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Luminescence decay of broadband emission from CdS quantum dots
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Journal of Luminescence 127 (2007) 499–507 www.elsevier.com/locate/jlumin
Luminescence decay of broadband emission from CdS quantum dots Lauren E. Shea-Rohwer, James E. Martin Sandia National Laboratories, P.O. Box 5800, MS-0892, Albuquerque, NM 87185-0892, USA Received 24 August 2006; received in revised form 21 February 2007; accepted 22 February 2007 Available online 7 March 2007
Abstract The stretched exponential photoluminescence decay of the energy-resolved broadband emission of purified and unpurified CdS quantum dots (QDs) made in reverse micelles is characterized as a function of photolysis time and thiol addition. Photolysis is found to proportionately increase both the lifetime and quantum yield of these QDs. This proportionality is consistent with a simple parallel channel model of the decay of the excited states. The ultimate QY of the purified sample is found to be as high as 24%, which is twice that previously reported for this preparation. At 70 1C both the QY and the lifetime increase by more than a factor of two, indicating that thermal quenching limits the QY at room temperature. Finally, the addition of alkanethiols is shown to red-shift and quench the emission while only modestly altering the lifetime. These thiolated QDs show an extremely large temperature dependence of QY, demonstrating stronger thermal quenching than the unfunctionalized QDs. r 2007 Elsevier B.V. All rights reserved. Keywords: Stretched exponential decay; Photoluminescence; CdS quantum dots; Quantum yield; Lifetime; Alkanethiols; Photolysis; Reverse micelles; Thermal quenching; White emission
1. Introduction In this paper we present the results of a quantitative study of the photoluminescence (PL) decay of the broadband, approximately white, emission of CdS quantum dots made from the reverse micellar synthesis reported by Lianos and Thomas [1] in 1986. The emission characteristics of these QDs are quite complex. Harruff and Bunker [2] have shown that the quantum yield (QY) of these QDs can be significantly increased by photolysis with UV light, and have noted that the broadband emission is strongly non-exponential, consistent with trap state emission. The effect of photolysis on the decay dynamics, and the relation of this to the QY, remains an open issue, and the purpose of this paper is to explore this and related issues. We focus on two types of samples: those prepared by following the Harruff and Bunker synthesis exactly; and those that were purified after this synthesis, but before photolysis. After these samples were fully photolyzed, the emission was Corresponding author. Tel.: +1 5058446627; fax: +1 5058458161.
E-mail address: [email protected] (L.E. Shea-Rohwer). 0022-2313/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2007.02.061
progressively quenched by titrating the solutions with alkanethiols, and the PL properties were monitored. We have measured both the PL decay and QY during the photolysis of both purified and unpurified QDs. In both cases the average lifetime was found to be proportional to the QY. In fact, the principal difference between the purified and unpurified QDs is their ultimate QY when fully photolyzed: the QY of the purified QDs reaches 24%, which is roughly twice that previously reported for broadband CdS QDs [2]. This proportionality can be understood qualitatively in terms of a model of parallel radiative and non-radiative decay channels, with the lifetime of the dark channel affected by photolysis. Measurements at low temperatures show that both the QY and the lifetime increase greatly, yet remain proportional, indicating that thermal quenching limits the QY of these materials at room temperature. Energy-resolved PL studies show that the lifetime decreases with increasing emission energy. Finally, the addition of alkanethiols is found to red-shift and quench the emission, but in this case the proportionality of the lifetime and QY does not hold. This strong thiol quenching does not occur at low
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temperatures, and we conclude that thiolated QDs show very strong thermal quenching of the emission at room temperature. There have been a number of related studies of the PL of CdS QDs. For example, the emission spectrum has been shown to be strongly affected by surface functionalization, synthesis conditions, solution pH, and water content [3–10]. When these factors result in a significant broadening of the emission bandwidth there is also a marked increase in the lifetime. The direct recombination of excitonic transitions are marked by small Stokes shifts and have been found to decay exponentially, with lifetimes of a few nanoseconds. In contrast, the broadband emission decays are much slower, and exhibit the strongly nonexponential decay characteristic of a distribution of trap states [2,3,8]. We have recently reported that broadbandemitting CdS QDs produced by surface functionalization with alkanethiols exhibit a stretched exponential luminescence decay [11]. The arithmetic average lifetime of this decay is on the order of 1 ms, much longer than that of the unfunctionalized QDs. The sensitivity of the lifetime to surface functionalization is also illustrated in a frequencydomain study by Lakowicz et al. [12], who found that blueemitting CdS nanoparticles stabilized by poly(aminoamine) starburst dendrimer had a very different lifetime (t ¼ 93 ns) than red-emitting, polyphosphate-stabilized CdS (t ¼ 10 ms). In time-domain studies of broad-emitting CdS QDs synthesized in reverse micelles, Kim et al. [8] found that surface modification with Cd(OH)2 increased the lifetime of the nonexponential decay. The PL decay time is also known to be dependent on the emission energy and sample temperature. White emission from ZnS–CdS co-colloids has been reported to have a multi-exponential decay, with an average relaxation time that decreases with emission energy [4]. Similar results have been reported for broadband-emitting CdS colloids [2]. Finally, low-temperature studies of CdS QDs have shown increases in both the emission intensity and lifetime [3], and a similar temperature dependence has been reported for CdS:Mn2+ [13] QDs. 2. Experimental 2.1. Synthesis Quantum dots were synthesized using the reverse micelle method described by Harruff and Bunker [2]. This was a modification of the Lianos and Thomas synthesis [1]. First, a solution of 0.2 M Cd(NO3)2 and a solution of 0.2 M Na2S are prepared in 1 mL deionized water. Next, in a glove box under nitrogen, 36 mL of each aqueous solution is injected into separate 5 mL solutions of 0.1 M dioctyl sulfosuccinate sodium salt (AOT) in heptane. The two solutions are allowed to stir for 1 h, and then mixed together. The assynthesized CdS QDs are 1.8–2.0 nm in diameter, as confirmed by TEM, and are very weakly luminescent. To increase their emission intensity, the samples are photolyzed
with 365 nm light at an intensity of 1.2 mW/cm2 for as much as 3 h. Some samples were purified before photolysis, by freezing the inverse micelle solutions at 30 1C. Over a period of weeks, ice crystals form that can be filtered out to leave a purified solution. These samples were photolyzed immediately after filtering. Some samples were titrated with dodecanethiol after photolysis. The emission intensity, absorbance and QY were measured for a range of thiol:CdS molar ratios. For comparison, narrow-band emitting CdS QDs were made by mixing a solution of Cd(NO3)2 in methanol containing 10 vol% pyridine with an equimolar solution of (NH4)2S in tetrahydrofuran (THF). This resulted in 2 nm QDs with narrow emission and a fast lifetime indicative of direct recombination. 2.2. Characterization Photoluminescence emission spectra were collected using a Horiba/Jobin-Yvon Fluorolog-3TM double grating–double grating fluorescence spectrophotometer. All samples were excited at 390 nm. A complete instrumental correction is performed on all spectra that includes corrections for factors such as wavelength-dependent PMT response and grating efficiencies, among other factors. Absorption spectra from 350 to 500 nm were obtained using a Perkin-Elmer Lambda 19TM UV/VIS/NIR spectrometer. Relative quantum yields were calculated from the integrated, corrected, emission spectra and the absorbed light at 390 nm within the emission volume. The absorbance values of both the sample and the reference were used to compute the light absorbed within the emission volume located in the center of a 1 cm path length square cuvette. Calling the integrals of the emission spectra for the sample and reference Is and Ir, respectively, and the absorbances As and Ar, the QY of the sample is QY ¼
I s Ar 10Ar 0:5 cm QYr , I r As 10As 0:5 cm
where QYr is the reference QY. (This expression is valid for absorbances in the range of our measurements, less than A ¼ 0.2 cm1.) A 5 104 M solution of quinine sulfate dihydrate in 1 N sulfuric acid was used as a reference standard, using the accepted QY of 54.6% [14]. Absolute QYs were determined using a measurement technique we developed that is based on exciting the sample with diffuse light within an integrating sphere [15]. The photoluminescent decay was measured using pulsed and steady-state excitation in the time domain, and was also measured by the phase shift method. Pulsed excitation refers to the case where the excitation is short compared to the shortest lifetime. DC excitation refers to the case where the pulse width is sufficiently long such that the luminescence reaches steady state before the light is shut off. In other words, the pulse width is longer than the longest lifetime the material exhibits.
