Charging and Discharging Channels in Photoluminescence

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Charging and Discharging Channels in Photoluminescence Intermittency of Single Colloidal CdSe/CdS Core/shell Quantum Dot Renyang Meng, Haiyan Qin, Yuan Niu, Wei Fang, Sen Yang, Xing Lin, Hujia Cao, Junliang Ma, Wanzhen Lin, Limin Tong, and Xiaogang Peng J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02448 • Publication Date (Web): 30 Nov 2016 Downloaded from http://pubs.acs.org on December 1, 2016

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The Journal of Physical Chemistry Letters

Charging and Discharging Channels in Photoluminescence Intermittency of Single Colloidal CdSe/CdS Core/shell Quantum Dot Renyang Meng,1 Haiyan Qin,*,1 Yuan Niu,1,2 Wei Fang,2 Sen Yang,2 Xing Lin,2 Hujia Cao,1 Junliang Ma,1 Wanzhen Lin,1 Limin Tong,2 and Xiaogang Peng*,1 1

Center for Chemistry of Novel & High-Performance Materials, Department of Chemistry, Zhejiang University, Hangzhou 310027, China.

2

State Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China.

*Corresponding Author Email: [email protected] Email: [email protected]

ACS Paragon Plus Environment

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ABSTRACT. Understanding photoluminescence (PL) intermittency of single quantum dot (QD)—intensity blinking by randomly switching between distinguishable brightness states under continuous excitation—has been a long-standing fundamental challenge and potential roadblock for their applications. Here we introduce a new analysis method for single-molecule spectroscopy that treats the blinking as photo-chemical/chemical processes (switching between neutral/bright and charged/dim states). It uncovers the channels for charging (bright to dim) and discharging (dim to bright) involved in PL blinking of single CdSe/CdS core/shell QDs. Both charging and discharging of the single CdSe/CdS core/shell QD possess a photochemical channel (~10-5-10-6 events/photon) that linearly depends on excitation in both single- and multi-exciton regime. These two linear channels coupled with a spontaneous discharging channel (~2 events/second) to dictate the QDs from non-blinking to gradually blinking under increasing excitation. For high quality CdSe/CdS core/shell QDs, Auger ionization of multi-exciton for both charging and discharging is negligible.

TOC GRAPHICS

KEYWORDS. Quantum Dots, Semiconductor Nanocrystals, Single-Dot Spectroscopy, Fluorescence Intermittency, Blinking Mechanism.


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Size-dependent luminescent properties of colloidal quantum dots (QDs)

1

promise them as

outstanding emissive materials. Photoluminescence (PL) intermittency of a single QD— randomly blinking by switching between distinguishable brightness states under constant excitation—was observed in 1996 2 and has then been a long standing mystery. Given constant excitation and continuous emission as pre-requisites for most applications of QDs as emitters, blinking casts significant doubts on their technical potential. Furthermore, blinking is an apparent roadblock for fundamental understanding and rational control of optical and optoelectronic properties of QDs.

It is known that charging of a neutral QD converts it from the bright state to an inefficient emission state—either dim or dark state. 2-4 Subsequent discharging of the dim/dark state would recover the bright state.

2-5

Inefficient PL of a dim/dark state is considered as a result of

nonradiative Auger recombination of a three-carrier excited state (a trion state).

2-8

Several

competitive charging mechanisms of a neutral QD are suggested, including Auger ionization of multi-exciton,

2, 4, 9-12

band-edge carrier ionization of single-exciton,

ionization prior to relaxation to form band-edge excitons.

8, 13

3, 11

and hot carrier

In comparison, discharging of the

dim state has been rarely investigated and suspected to be excitation-power independent. 2, 11

Identification of the blinking mechanism of QDs mostly relies on analysis of the PL intensity trajectory under constant excitation. Some reports further studied location and nature of the traps receiving the photo-generated charges of a quantum dot, which has not reached a general consensus at present. 14-20 If the charging (or discharging) involves only one elementary process, the bright (or dim) durations should follow single-exponential kinetics. Though single-


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exponential kinetics has been occasionally reported, and often approximated as power law statistics. selection of the bright-dim threshold,

15

21-23

24-26

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most cases are quite complex kinetics

As power law statistics may depend on

other statistic approaches excluding threshold selection,

such as change-point analysis 20, 27 and autocorrelation function, 28, 29 are proposed.

