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J. Phys. Chem. C 2008, 112, 10668–10673
Temperature Dependence of Photoluminescence Dynamics in Colloidal CdS Quantum Dots D. Kim,* T. Mishima, K. Tomihira, and M. Nakayama Department of Applied Physics, Graduate School of Engineering, Osaka City UniVersity, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan ReceiVed: January 29, 2008; ReVised Manuscript ReceiVed: May 11, 2008
We have investigated the temperature dependence of photoluminescence (PL) dynamics in CdS quantum dots (QDs) prepared by a colloidal method. A size-selective photoetching process and a surface modification technique with a Cd(OH)2 layer enabled us to prepare size-controlled CdS QDs with high PL efficiency. The PL decay profiles became slower with an increase in temperature, contrary to an ordinary behavior. We have revealed that such anomalous temperature dependence of the PL-decay profile is explained by a three-state model consisting of a ground-state and two excited states: a lower-lying bound-exciton state and a higherlying free-exciton state (the “dark-exciton state”) having an optically inactive triplet nature. 1. Introduction In the past two decades, semiconductor quantum dots (QDs) have attracted considerable attention to understand the size dependence of their physical and/or chemical properties.1–4 Semiconductor QDs exhibit distinct photoluminescence (PL) properties owing to quantum confinement effects on their electronic structures. One of the most characteristic PL properties of QDs is the observation of an optically passive state, the so-called dark-exciton state.5–12 The origin of the dark-exciton state is basically a spin triplet state that is forbidden for optical transitions by the spin-selection rule. In a bulk crystal, thermal effects inhibit the observation of the triplet-exciton state since the spin-exchange-splitting energy is usually smaller than 1 meV. On the contrary, in a QD system, the quantum confinement effect enhances the spin-exchange interaction, which results in a large splitting energy between the spin singlet and triplet states. In particular, the splitting energy in a smaller QD becomes considerably larger, becoming comparable to or exceeding the thermal energy at room temperature in some cases, owing to the strong quantum confinement effect. This effect is connected with our motivation in the present work. In Si QDs, the previous studies7,8,12 have reported clear evidence for the contribution of the spin-triplet exciton state to PL processes, where the exchange-splitting energy ranges from 5 to 20 meV depending on the QD size. In colloidal CdSe QDs, long radiative lifetimes (τR ∼ 1 µs at 10 K) relative to the exciton recombination time in bulk crystal were usually observed.5,6 Efros et al. theoretically revealed that a hexagonal crystal field, a nonspherical QD shape, and quantum-confinement-enhanced exchange interaction between the electron and the hole lift the degeneracy of the band-edge exciton states and result in a splitting into “bright”- and “dark”-exciton states.6 Ever since the synthesis of high-quality, size-tunable, and monodispersed CdSe QDs became established, detailed experimental results on the band-edge exciton states have been reported.5,6 In comparison with CdSe QDs, there have been few reports on the dark-exciton state in CdS QDs. Furthermore, the details of PL mechanisms in CdS QDs have not been settled. This * To whom correspondence should be addressed. E-mail: tegi@ a-phys.eng.osaka-cu.ac.jp.