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2.3. Pulsed excitation Pulsed excitation experiments used a 337 nm PTI GL3300TM N2 laser, with a pulse width of 600 ps. For some measurements, this was used to pump a PTI GL301TM dye laser with a pulse width of 500 ps and output selected at 390 nm. Two Thorlabs 210TM silicon photodiode detectors, with a response time less than 1 ns, were used—one detector was used to trigger the scope, the other measured the emission. The signals were averaged using a 1 GHz Tektronix TDS5104TM digital oscilloscope. When the emission was not energy-resolved, a UV-blocking interference filter was used in front of the emission detector. The input impedance of the detector signals was set to 50 O. To minimize residual ringing, we trimmed the input impedance of the emitted light detector channel with a 1.2 kO resistor in parallel with the 50 O scope impedance. The temperature dependence of the lifetime was studied at 70 and 25 1C. Band-pass filters (Newport 420, 440, 480, 530, 580 and 620 nm) were placed in front of the emitted light detector to study the emission energy dependence of the lifetime. 2.4. DC excitation UV LEDs and a 50 MHz HP8116TM signal generator were used to create longer pulses for the DC excitation experiments (see the appendix). Because of the lower light levels a Hamamatsu R7400PTM photomultiplier tube, with a response time of 1 ns, was used as a detector for these experiments, and was run in single photon counting mode. A separate Hamamatsu C3830TM high voltage power supply was used to limit PMT ripple. The signals were averaged using a 1 GHz Tektronix TDS5104TM digital phosphor oscilloscope. Two channels were used on the scope. One channel sampled the HP voltage supply, which was used as a low-noise trigger source for the scope. The other channel sampled the PMT signal. The input impedance for the PMT was set to 50 O and the input bandwidth was set to full. The emission light was detected after passing through a CVI long-pass filter that is used to block the scattered excitation light. For each experiment, the PMT dark voltage was recorded to enable accurate subtraction of the baseline.
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of these signals was determined from signal-averaged waveforms accumulated on the Tektronix TDS5104TM digital oscilloscope. With this system, measurements can be made at frequencies up to 10 MHz, which is the bandwidth of the PDA55 detectors. The frequency-dependent lifetime is given by the tangent of the phase shift divided by the modulation frequency o. 3. Results and discussion Much of this paper is concerned with the relationship of the photoluminescent lifetime to such factors as the QY and alkanethiol concentration. For this reason it is important to have an accurate method of determining the PL lifetime. For the CdS QDs produced in inverse micellar solutions, the luminescence is non-exponential, so the value of the lifetime depends on to which moment of the lifetime distribution the measurement couples. 3.1. Form of the decay The decay of the broadband emission is slow and nonexponential, which is consistent with the emission coming from surface trap states [2,3,8,11]. In Fig. 1 the emission spectrum of broadband QDs made in inverse micelles is compared to that of narrow band QDs, made by a metathesis reaction [16]. The difference in lifetimes is striking: the narrow band QDs have a lifetime of 4.5 ns (measured by the phase shift method) which is very fast compared to the broadband decay (Fig. 2a). The curvature of the decay on log-linear axes shows that the broadband emission is much slower than exponential, and
2.5. Frequency domain measurements The frequency dependent measurements were made using two Thorlabs PDA55TM silicon photodiode detectors. These have much greater sensitivity than the PDA 210 photodiodes, but have a smaller bandwidth. One was used to detect the modulated light from a 400 nm reference LED, the other was used to detect the modulated luminescence from the sample, which is illuminated with a second 400 nm LED. The emission light is detected after passing through a CVI long-pass filter that is used to block the excitation light alone. The difference between the phase
Fig. 1. A comparison between the emission spectra of narrow- and broadband-emitting CdS QDs. The narrow-band, blue-emitting QDs were made by a metathesis reaction, and the broadband-emitting QDs were synthesized in inverse micelles. The excitation wavelength was 390 nm.
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Fig. 3. The pulsed PL decay of a purified QD sample made in inverse micelles. This decay has a fast initial slope that is followed by a stretched exponential with two characteristic times. The excitation wavelength was 337 nm.
Fig. 2. (a) A comparison between the pulsed PL decay of narrow- and broadband-emitting CdS QDs. The blue-emitting QDs exhibit a fast decay with a 4.5 ns lifetime, whereas the broadband-emitting QDs exhibit a slow, non-exponential decay. (b) The slow emission is well characterized as a stretched exponential with b ¼ 0.5 and a characteristic time of 240 ns. For both samples, the emission light was detected after passing through a longpass interference filter that is used to block the excitation light.
where G is the gamma function. From this relation, it is clear that the observed value b ¼ 0.5 indicates that the trap states have a simple exponential distribution of lifetimes. Purified CdS QDs made by the Lianos and Thomas method show a complex SE decay with two characteristic times in Fig. 3. This behavior might seem improbable, but we have been able to reproduce this decay curve repeatedly for a variety of samples. The fast characteristic time is 81 ns and the slow characteristic time is 300 ns. The latter time is difficult to determine accurately, because the low amplitude of the signal in this time domain creates great sensitivity to the measured baseline. Because the primary objective of this paper is to determine the relationship of the PL decay to the QY, a practical method of quantifying the decay dynamics is needed. For the reasons explained in the appendix, we have chosen to compute the harmonic average lifetime /1/tS1 from the decay data, rather than the arithmetic average /tS. For non-exponential decay processes, the harmonic average can be much faster than the arithmetic average, but it is much less susceptible to experimental error. 3.2. Relationship of the lifetime to QY
in fact, Fig. 2b shows that for long times, it is stretched exponential (SE) in form, exp½ðt=tc Þb , with an exponent of b ¼ 0.5 and a characteristic time tc ¼ 240 ns. A stretched exponential tail is consistent with the relaxation time distribution [11] hðtÞ dt ¼
b exp½ðt=tch Þb=ð1bÞ , ð1 bÞG ð1 b=bÞ tch
(1)
We have shown that purification and photolysis of CdS reverse micellar solutions increases the QY [17]. This QY increase is also reflected in the PL decay. PL decay measurements made during photolysis show that the lifetime is proportional to the QY, Fig. 4. This proportionality is expected for a system where only the non-radiative, or dark, decay rate is affected by photolysis.