QDs applied for studying mechanisms of the PL blinking in literature varied a great deal. Here, we would concentrate on a series of high quality CdSe/CdS core/shell QDs in zinc-blende structure with 8 to 16 monolayers of the CdS shells, which are mono-exponential in PL decay dynamics, near unity in PL quantum yield, and nearly non-blinking in entire series.

30-32

This

series of QDs are sufficiently stable under relatively high excitation power and with high absorption cross section. We would further limit our systematic studies to charging/discharging kinetics of a QD. Studies on location or nature of the charges would be brief and only for supporting the kinetics model.

For convenience, CdSe/CdS core/shell QDs with x monolayers of CdS shell might be denoted as CdSe/xCdS QDs. Single-dot spectroscopy measurements are all performed on a home-built fluorescence microscopic system equipped with time-correlated single-photon counting (TCSPC) setup. QDs are excited by multiple pulsed lasers—a 450 nm laser being the default source—with tunable excitation repetition frequency (f) and variable number of photons absorbed per pulse for a single dot (〈N〉). Second order photon correlation measurements

33

(Figure S1) are applied for

confirmation of single-dot emission.


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Figure 1A illustrates PL intensity trajectories for a typical CdSe/16CdS QD at different levels of excitation power (〈N〉= 0.06-2, f = 1 MHz). From single-exciton to multi-exciton regimes, the PL intensity trajectory evolves from nearly non-blinking with a single bright state to bright-dim dual states blinking (also named as flickering 8). Increase of excitation power evidently accelerates the

Figure 1. PL properties of a single CdSe/16CdS QD. (A) Representative PL intensity time traces (black curves) of a single CdSe/16CdS QD under various excitation power (f = 1 MHz) with background noises (gray curves). Bin time is 30 ms. Distribution of the PL intensity is plotted to the right for each case. Bright and dim states are separated by dashed red lines. (B) Corresponding fluorescence lifetime-intensity distribution in color scale. Red (dark blue) corresponds to the most (the least) frequently occurring lifetimeintensity pair. ‘B’ and ‘D’ represent bright state and dim state, respectively. (C) PL decay curves of the photons from the bright (red curve) and dim state (blue curve) when 〈N〉 = 0.25. (D) PL decay curves of the photons from the bright (red curve) and dim state (blue curve) when 〈N〉 = 2. The inset is the early part of the decay curves.

bright-dim transition, and the bright and dim states tend to merge together as blinking getting very frequent, but the merged band can still be resolved under high time-resolution 34, 35 (Figure S2) and confirmed dual-state PL intermittency.


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The bright and dim states of the single CdSe/16CdS QD in Figure 1 possess a bin-averaged PL decay lifetime as ~70 and ~11 ns, respectively (Figure 1B). The bin-averaged lifetime value for the dim state is consistent with that of a negative trion emission.36 PL decay dynamics for both bright and dim states is nearly single-exponential at low excitation power (Figure 1C), and an additional bi- or multi-exciton component (~ 800 ps) occurs at high excitation power (Figure 1D and S3). Invisibility of this fast component in the bin-averaged PL decay lifetime plots (Figure 1B) suggests low PL quantum yield of the bi-exciton (or multi-exciton), consistent with the results obtained by second-order photon correlation measurements (Figure S1). This further indicates high efficiency of nonradiative Auger recombination of multi-exciton in the QDs.6

Previous results

30

revealed that high quality CdSe/CdS core/shell QDs employed in this work

significantly deviate from power law statistics. We notice that duration analysis is originated from the PL blinking of organic dyes, which is associated with high-frequency switching between singlet and triplet states—a photo-physical phenomenon.37 Due to their photochemical nature (charging and discharging), Figure 1 reveals that the probability of blinking of QDs is extremely low in comparison with that of organic dyes.37,

38

Nevertheless, this implies that

meaningful duration analysis based on single PL intensity trajectory would require extremely long experimental time for high optical quality QDs, especially in the single-exciton regime (see Figure 1A).

