J. Phys. Chem. B 2004, 108, 9027-9031
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Light Emission and Amplification in Charged CdSe Quantum Dots Congjun Wang,† Brian L. Wehrenberg,† Chui Y. Woo,‡ and Philippe Guyot-Sionnest*,† James Franck Institute, UniVersity of Chicago, Chicago, Illinois 60637, and Department of Physics and Astronomy, State UniVersity of New York at Stony Brook, Stony Brook, New York 11794 ReceiVed: March 5, 2004
Photoluminescence from charged colloidal CdSe quantum dots, with definite and controllable electron occupation, is observed. As charged nanocrystals still emit light but are transparent at the emission wavelength, the threshold for amplified stimulated emission is strongly reduced. We demonstrate 65% threshold reduction in charged CdSe nanocrystal films, and further reduction should be feasible. This opens new possibilities for achieving efficient lasing in these molecular-like systems.
1. Introduction One of the goals in molecular and colloidal quantum dot research is to develop “plastic” light-emitting devices and lasers.1-6 Light emission from colloidal quantum dots has led to photopumped lasers,1-4 light-emitting devices,5,6 biological labeling,7,8 and imaging.9,10 Future developments might involve electrically pumped lasers, a goal that is still elusive not only for the colloidal quantum dots but also for molecules and polymers. One basic difficulty is that charges quench the luminescence of small nanocrystal quantum dots,11 and are believed to cause unusual phenomena, such as blinking,12 luminescence wandering,13,14 and photoluminescence upconversion.15 Despite the advantageous tunable optical properties of colloidal quantum dots, they are effectively three-level systems. CdSe nanocrystals must first absorb one photon to reach population inversion,1 and other systems such as PbSe might require an even larger initial photon investment.16 Substantially lowering the stimulated emission threshold is therefore also of technological interest. Colloidal quantum dots17 share useful properties with conjugated molecules and polymers,18 such as the ease of solution processing, electroluminescence, photopumped lasing in the insulating regime, and conductivity by charging.18,19 However, molecular and polymeric systems in their conductive form are not yet known to demonstrate stimulated emission. Here, we report luminescence and improved stimulated emission with charged CdSe nanocrystal films. In concert with advances in achieving transport in these materials,19 this observation opens new possibilities for efficient lasing in these systems. 2. Experimental Section Colloidal CdSe nanocrystals with trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO) capping molecules are prepared according to ref 20. To provide a binding surface to CdSe nanocrystals on indium tin oxide (ITO) electrodes, a drop of 4-aminobutyldimethylmethoxysilane is placed on the ITO electrode, and the electrode is rinsed with methanol to remove excess silane before being heated to 120 °C for about 1 h. Optically clear thin films of nanocrystals on silane-treated ITO * To whom correspondence should be addressed. E-mail: pgs@ uchicago.edu. † University of Chicago. ‡ State University of New York at Stony Brook.
electrodes are prepared by drop casting a solution of nanocrystals in a 9:1 (v/v) mixture of hexane and octane. Thin films of nanocrystals are then immersed in a ∼3 mM 1,7-diaminoheptane in anhydrous methanol solution for ∼10 s, which are subsequently baked at 70 °C for several hours to cross-link nanocrystals in the closely packed arrays.21 A solution of 4-dicyanomethylene-2-methyl-6-p-diethylaminostyryl-4H-pyran (DCM) in methanol is used as a standard for quantum yield measurements. For electrochemical measurements, the ITO working electrodes are inserted in a glass test tube with the electrolyte solution (0.1 M tetrabutylammonium tetrafluoroborate in anhydrous N,N-dimethylformamide). The electrolyte salts are dried at 110 °C under vacuum overnight prior to use. A Ag wire and a Pt wire are used as the pseudoreference electrode and counter electrode, respectively. All the electrochemical potentials reported here are with respect to the Ag pseudoreference electrode. The cell is airtight and is maintained in a dry N2 atmosphere during the measurements. The cell can be cooled to -70 °C. A computer controls the potentiostat to provide steps in potential