The 12 K cathodoluminescence spectra of Er3+ doped into single crystals of aluminum nitride (2H-AlN) in the hexagonal phase are reported between 320 nm and 775 nm. The emission spectra represent transitions from the lower Stark level of 2P3/2 to the Stark levels of the 4I15/2, 4I13/2, 4I11/2, 4I9/2, 4F9/2, and 4S3/2 multiplet manifolds of Er3+(4f11). Emission spectra from 4S3/2 to 4I15/2 are also reported. All observed strong line emission are accounted for in terms of two principle sites, denoted site “a” and site “b”, with a few line spectra attributed to additional sites. A parameterized Hamiltonian that includes the atomic and crystal-field terms for Er3+(4f11)2S+1LJ was used to determine the symmetry and the crystal field splitting of the “a” and “b” sites. A descent in symmetry calculation was carried out to determine if distortion due to the size difference between Er, Al and the vacancies can be discerned. Modeling results assuming C3v and C1h are discussed. It appears that the sensitivity to a C1h model is not sufficient to invalidate the choice of C3v as an approximate symmetry for both sites. The g-factors reported from an EPR study of Er3+ in single-crystal AlN are in reasonable agreement with calculated g-factors for Er3+ in the “a” site assuming C3v symmetry.
© 2012 OSA
Interest in the detailed interpretation of the spectroscopic properties of wide band gap semiconductors such as the III-nitrides GaN and AlN doped with trivalent rare earth ions (RE3+) has grown rapidly in recent years as the optoelectronic properties of these materials have been successfully exploited in photonic devices [1–4]. Within the band gap of AlN (approximately 6.1 eV), numerous sharp-line absorption and emission spectra of the RE3+ ions are observed due to transitions within the 4fn subshell that is well shielded from the lattice by the filled 5s2 and 5p6 shells of the rare earth ion core [5–7]. The large optical window associated with hexagonal AlN is also transparent to the absorption and emission spectra arising from vacuum ultraviolet states of the RE3+ ions, transitions that are usually not observed in insulator hosts such as garnets, oxides and fluorides due to lattice absorption.
The physical properties of rare earth-doped AlN are attractive for purposes of application in that they have high fracture toughness, are relatively non-corrosive, and exhibit high thermal conductivity, although doping reduces the thermal conductivity somewhat [8,9]. Yet, the preparation and detailed optical characterization of the doped materials still provide challenges and opportunities that call for fundamental spectroscopic studies. The technologies of thin film, single crystal, and ceramic rare earth-doped AlN sample preparation and growth have improved greatly over recent years [10–12]. Experimental techniques that include specific wavelength laser excitation and up-conversion dynamics to probe observed multi-site RE3+ spectra can be carried out to investigate local RE3+ site symmetries together with methods of electron spin resonance (EPR), Zeeman spectroscopy, and site-selective combined excitation and emission spectroscopy [13–15]. Because of the importance of Er3+ as an infrared laser, its upconversion capabilities, and its use in fiber-optic amplifiers by the communications industry, we have carried out the following detailed crystal-field splitting analysis of the multi-site spectra of Er3+ in single crystal AlN.
We begin by reporting the multi-site cathodoluminescence (CL) spectra of Er3+ in single-crystal hexagonal phase AlN obtained at 12 K between 320 nm and 775 nm. The spectra represent emission transitions from the lower energy (Stark) level of Er3+(4f11) 2P3/2 to the Stark levels of the ground state, 4I15/2, and excited multiplet manifolds 4I13/2, 4I11/2, 4I9/2, 4F9/2 and 4S3/2. The CL spectra include transitions from both Stark levels of 4S3/2 to 4I15/2, which confirm the energy (Stark) level splitting of 4I15/2. All observed strong, sharp spectra are accounted for by assuming transitions from two Er sites, which we designate as principle sites “a” and “b”, with a few generally weak lines attributed to additional sites.
We also report refinements of the spectrofluorometric experiments and interpretation of Merkle et al. . These site selection data identify most of the 4I15/2, 4I13/2, 4I11/2 and 4I9/2 energy levels for Er3+ in the principal “a” site in a ceramic Er:AlN sample, and confirm levels derived from the CL data. Thus, the site selection data guide the identification of lines associated with one principle site in the CL spectra.