From a different viewpoint, the charging (bright to dim) and discharging (dim to bright) processes involved in a blinking cycle can be considered as photo-chemical (or chemical) kinetics. For any photo-chemical (or chemical) kinetics, its rate and rate constant are critical


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parameters for understanding its mechanism. Furthermore, the reaction order(s) of such a chemical (photo-chemical) process against the excitation photon density—the number of photons absorbed in unit time—should be insightful, given the process being associated with a single QD. Different from those blinking traces of QDs with continuous intensity distribution,

39, 40

blinking of the high quality CdSe/CdS core/shell QDs can be treated as binary blinking

the PL 30, 41

as

mentioned above. This simple blinking pattern makes the new analysis method involve only two types of switching events. ∞

ⓛ

+ n Bright (B) to dim (D): QD + n ⋅ hυ → QD + h , r( B→D) = ∑ kn (dhυ )

(1)

n=0

ⓛ

∞

n Dim (D) to bright (B): QD + n ⋅ hυ − e (or + h ) → QD , r( D→B) = ∑ k 'n (dhυ ) −

+

(2)

n =0

In Equations (1) and (2), both charging (“bright to dim”) rate ( r( B→D) ) and discharging (“dim to bright”) rate ( r( D→B) ) are expressed as a sum of a series of elementary kinetic processes against excitation photon density (dhv) with specific rate constants (kn and k’n). By identification of the number of photon (n) involved in an elementary process, we may distinguish different blinking mechanisms.

It should be pointed out that, if blinking involves multiple dim/dark states, similar equations could be formulated as long as the states are optically resolvable in the PL intensity trajectory. For those complex kinetics, one set of formulates between any two given states can be formulated, which shall reveal relationship between two states involved.


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The charging and discharging rates ( r( B→D) and r( D→B) ) are calculated as follows.

r( B→D) = N( B→D) / tB

(3)

r(D→B) = N(D→B) / tD

(4)

N(B→D) ( N(D→B) ) is the total number of “bright to dim” (“dim to bright”) events within the total bright duration tB (total dim duration tD) of a blinking trajectory (see Figure 2A).

Equations (3) and (4) shall collapse all data points in one PL intensity trajectory at a given excitation power into a single set of r(B→D) and r(D→B). This strategy treats each event of excitation as one repeating experiment of its kind, i.e., either QD at its bright state or QD at its dim state. Similar strategy is typical for chemical kinetics though it is unnecessary for analysis of the PL blinking of organic dyes.

By applying multiple excitation powers, one can then employ Equations (1) and (2) to obtain the reaction order(s) and corresponding rate constant(s) for either charging or discharging processes. It should be noted that, though it was analyzed differently, excitation-power dependence of single QD PL was studied previously. 2, 11, 21

Analysis reveals that the charging and discharging rates for the QD in Figure 1A linearly increase with excitation photon density in either single-exciton or multi-exciton regime (see Figure 2B). This indicates that both charging and discharging processes are irrelevant to Auger


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ionization involving bi- or multi-exciton. This is so because the order against excitation photon density of any Auger ionization should be 2 or greater.

In Figure 2B, the linear function of charging

goes

discharging

through

possesses

origin a

but

non-zero

intercept (1.8 events/second). This means that, in addition to the linear channel, discharging also possesses a “zero order” (or spontaneous) channel according to Equation

(2).

Results

on

varying

repetition frequency (f) (Figures 2C and Figure 2. Reaction kinetics of charging and discharging of PL blinking. (A) Schematic illustration for the calculation of the blinking rates. (B) Charging and discharging rates versus 〈N〉 and (C) variable f of a single CdSe/16CdS QD. (D) Charging and (E) discharging rates versus 〈N〉 for single CdSe/8CdS, CdSe/10CdS, and CdSe/16CdS QD. (F) Linear charging and discharging rate constants versus the shell thickness with inverse proportional fitting (dotted lines). (G) Spontaneous discharging rates k’0 versus the shell thickness with exponential fitting (dotted line). The error bars are calculated standard deviations for 20 single QDs for each sample.

S4) unambiguously confirm existence of a spontaneous (or non-photochemical) discharging channel, given the accurate zero point and linearity of the excitation photon density. The kinetics is found to be reproducible (Figures S4 and S5), and different CdS shell thicknesses does not

change the kinetics qualitatively (Figures 2D and 2E).


