Fluorescence correlation spectroscopy using quantum dots: advances,

challenges and opportunities

Romey F. Heuff, Jody L. Swift and David T. Cramb*

Received 22nd November 2006, Accepted 12th February 2007

First published as an Advance Article on the web 2nd March 2007

DOI: 10.1039/b617115j

Semiconductor nanocrystals (quantum dots) have been increasingly employed in measuring the

dynamic behavior of biomacromolecules using fluorescence correlation spectroscopy. This poses a

challenge, because quantum dots display their own dynamic behavior in the form of intermittent

photoluminescence, also known as blinking. In this review, the manifestation of blinking in

correlation spectroscopy will be explored, preceded by an examination of quantum dot blinking in

general.

1. Introduction

Semiconductor nanocrystals (quantum dots) are on the verge

of revolutionizing the field of biophotonics. The extreme

brightness and photostability of quantum dots have made

single biomolecule imaging almost trivial.1,2 The term ‘‘quan-

tum dot’’, was coined to represent the reduced dimensionality

of nanoscopic crystals made up of 100s to 1000s of unit cells,

with core diameters ranging from 1.5 nm–6 nm. At this length

scale, the confinement energy of the exciton (electron/hole

pair) is stronger than the Coulombic interaction, resulting in

quantization of the electronic energy. For optical transitions,

excitons are generated through the absorption of light. An

extensive and informative review of the optical properties of

single quantum dots is given in ref. 3. The optical gap of a

quantum dot is size-tunable in the visible to near infrared

region of the electromagnetic spectrum. After excitation,

emission of a photon occurs in the absence of other relaxation

pathways. Conveniently, the dots have broadband absorption,

making simultaneous excitation of a selection of different

color dots using a single wavelength light source possible.

Moreover, they have narrower emission profiles than organic

dye molecules, facilitating easier spectral separation of the

fluorescence signal. Thus, quantum dots have great potential

for multiplexing in biological assay applications, as well as in

imaging.

Quantum dots have been successfully used in long-term

biological imaging with little or no cytotoxic effects.4,5 To

date, quantum dots have been used for optical coding of

mammalian cells,6,7 in the formation of biosensors8 as diag-

nostic tools for cancer9,10 and in the development of rapid

screening techniques using multiplexed hybridization detec-

tion of DNA sequences.11 They have been used as donors for

fluorescence resonance energy transfer (FRET)12 and as fluoro-

phores in fluorescence lifetime imaging (FLIM)13 because of

their long lifetimes (10s of ns) compared to organic fluoro-

phores (1–5 ns). Near infrared dots have been used to map

sentinel lymph nodes,14 and dots in the visible region have

tracked the diffusion of individual glycine receptors at various

synaptic locations15 and so on.16

The chemical research of quantum dots has involved devel-

oping luminescent core materials and then adding a higher

bandgap shell to the core surface. The resultant core/shell

quantum dots were found to have superior optical properties.

One of the most widely studied core/shell quantum dots is

composed of CdSe/ZnS. CdSe/ZnS quantum dots are made in

hydrophobic highly coordinating organic solvents such as

trioctyl phosphine oxide (TOPO)17 and in order to render

them biologically compatible they need further surface mod-

ifications for water solubility and target specificity.18 A sche-

matic diagram of a core/shell quantum dot is displayed in Fig.

1. The ability to solubilize CdSe/ZnS dots in aqueous media by

use of an amphiphilic polymer or lipid coating while main-

taining a high quantum yield19 has led to their commercializa-

tion [Quantum Dot Corp and Evident Technologies]. A

peptide coating20 can also render the dots water-soluble, but

this formulation is not presently available commercially. Once

water solubilized, dots can be further functionalized to target

specific cellular surfaces or sites using receptor–ligand inter-

actions.21

Nowhere have the narrow spectral features of quantum dots

shown more potential for applications than in fluorescence

Fig. 1 Schematic diagram of a CdSe/ZnS core/shell quantum dot

which possesses a passivation layer. The exploded views reveal

increasing molecular detail.

Department of Chemistry, University of Calgary, 2500 University DrNW, Calgary, AB, Canada T2N 1N4. E-mail: dcramb@ucalgary.ca;Fax: +1 403 289 9488; Tel: +1 403 220 8138

1870 | Phys. Chem. Chem. Phys., 2007, 9, 1870–1880 This journal is �c the Owner Societies 2007

INVITED ARTICLE www.rsc.org/pccp | Physical Chemistry Chemical Physics

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(cross)correlation spectroscopy (F(X)CS) of biological sys-

tems. FCS and XCS are spectroscopic techniques that rely

on photostable fluorophores with high quantum yields to

study movement and molecular interactions at the single

molecule level. If multiple fluorophores can be excited simul-

taneously with a single wavelength and their emission is

spectrally distinguishable, then the technique is made even

more versatile. Quantum dots appear at first to be ideal

fluorophores for FCS and XCS applications, but despite their

distinct advantages over typical organic dye molecules, their

use in FCS has yet to be be fully realized. Intermittent

photoluminescence or ‘‘blinking’’ of quantum dots has limited

their use as an analytical tool pending a physical/mathematical

model for the FCS/XCS data, or at least adequate manipula-

tion of their photophysical properties to remove the intermit-

tency of photoluminescence.

Nevertheless, there have been several recent applications of

quantum dots in correlation spectroscopy applications. Initi-

ally, FCS was used almost exclusively to characterize the

concentration and size of biofunctionalized quantum

dots.22–24 Quantum dots have also been employed in XCS

studies of ligand–receptor binding.23,25 In both XCS studies,

the ligand–receptor investigated was the streptavidin–biotin

model system. Hwang and Wohland26 presented evidence for

binding between biotinylated fluorescein and a streptavidin

functionalized quantum dot (655 nm). In the other XCS work,

two-photon excitation of red and green quantum dots was

employed to examine the effect of large nanocrystals on the

streptavidin–biotin interaction.25 We found that the strepta-

vidin–biotin binding constant was reduced by approximately

five orders of magnitude when coupled to CdSe/ZnS quantum

dots. This difference was accounted for in part considering the

reduction in the forward reaction rate for binding due to the

bulk of the dots and the fraction of the dot surface which was

bioactive.25 In almost all of the above FCS and XCS studies,

there was evidence of anomalies in the data, particularly at

higher laser powers (which suggests high excitation rates). It is

possible that these anomalies resulted at least in part from this

so-called blinking behavior. Since intensity correlation studies

such as FCS are based on the statistical averaging of minute

fluctuations in the fluorescence intensity signal with time,

blinking on similar time scales may introduce complications

into the analysis of the FCS data. However, the anomalies in

FCS data may also provide some insight into the underlying

mechanisms behind fluorescence intermittency.

