LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

A

CXXXX American Chemical Society

Calibrating and Controlling theQuantum Efficiency Distributionof Inhomogeneously BroadenedQuantum Rods by Using a Mirror BallPer Lunnemann,*,†,§ Freddy T. Rabouw,‡ Relinde J. A. van Dijk-Moes,‡ Francesca Pietra,‡

Daniel Vanmaekelbergh,‡ and A. Femius Koenderink†

†Center for Nanophotonics, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands, ‡Condensed Matter and Interfaces, Debye Institute forNanomaterials Science, Princetonplein 1, 3584 CC Utrecht, The Netherlands, and §DTU Fotonik, Department of Photonics Engineering, Østedsplads 343, DK-2800,Denmark

Over the past decades, the develop-ment of bright single emittersacross the visible and near-infrared

spectrum has experienced major progress.Today there exist numerous different typeof single emitters such as organic dye mol-ecules, chemically synthesized II�VI nano-crystals, and epitaxially grown III�V semi-conductor quantum dots. Their usage spansfrom fluorescence microscopy,1,2 light emit-ting diodes,3 lasers, optical amplifiers,4,5 andquantum photonics.6,7 Especially the semi-conductor based emitters are promising dueto the possibility of tailoring their emissionwavelength through size, their exceptionallylarge oscillator strength, and the potential ofintegration with photonic structures usingtop down semiconductor fabrication, or bot-tomup self-assembly techniques. A commongoal is to optimize light emission and extrac-tion and to reduce undesirable nonradiative

decay processes. This may either be donethrough engineering of the electronic struc-ture of the emitter through a suitable choiceofmaterials and synthesis routes, or by tailor-ing the photonic environment.8�11 The ra-diative emission rate depends on the localdensity of optical states (LDOS), as givenby Fermi's golden rule,12,13 and may be con-trolled by structuring the surrounding ma-terial. Photonic crystals as well as plasmonicoptical antennas have been successfullydemonstrated to enhance and guide lightemission.8,9,14�16 To assess the success ofstrategies to improve emitters, whetherthroughchemistry orphotonics, it is essentialto have a method that determines radiativeand nonradiative decay rates, as well asquantumefficiencies in a rapid, yet calibratedmanner.An established technique to measure

the intrinsic nonradiative and radiative time

* Address correspondence toplha@fotonik.dtu.dk.

Received for review April 5, 2013and accepted June 26, 2013.

Published online10.1021/nn401683u

ABSTRACT We demonstrate that a simple silver coated ball lens

can be used to accurately measure the entire distribution of radiative

transition rates of quantum dot nanocrystals. This simple and cost-

effective implementation of Drexhage's method that uses nanometer-

controlled optical mode density variations near a mirror, not only

allows an extraction of calibrated ensemble-averaged rates, but for

the first time also to quantify the full inhomogeneous dispersion of

radiative and non radiative decay rates across thousands of nano-

crystals. We apply the technique to novel ultrastable CdSe/CdS dot-in-

rod emitters. The emitters are of large current interest due to their improved stability and reduced blinking. We retrieve a room-temperature ensemble

average quantum efficiency of 0.87 ( 0.08 at a mean lifetime around 20 ns. We confirm a log-normal distribution of decay rates as often assumed in

literature, and we show that the rate distribution-width, that amounts to about 30% of the mean decay rate, is strongly dependent on the local density of

optical states.

KEYWORDS: quantum dots . nanorods . quantum rods . quantum efficiency . Drexhage . optical density of states .decay-rate distribution

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

B

constants of an emitter is based on applying a well-defined change of the LDOS by changing the distanceof an emitter to a planar mirror, as pioneered byDrexhage et al.17 By measuring the fluorescence decayrate, which is the sum of nonradiative and radiativedecay constants, as a function of LDOS, it is possible toextract the contribution of nonradiative decay, sinceonly the radiative decay rate varies with LDOS. Asopposed to brightness comparisons or integratingspheremeasurements, Drexhage's method is absolute,requires no reference, and is artifact free. The methodhas been applied to rare earth ions,17�19 organic dyemolecules,20,21 epitaxially grown III�V semiconductorQDs,22�24 and chemically synthesized II�VI semicon-ductor QDs.20,25,26 Unfortunately, these experimentsare cumbersome to implement,25 requiring eitherelaborate deposition techniques, or sample-specificetching methodologies to vary the emitter�mirrordistance.22�24 One of the simplest reported implemen-tations of the technique is based on a gray-tonelithography to fabricate an inclined spacer layer ontop of the emitters.20 While the fabrication is relativelysimple, a required UV exposure may photobleachemitters already prior to testing. Furthermore, UVlithographymaterials tend to show strong backgroundfluorescence and involve solvents that put the integrityof the emitters at risk. Finally, we note that the methodis not suitable for calibrating an actual device; that is, itrequires a sample dedicated for calibration. Anothersimple implementation26 is based on measuring thedecay rate of emitters at two positions, one in frontof an PMMA�air interface and one with no interfaceby simply adding a droplet of index matched PDMSon top of the PMMA. While the method is simple, thecontrolled change of the LDOS is very small (∼15%),thus limiting the method to emitters with a largequantum efficiency. Second, the simplicity of onlymeasuring at two distances comes at the cost ofcompromising the robustness of the calibration(fitting a straight line to two points). Recently micro-mechanical techniques to vary emitter�mirror dis-tance were introduced, which avoid such chemistry-related issues, and are excellent for single-moleculestudies. However, micromanipulation is technicallychallenging and not easily scaled to obtain ensemblestatistics beyond a few tens of molecules.27�29