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Fig. 4. The lifetime is shown to be a linear function of the quantum yield for both purified and unpurified samples. The excitation wavelength for the QY measurements was 390 nm.
Although the SE decay indicates a distribution of lifetimes, to explain this proportionality qualitatively we consider a standard system with only two parallel channels of decay, one dark and one light, with lifetimes td and tl, respectively. For such a system, the measured relaxation time is tm ¼ t1td/(t1+td) and the QY is given by tm ¼ tl QY. The experimentally observed proportionality between tm and QY indicates that tl is unaffected by photolysis. For the purified sample the data in Fig. 4 gives tlffi62 ns/0.24ffi260 ns. The variable dark lifetime is related to the QY by td ¼ tlQY/(1QY). Before photolysis, the QY is 0.1, which gives a dark lifetime of only 29 ns. Photolysis ultimately increases this dark lifetime to 82 ns, at which point the QY is 0.24. The lifetime trends we report are similar to those observed by Chestnoy et al. [3] for 22 and 38 A˚ CdS colloids, despite the fact that these colloids were made by a method that does not employ micelles. Chestnoy et al. used a 1 kHz spark gap in H2 as an excitation source, which has a 20 ms tail. Their data were then deconvolved to remove the tail and fit to a biexponential. (They did not observe a stretched exponential decay for their colloids, but in part this might be due to the noise in their decay curves making a detailed analysis of the form of the decay problematic.) From the fit parameters, they compute a lifetime, but do not state what moment this is, though most probably it is the arithmetic average. Still, they observe a three-fold increase in the lifetime over the temperature range where we observe a two-fold increase. Non-exponential PL decay was observed by Kim et al. [8] from 17 A˚ CdS QDs synthesized in reverse micelles. The QD surfaces were modified with Cd(OH)2, resulting in an enhancement of the band-edge PL emission and an increase
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Fig. 5. Energy-resolved measurements of the PL decay from a purified sample show an increase in the lifetime at higher wavelengths. The decay curves are offset for clarity, with the longest wavelength emission furthest offset to the right. The excitation wavelength was 337 nm.
in the lifetime. From their slowest decay curve, obtained from a sample treated with 6 105 M of excess Cd2+ we obtain a harmonic average lifetime of 83 ns. This lifetime is within the range of our observations, but a direct comparison is not possible, because they do not report the QY of this sample. 3.3. Dependence of the lifetime on emission energy The dependence of the PL lifetime on the emission energy was explored using narrow pass filters. Analysis of the room temperature data in Fig. 5 for the purified sample show that even after energy discrimination, the tail of the PL decay is still stretched exponential, although the lifetime increases appreciably with decreasing emission energy, Fig. 6. The initial drop in the decay is very fast, and is probably due to direct exciton recombination. PL measurements at 70 1C, show the same energy dependence of the lifetime, and some other interesting features. First, the 530 nm emission data, Fig. 7, shows that the decay is much slower, and in fact the lifetime is twice as large. The QY also increases proportionately to 51%. But the logarithmic plot also shows that the decay is nearly exponential with b ¼ 0.80. At 70 1C, the relative amplitude of the fast initial decay is 50% larger than at 25 1C, and both of these observations point to a relative increase in direct recombination. 3.4. Effect of alkanethiols Finally, the effect of dodecanethiol addition was studied. The emission spectra of thiol-treated CdS QDs under
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Fig. 6. The dependence of the lifetime on emission wavelength and temperature is shown for the purified sample. The lifetimes are considerably longer at low temperature and higher wavelength. The excitation wavelength was 337 nm.
Fig. 8. (a) The change in the emission upon thiol addition to an unpurified sample. A progressive red-shift is apparent. (b) The effect of thiol addition on a purified sample is similar (excitation at 390 nm.)
Fig. 7. A comparison between the 530 nm PL decay of a purified sample at +25 and 70 1C shows that the latter decay is slower, though more exponential. The QY at the lower temperature is much higher—51%.
390 nm excitation are shown in Fig. 8 for unpurified and purified samples. The emission decreases similarly for each of these samples and is accompanied by a red-shift of roughly 35 nm. At very small thiol:CdS molar ratios, the measured emission of the purified sample actually increases, but unfortunately this is only due to a red-shift and slight increase in the absorption spectrum that increases the absorbance at the excitation wavelength, Fig. 9. This redshift is modest, only 14 nm. The absorbance of the
unpurified sample also red-shifts with thiol addition, though the absorbance starts to decrease at much lower thiol:CdS molar ratios than the purified sample. It is interesting to note that the absorbance of the unpurified sample is roughly three times smaller than that of the purified sample. This is consistent with a greater yield of nanoparticles in the purified sample. Alkanethiols strongly and monotonically quench the QY of both the purified and unpurified QDs at modest molar ratios of thiol, Fig. 10. Again, the lifetime is affected, but sub-proportionately, Fig. 11. For this reason, a simple parallel channel model, where the dark relaxation time is affected by thiol addition and the radiative channel is not, cannot explain the thiolated samples. Selected spectral
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Fig. 9. The absorbance of the purified sample increases and red-shifts with thiol addition.
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Fig. 11. Thiol addition decreases the PL lifetime, but the plot of lifetime vs. QY has a markedly non-zero intercept, which indicates that a simple two channel description is inadequate. Table 1 Peak emission wavelength and quantum yield of unpurified CdS QDs as a function of thiol molar ratio Thiol molar ratio
Peak emission wavelength (nm)
Quantum yield (%)
0 0.046 0.093 0.140 0.185 0.277 0.46 0.93 1.85 3.7
543.4 546.3 550.3 553.2 560.4 562.4 567 569.8 573.9 575
15 12.7 12.1 10.7 8.9 8.4 7.2 6.6 5.9 6.2
Table 2 Peak emission wavelength and quantum yield of purified CdS QDs as a function of thiol molar ratio Fig. 10. Thiol addition quenches the emission, causing the quantum yield to decrease.
properties of these samples are summarized in Tables 1 and 2. At 70 1C, the strong quenching effect of thiols nearly vanishes. Absolute measurements on a sample with sufficient thiol to quench the ambient QY to 4.1% show that the QY rises by a factor of 9, to 37%, which is quite close to the 51% value obtained for the parent, purified sample at this temperature. This QY increase is accompanied by a lifetime increase from 27 to 76 ns, which is far less than a factor of 9, showing once again that the emission decay of the thiolated QDs cannot be described simply.