situation in CdS QDs is mainly due to the fact that a defectrelated PL band is dominant in CdS QDs,13,14 except for in a few samples.11,15–17 Li et al. theoretically predicted that the optically passive 1P state becomes the ground hole state and that the splitting energy between the bright- and dark-exciton states in CdS QDs is much larger than that in CdSe QDs.18 Very recently, Demchenko and Wang reported that in CdS QDs, the dark-exciton state originates not from the P-like optically forbidden state but from exchange splitting.19 In ref 11, Yu et al. experimentally observed a large splitting energy between the bright- and dark-exciton states, which is ∼4 times larger than CdSe QDs. Although they measured decay profiles of the band-edge PL, the details of the recombination mechanism in CdS QDs have not been revealed until now. In order to understand the PL mechanism, it is necessary to conduct systematic studies of the temperature dependence of the PL spectrum and PL-decay profiles. Crooker et al. measured temperature-dependent PL decay times in colloidal CdSe QDs and discussed their experimental results, considering the thermal activation process from the dark-exciton state to the brightexciton state.20 However, most of the studies on PL properties of colloidal QDs have been limited to solution samples. Thus, little attention has been paid to the temperature dependence of PL properties so far because precise temperature-dependence experiments require film samples for controlled temperatures from ∼10 K to room temperature. In solution samples, such a wide range of temperatures is impossible in principle. In the present paper, we have investigated PL dynamics in surface-modified colloidal CdS QDs. CdS QDs with a narrow size distribution of ∼5% were prepared using a size-selective photoetching treatment.21–23 The intensity of the band-edge PL was remarkably increased by the surface modification of the QDs. In order to investigate the temperature dependence of the optical properties, we dispersed size-controlled and surfacemodified colloidal QDs into polyvinyl alcohol (PVA) films. The successful preparation of the size- and surface-controlled QDs enabled us to observe the precise temperature dependence of absorption spectra, PL spectra, and PL-decay profiles in CdS QDs. The PL-decay profiles became slower with an increase in temperature, which is contrary to ordinary behavior. This anomalous temperature dependence can be explained in terms of a three-state model including the dark-exciton state. It is
10.1021/jp8009172 CCC: $40.75 2008 American Chemical Society Published on Web 06/26/2008
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demonstrated that the dark-exciton state plays a major role in PL processes in CdS QDs even at room temperature. 2. Experimental Methods Colloidal CdS QDs were prepared by injecting H2S gas (0.2 mmol) into 100 mL of an aqueous solution containing 0.2 mmol Cd(ClO4)2 and 0.2 mmol sodium hexametaphosphate (HMP), which is a dispersive agent of colloids. CdS QDs grown in this manner have a wide size distribution of ∼30-40%. In order to reduce the size-distribution width, a size-selective photoetching treatment was performed by irradiating the sample solution with a monochromatic light.21–23 For the photoetching of the QDs, a 500-W Xe lamp was used as a light source. Monochromatic light was obtained using interference filters; the full-width at half-maximum intensity of the resulting monochromatic light was ∼10 nm. In PL spectra of CdS QDs prepared by the colloidal method, a surface-defect-related PL band is usually observed as the main PL band. A surface modification of QDs was performed to improve the PL properties. The QD surface was modified by the addition of Cd(ClO4)2 after adjusting the pH of the solutions to the alkaline region, which leads to formation of a Cd(OH)2 layer on the surface of the QDs.15 In order to investigate the temperature dependence of the optical properties, we dispersed colloidal QDs into polymer films as follows. The sample solution was mixed with a PVA aqueous solution. Then, the mixed solution was spread on a glass, and the excess water was evaporated by heating at 80 °C for 2 h. This process provided us film samples, that is, CdS QDs dispersed in PVA films. Absorption spectra were measured using a double-beam spectrometer with a resolution of 0.2 nm. For PL measurements, the 325-nm line of a He-Cd laser was used as the excitationlight source, and the emitted PL was analyzed with a single monochromator with the spectral resolution of 0.5 nm. For measurements of PL-decay profiles, third-harmonic-generation (THG) light (355 nm) of a laser-diode pumped yttrium aluminum garnet (YAG) laser with a pulse duration of 20 ns and a repetition of 10 kHz was used as the excitation light. The PL-decay profiles were detected with a streak-camera system. The sample temperature was controlled using a closed-cycle helium-gas cryostat. 3. Results and Discussions 3.1. Size-Selective Photoetching and Surface Modification of CdS QDs. Figure 1a shows the absorption and PL spectra of as-grown CdS QDs prepared by the colloidal method. The absorption structure is observed in a higher energy region than the band gap energy of ∼2.5 eV in a CdS bulk crystal, indicating the formation of CdS QDs. However, the spectral width of the absorption spectrum is very broad and no peak structure is observed because of the wide size distribution of the QDs. In the PL spectrum, the defect-related PL band with a large Stokes shift is dominant, and the band-edge PL band is negligibly weak. The observed absorption and PL spectra have been typical spectra of CdS QDs prepared by the colloidal method without surface modification.13,14 In order to solve the problem of the inhomogeneity of QD size, we performed size-selective photoetching.21,22 We irradiated monochromatic light obtained by using interference filters to the sample solution and increased the photon energy of the irradiation light in stages until a clear absorption peak was observed. After that, we performed surface modification of QDs by adding the Cd(ClO4)2 aqueous solution. Figure 1b shows
Figure 1. (a) Absorption and PL spectra for as-grown CdS QDs prepared by the colloidal method. (b) Absorption and PL spectra for CdS QDs after the photoetching process and after the surface modification.