Here, we report on an implementation of Drexhage'smethod that has two main benefits: First, the methodserves as simplification of a well-known measurementtechnique to calibrate the ensemble radiate decay rate.Without the need for lithography or sample-specificchemistry, the method allows for significant savings interms of measurement efforts, without compromisingthe fidelity. Second, andmore importantly, themethodallows retrieving information beyond ensemble-average rates. We demonstrate this benefit by showinghow the entire distribution of decay rates of a huge

ensemble of 105 quantum dots depends on the LDOS.We apply the method on a novel promising CdSe/CdSrod structure that shows a reduction of the universalphenomenon of fluorescence intermittency, that is,blinking. As with all currently available quantum dots,theensembles are very inhomogeneous, but byusing thismethod we demonstrate, for the first time, exactly howthe entire ensemble of rates are distributed andmodifiedby the LDOS using the massive acquired data set.The essence of our Drexhage method implementa-

tion is that we realize a precise yet low cost mirror thatcan be used to perform the entire measurement on asingle submillimeter size sample, and that may bereused on many samples. The mirror is created byevaporating a thin layer of silver onto a commerciallyavailable ball-lens. The spherical mirror is then put ontop of a thin glass substrate that is spin coated withemitters, see Figure 1.In the following section, we first show how rates for

an entire ensemble of 105 emitters are extracted.Subsequently, we uncover that the huge distributionof rates is not associated at all with a spread ofnonradiative decay, but rather a spread in intrinsicradiative decay rates in combination with a dipole-orientation dependence caused by the substrate.

RESULTS AND DISCUSSION

Figure 2 presents a map of the collected photoncounts of a confocal scan performed on a 400 � 400

Figure 1. (a) Illustration (not to scale) of the mirror config-uration. The silver coated ball lenses are mounted in a tripodconfiguration for easier handling and fixation of the position.Red spheres indicate the nanorods while green is the pumplight. The inset shows a TEM image of the nanorods (b) Crosssectional illustration of themeasurement setup (not to scale).

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

C

pixel grid covering a 115 μm � 115 μm square cor-responding to a step size of 290 nm. We observeconcentric rings with a low count region in the middlethat is identified as the center of the sphere. Weparticularly tuned the nanorod dilution such that atthe given collection area and step size we obtaininformation beyond the ensemble averaged rate.An example of a histogram of counts from points in aconcentric ring about the mirror center is presented inthe inset of Figure 2, together with the correspondingPoisson distribution. The clear mismatch between thetwo distributions clarifies that indeed the granularityof the image is not Poisson photon counting noise, aswould be expected from a homogeneous layer at thiscount rate. To estimate an upper bound to the meannumber of quantum dots probed per pixel, assumethat each NR yields the same intensity without photoncounting noise. Under this assumption, the entire dis-tribution in counts comes from the shot noise in thenumber N of NRs per pixel. Taking the ratio of width tomeanof the count distribution as estimate for (1/(ÆNæ)1/2),we find, for the points indicated in blue in Figure 2,that the mean ÆNæ is at most 1.2 NRs/px. This is an upperbound since the estimate ignores other evident sourcesof noise in the histogram. From this we conclude thatgranularity is associated with the discrete nature of theemitters. While in each pixel, we probe the decay rate ofapproximately oneor fewNRs, takingpixels in concentricrings around the spherical mirror center together willadd to an ensemble of many quantum dot-in-rodemitters at a fixed emitter�mirror separation distance(see Figure 2). In the central low count region, all NRs arein close vicinity to the metal surface. Radiative emis-sion is therefore quenched due to resonant couplingto the surface plasmons polariton (SPP) mode.19 Movingradially out from the center, the observed fringes inintensity are largely due to the standing wave thatthe pump laser and its reflection form at the interface.

The thin streak of lower counts within the left part of thefirst ring we attribute to a surface irregularity such as aminute scratch, on the mirror surface.For each position in Figure 2,we histogram the arrival

times of the detected photons relative to the laser pulsein bins of 1.32 ns (an 8-fold coarsening relative to thetiming card resolution). From the accumulated histo-gram, we extract a fluorescence decay rate by fitting asingle-exponential decay with an added background.Importantly, sincewe are counting the photons arrivingwithin specified time bins, our data are characterizedby having a Poissonian probability distribution withineach time bin. Using the maximum-likelihood fittingprocedure,30 Poissonian statistics implies minimizinga merit function of the form �∑i=1

N {D(ti)log[Fγ(ti)] �Fγ(ti)}, where D(ti) is the measured counts in the ithbin and Fγ is the fit function with fit parameter(s) γ.While this method is common practice in the field oftime correlated single photon counting, we note thatthe often used least squared residual merit functionapplies for Gaussian statistics. Although, for largecounts, the Poissonian distribution approaches theGaussian distribution, the correct choice of a merit func-tion implied by Poissonian statistics is crucial for ourexperiment with low counts. Examples of measureddecay traces and the fitted single exponential curve forthree isolated measurement positions are presented inFigure 3a. The location of these three pixels is indicatedin the complete map of extracted decay rates inFigure 3b. We find a clear modulation of the decayrate in concentric rings around the mirror center, with

Figure 3. (a) Examplemeasureddecay traces at three isolatedpositions, each collected over 20ms. A single exponential fit isshown as a black solid line. (b) The map of extracted decayrates versus lateral position under the mirror shows a clearmodulation. Blue pixels mark positions with counts below40where no fit was attempted. The three positions associatedwith panel a are indicated with a green circle (a, left), a cross(a, middle) and a plus (a, right).