2. Blinking and other photophysical properties of

quantum dot photoluminescence

Before examining fluorescence correlation spectroscopy more

formally, some background essential to better understand

blinking will be introduced. Blinking is observed for many

types of single emitters and is a fundamental photophysical

property of quantum dots. For quantum dots, the ‘‘off’’

periods in the fluorescence signal occur, limiting long-term

signal monitoring, despite continuous excitation conditions.

Blinking has been observed on time scales ranging from

approximately 200 ms to 100s of seconds and is thought to

arise from quantum dot ionization, which occurs even under

ambient lighting conditions.27 Organic dye molecules also

have intermittency events which typically follow exponential

statistics indicating a single dark, trap state, (often triplet)

which leads to well-defined blinking kinetic rates. In contrast,

power law distributions are observed for the time-dependent

probabilities of quantum dot blinking events, meaning that the

events occur over a vast range of time scales. This suggests that

blinking is a stochastic process. When averaged over many

excitation cycles, blinking will lower the steady state photo-

luminescence quantum yield. The photoluminescence quan-

tum yield has been shown to be sensitive to fluctuations in the

dot’s local environment, suggesting that molecules adsorbed to

the dot’s surface may change de-excitation pathways.28,29

Changes in the quantum yield have been observed for quan-

tum dot ensembles, either free in solution or immobilized on a

surface. Ensemble measurements include reversible photo-

induced photoluminescence enhancement,30,31 reversible

photobleaching,32,33 photo-darkening,32,33 electrochromic

properties34 and sub-populations of dark dots.23,24 Single

dot measurements tend to be related to dynamic changes in

photoluminescence and include; blinking,35–38 random fluc-

tuations of the emission wavelength and intensity-termed

spectral diffusion,39,40 fluctuating quantum yields41,42 and

long-term spectral shifts correlated with permanent photo-

bleaching.43

The photoluminescence intensity (count rate) per dot, an

example of which is displayed in Fig. 2a,44 can show sensitivity

to the mode of excitation (pulsed or continuous, one or two

photon), the intensity and energy of the excitation source (on

resonance or above-band excitation), as well as the exposure

time and the presence of strong oxidizing or reducing agents.45

A number of non-radiative relaxation pathways including

ionization and ionization suppression mechanisms exist in

quantum dots affecting their observed photoluminescence

properties and excited state lifetimes. These pathways may

be photo-, thermal- or chemically induced and either prevent

or promote radiative recombination of the exciton and dimin-

ish or enhance the quantum yield making energy transfer

mechanisms considerably more complex in nanocrystals than

either molecular systems or bulk materials. Correlation of

these other observables with blinking is still under investigation;

‘‘off’’ time distributions appear to be insensitive to environ-

mental conditions however ‘‘on’’ times deviate from power law

statistics and even switches to exponential statistics in the

absence of the ZnS capping agent.46 The power law distribution

of ‘‘off’’ times (Fig. 2b) suggests a random renewal process for

the recovery of the quantum dot back into the bright state. In

fact, one of the most surprising features about quantum dot

blinking is that in an ensemble of dots every dot is statistically

equivalent which is unanticipated given the ionization mechan-

ism proposed, as this should show obvious environmental

sensitivity. Systematic studies into the effects of environment

and excitation rates on ensemble fluorescence intermittency

using fluorescence correlation spectroscopy will prove useful.

3. FCS background

One method to analyze the fluctuations in fluorescence inten-

sity resulting from quantum dot blinking is to calculate the

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temporal intensity autocorrelation function.47 In the case

where the quantum dots are immobilized via coupling to a

surface, the resultant autocorrelation function should repre-

sent time correlations solely resulting from photophysical

changes, whereas for mobile dots diffusion will also affect

the autocorrelation decay. In general, the autocorrelation

analysis of fluctuations in the fluorescence intensity is also

known as Fluorescence Correlation Spectroscopy (FCS).

FCS is a sensitive technique employed mostly for the

detection of freely diffusing species. In the case of mobile

emitters, the fluorescence intensity time trace, or histogram, of

a well-defined interrogation volume will show intensity fluc-

tuations due to the exchange of fluorophores.47 Transit times

are a function of both solution temperature and viscosity as

well as the hydrodynamic radii of the emitters.47 If only a few

fluorophores are in the excitation volume at any one time, then

fluctuations due to diffusion are statistically significant47 and

any changes in the emission characteristics of the fluorophore

give rise to additional fluctuations, which will affect the FCS

signal. Information such as local concentrations, mobility

coefficients and rate constants for inter- or intra-molecular

reactions can be extracted by analyzing the fluorescence auto-

correlation decay.47

As mentioned above, periodic fluorescence intensity fluctua-

tions may be detected using auto-correlation analysis. This

analysis is akin to integrating the product of the fluctuation in

fluorescence intensity from the average value at a time t, dF(t),and that at a time (t + t), dF(t + t), where t is a variable lag

time. The product is averaged over t, to give the auto-correla-

tion value, G(t) as a function of t. In order to compare the

auto-correlation functions from different times or samples,

they are normalized using the average intensity, hFi. The

normalized ensemble averaged fluorescence intensity auto-

correlation function therefore is

GðtÞ ¼ hdFðtÞ�dFðtþ tÞihFðtÞi2

¼ hFðtÞ�Fðtþ tÞ � hFi2

hFi2

¼ hFðtÞ�Fðtþ tÞihFi2

� 1 ð1Þ

Rather than measuring dF(t), one often measures the changes

in fluorescence intensity, F(t). An autocorrelation of this

parameter delivers G(t) + 1, which can be plotted against tto yield the autocorrelation decay. For t = 0, the autocorrela-

tion amplitude can be defined as:

Gð0Þ ¼ hFðtÞ � hFii2

hFi2¼ variance

hFi2ð2Þ

Since both the variance and the mean fluorescence intensity

are proportional to NAve,

Gð0Þ ¼ 1

NAveð3Þ

where Nave is the average number of emitting species in the

interrogation volume. When the lag time is plotted logarith-

mically, the autocorrelation decay consists of three character-

istic regions defined by short, long and intermediate values of

t. A typical autocorrelation decay for a non-blinking organic

Fig. 2 (a) Typical intensity time trace of immobilized CdSe(ZnS) quantum dot fluorescence intermittency (blinking) at room temperature and (b)

at 10 K. (c) The normalized off-time probability distribution for one quantum dot (diamond) and averaged over 39 quantum dots (triangle). Inset

shows the distribution of fitting values for the power law exponent in the 39 quantum dots. The straight line in the main graph is a best fit to the

average distribution to eqn (5) with exponent, a B �1.5. Reprinted with permission from K. T. Shmizu, R. G. Neuhauser, C. A. Leatherdale,

S. A. Empedocles, W. K. Woo and M. G. Bawendi, Phys. Rev. B, 63, 205316, 2001. Copyright (2001) by the American Physical Society.

