Direct probe of spectral inhomogeneity reveals synthetic
tunability of single-nanocrystal spectral linewidths
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Cui, Jian, Andrew P. Beyler, Lisa F. Marshall, Ou Chen, Daniel
K. Harris, Darcy D. Wanger, Xavier Brokmann, and Moungi G.
Bawendi. “Direct probe of spectral inhomogeneity reveals
synthetic tunability of single-nanocrystal spectral linewidths.”
Nature Chemistry 5, no. 7 (June 2, 2013): 602-606.
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http://dx.doi.org/10.1038/nchem.1654
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Nature Publishing Group
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Thu May 26 20:40:20 EDT 2016
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Detailed Terms
Direct Probe of Spectral Inhomogeneity Reveals Synthetic Tunability of
Single-Nanocrystal Spectral Linewidths
Jian Cui, Andrew P. Beyler, Lisa F. Marshall, Ou Chen, Daniel K. Harris,
Darcy D. Wanger, Xavier Brokmann and Moungi G. Bawendi
Department of Chemistry, Massachusetts Institute of Technology
Cambridge, Massachusetts 02139, USA
May 1, 2013
Abstract
The spectral linewidth of an ensemble of fluorescent emitters is dictated by a combination of the single emitter linewidths and sample inhomogeneities. For semiconductor nanocrystals, efforts to tune ensemble linewidths for optical applications have focused primarily on eliminating sample inhomogeneities
because conventional single-molecule methods cannot reliably build accurate ensemble-level statistics for
single-particle linewidths. Photon-correlation Fourier spectroscopy in solution (S-PCFS) offers a unique
approach to investigating single-nanocrystal spectra with large sample statistics, without user selection
bias, with high signal-to-noise ratios, and at fast timescales. With S-PCFS, we directly and quantitatively deconstruct the ensemble linewidth into contributions from the average single-particle linewidth
and from sample inhomogeneity. We demonstrate that single-particle linewidths vary significantly from
batch to batch and can be synthetically controlled. These findings crystallize our understanding of the
synthetic challenges facing underdeveloped nanomaterials such as InP and InAs core/shell particles and
introduce new avenues for the synthetic optimization of fluorescent nanoparticles.
The past twenty years have seen great advances in the synthetic control over many critical properties
of colloidal semiconductor quantum dot nanocrystals (NCs) such as size polydispersity [1], quantum yield
[2], photostability [3] and photoluminescence intermittency [4]. Because of their unique and syntheticallytunable optical and electronic properties, these materials have been successfully implemented in applications such as biological imaging [5] and solid-state lighting [6] and hold promise in other applications such
as solar cells [7], photodetectors [8], and lasers [9].
However, most NC-based applications are still significantly limited in performance by the broad ensemble emission linewidth of NCs at room temperature [5] [6]. While the peak spectral energy of a
batch of nanocrystals is dictated by the average size of the particles [10], its spectral breadth is dictated
by a combination of sample inhomogeneity and the spectral linewidths of the single particles. To date,
progress in synthesizing spectrally-narrow NC batches has occurred primarily by reducing sample inhomogeneities without consideration for single-NC linewidths because we have lacked the experimental tools
and theoretical insight necessary to definitively determine the effects of synthesis on single-nanocrystal
monochromaticity [11] [12] [13].
Photon-correlation Fourier spectroscopy performed on emitters diffusing in solution (S-PCFS) offers a
unique approach for investigating the spectra of single nanocrystals with large sample statistics, without
user selection bias, with high signal-to-noise ratios, and at timescales fast enough to avoid the spectral
diffusion commonly observed in single-NC spectroscopy [14]. In this Article, we demonstrate that S-PCFS
can be used to efficiently and reliably measure the spectral profile of the average single nanocrystal within
an ensemble with statistical confidence, enabling the unambiguous characterization of the links between
synthetic methodologies and single-nanocrystal spectral linewidths.
1
Results
Theoretical Background of S-PCFS
The key to S-PCFS is measuring the energy differences between photons rather than measuring their
absolute energies [15]. When sampling an ensemble of particles freely diffusing through a small focal
volume, energy differences between photons emitted by the same particle reflect the single-NC spectral
profile. In contrast, photons emitted from different particles depend on the emission energies of each
particle and therefore reflect the inhomogeneously broadened ensemble spectrum. Because the detection
of photons originating from the same NC is statistically enhanced at timescales shorter than the particle
dwell time in the focal volume, the single-particle contribution can be disentangled from the ensemble while
maintaining ensemble-level statistics [16].
