We examined non-stoichiometric CaAlxSi(7-3x)/4N3:Eu2+ phosphors that were intentionally prepared with x = 0.7 ~1.3 to identify the origin of the deconvoluted Gaussian components that constitute the emission spectra of stoichiometric CaAlSiN3:Eu2+ phosphors. The Al/Si molar ratio around the Eu2+ activator caused the deconvoluted Gaussian peaks. The Eu2+ activator sites in Al-rich environments gave rise to the lower-energy emission peak, while those in Si-rich environments were related to the higher-energy emission peaks. Active energy transfer from the Eu2+ activator site in the Si-rich environment to the Eu2+ activator site in the Al-rich environment was confirmed. Particle swarm optimization was employed to estimate the nine unknown decision parameters that control the energy transfer process. All of the decision parameters were estimated within the range of reasonable values.
© 2010 OSA
Recently, considerable effort has been devoted to the development of nitride-based phosphors for use in light-emitting diodes (LED) [1-12]. CaAlSiN3:Eu2+, which will hereafter be denoted as CASIN, is one of the most successfully commercialized nitride phosphors for use in LED applications. Broad band-type emission in the red-light wavelength range enhances the color rendering index of white LEDs. Consequently, many investigations have aimed to develop a promising synthesis method for CASIN phosphors along with detailed structural analysis[4~12]; however, in-depth luminescence studies of CASIN phosphors are lacking. We have recently observed an interesting photoluminescence behavior: two-peak emission behavior and variation in decay behavior with respect to the emission wavelength . However, the origin of this two-peak emission behavior remains to be clarified. Likewise, the origin of each deconvoluted emission peak remains ambiguous. Because the host structure of CASIN provides Eu2+ activators that have only a Wyckoff site, it is difficult to envisage local structures that could be assigned to the deconvoluted emission peaks. In addition, decay curve variation with respect to the emission wavelength is of particular concern in relation to energy transfer between Eu2+ activators. However, detailed investigations regarding energy-transfer behavior and the ensuing quantitative analyses remain to be performed.
The inexplicable result that was reported previously  originated from failure to identify the local structures around the Eu2+ activator that caused the variation in decay behavior with respect to the emission wavelength. Thus, one of the most important purposes of the present investigation was to assign deconvoluted emission components to their corresponding local structures. The CASIN structure (Cmc21) exhibited random distribution of Al or Si ions around the Eu2+ activator at the Ca site (m). In addition, the CASIN structure might have inhomogeneous distribution of both oxygen impurities and cation vacancies around the Eu2+ activators. This unidentified diversity in the CASIN structure inevitably gives rise to a certain degree of inhomogeneous broadening. From a practical point of view, it is essential to examine every possible local structure around the Eu2+ activator and its consequence on PL behavior, because correct identification of local structures would make it possible to predict the exact shape and width of the emission (excitation or absorption) spectra of CASIN phosphors.
Although precise identification of all possible local structures was not achieved in the present study, the variation in both the shape and the width of the emission spectra could be explained in terms of local structures by examining artificially manipulated model phosphors. Non-stoichiometric CaAlxSi(7-3x)/4N3:Eu2+ phosphors with x = 0.7 ~1.3 were adopted as our model system, and their spectral distribution, structural refinement, and time-resolved emission spectra were extensively investigated. This model system was specially designed to monitor the effect of the Al/Si molar ratio around the Eu2+ activator site on the steady-state and time-resolved PL behaviors. Although slight deviations from the stoichiometric CASIN structure might induce unexpected defects or defect impurities, such as oxygen or cation vacancy, we succeeded in monitoring the PL behavior of non-stoichiometric CaAlxSi(7-3x)/4N3:Eu2+ phosphors as a function of the Al/Si molar ratio alone.
A non-linear rate equation model was developed to provide a reliable interpretation of the measured decay curve data, while taking the two-peak emission behavior into account. The quantitative decay analysis based on the rate equation model required a robust multi-dimensional optimization strategy, because the rate equation model involved estimation of nine unknown decision parameters. All of the decision parameters were key parameters, which both constituted the rate equations and played a significant role in understanding the energy-transfer behavior of the CASIN phosphors. However, it should be noted that conventional, mathematics-based local optimization strategies were not appropriate for the present quantitative decay analysis because the multi-dimensional search space consisted of many local optima. Consequently, we employed particle swarm optimization [14-16], a recently developed heuristic approach, to solve the rate equations. This strategy provided a reliable evaluation of all decision parameters, with estimates in a reasonable range of values.
