaC*CTOPO dt dC* S ) kdIC - kaC*CTOPO - hdC* dt V dh hd ) C* dt R

(3) (4) (5)

where kd and ka are the rate constants for desorption and adsorption of TOPO molecules from/to QDs surfaces, respectively. S and V are the spot area and the volume of the cylindrical light-condensed field, respectively; h is the film thickness, and hd is the overall mass-transfer coefficient for unstable QDs. Equation 5 corresponds to deposition rate k () dh/dt), which is constant during film formation (Figure 4). Then, C* should be constant; i.e., dC*/dt ) 0. The diffusion of stable QDs is faster than other processes in region 1, so we set C ) C0. From eq 4, we obtain

C* )

kdIC0V kaCTOPOV + hdS

(6)

Using eqs 5 and 6, we can explain the linear increase of k in terms of I in region 1 and C0 in Figure 6. Because the ratelimiting step in region 2 is the diffusion of stable QDs, all QDs in the light-condensed field are thought to be unstable above 2.0 × 102 kW cm-2; i.e., C* ) C0 in that region. From eq 5, we obtain hd as 1.9 × 10-2 m s-1. From eq 6, the inverse of eq 5 is

1 R 1 V + hdS) ) (k C k hd kdIC0V a TOPO

(7)

In the inset in Figure 7, the slope and intercept give the values of kd and ka as 1.1 × 102 cm2 kJ-1 and 2.2 × 107 m3 mol-1 s-1, respectively. In this analysis, we set CTOPO ) 0 in the suspension without TOPO addition, and this assumption did not significantly affect our results. See Appendix C for a detailed discussion. We estimated the photoreaction yield to form an unstable QD. The formation rate of destabilized QDs is kdIC0V, and the incoming rate of photons absorbed by QDs in the lightcondensed field is σIC0V, where σ is the absorption cross section of QDs. Then, kd/σ is the photoreaction yield for producing an unstable QD, which was estimated to be 5 × 10-5, using the

Figure 10. Values of incubation time in Figures (b) 5b and (0) 7b and the C0-control experiment (×) plotted in terms of C*. The inset shows a linear relationship between τ-1 and C*. The solid lines are the best-fitting result for these data as τ-1 ) 0.54C*.

converted value of kd ) 4.3 × 10-20 cm2 photon-1 and σ ) 8.1 × 10-16 cm2 dot-1. Incubation Period. An incubation period was one of the main features observed in film formation. From Figures 5-7, one can see that the laser intensity, concentration of QDs, and concentration of TOPO molecules affect the incubation time. In film formation in a dry process (e.g., physical/chemical vapor deposition), incubation time is expressed as the inverse of the partial pressure of the source gas.37,38 During the incubation time, adsorbates form not a continuous film, but small “islands” on the substrate. When the substrate is fully covered with islands, the film grows continuously, signaling the end of the incubation period.39 The difference in the adherence of adsorbates to the substrate and to the islands is thought to be one of the main origins of the incubation period.39 Our system was a wet process, but by analogy, C* corresponds to the partial pressure of the source gas in a dry process. In Figure 10, the obtained values of τ in Figures 5b and 7b are plotted in terms of C*. The values of τ obtained from the C0control experiment are also included. Despite the difference in experimental conditions, all data of τ are summarized along a single master curve. The inset shows the linear relation between τ-1 and C*. This implies that, during the incubation period, small QD islands form, identically to the dry process. Regardless of a wet or dry system, a common phenomenon is thought to occur at the initial stage of film formation. 5. Conclusion Under laser irradiation, TOPO-capped CdSe QDs formed a QD film. The deposition rate of the film depended on the laser intensity, the number density of QDs, and the concentration of TOPO molecules. We propose that the photons absorbed by

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QDs induce desorption of TOPO molecules, followed by formation of destabilized QDs. The latter attaches to a substrate and forms a QD film. On the basis of our proposed model, we determined the rate constants, kd and ka, and the mass transfer coefficient, hd, with a photoreaction yield of 10-5. Incubation time showed the same trend as film formation in a dry process, suggesting that small QD islands are formed during the incubation period. This technique of film formation can be a noble wet process for preparing a patterned QD film with a line width on the order of submicrons. Acknowledgment. This work was partly supported by a Research Fellowship from the Japan Society for the Promotion of Science. We thank the High-Voltage Electron Microscope Laboratory, School of Engineering, The University of Tokyo, for technical support for the transmission electron microscopy experiments. We also thank Professor S. Noda, The University of Tokyo, for helpful discussions. Appendix A Assuming that the light-condensed field is a cylinder, the boundary layer for mass transport is given as the radius of the cylinder.33 Because the side surface area of the cylinder, S′, is 10 times larger than the top surface area in our geometry, we can approximately describe the mass balance of QDs using the diffusion of QDs out of the bulk suspension as

RSk ) S ′

D (C - C) R 0

(A1)

where S ) πR2 and S′ ) 2πRh0. For the diffusion-limiting step, C is 0. Then, we obtain eq 1. Appendix B Random loose packing (RLP) is the lowest packing density for spheres without any attractive interactions.35 If spheres have attractive interactions, a looser packing structure than RLP is possible.35 In a QD film, a strong interaction between QDs is expected because of the desorption of TOPO molecules from their surfaces. The packing density of our QD film is therefore thought to be lower than the RLP. We tried to measure the packing density of our QD film by absorption measurements. The intensity of laser light transmitted through the glass substrate with/without a QD film was measured. Reliable data were not obtained because of complicated scattering and reflection around the QD film. We used RLP as the representative value for the QD film in our analysis. If we use a smaller packing density than the RLP, the values of hd, kd, ka, and the photoreaction yield become smaller than the values stated in the discussion. Appendix C Strictly speaking, free TOPO molecules are present even in the original suspension without TOPO addition because of an adsorption/desorption equilibrium. We evaluated the effect of the concentration of TOPO in the original solution. We redefined 0 the concentration of TOPO in the original solution as CTOPO . In this case, from eq 7, the slope a and the intercept b in the inset in Figure 7a are given by

a)

(

R ka hd kdIC0

0 b ) a CTOPO +

hdS kaV

(C1)

)

(C2)

0 If hdS/(kaV) , CTOPO , one can obtain the experimentally 0 determined maximum value of CTOPO in our model, which is

0 b/a ≈ 1.1 µM at most. For CTOPO is 0.9 µM, values of kd and ka that are about five times larger than those mentioned in the text are obtained. We want to have the order of the rate constants, and the approximation of CTOPO ) 0 in the original solution does not significantly affect our results.

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