S-PCFS experimentally implements this unique conceptual approach by combining the energy-resolving
capabilities of inteferometry with the time-resolving capabilities of Hanbury Brown and Twiss photon
correlation analysis (Figure 1). The interferometer converts spectral information into intensity fluctuations,
which are interpreted by photon correlation analysis as the energy difference ζ between photons as a
function of the time separation τ between them. Analogous to Fourier transform spectroscopy, where
the dependence of the output intensity on the interferometer path-length difference δ gives the intensity
interferogram, which is the Fourier transform of the spectrum s(ω), here, the dependence of the intensity
cross-correlation function on δ gives the “PCFS interferogram” g̃(δ, τ ), which is the Fourier transform of
the spectral correlation function p(ζ, τ ) (Equation 1).
Z
p(ζ, τ ) = h s(ω, t)s(ω + ζ, t + τ ) dωi
(1)
The spectral correlation p(ζ, τ ) can be interpreted as the distribution of energy differences ζ, for photons
of temporal spacing τ . Though the spectrum itself has been sacrificed to access spectral correlations at
timescales previously inaccessible to single-molecule spectroscopy, photon-correlation provides the means
of extracting single-emitter spectral information with ensemble-level statistics.
Traditional spectroscopy of particles diffusing in solution only provides the spectrum of the ensemble.
However, encoded in g̃(δ, τ ) are the spectral correlation functions psingle (ζ, τ ) for the average single emitter
and pens (ζ) for the ensemble [16] [17]. By analyzing g̃(δ, τ ) at timescales shorter and longer than the dwell
time of the particles within the focal volume, we decompose g̃(δ, τ ) into the contributions from the average
single emitter (g̃ single (δ, τ )) and from the ensemble (g̃ ens (δ)), which are related by Fourier transform to
their corresponding spectral correlation functions. We refer the reader to Section 1 of the Supplementary
Information and References [15] – [18] for more details regarding the theory and execution of this method.
In addition to high temporal and frequency resolution, S-PCFS overcomes many of the shortcomings
of traditional single-molecule spectroscopy. Assuming a single unique emitter within the focal volume at a
time, a measurement of 123 intensity correlation functions with 30 s integration times for particles with an
average dwell time of 300 µs has a throughput of ∼ 107 particles with no user selection bias. Furthermore,
because of short exposure times, low-intensity cw excitation, and a correction for fluctuations in the total
signal (see Supplementary Information Section 1), emission intermittency and bleaching are no longer
experimental concerns. Finally, integration time and temporal resolution are decoupled in PCFS, which
means that arbitrarily high signal-to-noise ratios can be obtained simply by increasing the integration time
for each correlation function.
Extracting Single-Nanocrystal Spectral Linewidths
Though S-PCFS directly measures spectral correlation functions, additional analysis is necessary to gain
insight into the underlying spectrum. Marshall et al. found that CdSe/CdZnS core/shell nanoparticles
exhibited no appreciable spectral diffusion at submillisecond timescales approaching the lifetime of the
emitters under low excitation flux and ambient conditions [17]. In the absence of spectral dynamics, the
2
single-particle spectral correlation function psingle (ζ, τ ) simply reduces to the energy autocorrelation of the
spectrum. Thus, the breadth of the spectral correlation function reflects the breadth of the underlying
spectrum. For both the single-particle and ensemble components, a broader spectral correlation p(ζ) means
a broader spectrum s(ω).
In order to obtain a quantitative spectral linewidth, we adopt a model to fit the data because, without
assumptions, the spectrum cannot mathematically be uniquely recovered from its autocorrelation. Knowing
that the single-NC spectrum at room temperature is a singly peaked, nearly symmetric function, we model
the spectral lineshape using a superposition of Gaussian functions and obtain a functional form to fit
g̃ single (δ, τ ). An effective spectral lineshape (ESL) can be calculated from the fit and its full-width at halfmaximum gives the effective “single-nanocrystal linewidth”. The ensemble component is fit similarly. See
Sections 2 and 3 of the Supplementary Information for more details and confirmation of the accuracy of
our analysis.