the absorption and PL spectra of the surface-modified CdS QDs after the photoetching process. The absorption spectrum is significantly different from that of the as-grown sample. The observation of an absorption peak indicates that the sizedistribution width of the CdS QDs is considerably small. The mechanism of the size-distribution reduction is as follows.21,22 Among the QDs of different sizes, the QDs whose exciton energies are resonant with the irradiation-light energy are photoetched. Since the exciton energy of the QD increases with a decrease in the QD size, the QDs to be photoetched become smaller by increasing the irradiation-light energy. This process results in narrowing the size distribution.21 In a previous paper,23 we demonstrated that line-shape analysis with use of combination of Gaussian line shapes of the excitonic absorption is a reasonable and convenient method for estimating the magnitude of the size-distribution width. The estimated mean diameter and size distribution are 4 nm and 5%, respectively, in the present case. It is obvious that the PL spectrum of the surface-modified QDs is drastically changed from that of the as-grown sample. The band-edge PL band is strongly activated by the surface modification and is observed as the main PL band, contrary to the fact that the defect-related PL band is dominant in the asgrown sample. We note that the surface modification enhances the band-edge PL intensity by 103 times. These results demonstrate the success of preparing the size- and surface-controlled CdS QDs. QDs dispersed in solutions have been the focus of most of the research so far. Thus, there has been little investigation of the temperature dependence of the PL properties of CdS QDs. We dispersed colloidal QDs into PVA films to measure the temperature dependence of optical properties. 3.2. Temperature Dependence of Absorption and PL Properties. Figure 2 shows the temperature dependence of absorption and PL spectra of CdS QDs dispersed in PVA films. Multiple absorption peaks, which originate from the groundstate and from the higher excited states of excitons in the CdS QDs, are observed clearly. Figure 3a shows the temperature dependence of the lowest absorption peak energy. It is wellknown that the temperature dependence of the exciton energy in direct-gap semiconductors can be described by Varshni’s law;24 E(T) ) E(0) - RT2/(T + β), where E(0) is the exciton energy at T ) 0 K, R is the temperature coefficient, and β is a parameter related to the Debye temperature of the crystal. The solid curve indicates the calculated result for the temperature dependence of the absorption energy, where the parameter
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Figure 4. Temperature dependence of temporal profiles of the bandedge PL.
Figure 2. Temperature dependence of absorption and PL spectra for CdS QDs dispersed in PVA films.
Figure 3. (a) Temperature dependence of the lowest absorption peak energy. The solid curve indicates the calculated result using Varshni’s law. (b) Temperature dependence of the integrated intensity of the bandedge PL.
values of R ) 3.9 × 10-4 eV/K and β ) 219 K in a CdS bulk crystal were used. The calculated result using the parameters in bulk crystal quantitatively explains the experimental result, which indicates that the observed temperature dependence is an intrinsic optical property of the CdS crystal. As shown in Figure 2, the band-edge PL is observed as a main PL band at every temperature. The observation of the bandedge PL allows us to investigate the PL properties of CdS QDs in detail. Figure 3(b) shows the temperature dependence of the integrated intensity of the band-edge PL band. We noted that the intensity of the band-edge PL band even at room temperature was almost half-that at 20 K, which means that the thermalquenching effect is very small. The above results demonstrate that the nonradiative process is remarkably suppressed in the surface-modified CdS QDs. Thus, it is possible to investigate the temperature dependence of the PL dynamics in detail. 3.3. Time-Resolved PL Study. Figure 4 shows the temporal profiles of the band-edge PL band at 40, 80, 100, 140, and 180 K. In this temperature range, temporal profiles become slower with an increase in temperature. In the usual case, as the temperature is increased, the nonradiative-decay rate becomes