Figure 2. Detected counts of a 400 by 400 step confocalscan corresponding to ∼115 μm � 115 μm scan. The bluering indicates points in a concentric ring around the sphe-rical mirror center that are histogrammed (top right, blue).On top, the corresponding Poisson distribution, scaled by0.2 is plotted (red). Themismatch between the distributionssignify that the granularity of the image is associated withthe discrete nature of the emitters rather than Poissonphoton counting noise.

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

D

the largest decay rates at positions in close vicinity tothe mirror surface. Blue pixels in the map mark posi-tions with below 40 counts in the entire decay trace,where no fit was attempted. To confirm that using asingle exponential function applies to the currentemitters, we carried out several measurements onsingle NRs far away from the mirror, integrating over150 s (see Supporting Information). The acquiredhistogram from the total set of data exhibited excel-lently single exponential behavior with an estimateddecay rate of 56.36 μs�1 and an associated standarddeviation of only (0.05%. While, the confidence inter-vals of the extracted decay rate at each pixel in Figure 3differ significantly primarily due to the span in countsranging from 40 counts to several hundreds, we notethat from the long integration time experiment onsingle NRs, the standard deviation of the estimatedrates of each 20 ms time frame was ca.(14% for each20 ms (see Supporting Information), thus confirmingthat indeed it is possible to establish decay ratedynamics with counts on the order of 100.31

To quantitatively extract radiative and nonradiativerates, we convert the pixel coordinates in the 2D mapto emitter�mirror separation, so that the data canbe compared to LDOS calculations. We identify thecontact point, F0, of the sphere with the substrateas the center of the rings in figure 2 with an estimatedaccuracy of 5 nm. Next, as a measure for the emitter�mirror separation we calculate the radial distanced from themirror surface to an emitter on the substrateas d(r) = (R2 þ |r � r0|

2)1/2 � R, where R denotes theradius of the coated ball lens. We bin all measurementpoints into a set of concentric bands di, defined byhaving emitter�mirror separation di � δd/2 e d(F) <di þ δd/2 . For each band, we calculate a histogram ofthe extracted decay rates, using a bin size of 2 μs�1. Theextracted decay rate histograms are plotted in Figure 4as a function of distance, using a δd = 34 nm. Eachhistogram typically contains decay rates fitted to ap-proximately 3000 pixels. We observe a wide spread indecay rates for each distance, with a mean decay rateof around 50 μs�1 (decay time 20 ns), and a relativedistribution width of about 50%. Since the statisticaluncertainty associated with the fitted decay rate ofeach pixel (typically ∼3 μs�1, comparable to a singlehistogrambinwidth) ismuch smaller than theobservedspread of decay rates, we attribute the width to inho-mogeneous broadening of the NRs. Notably, the entirehistogram clearly shifts depending on distance to themirror. To define the mean decay rate and the width ofthe distribution, the histogram at each distance is fittedwith a log-normal-distribution defined through

P(γ; μ,σ) ¼ 1γσ

ffiffiffiπ

p e�(lnγ� μ)2=σ2(1)

where σ and μ are the standard deviation and meanof lnγ, respectively. The most frequent decay rate,

γ0, and the standard deviation, Δγ, are related toμ and σ as

γ0 ¼ eμ� σ2(2)

Δγ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(eσ2� 1)e2μþσ2

p(3)

As seen from the inset in Figure 4, the log-normaldistribution describes our data excellently. The fittedmost frequent decay rate, γ0, is plotted with red circlesin Figure 4. The error bars indicate a 95% confidenceinterval ofγ0.We clearly resolve oscillations of themeandecay rate as well as the decay rate divergence at verysmall distances, as expected from the modulation ofthe LDOS at a metal interface. In the following we firstdiscuss the dependence of the mean decay rate ondistance to the mirror, and then further discuss thehistogram width.As in usual ensemble measurements, we combine

calculated LDOS and themeasuredmean decay rate tofit values for the intrinsic ensemble average γrad, and

Figure 4. (a) Measured decay rates as a function of distanceto the mirror. Plotted in gray colors is the histogram ofextracted decay rates for a given distance. The inset showsan example of the acquired histogram of decay rates at adistance 0.32 μm, indicated by the dashed box. Redmarkersindicate the extracted most frequent γ0 for each distancebased on a fitted normal distribution. The error bars indicatethe 95% confidence interval of the extracted decay rate γ0.The blue curve is a weighted fit based on eq 4 assuming acentral wavelength of 610 nmwith fitted quantum efficiencyη and intrinsic total decay rate, γtot

(¥) stated in the white box.(b) Red data points with error bars: the extracted standarddeviation, Δγ, of the log-normal distribution of decay rates.Dashed line: expectedhistogramwidthassumingan intrinsicradiative rate distribution width of Δγrad

(¥) = 7.5 μs�1, if allemitters would experience the same, mean LDOS. Solid blueline: effect of orientation-dependent LDOS, assuming thesame mean decay rate for all NRs, added to the dashed line.Orange dashed curve: as solid blue line, but also includingthe wavelength-spread induced LDOS variation. The wave-length inhomogeneity is unimportant in determining theLDOS dependence of the decay rate distribution width.