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dye molecule is given in Fig. 3. For very short lag times

diffusion is negligible and G(t) = G(0) (constant). For very

long lag times there is no correlation and the auto-correlation

function decays to a constant (either 0 or 1 depending on

whether G(t) or G(t) + 1 is plotted). On the millisecond time

scale and in the absence of photochemical processes, diffusion

through the focal volume (B1 mm3 for confocal applications)

occurs dominating the auto-correlation function, which decays

rapidly. Changes in the shape, amplitude or characteristic

decay time of the auto-correlation function may provide

information on underlying chemical, photophysical, confor-

mational or other changes for the fluorophore under investi-

gation.47 In FCS, the concentration of emitters is kept low so

that movement through the focal volume may be easily

detected. To improve statistical accuracy, the auto-correlation

decay is often built from hundreds of thousands of events.

The rapid growth in applications of FCS occurred after FCS

was applied using confocal microscopy. Confocal microscopy

allows for a very small volume of solution to be interrogated

(B1 fL). Small interrogation volumes are needed such that

only 1–100 molecules are examined. This small number results

in detectable fluctuations, which are easily analyzed using

FCS. A typical TPE-FCS experimental set-up is shown in

Fig. 4. The light source is a pulsed femtosecond laser, which

allows for the high peak intensities needed to drive two-photon

absorption. The laser beam is expanded to overfill the back

aperture of a high numerical aperture (NA 4 0.9) objective

lens. This results in a diffraction-limited focal spot. TPE

confines the excitation volume, the fluorescence from which

is collected back through the objective lens and directed to

Si : avalanche photodiode detectors. These detectors have the

high quantum efficiency (460%) and low background dark

noise necessary for single molecule detection. The count rate

signal from the detectors (single photon counting mode) is

usually directed to a hardware correlator card (ALV Langen

or Correlator.com), which calculates the autocorrelation and

cross-correlation signals. Event counters can also be used to

collect the count rate histograms from which the correlation

decays can be calculated, off line. The only difference between

this set-up and the one for single photon excitation is that the

laser used is operated in continuous mode and a pinhole is

placed at the image plane in front of the detector in order to

define the interrogation volume.

4. Details of previous FCS studies on quantum dots

Only a handful of fluorescence correlation studies on quantum

dots have been published to date22–25,48,49 despite the potential

for insight into the blinking mechanism. For example, since

the 1/G(0) represents the number of emitters in the interroga-

tion volume, a comparison of G(0)’s versus laser power would

provide insight into light-induced changes in quantum dots.

The most straightforward change would be in the number of

dots excited versus light intensity. Doose et al.22 compared the

photophysical and colloidal properties of different biocompa-

tible quantum dots using FCS. In their study, G(0) values were

examined at different laser powers for several different types of

water-soluble quantum dots and compared these results with

those from fluorescent beads and the organic dye rhodamine-

6-green (R6G). The latter of which is a common fluorescence

reference standard. Using a 532 nm continuous wave (cw)

laser to interrogate a 1 femto-litre focal volume in the power

range 1–1000 mW, they found that as a function of laser power,

G(0) decreases substantially more for the dots than it does for

the beads or R6G. The accepted rationalization for a decreas-

ing G(0) as a function of increasing laser intensity is an

increase in the interrogation volume resulting from excitation

saturation effects.50–53 Using alternating laser excitation

scheme fluorescence correlation spectroscopy (ALEX-FCS),

Doose et al.22 were able to rule out optical trapping, but not

power-dependent changes in blinking, as a source for the large

decrease in G(0) with excitation power. Additionally, they

observed abnormally large fluctuations in G(0) over a series

of measurements at low laser power. This could indicate

heterogeneity in particle brightness and was attributed to the

presence of small aggregates.22 Although blinking may be

responsible for these observations, it is difficult to prove,

because the autocorrelation function for both blinking and

diffusing has not been parameterized. Moreover, it has been

suggested that the autocorrelation decay including quantum

dot blinking may not be indistinguishable from one for diffu-

sion only.54 However, observations of the changes in the shape

Fig. 3 Count rate trajectory (a) and autocorrelation decay curve (b) for Alexa Fluor 594-labeled 40 BP DNA. In panel (b), the green–blue squares

represent the data and the red line a fit to that data using eqn (6). The DNA concentration is 120 nM and the fitted diffusion coefficient is

4.5 � 10�11 m2 s�1.

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of the autocorrelation decay, particularly at short lag times,

for quantum dots at higher excitation rates, suggests other-

wise.22–24 An example of the change in autocorrelation decay

shape found by Weiss and coworkers is reproduced in Fig. 5.22

They employed Monte Carlo calculations of diffusing and

blinking dots to simulate the anomalous shape of the auto-

correlation function. Unfortunately, no unique set of blinking

parameters for a given data set could be found.22

Larson et al.24 observed similar results for the changes in

G(0) values versus excitation rate (i.e. laser power) using two-

photon excitation FCS and attributed this to excitation

saturation. The auto-correlation curve for the quantum dots

in their study also changes shape with increasing laser power

(Fig. 1b. Larson et al.24), indicating that some photo-induced

process is occurring. Saturation can account for anomalous

changes in the value of G(0) versus power, but not for changes

in the shape of the autocorrelation decay.50–53,55 Such anom-

alous forms of the autocorrelation decay in the 1 ms–1 ms lag

time range, (B1 fL interrogation volumes) can only result

from concomitant periodic fluctuations in the fluorescence

intensity.

Given the above indirect observations of anomalies in the

autocorrelation decays, a direct observation of blinking in

mobile dots was needed. Confocal fluorescence coincidence

analysis (CFCA) measurements were applied to verify that

quantum dots blink when mobile in solution.23 The approach

premise used by Yao et al.23 was to label dots with organic

dyes in order to create an intensity trace for the dots transiting

the interrogation volume in one detection channel and then

observe quantum dot luminescence in the other. Since the

organic dye labels will not blink under low excitation rates,

events in the count rate histogram for the dye will reflect the

total transit time for the dot. Streptavidin coated 525 nm dots

were labeled with biotinylated Alexa fluor 594 dye molecules.