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The charging and discharging rate constants (k and k’, with n =1 for both) of the linear channels for QDs with different shell thickness are determined by the slope in the corresponding rate-〈N〉 plot using Equations (1) and (2) (Figures 2D and 2E). Statistic results of k’0 (the rate constant for the spontaneous discharging), k, and k ' for multiple dots from each shell thickness are summarized in Figures 2F and 2G. Though the ionization probability for both linear charging and discharging channels of single QD is rare (10-6 to 10-5), they are on the same order of magnitude observed using electrostatic force microscopy by the Brus’ group. 42

Results above (see Figures 2B, 2D, and 2E for examples) reveal that, by varying 〈N〉 in the range between 0.06 and 2, both charging and discharging rates universally increase with a linear function against excitation photon density. This implies that each photon-generated hole (or electron) contributes equally to the charging/discharging no matter whether it is in single- or multi-exciton regime. Experiments with varying excitation repetition frequency f further confirm this phenomenon. With a fixed number of photons absorbed by a QD in one pulse (〈N〉), the excitation power density (or the excitation rate) increases linearly with the increase of the laser repetition frequency. In order to avoid altering the yield of multi-excitation, the excitation repetition rate is kept to be much lower than the PL decay rate of the QDs. By fixing 〈N〉 within a relative low value (see the corresponding blinking trace in Figure 1A), linear dependence on photon density and identical rate constants (k, k ' , and k’0) are obtained by changing f (Figures 2C and S4).

The above results suggest hot-carrier charging/discharging for the linear channels, instead of band-edge (or the ground state of exciton/multi-exciton) carrier ionization. As shown in Figure


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1D, after relaxing to their ground states, the lifetimes of single-exciton and multi-exciton differ from each other by ~2 orders of magnitude. Thus, a band-edge carrier ionization channel with a universal rate constant (either k or k ' ) would be impossible to efficiently compete with both single-exciton

and

multi-exciton

recombination.

Further

evidences

for

hot-carrier

charging/discharging for the linear channels come

from

the

wavelength-dependent

excitation (Figure 3), which reveal strong increase of the rate constants—the slopes in the plots—with the increase of energy of the excitation photons. It should be pointed out that similar wavelength-dependence of PL blinking probability was observed by the other groups. 13, 21, 43

Figure 3. Excitation wavelength-dependent blinking rates. (A) The charging rates for “bright to dim” excited at 375, 445, and 517 nm of a single CdSe/16CdS QD. (B) The discharging rates for “dim to bright” excited at 375, 445, and 517 nm of a single CdSe/16CdS QD. Dotted lines are fitting functions.

Though results above cannot completely rule out band-edge exciton ionization, hot-carrier ionization should play an important role. Considering the hot-carrier ionization for both linear channels, we attempt to fit the photo-induced rate constants (k and k ' ) with a depletion-zone model. This simple model implies the probability of ionization should be inversely proportional to the CdS shell thickness of a QD, which offers decent fitting for both k and k ' (Figure 2F).

Results in Figure 3B further support existence of a spontaneous channel. Different from the slopes, the intercepts in Figure 3B are independent on the energy of excitation photons. This fact


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along with the small k’0 prompts us to consider a tunneling mechanism for the spontaneous discharging, which gives a reasonable fitting in Figure 2G.

Figure 2F shows that the probability of charging, or probability to initiate a blinking cycle by absorbing one photon, is rather low (10-5-10-6 events/photon) and decreases with the shell thickness. In comparison, with similar shell-thickness dependence, probability of the hot-carrier discharging is only about ~2 times larger (Figure 2F). This means that, if a QD is highly resistant to photo-initiated “bright to dim”, it would also be highly resistant to photo-initiated “dim to bright”. Therefore, without contribution of the spontaneous discharging channel, a QD should be in either long bright durations or long dim durations, which would be qualitatively different from the PL intensity trajectories in Figure 1A. Therefore, with a relatively low excitation power, it is the spontaneous discharging (Figure 2G, ~2 event/s in average) that substantially shortens the duration of the “dim” state. In literature, the Bawendi’s 44 and our 30 groups observed this type of nearly non-blinking behavior, i.e., with short “dim” durations—cutoff of the “dim” duration being ~1 s in both reports—and long “bright” durations for CdSe/CdS core/shell QDs. Such nearly non-blinking behavior was only confirmed recently for the CdSe/CdS core/shell QDs with near-unity PL quantum yield 30, 44 because it has to work with a low 〈N〉.

