Measuring Activation and Luminescence Time Scales of Upconverting

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Article

Measuring Activation and Luminescence Timescales of Upconverting NaYF:Yb,Er Nanocrystals 4

Ted A. Laurence, Yang Liu, Ming Zhang, Matthew J. Owen, Jinkyu Han, Ling-Dong Sun, Chun-Hua Yan, and Gang-yu Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07882 • Publication Date (Web): 27 Sep 2018 Downloaded from http://pubs.acs.org on September 29, 2018

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The Journal of Physical Chemistry

Measuring Activation and Luminescence Timescales of Upconverting NaYF4:Yb,Er Nanocrystals Ted A. Laurence,∗,† Yang Liu,‡ Ming Zhang,‡ Matthew J. Owen,‡ Jinkyu Han,† Lingdong Sun,¶ Chunhua Yan,¶ and Gang-yu Liu‡ †Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California, USA ‡University of California, Davis, California, USA ¶Peking University, Beijing, China E-mail: [email protected]

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Abstract Accurate determination of upconversion and luminescence lifetimes requires kinetic modeling of the complete time resolved response for upconversion luminescence of NaYF4 :Yb,Er nanocrystals. Prior investigations typically perform exponential fitting of the tail in the time profile or employ complex systems of differential equations to extract lifetimes. In order to simplify analysis while fitting the entire time-resolved response, this work introduces a set of simplified models that model the response as a convolution of upconversion and fluorescence processes. Models for two- and threephoton upconversion processes are developed and tested for NaYF4 :Yb,Er nanocrystals excited by a 980 nm laser. The results are presented for the transitions 2 H11/2 , 4 S3/2 → 4I 15/2

(530 nm, green emission), 4 F9/2 →4 I15/2 (650 nm, red emission) and 2 H9/2 →4 I15/2

(400 nm, blue emission). Even with the same number of fitting parameters, the twoand three-photon models resulted in better fitting than the simpler models of single and two convolved exponentials for 30 nm, 400 nm, and silica coated 30 nm nanoparticles. We provide evidence that the longest timescales (0.5-4 ms) are due to the luminescence of the final state, that the energy transfer waiting times leading to upconversion are shorter ( τ2 , then exp(−t/τ1 ) > exp(−t/τ2 ) for all t; the tail follows the lifetime of the first process τ1 and the rise follows the lifetime of the second process τ2 . On the other hand, if τ1 < τ2 , then exp(−t/τ1 ) < exp(−t/τ2 ) for all t; the tail follows the lifetime of the second process τ2 and the rise follows the lifetime of the first process τ1 . In summary, the longer process dominates

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the tail of the measurement and the shorter process dominates the rise regardless of the actual sequence of events. This result is independent of the details of the state diagram, and is a general result with two waiting time distributions. The discussion above does not include the instrument response effects, including the laser pulse width and shape. Modeling the instrument response includes convolving Eq. (3) with the measured instrument response. This convolution does not affect the results regarding the rise and tail of the measured response. Even for long pulses frequently used in studying upconversion processes, the same conclusion holds, and must be taken into account when performing experimental studies of upconversion processes.

Degenerate multi-step processes In the degenerate case, each of the n steps has identical waiting times, τ , the resulting distribution is the gamma distribution:

I(t) =

tn−1 exp(−t/τ ) (n − 1)!τ n

(4)

This case will be used in modeling the multiple excitation steps required for upconversion prior to luminescence, where we assume that the lifetimes of the donor sites transferring excitation to the acceptor site are all identical. This assumption for donor state lifetimes is not strictly true since the donor excitations will be transferred to different excited states, but provides a simplifying assumption that reduces the number of fitting parameters. 17,21,22

Three-step non-degenerate process For the fully non-degenerate case with 3 unequal waiting times τ1 , τ2 , and τ3 , we can recursively use Eq. 3 to obtain:

I(t) = I1 (t) ∗ I2 (t) ∗ I3 (t) =

τ22 I2 (t) τ32 I3 (t) τ12 I1 (t) + + (5) (τ1 − τ2 )(τ1 − τ3 ) (τ2 − τ1 )(τ2 − τ3 ) (τ3 − τ1 )(τ3 − τ2 )

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Using Eq. (5), it is possible to determine the identities of the rise time and decay times. The denominator for each term determine the sign in front of the lifetime responses I1 (t), I2 (t), and I3 (t). Assume τ1 > τ2 > τ3 . Then, the factors in front of I1 (t), I2 (t) and I3 (t) are positive, negative, and positive respectively. This means that the rise time follows τ2 , and the decay tail is the sum of two responses with lifetimes τ1 and τ3 . The amplitude of the decay with τ3 is less than the amplitude for τ1 ; if τ1 τ3 , then the amplitude for the decay with τ3 is insignificant, and we revert to the 2-step model. Two-photon upconversion process For upconversion luminescence, the same excited state lifetime of Yb3+ contributes to the energy transfer for 2 or 3 photon excitation of the Er3+ . 22 We assume that the lifetime of the state is same regardless of which state of Er3+ is the acceptor, although this is not likely to be strictly true. It is widely accepted that 2 H11/2 , 4 S3/2 → 4 I15/2 (green emission) transition is due to two-photon process, as shown in Fig. (2). In the Energy Diagram, this process starts with two photon ground state adsorption by Yb3+ (2 F7/2 → 2 F5/2 ) followed by twostep energy transfer upconversion to Er3+ (4 I15/2 → 4 F7/2 ), then Er3+ (4 F7/2 ) would rapidly relax to populate 2 H11/2 , 4 S3/2 , and finally emitting green light (2 H11/2 , 4 S3/2 → 4 I15/2 ). 22 For this case, two waiting times with τ2 = τY b3+ model the upconversion process, and one process with τ1 = τEr3+ models the luminescence. This is represented by:

I(t) =

tI2 (t) τ1 τ2 I2 (t) τ12 I1 (t) + − 2 (τ1 − τ2 ) (τ2 − τ1 ) (τ2 − τ1 )2

(6)

Similar to the more general case, if τ2 >> τ1 , we revert to the corresponding 2-step model. Three-photon upconversion process In this case, three successive photons cause a Er3+ ion to go into a higher excited state that quickly relaxes to the red luminescent state. 21,22 There are three identical waiting times for

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upconversion and one different waiting time for luminescence (the conversion from upper excited states to lower red-emitting states is assumed to proceed much faster than the other processes). 22 Previous work reported that 4 F9/2 → 4 I15/2 (red emission) transition is due to three-photon process, as shown in Fig. (2). In the energy diagram, this process starts with ground state absorption of Yb3+ (2 F7/2 → 2 F5/2 ) for three times followed by three-step energy transfer upconversion to Er3+ (4 I15/2 → 4 G, 2 K), then Er3+ (4 G, 2 K) would undergo back energy transfer to populate 4 F9/2 , and finally emitting red light (4 F9/2 → 4 I15/2 ). 22 In this case, τ1 equals to τEr3+ , would represent the luminescence process, and when τ2 is the luminescence process, and τ2 equals to τY b3+ , represents the upconversion process. This is represented below:

I(t) =

tτ1 I2 (t) τ12 τ2 I2 (t) τ13 I1 (t) t2 I2 (t) − + + 2τ2 (τ2 − τ1 ) (τ2 − τ1 )2 (τ2 − τ1 )3 (τ1 − τ2 )3

(7)