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

E

nonradiative decay rate γnr. Using F(d) to denote thecalculated LDOS enhancement relative to the LDOS inSiO2 in absence of themirror, we fit themeasuredmostfrequent decay rate γ0(d) to

γ0(d) ¼ γ(¥)totf1þ η[F(d) � 1]g (4)

The two fit parameters represent the ensemble-average total decay rate γtot

(¥) for the quantum dot-in-rod emitters in glass, in absence of the mirror, andthe ensemble-average quantum efficiency η (again inabsence of the mirror). The calculation of F(d) assumesa stratified structure consisting of a semi-infiniteglass substrate, vacuum, SiO2, and a semi-infinite Agslab. The assumption of a stratified parallel layeredstructure is well approximated from the fact that themaximum angle between the tangent of the mirrorand the glass interface is 1.4�. The calculations usesthe established integration methodology reported inref 32 and the parameters listed in Table 1. Therefractive indices of the SiO2 and Ag layer weremeasured by ellipsometry. As wavelength we takethe center emission wavelength from the measuredensemble emission spectrum, and take the emitterlocation as 20 nm above the glass substrate to accountfor the SiO2 shell.We find an excellent fit to themean decay rate when

we assume isotropically oriented transition dipolemoments, in good agreement with earlier results onCdS/ZnS quantum dots.25 In this work, Leistikow et al.simulated decay traces assuming a 2D degeneratedipole moment in each quantum dot in an isotropicensemble, exactly in a Drexhage geometry. Despite thedegeneracy, the conclusion is that rates fitted to thedecay traces should fit very well with the isotropicallyaveraged LDOS. This is opposed to self-assembledIII�V semiconductor quantum dots that are stronglyoriented parallel to the plane of growth.22 We get afitted ensemble-average total decay rate of γtot

(¥) = 49(3 μs�1 and an intrinsic ensemble-average quantumefficiency of η = 0.87 ( 0.08. Previous experimentalwork on CdSe/CdS NRs33,34 concluded on the basis ofstrongly polarized emission that the emission dipole ofNRs is oriented along the long axis of theNRs. However,owing to the thick SiO2 shell, the NRs in our experimentdo not necessarily lie flat on the surface, explainingthat the best fit is obtained assuming isotropic dipole

orientation. The fitted values show that at a mean totalfluorescence lifetime of 19 ns, and quantum efficiencyof around 90%, the CdSe dot in the CdS rod systemis highly promising for applications as a brightemitter. The fitted quantum efficiency is well abovethe ensemble quantum efficiency that we obtainfrom absorption/emission brightness measurements,in good agreement with previous ensemble studies ofquantum dots (QDs),20,25 because dark quantum dotsare counted in ensemble absorption, but not in emis-sion lifetime measurements. A subtle point here is thatthese particular quantum dot-in-rods in fact do nothave a completely dark state, but rather show inter-mittent switching between a bright state, and a graystate that is only approximately three times dimmerthan the bright state. As the nanorods in the gray statehave an estimated quantum efficiency around fourtimes lower than the bright state, and do contributeto the decay rate traces, the fitted η = 0.87 ( 0.08provides an underestimate for the actual quantumefficiency of the bright state.The main advantage of our newmethod to calibrate

fluorophores, in addition to simplicity, is that informa-tion beyond ensemble average rate and quantumefficiency is obtained, in the form of the full histogramof decay rates, comprising thousands of emitters. Wenow turn to a discussion of the histogram beyond theaverage rate. In previous reports, log-normal distribu-tions have been assumed to describe the decay ratedistribution of ensembles of quantum dots.20,35,36

However, in those reports only a single decay tracefor an entire ensemble of dots was recorded, whichwas fitted to the decay expected for a log-normaldistribution of rates. This procedure relies on anassumed distribution of rates, while in fact the ensem-ble-average decay transient that is measured mightbe fitted by many different nonsingle exponential fitfunctions. We here provide a method that can directlyprove or disprove the suitability of a particular ratedistribution. For this particular system, we find thatthe rates follow a log-normal distribution (see, forexample, the inset in Figure 4). Importantly, whenwe reverse the order of ensemble averaging, that is,fitting pixel-averaged decay traces with a decay lawfor log-normally distributed rates, we find a similarmost frequent decay rate and distribution width,which provides an a posteriori validation of previousapproaches.20,35,36

Considering Figure 4, the width of the decay ratedistribution evidently varies with LDOS, that is, withmirror�emitter separation. At small separations to themirror, where the mean decay rate depends stronglyon the distance to the mirror, we find a strong changein the width of the rate distribution that follows theLDOS variation. An LDOS dependence of the distribu-tion width is induced through various mechanisms.To first order, the combined effect of LDOS on the width

TABLE 1. Parameters Used for Calculating the LDOSa

parameter value

*thickness SiO2 35 nm*refractive index SiO2 1.523*refractive index Ag 0.0751 þ i4.191height above glass substrate of emitter 20 nm*centre emission wavelength 610 nm

a Parameters marked by an asterisk (/) indicate a measured quantity, while thosewithout are estimates.

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

F

can be written as

Δγ(z) ¼ Δγnr þΔγ(¥)rad 3 F(z)þ γ(¥)rad 3ΔF(z) (5)