Thiol molar ratio
Peak emission wavelength (nm)
Quantum yield (%)
0 0.46 0.93 1.4 2.3 3.7 6.0 9.3
530 544.7 550.3 553.5 556.7 559.1 561.5 566.2
20.3 14.8 10.3 8.6 7.3 6.6 5.8 4.5
It would be interesting to determine if other surface active agents might increase the QY of these broadband emitters. Future work will focus on the effect on the PL of a variety of surface-active ligands.
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4. Conclusions The stretched exponential photoluminescent decay of the broadband emission of purified and unpurified CdS QDs made in reverse micelles has been characterized as a function of photolysis and thiol addition. During photolysis, the lifetime was found to increase in proportion to the QY, which is consistent with a parallel channel model of decay where only the lifetime of the non-radiative channel is affected by photolysis. The QY of the purified sample was found to be as high as 24%, which is twice that reported for this preparation [2,8]. Measurements at 70 1C give a QY of 51% for this sample, and a proportionately increased lifetime. Energy-resolved PL studies show that the PL decay is still stretched exponential, but with a lifetime that decreases with increasing emission energy. Finally, the addition of alkanethiols redshifts and quenches the emission, and gives a subproportional dependence of the lifetime on QY. These thiolated QDs show an extremely large temperature dependence of QY. Future studies will focus on determining if other ligands can increase the QY, while retaining the broadband emission characteristics.
Fig. 12. When the pulsed decay curve in Fig. 3 is multiplied by time the product has significant amplitude out to long times. The integral of this product (right axis) exhibits slow convergence, making the determination of the arithmetic average relaxation time from pulsed PL decay data impractical. All that can be ascertained is that this lifetime is greater than 350 ns.
Acknowledgments Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract no. DE-AC04-94AL85000. Appendix In many cases, a luminescent decay can be modeled as a sum of exponential processes characterized by a distribution R 1 of relaxation times h(t), normalized such that 0 hðtÞ dt ¼ 1. When the duration of the excitation pulse is short compared to the fastest relaxation time in the spectrum, the photoluminescent decay is given by Z 1 S p ðtÞ ¼ t1 et=t hðtÞ dt, (A.1) 0
where the radiated light is normalized such that R1 time p ðtÞ dt ¼ 1. The arithmetic average 0 SR R 1 Rrelaxation 1 1 tR0 ¼ 0 t hðtÞ dt is then given by 0 t0 S p ðtÞ dt dt0 ¼ 1 0 t S p ðtÞ dt, so in principle one can extract the arithmetic average lifetime from the experimental data. In practice, this does not work well for these samples because of the poor convergence of t Sp(t), as shown in Fig. 12. Attempting to extract the arithmetic average lifetime from t Sp(t) gives a lifetime b350 ns, which we will show in the following is too large. The accuracy of this approach is also poor because the low-amplitude, long-time tail of t Sp(t) is very sensitive to the baseline. A more practical approach R 1 is to compute the harmonic average lifetime th ¼ 1= 0 t1 hðtÞ R 1dt. For pulsed excitation, this lifetime is given by 0 Sp ðtÞ dt=S p ð0Þ, an
Fig. 13. A comparison between the PL decay with pulsed and steady-state excitations. The pulsed excitation gives a harmonic average lifetime of 74 ns, whereas an arithmetic average lifetime of 180 ns is obtained from the steady-state data.
expression that is much easier to evaluate than the arithmetic average. The harmonic average will be much smaller than the arithmetic average. For example, integrating Sp(t) in Fig. 12 gives a harmonic average lifetime of 69 ns. Pulsed excitation is actually not the method of choice for the determination of the arithmetic average lifetime: both
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Applying this result to data for the purified QD sample gives t0 ¼ 180 ns, which is much longer than the harmonic average of 74 ns obtained from the pulsed data in Fig. 13. Frequency-domain measurements were made to try to more accurately determine the arithmetic average lifetime, which is directly obtained from the phase shift at asymptotically low frequencies. These measurements, Fig. 14, give an arithmetic average lifetime of 150 ns. This value is more accurate than the steady-state excitation data, because these data were not deconvolved from the system response. The LED itself, as driven with the HP signal source, and as measured with the PMT, shuts off in about 20 ns. We conclude that the arithmetic average lifetime is essentially twice the harmonic average.
References Fig. 14. Frequency-domain lifetime measurements indicate an arithmetic average lifetime of 150 ns (zero-frequency limit).
frequency domain measurements at asymptotically low frequencies and time-domain measurements with long duration excitations are more direct. We discuss the timedomain measurements first. When a sample exhibits a broad distribution of lifetimes, the PL decay depends on the duration of the excitation. This effect is significant in the broadband QDs investigated here. Fig. 13 shows a comparison of the PL decay with pulsed excitation (600 ps pulse), and after being illuminated sufficiently long (1 ms) for the emission to reach steady state. With steady-state excitation the observed PL decay is roughly 2 slower than in the pulsed experiments. The arithmetic average lifetime is more easily extracted from steady-state excitation data because this preferentially populates the slowest relaxation processes [11]. In terms of the distribution of relaxation times, the steady-state PL decay is given by Z 1 S c ðtÞ ¼ et=t hðtÞ dt. (A.2) 0
R1 The simple integral t0 ¼ 0 S c ðtÞ dt=Sc ð0Þ of the normalized decay now gives the arithmetic average lifetime.
