1. Introduction

Long persistent luminescence (LPL) is a “self-sustained” luminescence phenomenon whereby luminescence can last for minutes to hours at room temperature after the stoppage of the excitation. For long persistent phosphors (LPPs), the energy stored in suitable traps could be released which was induced by thermal energy available at room temperature. To date, LPPs have received much attention and interests due to their wide application, e.g., such as emergency escape routes and exit signs, optical energy media, thermal sensors [1–6]. Besides the traditional applications, new fields of interest emerged in medical field such as cancer photodynamic therapy, cancer diagnoses and in vivo imaging [7–10]. ZnS:Cu persistent phosphor was first applied for making watch dials in the middle of 1990s [3,11]. In 1996, a new persistent aluminate material (SrAl₂O₄:Eu²⁺, Dy³⁺) was reported by Matsuzawa. et al, which can emit in visible for 10h after ceasing the irradiation and gave us a new benchmark for the performance of persistent luminescence materials [12]. Since then, this new finding boosted the research on the persistent luminescence phosphors and so many efficient persistent luminescence materials were discovered based on stable aluminate and silicate materials, i.e. CaAl₂O₄:Eu²⁺, Nd³⁺ [13], Sr₄Al₁₄O₂₅:Eu²⁺, Dy³⁺ [14], and Sr₂MgSi₂O₇:Eu²⁺, Dy³⁺ [15]. Meanwhile, a large amount of the trivalent rare-earth (R³⁺) -doped LPPs were also found such as CaTiO₃:Pr³⁺ [16], Y₂O₂S:Eu³⁺, Mg²⁺, Ti⁴⁺ [17], and Ca₂SnO₄:Sm³⁺ [18]. However, neither the persistent luminescence nor the afterglow times are less than that of Eu²⁺-doped LPPs. More importantly, the details of the nature and distribution of the traps in R³⁺-doped LPPs are still a subject of challenge, which are critical to explore and design the desired long persistent phosphors. Based on our team’s works about R³⁺-doped long persistent phosphors such as Sr₃Al₂O₅C_l2:Pr³⁺ [19], CdGeO₃:Tb³⁺ [20], La₃GaGe₅O₁₆:Pr³⁺ [21], BaZrSi₃O₉:R³⁺ (R = Eu, Sm, Dy, Tb and Pr) [22], SrZrO₃:Pr³⁺ [23] etc, a doubt comes to my mind that how to improve the phosphorescence performance of R³⁺-doped LPPs. A persistent luminescence requires the presence of abundant traps able to intercept free carriers, and to immobilize them for an appropriate time. Thus, how to enhance the lattice defects (oxygen vacancies) or the impurities is key to optimize the phosphorescence performance of R³⁺-doped LPPs. Obviously, the lattice defects largely depend on the proportion of the starting prepared materials and the synthesis condition, for example, the fabrication atmosphere or the sintering temperature. The chief reason why La₃GaGe₅O₁₆ compound is selected to be the host is that this host is rich in the bridging oxygen and could be the potentially suitable for R³⁺-doped long persistent phosphors.

As shown in Fig. 1(a), there are five types of the bridging oxygen (O) based on the crystal structure of La₃GaGe₅O₁₆, as denoted O₁~O₅. O₁ is located between the tetracoordinated and hexacoordinated germanium (GeO₄ and GeO₆); O₂ lies between the tetracoordinated gallium (GaO₄) and the hesacoordinated germanium (GeO₆); O₃ comes from the joint between the tetracoordinated gallium (GaO₄) and pentacoordinated germanium (GeO₅); O₄ exists between two pentacoordinated germanium (GeO₅); O₅ originates between the tetracoordinated germanium and pentacoordinated germanium (GeO₅). On the other hand, Ge-O and Ga-O units are the basic framework of the structure, so the formation of Ge vacancies (V_Ge) and Ga vacancies (V_Ga) are both energetically costly. Meanwhile, the La vacancies (V_La) in this host can hardly occur as well, because La layers are located in a loose and comfortable space. As far as we know, oxygen vacancies, concerning linking (bridging) oxygen, cost the lower energy than the formation of other vacancy defects and thus stand out as a most likely cause of the observed persistent luminescence in Sr₂MgSi₂O₇ [24,25]. If it is true in the case of La₃GaGe₅O₁₆ phosphor, we expect that the reducing atmosphere will lead to a good performance of La₃GaGe₅O₁₆ phosphor, since there are various types of bridging oxygen in La₃GaGe₅O₁₆ host and the oxygen vacancies may be presented in high concentration under high-temperature reducing atmosphere annealing conditions. Therefore, oxygen vacancies are considered as candidates for the lattice defects in La₃GaGe₅O₁₆ host. In order to gain a theory about the trapping of charge carriers at oxygen vacancies, Freysoldt et al gave us a concrete procedure that how density functional theory (DFT) calculations with periodic boundary conditions are performed on supercells containing an oxygen vacancy [26].