Recent emission channeling experiments and lattice location studies of RE3+ in 2H-AlN by Vetter et al.  indicate that the main sites for RE3+ ions doped into hexagonal AlN occupy vacant cation (Al) sites, although a number of substitutional minority sites are found as well. Yang et al. , after reviewing possible local sites for Er3+ in single crystal hexagonal AlN, concluded that C3v symmetry for Er3+ in a sample with a concentration of about 1016 cm−3 agreed with their EPR analysis. Such low RE3+ doping, however, precludes observation of the details of the weak 4f11 spectrum of Er3+. A much larger concentration of Er3+ is needed to observe, analyze, and model the optical spectroscopy.
However, for larger amounts of Er3+, the local site symmetry can be distorted during crystal growth since the radius of Er3+ is larger than the radius of the Al3+ it replaces. This causes stress on the surrounding environment. In fact, local-density functional modeling by Petit et al.  suggests that a neighboring oxygen ion or neighboring nitrogen vacancy next to Er3+ may substitute for a basal-plane N to form complexes such as Er3+-ON or Er3+-VN with C1h symmetry. In effect, the Er3+ ions that occupy Al vacancies of C3v symmetry may shift along the c-axis toward the basal plane into a site of C1h symmetry in order to reduce the local stress associated with its size. Thus, the site symmetry of Er3+ in the present study could be C3v or lower, possibly depending on the amount and distribution of Er3+ ions in the lattice.
To identify the appropriate symmetry, we performed descent in symmetry calculations from C3v to C3 (assuming the mirror plane symmetry is broken) and from C3v to C1h (assuming the mirror plane remains, but the three-fold rotation symmetry axis is broken). The crystal-field splitting of the energy levels of Er3+ in each site is modeled assuming each of these symmetries, as discussed in section 4.
2. Experimental details
Single crystals of hexagonal phase aluminum nitride (2H-AlN) doped with trivalent erbium were grown by a temperature gradient method under high temperature and high pressure  with the use of a belt-type high pressure, high temperature (HP-HT) apparatus designed to grow materials having similar physical crystalline properties [20,21]. Li3AlN2, together with Ba3Al2N4, was used as the solvent. The solvent was mixed with ErF3 and packed into a molybdenum sample chamber. Both steps were carried out under a dry nitrogen atmosphere. The assembled cell was then compressed to 6.5 GPa and heated to 1400 °C for 4.5 hours and quenched to room temperature by shutting off the heater power supply. The end product resulted in lightly colored crystals with diameters up to 0.4 mm and a maximum size of less than 0.5 mm on a side parallel to the c-axis.
The crystal structure was confirmed by x-ray diffraction (XRD) with a Bruker AXS D8 Advance, which is equipped with a Cu K-alpha x-ray source. Figure 1 shows a typical XRD pattern of the Er3+-doped AlN crystals mounted on a silicon substrate using silver paste. None of the XRD measurements indicated the formation of any other phase, including rare-earth rich phases within the AlN crystals. The hexagonal structure (wurzite phase) of AlN was confirmed [22,23]. The space group is , with both Al and N occupying C3v sites in the unit cell. Earlier emission channeling experiments  identify the location of the majority of RE3+ as substituting for Al3+ in cation vacancies, some of which may form complexes with nitrogen vacancies.
The CL spectra were obtained from crystals mounted on the head of a closed-cycle helium refrigerator positioned within a vacuum chamber. An electronically controlled calibrated resistive heater was maintained at a selected sample temperature while the spectra were recorded. The CL spectra were obtained at several temperatures from approximately 12 K to room temperature in order to record any temperature dependence in the spectra. A SPECS Eq. (22) Auger electron gun was used as the excitation source that produced electrons having energies between 100 eV and 5 keV and beam currents between 0.01µA and 150 µA. The CL spectra were produced by electrons excited to 5 keV with a beam current of 2 µA/mm2. The emission was passed through a quartz window and a pair of UV-coated lenses before reaching the entrance slit of a 1.0 m Czerny-Turner spectrograph (Jobin-Yvon 1000M). The spectrograph was equipped with holographic gratings blazed at 250 nm with 1200 lines/mm and at 1000 nm with 600 lines/mm, and calibrated using a Hg arc standard. Resolution of the spectra was better than 0.05 nm for the sharpest transitions. Detection was carried out with a nitrogen-cooled CCD camera that recorded the spectra between 300 nm and 1000 nm. Uncertainty in the wavelength measurements was approximately 0.02 nm. The methods used to record the CL spectra are similar to the methods we reported earlier [24–28].