and simultaneously records the electrochemical current and auxiliary inputs from photodiodes and photomultipliers. For the experiments reported here, ∼6.8 nm diameter TOP/ TOPO-capped CdSe nanocrystals with the first exciton peak at 632 nm at room temperature are studied. For the optical bleach measurements, a 635 nm laser diode is used to probe the visible absorption of the CdSe thin films. A silicon photodiode simultaneously detects the 635 nm beam that passes through the nanocrystal thin films and a reference beam to obtain the change of absorption at the shoulder of the first exciton peak. For certain studies, visible absorption spectra of nanocrystal films are measured with a fiber optic spectrometer. In the continuous wave (cw) photoluminence (PL) experiments, the 514 nm beam from an Ar+ laser is used as excitation source, and the PL of CdSe films is collected at ∼90° by a photomultiplier tube. Pulsed PL spectra from charged nanocrystals and stimulated emission are investigated with a pulsed laser (25 Hz, 532 nm, 9 ps). The emission intensity from each laser shot is recorded by two photomultiplier tubes equipped with separate monochromators to monitor light intensity at two different emission wavelengths simultaneously. The cross-linked nanocrystal thin films are extremely robust.21 In our experiments, these films have not shown the slightest indication of photodegradation over an extended period of
10.1021/jp0489830 CCC: $27.50 © 2004 American Chemical Society Published on Web 05/28/2004
9028 J. Phys. Chem. B, Vol. 108, No. 26, 2004
Figure 1. Room-temperature measurements of the response of a CdSe nanocrystal thin film upon charging and discharging. The electrochemical potential is stepped from -0.55 to -1.15 V at t ) 0 ms and returned to -0.55 V at t ) 6000 ms. (A) Visible absorption changes (-∆R/R). (B) PL response. (C) Simultaneously recorded electrochemical current. Current from polarization was subtracted in (C).
experiments. As a measure of stability, the film that we looked at the longest was excited for more than one million laser shots, and exhibited no deterioration whatsoever. The performance of the film does not degrade as long as the electrochemical cell is kept in a dry and oxygen-free environment. 3. Results and Discussion A. Fluorescence from Charged Nanocrystals. Light emission from charged colloidal nanocrystals has been invoked in two papers,22,23 but without direct evidence or control of the number or nature of charges. Previous experiments on reduced CdSe nanocrystals showed that PL was vastly quenched, by many orders of magnitude, after charge injection.11,24-26 These studies also demonstrated that the PL of nanocrystals remained strongly quenched well after the electrons were removed from the quantum state, 1Se. This observation indicated that the electrons in the quantum states were not the main source of nonradiative recombination, and it was suggested instead that charged surface states were responsible for most of the PL quenching. However, in these earlier studies, the kinetics of charging were not resolved and it was not possible to determine if the nonradiative channels arose more slowly than or as fast as the charge injection into the quantum states. With recent progress in electrochemical charge injection,21 it is now feasible to rapidly charge all the nanocrystals composing a film of ∼200 nm thick on time scales of ∼100 ms. This development allows us to resolve the kinetics of PL quenching as electrons are injected into the nanocrystals. Figure 1 shows the time trace of a typical experiment. The ∼6.8 nm diameter CdSe nanocrystal thin film (∼100 nm thick) is excited by a continuous 514 nm beam. The exciton bleach (Figure 1A), the peak emission intensity (Figure 1B), and the current (Figure 1C) are recorded with a time resolution of 3 ms as the electrochemical potential is stepped. By inspection, the kinetics of charging and discharging of the 1Se state, measured
Wang et al.
Figure 2. Absorbance bleach (bottom panels) and 1/PL intensity (upper panels) as a function of time as a negative potential is applied at (A) room temperature and (B) -70 °C. The inset in (B), which is a zoomin of the 1/PL kinetics, clearly illustrates the nonmonotonic PL response upon charging. Applied potentials: dotted lines, (A) -0.60 V and (B) -0.70 V; dashed lines, (A) -0.90 V and (B) -0.92 V; solid lines, (A) -1.15 V and (B) -1.4 V.