Figure 2 provides an example of our data analysis. The measured g̃ single (δ, τ ' 5 µs) is plotted in blue
in Figure 2a for a batch of CdSe/CdS core/shell particles. We highlight the high signal-to-noise ratio at
τ ' 5 µs, which is at least 3 orders of magnitude faster in temporal resolution than conventional singlemolecule spectroscopy can achieve. Plotted in red is the fit to our model. Figure 2b shows that the fit is
well-conserved to the spectral correlation psingle (ζ, τ ' 5 µs). The effective spectral lineshape calculated
from this fit is shown in Figure 2c.
Variability and Tunability of Single-Nanocrystal Linewidths
Having demonstrated how S-PCFS can be used to measure the spectral linewidth of the average single
NC, we apply our method to explore the dependence of this linewidth on several nanocrystal parameters
in core/shell particles. We present three experiments that illustrate how single-NC linewidths vary in ways
that challenge our current understanding of the spectra of nanomaterials.
First, we investigate the effect of the core composition on the single-NC linewidth. Given that different
material compositions are associated with different effective masses, dielectric constants, deformationpotential coupling, and other properties that affect the materials’ response to optical excitations, changing
the core composition was expected to have a significant effect on spectral linewidths [19]. In this experiment,
we compare CdSe, InP, and InAs core/shell particles. InP was chosen because it is a Cd-free alternative to
CdSe and InAs was chosen for its emission tunability into the near-infrared. These materials are of great
interest for applications in displays, solid-state lighting [20], and biological imaging [21].
In Figure 3, we overlay the single-NC and ensemble spectral correlation functions for CdSe, InP, and
InAs core/shell particles. The ensemble spectral correlations confirm what is often observed in InP and InAs
nanocrystals – their ensemble spectra are much broader than those of CdSe particles [22] [23]. Surprisingly,
however, the single-NC linewidths are nearly the same. This result shows that differences in the materials
properties of the core composition do not necessarily have a dramatic effect on single-NC linewidths.
In the second experiment, however, we discover large batch-to-batch variations in the average single-NC
R
linewidths of three sample batches of commercial CdSe core/shell particles (Qdots)(Figure
4a). Although
variation in the room-temperature spectral linewidth of single nanocrystals has been previously observed
[14], this is the first report of variation in the average spectral linewidth of single nanocrystals between
synthetic batches. More importantly, these large single-NC linewidth variations exist despite their same
core material composition (CdSe) [24].
The first two experiments reveal that the core material composition does not solely dictate the singleNC linewidth, but instead, that other aspects of the core/shell architecture can have a predominant effect.
We can begin to understand the structural origins of these linewidth variations through controlled synthesis
in conjunction with S-PCFS.
In our third and final experiment, we demonstrate that the single-NC linewidth can be altered considerably by the adjustment of a synthetically-controllable structural parameter. In Figure 4b, we observe
that the single-NC linewidth increases substantially for CdSe/CdS particles undergoing shell growth. In
fact, Table 1 shows that the single-NC linewidth increases monotonically from 64 meV (1.8 monolayers) to
3
an astonishing 92 meV (10 monolayers). This result does not necessarily imply that all single-NC linewidth
variations, such as those observed in the second experiment, are caused by differences in shell thickness.
Rather, it provides one instance in which the single-NC linewidth can be strongly influenced by structural
features of core/shell particles. This experiment brings to light the feasibility of synthetic control over the
single-NC linewidth.
Discussion
Our findings have far-reaching implications for our understanding of the spectra of both single nanocrystals
and nanocrystal ensembles. First, and most importantly, we have shown that the room-temperature singleNC linewidth varies considerably from batch to batch in a synthetically controllable fashion (Figure 4).
In fact, the broadest single-NC linewidth measured for the CdSe/CdS particles is even broader than the
ensemble linewidth for several of the other CdSe particles (Table 1). Furthermore, single-NC linewidth
synthetic tunability should be possible for nanoparticles with cores other than CdSe because the single-NC
linewidth is not dictated solely by the core composition; other aspects of the core/shell architecture can
greatly alter the single-NC linewidth.
The direct consequence of these results is that the effect of the single-NC linewidth on the ensemble
spectral linewidth cannot be ignored. Throughout the literature, changes in the ensemble spectral linewidth
have often been attributed to changes in the size distribution of the particles [22]. However, our third
experiment demonstrates that this conclusion is unwarranted. In the case of our CdSe particles undergoing
CdS shell growth, the increase in the ensemble linewidth is due primarily to broadening of the single-NC
linewidth (Table 1).