2. Experimental procedures
CaAlxSi(7-3x)/4N3:Eu2+ phosphor samples with x = 0.7 ~1.3, which were adopted as our model system in the present investigation, were prepared by a typical solid-state reaction method. Raw materials such as Ca3N2, AlN, α-Si3N4, and EuN were dry mixed in a glove box with oxygen and a moisture content maintained below 1 ppm. The Eu2+ concentration was fixed at 0.02 in each sample. The mixed raw materials were fired at 1800 °C under a pressurized N2 gas environment (10 atm). The fired samples were ground and subjected to X-ray diffraction (XRD), energy dispersive spectroscopy (EDS), continuous wave photoluminescence (CWPL), and time-resolved photoluminescence (TRPL). CWPL was measured using an in-house spectroscope equipped with a xenon lamp with an excitation wavelength of 390 nm. The time-resolved emission spectra of the CaAlxSi(7-3x)/4N3:Eu2+ phosphors were also measured using an in-house photoluminescence system that included a picosecond Nd:yttrium aluminum garnet (YAG) laser with a pulse repetition frequency of 10 Hz and a charge-coupled device sensor with a time resolution of 10 ns. An excitation wavelength of 355 nm was produced by tripling the 1066 nm frequency of the Nd:YAG laser.
3. Results and discussion
3.1 Spectral and structural analyses
Figure 1(a) shows the steady-state emission spectra measured at CW excitations for CaAlxSi(7-3x)/4N3:Eu2+ Phosphors with x = 0.7 ~1.3. The photographs taken at an excitation wavelength of 365 nm are shown in the inset of Fig. 1(a). It is apparent that the emission spectra for lower x values can be deconvoluted into two distinct Gaussian peaks. It was verified that the best least-square fit was obtained by using two Gaussian peaks rather than three or more Gaussian peaks. Figure 1(b) shows the deconvoluted emission spectrum for CaAl0.7Si1.225N3 (x = 0.7). The variation in x (i.e., the Al/Si molar ratio) gave rise to conspicuous differences in spectral shape. As x increased, the higher energy contribution diminished and, ultimately, disappeared from the emission spectra. Both Gaussian components were proven to originate from the CaAlxSi(7-3x)/4N3:Eu2+ phosphors. It was obvious that they were not related to the formation of a second phase, because no phase detected in our XRD measurements emitted in the wavelength range of interest.
As shown in Figs. 2(a) and 2(b), we refined the XRD patterns for two representative samples, CaAl0.7Si1.225N3 (x = 0.7) and CaAl1.2Si0.85N3 (x = 1.2); hereafter, the former will be denoted as N-CASIN-0.7 and the latter as N-CASIN-1.2. A major constituent phase retained the CASIN structure despite detection of impurities. Both samples contained an AlN phase as an impurity, and only N-CASIN-1.2 included both an AIN and a Ca3AlN3 phase.
The refined atomic position and the occupancy data are presented in Table 1 along with Ca-N bond length data. In particular, the Al/Si occupancy ratio and the average Ca-N bond length in Table 1 are of interest. The occupancy of the other constituent atoms was fixed during refinement, so that we could monitor only the Al/Si occupancy ratio in the CASIN structure. The refined Al/Si occupancy ratio was similar to the starting composition as well as the energy dispersive spectroscopy (EDS) composition analysis, which is given in Table 2 . The average Ca-N bond length for N-CASIN-0.7 was slightly greater than that for N-CASIN-1.2, which also coincided with the emission spectrum measurement. These results indicate that a higher energy component was observed only for N-CASIN-0.7. It is well known that the smaller the polyhedron around the activator, the higher the emission energy[17-21], which will be discussed in greater detail later in this subsection. It seems to be impractical to distinguish aluminum and silicon in the Rietveld refinement of powder x-ray diffraction patterns due to similar electron density.
The Rietveld refinement process involving different Al/Si ratio was implemented just to see the effect on Ca-N polyhedron size and eventually to check if the resultant Ca-N polyhedron size coincides with the PL data. In this regard, a reasonable result was obtained with an acceptable fitting quality (Rwp = 12.1, Rp = 11.0). The EDS data in Table 2 also provided useful information about the oxygen content. However, the EDS results cannot be used for correct quantitative analyses but for rough measures because of the presence of impurity phases. If the greater oxygen content was induced by a greater Al/Si ratio to meet the electrical neutrality requirement, the high-energy emission component would have been activated for the higher Al/Si ratios, causing a blue-shift in emission. However, the observed result was the opposite of this hypothetical result. That is, the higher Al/Si ratio deactivated the high-energy component and a red-shift was observed. Namely, in contrast to our prior expectation, which was based on electrical neutrality, the EDS measurement showed that the oxygen contents of N-CASIN-0.7 and N-CASIN-1.2 were similar, and the emission spectra showed a clear red shift as the Al/Si ratio increased. Consequently, factors other than oxygen contamination might explain the experimental data.
