Power-law carrier dynamics in semiconductor nanocrystals at nanosecond time scales ∗ P. H. Sher and J. M. Smith Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK P. A. Dalgarno and R. J. Warburton School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK 8 0 X. Chen and P. J. Dobson 0 Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ,UK 2 n S. M. Daniels, N. L. Pickett, and P. O’Brien a School of Chemistry, University of Manchester, Oxford Road, Manchester M13 3PL, UK J (Dated: February 4, 2008) 7 2 Wereporttheobservationofpowerlawdynamicsonnanosecondtomicrosecondtimescalesinthe fluorescencedecayfrom semiconductornanocrystals, anddrawacomparison betweenthisbehavior ] andpower-lawfluorescenceblinkingfrom singlenanocrystals. Thelinkissupportedbycomparison r e ofblinkingandlifetimedatameasuredsimultaneouslyfromthesamenanocrystal. Ourresultsreveal h that the power law coefficient changes little over the nine decades in time from 10 ns to 10 s, in t contrast with thepredictions of some diffusion based models of power law behavior. o t. PACSnumbers: a m - The following article has been submitted to Applied a random walk or diffusion process [2, 3, 6, 7, 8], whilst d PhysicsLetters. If it is published, it will be found online others propose static models with a distribution of trap n at http://apl.aip.org statesin the volume surroundingeachnanocrystal[4,9]. o Some works [6, 7] have suggested that a signature of a c Powerlawdynamicsobservedinthefluorescenceblink- [ ing behavior of single semiconductor nanocrystals have diffusion process would be a reduction in the power law received much recent attention. Both the fluorescence gradientatsub-100µstime scalessuchthat−1<µ<0. 5 v on and off periods havebeen shownto follow power law In this Letter we present evidence that power law be- 2 distributions,withtheprobabilitydensityofmeasuringa havior can be observed on nanosecond to microsecond 9 periodofdurationτ givenby P(τ)=µτµτ−(1+µ),where time scales in time-resolved photoluminescence (TRPL) b 2 µ is the time independent power law coefficient, and τ experiments performed on both single nanocrystals and b 4 is the temporal resolution of the measurement appara- ensembles, thereby providing a new time scale on which 0 tus. The observed behaviour is particularly robust for to study the phenomenon. We used a standard time- 6 the fluorescence off durations which show values of µ correlated single photon counting (TCSPC) apparatus 0 / between about 0.4 and 0.8 over time scales from 100 µs with timing resolution tres ≃ 500 ps to measure room at to 100 s [1, 2, 3]. Autocorrelation measurements of en- temperature TRPL of three different nanocrystal types: m semblefluorescencehavesuggestedthatthe behaviorex- bareCdSenanocrystals(sampleA);CdSe/ZnScore-shell - tends to time scales as short as 1 µs [4]. The behavior is structures(sampleB);andZn0.5Cd0.5S/CdSe/ZnStriple d of significant practical importance, since the occurrence layer structures (sample C). The core-shells were fabri- n oflongfluorescenceoff durationsleadstostatisticalage- catedbystandardmethods;thefabricationprocedurefor o ing (reversible photobleaching) in the fluorescence from the bare nanocrystals and the triple layer structures are c ensembles of emitters [5], raising serious obstacles to the described elsewhere [10, 11]. All of the samples showed : v realizationofinexpensiveoptoelectronicdevicesbasedon strongensemble luminescence ataround600nm withno i X nanocrystal/polymer composites. deep trap luminescence, but importantly were not opti- mized for high quantum yield so that long fluorescence r The blinkingitselfis thoughtto be causedbythe hop- a on times were absent. Samples for photoluminescence ping of carriers between the quantum confined state in measurementswerecreatedbyspincastingfromsolution the nanocrystal and surrounding trap sites: when the onto quartz substrates. Single nanocrystals were identi- nanocrystalisinachargedstate,fluorescenceisquenched fied by their homogeneously broadened PL spectra with bystrongnon-radiativeAugerprocessesfacilitatedbythe Lorentzian line shapes. extra confined carrier. However the origin of the power lawbehaviorisstillamatterofsomedebate. Severalsug- Figure 1 shows fluorescence decay