Measurements and Fitting For each sample, three measurements were taken with increasing laser power. The laser intensities used are similar to those reported in the supplemental information of Zhang et al. 23 For our 980 nm excitation, we used 10 µs pulses operating at 500 Hz. Beam area is estimated to be 1.8 × 10−8 cm2 . For total averaged excitation powers of 6, 78, and 256 µW, the corresponding pulse fluences and pulse intensities are 0.7, 9, and 28 J/cm2 , and 0.07, 0.9, and 2.8 MW/cm2 . The lifetime curve is measured independently three times for 1 s every 2 nm between 400 and 900 nm. These data provide sufficient spectral resolution, reproducibility and signal to successfully fit and determine the lifetime curves. Directly modulating the laser allows for tunable pulse widths with high extinction, providing a large dynamic range in the intensity of over 3 orders of magnitude, allowing for more robust discrimination between models. We compare fits of the time-resolved response of the three different REN samples (REN 30, REN 400, and REN/silica) using five fitting models. The first model is a single expo13



nential decay as is typically used to model a simple fluorescence decay of a singlet state. The second model is the two-step waiting time model, consisting of the convolution of two exponentials: one to excite and one to decay; we call this the “two-step” model. The third and fourth models are the multiple photon energy transfer models that we discussed in Equations (6) and (7); since we restrict all but one of the waiting times to be the same, these models have the same number of fitting parameters as the two-step model. The fifth model is the three-step non-degenerate process of Equation 5, and requires one additional fitting parameter. The fitting procedures use the maximum likelihood methodology discussed in Ref. 34 . We perform the fits using the maximum likelihood estimator for Poisson random variables, which PN P 34 xi is has a figure of merit of the form χ2MLE = 2 N i=1,xi 6=0 xi ln(fi /xi ). i=1 (fi − xi ) − 2 a histogram data set of length N , and fi is the model. This reduces to the standard least squares χ2 in the limit of large xi . We use the fitting optimization routine from Ref. 35 , specifying a Poisson random variable. For the “two convolved exponential”, “two-photon upconversion”, and “three-photon upconversion” models, there are the same number of fitting parameters, making fitting comparisons between these models more rigorous: any decreases in the goodness of fit χ2MLE suggests a better model, not just an improved fit due to a higher degree of freedom in the fit. In each case, there are two lifetimes τ1 and τ2 , an amplitude for the decay, and a constant background term. τ2 has a different meaning for each model: for “two-step waiting time model”, τ2 is a single exponential waiting time convolved with the exponential τ1 ; for “twophoton upconversion”, τ2 is the lifetime of two separate exponential waiting times, which are then convolved with a waiting time with lifetime τ1 ; and “three-photon upconversion” is similar to the two-photon upconversion except that there are three separate exponential waiting times. The convolution-based models discussed in the Theory section are calculated for the fitting model by performing fast Fourier transform (FFT)-based numeric convolutions of

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exponentials. As an example, for the three photon upconversion model, single exponential decays with time constants τ1 and τ2 are calculated using Eq. (1.1) from Ref. 31 . The decay with time constant τ2 is convolved with itself twice, convolved again with the decay with time constant τ1 , and then with the instrument response. A constant term is then added. The other models are calculated in a similar fashion. We restricted values of the parameters to use all available information. Although a varying constant term was added, the variation was restricted to be within 3 standard deviations from a separately measured background value. Deviations from the fit at the tails of the fit indicate inadequacies in the modeling rather than experimental background. Additionally, the fitted lifetime components were restricted to being positive. There was a fitted amplitude for each model that did not vary significantly, and is not listed in the data tables.

Comparing Results from fitting 5 kinetics models Comparing fitting models Figures 3, 4, and 5 show the fits using the models described above from one measurement of the REN 400 sample for the green, red, and blue photoluminescence peaks shown in Fig. 2. In the figures, we show the results with the highest excitation energies, which have the highest signal levels and are thus more demanding on accurate fitting models. Tables 1, 2 and 3 show the values from these fits as well as for lower pulse energy of 9 J/cm2 and the REN 30 and REN/silica samples. In the tables, the total amplitude and constant background fitting parameters are not shown. The amplitude is the number of photons measured minus the background, and the constant background value is restricted to a narrow range based on separate background measurements. The single exponential fit (labeled 1 Exp) was very poor, with a χ2MLE of 300, whereas the other models yielded much better fits. By convolving two or more exponentials, the fits as measured by difference between data and fit and χ2MLE