Both dots and dye labels were excited using a 488 nm laser

(100 mW, cw) and were observed as bursts in the photon count

rate histogram for either the red channel (labelled dark dots),

the green channel (unlabelled bright dots) or both channels

(labelled bright dots). Intermittency in the green channel due

to quantum dot blinking was observed and the probability of

observing a blinking event is increased from 14% to 35% by

lengthening the transit time from 1 ms to 10 ms, via increasing

solution viscosity.23 Sub-populations of dark dots were also

measured using two-photon excitation correlation spectro-

scopy and agreed with the results from CFCA.23 The relative

numbers of dark and bright dots remained unchanged with

respect to transit time, suggesting that dark dots are not in a

temporary ‘‘off’’ state.23 The overall percentage of bright dots

in a sample ranges from 30% to greater than 90%, depending

on the quantum dot production batch, and follows the trend

with the bulk quantum yield of the dots used in this study.23

In contrast to the above experiments, the majority of

quantum dot blinking data has been recorded for immobilized

dots. Blinking behavior is often used as the distinguishing

criteria with which one identifies single emitters. However, the

observation of anti-bunching in photon correlation measure-

ments is now considered a more definitive indicator that a

single quantum emitter is being investigated.37,38 Messin

et al.38 reported that the correlation curve of a single CdSe

(i.e. no shell) quantum dot intensity time trace reflected anti-

bunching at short lag times and was relatively horizontal

Fig. 4 Schematic of two-photon excitation fluorescence correlation

spectroscopy experimental set-up. A neutral density filter (NDF) is

utilized to attenuate the power originating from the titanium sapphire

laser excitation source. Beam expanders (BE) ensure the overfilling of

the higher numerical aperture lens (NA). Dichroic optics (D) are

utilized to direct the beam to and from the objective lens, and a broad

band filter (BBF) allows for the separation of emission and excitation

light. A tube lens (TL) on the side of the microscope directs the

emission to the detection cube, where a second dichroic is used to

separate the green and red emission. Band pass filters (BBF’s) are used

to ensure only emission fluorescence reaches the avalanche photo-

diodes (APD).

Fig. 5 Typical FCS curves for quantum dots at various one-photon

excitation powers. Correlation functions of the quantum dots (inset)

are normalized to g2(t) (main graph). Two distinct effects are visible

with increasing excitation power: (1) the shape of the FCS curve

changes significantly; (2) g2(0) decreases with increasing power. Re-

printed with permission from S. Doose, J. M. Tsay, F. Pinaud and

S. Weiss, Anal. Chem., 2005, 77(7), 2235. Copyright 2005 American

Chemical Society.

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between 200 ns and 100 ms indicating the absence of blinking

in this time range. Beyond 100 ms the curve decayed slowly

until the measurement time was approached and the decay fell

abruptly, but not asymptotically to zero. This suggests that

blinking of mobile dots under similar circumstances would be

challenging to deconvolute from the diffusion influenced

autocorrelation decay, as was previously proposed by

Pelton et al.54

In general, since quantum dot blinking is a stochastic

process, there is no characteristic time scale over which the

process occurs and the effect of quantum dot blinking on the

ensemble averaged auto-correlation function has not been

derived parametrically.56 The auto-correlation function mea-

sured for any portion of the intensity time trace will be

different than the next, exhibiting ergodicity breaking for the

single emitter due to the random nature of the intermittency. It

will be of interest to determine whether or not the anomalies

observed for ensemble average fluorescence autocorrelation

decay for mobile quantum dots behave in a similar fashion as

the ensemble average autocorrelation decays for immobilized

quantum dots.

5. Further examination and modeling of quantum

dot blinking

(a) Fluorescence intensity histogram analysis

The time traces of fluorescence intensity (or count rate histo-

grams) for single immobilized quantum dots can be analyzed

directly. Such analysis reveals that blinking is best described as a

stochastic renewal process, since ‘‘on’’ and ‘‘off’’ time probabil-

ity density distributions follow power law statistics with expo-

nents between �1.4 and �1.9, depending on the measurement

conditions.35,44,57,58 The probability density is given as:

Pðtoff=onÞ ¼No: of times ‘‘toff=on’’Total time ‘‘off=on’’

ð4Þ

and the power law distribution is

PðtÞ ¼ Ata ð5Þ

where A is a proportionality factor. The smallest ‘‘on’’ or ‘‘off’’

time that may be observed is limited by the width of the

measurement window (data collection time bin size) or time

resolution of the experiment. Bin sizes are chosen so that a

distinction can be made between a period where a photon has

not been emitted and a dark period where photon emission is

expected, the latter of which defines a true ‘‘off’’ time and the

former represents the emission lifetime. Typically bin sizes

range from 50 ms to 10 ms depending on the count rate of the

sample which varies considerably with excitation conditions.

While blinking ‘‘off’’ occurs more frequently with increasing

temperature and laser intensity, recovery from the ‘‘off’’ state

appears to be insensitive to experimental conditions.35,44,59 A

maximum ‘‘off’’ time is difficult to define or observe from a

single count rate histogram as the duration of the measure-

ment is limited by long term drift of the apparatus35 as well as

photobleaching of the dot.43

Since no upper bound for the ‘‘off’’ times could be deter-

mined from the single intensity time traces, the renewal

process was considered to be non-ergodic and unpredictable.58

Non-ergodic behaviour implies that the auto-correlation ana-

lysis of the fluorescence intensity fluctuations of a single

immobilized emitter, averaged over a sufficiently long obser-

vation time will not be the same as the auto-correlation

function of an intensity time trace of an ensemble of emitters

sampled for a much shorter time period. In contrast to this

prediction, Wiseman and coworkers60 using image correlation

spectroscopy (ICS), were able to show, in principle, that

individual blinking parameters were extractable from the

auto-correlation analysis of large ensembles of immobilized

dots. They showed that the auto-correlation function of the

count rate histogram from single emitters were reproducible,

provided histograms with a well represented range of ‘‘on’’

and ‘‘off’’ times were chosen. In a different but similar study,

Pelton et al.54 used Fourier analysis of the time fluctuations of

ensemble measurements. For a limited frequency (or time)

range, they could extract blinking statistics of single dots for

immobilized and mobile emitters. These latter studies54,60 and

observations of fluorescence decay for immobilized ensem-

bles32 indicate that a maximum ‘‘off’’ time in quantum dot

blinking does exist and these systems are not completely non-

ergodic.