Results in Figure 2G imply that, as the CdS shell thickness increases, the spontaneous discharging channel became inefficient exponentially. To ensure a decent recovery of the bright state from the charged/dim state of those “giant QDs”,

45, 46

the excitation power should be

reasonably high. This would simultaneously increase the probability of “bright to dim”. Overall, the PL intensity trajectory would thus become frequently switching between a bright state and a


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“not so dark” dim state.

45

With low temporal resolution, these two states merge into a broad

intensity band in the trajectory. In fact, for CdSe/16CdS core/shell QDs, such type of nonblinking could be reproduced by increasing the excitation power (Figure S7).

High excitation power, such as 〈N〉 = 2 in Figure 1A, results in relatively high frequency of blinking, which can be applied for the traditional “on” and “off/dim” duration statistics. Though the scattered data might indicate a narrow distribution of time constants,

20

2, 24, 37

a single-

exponential and double-exponential distribution can respectively fit the “bright” and “dim” durations reasonably (Figure S8). The fitting parameters are consistent with those in Figure 2B. In literature, quasi single-exponential distribution of “bright” durations was reported by several groups

21-23, 35

though most publications reported a multi-exponential (approximated as power

law) distribution. 24-26

It should be pointed out that, though power law statistics has been proposed to represent complex multi-exponential distribution of the durations, they are mathematically different from each other.

47

Mathematically, it requires infinite numbers of exponentials to fit the entire range of a

power-law function. A given part of a power-law function within a limited time range and a finite set of single-exponential functions can be numerically the same, which is likely the case for the duration statistical analysis. However, combination of a finite number of singleexponentials would be convergent in its first moment, but power law distribution would be analytically divergent (see Supporting Information). For a high quality QD with a finite size, the number of charging/discharging channels—the number of exponential components in the rates—


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should be limited. These facts imply that power law statistics should only be an approximate representation of the charging/discharging processes of single QD.

Efficient and well-defined discharging channels, especially the spontaneous channel, imply that the trapped charge should be at close proximity to the nanocrystal-ligand interface of a QD, similar to that suggested in literature.16-18, 48 Thiolates—well-known hole-trapping ligands—are placed onto the QDs, which indeed accelerates blinking.

49

By placing a monolayer of ZnS—a

very wide-bandgap semiconductor—between the CdSe/CdS core/shell QD and its ligands, the blinking is significantly suppressed (Figure S9).

In summary, quantitative measurements combined with a new analysis method can resolve different channels involved in the PL blinking of single QDs. For mostly developed CdSe/CdS core/shell QDs, Auger ionization of multi-excitons is not playing a noticeable role in both charging and discharging though nonradiative Auger recombination does occur efficiently for either bi-excitons or trions. The model and conclusions presented here might be applicable for high quality QDs, but might not be directly applicable for QDs with poorly-defined defects or under special experimental conditions, e.g. QDs with B-type blinking.

50

However, the results

disclosed here should still shed some light for understanding various phenomena associated with the PL blinking of all types of QDs. The results here indicate that QDs with non-blinking properties and high fluorescence quantum yield under continuous excitation are realistic as long as the photo- and electro-excitation is not excessive. Furthermore, the mechanisms provide guidelines for designing next generation of non-blinking QDs, which covers nearly the entire visible window. 51


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Experimental Methods Synthesis and ligand exchange of CdSe/CdS core/shell QDs. The zinc-blende CdSe/CdS core/shell QDs with different shell thicknesses were synthesized using the published procedures.30 For the ligand exchange procedure, the original ligands were replaced by 1dodecanethiol for the CdSe/8CdS sample. An excess of thiol ligands (400 molecules per nanocrystal) were added into the CdSe/CdS QD solution and reacted for ~ 3 hours to ensure completion of the ligand exchange.49 Synthesis of CdSe/CdS/ZnS core/shell/shell QDs. After targeted CdSe/CdS QDs had been synthesized,

no

further

purification

was

performed.