[1] P. Lianos, J.K. Thomas, Chem. Phys. Lett. 125 (3) (1986) 299. [2] B.A. Harruff, C.E. Bunker, Langmuir 19 (2003) 893. [3] N. Chestnoy, T.D. Harris, R. Hull, L.E. Brus, J. Phys. Chem. 90 (1986) 3393. [4] L. Spanhel, M. Haase, H. Weller, A. Henglein, J. Am. Chem. Soc. 109 (1987) 5649. [5] U. Resch, A. Eychmuller, M. Haase, H. Weller, Langmuir 8 (1992) 2215. [6] M. Hamity, R.H. Lema, C.A. Suchetti, J. Photochem. Photobiol. A 133 (2000) 205. [7] C.-W. Wang, M.G. Moffitt, Langmuir 20 (2004) 11784. [8] D. Kim, M. Miyamoto, T. Mishima, M. Nakayama, J. Appl. Phys. 98 (2005) 083514. [9] M. Tata, S. Banerjee, V.T. John, Y. Waguespack, G.L. McPherson, Colloid Surf. A 127 (1997) 39. [10] J. Zhang, L. Sun, C. Liao, C. Yan, Solid State Commun. 124 (2002) 45. [11] J.E. Martin, L.E. Shea-Rohwer, J. Lumin. 121 (2006) 573. [12] J.R. Lakowicz, I. Gryczynski, Z. Gryczynski, C.J. Murphy, J. Phys. Chem. B 103 (1999) 7613. [13] A.A. Bol, R. van Beck, J. Ferwerda, A. Meijerink, J. Phys. Chem. Solids 64 (2003) 247. [14] R.A. Velapoldi, K.D. Mielenz, A Fluorescence Standard Reference Material: Quinine Sulfate Dihydrate, NBS Special Publication, 1980, pp. 260–264. [15] L.S. Rohwer, J.E. Martin, J. Lumin. 115 (2005) 77. [16] B.A. Ridley, B. Nivi, J.M. Jacobson, Science 286 (1999) 746. [17] L.E. Shea-Rohwer, J.E. Martin, J. Lumin., submitted for publication.
Journal of Luminescence 127 (2007) 499–507 www.elsevier.com/locate/jlumin
Luminescence decay of broadband emission from CdS quantum dots Lauren E. Shea-Rohwer, James E. Martin Sandia National Laboratories, P.O. Box 5800, MS-0892, Albuquerque, NM 87185-0892, USA Received 24 August 2006; received in revised form 21 February 2007; accepted 22 February 2007 Available online 7 March 2007
Abstract The stretched exponential photoluminescence decay of the energy-resolved broadband emission of purified and unpurified CdS quantum dots (QDs) made in reverse micelles is characterized as a function of photolysis time and thiol addition. Photolysis is found to proportionately increase both the lifetime and quantum yield of these QDs. This proportionality is consistent with a simple parallel channel model of the decay of the excited states. The ultimate QY of the purified sample is found to be as high as 24%, which is twice that previously reported for this preparation. At 70 1C both the QY and the lifetime increase by more than a factor of two, indicating that thermal quenching limits the QY at room temperature. Finally, the addition of alkanethiols is shown to red-shift and quench the emission while only modestly altering the lifetime. These thiolated QDs show an extremely large temperature dependence of QY, demonstrating stronger thermal quenching than the unfunctionalized QDs. r 2007 Elsevier B.V. All rights reserved. Keywords: Stretched exponential decay; Photoluminescence; CdS quantum dots; Quantum yield; Lifetime; Alkanethiols; Photolysis; Reverse micelles; Thermal quenching; White emission
1. Introduction In this paper we present the results of a quantitative study of the photoluminescence (PL) decay of the broadband, approximately white, emission of CdS quantum dots made from the reverse micellar synthesis reported by Lianos and Thomas [1] in 1986. The emission characteristics of these QDs are quite complex. Harruff and Bunker [2] have shown that the quantum yield (QY) of these QDs can be significantly increased by photolysis with UV light, and have noted that the broadband emission is strongly non-exponential, consistent with trap state emission. The effect of photolysis on the decay dynamics, and the relation of this to the QY, remains an open issue, and the purpose of this paper is to explore this and related issues. We focus on two types of samples: those prepared by following the Harruff and Bunker synthesis exactly; and those that were purified after this synthesis, but before photolysis. After these samples were fully photolyzed, the emission was Corresponding author. Tel.: +1 5058446627; fax: +1 5058458161.
E-mail address: [email protected] (L.E. Shea-Rohwer). 0022-2313/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2007.02.061
progressively quenched by titrating the solutions with alkanethiols, and the PL properties were monitored. We have measured both the PL decay and QY during the photolysis of both purified and unpurified QDs. In both cases the average lifetime was found to be proportional to the QY. In fact, the principal difference between the purified and unpurified QDs is their ultimate QY when fully photolyzed: the QY of the purified QDs reaches 24%, which is roughly twice that previously reported for broadband CdS QDs [2]. This proportionality can be understood qualitatively in terms of a model of parallel radiative and non-radiative decay channels, with the lifetime of the dark channel affected by photolysis. Measurements at low temperatures show that both the QY and the lifetime increase greatly, yet remain proportional, indicating that thermal quenching limits the QY of these materials at room temperature. Energy-resolved PL studies show that the lifetime decreases with increasing emission energy. Finally, the addition of alkanethiols is found to red-shift and quench the emission, but in this case the proportionality of the lifetime and QY does not hold. This strong thiol quenching does not occur at low
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temperatures, and we conclude that thiolated QDs show very strong thermal quenching of the emission at room temperature. There have been a number of related studies of the PL of CdS QDs. For example, the emission spectrum has been shown to be strongly affected by surface functionalization, synthesis conditions, solution pH, and water content [3–10]. When these factors result in a significant broadening of the emission bandwidth there is also a marked increase in the lifetime. The direct recombination of excitonic transitions are marked by small Stokes shifts and have been found to decay exponentially, with lifetimes of a few nanoseconds. In contrast, the broadband emission decays are much slower, and exhibit the strongly nonexponential decay characteristic of a distribution of trap states [2,3,8]. We have recently reported that broadbandemitting CdS QDs produced by surface functionalization with alkanethiols exhibit a stretched exponential luminescence decay [11]. The arithmetic average lifetime of this decay is on the order of 1 ms, much longer than that of the unfunctionalized QDs. The sensitivity of the lifetime to surface functionalization is also illustrated in a frequencydomain study by Lakowicz et al. [12], who found that blueemitting CdS nanoparticles stabilized by poly(aminoamine) starburst dendrimer had a very different lifetime (t ¼ 93 ns) than red-emitting, polyphosphate-stabilized CdS (t ¼ 10 ms). In time-domain studies of broad-emitting CdS QDs synthesized in reverse micelles, Kim et al. [8] found that surface modification with Cd(OH)2 increased the lifetime of the nonexponential decay. The PL decay time is also known to be dependent on the emission energy and sample temperature. White emission from ZnS–CdS co-colloids has been reported to have a multi-exponential decay, with an average relaxation time that decreases with emission energy [4]. Similar results have been reported for broadband-emitting CdS colloids [2]. Finally, low-temperature studies of CdS QDs have shown increases in both the emission intensity and lifetime [3], and a similar temperature dependence has been reported for CdS:Mn2+ [13] QDs. 2. Experimental 2.1. Synthesis Quantum dots were synthesized using the reverse micelle method described by Harruff and Bunker [2]. This was a modification of the Lianos and Thomas synthesis [1]. First, a solution of 0.2 M Cd(NO3)2 and a solution of 0.2 M Na2S are prepared in 1 mL deionized water. Next, in a glove box under nitrogen, 36 mL of each aqueous solution is injected into separate 5 mL solutions of 0.1 M dioctyl sulfosuccinate sodium salt (AOT) in heptane. The two solutions are allowed to stir for 1 h, and then mixed together. The assynthesized CdS QDs are 1.8–2.0 nm in diameter, as confirmed by TEM, and are very weakly luminescent. To increase their emission intensity, the samples are photolyzed