by the exciton bleach and recovery (Figure 1A), do not follow closely the fluorescence quenching (Figure 1B). To examine more clearly the different kinetics, Figure 2A shows the visible exciton bleach and the inverse of PL intensity plotted as a function of the logarithm of time. Figure 2A illustrates three different potentials corresponding to zero, one, and two electrons charging in the 1Se state of each nanocrystal. At all potentials there is a clear difference between the kinetics of charging the 1Se state and the fluorescence quenching. 1/PL rather than PL is shown here because 1/PL is a better measure of the increase of nonradiative recombination rates knr, as 1/PL ) (kr + knr)/kr is linearly proportional to knr. A logarithmic growth of the nonradiative rate is now evident, which occurs mostly after the nanocrystals have all achieved a steady-state occupation in the 1Se state. By cooling the sample, the overall kinetics become slower and we can further distinguish the effects of charges on the 1Se state and the fluorescence quenching (Figure 2B). The effect becomes very striking, as the PL is even seen to increase upon about one electron occupation, for a short time, before nonradiative rate buildup eventually takes over (Figure 2B, inset). The observation above that charged films fluoresce with effficiency similar to or even higher than that of uncharged films is surprising because Auger relaxation should strongly reduce the fluorescence efficiency.1,11 For an isolated nanocrystal of the size studied, the one-electron Auger rate is about (400 ps)-1. Taking a typical radiative lifetime of 20 ns, one-electron charging would give a quenching factor of ∼50. There are two plausible explanations why the Auger process plays a minor role here. First, the negatively charged exciton S- is always a singlet state, and it should have a faster radiative relaxation than the neutral exciton S. Second, energy transfer within the film and other nonradiative processes lead to an average lifetime that is already much shorter than the isolated nanocrystal lifetime. This is borne out by the fact that the measured quantum yield of the films is about 1.0%. Alternative explanations might be that (i) the improved luminescence upon charging might arise from the filling of “trap” states below the 1Se level [however, this interpretation
Light Emission in Charged CdSe Quantum Dots
Figure 3. -∆R/R and 1/PL as a function of charges flowing into (A) and out of (B) the nanocrystal film at room temperature (applied potential -1.15 V; solid curves, 1/PL; dotted curves, -∆R/R). The dashed line in (A) is a guide to the eye, demonstrating that the 1/PL is nearly linearly proportional to the injected charges after the 1Se state is fully occupied.
is inconsistent with the experimental observation that at potentials just below the 1Se it is a weak luminescence quenching, not enhancing, that takes place (dotted curves in the upper panels of Figure 2)] and (ii) the observed fluorescence is representative of a few bright but electrically isolated nanocrystals, while all electrically connected nanocrystals are dark. As spectral data show later, the fact that different average charging leads to very different average PL spectra eliminates this possibility. Figure 3A shows the same room-temperature data as the solid curves in Figure 2A, but plotted as a function of the integrated charge after the potential step. This graph indicates that a small amount of charge (∼12 µC) already leads to the full occupation of the 1Se state (-∆R/R ≈ 1),21 while the additional charges correlate approximately linearly with the increase of the nonradiative rates. In contrast, on the recovery side (Figure 3B), there is less current associated with the fluorescence recovery and there is no clear correlation between the long-term behavior of 1/PL and the integrated charge. On the basis of the evidence above, we propose that the longterm PL quenching is related to the buildup of nonradiative recombination surface sites created mostly by reduction from the 1Se electrons. The logarithmic rather than linear growth of the quench suggests that the surface sites are repulsive and therefore possibly charged, although they are disconnected from the electrodes by high barriers. The slowing of the quenching at low temperature is consistent with an activation barrier associated with the surface reduction process. When the 1Se electrons of the nanocrystals are removed, the quenching surface sites are slowly oxidized to their initial state by impurities in solution, and the PL recovers. At present, we do not have a chemical identification of the surface sites. For future work and applications, these surface sites need to be identified and eliminated, possibly by devising a different surface chemistry of the nanocrystals. B. Emission Spectrum of Charged Colloidal Nanocrystals. To investigate the emission spectrum and the amplified stimulated emission (ASE) in charged nanocrystal films, the sample is photoexcited by 9 ps laser pulses at 532 nm and a 25 Hz repetition rate. The emission from each laser pulse provides a data point every 40 ms. The bleach of the first exciton absorption
J. Phys. Chem. B, Vol. 108, No. 26, 2004 9029
Figure 4. PL and visible absorption spectra of neutral and charged nanocrystal films at -70 °C: dotted curves, neutral nanocrystals; dashed curves, nanocrystals with on average one electron in the 1Se state of each dot (V ) -0.9 V, -∆R/R ≈ 0.5); solid curves, two electrons in each nanocrystal (applied potential -1.4 V, -∆R/R ≈ 1). The arrow in the absorption spectra panel indicates the position of the excitation (532 nm) for PL measurement. A sharp artifact due to fluorescence of the substrate electrode at 580 nm was removed. Inset: schematics of transitions in doubly charged nanocrystals.