Recently, a method for determining the maximum values for

the ‘‘on’’ and ‘‘off’’ times via recording the fluorescence decay

of an ensemble of immobilized quantum dots was published by

Bawendi and co-workers.32,33 The maximum ‘‘off’’ times

determined from their fluorescence decays were on the order

of many 1000s of seconds, much longer than typical observa-

tion times for single dots measurements. It appears that

blinking occurs over ten orders of magnitude in time

(10�6 up to 104 s).

(b) Spectral analysis and blinking

Since most experimental set-ups used to examine the fluores-

cence of quantum dots employ band pass emission filters, one

must examine the possibility that an off event is equivalent to a

transient shifting of the emission spectrum beyond the filter’s

cut-off wavelength. Blinking has been associated with small

reversible spectral shifts of a few nm which is also known as

spectral diffusion,39,40 in contrast to much larger spectral shifts

(10s of nm) which occur prior to permanent photobleaching

events.43 These small shifts should not significantly affect

detectability in a typical fluorescence experiment.

(c) Effect of environment/capping on other photophysical

characteristics

Blinking statistics suggest that the rate of sampling into the

‘‘off’’ state is increased with increasing temperature or laser

power, suggesting a barrier which activation energy is required

to cross.35 Recovery from the ‘‘off’’ state appears to be

independent of all environmental influences. Systematic inves-

tigations into the variance of the power law exponent with

environment are required. A value other than �0.5 for the

power law exponent of the ‘‘on’’ and ‘‘off’’ time distributions

infers that the process is not purely random, and that other

secondary interactions are occurring.61 The rate of photodes-

truction of a quantum dot can be directly correlated to the

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number of layers of capping material limiting the ‘‘off’’ times

present, being much slower for increasing numbers of layers.42

This suggests that capping layers are not grown epitaxially but

rather they contain grain boundaries through which oxygen

may diffuse into the core in order to promote destructive

oxidation.42

Other phenomenon observed for quantum dots making

them different from organic dye molecules include reversible

photo-induced photoluminescence enhancement,29,30 reversi-

ble photobleaching and photo darkening,31,32 as well as fluc-

tuating quantum yields23,28 and fluctuating and multiple

excited state lifetimes.31,62–65 Zhang et al.66 using intensity

changepoint reconstruction of the single emitter count rate

histogram could determine a positive, but not linear, correla-

tion of intensity with lifetime. Their results also indicate that a

pure stochastic model for quantum dot fluorescence intermit-

tency is inadequate and that a distribution of emission states

must exist. This is similar to the conclusions of Watkins and

Yang67 and Margolin et al.58 that the underlying mechanism

for blinking in quantum dots is the result of a distribution of

trap sites in either energy or space.

6. Excitation rate dependence of anomalous

fluorescence autocorrelation signals

In our group, we have examined the two-photon excitation

fluorescence autocorrelation decays of mobile quantum dots.

We observe an anomalous shape in the autocorrelation decay,

which appears to be a function of the excitation rate. Typical

laser power dependent autocorrelation decays are displayed in

Fig. 6. This figure shows a series of auto-correlation decays

which depict the dependence of green quantum dot autocor-

relation decay on laser power (i.e. excitation rate). As the laser

power is increased, a change appears in the autocorrelation

function in the 0.01 to 0.5 ms region. For the green quantum

dots, this effect then reaches an asymptote at approximately

60 mW.

In Fig. 7, two autocorrelation decays are displayed for

closer inspection. These are from a 2 nM solution of strepta-

vidin-functionalized green quantum dots (lem = 525 nm) in

borate buffer, at two different laser powers of 10 mW and

70 mW, and are plotted on two different amplitude scales. This

is necessary since the correlation function amplitude, G(0), is

strongly dependant upon laser power, and differences in the

shapes of the decay curves at short lag times, (t), are more

easily compared in such a plot. The 10 mW curve is shown in

black squares and is easily fitted using the normal expression

for diffusion.68

GðtÞ ¼ Gð0Þ 1þ 8Dto2

R

� ��11þ 8Dt

o2A

� ��1=2ð6Þ

where, t is the lag time, D is the diffusion constant, oR is the

laser beam waist at its focus and oA is the depth of focus. The

concentration and diffusion coefficient of the 525 nm

Fig. 6 Autocorrelation data at four different laser powers (9, 30, 60 and 203 mW) showing the development of the anomalous shape of the decay

curve. The diffusion only model best fit line is shown (black line) for comparison. The red channel data is for a solution that is approximately 1 nM

in 605 nm biotinylated Qdots (red channel) and 1 nM 525 streptavidin coated Qdots (green channel) in ultrapure (i.e. 18 MO) water.

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streptavidin coated quantum dots at 10 mW, using 3.3 fl for

the focal volume, were 2.1 nM and 3.5 � 10�11 m2 s�1,

respectively.

The 70 mW auto-correlation decay is represented by the

blue circles. Failure of the auto-correlation decay to form a

plateau at short lag times indicates the presence of a short

time-scale phenomenon, consistent with the blinking observed

by others for surface immobilized dots.3 The auto-correlation

amplitude at 70 mW cannot be fitted with eqn (6).

In order to parameterize the auto-correlation functions at

higher excitation rates, a model was developed to accommo-

date the anomalous shape of the autocorrelation decay. Such a

model allows a somewhat quantitative comparison of auto-

correlation decays under varying experimental conditions.

There is as yet no analytic expression connecting temporal

fluorescence intensity blinking (described by a power law

probability density distribution) with the temporal fluores-

cence intensity autocorrelation function. However, one can

begin with the premise that at higher excitation rates, there is

an increasing probability of observing blinking events in the

10 ms–10 ms time range. Beyond approximately 10 ms, the

fluorescence intensity dynamics are dominated by fluctuations

due to the quantum dots diffusing into and out of the TPE

volume. Thus, the form of model autocorrelation function can

be given in general:

GðtÞ ¼ Gdiff ðtÞ� 1þ F�gblinkðtÞ1� F

� �ð7Þ

where F represents the fraction of dots with detectable fluctua-

tions not described by the diffusion (i.e. eqn (6)). gblink(t) is thefunction that models the anomalous shape of the autocorrela-

tion decay. The form of gblink(t) that best describes this shapewas found empirically to be:

gblinkðtÞ ¼ Ata�2 ð8Þ

To fit the model function to the data, parameters a, A, F, oR

and oA were allowed to float. The parameters were optimized

via least squares analysis using the software package, Origin.

The resulting fit using eqn (7), is given for the 70 mW data, as

black line in Fig. 7.