with 365 nm light at an intensity of 1.2 mW/cm2 for as much as 3 h. Some samples were purified before photolysis, by freezing the inverse micelle solutions at 30 1C. Over a period of weeks, ice crystals form that can be filtered out to leave a purified solution. These samples were photolyzed immediately after filtering. Some samples were titrated with dodecanethiol after photolysis. The emission intensity, absorbance and QY were measured for a range of thiol:CdS molar ratios. For comparison, narrow-band emitting CdS QDs were made by mixing a solution of Cd(NO3)2 in methanol containing 10 vol% pyridine with an equimolar solution of (NH4)2S in tetrahydrofuran (THF). This resulted in 2 nm QDs with narrow emission and a fast lifetime indicative of direct recombination. 2.2. Characterization Photoluminescence emission spectra were collected using a Horiba/Jobin-Yvon Fluorolog-3TM double grating–double grating fluorescence spectrophotometer. All samples were excited at 390 nm. A complete instrumental correction is performed on all spectra that includes corrections for factors such as wavelength-dependent PMT response and grating efficiencies, among other factors. Absorption spectra from 350 to 500 nm were obtained using a Perkin-Elmer Lambda 19TM UV/VIS/NIR spectrometer. Relative quantum yields were calculated from the integrated, corrected, emission spectra and the absorbed light at 390 nm within the emission volume. The absorbance values of both the sample and the reference were used to compute the light absorbed within the emission volume located in the center of a 1 cm path length square cuvette. Calling the integrals of the emission spectra for the sample and reference Is and Ir, respectively, and the absorbances As and Ar, the QY of the sample is QY ¼
I s Ar 10Ar 0:5 cm QYr , I r As 10As 0:5 cm
where QYr is the reference QY. (This expression is valid for absorbances in the range of our measurements, less than A ¼ 0.2 cm1.) A 5 104 M solution of quinine sulfate dihydrate in 1 N sulfuric acid was used as a reference standard, using the accepted QY of 54.6% [14]. Absolute QYs were determined using a measurement technique we developed that is based on exciting the sample with diffuse light within an integrating sphere [15]. The photoluminescent decay was measured using pulsed and steady-state excitation in the time domain, and was also measured by the phase shift method. Pulsed excitation refers to the case where the excitation is short compared to the shortest lifetime. DC excitation refers to the case where the pulse width is sufficiently long such that the luminescence reaches steady state before the light is shut off. In other words, the pulse width is longer than the longest lifetime the material exhibits.
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2.3. Pulsed excitation Pulsed excitation experiments used a 337 nm PTI GL3300TM N2 laser, with a pulse width of 600 ps. For some measurements, this was used to pump a PTI GL301TM dye laser with a pulse width of 500 ps and output selected at 390 nm. Two Thorlabs 210TM silicon photodiode detectors, with a response time less than 1 ns, were used—one detector was used to trigger the scope, the other measured the emission. The signals were averaged using a 1 GHz Tektronix TDS5104TM digital oscilloscope. When the emission was not energy-resolved, a UV-blocking interference filter was used in front of the emission detector. The input impedance of the detector signals was set to 50 O. To minimize residual ringing, we trimmed the input impedance of the emitted light detector channel with a 1.2 kO resistor in parallel with the 50 O scope impedance. The temperature dependence of the lifetime was studied at 70 and 25 1C. Band-pass filters (Newport 420, 440, 480, 530, 580 and 620 nm) were placed in front of the emitted light detector to study the emission energy dependence of the lifetime. 2.4. DC excitation UV LEDs and a 50 MHz HP8116TM signal generator were used to create longer pulses for the DC excitation experiments (see the appendix). Because of the lower light levels a Hamamatsu R7400PTM photomultiplier tube, with a response time of 1 ns, was used as a detector for these experiments, and was run in single photon counting mode. A separate Hamamatsu C3830TM high voltage power supply was used to limit PMT ripple. The signals were averaged using a 1 GHz Tektronix TDS5104TM digital phosphor oscilloscope. Two channels were used on the scope. One channel sampled the HP voltage supply, which was used as a low-noise trigger source for the scope. The other channel sampled the PMT signal. The input impedance for the PMT was set to 50 O and the input bandwidth was set to full. The emission light was detected after passing through a CVI long-pass filter that is used to block the scattered excitation light. For each experiment, the PMT dark voltage was recorded to enable accurate subtraction of the baseline.
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of these signals was determined from signal-averaged waveforms accumulated on the Tektronix TDS5104TM digital oscilloscope. With this system, measurements can be made at frequencies up to 10 MHz, which is the bandwidth of the PDA55 detectors. The frequency-dependent lifetime is given by the tangent of the phase shift divided by the modulation frequency o. 3. Results and discussion Much of this paper is concerned with the relationship of the photoluminescent lifetime to such factors as the QY and alkanethiol concentration. For this reason it is important to have an accurate method of determining the PL lifetime. For the CdS QDs produced in inverse micellar solutions, the luminescence is non-exponential, so the value of the lifetime depends on to which moment of the lifetime distribution the measurement couples. 3.1. Form of the decay The decay of the broadband emission is slow and nonexponential, which is consistent with the emission coming from surface trap states [2,3,8,11]. In Fig. 1 the emission spectrum of broadband QDs made in inverse micelles is compared to that of narrow band QDs, made by a metathesis reaction [16]. The difference in lifetimes is striking: the narrow band QDs have a lifetime of 4.5 ns (measured by the phase shift method) which is very fast compared to the broadband decay (Fig. 2a). The curvature of the decay on log-linear axes shows that the broadband emission is much slower than exponential, and
2.5. Frequency domain measurements The frequency dependent measurements were made using two Thorlabs PDA55TM silicon photodiode detectors. These have much greater sensitivity than the PDA 210 photodiodes, but have a smaller bandwidth. One was used to detect the modulated light from a 400 nm reference LED, the other was used to detect the modulated luminescence from the sample, which is illuminated with a second 400 nm LED. The emission light is detected after passing through a CVI long-pass filter that is used to block the excitation light alone. The difference between the phase
Fig. 1. A comparison between the emission spectra of narrow- and broadband-emitting CdS QDs. The narrow-band, blue-emitting QDs were made by a metathesis reaction, and the broadband-emitting QDs were synthesized in inverse micelles. The excitation wavelength was 390 nm.
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Fig. 3. The pulsed PL decay of a purified QD sample made in inverse micelles. This decay has a fast initial slope that is followed by a stretched exponential with two characteristic times. The excitation wavelength was 337 nm.
