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Continuous Distribution of Emission
States from Single CdSe/ZnS Quantum
Dots
Kai Zhang,
†
Hauyee Chang,
†,‡
Aihua Fu,
†
A. Paul Alivisatos,
†,§
and Haw Yang*
,†,
|
Department of Chemistry, UniVersity of California at Berkeley, and Materials Sciences
DiVision and Physical Biosciences DiVision, Lawrence Berkeley National Laboratory,
Berkeley, California 94720
Received March 1, 2006
ABSTRACT
The photoluminescence dynamics of colloidal CdSe/ZnS/streptavidin quantum dots were studied using time-resolved single-molecule
spectroscopy. Statistical tests of the photon-counting data suggested that the simple “on/off” discrete state model is inconsistent with
experimental results. Instead, a continuous emission state distribution model was found to be more appropriate. Autocorrelation analysis of
lifetime and intensity fluctuations showed a nonlinear correlation between them. These results were consistent with the model that charged
quantum dots were also emissive, and that time-dependent charge migration gave rise to the observed photoluminescence dynamics.
Colloidal semiconductor nanocrystals, or quantum dots
(QDs), have been the focus of much research effort in the
past decade. The development of these colloidal dots has
allowed the concepts of quantum confinement and dimen-
sional control of electronic and optical properties to find
entirely new areas of application, for instance in fluorescent
labeling of biological specimens. At the single-particle level,
however, colloidal QDs exhibit surprisingly complicated
time-dependent behavior in their photoluminescence (PL)
characteristics.
The first report of PL on-off intermittency from individual
QDs attributed the off period in a PL time trace to a
photoionized, charged state, and the off-to-on process to
reneutralization of the particle.1QD PL suppression by
photoionization is thought to result from an Auger-assisted
process.2This picture of photon-assisted charging was
confirmed by direct measurement of particle charges using
electrostatic force microscopy.3,4 The precise nature of the
charged state, however, remains unclear. The formation and
stabilization of charges in ZnS capped CdSe core-shell QDs
may involve electrons or holes that are trapped in states at
the surface of the CdSe core or at the surface of the ZnS
shell.5,6 Relocation of the external charge is thought to cause
the emission spectrum to vary with time.7
Statistical analyses of PL time trajectories from single QDs
provide further insight into the underlying dynamics. Within
the two-state framework, both the on- and off-state resident
times were found to exhibit a power-law distribution which,
in turn, may imply either an exponential distribution of trap
depths or a dynamically varying rate of reneutralization.8,9
To explain the prolonged on time, the neutral-on and
charged-off two-state model was recently extended to a three-
state model, permitting PL from a charged state where the
charge is trapped far away from the core.10 Taking together
the notion that charged QDs are also emissive and that there
exists a distribution of surface charge traps, one would expect
that location of surface charges should affect the emission
intensities11 such that they are not strictly on and off.
A schematic configuration for single-molecule optical
experiments is illustrated in Figure 1. Qdot655 streptavidin
conjugates from Quantum Dot Corp. (now Invitrogen, 1002-
1, lot no. 0104-0034) were used in this study. These QDs
were comprised of a core of CdSe capped by a layer of ZnS.
This core-shell material is further coated with a polymer
shell that allows conjugation of streptavidin. Transmission
electron microscopy (TEM) characterization of the morphol-
ogy for the same sample lot used in this study showed that
the average length, width, and aspect ratio were 11.9 (2.3
nm (19%), 6.95 (0.88 nm (13%), and 1.72 (0.37 (22%),
respectively (cf. Figure 1, inset B). Included in the paren-
theses are relative standard deviations. These TEM results
indicate that shape variations in individual QDs cannot be
ruled out in explaining the results from individual QDs.
The evaluation of single molecule trajectories can be
dramatically influenced by the time scale of binning (see
Figure 2 for an example of how a distribution of intensity
†Department of Chemistry, University of California at Berkeley.
‡Current address: Xradia Inc., Concord, CA.
§Materials Sciences Division, Lawrence Berkeley National Laboratory.
|Physical Biosciences Division, Lawrence Berkeley National Laboratory.