 

Fig. 1 View of the structure of La₃GaGe₅O₁₆ compound and the different cation are shown, respectively.

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In our previous works, we presented the photoluminescence and phosphorescence properties of La₃GaGe₅O₁₆ host and also observed a pink persistent luminescence from La₃GaGe₅O₁₆:Pr³⁺ [21]. In this paper, we observed a green long persistent luminescence from La₃GaGe₅O₁₆:Tb³⁺ phosphors due to the defect related emission, and the 4f - 4f transitions of Tb³⁺. We tried to tune the multicolor persistent luminescence by doping Tb³⁺ concentration in La₃GaGe₅O₁₆. In order to improve the phosphorescence performance, we prepared the La₃GaGe₅O₁₆:Tb³⁺ phosphors under different flowing gas atmospheres and modified the composition around Tb³⁺ by adjusting the Ge/O content. For better understand the nature of traps involved in trapping and releasing processes, La₃GaGe₅O₁₆:Tb³⁺ phosphors were studied by a combination of both experiments and first-principle calculation.

2. Experimental

2.1 Synthesis

The samples were prepared by a two-step traditional solid-state reaction. La₂O₃(99.99%), Ga₂O₃ (99.99%), GeO₂ (99.99%) and Tb₂O₃ (99.99%) were used as starting materials. After the raw materials were weighed according to the composition of La_3(1-x)GaGe₅O₁₆:xTb³⁺ (x = 0, 0.001, 0.005, 0.01, 0.03, 0.05, 0.07, and 0.09, etc) and La_2.99GaGe_5(1-x)O₁₆:0.01Tb³⁺ (−0.05≤x≤0.05), the powders were mixed and milled thoroughly for 1h in an agate mortar and prefired at 900 °C for 8 h in air. After ground again, the mixtures were sintered at 1300 °C for 12 h under different atmospheres such as vacuum, air, 100% N₂ and 5%H₂/95% N₂. After being cooled down to room temperature naturally, the as-prepared powder samples were obtained.

2.2 Measurement

The phase purity of the prepared phosphors was measured by an X-ray diffractometer with Cu Ka radiation (wavelength = 0.15406 nm) at 36 kV tube voltage and 20 mA tube current. Room-temperature photoluminescence excitation, emission spectra and afterglow spectra of all the samples were measured by a Hitachi F-7000 Fluorescence Spectrophotometer equipped with a 150 W xenon lamp as excitation source. The persistent luminescence spectrum was also measured using the spectrophotometer by shutting off the Xe lamp. The decay curves were measured by a GFZF-2A single-photo-counter system. The thermoluminescence (TL) spectrum was measured with a FJ-427A1 thermoluminescence reader and analyser system. For the TL glow curve measurements, the heating rate was 1°C/s and the range of the measurement is from room temperature to 300°C. A delay for 3 min was used between the irradiation and measurement. All measurements were carried out at room temperature except for the TL spectrum. Electron paramagnetic resonance (ESR) spectra were recorded with an X-band spectrometer (Bruker A300) at 100K before and after irradiation by a xenon lamp. The afterglow images were recorded with a classic Reflex digital camera (Nikon camera) with the same exposure time.

The representative XRD pattern of La₃GaGe₅O₁₆: Tb³⁺ is shown in Fig. 10 in the Appendix. Our calculations were based on DFT within the generalized gradient approximation (GGA) [26] combined with the projector augment wave (PAW) method as implemented in VASP code [27,28]. The valence configurations of O, Ga, Ge, and La were 2s²2p⁴, 4s²4p¹, 4s²4p², and 5d¹6s², respectively. A plane-wave basis set with an energy cutoff of 400eV was adopted. Considering the size of the cell used (Fig. 11 in the Appendix), a 3 × 2 × 1 monkhorst-Pack k-point mesh was used for integrations over the Brillouin zone. The ionic positions were fully relaxed until the residual force acting on each ion was less than 0.01eV/ Ǻ. The calculated crystal structure was optimized based on the experimental data, as shown in (see Fig. 12 in the Appendix). The optimized lattice parameters are a = 4.827 Å, b = 8.090 Å, c = 15.707 Å, α = 90.76°, β = 94.01°, and γ = 90.01°, respectively, in good agreement with the experimental results. Test calculations show that the energy difference to be within 0.2 eV by using 150- and 450-atom supercells for one sample. Therefore, oxygen vacancies were simulated by removing one O atom from a 150-atom supercell with periodic boundary conditions, corresponding to the defect concentration of 1% for oxygen vacancies.

