High-Resolution Line Width Measurement of Single CdSe

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2009, 113, 5345–5348 Published on Web 03/17/2009

High-Resolution Line Width Measurement of Single CdSe Nanocrystals at Long Time Scales Bradley N. Littleton,† Mark J. Ferne´e,*,† Daniel E. Go´mez,‡,§ Paul Mulvaney,‡ and Halina Rubinsztein-Dunlop† Centre for Quantum Computer Technology, School of Physical Sciences, The UniVersity of Queensland, Queensland, Australia 4072, and School of Chemistry, The UniVersity of Melbourne, ParkVille, Victoria, Australia 3010 ReceiVed: January 30, 2009; ReVised Manuscript ReceiVed: March 04, 2009

Band-edge photoluminescence from single CdSe/CdZnS nanocrystals was analyzed using a confocal Fabry-Perot spectrometer with long exposure times. Due to spectral diffusion, direct detection of the line shape was not possible. However, the contrast observed in the resulting signal provided a rigorous upper bound to the single nanocrystal line width as low as 20.7 ( 0.5 µeV. This result is in excellent agreement with an asymptotic upper limit to the spectral diffusion broadened line width found at millisecond time scales, extending this time scale by 4 orders of magnitude. This indicates that spectral diffusion commonly observed at long time scales results from a physical process different from that/those responsible for the asymptotic limit. Introduction Semiconductor nanocrystal (NC) quantum dots display size tunable, atomic-like optical transitions from the lowest energy excitonic states, are relatively easy to synthesize, and have large oscillator strengths.1 They are therefore promising as “artificial atom” structures for a range of photonic and quantum optical technologies, in addition to their common application in biology as fluorescent markers.2 Knowledge of the coherence time of excitations in these systems is particularly important for applications to quantum information processing3,4 and cavity quantum electrodynamics5-7 studies. The coherence time of the exciton level can be determined either in the frequency domain by measuring the homogeneous line width or in the time domain using pump/probe techniques. In either case the phenomenon of spectral diffusion (SD) usually obscures these measurements. SD is caused by electric field fluctuations in the exciton’s local environment that induce a spectral line shift due to the quantum confined Stark effect.8 This finding is contrary to what was expected for strongly quantum confined systems9 and implies the presence of large internal electric fields in these materials. However, the presence of large internal fields only implies sensitivity to external charge noise and gives no indication of the time scale of the external fluctuations. At cryogenic temperatures, SD has been found to depend on the energy of the nonresonant pump but is otherwise independent of temperature below 50 K, indicating that hotcarrier relaxation provides the energy that drives SD.10-12 * To whom correspondence should be addressed. E-mail: fernee@physics. uq.edu.au. Fax: +617 3365 3425. † The University of Queensland. ‡ The University of Melbourne. § Current address: Materials Science and Engineering, CSIRO, Clayton South, VIC, 3169.

10.1021/jp900887r CCC: $40.75

SD was first overcome in an ensemble measurement of the homogeneous line width using a spectral hole burning technique,13 establishing a line width of 6 µeV. In particular, SD was overcome in this experiment by modulating the lasers at around 1 MHz. This indicates that the majority of SD in the probed NC’s was occurring over time scales longer than 1 µs. However, as this was an ensemble measurement, the time scale should not be relevant to instabilities in single NCs. Recently a novel technique combining both high spectral and temporal resolution (photon-correlated-Fourier-spectroscopy14) has been applied to single CdSe NCs.15 Using short microsecond time scales in order to avoid SD, a narrow 6.5 µeV line width was found. Furthermore, broadening caused by SD was found to approach an upper value of ∼12 µeV for timescales beyond a millisecond, which we shall refer to as the “asymptotic limit”. It is noteworthy that this asymptotic limit to the SD broadened line width is far narrower than any previous report (due primarily to resolution-limited measurements16,17). These resolution-limited experiments operated on time scales of seconds17 to minutes,16 far longer than those used to establish the SD upper limit. At these comparatively long time scales large spectral jumps are evident17 and spectral line widths can exceed 1 meV. Clearly, somewhere between the millisecond and minute time scales this asymptotic limit must beak down. Here we probe SD at a long 30 s time scale (which is comparable with time scales of previous reports on SD16,17) using a high-resolution scanning confocal Fabry-Perot (F-P) spectrometer. As SD during an exposure randomly probes the F-P instrument function and many exposures are required to scan over a spectral line, SD then precludes this standard mode of spectroscopy. However, we use a technique of contrast detection to establish a rigorous upper bound to the line width in the presence of SD. Contrary to expectation, we find a narrow line width comparable with the previously determined 12 µeV  2009 American Chemical Society