is again simultaneously recorded to measure the occupation of the 1Se state.19,21 Figure 4 first shows the low-pump-power emission spectra of a thin film of nanocrystals with one and then two electrons in the 1Se state. The data points are averages of the emission intensity for 30 consecutive laser shots after the visible bleach has stabilized ∼0.3 s after the required electrochemical potential is applied, and before PL quenching is too extensive. Consistent with the results of Figure 2, the emission of the S exciton with on average one electron per dot, S-, is nearly identical in strength and line shape to that of the neutral nanocrystals. On the other hand, the emission of the S exciton with two electrons, S2-, is red-shifted by about 4 nm, or 13 meV. Furthermore, a new emission peak, P2-, appears around 590 nm. This emission is not due to a binary size distribution as verified by transmission electron microscopy and PL of dilute solutions of the nanocrystals. P2- is instead assigned to the radiative recombination of the electron in the 1Pe state and a hole in either the 1Sh,3/2 or 1Ph,3/2 states.23 P2- is only ∼0.14 eV blue-shifted from S2-, yet the 1Pe-1Se separation is ∼0.2 eV. The smaller shift could be due to the effect of the charges on the excitonic energies.23,27 This could also explain the ≈0.08 eV stabilization of P exciton absorption shoulder seen in Figure 4. The P2- emission peak further confirms that the observed PL is from doubly charged nanocrystals. The red shift of S2- from S and S- is in qualitative agreement with theoretical predictions that the emission of a doubly charged quantum dot is more red-shifted due to Coulomb interactions.27 A S2- shift of ∼85 meV has been predicted for 3.85 nm diameter CdSe nanocrystals. The nanocrystals used here are about twice as large in diameter, and the weaker Coulomb interaction may account for the difference in the emission shift. C. Reduced Threshold for Stimulated Emission in Charged Nanocrystals. At higher pump power, robust ASE is observed in the cross-linked nanocrystal films. In our experiments, films have been irradiated with more than one million laser shots without noticeable photodegradation. In neutral nanocrystals, the gain-narrowed ASE peak is red-shifted from the photolu-
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Figure 5. ASE spectra of neutral (dotted line) and charged (solid line) nanocrystal solids with two electrons in the 1Se state (applied potential -1.4 V, -∆R/R ≈ 1) at -70 °C. The strong and narrow peak at ∼648 nm is the ASE. The excitation intensity is 5.65 mJ/cm2. A cutoff filter at 610 nm is used.
Figure 6. PL peak intensity (630 nm, triangles) and ASE peak intensity (648 nm, circles) as a function of pump fluence at -70 °C. Open symbols are for values measured on a neutral nanocrystal film, and solid symbols are for values from the same film when two electrons are injected into each dot (applied potential -1.4 V, -∆R/R ≈ 1). The lines are guides to the eye. Inset: PL spectra measured at an excitation intensity of 0.54 mJ/cm2 (indicated by the arrow in the main panel) of the film before (dashed line) and after (solid line) charging, demonstrating the development of ASE in a charged film below the threshold for a neutral film. A cutoff filter at 610 nm is used.
minescence peak (Figure 5), a result of the fact that the stimulated emission is from dots with two or more excitons.1,23 For doubly charged nanocrystals, the low-pump-power ASE (solid curve in the inset in Figure 6) is less markedly red-shifted from the S2- emission peak (Figure 4), which is expected for a single-exciton S2- gain regime. With two electrons in the 1Se state, the nanocrystals are transparent at the emission wavelength and the threshold for ASE is lowered. Effectively, the nanocrystals become four-level systems. ASE thresholds identified by the onset of line narrowing and the change of slope efficiency are reproducibly reduced by more than 50% for charged films of this size of nanocrystals. In Figure 6, the thresholds are 1.06 mJ/cm2 for neutral nanocrystals and 0.35 mJ/cm2 for doubly negatively charged nanocrystals, giving a reduction of 65%. The ASE threshold follows closely the injection of electrons into the 1Se state (Figure 7A). At potentials below the 1Se level,
Wang et al.