NANO
LETTERS
2006
Vol. 6, No. 4
843-847
10.1021/nl060483q CCC: $33.50 © 2006 American Chemical Society
Published on Web 03/21/2006
levels can be obscured by binning artifacts). The recently
developed changepoint method provides a statistically un-
biased and systematic method for analyzing such trajecto-
ries.12 In this method, the time instances at which the
emission intensity changes are accurately determined, one
photon at a time, using a log-likelihood ratio test, to reveal
new features such as intensity levels and fast transitions that
are likely to be blurred by binning. Bayesian information
criteria are employed to determine the number of discrete
intensity levels that are supported by the experimental data.
Here we apply this method to single QD photon emission
trajectories, to determine the nature of the intensity distribu-
tions.
The changepoint reconstructed intensity and lifetime
trajectories for the QD in Figure 2 are shown in Figure 3.
Visually, the reconstructed trajectory follows the binned raw
photon data very well. To assess the extent to which
dynamical information is recovered, fluctuation correlation
of 100-µs binned trajectory is compared with that of
changepoint reconstructed trajectory. Figure 4A shows that
dynamics from 1.8 ms to the length of the entire trajectory
(688 s) are quantitatively recovered. The relatively slowly
varying time-correlation curve on the 2-ms to 1-s time scales
(cf. Figure 4) is indicative of a prolonged bright state. This
is in agreement with the model for ZnS capped CdSe QDs
proposed by Verberk et al.,10 who extended the two-state
model (neutral-on and charged-off) to permit PL from a
charged state if the charge is trapped far away from the CdSe
core. The trapped charge in the emissive state frustrates
further photoionization via a Coulomb-blockade mechanism,
thereby allowing for a prolonged on state.
The luminescence lifetime in each changepoint determined
intensity segment can also be estimated14 and appears to be
positively correlated with the emission intensity (cf. Figure
3), indicative of dynamical quenching pathways.15,16 More
quantitative evaluation is made by comparing their respective
correlation functions. As illustrated in Figure 4, the intensity
and lifetime fluctuations exhibit significant differences on
time scales greater than 17 ms. To examine if the discrete-
Figure 1. Schematic of the single-molecule microscope and TCSPC photon registration scheme. Inset A shows a representative image of
single QDs, where blinking during raster scanning is evident (the dark, horizontal lines within each bright spot). Inset B is a representative
TEM image of the CdSe/ZnS/streptavidin quantum dots. Distributions of crystal length, width, and aspect ratio counted from more than
200 QDs are also shown. For each detection event, the time period between two sequentially detected photons (the interphoton duration,
∆) and the time lapse between the excitation pulse and the detection of luminescence photon (the microtime) are recorded and stored in a
computer for later data analysis.
Figure 2. A 11-min time-resolved trajectory of a single QD at
various bin times, illustrating how statistical characteristics are
affected by the choice of bin times. For example, shown on the
right of each time trace is the corresponding intensity histogram,
the shape of which apparently changes with bin time. The data
were taken using a time-stamped time-correlated single-photon
counting setup (cf. Figure 1).
844
Nano Lett.,
Vol. 6, No. 4, 2006
state model is suitable for describing the emission behavior
of single QD, we first find the most likely number of intensity
states that is supported by experimental data using the
Bayesian information criterion (BIC)12
where Ncp is the number of intensity change points, Nis the
number of photons contained in the trajectory, and LGis the
log-likelihood which evaluates how closely the nG-state
reconstructed intensity trajectory matches the original data.
The most likely minimum number of states that describe the
experimental time trace is nG
max that maximizes BIC. For
example, the QD shown in Figure 3 is found to be best
described by as few as three distinct states. While the number
of states determined by BIC analysis varies from particle to
particle, we found it generally true that a simple two-state
model is inadequate for describing the photophysics of a
single QD.
To investigate if photons within each BIC categorized
intensity group arise from the same emission state, we
examine the exponentiality of interphoton duration using a
Kolmogorov-Smirnov test.17 The hypothesis that the dis-
tribution is exponential is rejected with an error rate of Rif
where F*(∆m))∫0
∆m(1/∆h)e
(-∆/∆h)d∆is the cumulative
exponential distribution function with ∆h)1/n∑m)1
n∆m,
and Sn(∆m))m/nis the sample cumulative sum of ordered
interphoton durations {∆1e‚‚‚ e∆me‚‚‚ e∆n}.Inthe
current work, Ris chosen to be 1% and the critical value is
computed using R=1.25/N1/2 for Ne10 000. This
simplified test allows one to rapidly assess the confidence
level for the assignment of a discrete state or of a continuous
distribution, thereby placing visual examination (cf. Figure
5) on a statstically more robust footing. As an example of
this test, results for the QD on Figure 2 are summarized in
Table 1, suggesting that photons within each BIC group do
not arise from a single state with the same emission intensity.