Here, the first two terms describe the effect of anintrinsic inhomogeneous broadening, for instance dueto size and shape dispersion, separated in a LDOS-insensitive nonradiative contribution Δγnr as well asa LDOS-dependent radiative rate distribution. If allsources are subject to the same LDOS variation, allthe radiative rates within the distribution are multi-plied by the LDOS. Therefore, if all sources are highlyefficient, the width of the distribution is directly pro-portional to the LDOS at the emission frequency,so that the width scales as Δγ = Δγ¥ 3 F(z). Conversely,the width of the rate distribution would remain inde-pendent of distance if the spread is purely due to adistribution in nonradiative decay constants, Δγnr. Thethird term in eq 5 accounts for a second effect thatalso affects the distribution, namely, that the mirroroffers a different LDOS for different transition dipolemoment orientations, and emitters with different emis-sion wavelengths in the inhomogeneous ensemble.To investigate the role of dipole moment orientationsand emitter wavelengths we have calculated the var-iation ΔF in LDOS for the two scenarios: (1) taking intoaccount the randomdipole orientation, while assumingthat all emitters emit with the samewavelength, and (2)taking into account the measured inhomogeneouslybroadened ensemble spectrum, while assuming thatall emitters experience the orientationally averagedLDOS. For evaluation of the first scenario, we notethat from the calculated LDOS at parallel and per-pendicular dipole orientation relative to the substratenormal, the rate at any dipole orientation is completelyknown,37 and hence the distribution. We find that theLDOS distribution induced through inhomogeneousbroadening of the emission wavelength is negligiblecompared to the distribution caused by orientationaleffects.In Figure 4b we plot the different contributions to

the measured histogram width, and compare thesewith the data. The intrinsic inhomogeneous decay ratedistribution, corresponding to NRs in a homogeneousdielectric environment, contributes approximately halfof the observed width. The other half is contributed bythe orientation dependence of the local density ofstates. Setting the intrinsic inhomogeneous broaden-ing of the radiative decay rate to a width Δγrad

(¥) =7.5 μs�1 we find a reasonable agreement with themeasurements except for distances close to themirror.Interestingly, we found the best fit setting Δγnr = 0,implying thatmost broadening is causedby a spread ofradiative decay rates, and not nonradiative effects. Thisassessment is first consistent with the high quantumefficiency fitted to the mean decay rate, which indi-cates that nonradiative contributions are negligible,

and second indicates that for the fastest decayingemitters in the ensemble, the quantum efficiency isnot necessarily lower than for the slowest ones. Withregard to the contribution of dipole orientation, wenote thatΔFθ does not vanish far away from themirror,as a result of the glass substrate causing a dipole-orientation dependence on the LDOS even in theabsence of the mirror. It might be argued that the factthat half of the decay rate distribution width is due toorientation dependence at the glass�air interface, andnot to a difference in oscillator strength, is an artifact ofthe measurement method. However, we argue thatthis is by no means a limitation. First, as the glass�airinterface is completely understood, the measurementcan be corrected for the orientation dependence, sothat the calibration still gives complete access to theentire intrinsic distribution that is otherwise comple-tely inaccessible by any other method. This correctionis applicable in any casewhere the intrinsic distributionis comparable in width to the orientational spreadin LDOS. Second, the experiment could easily bemodified to use an immersion liquid between balland sample, removing the intrinsic orientation depen-dence. Third, and most importantly, if the presence ofthe glass�air interface is to be deemed an artifact, itmust be realized that it is in fact an artifact common toalmost all state-of-the-art single quantum dot studies.Almost all state-of-the-art single quantum dot studiesaimed at quantifying charge dynamics, Auger recom-bination, blinking, spectral wandering, etc. are carriedout right at the interface of a glass microscope slide(e.g. see refs 31, 33, and 38�40). The distribution weuncover is hence directly representative for all suchstudies, and conversely, it is an important realizationthat all such studies will result in widely distributedvalues of extracted parameters, unless the measure-ment is corrected for the glass�air interface and itsLDOS.

CONCLUSION

We have demonstrated a novel implementation ofthe Drexhage experiment for extracting the ensemble-average radiative decay rate and quantum efficiency ofdipole emitters. On one hand, the method serves as asimplification of a well-known measurement tech-nique that allows for momentous savings in measure-ments efforts. In our method, the measurementprocedure is still sequential, as we aim to uncover anentire ensemble statistics. However if just ensemble-average data are desired, by using a streak camera onecould collect the entire data set in a single shot in amatter of seconds. On the other hand, these hugesavings in simplicity open up new and exciting possi-bilities, for instance, that of acquiring so far inaccessibleinformation of the entire distribution of decay tracesfrom a huge ensemble with 104 to 105 emitters, andits dependence on the local density of optical states.

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

G

Themethod is based on the use of a very simplemetal-coated ball lens to create a controlled local density ofoptical states variation. We applied this method to atype of CdSe/CdS dot-in-rod nanocrystals, a novelstructure that holds promise to show excellent photo-stability and the absence of a true dark state, andaccording to our measurement has a quantum effi-ciency of 80% or above. We anticipate our method tohave many applications, since the ball lens is not onlyeasily fabricated but also can simply be placed on topof, and subsequently removed from, any sample sub-strate. This advantage moves Drexhage calibrationfrom a tedious system specific fabrication procedureto be applied on dedicated test samples to a methodthat could even be applied on actual completelyfunctional devices, such as for instance III-nitridelight-emitting diodes and organic light-emittingdiodes. Furthermore, we have demonstrated that thisnew technique provides a unique opportunity to un-cover photophysical parameters beyond ensemble-averaged decay traces. By carefully chosen dilutionwe operate at just one or a few quantum dot-in-rodemitters per pixel, while we can still collect significantensemble statistics owing to the large number of pixelsfor which we obtain signal. Indeed, we obtain a full

distribution of decay times from single exponential fitsto pixels that each represent a signal from just one or afew emitters. In previous works, several authors haveadvocated that in measurements of larger ensemblesthe distribution of rates causes the average decay traceto be not single exponential, but best fitted with a log-normal distribution. In our work we go beyond thisindirect evidence as we reverse the order of fittingdecay constants and assemble ensemble data. For theparticular quantum dot-in-rod system we study, ratedistributions are log-normal, and we confirm that alog-normal fit to ensemble-averaged decay traces isindeed consistent with the full log-normal distributionof histogrammed rates.20,25,35 In the system studiedhere, the inhomogeneously broadened width of thedecay rate distribution is due in equal parts to anintrinsic distribution in the radiative rate and also adipole-orientation dependence caused by the planarsubstrate, while nonradiative decay rate effects arenegligible. We expect that this method to go beyondensemble average quantities will find wider use tocharacterize a plethora of solid state emitters of currentinterest, and can be further extended to also deal with,for example, the statistics of blinking or quantifyingdecay rates for bright and gray states separately.