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Figure 1. Spectral diffusion of a typical single NC at 5 K (5 s exposure, 9 Wcm-2 pump irradiance at 532 nm). (a) Kinetic series of 150 spectra. (b) 10 successive spectra extracted from the kinetic series (spectra offset for clarity). The dark spectrum is dominated by a peak close to the resolution limit. (c) The average spectrum after aligning spectra according to their peak position (fwhm ∼ 300 µeV).

asymptotic limit, suggesting that the commonly observed SD occurs with a characteristic time scale of the order of the experimental integration time. Experimental Methods We use CdSe/CdZnS core/graded shell NC obtained from a commercial supplier (Invitrogen ITK655, R ∼ 4 nm core18) with NCs being directly deposited on a crystal quartz substrate for use in a cryostat as described previously.17 All NCs observed with a standard grating spectrometer (80 µeV spectral resolution) exhibit spectral wandering over a 1-2 meV range.17 A typical kinetic series of spectra is shown in Figure 1a. Within that series, some individual spectra can have resolution-limited line widths (see Figure 1b). However, even after correcting for spectral peak movement, the average spectral line width is usually of the order of 300 µeV,17 as seen in Figure 1c. This indicates that SD occurring during the integration time is still the primary contribution to the line width. The experimental setup for the F-P spectroscopy is shown in Figure 2a. The sample was excited and observed in an

Letters

Figure 2. Confocal cryogenic microscope for F-P spectroscopy. (a) NCs are located by sample translation. Elements are a dichroic beam splitter, DBS, 90/10 beam splitter, BS, Raman edge long pass filter, LP, and the scanning F-P spectrometer. (b) The output from the F-P spectrometer we would expect to see from a NC with stable spectral emission characterized by a fwhm of 5.00 ( 0.13 GHz (20.7 ( 0.5 µeV). Here the F-P spectrometer is scanned over four free spectral ranges and the shaded area indicates the contrast error for the data reported in Figure 3. The dashed lines represent the instrument function of the F-P.

epifluorescence geometry with a super long working distance objective lens (Nikon, 100× NA 0.7) Excitation was via a diodepumped solid state laser at 532 nm, focused to a point on the sample. The resulting NC photoluminescence was separated using Raman edge filters and divided by a beamsplitter, with 90% of the signal being imaged into a confocal F-P spectrometer (Thorlabs) before being reimaged onto a peltier cooled electron-multiplied CCD (Andor Ixon EMCCD). The remaining 10% was imaged directly onto a second EMCCD to monitor the emission intensity of the dot. The F-P spectrometer (10 GHz free spectral range (FSR), finesse ) 170) was aligned such that its midpoint was coincident with the image of the sample. A simulated output from the scanning F-P is indicated in Figure 2b, for a scan range of 4 FSR’s. This was generated using the line width parameter determined from the experiment output in Figure 3, using eq 1 (below) and represents the line shape that would be generated by scanning the F-P in the absence of SD. (Note: For the experiment we limited the scan range to 1 FSR using a sawtooth voltage ramp.) Due to SD, it is not possible to measure the line shape directly as depicted in Figure 2b, so we developed a method of contrast analysis that provides a rigorous upper bound to the line width, given sufficient throughput from the F-P. This method offers significant benefits in the presence of SD, enabling the use of the high resolution F-P spectrometer without the requirement