data for three sin- gestionshavebeenmadefordynamicmodelsthatrelyon gle nanocrystals and an ensemble of each of the sample types A, B, and C. The same data (black squares) are displayed on semi-logarithmic axis in the left hand col- umnandfully logarithmicaxesintherighthandcolumn ∗[email protected] of the figure. Power law behaviour appears as a straight 2 FIG. 1: (color online) TRPL data from semiconductor nanocrystals on semi-logarithmic (left column) and logarith- mic (right column) axes. The three rows correspond to the differentnanocrystalstructuresA,BandC.Alldatasetsare FIG. 2: (color online) TCSPC and blinking data histograms from single nanocrystals except for the uppermost in each on common logarithmic axes for fourteen different single window which is from an ensemble. The black scatter plots nanocrystals. The increments on both axes of the figure cor- are raw data, the gray scatter plots are results of our Monte respond to factors of ten. (Inset) three level system used to Carlo simulation, and the solid red lines are analytical biex- simulate the tails of the TRPL data. Level 0 represents the ponential fits. In all cases, t = 0 corresponds to the peak of nanocrystal ground state; level 1 the quantum confined ex- theTRPL signal. citon; and level 2 the charged fluorescence off state. τrad is theradiative lifetime thatcorresponds totheslower decayin theoriginalbiexponentialfit. Thetwonewfittingparameters line of gradient −(µ+1) on the fully logarithmic axes. are the lifetime for escape from the exciton state to the fluo- Previously, single nanocrystal fluorescence decays have rescence off state, labeled τesc,and thepowerlaw coefficient beenfittedwithbiexponentialfunctions withlifetimes of µ. about 1 ns and 15 ns, attributed to Auger and radiative recombination processes respectively [12]. Fitting biex- ponential functions to our data (solid red lines in Fig.1) of the carriersescapes from the nanocrystal,similarly to reveals excellent agreement up to about 50 ns after the thefluorescenceoff statethatisresponsibleforthesingle excitation pulse, but for longer delays the fluorescence nanocrystal blinking phenomenon. consistently decays more slowly than the biexponential An empirical Monte Carlo (MC) model that produces function. thesuggestedpower-lawbehaviorisshownschematically The presence of this slow tail indicates that between in the inset of Fig.2. Times spent in the fluorescence excitation and emission, the photogenerated exciton can off state are generated using the function ti = tbxi−1/µ entera‘dark’statefromwhichitcannotradiate. Wedo where xi is a random variable in the range 0 < xi < 1, not believe this state to be the ‘dark’ spin configuration andtbistheminimummeasurabletrappingduration[17], of the confined exciton ground state since the lowest en- which in our experiment is equal to tres. For each MC ergy ‘bright’ exciton states for nanocrystals of this size iteration the system is initialized in the exciton state at lie less than 5 meV (≪ kT) higher in energy [13], and time t = 0 and is allowed to evolve until it undergoes the spinrelaxationtime is fast comparedwiththe radia- radiative recombination to the ground state. tive lifetime [14, 15]. That the tail results from a large Fits of our MC simulation data sets to the measured homogeneous line width as suggested in the recent work TRPL data are shown as grey scatter graphs overlaying by Rothe et al [16] appears unlikely since homogeneous the experimental data in Fig.1. In all cases the model broadening at room temperature is dominated by rapid provides exact fits to the experimental data for time de- dephasing of the exciton and not population decay. We lays greater than about 10 ns. The underestimation of therefore believe that the dark state occurs when one the single nanocrystal experimental data at short time 3 data records a timing event for only about 4% of the TABLE I: Fitting parameters τrad, τesc, and µ for the best excitation pulses, so that F ≃ 25. The result of this fitstothedatashown in Fig. 1,andfor theaverageµvalues 2 scaling is therefore to shift the TCSPC data up the y- fromtheblinkingdatainFig. 