Figure 7. ASE threshold shift upon charge injection at -70 °C: (A) ASE threshold (solid circles) and the absorption change at the first exciton peak (open triangles) as a function of applied potentials; (B) light intensity at the ASE peak of 648 nm, as a function of time after charge injection, at different applied potentials. The laser pump power (0.82 mJ/cm2) is below the ASE threshold of the uncharged film.
the ASE threshold increases slightly due to slight quenching of luminescence by charging trapped states, while the lowest threshold is reached at the potential where two electrons are injected into each nanocrystal. At optical pump powers below the ASE threshold in the neutral state, pulsing the applied electrochemical potential leads to bright ASE. The brightest ASE is again observed for potentials corresponding to double charging. At higher potentials, the ASE deteriorates quickly because of the rapid buildup of nonradiative recombination and the increase of the Auger rate (Figure 7B). It is worth speculating on the intrinsic limitations of threshold reduction by charging. In neutral nanocrystal films, population inversion threshold requires a pump intensity that generates one electron-hole pair in each nanocrystal. With doubly charged nanocrystals, population inversion is achieved with arbitrarily low pump intensity. However, population inversion alone is not sufficient to realize stimulated emission. For gain to develop, the excitons must have a lifetime longer than the travel time of photons in the gain medium. The threshold for ASE in neutral nanocrystals is then given by Neh > 1 + A/2, where Neh is the pump induced exciton population in each nanocrystal, and A is the ratio of ASE buildup time τs and exciton lifetime T1 (radiative and nonradiative). τs is given by nr/σgFc, where nr is the sample refractive index, σg is the optical gain cross-section, F is the nanocrystal density in the film, and c is the light velocity.1 In doubly charged nanocrystals, population inversion is already achieved and the threshold for ASE becomes Neh ≈ A/2. A is possibly different as T1 and σg will likely differ from the uncharged case. For our size of nanocrystals, using σg ∼ 2 × 10-17 cm2 (ref 1) and T1 ) 100 ps, we estimate that A ∼ 0.02, such that the maximum threshold reduction could be ∼99% compared to the measured 65%. The discrepancy could be due to optical losses in the film, such as scattering or residual absorption at the emission wavelength. The latter could arise from the tail of higher interband optical transition or from high energy intraband transitions. We note that, as observed in Figure 7, adding more than two electrons per CdSe nanocrystal is not expected to lead to further improvement. Indeed, transparency is not improved while Auger relaxation speeds up28, giving rise to increased ASE threshold.
Light Emission in Charged CdSe Quantum Dots Thin films of 5.5 nm diameter CdSe nanocrystals were also studied. The maximum reduction of the ASE threshold in these films was only ∼15%. We expect that, for small nanocrystals, the competition between the Auger rate and the ASE buildup time is the limiting factor for reducing the threshold, rather than the population inversion. This arises due to the faster Auger process in smaller nanocrystals, because the Auger rate scales with nanocrystal size as ∼R3, where R is the radius of the nanocrystal.1 Additionally, smaller nanocrystals have more negative reduction potentials24,25 and are less electrochemically stable. The PL quenching at more negative potentials is faster, and this could also adversely affect the reduction of the ASE threshold by charging. 4. Conclusion In summary, photoluminescence of CdSe colloidal quantum dots has been observed in the neutral and one-electron- and twoelectron-reduced states. Strikingly, the photoluminescence of doubly charged nanocrystals shows emission from both P and S excitons with similar intensity. After some time, the buildup of nonradiative centers ultimately quenches the photoluminescence. The buildup of these nonradiative recombination centers is effectively suppressed by cooling the electrolyte, in accord with the generally improved electrochemical stability of the nanocrystals at lower temperatures. Nanocrystals cooled to ∼-70 °C exhibit a markedly reduced pumping energy threshold for stimulated emission when in the doubly charged state. Further investigations of related systems with improved surface chemistry such as core/shell materials and reduced Auger rates such as rods3 may lead to additional improvements. It should also be noted that some materials such as PbSe have been reported to require multiexciton excitation to achieve stimulated emission.16 In this case, the negative or positive charging of the nanocrystals29 should lead to even more dramatic improvements in the lasing performance. The lowered lasing threshold of charged and conducting colloidal nanocrystals opens vastly expanded possibilities for colloidal quantum dots as lasing media. Acknowledgment. We thank Dr. M. Pelton for helpful discussions. This work was funded by the U.S. National Science Foundation (NSF) under Grant DMR-0108101. We made use of the NSF Materials Research Science and Engineering Center (MRSEC) Shared Facilities supported by NSF under Grant DMR-0213745. C.Y.W. acknowledges financial support from the MRSEC Research Experience for Undergraduates Program at the University of Chicago.