larger, so that the PL intensity and the PL decay time are decreased. As shown in Figure 3b, the intensity of the bandedge PL band is slightly decreased with an increase in temperature, although the influence of thermal quenching is very small. Nevertheless, the observed decay profiles become longer, which is contrary to the above scenario. In order to explain the anomalous temperature dependence of the decay profiles, we have to consider that at least two radiative states contribute to PL processes: a lower-lying emitting state with a relatively fast decay profile and an upper-lying emitting state with a relatively slow decay profile. On the basis of this model, we can expect that the population in the upper state with a slow decay component is increased with an increase in temperature by the thermal excitation from the lower state with a fast decay component, leading to prolongation of the decay profiles. The PL-decay profile has a slow decay time in the order of hundreds of nanoseconds. This long decay-time component suggests that the optically passive state, the so-called darkexciton state, contributes to the PL process. Thus, we attribute the upper-lying emitting state with a slow decay component to the dark-exciton state. Since the dark-exciton state is a “freeexciton” state, we have to consider a “bound-exciton” state as the origin of the lower-lying emitting state. In fact, the surfacerelated shallow-bound state has been discussed in CdSe,25–27 CdTe,28,29 and InP QDs30 so far. Nirmal et al. reported the surface localization of photoexcited excitons in CdSe QDs by measuring size-selective PL spectra and PL-decay profiles.25 Califano et al. suggested that that surface states greatly influence the PL-decay times in colloidal CdSe QDs.27 Wang et al. reported the contribution of surface states to the PL process by measuring time-resolved PL in highly luminescent CdSe QDs.26 Furthermore, Wang et al. provided a proof of the existence of surface states from the results of up-converted PL with an ultrashort time resolution in CdTe QDs.28 Thus, we attribute the lower-emitting state with a fast decay component to the shallow-bound-exciton state belonging to the bright-exciton state. 3.4. Three-State Model Including Dark-Exciton State. In order to explain the anomalous temperature dependence of the decay profiles, we propose the three-state model shown in Figure 5a: a ground state |g> and two excited states of a lower-lying shallow-bound-exciton state |Bx> and a higher-lying darkexciton state |Dx>. Here, the bound-exciton state |Bx> lies below the dark-exciton state |Dx> by an energy spacing of ∆E. Li et al. theoretically predicted the existence of the dark-exciton state in CdS QDs.18 According to their calculations, the splitting energy between the bright- and dark-exciton states in CdS QDs with a radius of ∼2 nm is ∼40 meV. Demchenko and Wang reported the comparable exchange splitting energy in CdS
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Figure 6. Temporal profiles of the band-edge PL at 80 and 140 K (open circles). The solid curves indicate the best fits with a combination of one monoexponential and one stretched exponential functions.
Figure 5. (a) Schematic energy levels of the three-state model in CdS QDs. (b) Calculated result for the temperature dependence of the decay time using eq 1.
QDs.19 It is noted that this value is much larger than the thermal energy at room temperature. We assumed a Boltzmann distribution of excitons between the bound-exciton state |Bx> and the dark-exciton state |Dx> on the basis of a statistical ensemble of QDs.20 Under such conditions, the rate equation for the total number of the excitons N is given as
nDx nBx dN )dt τDx τBx
(1)
where nDx (nBx) and 1/τDx (1/τBx) denote the exciton number and the radiative-decay rate of the dark-exciton state |Dx> (the bound-exciton state |Bx>), respectively. By considering the density of states, gDx for |Dx> and gBx for |Bx>, the ratio of the exciton number between |Dx> and |Bx> is given as
(
nDx gDx ∆E ) exp nBx gBx kBT
)
(2)
From equations 1 and 2, we obtain the decay rate, 1/τ, as
(
gDx 1 1 ∆E + exp kBT 1 τBx gBx τDx ) gDx τ ∆E 1+ exp gBx kBT
(
)
)
(3)
Figure 5b shows the calculated result for the temperature dependence of the decay time using equation 3 with τDx ) 1300 ns, τB ) 25 ns, ∆E ) 5 meV, and gDx/gBx ) 75. We note that these parameter values are related to the experimental results described below. The calculated result qualitatively explains the experimental one; namely, the PL decay becomes slower with an increase in temperature. Further quantitative analysis will be discussed below. 3.5. Analysis of Multiple-Exponential-Decay Profiles. The observed decay profiles consist of multiple-exponential components as shown in Figure 4. The superposition of PL bands with different decay-time constants results in multiple-exponential decay. In order to discuss the PL-decay profiles quantitatively, we analyzed them by a Kohlraush-WilliamsWatts-type function.31 The best fits were obtained with a combination of one monoexponential and one stretched expo-
Figure 7. Temperature dependence of the decay time of τ1 and 〈τ2〉.