2. Thenumbersinparentheses axisofthelogarithmicplotbyabouttendecadeswithout represent estimated error bars for thevalues stated. distortion to the curve shape. Although there is clearly a large time gap between Sample τrad(ns) τesc(ns) µ µblink the two data sets and some variation between individual Aens 14 (2) 2 (1) 0.50 (0.05) 0.54 (0.05) A1 14 (2) 2.5 (1) 0.50 (0.1) nanocrystals,ineachcasetheirrelativepositionssuggest A2 14 (2) 4 (1) 0.50 (0.1) thatthepowerlawdecayattheshortandlongtimescales A3 20 (2) 5 (1) 0.50 (0.1) measured here may be continuous across the entire time Bens 14 (2) 2.5 (1) 0.63 (0.05) 0.67 (0.05) rangewithµ≃0.5throughout. Thereisalsosomecorre- B1 14 (2) 7 (1) 0.63 (0.1) lation between the values of µ measured on the different B2 20 (2) 3 (1) 0.63 (0.1) time scales. The mean values measured from the blink- B3 12 (2) 7 (1) 0.63 (0.1) ingdata,listedalongsidetheensemblefittingparameters Cens 17 (2) 6 (1) 0.50 (0.05) 0.37 (0.05) for each of the three nanocrystal types in Table I, agree C1 17 (2) 10 (2) 0.50 (0.1) well with those fitted to the ensemble TRPL tails, with C2 17 (2) 10 (2) 0.50 (0.1) nanocrystals of type B (core-shells) providing a notice- C3 17 (2) 10 (2) 0.50 (0.1) ablylargervalueofµinbothmeasurements. Thisdegree ofcorrespondencebetweenthetwodatasetsprovidesfur- ther evidence that the tail in the fluorescence decay is a delays results because our model neglects Auger limited result of the same trapping behavior that causes fluores- fluorescence. The fitting parameters for the twelve MC cence blinking. We note that in contrast with the pre- data sets in Fig.1 are listed in Table I. In each case we dictions madeinthe diffusion basedmodels ofreferences have takenµ value fromthe ensemble fit. The tabulated [6]and[7]thevaluesofµappearquitesimilaronthe100 parameters reveal that most of the differences between ns time scale to those found in the blinking data. the data sets are primarily attributable to differences in To conclude, our study provides evidence that the τ , which is determined by the degree of surface passi- esc same carrier trapping dynamics that lead to power law vation of the individual nanocrystals. That all values of statisticsinfluorescenceblinkingofsinglesemiconductor τ fitted are smaller than τ shows that the off state esc rad nanocrystals can be observed on much faster time scales plays an important role. influorescencedecayexperiments,openingupnewpossi- Toprobetherelationshipbetweenthe fluorescencede- bilitiesfortestingthevarioustheoreticalmodelsofpower cay function and distribution of off times from blinking lawbehavior. Wehopethataswellfurtheringtheunder- measurements, we performed both experiments simulta- standingofcarrierdynamicsinsemiconductornanocrys- neously on the same nanocrystal. Pulsed excitation at tals, our approach may prove fruitful in the analysis of a repetition rate of 500 kHz allowed us to use a TRPL thenon-exponentialfluorescencedecaysofothercolloidal timerangeof1µsandablinkingsamplingtime of50ms and molecular systems. with clear distinction between the fluorescence on and off states. Figure3showsbothTCSPCandfluorescence off histogramsforfourteensinglenanocrystalsofthedif- ferent types. Acknowledgments We have scaled the TCSPC data in Fig. 2 to enable thetwodatasetstobepresentedonthesamey-axis. The scalingfactorusedisthe productoftwosub-factors–the Funding for this work was provided by the United first, F , corrects for the difference between the widths Kingdom Engineering and Physical Sciences Research 1 of the time bins, generally50 ms for blinking and 200ps Council,theRoyalSocietyofEdinburgh,theRoyalSoci- for TCSPC, giving F =2.5×108, while the second, F , ety of London, and Oxford University’s Research Devel- 1 2 corrects for the difference in the measurement efficiency opmentFund. WewouldliketothankPicoQuantGmbH of the twomethods. Whilst the blinking data recordsall for the loan of a pulsed laser for the single nanocrystal of the off periods with duration > 100 ms, the TCSPC measurements. [1] M.Kuno,D.P.Fromm,H.F.Hamann,A.Gallagherand (2005). D.J. Nesbitt,J. Phys.Chem 112, p.3117 (2000). [4] R.Verberk,A.M.vanOijen,M.Orrit,Phys.Rev.B66, [2] K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. 233202 (2002). A. Empedocles, W. K. Woo, and M. G. Bawendi, Phys. 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