Significantly, the value of a = 1.5 was found for all

anomalous autocorrelation decay fits. Although this region

of the autocorrelation decay is where triplet state blinking

effects appear for organic molecules, the short time behavior

for the quantum dots cannot be modeled adequately using a

standard singlet–triplet type coupling, which results in an

exponentially decaying contribution to the autocorrelation

function.69

At short times, changes in the value of G(t) are dominated

by blinking (t�1/2), because the diffusional contribution to

G(t) is constant. At times approaching the transit time, the

decay of G(t) is dominated by diffusional decay, which goes

like t�3/2. The change in excitation volume due to the higher

laser intensity is accounted for by also allowing the parameters

oR and oA to float, while holding the concentration and

diffusion coefficient constant at those values obtained with

eqn (6) at 10 mW.

The previous study of mobile quantum dots by Doose

et al.22 examined the possibility of factors other than blinking,

such as optical trapping and changes in concentration that

could influence the shape of the autocorrelation decay in a

laser power dependent manner. They determined that the

effect on the autocorrelation decay could not be explained

without accounting for blinking. To further test whether or

not the changes in the autocorrelation decays observed in the

present study result from blinking, fluorescence cross-correla-

tion spectroscopy of physically bound, but spectrally distinct

pairs of dots was used. Blinking should not be evident in the

cross-correlation signal unless the blinking between two joined

dots is synchronized.

The cross-correlation decay for physically bound dots of

different colors was measured for a series of laser powers. The

resulting cross-correlation decay curves for a solution of

605 nm biotinylated dots (QDB) and 525 nm streptavidin

coated dots (QDS), as a function of laser power, is given in

Fig. 8. The cross-correlation amplitude of two linked dots does

Fig. 7 Autocorrelation decays for a 10 nM solution of streptavidin

coated quantum dots (lem = 525 nm). The black squares (left scale)

represent the decay recorded for a laser excitation power of 10 mW

(two-photon excitation at 780 nm) at the back aperture of the objective

lens. The blue circles (right scale) represent the decay for a laser power

of 70 mW. The red and black lines are the best fits of the model given

by eqn (6) and (7), to the 10 mW and 70 mW decays, respectively.

Fig. 8 Cross correlation data at four different laser powers (13, 30, 60

and 203 mW) showing that the shape of the decay curve does not

deviate as it does in the autocorrelation analysis (see Fig. 6) of the

same solution. This suggests that the anomalous shape of the auto-

correlation curves in Fig. 6 is not due to saturation effects.

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not exhibit the ‘‘blinking effect’’ even with increased laser

power. This is not surprising since the blinking events from

each dot in the pair are not expected to be synchronized. The

QDB–QDS pair displayed no other evidence of electronic

coupling (i.e. no FRET signal between them). The cross

correlation data were fitted using eqn (6), which is a reason-

able approximation, assuming mostly 1 : 1 association of the

red and green dots. Eqn (6) does not explicitly account for

saturation effects,50,53 but appears to model the cross-correla-

tion data adequately by allowing the volume parameters to

float. The four cross-correlation plots are, in fact, from the

same solution and laser powers as those presented in Fig. 6.

The behavior in the absolute amplitude of the correlation

functions is similar. In going from 9 mW to 203 mW, the G(t)at 10�2 ms drop by a factor of slightly greater than 3. Such

behavior is rationalized in terms of an increase in the TPE

observation volume due to saturation of two-photon excita-

tion.50,53 Therefore, it is clear that the dots in the power studies

are under the influence of excitation saturation. However,

there is no evidence that saturation will lead to the changes

in the shape of the autocorrelation decay signal at short

times observed both by us (Fig. 6) and Weiss and co-workers

(Fig. 5).22

If we consider that the anomalous shape of the autocorrela-

tion decays shown in Fig. 5 and 6 results from quantum dot

blinking and not artifact, then it is interesting that the lag time

(ta�2) dependence of that part of the autocorrelation decays,

with a = 1.5 is similar to the dependence observed by Orrit

and coworkers.70 They reported a dependence of t�0.3 for

single uncapped, immobile CdS quantum dots. We measure

the ensemble average behavior, rather than the autocorrela-

tion decay for a single dot. Autocorrelation analysis of en-

sembles of CdSe quantum dots on surfaces has revealed

similar behavior.60 However, a different empirical model was

used for evaluation of lag times, which were recorded for the

range 0.1–30 s. As noted above, Weiss and co-workers ob-

served similar anomalous autocorrelation decay shapes for

mobile CdSe dots using one photon excitation FCS.22 More-

over, they observed that the anomalous shape depended on

excitation rate (i.e. laser power applied to the sample).

It would be of interest also to determine whether or not the

changes in short time correlation persist at longer times.

However, changes due to blinking are difficult to deconvolute

from the diffusional decay of the correlation functions.54 The

longer time correlation function behavior can be examined by

comparing the change in TPE volume dwell times, tD, forautocorrelation and cross-correlation decays as a function of

excitation rate. The dwell time in the excitation volume is

defined as:50

tD ¼o2

R

8Dð10Þ

Given that the cross-correlation signal is independent of

blinking dynamics, the dependence of dwell time versus laser

power should reflect only excitation saturation. In the case of

the autocorrelation decay, blinking dynamics with the same

characteristic time as the diffusional exchange in the excitation

volume could be convoluted and therefore, are potentially

measurable. For these measurements, we have again used the

same solution as that used to collect the data displayed in Fig.

6 and 8. In this solution a low degree of binding was main-

tained such that the autocorrelation decays represent mostly

free red and green quantum dots. Thus, the absolute values of

the dwell times are different for the red dots, green dots

(autocorrelation) and red–green bound dots (cross-correla-

tion). For comparison of tD versus excitation rate, the dwell

times were normalized to their values at the lowest laser

power, 9 mW. In Fig. 9 (tau-power), we find that the normal-

ized dwell times all follow the same power dependence within

measurement error. Thus, it appears that the phenomenon

that results in an anomalous shape of the autocorrelation

signal at short times, does not significantly affect the auto-

correlation signal at long lag times.

The similarity of excitation rate dependence between our

results and those of Weiss and coworkers22 is striking, despite

the different methods of excitation; two-photon versus one-

photon, respectively. Additionally, for an ensemble of surface-

bound quantum dots, Wiseman and workers60 also observed a

dependence of the blinking derived autocorrelation function

on excitation rate. These FCS-based results taken together

with fluorescence histogram analysis35,44,57,58 strongly support

that blinking behavior is related to excitation rate. For mobile

quantum dots, the interrogation window is limited by the

average transit time through the FCS detection volume,

typically a few milliseconds. The dots’ behavior over this time

window is then averaged over the many transit events of

different dots. The main advantage of FCS analysis of

quantum dots is that rare events in the time regime of 1 msto 1 ms can be accumulated and therefore detected. This is

challenging for a typical fluorescence histogram collection

Fig. 9 Normalized correlation decay times versus laser power. The

inset displays the fitted decay times for the autocorrelation of the red

detection channel (red dots), green detection channel (green dots) and

cross-correlation of the red and green channels (yellow dots). These

decays times are normalized (main graph) to their values at the lowest

power tD/tD (9 mW). The plots indicate that the changes in normal-

ized decay times with laser power are the same within error, which

suggests that these changes result from two-photon excitation satura-

tion, rather than blinking. These parameters were determined from

autocorrelation and cross-correlation analysis of a solution that was

approximately 1 nM in 605 nm biotinylated Qdots and 1 nM

525 streptavidin coated Qdots in ultrapure water, i.e. same as for

Fig. 6 and 8.