Figure 3 shows the time resolved photoluminescence (TRPL) spectra for CaAlxSi(7-3x)/4N3:Eu2+ phosphors with x = 0.7 ~1.3. Each TRPL spectrum contained two distinctive Gaussian peaks, as was also the case in the CWPL spectra. Figures 4(a) and 4(b) show the deconvoluted TRPL spectra for N-CASIN-0.7 and N-CASIN-1.2 at two different delay times — 40 nsec and 0.52 μsec — after the cessation of the excited light pulse. Similar to the CWPL spectra, the higher energy component vanished as x increased. In particular, for N-CASIN-1.2, the higher energy component almost disappeared at the delay time of 0.52 μsec. The most interesting TRPL result was the variation in decay rate with respect to the detection wavelength for both N-CASIN-0.7 and N-CASIN-1.2. Shorter detection wavelengths resulted in faster decay rates. The decay curves for N-CASIN-0.7 were detected at 525 and 700 nm (2.36 and 1.77 eV) and at 525 and 725 nm (2.36 and 1.71 eV) for N-CASIN-1.2, as shown in Fig. 4(a) and 4(b). The wavelength-dependent decay behavior was closely related to the energy transfer between activators in different environments. This result will be discussed in more detail along with rate equation calculation in the following subsection. An analogous result has also been observed in other similar phosphor systems such as Sr2Si5N8:Eu2+ and (Sr,Ba)2SiO4:Eu2+[22-24]. However, there is a clear difference between CASIN and the other phosphors. The CASIN structure provides only a Wyckoff site for the accommodation of Eu2+ activators, while the aforementioned phosphors have two distinct Wyckoff sites for the activator accommodation, each of which has been assigned to the deconvoluted Gaussian peaks in the observed CWPL and TRPL spectra. It is thus necessary to identify the origin of the deconvoluted Gaussian peaks observed in both the CWPL and TRPL spectra of non-stoichiometric CASIN phosphors. Because the CASIN structure has only a Wyckoff site for Eu2+ activators, we aimed to clarify how various local structures around the Ca2+ (Eu2+) site should be divided into two representative categories, which are well matched to the deconvoluted Gaussian peaks. According to the structural refinement and compositional analysis of N-CASIN-0.7 and N-CASIN-1.2, we determined that the Al/Si molar ratio around the Eu2+ activator played a significant role in assigning the deconvoluted Gaussian peaks. More importantly, the non-stoichiometric CASIN phosphors adopted as our model system made it much easier to find the origin of the deconvoluted Gaussian peaks in the observed CWPL and TRPL spectra. We confirmed that the high-energy emission diminished as the Al/Si molar ratio increased, which indicates that the Al-rich local environments around the Eu2+ activator resulted in lower energy emission, while a Si-rich local environment led to higher energy emission.
The above-described assignment of the deconvoluted Gaussian peaks can be explained by Dorenbos’ analysis[17-21], wherein the centroid shift and crystal field splitting was monitored with respect to neighboring ions for the Ce3+ doped system. Although the exact Stokes shift was not estimated, the Dorenbos’ analysis on centroid shift and crystal field splitting could explain approximately the observed emission spectra. Dorenbos reported that Al3+ gave rise to a larger centroid shift than Si4+ for a Ce3+-doped oxide system . The same result should be observed for the present non-stoichiometric CASIN system, because Dorenbos’ analysis of Ce3+-doped systems can be applied to Eu2+-doped systems . In addition to Dorenbros’ analysis of centroid shift, that of crystal field splitting was also in good agreement with our experimental data. The crystal field splitting of the 5d level was controlled by the distance to the nearest anion ligands. Based on Rietvelt refinement, the average Ca-N bond length for N-CASIN-1.2 was slightly shorter than that for N-CASIN-0.7, as can be seen in Table 1. Although a clear separation between the local environments, which leads to the higher and lower energy emissions, was practically impossible, the average Ca-N bond length might be a good indicator of the plausible assignment of deconvoluted emission spectra to their corresponding local environments. For example, an Al-rich local environment induced a smaller polyhedron around the Eu2+ activator, which was assigned to the lower energy emission, while a Si-rich local environment led to a larger polyhedron and a higher energy emission. Both the centroid shift and crystal field splitting analyses were in good agreement with our experimental data and provided a plausible explanation of the two-peak emission behavior.