nential function: A1 exp(-t/τ1) + A2 exp[-(t/τ2)β]. Here, the parameters A1 and A2 represent the relative weighting of the exponential component and stretched exponential decay one. Two examples of the analysis are shown in Figure 6. It is evident that the PL-decay profiles are reasonably explained by the fitting model in the whole time range, where the change of the PL intensity is of about three orders. It is noted that all of the decay profiles can be fit with the same value of β ∼ 0.48. In general, β < 1 represents the statistical distribution of exponential components with different decay times, which seems to be mainly due to the random size distribution of QDs in this case. The visible PL, the so-called S band, in porous Si is a typical case for which the PL decay is well described by a stretched exponential function.32–34 Mauckner et al. presented a simple approach to evaluating the distribution of decay time and the statistical average PL-decay time 〈τ〉 from experimentally observed stretched-exponential PL decays.33 We estimated an average decay time of 〈τ2〉 using their treatment. Figure 7 shows the temperature dependence of 〈τ2〉 and the fast decay time of τ1 estimated from the single exponential function. The slow decay time of 〈τ2〉 becomes slower with an increase in temperature up to 160 K, while the value of τ1 does not change remarkably. The tendency of 〈τ2〉 to increase with temperature in the temperature range up to 160 K well corresponds to the temperature dependence of τ calculated using equation 3. Thus, we assigned the slow decay time of 〈τ2〉 to the decay time that is characterized by the three-state model described above. We considered the inhomogeneity of ∆E, which corresponds to the energy difference between the dark-exciton state and the boundexciton state, as the origin of the distribution of the decay time. It is evident from equation 3 that the PL-decay profiles in QDs with smaller ∆E values exhibit longer components. The fast decay time of τ1 is 30∼40 ns, which is comparable to a decay time of a bright-exciton state in CdSe QDs. Crooker
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Figure 9. Temperature dependence of the decay time of 〈τ2〉 (closed circles). The broken and solid curves indicate calculated results for the temperature dependence of the decay time using eq 1 without and with consideration of the nonradiative decay rate, respectively.
Figure 8. (a) Temperature dependence of the stretched-exponential component, exp[-(t/τ2)β2], where τ2 and β2 are the best-fit parameters for the observed PL-decay profiles. (b) Calculated result for the temperature dependence of the decay time using equation 1 at τDx ) 1300 ns, τBx ) 25 ns, and gDx/gBx ) 75. For ∆E, an appropriate Gaussian distribution with a mean value of 40 meV and with a dispersion of 30 meV was assumed.
et al. measured the temperature dependence of PL-decay profiles in CdSe QDs and reported that the decay time of 20 ns at room temperature almost corresponds to the decay time of the brightexciton state.20 Fisher et al. also observed a decay time of 20-40 ns using a single QD spectroscopy technique at room temperature and reported that the decay time hardly changes with the size of QDs.35 Thus, we attribute the fast decay component of τ1 to the decay time of a bright-exciton state in CdS QDs. Hereafter, we further discuss the temperature dependence of the slow-decay component that is characterized by the stretchedexponential decay. Figure 8a shows the temperature dependence of the stretched-exponential component, exp[-(t/τ2)β], where τ2 and β used here are the best-fit parameters evaluated from the observed PL-decay profiles. As mentioned above, the distribution of ∆E results in a distribution of the decay time. We calculated the PL-decay profiles on the basis of equation 3 with the assumption of a distribution of ∆E. The solid curve in Figure 8b represents the calculated result at τDx )1300 ns, τBx )25 ns, and gDx/gBx ) 75. For ∆E, we assumed an appropriate Gaussian distribution with a mean value of 40 meV and with a dispersion of 30 meV. The calculated results quantitatively explain the temperature dependence of the slow component of the PL-decay profiles. Thus, the dynamics of the band-edge PL in CdS QDs can be explained in terms of the present threestate model including the dark-exciton state and bound-exciton one. 3.6. Influence of a Nonradiative-Recombination Process. Finally, we quantitatively discuss the temperature dependence of 〈τ2〉 based on the three-state model. As the temperature increased up to 160 K, 〈τ2〉 became longer as shown in Figure 9, where closed circles denote the temperature dependence of 〈τ2〉. Then, 〈τ2〉 is almost constant between 160 and 200 K. A further increase in temperature causes a decrease in 〈τ2〉. The broken curve represents the calculated result of τ on the basis of equation 3 at τDx ) 1300 ns, τBx ) 25 ns, gDx/gBx ) 75, and ∆E ) 5 meV. The calculated result quantitatively explains the temperature dependence of 〈τ2〉 up to 160 K. At temperatures