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S(ωNC, γ)∝

∫ Γ(ω) exp(-(ω - ωNC)24 ln 2/γ2) dω (1)

where ωNC is the center frequency of the NC emission and γ is the fwhm. The ratio between the two cases of being optimally in resonance (ωNC ) n∆ω, n∈N) and out of resonance (ωNC ) (n + 1/2)∆ω) is therefore given by

C(γ) )

Figure 3. Fabry-Perot spectrometer throughput. (a) Variation in the F-P throughput with a 30 s exposure (red dots), compared to the NC luminence using a 10 s exposure (blue solid line). Pump irradiance ) 40 W cm-2. (b) The contrast (eq 1) vs NC line width. (Inset: The high contrast region bounded by the finesse and the FSR of the resonator.)

for scanning over the entire line shape. In essence, every F-P throughput measurement can be used to obtain an estimate of the NC line width as described below. This benefit is that the NC throughput from the F-P can be monitored continuously in order to capture any events where SD has a minimal influence, in the same way that continuously monitoring single NC spectra usually results in a few spectra at the resolution limit of the spectrometer, as highlighted in Figure 1b. Results and Discussion Neglecting the small losses in the mirrors of the F-P, we can model its instrument function simply as an Airy function

(

Γ(ω) ) 1 +

( ))

4F2 2 πω sin ∆ω π2

-1

where F is the F-P finesse and ∆ω is the FSR (in units of angular frequency). If we make the assumption that the NC being measured has a Gaussian line shape (which has the lowest kurtosis of any physically plausible line shape and hence will give the largest estimate of width for the observed contrast), then the signal, S, received through the F-P will be proportional to

S(0, γ) S(∆ω/2, γ)

(2)

setting n ) 0 for simplicity. This represents the largest NC line width that will result in the observed contrast, and hence is an upper bound on the true line width. A plot of C(γ), calculated with parameters relevant to this experiment, is shown in Figure 3b. As we are calculating a ratio of maximum and minimum signals, the curve has an asymptote at C ) 1. The region bounded by C(γ/∆ω ) 1) and C(γ/∆ω) ) F (see Figure 3b, inset) defines a region of rapid change in contrast in which we are able to estimate the line width with maximum precision. In practice, the maximum signal ratio we can observe is much less than F, as it is governed by the signal-to-noise ratio, which is in turn limited by the low signal levels available from a single NC. A number of individual quantum dots were investigated and, as expected from lower resolution observations of the sample, only a small proportion (∼10%) displayed a discernible contrast in F-P throughput. Data from the NC displaying the largest contrast is shown in Figure 3a. This data displays characteristic single quantum dot blinking, whereas the fluctuations in the F-P throughput are also caused by SD. Anticorrelations between the NC luminosity and the F-P throughput are due to random changes of the overlap between the NC spectrum and the F-P instrument function over the duration of the experiment. By normalizing the signal through the F-P by the NC luminosity and solving eq 2 for the maximum/minimum signal ratio, we calculate an upper bound for the line width of this NC to be 5.00 ( 0.13 GHz (20.7 ( 0.5 µeV). This corresponds to a lower limit on the lifetime of 200 ( 10 ps. The relatively high precision of these bounds is due in large part to the slope of C(γ) at the value measured in the experiment. For the degree of spectral diffusion that we typically observe17 (see also Figure 1), it is quite unlikely that the NC will be spectrally stable over a whole 30 s exposure, and any SD will reduce the observed contrast. Thus, solving eq 2 using the observed contrast will result in a conservative (though rigorous) upper bound. Ultimately, if the SD is rapid compared to exposure time of the detector (or equivalently, if the line width is large with respect to the FSR) no contrast in the F-P throughput will be observed. Overall, the use of the scanning F-P in conjunction with the contrast method outlined above provides a high resolution estimate of the homogeneous line width that requires only two measurements in a kinetic series (although other measurements are required to establish the signal-to-noise ratio). This then provides a measurement of the line width similar to that which can be obtained from a single spectrum shown in Figure 1b but with far greater resolution. A question that must be asked is to what degree is this result significant? All the NCs that display visible contrast through the F-P must have line widths bound below 10 GHz (the FSR of the F-P). In fact, any throughput suggests a narrow line width, as the finesse of the cavity is sufficient to act as an OD 2 attenuator for emission broader than the FSR. Furthermore, we have observed hundreds of single NCs at 5 K17 by dispersing