3.2 Rate equations for decay analysis
In the previous subsection, we assigned the deconvoluted Gaussian components that constitute the emission spectra of CASIN phosphors to their corresponding local environments. The higher energy component that originated from Si-rich environments with shorter average Ca-N bond length was referred to as P1, and the site from which P1 originated was referred to as Ca1. On the other hand, Al-rich environments and the slightly longer average Ca-N bond length were referred to as Ca2, and the lower energy emission component from the Ca2 sites was denoted P2. The most interesting result was the energy transfer from Ca1 to Ca2, which was detected in the decay curves monitored at various emission wavelengths. Thus, we observed that the longer the emission wavelength, the slower the decay. This result indicates active energy transfer from the Eu2+ activators at Ca1 sites to those at Ca2 sites, and can be explained by the general principle that the donor (Eu2+ activators at Ca1 sites) decays faster than the acceptor (Eu2+ activators at Ca2 sites).
Figures 5(a) and 5(b) show typical donor and acceptor decay curves measured at different emission wavelengths for N-CASIN-0.7 and N-CASIN-1.2, respectively. In an attempt to provide a quantitative interpretation of the decay behavior based on energy transfer, rate equations were set up, wherein the Eu2+ activators were categorized into two types. The first category was for regular Eu2+ ions located at the characteristic site of the host lattice with no adjacent quenching (or killer) sites. The criterion that we used to identify regular Eu2+ ions was based on whether the primary energy transfer occurs with other Eu2+ ions or killer sites. If the energy transfer rate from Eu2+ ions to other Eu2+ ions is much faster than the rate of energy transfer to killer sites, then we can regard them as regular Eu2+ ions. The number density of Eu2+ ions in this category was designated as . The superscript of ρ indicates whether Eu2+ ions are in a ground (4f7) or an excited state (4f65d1), and the subscript indicates whether Eu2+ ions are located at either the Ca1 or the Ca2 site. The regular Eu2+ ions are not susceptible to direct quenching by killer sites, but are apt to interact with their neighboring Eu2+ ions. Consequently, inter-activator energy transfer takes place.
When a killer site is located near an excited Eu2+ ion, inter-activator energy transfer does not occur, but, rather, direct quenching is dominant. This category of Eu2+ ions, which are located near killer sites, are defined as defective Eu2+ ions. The killer sites were not identified, but were presumed to be defects or impurities in the host lattice. Eu2+ ions at perturbed, non-emitting Eu2+ sites, the symmetry of which deviated from that of the characteristic Ca1 or Ca2 sites of the host lattice due to defects, were also killer sites . The number density of defective Eu2+ ions was designated as . It should be noted that categorization of the activator into regular and defective ions was required to explain the early stage of the acceptor decay curve. Without this classification, a conspicuous rising would occur during the initial stage of the calculated acceptor decay curve, which would be inconsistent with the actual measured decay curve. In fact, no dramatic rising was observed in the actual measured decay curve, as shown in Figs. 5(a) and 5(b). This issue will be discussed in more detail later in this section.
The rate equations consisting of and were derived as follows:26], and the oscillator strength of the 4f-5d transition for Eu2+ in some oxide hosts [27,28]. Although we failed to determine the exact G value for N-CASIN-0.7 and N-CASIN-1.2, our estimate is reasonable because the variation in G does not affect the shape of the decay curve, but, rather, has a dramatic influence on the overall number density. Considering our use of normalized decay curves for the least-square fitting process, a rough estimation of G would not affect the determination of other more important parameters. KrCa1(1/τCa1) and KrCa2(1/τCa2) are the radiative decay rates for P1 and P2, which are presumed to vary with respect to the activator site environment. Kn is the non-radiative decay rate of defective Eu2+ ions, which represents direct quenching by killer sites. is the energy transfer constant of interactions between Eu2+ ions, wherein the subscripts x and y stand for the Ca1 and Ca2 sites in the host lattice, respectively. The energy transfer constant () should never be misunderstood to be identical to the energy transfer rate. In fact, the non-radiative energy transfer rate is and .