This conclusion leads us to consider an alternative scenario
where the emission state is continuously distributed and
evolves with time.
To further characterize single QDs, we construct prob-
ability distributions of emission intensity (Iˆ) and lumines-
cence lifetime (τˆ), as well as their joint distribution function,
fluorescence lifetime-intensity distribution (FLID) map for
each QD
where σˆIi
2and σˆτi
2are respectively the expected variance for
intensity and lifetime in the ith changepoint segment. As an
example, the QD shown in Figure 2 is analyzed in Figure
Figure 3. (A) Typical result of changepoint reconstruction (with
95% confidence) for time-dependent emission intensity from a
single QD. The 3.5-ms binned intensity trace is shown in gray and
the reconstructed one as thick horizontal segments. Note those fast
transitions that are otherwise obscured by photon counting noise
are successfully recovered. (B) Luminescence lifetime from each
changepoint segment. Subpanels a-c: Representative microtime
histograms for different luminescence lifetimes (O), in which the
maximum likelihood fits are overlaid as solid lines.
Figure 4. (A) Comparison of intensity fluctuation correlation of
photon-counting trajectory (b) with that of changepoint recovered
trajectory (s). The zoomed difference trajectory is displayed at
the bottom where the 95% error bounds (‚‚‚) indicate that
information of intensity dynamics greater than 1.8 ms is quantita-
tively recovered. The correlation curve appears relatively flat at
short times, similar to those that have been reported for ZnS capped
CdSe nanocrystals.13 (B) Comparison of intensity (s) and lifetime
(‚-‚) fluctuation correlations of the changepoint-recovered trajec-
tory. While the faster dynamics (<17 ms) of emission intensity
and luminescence lifetime appear indistinguishable with 95%
confidence (‚‚‚), they are clearly different at longer times. The QD
shown in Figure 2 is used for this figure.
P(Iˆ,τˆ) )∑
i
1
2πσˆIiσˆτi
exp
[
-(I-Iˆi)2
2σˆIi
2
]
exp
[
-(τ-τˆi)2
2σˆτi
2
]
BIC )2LG-(2nG-1) ln Ncp -Ncp ln N
D)max
1emen{|F*(∆m)-Sn(∆m)|}>R
Nano Lett.,
Vol. 6, No. 4, 2006 845
5A. The top panel displays the overall Iˆdistribution, which
roughly exhibits two clusters. The lower-intensity cluster
peaks at ∼240 counts/s whereas the high-intensity one peaks
at ∼1700 counts/s with significantly more weight. This is
expected by visual examination of the raw trajectory, which
indicates that this particular QD spends significantly more
time on the “bright” state than on the “dark” state. There is,
however, finite probability of finding this particle at inter-
mediate intensity levels. While QDs have been shown to
possess a permanent dipole,18 it is unlikely that the observed
intensity distribution arises from dipole reorientation because
the overall polarization effect from our experimental setup
is about 10%, much less than observed intensity variations.
Turning to the emission lifetime, τˆ, its distribution on the
right panel appears to cluster around ∼25 ns, consistent with
the ∼20-ns room-temperature PL lifetime measurements of
high-intensity states.15,16,19 The correlation between Iˆand τˆ
is visualized by the FLID map displayed in Figure 5. In the
range between Iˆ)240 counts/s and Iˆ)1500 counts/s, τˆ
appears to depend linearly on Iˆ. At higher intensities (∼1500
counts/s eIˆe∼2100 counts/s), however, τˆ appears to
fluctuate around τˆ)25 ns instead of following the same
linear trend. This observation is consistent with the time-
correlation analysis in Figure 4, which shows that dynamics
of PL lifetime are quantitatively different from those of
intensity fluctuations.
In general, both the luminescence lifetime and emission
intensity are distributed continuously (cf. Figure 5A-C).