5348 J. Phys. Chem. C, Vol. 113, No. 14, 2009 the output with a 300 mm grating spectrometer and detecting individual spectra with a CCD camera16,17 (such as shown in Figure 1) and have not found a single NC that did not exhibit SD. So it is unlikely that these are anomalously stable NCs. In fact, SD is apparent in the data of Figure 3a. Upper bounds for other NCs exhibiting F-P throughput also indicate line widths approximately 1 order of magnitude narrower than the average line width shown in Figure 1c. Thus we suggest that this result is representative of the underlying line width of the NCs. The key result is not the line width, per se, but the time scale over which it is obtained. Our exposure time is approximately 4 orders of magnitude longer than that used to determine the 12 µeV asymptotic limit to the SD broadened line width.15 At this longer time scale the average SD-induced line width is >300 µeV (averaged over >100 successive spectra acquired from a single NC), an increase of more than an order of magnitude over the asymptotic limit. Thus there must be a departure from the 12 µeV asymptotic limit at some longer time scale. Our F-P results thus extend the asymptotic limit out to time scales comparable to the spectral acquisition time of this experiment. If the large SD fluctuations commonly observed (as shown in Figure 1) extend to time scales considerably shorter than the exposure time, we would not see any F-P throughput due to SD-induced spectral broadening. In effect, this result restricts the time scale of the large SD variations to approximately that of the experiment, which is supported by the discrete jumps observed in Figure 1. Furthermore, this conclusion is supported by a statistical analysis of SD which reveals correlations attributed to a long characteristic time scale between jumps.19 The process of SD can have two effects on the observed spectrum, either broadening the line width or causing discrete random jumps of the spectral line. What discriminates these two effects is the spectral acquisition time relative to the spectral fluctuation rate. In general we tend to observe both of these effects in single NCs, with the data in Figure 1, panels a and b, illustrating the commonly observed random jump behavior16,17 as well as an average broadening (Figure 1c), although we have noted individual resolution limited spectra (Figure 1b).17 Our results with the F-P delve beyond our previous resolution limit (80 µeV) and indicate that the underlying line width is approximately that given by the aforementioned asymptotic limit. Thus the F-P results suggest that the physical processes responsible for the SD illustrated in Figure 1 are distinct from those that give rise to the asymptotic limit as they occur at vastly different time scales. Finally we speculate on the origin of the two SD processes. The fast process that gives rise to the aforementioned 12 µeV asymptotic limit is likely to involve environmental charge motion/fluctuations in shallow potentials15 with relatively high excitation probabilities. However, the longer time scale of the SD reported here indicates that deeper potentials are involved, which would reduce the excitation probability. A possible candidate for this process is the generation of fluctuating dipole fields caused by photoinduced desorption (and subsequent readsorption) of surface passivating molecules.20 Previous reports indicating that SD (observed at the second to minute time scale, as shown in Figure 1) is independent of temperature below 50 K10-12 suggest surface potentials on the order of tens