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Photon Counts

REN 400, 28 J/cm

Difference

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4

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2 Data: 510 to 564 nm 1 Exp 2 Step 2 Photon 3 Photon 3 Step

1000 0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Time Delay (ms)

Figure 3: Fits of time-resolved response for response between 510 and 564 nm for the REN 400 sample with 28 J/cm2 excitation. Five fits are shown: single exponential (1 Exp), the two-step waiting time model (2 Step), the two-photon upconversion model (2 Photon), the three-photon upconversion model (3 Photon), and the three step waiting time model (3 Step). Difference plots (subtracting fit minus data) are shown for all models except the single exponential model, which yielded a poor fit. improve considerably. In the plot showing the difference of the data and fit, we exclude the single exponential fit since it would obscure the differences between the remaining plots. As seen in Table 1, the longest lifetime τ1 is consistent between the fits. Changing the pulse energy does change the fitted lifetime by 15%, but the change is not large, with a change similar to that observed in the supplemental information from Chan et al. 36 The differences between the remaining models are seen at the rise time and peak of the response. For the green luminescence, the rise times of the time-resolved response are nearly always better fit with models involving more than two waiting times, as seen In Figure 3 and the Table 1. These models include the two- and three-photon models and the three-step non-degenerate models. With one exception, the χ2MLE values for the two-step model are higher than the values for the other models. On the other hand, there was no significant difference found between the χ2MLE values obtained for the other three models, even with the additional fitting parameter used in the three-step model. This suggests that we can16


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Photon Counts

REN 400, 28 J/cm

Difference

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10

3

500 0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Time Delay (ms)

Figure 4: Fits of time-resolved response for response between 640 and 690 nm for the REN 400 sample with 28 J/cm2 excitation, similar to Figure 3. not uniquely identify which of these three models is best from an individual time-resolved response. However, we do find evidence that more than two steps are required to obtain the upconversion luminescence by fitting an individual time-resolved response. This evidence for multiple steps does not rely on the intensity dependence of the luminescence or the relationship with other luminescence peaks. This provides additional support that there is a multi-step process involved in upconversion photoluminescence, as discussed and modeled elsewhere. 17,22 For each of the fits, deviations from each model are observed at the rise time and near the peak of the response. These deviations may be due to heterogeneity within or between nanoparticles or from inadequacies in the models due to the assumption of constant rates. Additional comparisons with more complete kinetic models 21 likely can distinguish between these two possible causes for deviations. For the fitted values of τ2 and τ3 , the total waiting time before reaching the final luminescent states adds to a consistent waiting time regardless of the model. For example, for the REN 400, 28 J/cm2 case, the two-step model has a waiting time of τ2 = 0.042 ms. For the two photon model, there are two waiting times modeled with τ2 = 0.021 ms each, for a

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Photon Counts

REN 400, 28 J/cm 10

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10

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Difference

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25 0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Time Delay (ms)

Figure 5: Fits of time-resolved response for response between 400 and 414 nm for the REN 400 sample with 28 J/cm2 excitation, similar to Figure 3. total of 0.042 ms. For the three photon model, there are three waiting times modeled with τ2 = 0.016 ms each, for a total of 0.048 ms. For the three-step model, adding τ2 = 0.019 ms and τ3 = 0.024 ms gives a total waiting time of 0.043 ms. This consistency suggests that any differences found in the χ2MLE of the fits provide a robust measurement of the consistency between the simplified models and the physical mechanisms. In particular, the quality of the fits suggest that more than two steps are required to obtain the upconversion luminescence. In the difference plot from Figure 3, the difference for the two-step model is highest right at the beginning of the time-resolved response. This is consistent with the model failing to capture multiple steps before obtaining luminescence, since the two-step model assumes a single exponential rise time. The single exponential rise time would have a faster initial rise than the other models, producing an initial rise of the model above the other models. This pattern is seen throughout the difference plots of the remaining figures. Similar to the discussions pertaining to Eq. 3, the tail of the time-resolved response is the longest of all timescales involved, regardless of the order of these processes. This is also true for the 3-step equations such as Eq. 5. Previous approaches often implicitly assume that the