J. Phys. Chem. B, Vol. 108, No. 26, 2004 9031 References and Notes (1) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H.-J.; Bawendi, M. G. Science 2000, 290, 314-317. (2) Eisler, H.-J.; Sundar, V. C.; Bawendi, M. G.; Walsh, M.; Smith, H. I.; Klimov, V. I. Appl. Phys. Lett. 2002, 80, 4614-4616. (3) Htoon, H.; Hollingworth, J. A.; Malko, A. V.; Dickerson, R.; Klimov, V. I. Appl. Phys. Lett. 2003, 82, 4776-4778. (4) Kazes, M.; Lewis, D. Y.; Ebenstein, Y.; Mokari, T.; Banin, U. AdV. Mater. 2002, 14, 317-321. (5) Schlamp, M. C.; Peng, X. G.; Alivisatos, A. P. J. Appl. Phys. 1997, 82, 5837-5842. (6) Mattoussi, H.; Radzilowski, L. H.; Dabbousi, B. O.; Thomas, E. L.; Bawendi, M. G.; Rubner, M. F. J. Appl. Phys. 1998, 83, 7965-7974. (7) Bruchez, M.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013-2016. (8) Chan, W. C. W.; Nie, S. Science 1998, 281, 2016-2018. (9) Dubertret, B.; Skourides, P.; Norris, D. J.; Noireaux, V.; Brivanlou, A. H.; Libchaber, A. Science 2002, 298, 1759-1762. (10) Larson, D. R.; Zipfel, W. R.; Williams, R. M.; Clark, S. W.; Bruchez, M. P.; Wise, F. W.; Webb, W. W. Science 2003, 300, 14341436. (11) Shim, M.; Wang, C.; Guyot-Sionnest, P. J. Phys. Chem. B 2001, 105, 2369-2373. (12) Nirmal, M.; Dabbousi, B. O.; Bawendi, M. G.; Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Nature 1996, 383, 802-804. (13) Blanton, S. A.; Dehestani, A.; Lin, P. C.; Guyot-Sionnest, P. Chem. Phys. Lett. 1994, 229, 317-322. (14) Empedocles, S. A.; Norris, D. J.; Bawendi, M. G. Phys. ReV. Lett. 1996, 77, 3873-3876. (15) Poles, E.; Selmarten, D. C.; Miæiæ, O. I.; Nozik, A. J. Appl. Phys. Lett. 1999, 75, 971-973. (16) Schaller, R. D.; Petruska, M. A.; Klimov, V. I. J. Phys. Chem. B 2003, 107, 13765-13768. (17) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. ReV. Mater. Sci. 2000, 30, 545-610. (18) Heeger, A. J. Mater. Res. Soc. Bull. 2001, 26, 900-904. (19) Yu, D.; Wang, C.; Guyot-Sionnest, P. Science 2003, 300, 12771280. (20) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706-8715. (21) Guyot-Sionnest, P.; Wang, C. J. Phys. Chem. B 2003, 107, 73557359. (22) Shimizu, K. T.; Woo, W. K.; Fisher, B. R.; Eisler, H. J.; Bawendi, M. G. Phys. ReV. Lett. 2002, 89, 117401-117404. (23) Achermann, M.; Hollingsworth, J. A.; Klimov, V. I. Phys. ReV. B 2003, 68, 245302. (24) Wang, C.; Shim, M.; Guyot-Sionnest, P. Science 2001, 291, 23902392. (25) Wang, C.; Shim, M.; Guyot-Sionnest, P. Appl. Phys. Lett. 2002, 80, 4-6. (26) Shim, M.; Guyot-Sionnest, P. Nature 2000, 407, 981-983. (27) Franceschetti, A.; Zunger, A. Phys. ReV. B 2000, 62, R16287R16290. (28) Klimov, V. I.; Mikhailovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Science 2000, 287, 1011-1013. (29) Wehrenberg, B. L.; Guyot-Sionnest, P. J. Am. Chem. Soc. 2003, 125, 7806-7807.