Conversely, it has been speculated that the broad ensemble spectral linewidths of InP and InAs
core/shell particles may be dictated by broad single-NC linewidths rather than by sample inhomogeneities.
Figure 3 and Table 1 reveal that the dramatically different ensemble spectral linewidths belie nearly identical single-NC spectra. The broad ensemble spectra of InP and InAs core/shell particles are limited not
by the intrinsic properties of these materials, but rather by the inhomogeneities among the particles in
the sample. Thus, the synthesis of InP and InAs core/shell particles with ensemble spectral linewidths as
narrow as CdSe should be achievable via the reduction of sample inhomogeneities.
These insights could not have been conclusively drawn using traditional characterization tools. A
comparison of Table 1 and Supplementary Figure S2 shows that both single-NC and ensemble spectral
linewidths have little correlation with shell morphology in core/shell particles. Because transmission electron microscopy (TEM) cannot easily resolve the core from the shell, and because it relies on single-particle
examination, it cannot provide an ideal measure of the degree of inhomogeneity within a synthetic batch.
S-PCFS, on the other hand, provides a quantitative comparison of the single-NC and ensemble linewidths
and is thus a direct probe of the degree of spectral inhomogeneity within a sample. This technique has
allowed us to conclude that the single-NC linewidth and the sample polydispersity are independent and
synthetically controllable parameters.
Finally, the single-NC linewidth variations that we observe challenge our current understanding of
the physical origin of single-nanocrystals emission spectra. The breadth of the single emitter spectrum
originates from broadening of the lifetime-limited natural emission spectrum by intrinsic and extrinsic
interactions with the environment [25]. In the context of nanocrystals, the single-NC linewidth is believed
to arise from a combination of photoinduced spectral diffusion (extrinsic) and exciton-phonon interactions
(intrinsic) [26]. However, spectral diffusion has been found to be negligible in core/shell particles at the
timescales investigated in the present work [17]. Thus, our results directly reflect the intrinsic single-NC
spectral broadening mechanisms such as excitonic coupling to phonons within the nanoparticle, [27] [28]
to vibrations in the ligands on the surface, and to the bath solvent itself [29] [30].
The single-NC linewidth broadening with shell growth observed in the CdSe/CdS particles is consistent
with an increased “Frölich-like” exciton-phonon interaction due to the spatial separation between the electron and hole in these quasi-type-II heterostructures [31] [32]. Our results suggest that the batch-to-batch
4
variations in single-NC emission linewidths measured by S-PCFS originate from a delicate interplay between various parameters that affect exciton-phonon interactions within the core/shell/ligand architecture.
Conclusions
In this Article, we have demonstrated that S-PCFS enables the simultaneous characterization of ensemble
and single-emitter spectral properties with unprecedented clarity. With this new class of single-molecule
spectroscopy, we have discovered batch-to-batch variability and synthetic tunability in room-temperature
single-nanocrystal emission linewidths. Our work highlights the fundamental importance of the single-NC
spectral linewidth when characterizing and optimizing nanocrystals for applications. With the use of SPCFS as a high-throughput characterization tool, synthetic chemists can rapidly and quantitatively assess
synthetic methodologies for the rational design of future nanostructures. In fact, our technique is already
being used to help develop a new generation of nanoparticles with superior optical properties [33].
We also emphasize the broad applicability of S-PCFS. Coupled with the rich and unexplored physics
now accessible by our method, we anticipate that S-PCFS may serve as a platform for new perspectives
on the synthesis of nanomaterials of exceptional quality. Finally, we note that though our efforts have
focused on semiconductor core/shell nanoparticles, our method can be easily extended to to characterize
the inhomogeneities in and to probe the underlying physics of myriad fluorescent systems.
5
Methods
Experimental Details
Each sample was prepared by diluting a concentrated stock solution into a hexanes solution containing
excess cadmium oleate and decylamine, which help prevent aggregation. A thin flat capillary tube containing a dilute solution of the nanocrystal sample was mounted onto a water-immersion objective. A cw
laser at 457 nm was used in conjunction with a pellicle beamsplitter and a dielectric notch or long-pass
filter in order to achieve sensitivity across the visible spectrum.