Higher-intensity states tend to exhibit longer luminescence
lifetimes, whereas lower-intensity states exhibit shorter life-
times. There is, however, no obvious linear relationship
between lifetime and intensity. For example, in parts A and
B of Figure 5, the τˆ/Iˆslope gradually decreases at higher
intensities. For some particles, on the other hand, the slope
becomes steeper at higher intensities as shown in Figure 5C.
Overall, there exists a wide distribution of FLID patterns
which vary from particle to particle. This, in turn, suggests
that FLID can be an effective tool to unravel the character-
istics of individual particles or molecules in general.
Our analysis of experimental results suggests that PL
intermittency of a single QD is inconsistent with discrete-
state models. Instead, single QD PL should be considered
as emanating from a distribution of emissive states, giving
rise to the observed broad intensity distribution. While
mechanisms including photoinduced reorganization of mo-
lecular absorbates at the surface,20 and photooxidation related
shape changes21 may also be operative, here we rationalize
the experimental observation generalizing the model pro-
posed by Verberk et al. to allow the characteristics of the
charge trapping state to vary as a function of time (cf. Figure
5D). The trapped charge is expected to modify the electronic
structure of the QD,11 likely to cause changes in the
absorption cross section and radiative lifetime. As a result,
both the radiative and nonradiative decay rates may change
as a function of time to give rise to the broad, time-varying
intensity distribution and distinct fluctuations in intensity and
lifetime. The broad distribution in emission intensity can be
understood as resulting from a distribution of positive charge
traps at the core-shell interface, or at the shell-streptavidin
layer. Over time, the charged QD may reneutralize but is
quickly photoionized under the excitation laser illumination,
or the charge may persist but migrate among the localized
trapping states, likely via a thermally activated process.22
Electrostatic force microscopy (EFM) shows single CdSe
nanocrystal can devolop a positive charge upon exposure to
weak, ambient light. Measurements taken during photoex-
citation show photoionization of individual nanocrystals.4A
fundamental understanding of the PL dynamiacs from a
single QD could eventually provide clues for a rational design
of nanostructures with tailored optical properties.23
Acknowledgment. We thank Professor E. Sa´nchez for
the generous gift of a scanning program. H.Y. acknowledges
financial support from the Office of Science, U.S. Depart-
Figure 5. (A-C) Representative fluorescence lifetime-intensity
distribution (FLID) of QDs. (A) is the QD shown in Figure 2. The
overall intensity distribution is shown on the top panel while that
of lifetime distribution is on the right panel. Darker color represents
longer dwelling time. A 50-ms binned photon trajectory is also
displayed in the inset as reference. The contour lines are for eye
guides only. (D) Illustration for the formation of a continuous
distribution of bright states. Photoionization induced charge can
migrate between different surface trapping sites. These charged
states where the positive trapping sites are away from the core,
can still emit photons when excited, giving rise to various PL
intensity. The QD switches to a dark state when the charge stays
at the center of the QD, or when there are multiple charges such
that nonradiative recombination becomes the dominant relaxation
path.10
Table 1. Kolmogorov-Smirnov Test of Exponentiality for
Every 10 000 Photons in the Time Trajectoriesa
state NnI(counts/s) D0.01
QD1 956749 10000 1806 0.0151 0.0125
QD2 78690 10000 1089 0.0176 0.0125
QD3 17784 10000 206 0.0399 0.0125
aNis the total number of photons found in each state, nis the number
of photons used in each exponentiality test, Iis the average intensity of
that BIC state. QD1, QD2, and QD3 are the intensity states for QD. These
assignments are based on the BIC-grouped analysis.
846
Nano Lett.,
Vol. 6, No. 4, 2006
ment of Energy, under Contract DE-AC03-76SF00098, from
the National Science Foundation, and from the University
of California at Berkeley. A.P.A. acknowledges support by
NIH National Center for Research Resources through the
University of California, Los Angeles, subaward agreement
0980GCD709 through the U.S. Department of Energy under
Contract No. DE-AC03-76SF00098, and by DOD Advanced
Research Project Agency under award No. 066995.
Supporting Information Available: Materials, descrip-
tions of experimental details, and data analysis algorithms.
This material is available free of charge via the Internet at
http://pubs.acs.org.
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NL060483Q
Nano Lett.,
Vol. 6, No. 4, 2006 847