higher than 160 K, the calculated result still increases gradually, while 〈τ2〉 begins to decrease. The discrepancy between the calculated and the experimental results is considered to be due to the influence of the nonradiative recombination process because equation 3 represents only the “radiative” decay rate in the three-state model. The band-edge PL intensity slightly decreases with an increase in temperature, as shown in Figure 3b, in the temperature range between 20 and 150 K. Then, there is a plateau region between 150 and 200 K. A further increase in temperature reduces the PL intensity. On the other hand, the decay profiles are prolonged with an increase in temperature up to 200 K. At temperatures higher than 200 K, the PL-decay profiles become faster. The above experimental results indicate that the nonradiative decay process affects PL dynamics at temperatures higher than 200 K: the so-called thermal quenching. Thus, we take into account the temperature dependence of the nonradiative decay rate, 1/τnr(T), in the form of a well-known thermalactivation type, which is given as
( )
Ea 1 1 ) exp τnr(T) τnr(T ) 0) kBT
(4)
where Ea represents the thermal-activation energy for the nonradiative process. We calculated the temperature dependence of τ(T), which is defined as
1 1 1 ) + τ(T) τr(T) τnr(T)
(5)
where 1/τr(T) is given by eq 3. The solid curve in Figure 9 represents a calculated result with use of the fitting parameters of τnr(T ) 0) ) 30 ns and Ea ) 100 meV. The calculated result quantitatively explains the temperature dependence of 〈τ2〉. Thus, a slight decrease in 〈τ2〉 at temperatures higher than 200 K can be understood consistently by taking into account such a nonradiative process. It is noted that PL decay profiles exhibit a long decay time of hundreds of nanoseconds even at room temperature, which demonstrates the large contribution of the dark-exciton state to PL processes. This is owing to the large splitting energy between the bright- and dark-exciton states in CdS QDs compared with other semiconductor QDs such as CdSe, CdTe, and Si QDs. The existence of the slow component even at room temperature is an intrinsic feature peculiar to CdS QDs. 4. Conclusion We have investigated temperature-dependent PL dynamics in CdS QDs with a high PL efficiency. The intensity of the
Photoluminescence in Colloidal CdS Quantum Dots band-edge PL at room temperature is almost half-that at 20 K, which demonstrates remarkable suppression of the nonradiative process in the surface-modified CdS QDs. The decay profiles of the band-edge PL exhibit characteristic temperature dependence; they become slower with an increase in temperature. The temperature dependence of the PL-decay profiles is successfully explained in terms of a three-state model including the darkexciton and bound-exciton states. At higher temperatures, the thermal population of the higher-lying dark-exciton state is significant, and the decay time becomes longer. CdS QDs exhibit fairly long decay profiles in contrast with other semiconductor QDs. A noteworthy result in the PL decay profiles is the observation of a long decay time of hundreds of nanoseconds even at room temperature. This is owing to the large splitting energy between the bright- and dark-exciton states in CdS QDs. Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific research from Japan Society for the Promotion of Science. References and Notes (1) Woggon, U. Optical Properties of Semiconductor Quantum Dots; Springer: New York, 1996. (2) Yoffe, A. D. AdV. Phys. 2001, 50, 1. (3) Masumoto, Y.; Takagahara, T. Semiconductor Quantums Dots; Springer: New York, 2002. (4) Klimov, V. I. Semiconductor and Metal Nanocrystals; Marcel Dekker: New York, 2004. (5) Nirmal, M.; Norris, D. J.; Kuno, M.; Bawendi, M. Phys. ReV. Lett. 1995, 75, 3728. (6) Efros, A. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. Phys. ReV. B 1996, 54, 4843. (7) Reboredo, F. A.; Franceschetti, A.; Zunger, A. Phys. ReV. B 2000, 61, 13073. (8) Takeoka, S.; Fujii, M.; Hayashi, S. Phys. ReV. B 2000, 62, 16820. (9) Besombes, L.; Marsal, L.; Kheng, K.; Charvolin, T.; Dang, L. S.; Wasiela, A.; Mariette, H. J. Cryst. Growth 2000, 214, 742. (10) Halperin, E. J.; Awschalom, D. D.; Crooker, S. A.; Efros, A. L.; Rosen, M.; Peng, X.; Alivisatos, A. P. Phys. ReV. B 2001, 63, 205309.
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