PL emission was collected through the same objective and focused through a pinhole to obtain a welldefined focal volume as in fluorescence correlation spectroscopy (FCS) [34]. The beam was recollimated
and directed to a two-output Michelson interferometer. In the interferometer, the beam was split, sent
to two orthogonal paths, recombined at the beam splitter and focused onto two single-photon counting
modules (PerkinElmer now Excelitas Technologies). On one arm of the interferometer, a retroreflector was
mounted on a linear stage that defined the path-length difference δ. On the other arm was a retroreflector
mounted with a piezoelectric actuator that translated it back and forth over short distances (“dithering”).
Correlation functions were obtained through a digital correlator (ALV-7004/FAST).
Each S-PCFS experiment consisted of 123 correlation measurements over 81 path-length differences.
Each step of the linear stage increased the path-length difference δ by 1 µm, thus covering path-length
differences from -40 µm to +40 µm. The path-length differences selected for these measurements provide
sufficient spectral resolution for all samples measured here. The instrument function of the interferometer
is less than 15 µeV .
The center 21 positions were measured three times and the correlation function values were averaged
after correcting for diffusion and the ensemble spectral correlation. The ensemble component was selected
at τ ∼ 100 ms, a timescale much longer than the average particle dwell time in the focal volume. The
PCFS interferogram g̃ single (δ, τ ) was then averaged over τ = 1 − 10 µs and reported as τ ' 5 µs. The piezo
actuator, receiving an input from a function generator, translated the mirror over a distance of ∼2 emission
wavelengths with a frequency of 0.04 Hz or 0.06 Hz. Afterpulse correction was performed as described in
[17] except no short-time fitting was performed.
Transmission electron microscopy was performed on a JEOL 200CX General Purpose TEM operating at
120 kV and on a JEOL 2010 Advanced High Performance TEM operating at 200 kV. Ensemble fluorescence
spectra were measured on a Fluoromax-3 (Horiba Jobin Yvon).
Samples
The synthesis of InAs/ZnS and CdSe/CdS core/shell particles are described in the Supplementary Information. The emission maximum of the InAs/ZnS particles was 710 nm and the emission maxima of the
CdSe/CdS particles were between 600 and 620 nm.
R 545 (SKU No. Q21791MP, Lot No. 801737), Qdot
R 605 (SKU No.
Commercial CdSe samples Qdot
R
Q21701MP, Lot No. 786124), and Qdot 655 (SKU No. Q21721MP, Lot No. 691974) were purchased
from Invitrogen (now Life Technologies).
The InP sample was obtained from QD Vision, Inc.
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Acknowledgements
This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division
of Materials Sciences and Engineering under Award DE-FG02-07ER46454 and by the National Institutes
of Health through the MIT Laser Biomedical Resource Center under Award P41EB015871-26A1. J.C.
gratefully acknowledges support from the National Science Foundation Graduate Research Fellowship
Program. D.D.W. gratefully acknowledges support from the Fannie and John Hertz Foundation. The
authors thank QD Vision, Inc. for providing the InP core/shell sample and José Cordero for help with
synthesis.
Author contributions
J.C., L.F.M., X.B., and M.G.B. conceived of and designed the experiments. J.C. performed the S-PCFS
experiments. O.C. and D.K.H. synthesized the CdSe/CdS and InAs/ZnS nanoparticles. D.D.W. and
O.C. performed transmission electron microscopy. J.C. and A.P.B. analyzed the data with guidance from
L.F.M., X.B., and M.G.B. The manuscript was written by J.C. and A.P.B. with contributions from all
authors.
8
Additional information
The authors declare no competing financial interests. Supplementary information accompanies this paper on www.nature.com/naturechemistry. Reprints and permissions information is available online at
www.nature.com/reprints. Correspondence and requests for materials should be addressed to M.G.B.
9
Tables
Single-Nanocrystal and Ensemble Effective Spectral Linewidths.
Sample
R 545
Qdot
R 605
Qdot
R 655
Qdot
InP core/shell
InAs/ZnS
CdSe/CdS 1.8 ML†
CdSe/CdS 4.0 ML*
CdSe/CdS 6.5 ML
CdSe/CdS 10.0 ML
Single-NC linewidth (meV)
70
42
60
73
76
64
69
82
92
Ensemble linewidth (meV)
138
75
90
178
151
87
84
102
124
†This sample is included in Figure 2
*This sample is included in Figure 3
10
Figures
cw laser
dielectric filter
piezo actuator
achromats
capillary
δ
objective
pellicle
pinhole
linear stage
beam splitter
digital
correlator
APD
Figure 1: Experimental Setup. In S-PCFS, we pass the fluorescence from particles diffusing through a small
focal volume through an interferometer. With correlation analysis of the intensities at both outputs, the spectral
correlation function for the average single particle can be distinguished from the spectral correlation function for the
ensemble.