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experiment, where blinking probabilities are reported

over 10�3–102 s.35,44,57,58

7. Closing remarks

There are several intriguing possibilities for FCS to add to the

understanding and mitigation of quantum dot blinking. More

autocorrelation analysis in the time range 1 ms–1 ms of sur-

face-bound ensemble quantum dots would be illuminating.

The one study thus far38 reported mildly decaying autocorre-

lation data in this time range for uncapped CdS quantum dots.

FCS detection of mobile quantum dot blinking will provide a

mechanism to report on the changes in quantum dots’ re-

sponses to their environment. For example, our ongoing

studies involve using FCS to measure blinking in solutions

of varying ionic strength. Changing the quantum dots’ local

electronic environment should affect blinking, if ionization of

the dots is involved in the blinking process. Additionally, it is

clear that surface chemistry plays a major role in quantum dot

blinking.28,29,71 The addition of surface active agents to the

quantum dot solutions should affect blinking behavior as

measured by FCS. It will be interesting to determine whether

or not there is a difference between reducing and oxidizing

surfactants on blinking. Finally, it may be possible to send

quantum dots into dark states electrochemically,34 the kinetics

of which should be measurable using FCS.

Acknowledgements

The authors acknowledge the financial support of NSERC

through an AGENO grant and the Alberta Ingenuity Fund for

a graduate scholarship (JLS). We also acknowledge helpful

discussions with Professor Cecile Fradin (McMaster).

References

1 P. Alivisatos, Nat. Biotechnol., 2004, 22(1), 47–52.2 S. Courty, C. Luccardini, Y. Bellaiche, G. Cappello and M.Dahan, Nano Lett., 2006, 7, 1491–1495.

3 D. E. Gomez, M. Califano and P. Mulvaney, Phys. Chem. Chem.Phys., 2006, 8, 4989–5011.

4 J. K. Jaiswal, H. Mattoussi, J. M. Mauro and S. M. Simon, Nat.Biotechnol., 2003, 21, 47–51.

5 F. Chen and D. Gerion, Nano Lett., 2004, 4, 1827–1832.6 L. C. Mattheakis, J. M. Dias, Y. J. Choi, J. Gong, M. P. Bruchez,J. Liu and E. Wang, Anal. Biochem., 2004, 327, 200–208.

7 X. Gao, W. C. W. Chan and S. Nie, J. Biomed. Optics, 2002, 7(4),532–537.

8 I. L. Medintz, A. R. Clapp, H. Mattoussi, E. r. Goldman, B. Fisherand J. M. Maurio, Nat. Mater., 2003, 2, 630–638.

9 R. Baklova, H. Ohba, Z. Zhelev, T. Nagase, R. Jose, M. Ishikawaand Y. Baba, Nano Lett., 2004, 4, 1567–1573.

10 X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J.J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir and S. Weiss,Science, 2005, 307, 538–544.

11 R. Robelek, L. Niu, E. L. Schmid and W. Knoll, Anal. Chem.,2004, 76, 6160–6165.

12 A. R. Clapp, I. L. Medintz, J. M. Mauro, B. R. Fisher, M. G.Bawendi and H. Mattoussi, J. Am. Chem. Soc., 2003, 126, 301–310.

13 H. E. Grecco, K. A. Lidke, R. Heintzmann, D. S. Lidke, C.Spagnuolo, O. E. Martinez, E. A. Jares-Erijman and T. M. Jovin,Microsc. Res. Tech., 2004, 65, 169–179.

14 S. Kim, Y. T. Lim, E. G. Soltesz, A. M. DeGrand, J. Lee, A.Nakayama, J. A. Parker, T. Mihaljevic, R. G. Laurence, D. M.Dor, L. H. Cohn, M. G. Bawendi and J. V. Frangioni, Nat.Biotechnol., 2004, 22, 93–96.

15 M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau and A.Triller, Science, 2003, 302, 442–445.

16 W. J. Parak, D. Gerion, T. Pellegrino, D. Zanchet, C. Micheel, S.C. Williams, R. Boudreau, M. A. Le Gros, C. A. Larabell and A.P. Alivisatos, Nanotechnology, 2003, 14, R15–R27.

17 w. C. W. Chan, D. J. Maxwell, X. Gao, R. E. Bailey, M. Han andS. Nie, Curr. Opin. Biotechnol., 2002, 13, 40–46.

18 W. C. W. Chan and S. Nie, Science, 1998, 281, 2016–2018.19 C. B. Murray, D. J. Norris andM. G. Bawendi, J. Am. Chem. Soc.,

1993, 115, 8706–8715.20 F. Pinaud, D. King, H. P. Moore and S. Weiss, J. Am. Chem. Soc.,

2004, 126, 6115–6123.21 S. J. Rosenthal, I. Tomilinson, E. M. Adkins, S. Schroeter, S.

Adams, L. Swafford, J. McBride, Y. Wang, L. J. DeFelice and R.D. Blakely, J. Am. Chem. Soc., 2002, 124, 4586–4594.

22 S. Doose, J. M. Tsay, F. Pinaud and S. Weiss, Anal. Chem., 2005,77(7), 2235–42.

23 J. Yao, D. R. Larson, H. D. Vishwasrao, W. R. Zipfel and W. W.Webb, PNAS, 2005, 102, 14284–14289.

24 D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P.Bruchez, F. W. Wise and W. W. Webb, Science, 2003, 300,1434–1436.

25 J. L. Swift, R. F. Heuff and D. T. Cramb, Biophys. J., 2006, 90,1396–1410.

26 L. C. Hwang and T. Wohland, ChemPhysChem, 2004, 5, 549–551.27 T. D. Krauss, S. O’Brian and L. E. Brus, J. Phys. Chem. B, 2001,

105, 1725–1733.28 C. Bullen and P. Mulvaney, Langmuir, 2006, 22, 3007–3013.29 J. A. Gaunt, A. E. Knight, S. A. Windsor and V. Chechik, J.