Our rate equations involved four non-linear terms that describe the energy transfer between the Eu2+ activators of various types: regular Ca1 to regular Ca2, regular Ca1 to defective Ca1 (and Ca2), and regular Ca2 to defective Ca2. Energy transfer from defective to regular or to defective sites was not considered here because the defective activators are apt to be directly quenched by the killer site. Backward energy transfer from Ca2 to Ca1 was ignored because of the negligible spectral overlap, and migration between the same type of activators was also ignored. We categorized the donors into four different types and possible energy transfer routes between them are included in our rate equations. This means that a certain degree of migration effect was already taken into account partly in the present rate equation model, even though we failed to accommodate a complete consideration of migration. We only adopted three independent energy transfer constants that represented the following energy transfers: Ca1 → Ca1 (), Ca2 → Ca2 () and Ca1 → Ca2 () interactions (energy transfer routes). Because the energy transfer that occurred between Eu2+ activators of particular types was examined in the present investigation, the inhomogeneous distribution of Eu2+ activators in the crystalline host was an important issue. However, in CASIN hosts, the four characteristic activator sites, i.e., regular Ca1, defective Ca1, regular Ca2 and defective Ca2, all belong to an identical Wyckoff site, so that the acceptor distribution around a donor is identical, irrespective of which activator sites were considered the donor sites. Accordingly, all four energy transfer constants should involve the same acceptor distribution function. As a distribution function, we adopted the angular-class model proposed by Vásquez[25,29-32], which predicts a non-radiative energy-transfer rate based on an inhomogeneous distribution of activators in the crystalline host. The primary determinant of the energy transfer constant is not the distribution function, but some other factor included in because the distribution function included in every is identical. is comprised of the product of the radiative decay rate of the donor, the spectral overlap, the oscillator strength of the acceptor, and the acceptor distribution function.
Reproduction of the decay curves was accomplished using the well-known Runge-Kutta method , followed by least-square-fitting (LSF). The donor (P1) and acceptor (P2) decay curves were simultaneously subjected to LSF by use of the following relationships:
After establishing a plausible rate equation model, the ensuing LSF process for the evaluation of decision parameters was the next step. Simultaneous LSF of both the donor and acceptor decay curves is difficult, even if the rate equation model proposed above was reasonable from a theoretical point of view. There were nine unknown decision parameters to be determined in the LSF process: the radiative decay rates for donor and acceptor (KrCa1 and KrCa2), the energy transfer constants (, = ), the non-radiative decay rate of defective Eu2+ ions (Kn), the contribution of Ca1 (RCa1), the fraction of defective Eu2+ activators (q), the P2 contribution to the 525-nm decay curve (m), and the P1 contribution to the 700-nm (or 725-nm) decay curve (n). Inclusion of such a large number of decision parameters in the LSF process is unusual because it is practically impossible to achieve a satisfactory optimization by use of conventional, mathematics-based, local optimization strategies, which require instantaneous evaluation of Hessian and Jacobian matrices. To overcome this complication we adopted a heuristics-based optimization method — the so-called particle swarm optimization (PSO) [14~16], which is a population-based heuristic inspired by swarm behavior (or swarm intelligence). PSO is comparable to the genetic algorithm (GA), but is better suited than GA to optimization with a continuous decision parameter space. Because the present optimization process that included nine decision parameters constituted a continuous nine-dimensional decision space, use of PSO was appropriate.
Figure 5(a) and 5(b) show the measured and calculated decay curves with acceptable fitting quality. The best-fitted parameters obtained from the PSO process were all reasonable, as shown in Table 3 . The radiative decay rates for the two distinct local environments, KrCa1 and KrCa2, were determined to be similar to one another within the same order of magnitude, though we set them as independent free parameters in the PSO process. The non-linear energy-transfer terms in the rate equation, which were of particular interest, were coupled with two energy-transfer constants (, = ). for N-CASIN-1.2 was much greater than that for N-CASIN-0.7 while ( = ) did not differ significantly between N-CASIN-0.7 and N-CASIN-1.2. This result indicates that the energy transfer from Ca1 to Ca2 was enhanced as the Al/Si ratio around the activator increased. The estimated RCa1 was also noteworthy because N-CASIN-1.2 had a lower RCa1 value than N-CASIN-0.7. RCa1 showed an inverse relationship with the Al/Si ratio, i.e., the higher the Al/Si ratio, the lower the RCa1 value. This result coincided with the spectral measurement, which showed a reduction in the high-energy emission (P1) at higher Al/Si ratios that ultimately caused a red shift. The fraction of defective Eu2+ activators (q) was indicative of the killer concentration (defects or defect impurities). The m and n values were estimated to be close to 1, which were quite reasonable considering the spectral deconvolution shown in Figs. 4(a) and 4(b). Thus, the detection wavelengths used for donor and acceptor decay were far enough from each other to allow adequate separation. The time evolution of the donors in the four different local environments, i.e., and curves, was calculated based on the fitting results for N-CASIN-0.7 and N-CASIN-1.2 (Fig. 6 ). It should be noted that separate experimental measurements for the and curves were unavailable.