11
a)
b)
FFT data
FFT fit
psingle(ζ)
~
gsingle(δ)
0.3
0.2
0.1
-600
-200
0
200
400
Energy Separation ζ (meV)
c)
0
-0.01
0
0.01
600
From Fit
0.03
ESL
-0.03
Fit Residual
-400
Linewidth
0.01
0
-0.01
-0.03
-0.01
0
0.01
Path-length Difference δ (mm)
0.03
-200
-100
100
0
Energy ω (meV)
200
Figure 2: Demonstration of S-PCFS Data Analysis. a) Single-emitter PCFS interferogram g̃ single (δ, τ ' 5 µs)
along with fit and fitting residual. Note the high signal-to-noise ratio at a timescale more than 3 orders of magnitude
faster than conventional methods can access. b) The Fourier transform of g̃ single (δ, τ ' 5 µs) gives the spectral
correlation psingle (ζ, τ ' 5 µs). The good fit is conserved through the transform. c) The effective spectral lineshape
(ESL) is calculated from the initial fit to g̃ single (δ, τ ' 5 µs) and its full-width at half-maximum is the effective
“single-nanocrystal linewidth”.
p(ζ)
CdSe single
CdSe ensemble
InP single
InP ensemble
InAs single
InAs ensemble
-400
-200
0
200
Energy Separation ζ (meV)
400
Figure 3: Comparison of Different Core Materials Composition. Single-particle (solid line) and ensemble
(dotted line) spectral correlation functions p(ζ, τ ' 5 µs) for core/shell particles with CdSe (blue), InP (red), and
InAs (violet) cores. Despite very different material properties and ensemble spectral linewidths, the single-nanocrystal
spectral linewidths are very similar.
12
a)
® 545
® 605
® 655
psingle(ζ)
Qdot
Qdot
Qdot
-200
-100
0
100
Energy Separation ζ (meV)
1.8 ML
4.0 ML
6.5 ML
10.0 ML
Shell Growth
p
single
(ζ)
b)
200
-200
-100
0
100
Energy Separation ζ (meV)
200
Figure 4: Comparison of Samples with CdSe Cores. a) Single-particle spectral correlation functions
R
psingle (ζ, τ ' 5 µs) for the commercial CdSe particles (Qdots).
There is great variation in the linewidths with no obvious trend according to size or shell morphology. b) Single-particle spectral correlation functions psingle (ζ, τ ' 5 µs)
for the CdSe/CdS core/shell particles during shell growth. The linewidth increases monotonically with shell growth.
13
Direct Probe of Spectral Inhomogeneity Reveals Synthetic Tunability of
Single-Nanocrystal Spectral Linewidths
Supplementary Information
Jian Cui, Andrew P. Beyler, Lisa F. Marshall, Ou Chen, Daniel K. Harris,
Darcy D. Wanger, Xavier Brokmann and Moungi G. Bawendi
1
Explanation of Notation
In S-PCFS, the intensities at both outputs of the interferometer are measured and the intensity crosscorrelation function g × (δ, τ ) is calculated at different interferometer path-length differences δ for temporal
spacings between photons τ . Reference [1] introduces the governing equation of S-PCFS, which relates
g × (δ, τ ) to the single-emitter and ensemble spectral correlation functions.
n
o
1
g × (δ, τ ) = g (2) (τ ) − F T pens (ζ) + g (2) (τ ) − 1 psingle (ζ, τ )
2
ζ→δ
(1)
This is equivalent to the governing equation in [2] where g (2) (τ ) = g FCS (τ ) represents the autocorrelation
function of the total intensity before entering the interferometer. This correlation function describes
fluctuations in the total signal and accounts for the diffusion of the particles as in fluorescence correlation
spectroscopy (FCS) [3] as well as fluctuations in the single-emitter signal (e.g. “blinking”).