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Photon Counts

REN 30, 28 J/cm

Difference

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10

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5000


0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Time Delay (ms)

Figure 6: Fits of time-resolved response for response between 510 and 564 nm for the REN 30 sample with 28 J/cm2 excitation, similar to Figure 3. tail of the time-resolved response is due to the final luminescence response. However, this work suggest that further evidence is necessary to validate. Based on previous models, 17,22 we expect the time-resolved response to have 2 or 3 exponential waiting times for energy transfers from the excited state of Yb3+ to the excited state of Er3+ , which then emits after another exponential waiting time. We modeled the transfer of excitation from Yb3+ as two or three exponentials with identical waiting times τ2 . In Tables 1- 3, we find that the fits with the two and three photon upconversion models were significantly better than the two convolved exponential model in most cases, although the differences between the two and three photon upconversion models does not appear significant enough to draw conclusions about which model is better. In all cases, attempting to fit the data with τ2 > τ1 either led fits with τ2 < τ1 or converged to a local rather than global minimum of χ2MLE . This suggests that the longest waiting time must be τ1 , which is a single exponential process, which we suggest is the luminescence process. These fits provide additional evidence that the luminescence step is typically the longest decay, and dominates the tail of the response as was previously generally assumed.

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Photon Counts

REN/silica, 28 J/cm 10

4

10

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2

Difference

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10 2500 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0 2500 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Time Delay (ms)

Figure 7: Fits of time-resolved response for response between 510 and 564 nm for the REN/silica sample with 28 J/cm2 excitation, similar to Figure 3. For the red luminescence peak from Figure 2, we find a similar pattern as for the green luminescence peak, except that the difference between the quality of fits (χ2MLE ) for the twostep model are even larger (see Figure 4 and Table 2). As before, the difference plot for the two-step model shows the largest deviation right at the beginning of the time-resolved response (Figure 4). The blue luminescence peak from Figure 2 does not in general show a significant difference between the models, except for the higher energy excitation (28 J/cm2 ) for the REN 30 and REN/silica samples. Again, these show poorer fits for the two-step model than for the others. For smaller upconverting nanoparticles, the lifetimes observed are shorter, as observed previously. 17 For the REN 30 sample, the fits follow the same pattern as for the REN 400 sample (Figure 6 and Tables 1-3), but with shorter timescales for τ1 , τ2 and τ3 . Although the values for the timescales are shorter for smaller nanoparticles as measured previously, 17 the values measured for the decay times are faster here than what were measured previously. For REN 30, the surface area to volume ratio is 0.1 nm−1 , corresponding to rates near 2000 s−1 from Figure 4 of Ref. 17 , or a lifetime of about 0.5 ms. The lifetimes measured

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Table 1: Fitted values for 530 nm emission. χ2MLE is goodness of fit. τ1 , τ2 , and τ3 are single exponential lifetimes of successive processes required for luminescence in each model. For the “2 Step” and “3 Step” models, there is one step for each fitted lifetime. For the “2 Photon” model, there is one step with lifetime τ1 and two steps with identical lifetimes τ2 . For the “3 Photon” model. there are three steps with identical lifetimes τ2 . Values shown are averages over repeated measurements, with variability of approximately 5%. Sample, Kinetic Excitation Fluence Model REN 400 2 Step 2 28 J/cm 2 Photon 3 Photon 3 Step REN 400 2 Step 9 J/cm2 2 Photon 3 Photon 3 Step REN 30 2 Step 2 28 J/cm 2 Photon 3 Photon 3 Step REN 30 2 Step 9 J/cm2 2 Photon 3 Photon 3 Step REN/silica 2 Step 28 J/cm2 2 Photon 3 Photon 3 Step REN/silica 2 Step 9 J/cm2 2 Photon 3 Photon 3 Step