Site selection spectroscopy was performed on ceramic Er:AlN material, as exemplified in Fig. 2 and described in , using techniques very similar to those reported therein. Upgrades to the optical cryostat facilitated measurements at temperatures both lower and higher than the 20 K at which most spectra in that work were taken. Fluorescence spectra were taken with spectral band pass as narrow as 0.3 nm, and excitation wavelengths could be selected to a typical specificity of 0.2 nm.
3. Data analysis
The multi-site CL spectral lines obtained at 12 K between 320 nm and 775 nm are listed in Table 1 (column 2) for Er3+(4f11) energy levels, including the ground state, 4I15/2, and excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2, and 4S3/2. Using empirical methods of energy differences between transition energies and temperature dependent peak characteristics, more than 97% of the spectra reported in column 2 can be accounted for in terms of two sites, with the remaining 3% of the spectra likely associated with other Er sites for which there is insufficient data for analysis. The transitions numbered in column 5 are identified as site “a” under cols. 6-8 and site “b” under cols. 9 and 10. Column 5 identifies the transition from the lower energy (Stark) level of 2P3/2 to one of the J + 1/2 terminal Stark levels within each 2S+1LJ multiplet manifold listed in column 1. The transition numbers also correspond to the emission peaks identified in Figs. 3 through 9.
The experimental Stark levels inferred from CL of the single crystal material may be compared with those inferred from site selection spectroscopy of the ceramic. To facilitate this comparison, higher resolution temperature-dependent measurements for selected excitation wavelengths have been used to refine the level assignments for the principal site reported in Merkle et al. . The great majority of the assignments are confirmed, and are within one or two wave numbers of the originally reported values, as may be seen by comparing column 7 of Table 1 with . In the case of the 4I9/2 manifold, our new data shift the energy levels lower by as much as 6 cm−1, but the splittings are only subtly changed. However, there are a few exceptions to this overall agreement, which can affect the assignment of levels in the CL data and the fitting of crystal field theory to the data.
The first reassignment occurs in the 4I15/2 manifold. Fluorescence spectra of Er3+ in the principal site for several different wavelengths in its excitation spectrum indicate that the 1558.25 nm fluorescence line’s intensity at the lowest temperatures is weak and inconsistent, though as the temperature is increased it grows rapidly, as exemplified in Fig. 2. This supports ’s prediction of hot bands at about that wavelength, but calls into question its assignment of an energy level at 98 cm−1 based on this line. However, a moderately weak fluorescence line at 1544.5 nm is much more consistent for different principal site excitation wavelengths and its intensity varies only weakly with temperature, as can be seen in Fig. 2. This is much more consistent with expectations for a transition from the lowest 4I13/2 level. On the basis of this transition, we conclude that the fourth energy level in 4I15/2 is not at 98 cm−1, but rather is at 43 cm−1.
The other reassignments resulting from our refined site selection spectra involve 4I11/2 states. A detailed excitation spectrum of the principal site fluorescence refines the energy of the transition reported as 10108 cm−1 in  to 10105 cm−1, and reveals three additional excitation transitions at 10150, 10170 and 10187 cm−1. The final two of these agree satisfactorily with energy levels assigned from the CL data, but the transition energies 10105 and 10150 cm−1 cannot plausibly be associated with any CL feature. In addition, the crystal field modeling to be reported in a later section cannot account for these features if they represent ground state absorption.
The existence of 4I15/2 states at 43 and 135 cm−1 suggests explanations for these excitation lines in terms of hot band absorption. The 10105 cm−1 line is satisfactorily consistent with a transition from the level at 135 cm−1 to that observed in CL at 10237 cm−1, and 10150 cm−1 is consistent with a transition between the levels at 43 and 10193 cm−1. We conclude that the 4I11/2 levels observed by site selection spectroscopy are the five given in column 7 of Table 1.