Here, we introduce the notation g̃(δ, τ ) as the Fourier transform of the spectrally-relevant component
of the cross-correlation function. This is equivalent to the “δ-dependent component” of g × (δ, τ ) because
g (2) (τ ) arises from the sum of the detector intensities and should show no dependence on the interferometer
path-length difference.
n
o
g̃(δ, τ ) = F T pens (ζ) + g (2) (τ ) − 1 psingle (ζ, τ )
(2)
ζ→δ
g̃(δ, τ ) is the “PCFS interferogram” that is equivalent to the Fourier transform of the “diffusion weighted
spectral correlation” described in [2].
We
have further
τ ) into its single-emitter and ensemble components. This gives us g̃ single (δ, τ ) =
single
split g̃(δ,ens
FT p
(ζ, τ ) ζ→δ and g̃ (δ) = F T {pens (ζ)}ζ→δ . The ensemble component does not have a τ dependence because it is determined by the statistics of different particles entering and exiting the focal volume,
which is governed by Poisson statistics.
2
Fitting
In the absence of spectral dynamics, p(ζ, τ ) is the spectral autocorrelation. For both the single-NC and
ensemble components, we have assumed here that the true spectral lineshape s(ω) is well-approximated
by an effective spectral lineshape composed of the summation of an arbitrarily large number of Gaussian
functions. In practice, we find that for all samples measured here, both g̃ single (δ) and g̃ ens (δ) are well-fit
by a spectrum composed of the sum of two Gaussian functions with amplitudes A, B and widths c, d,
but centered at the same frequency ωo as follows. The inclusion of additional Gaussian functions into the
model does not improve the fit.
s(ω) = Ae−
(ω−ωo )2
2c2
1
+ Be−
(ω−ωo )2
2d2
(3)
The model gives a spectral correlation p(ζ) that is a sum of three Gaussians: one term from the
first Gaussian, the second term from the second Gaussian and a cross-term. Fourier transform to g̃(δ)
gives another sum of three Gaussians resulting in the fitting equation below. The absence of the center
frequency ωo in the fitting equation indicates that absolute frequencies are indeed lost but information
regarding spectral breadth is conserved.
2 2 2
2 2 2
2 2
2 2
g̃ single/ens (δ) = 2π A2 c2 e−4π c δ + B 2 d2 e−4π d δ + 2ABcde−2π (c +d )δ
(4)
In Figure 2c, the ratio of the areas of the two Gaussians is approximately 2:1, indicating that both
Gaussians contribute significantly to the fitting.
3
Ensemble Spectrum: S-PCFS vs. Fluorometer
Ensemble Spectral Correlations
a)
-300
Fluorometer Spectrum vs. S-PCFS ESL
b)
S-PCFS
Fluorometer
-100
0
100
Energy separation ζ (meV)
300
-200
S-PCFS
Fluorometer
-100
0
100
Energy spread (meV)
200
Figure S1: Comparison of Fluorescence Data from S-PCFS and Fluorometer a) Spectral correlations for
the ensemble spectrum of CdSe/CdS core/shell particles with 4.0 monolayers of CdS taken by both S-PCFS and the
fluorometer agree well with each other. b) Though the effective spectral lineshape for the ensemble calculated from
fitting to the PCFS interferogram cannot capture the slight asymmetry of the spectrum, the linewidths are nearly
identical.
To illustrate the accuracy of S-PCFS and our fitting, we compare the ensemble component obtained
through S-PCFS to the ensemble spectrum obtained through a conventional fluorometer for the same batch
of particles. As also shown in [2], pens (ζ) obtained from S-PCFS is remarkably consistent with the energy
autocorrelation of the spectrum obtained through traditional spectroscopy (Supplementary Figure S1a).
In Supplementary Figure S1b, we plot the effective spectral lineshape (ESL) calculated from our fit to the
S-PCFS data to the actual spectrum from the spectrometer. Because our model is based on overlapping
Gaussians, it cannot account for the slight asymmetry in the spectrum. However, the linewidths are nearly
identical, giving credence to our method.
2
4
Transmission Electron Microscopy
a)
50 nm
d)
b)
c)
50 nm
50 nm
e)
f)
50 nm
R 545, b) Qdot R 605, c) Qdot R 655, d) InP
Figure S2. Transmission Electron Micrographs a) Qdot
core/shell particle, e) CdSe with 4.0 monolayers CdS shell, f) CdSe with 10.0 monolayers CdS shell
5
InAs/ZnS Synthesis
A 0.05 M indium myristate (InMy3 ) stock solution was made by adding 5 mmoles indium(III) acetate
(99.99%, Alfa Aesar) and 15 mmoles myristic acid (98%, Spectrum Chemicals) to 100 mL of 1-octadecene
(90%, technical grade from Sigma Aldrich).