Fig. 2. (a) A comparison between the pulsed PL decay of narrow- and broadband-emitting CdS QDs. The blue-emitting QDs exhibit a fast decay with a 4.5 ns lifetime, whereas the broadband-emitting QDs exhibit a slow, non-exponential decay. (b) The slow emission is well characterized as a stretched exponential with b ¼ 0.5 and a characteristic time of 240 ns. For both samples, the emission light was detected after passing through a longpass interference filter that is used to block the excitation light.
where G is the gamma function. From this relation, it is clear that the observed value b ¼ 0.5 indicates that the trap states have a simple exponential distribution of lifetimes. Purified CdS QDs made by the Lianos and Thomas method show a complex SE decay with two characteristic times in Fig. 3. This behavior might seem improbable, but we have been able to reproduce this decay curve repeatedly for a variety of samples. The fast characteristic time is 81 ns and the slow characteristic time is 300 ns. The latter time is difficult to determine accurately, because the low amplitude of the signal in this time domain creates great sensitivity to the measured baseline. Because the primary objective of this paper is to determine the relationship of the PL decay to the QY, a practical method of quantifying the decay dynamics is needed. For the reasons explained in the appendix, we have chosen to compute the harmonic average lifetime /1/tS1 from the decay data, rather than the arithmetic average /tS. For non-exponential decay processes, the harmonic average can be much faster than the arithmetic average, but it is much less susceptible to experimental error. 3.2. Relationship of the lifetime to QY
in fact, Fig. 2b shows that for long times, it is stretched exponential (SE) in form, exp½ðt=tc Þb , with an exponent of b ¼ 0.5 and a characteristic time tc ¼ 240 ns. A stretched exponential tail is consistent with the relaxation time distribution [11] hðtÞ dt ¼
b exp½ðt=tch Þb=ð1bÞ , ð1 bÞG ð1 b=bÞ tch
(1)
We have shown that purification and photolysis of CdS reverse micellar solutions increases the QY [17]. This QY increase is also reflected in the PL decay. PL decay measurements made during photolysis show that the lifetime is proportional to the QY, Fig. 4. This proportionality is expected for a system where only the non-radiative, or dark, decay rate is affected by photolysis.
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Fig. 4. The lifetime is shown to be a linear function of the quantum yield for both purified and unpurified samples. The excitation wavelength for the QY measurements was 390 nm.
Although the SE decay indicates a distribution of lifetimes, to explain this proportionality qualitatively we consider a standard system with only two parallel channels of decay, one dark and one light, with lifetimes td and tl, respectively. For such a system, the measured relaxation time is tm ¼ t1td/(t1+td) and the QY is given by tm ¼ tl QY. The experimentally observed proportionality between tm and QY indicates that tl is unaffected by photolysis. For the purified sample the data in Fig. 4 gives tlffi62 ns/0.24ffi260 ns. The variable dark lifetime is related to the QY by td ¼ tlQY/(1QY). Before photolysis, the QY is 0.1, which gives a dark lifetime of only 29 ns. Photolysis ultimately increases this dark lifetime to 82 ns, at which point the QY is 0.24. The lifetime trends we report are similar to those observed by Chestnoy et al. [3] for 22 and 38 A˚ CdS colloids, despite the fact that these colloids were made by a method that does not employ micelles. Chestnoy et al. used a 1 kHz spark gap in H2 as an excitation source, which has a 20 ms tail. Their data were then deconvolved to remove the tail and fit to a biexponential. (They did not observe a stretched exponential decay for their colloids, but in part this might be due to the noise in their decay curves making a detailed analysis of the form of the decay problematic.) From the fit parameters, they compute a lifetime, but do not state what moment this is, though most probably it is the arithmetic average. Still, they observe a three-fold increase in the lifetime over the temperature range where we observe a two-fold increase. Non-exponential PL decay was observed by Kim et al. [8] from 17 A˚ CdS QDs synthesized in reverse micelles. The QD surfaces were modified with Cd(OH)2, resulting in an enhancement of the band-edge PL emission and an increase
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Fig. 5. Energy-resolved measurements of the PL decay from a purified sample show an increase in the lifetime at higher wavelengths. The decay curves are offset for clarity, with the longest wavelength emission furthest offset to the right. The excitation wavelength was 337 nm.
in the lifetime. From their slowest decay curve, obtained from a sample treated with 6 105 M of excess Cd2+ we obtain a harmonic average lifetime of 83 ns. This lifetime is within the range of our observations, but a direct comparison is not possible, because they do not report the QY of this sample. 3.3. Dependence of the lifetime on emission energy The dependence of the PL lifetime on the emission energy was explored using narrow pass filters. Analysis of the room temperature data in Fig. 5 for the purified sample show that even after energy discrimination, the tail of the PL decay is still stretched exponential, although the lifetime increases appreciably with decreasing emission energy, Fig. 6. The initial drop in the decay is very fast, and is probably due to direct exciton recombination. PL measurements at 70 1C, show the same energy dependence of the lifetime, and some other interesting features. First, the 530 nm emission data, Fig. 7, shows that the decay is much slower, and in fact the lifetime is twice as large. The QY also increases proportionately to 51%. But the logarithmic plot also shows that the decay is nearly exponential with b ¼ 0.80. At 70 1C, the relative amplitude of the fast initial decay is 50% larger than at 25 1C, and both of these observations point to a relative increase in direct recombination. 3.4. Effect of alkanethiols Finally, the effect of dodecanethiol addition was studied. The emission spectra of thiol-treated CdS QDs under
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Fig. 6. The dependence of the lifetime on emission wavelength and temperature is shown for the purified sample. The lifetimes are considerably longer at low temperature and higher wavelength. The excitation wavelength was 337 nm.
Fig. 8. (a) The change in the emission upon thiol addition to an unpurified sample. A progressive red-shift is apparent. (b) The effect of thiol addition on a purified sample is similar (excitation at 390 nm.)
Fig. 7. A comparison between the 530 nm PL decay of a purified sample at +25 and 70 1C shows that the latter decay is slower, though more exponential. The QY at the lower temperature is much higher—51%.
390 nm excitation are shown in Fig. 8 for unpurified and purified samples. The emission decreases similarly for each of these samples and is accompanied by a red-shift of roughly 35 nm. At very small thiol:CdS molar ratios, the measured emission of the purified sample actually increases, but unfortunately this is only due to a red-shift and slight increase in the absorption spectrum that increases the absorbance at the excitation wavelength, Fig. 9. This redshift is modest, only 14 nm. The absorbance of the
unpurified sample also red-shifts with thiol addition, though the absorbance starts to decrease at much lower thiol:CdS molar ratios than the purified sample. It is interesting to note that the absorbance of the unpurified sample is roughly three times smaller than that of the purified sample. This is consistent with a greater yield of nanoparticles in the purified sample. Alkanethiols strongly and monotonically quench the QY of both the purified and unpurified QDs at modest molar ratios of thiol, Fig. 10. Again, the lifetime is affected, but sub-proportionately, Fig. 11. For this reason, a simple parallel channel model, where the dark relaxation time is affected by thiol addition and the radiative channel is not, cannot explain the thiolated samples. Selected spectral
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Fig. 9. The absorbance of the purified sample increases and red-shifts with thiol addition.