3. Results and discussion

3.1 Color tuning of persistent luminescence

The photoluminescence properties of La₃GaGe₅O₁₆:Tb³⁺ were not discussed in detail, but the excitation and emission spectra were presented (see Fig. 13 in the Appendix). As shown in Fig. 2(a), La₃GaGe₅O₁₆:Tb³⁺ gives a combined parts including the host emission and the Tb³⁺ characteristic emission. Thus, we can tune the persistent luminescence by changing the Tb³⁺ doping concentration. In our previous work, La₃GaGe₅O₁₆ is proved to be a new self-activated luminescent host [21]. From Fig. 2, we can see that the host emission decreases with the increasing doping content of Tb³⁺, indicating that energy transfer from the host to Tb³⁺ ions occurs but it is inefficient. As the result of the different doping content, the persistent luminescence is observed to vary from cyan to green as shown in Fig. 2(b). We also give the persistent emission spectra of La_3(1-x)GaGe₅O₁₆:xTb³⁺ as a function of the afterglow time (see Fig. 14 in the Appendix).

 

Fig. 2 (a) the persistent luminescence of La_3(1-x)GaGe₅O₁₆:xTb³⁺ with different doping concentration (x = 0.1%, 0.2%, 0.3%, 0.5%, 1.0% and 1.5%) measured immediately after stopping the light source (excitation slit Δλ = 10 nm, emission slit Δλ = 10 nm); (b) CIE chromaticity coordinates of the Tb³⁺-doped samples.

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3.2 Phosphorescence properties

Usually, the thermoluminescence (TL) method is considered as an efficient tool to probe the traps, such as the evaluating for the depth and density of traps in host material [29,30]. Clearly, knowing the depth and density of traps is crucial when trying to understand the mechanism of persistent luminescence, and when developing new afterglow materials. To gain insight into the trapping and releasing processes involved in the persistent phosphor La₃GaGe₅O₁₆:Tb³⁺, we conducted a series of TL measurements by varying the delay time after the excitation and the thermal cleaning temperature. The TL curves of a typical sample La₃GaGe₅O₁₆:0.015Tb³⁺ at different delay times (t = 0.5, 1, 3, 5, 7 and 10 min) are shown in Fig. 3(a). Obviously, the TL bands have a large shift from lower temperature to higher temperature with the elapse of time. It is caused by the lacking of low-temperature tail because the charge carriers escape from shallower traps much faster than that in deep ones. In addition, it reveals that TL band is composed of a series of traps with continuous distribution and close depths. With the longer time, the depth of predominated TL band becomes deeper and deeper.

 

Fig. 3 (a) TL glow curves of La_2.99GaGe₅O₁₆:1.0%Tb³⁺ measured by varying the delay time ; (b) TL glow curves by preheating the La_2.99GaGe₅O₁₆:1.0%Tb³⁺ sample at the different thermal cleaning temperature; (c) Initial rise analysis of the corresponding TL glow curves; (d) Trap depth distribution of La_2.99GaGe₅O₁₆:1.0%Tb³⁺ sample.

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To further probe the energy distribution of traps, it is imperative to vary the preheating temperature at which the sample is excited. If a phosphor is excited at a higher temperature with a continuous trap depth distribution, only deeper fractions of the traps are filled. The shallower traps are immediately bleached due to the increased thermal energy available. TL glow curves of La₃GaGe₅O₁₆:0.015Tb³⁺ sample were collected after preheated at different preheating temperature in Fig. 3(b). This sample was first irradiated for 1 min at 300K and then heated to a certain temperature (T_stop) to partially clean the occupied traps. From Fig. 3(b), the gradual deepening of the trap depth for increasing T_stop proves the presence of a continuous trap distribution in La₃GaGe₅O₁₆:Tb³⁺ phosphor.