The synthesis of the InAs/ZnS core/shell particles was adapted from [4]. 3 mL of 0.05 M InMy3 stock
solution (0.15 mmoles) was added to a 15 mL four-neck round bottom flask attached to a Schlenk line.
The solution was heated to 100◦ C and the flask was evacuated to a pressure of 100 mtorr.
The injection syringe was prepared by mixing 0.115 mmoles tris(trimethylsilyl)arsine (TMS3 As) prepared as described previously [5] with 0.75 mL tri-n-octylphosphine (98%, Strem) in a nitrogen glovebox. Overcoating syringes were prepared by adding 1.1 mmoles diethylzinc (99%, Strem) with 5 mL
tri-n-octylphosphine (98%, Strem) and 1 mmole bis(trimethylsilyl)sulfide (99%, Strem) with 5 mL tri-nocrylphosphine (98%, Strem).
The TMS3 As solution was rapidly injected into the vigorously stirred InMy3 solution at 150 ◦ C and
promptly heated to 250◦ C for 40 min. The solution was cooled to 175◦ C for overcoating. The overcoating
solutions were injected dropwise at 1.5 mL/hr.
3
6
CdSe/CdS Synthesis
A detailed description of the CdSe/CdS synthesis can be found in [6].
CdSe cores were synthesized by a modification of the method described in [7]. For the shell growth
reaction, a hexane solution containing 100 nmol of CdSe nanocrystals were loaded in a mixture of 3 mL 1octadecene (ODE, 90%, Alfa Aesar) and 3 mL oleylamine (OAm, 70%, Aldrich). The reaction solution was
degassed under vacuum at room temperature for 1 hr and then at 120 ◦ C for 20 min to totally remove the
hexane, water and oxygen inside the reaction solution. After that, the reaction solution was heated up to
the growth temperature under nitrogen flow and magnetic stirring. Once the reaction solution was heated
to 240 ◦ C, a desired amount of Cd-oleate (dilute in 6 mL ODE) and one equivalent amount of octanethiol
(dilute in 6 mL ODE) were infused into the growth solution with a rate of 3 mL/hr using a syringe pump.
Shortly after starting addition, the reaction temperature was further elevated to 310 ◦ C and maintained
for the rest of the reaction. Precursor addition was stopped for ∼5 min at a time to take aliquots. The
resulting CdSe/CdS core/shell QDs were precipitated with acetone addition and the redispersed in hexane.
The particles were further purified by precipitation-redispersion for two more rounds and finally suspended
in ∼5 mL hexanes.
References
[1] Brokmann, X., Marshall, L. F. & Bawendi, M. G. Revealing single emitter spectral dynamics from
intensity correlations in an ensemble fluorescence spectrum. Opt. Exp. 17, 4509–4517 (2009).
[2] Marshall, L. F., Cui, J., Brokmann, X. & Bawendi, M. G. Extracting Spectral Dynamics from Single
Chromophores in Solution. Phys. Rev. Lett. 105, 053005 (2010).
[3] Haustein, E. & Schwille, P. Fluorescence Correlation Spectroscopy: Novel Variations of an Established
Technique. Annu. Rev. Biophys. Biomol. Struct. 36, 151–169 (2007).
[4] Allen, P. M. et al. InAs(ZnCdS) Quantum Dots Optimized for Biological Imaging in the Near-Infrared.
J. Am. Chem. Soc. 132, 470–471 (2010).
[5] Wells, R. L., Self, M. F., Johansen, J. D., Laske, J. A., Aubuchon, S. R., Jones, L. J., Cowley, A.
H. and Kamepalli, S. (2007) Tris(Trimethylsilyl)Arsine and Lithium Bis(Trimethylsilyl)Arsenide, in
Inorganic Syntheses, Volume 31 (ed A. H. Cowley), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi:
10.1002/9780470132623.ch25
[6] Chen, O. et al. Compact high-quality CdSe-CdS core-shell nanocrystals with narrow emission
linewidths and suppressed blinking. Nature Mater. Advance Online (2013).
[7] Carbone, L. et al. Synthesis and Micrometer-Scale Assembly of Colloidal CdSe/CdS Nanorods Prepared by a Seeded Growth Approach. Nano Lett. 7, 2942–2950 (2007).
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