MATERIALS AND METHODSWe use a high tolerance ball lens from Edmund Optics, with a

diameter of 4.00 mm, a diameter tolerance of þ0.0/�3.00 μm,and a maximal deviation from a sphere of 2 μm. The ball lens iscoated by physical vapor deposition of a 5 nm Ge adhesionlayer, followed by 100 nm Ag. Finally, as a protection againstscratches and oxidation, a 35 nm layer of SiO2 is evaporatedonto the sphere. For easier handling and to prevent the ball lensfrom rolling over the sample, we glued three identical balllenses onto a cover glass slide in a tripod configuration prior tocoating. A few considerations restrict the choice of radius of thespherical lens. In our measurement scheme, the distance to themirror is increased by moving out from the contact pointbetween the substrate and mirror. First, in order for the config-uration to best approximate a planar mirror for which the LDOSis easily calculated, we require that the radius be much largerthan the emission wavelength. Second, we require that themaximum difference in vertical distance within the width ofthe signal collection area (in our case a diffraction-limited focus)be much smaller than the emission wavelength. Both of theserequirements are easily fulfilled using macroscopic ball lenseswith diameters of ∼1 mm.Following a previous work,33 we synthesized CdSe/CdS dot-

in-rod structures, that is, a spherical CdSe core embedded in arod shaped CdS shell, for use as emitters. The CdSe core has adiameter of 3.2 nm, and the shell has the dimensions of 5.6 nmand 21 nm along the short and long axis, respectively. Thenanorods (NRs) are covered by 15�20 nm of silica followingref 41. The SiO2 coating imparts water solubility while providingan inert protection layer to reducedegradation of optical proper-ties in aqueous environments. Moreover, for our experiment, theSiO2 layer hinders electric coupling between clustered rods andreduces aggregation when placing NRs on substrates. The NRsshow an ensemble emission spectrumwith a center wavelengthof 610 nm and a full width at half-maximum of ∼50 nm. Thiswidth is largely due to size inhomogeneity, as single quantumdot-in-rod emitters of this type have spectral widths of around

10 nm (at room temperature, and at the pixel integration timesused in this work), see Supporting Information. Since the silicacoating makes the NRs hydrophilic, in order to achieve a homo-geneously distributed single layer of NRs, we use a Piranhacleaned glass substrate followed by a 5 min bath in HCl (38%)to render the surface hydrophilic. The NRs are subsequentlyspin-coated onto the substrate (500 rpm for 30 s) from a dilutedethanol dispersion using carefully tuned spin parameters anddilution to achieve a single layered homogeneous distributionwith a density of order 1�10 μm�2.We use a confocal fluorescence lifetime imaging microscope,

described in an earlier work,10 in which a piezo stage allowstranslational scanning relative to the laser focus of the samplesubstrate containing a dilute surface coverage with the emit-ters, plus mirror tripod. Thereby, at different lateral positions weaddress emitters at a different vertical separation to the mirrorsurface. The excitation source is a 532 nm, linearly polarizedpulsed laser, with a pulse duration <10 ps and a repetition rateof 10 MHz, that is focused to a diffraction limited spot usinga 100� oil-immersion objective (NA = 1.4). To avoid excessiveblinking, creation of biexcitons and saturation of our emitterswe use a low pump power of ∼10 nW. The collected fluores-cence is focused onto a 20 μm silicon avalanche photodiode(IdQuantique ULN) that is connected to a Becker and HicklDPC230 timing card registering the arrival times of laser pulsesand fluorescence photons with 165 ps resolution. The sum ofbackground and dark counts was measured to be ∼4 counts/s.We scan with a step size of around 300 nm, comparable to thediffraction limit, and with a scan speed (50 Hz pixel clock) that isa trade off between focus drift and sufficient collection time perpixel to fit a lifetime to the detected signal.

Conflict of Interest: The authors declare no competingfinancial interest.

Acknowledgment. We are grateful to M. Frimmer andA. Mohtashami for help in the initial stages of the project. Thiswork is part of the research program of the “Foundation forFundamental Research on Matter (FOM)”, which is financially

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

H

supported by the “The Netherlands Organization for ScientificResearch (NWO)”. A.F.K. gratefully acknowledges a NWO-Vidigrant for financial support. P.L. acknowledges support by theCarlsberg Foundation as well as the Danish Research Council forIndependent Research (Grant No. FTP 11-116740).

Supporting Information Available: Measured spectra of sin-gle nanorods as well as ensemble; decay rate analysis of a singlenanorod. Thismaterial is available free of charge via the Internetat http://pubs.acs.org.

REFERENCES AND NOTES1. Resch-Genger, U.; Grabolle, M.; Cavaliere-Jaricot, S.;

Nitschke, R.; Nann, T. Quantum Dots versus Organic Dyesas Fluorescent Labels. Nat. Methods 2008, 5, 763–75.

2. Lichtman, J. W.; Conchello, J.-A. Fluorescence Microscopy.Nat. Methods 2005, 2, 910–9.

3. Caruge, J. M.; Halpert, J. E.; Wood, V.; Bulovi�c, V.; Bawendi,M. G. Colloidal Quantum-Dot Light-Emitting Diodes withMetal-Oxide Charge Transport Layers.Nat. Photonics 2008,2, 247–250.