Instead

of

the

cadmium

diethyldithiocarbamate precursor solution, zinc diethyldithiocarbamate (Zn(DDTC)2) was used for ZnS outer monolayer growth. For example, the growth of a single monolayer of ZnS outside the CdSe/8CdS, 0.63 mL of Zn(DDTC)2 - dodecane - amine solution (0.1 mmol/mL) was injected into CdSe/CdS QDs solution at 80 °C. The temperature was set at 150 °C for 20 minutes for growth of the ZnS shell. Optical measurements on single QDs. For single-dot spectroscopy experiments, a diluted QD solution with 3% PMMA in toluene by weight was spun casted on a clean glass coverslip. Single QD optical measurements were performed using a home-built epi-illumination fluorescence microscope system equipped with a 63x oil immersion objective (Zeiss, NA = 1.46) and suitable spectral filters. A 450 nm pulsed laser (PicoQuant, ~50 ps) with tunable excitation repetition frequency was used as the default excitation light source.


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Using a turnover mirror, the photoluminescence signals of single QDs were collected and sent to an EMCCD camera (Andor, iXon3 DU-897) or a time-correlated single-photon counting (TCSPC) system for blinking or time-resolved measurements. Excitation wavelength-dependent measurements for single QDs were carried out by an Olympus IX 83 microscope with a 60x oil immersion objective (NA = 1.49). A series of pulsed picosecond lasers (A.L.S. GmbH, PiL037X, PiL044X and PiL051X) were used as the excitation sources. Using suitable dichroic beamsplitter and long-pass filter (Semrock), the emission signals from the QDs were collected and sent to an EMCCD (Andor, iXon Ultra 897). All optical measurements were performed at room temperature under low relative humidity (< 40 %). More detailed descriptions of methods used in this work could be found in Supporting Information.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Experimental conditions and methods for data analysis; mathematical analysis of power-law and exponentials; antibunching curve; blinking traces with different bin times, repetition rates, shell thicknesses, excitation power and QD systems; duration probability densities; trion properties.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]


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*Email: [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (NSFC, No. 21233005, 21303159, 21573194 and 91433204) and Fundamental Research Funds for the Central Universities (2014FZA3006). REFERENCES (1) Brus, L. E. Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state. J. Chem. Phys. 1984, 80, 4403-4409. (2) Nirmal, M.; Dabbousi, B. O.; Bawendi, M. G.; Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Fluorescence intermittency in single cadmium selenide nanocrystals. Nature 1996, 383, 802-804. (3) Efros, A. L.; Rosen, M. Random telegraph signal in the photoluminescence intensity of a single quantum dot. Phys. Rev. Lett. 1997, 78, 1110-1113. (4) Krauss, T. D.; Brus, L. E. Charge, polarizability, and photoionization of single semiconductor nanocrystals. Phys. Rev. Lett. 1999, 83, 4840-4843. (5) Efros, A. L. Nanocrystals: Almost always bright. Nat. Mater. 2008, 7, 612-613. (6) Wang, L. W.; Califano, M.; Zunger, A.; Franceschetti, A. Pseudopotential theory of Auger processes in CdSe quantum dots. Phys. Rev. Lett. 2003, 91, 056404. (7) Spinicelli, P.; Buil, S.; Quelin, X.; Mahler, B.; Dubertret, B.; Hermier, J. P. Bright and Grey States in CdSe-CdS Nanocrystals Exhibiting Strongly Reduced Blinking. Phys. Rev. Lett. 2009, 102, 136801. (8) Galland, C.; Ghosh, Y.; Steinbruck, A.; Sykora, M.; Hollingsworth, J. A.; Klimov, V. I.; Htoon, H. Two types of luminescence blinking revealed by spectroelectrochemistry of single quantum dots. Nature 2011, 479, 203-7. (9) Chepic, D. I.; Efros, A. L.; Ekimov, A. I.; Vanov, M. G.; Kharchenko, V. A.; Kudriavtsev, I. A.; Yazeva, T. V. Auger Ionization of Semiconductor Quantum Drops in a Glass Matrix. J. Lumin. 1990, 47, 113-127. (10) Klimov, V. I.; McBranch, D. W. Auger-process-induced charge separation in semiconductor nanocrystals. Phys. Rev. B 1997, 55, 13173-13179.


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