Figure 3 includes peaks 1 through 14 from the 12 K CL spectrum that represent transitions from the lower Stark level of 2P3/2 to the ground state manifold 4I15/2. Peak 1 is a shoulder that represents the transition from the initiating Stark level in 2P3/2 at 31076 cm−1 to the ground state Stark level of Er3+ in the “a” site (Table 1). Peak 2 consists of two unresolved transitions, one transition from the initiating Stark level in 2P3/2 at 31069 cm−1 to the ground state Stark level of Er3+ in the “b” site and a second transition from the initiating Stark level of Er3+ in the “a” site to the first excited Stark level at approximately 7 cm−1. This analysis of the splitting is confirmed by the site selection data in Table 1 (column 7) for Er3+ in the “a” site. The overlap of these peaks requires deconvolution of the spectra for peaks 1 and 2. The uncertainty in separation between peaks is less than a wave number, so that in Table 1 we list the energy for both transitions as 31069 cm−1. To further support this assignment we have observed emission spectra from 4S3/2 to 4I15/2 for Er3+ in the “a” site that unambiguously identifies the 7 cm−1 splitting between the ground state and the first excited Stark level. Emission peaks at 321.9 nm and 322.14 nm in Table 1 are very weak. They establish Stark levels at 30 cm−1 and 43 cm−1, respectively, that are confirmed by site selection spectroscopy. The emitting level of the “b” site can also be established from energy differences from that site to lower energy Stark levels established from emission by 4S3/2.
The CL emission spectra shown in Fig. 4 for peaks 42 through 55 were analyzed as transitions from both Stark levels of 4S3/2 to the Stark levels of the 4I15/2 manifold for Er3+ in both sites. The figure includes detector noise due to the narrow slits required to resolve the transitions observed from the two emitting Stark levels of the 4S3/2 manifold in both sites to eight expected terminal Stark levels of 4I15/2. Analysis of the CL spectrum confirms all eight Stark levels of the 4I15/2 manifold reported in both sites in Table 1. The splitting of the 4S3/2 manifold is 20 cm−1 (site “a”) and 18 cm−1 (site “b”). This splitting is shown in Fig. 5 and Table 1. We list only emission from 2P3/2 in Table 1 since the emission from 4S3/2 simply confirms the splitting of the ground state manifold.
Perhaps the simplest spectra analyzed that demonstrate the dominance of two Er3+ sites in this crystal are the spectra shown in Fig. 5, representing the sharp, well defined transitions from the lower Stark level of 2P3/2 to the two Stark components of 4S3/2. The four peaks (65 through 68) identify the splitting of the 4S3/2 in the “a” and “b” sites and provide the energies for the emitting Stark levels used to analyze the crystal-field splitting of the 4I15/2 manifold described in the preceding paragraph. The difference in energy between the multiplet barycenters of 4S3/2 of Er3+ in the “a” and “b” sites is comparable to the energy shift found between the ground-state Stark level of Er3+ in both sites as well, suggesting the impurity traps represented by these two sites have nearly the same depth.
The spectra representing transitions from 2P3/2 to 4I11/2 are shown in Fig. 6 . At first glance, it appears that exactly J + 1/2 expected peaks (27 through 32) are observed for a single site. However, a closer look indicates that each peak appears to have a discernible shoulder, suggesting that the peaks may be deconvoluted into two peaks with nearly the same energy. The results from deconvolution suggest the experimental Stark levels for this manifold for the “a” and “b” sites reported in Table 1. Stark levels 10192 cm−1 and 10211 cm−1 in the “a” site are similar to levels assigned by analysis of the site selection spectra. The experimental Stark levels for 4I11/2 of Er3+ in both sites are also in reasonable agreement with calculated energy values listed in columns 8 and 10 of Table 1 that are based on the modeling studies described in the following section.
Figures 7 and 8 show the 12 K CL emission spectra representing transitions from 2P3/2 to 4I9/2, and 2P3/2 to 4F9/2, respectively. The transitions are represented by peaks 33 through 41 and peaks 56 through 64. Peak 33 is very weak and broad, and probably represents two separate transitions observed in the spectrum between 530 and 531 nm. In Fig. 7, five strong peaks can be assigned to transitions that identify five Stark levels within the 4I9/2 “a” site manifold based on comparison with levels determined by site selection spectra listed in column 7 of Table 1. The remaining peaks and terminal Stark levels are identified with the “b” site, with the exception of peak 38 which is presently unassigned. In Fig. 8, nine peaks and a shoulder (on peak 54) are observed and ten terminal Stark levels are expected from the 2P3/2 to 4F9/2 in those sites.