An initial rising method, proposed by Van den Eeckhout et al [31,32], is further applied to the measured TL curves to uncover how the trap depth of La₃GaGe₅O₁₆:Tb³⁺ phosphor distributes [32]. Briefly, this method for estimating trap depths starts from a assumption that the concentration of trapped electron on the low-temperature side of the TL curves remains relatively constant; only a tiny fraction of the charge carriers can escaped under the small amount of thermal energy available. Thus, the TL intensity (I(t)) can be approximately expressed as:

Figure 4 gives the TL glow curves of La_2.99GaGe₅O₁₆:0.01Tb³⁺ synthesized under different synthesis atmosphere (5%H₂ + 95%N₂, 100% N₂, vacuum and the air). For comparison, TL glow curve of La₃GaGe₅O₁₆ host was also given. As a rule, each TL peak stands for a kind of trapping center and the relative trap density or trapping capacity is roughly proportional to the integral TL intensity [33–35].Compared the TL curves between La_2.99GaGe₅O₁₆:0.01Tb³⁺ and La₃GaGe₅O₁₆ host (which were prepared in air), we infer that intrinsic defects might play main role in the persistent luminescence because TL curve of Tb³⁺-doped La₃GaGe₅O₁₆ is similar to that of La₃GaGe₅O₁₆ host. For further prove our speculation, we made a comparison about the TL curves of La_2.99GaGe₅O₁₆:0.01Tb³⁺ synthesized in a vacuum and air, and found the persistent performance prepared in the vacuum is much superior to that in air. Thus, oxygen vacancies might be considered as candidates for the lattice defects in La₃GaGe₅O₁₆ host under high-temperature annealing conditions. If it is true in the case of La₃GaGe₅O₁₆ phosphor, a better persistent performance of La₃GaGe₅O₁₆:Tb³⁺ phosphor can be expected in a reducing atmosphere. Therefore, we tried to synthesize the La₃GaGe₅O₁₆:Tb³⁺ phosphors under the reducing flowing gas atmosphere (5%H₂/95%N₂) to improve the phosphorescence performance. From Fig. 4, we can see the integral TL intensity of La₃GaGe₅O₁₆:Tb³⁺ synthesized in the reduction atmosphere (5%H₂ + 95%N₂), is the largest compared with other two samples, suggesting this sample presents the best performance in the persistent luminescence. The reason for this is that the traps might be closely related with the oxygen vacancies (V_O). In other word, V_O can be developed helpfully when La₃GaGe₅O₁₆:Tb³⁺ was prepared in the reduction atmosphere (5%H₂ + 95%N₂), however V_O is suppressed partially when in an oxygenated atmosphere (the air). This is why La₃GaGe₅O₁₆:Tb³⁺ samples synthesized at different atmosphere give the different behaviors in persistent luminescence. Thus, a conclusion might be made that the trapping center probably originates from the intrinsic defects not the extrinsic defects. Both the position and the shape of TL curves are the same besides the intensity of the TL curves. The role of the doping Tb³⁺ ions might be dual, as they can modify the intrinsic defects or enrich the instinct defects in the host and sever as luminescent centers as well. So, the integral TL intensity of La₃GaGe₅O₁₆:Tb³⁺ samples are higher than that of La₃GaGe₅O₁₆ host.

 

Fig. 4 TL glow curves of La₃GaGe₅O₁₆:Tb³⁺ synthesized at different atmosphere (a:5%H₂ + 95%N₂, b: 100% N₂, c: the air and d: vacuum).

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By adjusting the Ge/O content ratio slightly, we aim to prolong the afterglow time and intensity of the La₃GaGe₅O₁₆:Tb³⁺ by modifying composition around Tb³⁺, since the intrinsic traps of host probably play an important role in the persistent luminescence. Thus, we prepared a series of Tb³⁺-doped La₃GaGe_5+xO_16+4x (−0.05≤x≤0.05) samples in the reduction atmosphere (5%H₂ + 95%N₂). The XRD patterns of La₃GaGe_5+xO_16+4x (−0.05≤x≤0.05) samples were presented (see Fig. 15 in the Appendix), proving that small Ge/O content deficiency can still maintain the crystal structure intact. The persistent luminescence and afterglow times of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05) are presented in Fig. 5(a) and 5(b). From Fig. 5(a) and 5(b), one can see that Ge/O content deficiency benefits to improve the persistent luminescence and afterglow time, whereas these samples, a composition of Ge/O content excess, exhibit poorer afterglow properties. This one aspect demonstrates the persistent luminescence of La₃GaGe₅O₁₆:Tb³⁺ is closely related to the intrinsic defects in host. Thus, we can make a assumption that composition with slight Ge/O content deficiency is of importance for La₃GaGe₅O₁₆:Tb³⁺ to enrich the traps concentration. In order to further prove our proposed assumption, the TL glow curves of La_2.99GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05) were measured. As shown in Fig. 5(c), the integral intensity of TL glow curves gives a trend of increasing as the value of x decreases, indicating that composition of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ samples with slight Ge/O content deficiency contributes to enriching the traps concentration. Furthermore, new TL bands peaked in the higher-temperature region were detected when the Ge/O content is deficient. However, this is only the first insight. A detailed analysis of the TL curves should adopt the deconvolution method based on the Gaussian equation. Thus, a good agreement between the experimental and calculated glow curves was obtained by using the above method. As shown in Fig. 5(d), the TL glow curve of La_2.99GaGe_4.95O_15.2:0.01Tb³⁺ consists of three bands located at 345K, 393K, and 420K. By comparing the TL curves of La_2.99GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05), the TL band located at 345K should be attributed to the trapping center of oxygen vacancies. The other TL bands located at 393K, and 420K are so weak that they can make a little contribution for the persistent luminescence; and these two new TL bands might be caused by the new oxygen vacancies because there are various types of bridging oxygen in La₃GaGe₅O₁₆ host, as illustrated in Fig. 1.