4. vanDer Poel,M.;Moerk, J.; Somers, A.; Forchel, A.; Reithmaier,J. P.; Eisenstein, G. Ultrafast Gain and Index Dynamics ofQuantum Dash Structures Emitting at 1.55 μm. Appl. Phys.Lett. 2006, 89, 81102.

5. Eliseev, P.; Li, H.; Liu, T.; Newell, T.; Lester, L.; Malloy, K.Ground-State Emission and Gain in Ultralow-ThresholdInAs�InGaAs Quantum-Dot Lasers. IEEE J. Sel. Top. Quant.Electron. 2001, 7, 135–142.

6. Claudon, J.; Bleuse, J.; Malik, N. S.; Bazin, M.; Jaffrennou, P.;Gregersen, N.; Sauvan, C.; Lalanne, P.; Gérard, J.-M. AHighlyEfficient Single-Photon Source Based on aQuantumDot ina Photonic Nanowire. Nat. Photonics 2010, 4, 174–177.

7. Hennessy, K.; Badolato, a.; Winger, M.; Gerace, D.; Atatüre,M.; Gulde, S.; Fält, S.; Hu, E. L.; Imamoglu, A. QuantumNature of a Strongly Coupled Single QuantumDot�CavitySystem. Nature 2007, 445, 896–9.

8. Lund-Hansen, T.; Stobbe, S.; Julsgaard, B.; Thyrrestrup, H.;Sunner, T.; Kamp, M.; Forchel, A.; Lodahl, P. ExperimentalRealization of Highly Efficient Broadband Coupling ofSingle Quantum Dots to a Photonic Crystal Waveguide.Phys. Rev. Lett. 2008, 101, 1–4.

9. Julsgaard, B.; Johansen, J.; Stobbe, S.; Stolberg-Rohr, T.;Sunner, T.; Kamp, M.; Forchel, A.; Lodahl, P. DecayDynamics of Quantum Dots Influenced by the LocalDensity of Optical States of Two-Dimensional PhotonicCrystal Membranes. Appl. Phys. Lett. 2008, 93, 094102.

10. Frimmer, M.; Chen, Y.; Koenderink, A. F. Scanning EmitterLifetime Imaging Microscopy for Spontaneous EmissionControl. Phys. Rev. Lett. 2011, 107.

11. Frimmer, M.; Koenderink, A. F. Superemitters in HybridPhotonic Systems: A Simple Lumping Rule for the LocalDensity of Optical States and Its Breakdown at the UnitaryLimit. Phys. Rev. B 2012, 86, 235428.

12. Sprik, R.; van Tiggelen, B. A.; Lagendijk, A. Optical Emissionin Periodic Dielectrics. Eur. Phys. Lett 1996, 35, 265–270.

13. Loudon, R. The Quantum Theory of Light, 3rd ed.; OxfordUniversity Press: Oxford, 2000; p 448.

14. Lodahl, P.; van Driel, A. . F.; Nikolaev, I. S.; Irman, A.;Overgaag, K.; Vanmaekelbergh, D.; Vos, W. L. Controllingthe Dynamics of Spontaneous Emission from QuantumDots by Photonic Crystals. Nature 2004, 430, 654–657.

15. Kühn, S.; Håkanson, U.; Rogobete, L.; Sandoghdar, V.Enhancement of Single-Molecule Fluorescence Using aGold Nanoparticle as an Optical Nanoantenna. Phys. Rev.Lett. 2006, 97, 017402.

16. Anger, P.; Bharadwaj, P.; Novotny, L. Enhancement andQuenching of Single-Molecule Fluorescence. Phys. Rev. Lett.2006, 96, 113002.

17. Drexhage, K.; Fleck, M.; Shäfer, F.; Sperling, W. Beeinflus-sungder Fluoreszenz eines Europium-chelates durch einenSpiegel. Ber. Bunsen. Phys. Chem 1966, 20, 1179.

18. Snoeks, E.; Lagendijk, A.; Polman, A. Measuring and Mod-ifying the Spontaneous Emission Rate of Erbium near anInterface. Phys. Rev. Lett. 1995, 74, 2459–2462.

19. Amos, R. M.; Barnes, W. L. Modification of the SpontaneousEmission Rate of Eu3þ Ions Close To a Thin Metal Mirror.Phys. Rev. B 1997, 55, 7249–7254.

20. Kwadrin, A.; Koenderink, A. F. Gray-Tone LithographyImplementation of Drexhage's Method for CalibratingRadiative and Nonradiative Decay Constants of Fluoro-phores. J. Phys. Chem. C 2012, 116, 16666–16673.

21. Danz, N.; Heber, J.; Bräuer, A.; Kowarschik, R. FluorescenceLifetimes of Molecular Dye Ensembles Near Interfaces.Phys. Rev. A 2002, 66, 063809.

22. Johansen, J.; Stobbe, S.; Nikolaev, I.; Lund-Hansen, T.;Kristensen, P.; Hvam, J. M.; Vos, W.; Lodahl, P. Size Depen-dence of the Wavefunction of Self-assembled InAsQuantumDots fromTime-ResolvedOpticalMeasurements.Phys. Rev. B 2008, 77, 073303.

23. Stobbe, S.; Johansen, J.; Kristensen, P.; Hvam, J. M.; Lodahl,P. Frequency Dependence of the Radiative Decay Rate ofExcitons in Self-Assembled Quantum Dots: Experimentand Theory. Phys. Rev. B 2009, 80, 1–14.