Five of these transitions were assigned to the “a” site and the remaining five to the “b” site using methods of energy differences. Peaks in both figures are sharp and relatively intense, and limited by spectral resolution of the spectrograph, suggesting they may have relatively large emission cross sections. The difference in manifold splitting of 4I9/2 and 4F9/2 provides an important distinction between sites in the subsequent modeling studies of the crystal-field splitting of these states.
The CL emission spectra, representing transitions from 2P3/2 to 4I13/2 (levels 15 through 26 in Fig. 9 ), are perhaps the most difficult to analyze in the entire set of data given the number of similar energy differences between Stark levels and the inhomogeneous broadening of the peaks. Ambiguity is greatly reduced by comparing the peaks and transitions that give the experimental energy level scheme of Stark levels selected for the “a” site in Table 1 (column 6) with the experimental Stark levels for the 4I13/2 manifold analyzed from the site selection spectroscopy. The remaining peaks and subsequent terminal Stark levels then can be assigned by process of elimination to Stark levels of Er3+ in the “b” site, in column 9 of Table 1. The experimental Stark levels expected for 4I13/2 for Er3+ in both “a” and “b” sites in Table 1 agree well with the assignments made from the site selection spectroscopy and with the results of the crystal-field modeling studies reported in the next section.
4. Modeling the crystal field splitting
The 34 identified experimental Stark levels for each of the two principle (“a” and “b”) sites, representing every Stark component of the seven lowest-energy multiplet manifolds of Er3+ along with the lowest Stark component of the emitting 2P3/2 multiplet in single-crystal hexagonal phase AlN, are reported in Tables 2 and 3 for the main “a” and “b” sites, respectively. These energy levels are modeled using a parameterized Hamiltonian written in standard practice [29,30] that consists of spherically symmetric “atomic” contributions given by,
, , , , , , , , and. As with C3 symmetry, one of the 15 crystal-field parameters can be set to zero via appropriate rotation about the parametrization z-axis, with standard convention setting . This results in 14 independent crystal-field parameters in C1h symmetry. The experimental Stark levels are modeled through use of a Monte Carlo method [31,32] in which each of the independent crystal-field parameters is given random starting values between −1000 and + 1000 cm−1 and optimized using standard least-squares fitting between calculated and experimental levels.
Based on 34 Stark levels for each site and assuming C3v site symmetry for the Er3+ ion, the final overall standard deviation between calculated-to-experimental Stark levels for site “a” is 8.7 cm−1 (rms error = 7.0 cm−1) and for the same number of Stark levels for site “b”, the overall standard deviation is 8.3 cm−1 (rms error = 6.7 cm−1). Table 2, columns 4-7 compare the modeling results for site “a” with experimental energy values given in column 2. Calculated irreducible representations (irreps) (Γ1/2 and Γ3/2) and the largest MJ components are given for each doublet level as determined by the best fit of the data to C3v symmetry. The results for site “b” are given in Table 3 using the same format as for Table 2. The atomic and crystal-field parameters that are used to obtain these results are given in Table 4 . Six of the 20 atomic parameters were allowed to vary in the fitting process, along with all six crystal-field parameters. Parameter uncertainties for these twelve parameters are given in parentheses after the parameter values. The other 14 atomic parameters were held fixed at previously determined values. Stark levels calculated using these parameters are also given in Table 1, columns 8 and 10.
When we carried out the modeling calculations assuming C3 site symmetry for the Er3+ ion, there was no significant improvement in the calculated-to-experimental fitting, with higher standard deviations for both the site “a” and “b” fittings.
Modeling calculations using C1h site symmetry showed a modest improvement in the fittings, with the standard deviation for the site “b” fitting decreasing from 8.3 to 7.6 cm−1 (rms error decreasing from 6.7 to 4.9 cm−1). For the site “a” fitting, the standard deviation was almost unchanged (going from 8.7 to 8.8 cm−1), though the rms error decreased from 7.0 to 5.7 cm−1. The right-hand columns of Tables 2 and 3 present the energy level calculations using C1h symmetry. As can be seen from these two tables, the additional crystal-field parameters allowed in C1h symmetry improve the energy level calculations for specific levels of 4I15/2 and 4I13/2 multiplets.