χ2MLE 18 12 13 12 1.6 1.6 2.4 1.3 61 38 33 38 9.2 4.9 4.3 5.8 42 36 33 36 5.7 3.8 3.4 3.8

τ1 (ms) τ2 (ms) 0.45 0.46 0.46 0.46 0.53 0.54 0.55 0.53 0.125 0.127 0.127 0.127 0.118 0.123 0.125 0.128 0.117 0.114 0.115 0.114 0.105 0.107 0.109 0.108

0.042 0.021 0.016 0.019 0.069 0.036 0.024 0.060 0.030 0.015 0.011 0.015 0.038 0.019 0.013 0.017 0.019 0.012 0.009 0.011 0.029 0.015 0.011 0.015

τ3 (ms) NA NA NA 0.024 NA NA NA 0.010 NA NA NA 0.015 NA NA NA 0.020 NA NA NA 0.014 NA NA NA 0.015

here of 0.11 to 0.13 ms are shorter, although a higher excitation intensity may play a role in the change. There is an interesting deviation from the models at longer timescales for the green luminescence for the REN30 sample (Figure 6). This is not due to inadequate background subtraction, and may indicate either inhomogeneity in the samples or depletion of other states that quench the green luminescence. Although not as dramatic, the long-time

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χ2MLE 6.1 2.2 5.7 1.4 1.6 1.2 1.6 1.1 38 7.8 5.0 7.8 3.8 1.3 1.1 1.3 17 6.0 4.2 6.0 2.4 1.2 1.1 1.2

τ1 (ms) τ2 (ms) 0.56 0.61 0.63 0.59 0.57 0.72 0.77 0.68 0.284 0.30 0.302 0.30 0.309 0.327 0.335 0.327 0.267 0.273 0.276 0.273 0.289 0.303 0.309 0.302

0.15 0.066 0.042 0.109 0.28 0.10 0.064 0.11 0.073 0.034 0.022 0.034 0.094 0.042 0.029 0.042 0.051 0.025 0.017 0.025 0.072 0.034 0.023 0.034


deviation is present for the REN 400 sample (Figure 3). The deviation is not significant for the blue or red luminescence. For the REN/silica sample, the fits are very similar to those for the REN30 sample, except even shorter lifetimes are found, and the deviation from the fits at longer times is larger (Figure 7 and Tables 1-3). The decrease in lifetime found for adding the silica

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χ2MLE 1.2 1.1 1.3 1.2 1.2 1.2 1.2 1.2 2.3 1.6 1.5 1.6 1.2 1.1 1.1 1.1 2.9 2.2 2.0 2.2 1.1 1.1 1.1 1.1

τ1 (ms) τ2 (ms) 0.289 0.296 0.341 0.333 0.543 0.589 0.554 0.550 0.083 0.089 0.092 0.089 0.076 0.085 0.097 0.093 0.084 0.085 0.085 0.085 0.080 0.074 0.078 0.075

0.050 0.025 0.015 0.024 0.027 0.13 0.011 0.018 0.042 0.021 0.015 0.021 0.053 0.025 0.016 0.023 0.028 0.015 0.011 0.015 0.040 0.021 0.015 0.021


layer is smaller than was found previously 17 when comparing the REN30 and REN/silica samples. The additional quenching for the REN/silica sample over the uncoated sample was attributed to defect-dependent rates, where there are more defects in the silica coated samples and smaller nanoparticles. 17 Since the long-timescale deviation is larger for the REN/silica sample than for the REN30 sample, and deviations for both are larger than for

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the REN400 sample, we suggest that the deviation is more likely due to heterogeneity within the samples due to defects rather than inadequate kinetics modeling.