24. Andersen, M. L.; Stobbe, S.; Sorensen, A. S.; Lodahl, P.StronglyModified Plasmon�Matter InteractionwithMeso-scopic Quantum Emitters. Nat. Phys. 2010, 7, 215–218.

25. Leistikow, M.; Johansen, J.; Kettelarij, A.; Lodahl, P.; Vos, W.Size-Dependent Oscillator Strength and Quantum Effi-ciency of CdSe Quantum Dots Controlled via the LocalDensity of States. Phys. Rev. B 2009, 79, 1–9.

26. Brokmann, X.; Coolen, L.; Dahan, M.; Hermier, J. Measure-ment of the Radiative and Nonradiative Decay Rates ofSingle CdSe Nanocrystals through a Controlled Modifica-tion of their Spontaneous Emission. Phys. Rev. Lett. 2004,93, 107403.

27. Buchler, B.; Kalkbrenner, T.; Hettich, C.; Sandoghdar, V.Measuring the Quantum Efficiency of the Optical Emissionof Single Radiating Dipoles Using a Scanning Mirror. Phys.Rev. Lett. 2005, 95, 063003.

28. Frimmer, M.; Mohtashami, A.; Koenderink, A. F. Nanome-chanical Method to Gauge Emission Quantum YieldApplied to NV-Centers in Nanodiamond. arXiv 2012, 11.

29. Chizhik, A. I.; Chizhik, A. M.; Khoptyar, D.; Ba, S.; Meixner,A. J.; Enderlein, J. Probing the Radiative Transition of SingleMolecules with a Tunable Microresonator. Nano Lett. 2011,11, 1700–1703.

30. Bajzer, Z.; Therneau, T. M.; Sharp, J. C.; Prendergast, F. G.Maximum Likelihood Method for the Analysis of Time-Resolved FluorescenceDecay Curves. Eur. Biophys. J.1991,20, 247–262.

31. Galland, C.; Ghosh, Y.; Steinbruck, A.; Sykora, M.;Hollingsworth, J. a.; Klimov, V. I.; Htoon, H. Two Types ofLuminescence Blinking Revealed by Spectroelectrochem-istry of Single Quantum Dots. Nature 2011, 479, 203–7.

32. Paulus, M.; Gay-Balmaz, P.; Martin, O. J. F. Accurate andEfficient Computation of the Green's Tensor for StratifiedMedia. Phys. Rev. E 2000, 62, 5797–5807.

33. Carbone, L.; Nobile, C.; De Giorgi, M.; Sala, F. D.; Morello, G.;Pompa, P.; Hytch, M.; Snoeck, E.; Fiore, A.; Franchini, I. R.;et al. Synthesis and Micrometer-Scale Assembly ofColloidal CdSe/CdS Nanorods Prepared by a SeededGrowth Approach. Nano Lett. 2007, 7, 2942–50.

34. Talapin, D. V.; Koeppe, R.; Gotzinger, S.; Kornowski, A.;Lupton, J. M.; Rogach, A. L.; Benson, O.; Feldmann, J.; Weller,H. Highly Emissive Colloidal CdSe/CdS Heterostructures ofMixed Dimensionality. Nano Lett. 2003, 3, 1677–1681.

35. van Driel, A. F.; Nikolaev, I.; Vergeer, P.; Lodahl, P.;Vanmaekelbergh, D.; Vos, W. L. Statistical Analysis of Time-Resolved Emission from Ensembles of SemiconductorQuantumDots: Interpretationof Exponential DecayModels.Phys. Rev. B 2007, 75, 035329.

36. Nikolaev, I.; Lodahl, P.; van Driel, A. F.; Koenderink, A. F.;Vos, W. L. Strongly Nonexponential Time-ResolvedFluorescence of Quantum-Dot Ensembles in Three-Dimensional Photonic Crystals. Phys. Rev. B 2007, 75,115302.

37. Vos, W. L.; Koenderink, A. F.; Nikolaev, I. S. Strong Depen-dence of the Pptical Emission Rates of a Two-LevelQuantum Emitter in Any Nanophotonic Environment on

ARTIC

LE

LUNNEMANN ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX

www.acsnano.org

I

the Orientation of the Transition Dipole Moment. Phys.Rev. A 2009, 80, 053802.

38. Galland, C.; Ghosh, Y.; Steinbruck, A.; Hollingsworth, J. a.;Htoon, H.; Klimov, V. I. Lifetime Blinking in NonblinkingNanocrystal Quantum Dots. Nat. Commun. 2012, 3, 908.

39. Spinicelli, P.; Buil, S.; Quélin, X.; Mahler, B.; Dubertret, B.;Hermier, J.-P. Bright and Grey States in CdSe�CdS Nano-crystals Exhibiting Strongly Reduced Blinking. Phys. Rev.Lett. 2009, 102, 1–4.

40. Cordones, A. a.; Bixby, T. J.; Leone, S. R. Evidence forMultiple Trapping Mechanisms in Single CdSe/ZnS Quan-tumDots from Fluorescence Intermittency Measurementsover aWide Range of Excitation Intensities. J. Phys. Chem. C2011, 115, 6341–6349.

41. Koole, R.; van Schooneveld, M. M.; Hilhorst, J.; Ade MelloDonegá, C.; Hart, D. C. E.; van Blaaderen, A.; Vanmaekelbergh,D.; Meijerink, A. On the Incorporation Mechanism ofHydrophobic Quantum Dots in Silica Spheres by a ReverseMicroemulsion Method. Chem. Mater. 2008, 20, 2503–2512.

ARTIC

LE