Letters of meV. This is approximately 3 orders of magnitude deeper than the potentials attributed to SD that contributes to the 12 µeV asymptotic limit15 and is in good agreement with the disparity in time scale we report here. Conclusion In summary, we have performed high resolution measurements of the line width of single CdSe/CdZnS core/graded shell NCs at 5 K using Fabry-Perot spectroscopy. Due to the presence of SD during the measurement, a measurement of the spectral line shape was not possible. Nevertheless, a rigorous upper bound to the line width of 20.7 ( 0.5 µeV was found, which is consistent with a previously reported asymptotic upper limit for SD of ∼12 µeV determined at a millisecond time scale, but extending this time scale by up to 4 orders of magnitude. That a SD broadened line width detected at a millisecond time scale is still detectable at this time scale indicates that the additional SD-induced broadening most commonly detected only occurs at time scales comparable to the experimental exposure time of seconds to minutes. Such a large disparity in time scales suggests that the SD most commonly detected results from a different physical process to that contributing to the previously determined asymptotic limit. Acknowledgment. B.N.L. and M.J.F. thank the Australian Research Council for their financial support. References and Notes (1) Alivisatos, A. P. Science 1993, 271, 933–937. (2) Michalet, X.; Pinaud, F.; Lacoste, T. D.; Dahan, M.; Bruchez, M. P.; Alivisatos, A. P.; Weiss, S. Single Mol. 2001, 2, 261–276. (3) Press, D.; Ladd, V.; B Zhang, B.; Yamamoto, Y. Nature 2008, 456, 218–221. (4) Li, X. Q.; Wu, Y. W.; Steel, D.; Gammon, D.; Stievater, T. H.; Katzer, D. S.; Park, D.; Piermarocchi, C.; Sham, L. J. Science 2003, 301, 809–811. (5) Park, Y.-S.; Cook, A. K.; Wang, H. Nano Lett. 2006, 6, 2075– 2079. (6) Greentree, A. D.; Salzman, J.; Prawer, S.; Hollenberg, L. Phys. ReV. A 2006, 73, 013818. (7) Ferne´e, M. J.; Rubinsztein-Dunlop, H. Phys. ReV. B 2006, 74 (11), 115321. (8) Empedocles, S. A.; Bawendi, M. G. Science 1997, 278, 2114–7. (9) Empedocles, S. A.; Neuhauser, R.; Shimizu, K.; Bawendi, M. G. AdV. Mater. 1999, 11, 1243–56. (10) Empedocles, S. A.; Bawendi, M. G. J. Phys. Chem. B 1999, 103, 1826–30. (11) Muller, J.; Lupton, J. M.; Rogach, A. L.; Feldmann, J.; Talapin, D. V.; Weller, H. Phys. ReV. Lett. 2004, 93, 167402. (12) Muller, J.; Lupton, J. M.; Rogach, A. L.; Feldmann, J.; Talapin, D. V.; Weller, H. Phys. ReV. B 2005, 72, 205339. (13) Palinginis, P.; Tavenner, S.; Lonergan, M.; Wang, H. Phys. ReV. B 2003, 67, 201307(R). (14) Brokmann, X.; Bawendi, M. G.; Coolen, L.; Hermier, J.-P. Opt. Express 2006, 14, 6333. (15) Coolen, L.; Brokmann, X.; Spinicelli, P.; Hermier, J.-P. Phys. ReV. Lett. 2008, 100, 027403. (16) Empedocles, S. A.; Norris, D. J.; Bawendi, M. G. Phys. ReV. Lett. 1996, 77 (18), 3873–3876. (17) Fernée, M. J.; Littleton, B. N.; Cooper, S.; Rubinsztein-Dunlop, H.; Gómez, D.; Mulvaney, P. J. Phys. Chem. C 2008, 112, 1878–1884. (18) Liptay, T. J.; Marshall, L. F.; Rao, P. S.; Ram, R. J.; Bawendi, M. G. Phys. ReV. B 2007, 76, 155314. (19) Fern´ee, M. J.; Littleton, B. N.; Plakhotnik, T.; Rubinsztein-Dunlop, H.; Go´mez, D.; Mulvaney, P. (in preparation). (20) Fomenko, V.; Nesbitt, D. J. Nano Lett. 2008, 8, 287–293.

JP900887R