Discussion The decay times τ1 which we identify as luminescence lifetimes of the final, luminescent state, are significantly longer than the values found for τ2 . Additionally, the values for τ1 have more variation between samples (more than an order of magnitude) compared to the variation found in τ2 . This is consistent with the suggestion that τ1 can be identified with the luminescent state, where lifetime variations would be dominated by the quenching present due to the surface-to-volume ratios that vary with REN size. 17 The smaller variations in the values for τ2 are consistent with the timescales being set by the proximity of Yb3+ to act as donors to Er3+ . The accepted mechanism for green emission from the 530 nm line is attributed to twophoton transfers from Yb3+ to Er3+ , whereas a likely mechanism for the 650 nm red emission involves three-photon transfers from Yb3+ to Er3+ . 22 This would suggest that the two-photon upconversion model and the three-step waiting times models would be appropriate for Table 1, and the three-photon upconversion model would be appropriate for Table 2. The same state of Yb3+ provides the transfers for each of the upconversion steps, therefore we expect for a given sample that the lifetimes τ2 to be the most similar for the two-photon upconversion model for 530 nm (Table 1) and the three-photon upconversion model for 650 nm (Table 2). Although we do not find significant differences between these models, we do find that a twostep waiting time model does not fit the data as well. We find that the total waiting times found to reach the final luminescent state are consistent between models, and we suggest that these values correspond to the waiting times for transfers from the excited states of Yb3+ to Er3+ . It will be instructive to study how results from these fits can be used in combination with more sophisticated models that contain a much larger number of parameters, such as

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those described in Refs. 17,21 . We have found deviations from our models for the longer-time response of green luminescence. These deviations from the models is stronger for the smaller REN30 and REN/silica samples than for the REN 400 sample. We suggest that this may be due to the heterogeneity found near the surface of the nanoparticles causing additional defects, and affecting the rates of processes for the excited states of Yb3+ to Er3+ . Additionally, this may be due to the depletion of other states that affect the quenching rates of the final luminescent state. Further comparisons to more complete kinetic models can distinguish between these possibilities.

Conclusion For time-resolved photoluminescence measurements of RENs, it is important to fit the entire time-dependent curve. This permits accounting for uncertainties arising from the convolution of multiple exponential processes in series, and obtaining information about the underlying processes from more sophisticated lifetime models. In upconversion luminescence, we show that identifying the timescales associated with each step in the process is not trivial, since the observed rise times and fall times in the time-resolved response depend on which lifetimes are longer or shorter, not on the sequence of events. By fitting the entire time-resolved response, we can extract the timescales which then must be associated with the events in the luminescence process using other evidence. Using this approach, we found evidence that the luminescent state of the Er3+ ions are the longest lived states and thus determine the decay timescale of the lifetime tails. We also found that multiple step activation models provides better fits than other models, consistent with previous models of the upconversion luminescence process. We observed deviations from the model for the green luminescence at longer timescales which cannot be explained due to background. This can either be due to inhomogeneity in the sample or within the nanoparticle, or from depletion of other states that quench the green luminescence.

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The methodology of fitting the entire time-resolved response will be valuable for understanding and manipulating the mechanisms of upconversion in REN samples. In addition to using these models to understand bulk photodynamics, the models are appropriate for use in detection with fewer photons. For example, these models would be beneficial for measurements of the time-resolved response of single upconverting nanoparticles, 37 possibly under conditions where F¨orster Resonance Energy Transfer occurs. 38

Acknowledgement This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. This work is support in part by Gordon and Betty Moore Foundation (GYL), National Institute of Health (R21 ES025350) Y.L. was supported in part by a UCD-LLNL Joint Graduate Mentorship Award.

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Graphical TOC Entry TOC Graphic

Photons

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

3

0.0

0.5

1.0

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Time Delay (ms)

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Measuring Activation and Luminescence Time Scales of Upconverting

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