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Fig. 11. Thiol addition decreases the PL lifetime, but the plot of lifetime vs. QY has a markedly non-zero intercept, which indicates that a simple two channel description is inadequate. Table 1 Peak emission wavelength and quantum yield of unpurified CdS QDs as a function of thiol molar ratio Thiol molar ratio
Peak emission wavelength (nm)
Quantum yield (%)
0 0.046 0.093 0.140 0.185 0.277 0.46 0.93 1.85 3.7
543.4 546.3 550.3 553.2 560.4 562.4 567 569.8 573.9 575
15 12.7 12.1 10.7 8.9 8.4 7.2 6.6 5.9 6.2
Table 2 Peak emission wavelength and quantum yield of purified CdS QDs as a function of thiol molar ratio Fig. 10. Thiol addition quenches the emission, causing the quantum yield to decrease.
properties of these samples are summarized in Tables 1 and 2. At 70 1C, the strong quenching effect of thiols nearly vanishes. Absolute measurements on a sample with sufficient thiol to quench the ambient QY to 4.1% show that the QY rises by a factor of 9, to 37%, which is quite close to the 51% value obtained for the parent, purified sample at this temperature. This QY increase is accompanied by a lifetime increase from 27 to 76 ns, which is far less than a factor of 9, showing once again that the emission decay of the thiolated QDs cannot be described simply.
Thiol molar ratio
Peak emission wavelength (nm)
Quantum yield (%)
0 0.46 0.93 1.4 2.3 3.7 6.0 9.3
530 544.7 550.3 553.5 556.7 559.1 561.5 566.2
20.3 14.8 10.3 8.6 7.3 6.6 5.8 4.5
It would be interesting to determine if other surface active agents might increase the QY of these broadband emitters. Future work will focus on the effect on the PL of a variety of surface-active ligands.
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4. Conclusions The stretched exponential photoluminescent decay of the broadband emission of purified and unpurified CdS QDs made in reverse micelles has been characterized as a function of photolysis and thiol addition. During photolysis, the lifetime was found to increase in proportion to the QY, which is consistent with a parallel channel model of decay where only the lifetime of the non-radiative channel is affected by photolysis. The QY of the purified sample was found to be as high as 24%, which is twice that reported for this preparation [2,8]. Measurements at 70 1C give a QY of 51% for this sample, and a proportionately increased lifetime. Energy-resolved PL studies show that the PL decay is still stretched exponential, but with a lifetime that decreases with increasing emission energy. Finally, the addition of alkanethiols redshifts and quenches the emission, and gives a subproportional dependence of the lifetime on QY. These thiolated QDs show an extremely large temperature dependence of QY. Future studies will focus on determining if other ligands can increase the QY, while retaining the broadband emission characteristics.
Fig. 12. When the pulsed decay curve in Fig. 3 is multiplied by time the product has significant amplitude out to long times. The integral of this product (right axis) exhibits slow convergence, making the determination of the arithmetic average relaxation time from pulsed PL decay data impractical. All that can be ascertained is that this lifetime is greater than 350 ns.
Acknowledgments Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract no. DE-AC04-94AL85000. Appendix In many cases, a luminescent decay can be modeled as a sum of exponential processes characterized by a distribution R 1 of relaxation times h(t), normalized such that 0 hðtÞ dt ¼ 1. When the duration of the excitation pulse is short compared to the fastest relaxation time in the spectrum, the photoluminescent decay is given by Z 1 S p ðtÞ ¼ t1 et=t hðtÞ dt, (A.1) 0
where the radiated light is normalized such that R1 time p ðtÞ dt ¼ 1. The arithmetic average 0 SR R 1 Rrelaxation 1 1 tR0 ¼ 0 t hðtÞ dt is then given by 0 t0 S p ðtÞ dt dt0 ¼ 1 0 t S p ðtÞ dt, so in principle one can extract the arithmetic average lifetime from the experimental data. In practice, this does not work well for these samples because of the poor convergence of t Sp(t), as shown in Fig. 12. Attempting to extract the arithmetic average lifetime from t Sp(t) gives a lifetime b350 ns, which we will show in the following is too large. The accuracy of this approach is also poor because the low-amplitude, long-time tail of t Sp(t) is very sensitive to the baseline. A more practical approach R 1 is to compute the harmonic average lifetime th ¼ 1= 0 t1 hðtÞ R 1dt. For pulsed excitation, this lifetime is given by 0 Sp ðtÞ dt=S p ð0Þ, an
Fig. 13. A comparison between the PL decay with pulsed and steady-state excitations. The pulsed excitation gives a harmonic average lifetime of 74 ns, whereas an arithmetic average lifetime of 180 ns is obtained from the steady-state data.
expression that is much easier to evaluate than the arithmetic average. The harmonic average will be much smaller than the arithmetic average. For example, integrating Sp(t) in Fig. 12 gives a harmonic average lifetime of 69 ns. Pulsed excitation is actually not the method of choice for the determination of the arithmetic average lifetime: both
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Applying this result to data for the purified QD sample gives t0 ¼ 180 ns, which is much longer than the harmonic average of 74 ns obtained from the pulsed data in Fig. 13. Frequency-domain measurements were made to try to more accurately determine the arithmetic average lifetime, which is directly obtained from the phase shift at asymptotically low frequencies. These measurements, Fig. 14, give an arithmetic average lifetime of 150 ns. This value is more accurate than the steady-state excitation data, because these data were not deconvolved from the system response. The LED itself, as driven with the HP signal source, and as measured with the PMT, shuts off in about 20 ns. We conclude that the arithmetic average lifetime is essentially twice the harmonic average.
References Fig. 14. Frequency-domain lifetime measurements indicate an arithmetic average lifetime of 150 ns (zero-frequency limit).
frequency domain measurements at asymptotically low frequencies and time-domain measurements with long duration excitations are more direct. We discuss the timedomain measurements first. When a sample exhibits a broad distribution of lifetimes, the PL decay depends on the duration of the excitation. This effect is significant in the broadband QDs investigated here. Fig. 13 shows a comparison of the PL decay with pulsed excitation (600 ps pulse), and after being illuminated sufficiently long (1 ms) for the emission to reach steady state. With steady-state excitation the observed PL decay is roughly 2 slower than in the pulsed experiments. The arithmetic average lifetime is more easily extracted from steady-state excitation data because this preferentially populates the slowest relaxation processes [11]. In terms of the distribution of relaxation times, the steady-state PL decay is given by Z 1 S c ðtÞ ¼ et=t hðtÞ dt. (A.2) 0
R1 The simple integral t0 ¼ 0 S c ðtÞ dt=Sc ð0Þ of the normalized decay now gives the arithmetic average lifetime.
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