Table 5 presents the C1h crystal-field parameters determined for both sites “a” and “b”. For comparison, the C3v parameters, transformed to the coordinate system used by the C1h parametrization by Euler rotations α = 90°, β = 90°, are given to the left of the C1h parameters for each site. The fitting improvement using C1h parameters is statistically significant, indicating that the true site symmetry for both the “a” and “b” sites is most likely C1h. However, as can be seen from Table 5, the uncertainties in the values of the C1h crystal-field parameters are large, and in most cases are larger than the difference between the C3v and the C1h parameter values. The large parameter value uncertainties means that the wavefunctions generated by the C1h Hamiltonian will be less reliable for the purposes of deducing other properties of the systems, such as calculated Zeeman splittings. The relatively small differences between the C3v and the C1h parameter values indicate that it is reasonable to use an approximate C3v symmetry to model these systems.
Using wavefunctions generated from the C3v modeling studies for both sites, we calculated the Zeeman splitting and g-factors for the Stark levels of the ground 4I15/2 manifold. The Zeeman splitting calculated for an external magnetic field of 0.15 T, along with resulting calculated g-values (g|| and g⊥), are listed in Table 6 for site “a” and in Table 7 for site “b”. We have compared these calculated results with experimental values for g|| and g⊥ obtained from an investigation of the EPR spectrum on single-crystal Er3+ in AlN . Only one Er3+ site was observed in the EPR study, with experimental g-values for the ground state Stark level reported as g|| = 4.337 and g⊥ = 7.647. The experimental g-values agree with the calculated values g|| = 5.5 and g⊥ = 6.1 given in Table 6 for site “a”, and do not agree with the calculated values g|| = 14.7 and g⊥ = 1.0 given in Table 7 for site “b”. We therefore conclude that the Er3+ ions occupy site “a” in the dilute sample used for the EPR study.
5. Summary and conclusions
With support from analyses of site-selective spectroscopy, the cathodoluminescence (CL) spectra of Er3+(4f11) in single-crystal hexagonal phase of AlN have been assigned to two principal sites in the lattice. The 12 K CL spectrum obtained between 320 nm and 775 nm was analyzed for the J + 1/2 Stark levels of the ground-state 4I15/2 and excited state 4I13/2, 4I11/2, 4I9/2, 4F9/2, and 4S3/2 multiplet manifolds. The emission to the Stark levels of these manifolds came from the lower-energy Stark level of the 2P3/2 multiplet, with additional data coming from the 4S3/2 → 4I15/2 emission. More than 97% of the observed CL spectra were accounted for in terms of the two principal sites. More than 65 peaks and shoulders were evaluated and a number of deconvolution studies were carried out on problematic features.
A crystal-field splitting calculation was carried out for each site using a parameterized Hamiltonian that included atomic and crystal-field terms for states of Er3+(4f11)2S+1LJ. The identification of two Er3+ sites in AlN suggested a descent in symmetry calculation from C3v to C1h for each site, since Er3+ has a larger ionic radius than Al3+, and is expected to cause stress on the surrounding environment, especially when doped into AlN in sufficient quantities to observe the optical spectrum of the 4f → 4f transitions. Likewise, Er3+ may substitute for a basal-plane N to form complexes such as Er3+-ON or Er3+-VN with C1h symmetry. Er3+ ions in Al3+ sites may shift along the c-axis toward the basal plane into a site of C1h symmetry to lower the energy of Er3+ as a trap impurity in AlN. The modeling of the Er3+ site symmetry gave interesting results, as shown in Table 5. For site “a” the C1h crystal-field fitting gave a slightly higher standard deviation than obtained for C3v symmetry, while for site “b” the C1h fitting gave a statistically-significant lower standard deviation than for C3v symmetry. However, for most of the crystal-field parameters given in Table 5, the difference between the C3v and C1h symmetry parameter values is less than the statistical uncertainty in the C1h symmetry crystal-field parameters. Therefore, we conclude that C3v remains a reasonable approximate symmetry for Er3+ ions in both sites of AlN, and that wavefunctions generated using the assumption of C3v symmetry may be used reasonably for calculation of other optical properties, such as Zeeman splittings of the states.
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