It was readily apparent that active energy transfer between Ca1 and Ca2 occurred. This type of energy transfer, which has been called site-to-site energy transfer , was clearly evidenced by the variation in decay rate with respect to the detection wavelength. Site-to-site energy transfer might involve a variety of local environments, so that precise classification of the local environment might lead to a more complicated rate equation model along with more terms and more decision parameters. In the present investigation, however, we adopted only two local environments, which were simplified as a Si-rich environment (Ca1) and an Al-rich environment (Ca2). Accordingly, only two Gaussian emission components (P1 and P2) were deconvoluted in an attempt to implement our quantitative analysis of the decay curves. In fact, this simplification was based on the fact that the two-peak deconvolution yielded the best fit compared with other deconvolution cases that involved more Gaussian components. Furthermore, the analysis based on the two-peak simplification could be generalized and applied to more complicated systems that involved more Gaussian components, resulting in a more refined classification of the local environments.
As mentioned above, an unexpected result in the decay measurements was the absence of a significant increase (so-called rising) during the initial stage of acceptor decay, while energy transfer between donor and acceptor was dominant. The conventional rate equation model of energy transfer that simply includes donor and acceptor pairs cannot adequately explain the absence of the initial-stage-rising in the actual, measured acceptor decay curves. On the other hand, adoption of both regular and defective activators as separate terms in the rate equation model resolved this complication. As a result, it was possible to obtain agreement between the rate equation model and the experimental decay data over a long-range time scale, i.e., up to 2 μsec, which covered nearly four decades in the intensity scale. Of course, the rising clearly appeared in the calculated acceptor decay curve at regular Ca2 sites (), as shown in Fig. 6. It should be noted that the measured decay curve was the sum of both the regular and defective activator decay curves. Accordingly, the increasing region of the curve was not evident in the measured acceptor decay curve represented by , wherein the latter term (the donor contribution) can be ignored because the estimated n value was nearly 1. Another advantage of the adoption of both regular and defective activators as separate terms in the rate equation model was the estimation of relative fraction of defective Eu2+ activators (q). The estimated q value should be related to the killer site concentration. Consequently the adoption of defective activator terms in the rate equation made it possible to roughly predict the defect concentration in the host.
We examined non-stoichiometric CASIN phosphors to assign the deconvoluted Gaussian components that comprise the emission spectrum to their corresponding local environments. The Al/Si molar ratio around the Eu2+ activator was a key parameter in assigning the deconvoluted Gaussian peaks. The high Al/Si ratio near the Eu2+ activator abolished the high energy peak. The Eu2+ activator site in an Al-rich environment with a smaller average Ca-N distance was assigned to the lower energy emission peak, while that in a Si-rich environment with a longer average Ca-N distance was assigned to the higher energy emission peak.
The energy transfer between Eu2+ activators in Si- and Al-rich environments was also taken into account. Decay curve analysis along with rate equation modeling confirmed active energy transfer from the Eu2+ activator site in the Si-rich environment (donor) to the Eu2+ activator site in the Al-rich environment (acceptor). In particular, numerical computation based on particle swarm optimization was implemented to solve the rate equations with nine unknown decision parameters and to correctly evaluate the decision parameters. Use of this strategy gave precise donor and acceptor decay curves with outstanding fitting quality along with plausible best-fitted parameters. The estimated energy-transfer rate, radiative decay rate, defect concentration, and relative contribution of each local environment were all within a reasonable range of values. Decay curve fitting with the quality reported in the present study is extremely rare in the published literature, especially for simultaneous treatment of the donor and acceptor decay curves for Eu2+ activator systems. In this context, our energy-transfer modeling and the ensuing PSO process resulted in excellent agreement between the calculated and experimental results.
This work was supported by the IT R&D Program of MKE/IITA (2009-F-020-01) and partly supported by the WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology.
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