Colloid Interface Sci., 2005, 290, 437–443.30 T. Uematsu, S. Maenosono and Y. Yamaguchi, J. Phys. Chem. B,

2005, 109, 8613–8618.31 M. Jones, J. Nedeljkovic, R. J. Ellingson, A. J. Nozik and G.

Rumbles, J. Phys. Chem. B, 2003, 107, 11346–11352.32 I. Chung and M. G. Bawendi, Phys. Rev. B: Condens. Matter,

2004, 70, 165304.33 I. Chung, J. B. Witkoskie, J. Cao and M. G. Bawendi, Phys. Rev.

E, 2006, 73, 011106.34 C. Wang, M. Shim and P. Guyot-Sionnest, Science, 2001, 291,

2390–2392.35 M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher and D. J.

Nesbitt, J. Chem. Phys., 2001, 115, 1028–1040.36 G. Galli, A. Puzder, A. J. Williamson, J. C. Grossman and L.

Pizzagalli, Structural and electronic properties of quantum dotsurfaces. www.nsti.org/publ/MSM2002/382.pdf.

37 P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F.Strouse and S. K. Buratto, Nature, 2000, 406, 968–970.

38 G. Messin, J. P. Hermier, E. Giacobino, P. Desbiolles and M.Dahan, Opt. Lett., 2001, 26, 1891–1893.

39 R. G. Neuhauser, K. T. Shimizu, W. K. Woo, S. A. Empedoclesand M. G. Bawendi, Phys. Rev. Lett., 2000, 85, 3301–3304.

40 S. A. Empedocles, D. J. Norris and M. G. Bawendi, Phys. Rev.Lett., 1996, 77, 3873–3876.

41 U. Banin, M. Bruchez, A. P. Alivisatos, T. Ha, S. Weiss and D. S.Chemla, J. Chem. Phys., 1999, 110, 11995–1201.

42 B. R. Fisher, H. J. Eisler, N. E. Stott and M. G. Bawendi, J. Phys.Chem. B, 2004, 108, 143–148.

43 W. G. J. H. M. van Sark, P. L. T. M. Frederix, D. J. Van denHeuvel, H. C. Gerritsen, A. A. Bol, J. N. J. van Lingen, C. deMello Donega and A. Meijerink, J. Phys. Chem. B, 2001, 105,8281–8284.

44 K. T. Shmizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empe-docles, W. K. Woo and M. G. Bawendi, Phys. Rev. B: Condens.Matter, 2001, 63, 205316.

45 S. Hohng and T. Ha, J. Am. Chem. Soc., 2004, 126, 1324–1325.46 A. L. Efros and M. Rosen, Phys. Rev. Lett., 1997, 78, 1110–

1113.47 P. Schwille, Cell Biochem. Biophys., 2001, 34, 383–405.48 T. Liedl, S. Keller, F. C. Simmel, J. O. Radler and W. J. Parak,

Small, 2005, 1(10), 997–1003.49 J. A. Rochira, M. V. Gudheti, T. J. Gould, R. R. Laughlin, J. L.

Nadeau and S. T. Hess, J. Phys. Chem., 2007, 111, 1695–1708.50 K. Berland and G. Shen, Appl. Opt., 2003, 42, 5566–5576.51 I. Gregor, D. Patra and J. Enderlein, ChemPhysChem, 2005, 6,

164–170.

This journal is �c the Owner Societies 2007 Phys. Chem. Chem. Phys., 2007, 9, 1870–1880 | 1879

Dow

nloa

ded

by U

nive

rsity

of

Cal

gary

on

03 J

uly

2012

Publ

ishe

d on

02

Mar

ch 2

007

on h

ttp://

pubs

.rsc

.org

| do

i:10.

1039

/B61

7115

J

View Online

52 S. T. Hess and W. W. Webb, Biophys. J., 2002, 83, 2300–2317.

53 A. Nagy, J. Wu and K. M. Berland, Biophys. J., 2005, 89,2077–2090.

54 M. Pelton, D. G. Grier and P. Guyot-Sionnest, Appl. Phys. Lett.,2004, 85, 819–821.

55 V. Iyer, M. J. Rossow and M. N. Waxham, J. Opt. Soc. Am. B,2006, 23, 1420–1433.

56 G. Margolin and E. Barkai, J. Chem. Phys., 2004, 121, 1566–1577.57 M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher and D. J.

Nesbitt, J. Chem. Phys., 2000, 112, 3117–3120.58 G. Margolin, V. Protasenko, M. Kuno and E. Barkai, http://

arxiv.org/list/cond-mat/cond-mat/050612v2, 2006.59 J. Tang and A. Marcus, J. Chem. Phys., 2005, 123, 054704(12).60 A. I. Bachir, N. Durisic, B. Hebert, P. Gr +utter and P. W. Wiseman,

J. Appl. Phys., 2006, 99, 064503-1(7).61 C. Godreche and J. M. Luck, J. Stat. Phys., 2000, 104, 489–524.62 M. Dahan, T. Laurence, F. Pinaud, D. S. Chemla, A. P. Alivistos,

M. Sauer and S. Weiss, Opt. Lett., 2001, 26, 825–827.

63 X. Brokmann, L. Coolen, M. Dahan and J. P. Hermier, Phys. Rev.Lett., 2004, 93, 107403-1(4).

64 G. Schlegel, J. Bohnenberger, I. Potapova and A. Mews, Phys.Rev. Lett., 2002, 88, 137401-1(4).

65 W. Z. Lee, G. W. Shu, J. S. Wang, J. L. Shen, C. A. Lin, W. H.Chang, R. C. Ruaan, W. C. Chou, C. H. Lu and Y. C. Lee,Nanotechnology, 2005, 16, 1517–1521.

66 K. Zhang, H. Chang, A. Fu, A. P. Alivisatos and H. Yang, NanoLett., 2006, 6, 843–847.

67 L. P. Watkins and H. Yang, J. Phys. Chem. B, 2005, 109, 617–628.

68 J. L. Swift, T. E. S. Dahms and D. T. Cramb, J. Phys. Chem. B,2004, 108, 11133–11138.

69 C. Eggeling, A. Volkmer and C. Seidel, ChemPhysChem, 2005, 6,791–804.

70 R. Verberk, A. M. van Oijen and M. Oritt, Phys. Rev. B: Condens.Matter, 2002, 66, 233202.

71 J. A. Kloepfer, S. E. Bradforth and J. L. Nadeau, J. Phys. Chem. B,2005, 109, 9996–10003.

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