 

Fig. 5 (a) The emission images of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05) recorded by a classic Reflex digital camera with the same exposure time varying with the different afterglow time (t = 0.5, 3, 5, 10 and 15 min); (b) the afterglow curves of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05) samples; (c) TL glow curves of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ (−0.05≤x≤0.05) sample (Irradiation time: 2 min; delay time: 3 min and heating rate:1°C/s); (d) deconvolution of the TL glow curve of the La₃GaGe_4.95O_15.20:0.01Tb³⁺ sample.

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3.3 Defects and traps

As far as we know, effects, either intrinsic or extrinsic defects or both of them, play important roles in energy storage of persistent luminescence. Therefore, understanding of defect properties is indispensable for further development and applications of certain potential persistent phosphors. In order to distinguish between the extrinsic and intrinsic defects, further investigation of trap types should be the key to unlock the puzzle. Figure 6 gives the ESR spectra of La₃GaGe₅O₁₆ host and La₃GaGe₅O₁₆:0.01Tb³⁺ sample before and after irradiation measured at 100K. A sharpening signal at g = 3.9176, g = 3.6985 (Trap І) and a weak one at g = 1.9588 (Trap П) were detected after irradiation, in contrast to a lack of signal before irradiation in the inset of Fig. 6.The width and constriction of the signals remain practically unchanged between La₃GaGe₅O₁₆ host and La₃GaGe₅O₁₆:0.01Tb³⁺ sample. This implies that nothing is changed in the trap types and also means the doping Tb³⁺ ions don’t induce the extrinsic defects or traps. These two signals are attributed to oxygen vacancies [37–39]. Except for the signals of oxygen vacancies, others signals were not observed in Fig. 6. Thus, it is proved that oxygen vacancies are considered as candidates for the lattice defects in La₃GaGe₅O₁₆ host. The intensity of the EPR signal varies obviously between them, confirming the assumption we proposed in above section that the doping Tb³⁺ ions can modify the intrinsic defects or enrich the instinct defects in the host. Thus, the role of the extrinsic defects can be overlooked in persistent luminescence, and this afterglow phenomenon probably originates from the oxygen vacancies. However, which kind of of the bridging oxygen vacancies (O) play the key role in this persistent phosphor? The answer comes upon total-energy calculations (see the following section).

 

Fig. 6 The trap types: EPR spectra of La₃GaGe₅O₁₆ host and La₃GaGe₅O₁₆:0.015Tb³⁺ sample recorded at 100K after irradiation; inset show the EPR spectra of La₃GaGe₅O₁₆ host before irradiation.

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3.4 Electronic structures

Understanding the electronic structures of the host material and its lattice defects is essential to control the carrier trapping and detrapping process in the persistent phosphors [33–35]. Before investigating the lattice defects in La₃GaGe₅O₁₆, we first studied the electronic structure of perfect La₃GaGe₅O₁₆ crystal. Calculated band structure and density of states of La₃GaGe₅O₁₆ are shown in Fig. 7(a) and 7(b). We see that La₃GaGe₅O₁₆ is an insulator with an indirect gap: the valence band maximum (VBM) composed of O 2p orbitals is at the V point and the conduction band minimum (CBM) characteristic of Ge 4s orbitals is at the Γ point; the band-gap energy was calculated to be 3.2002 eV. In order to compare this with the experimental band gap values, we calculated the measured value of 4.352 eV for La₃GaGe₅O₁₆ host based on the diffuse reflection spectrum (see Fig. 16 in the Appendix). The obtained value for La₃GaGe₅O₁₆ is 4.352 eV. This value is actually the optical gap rather than the electronic band gap. Considering the uncertainty of the experiment, the actual electronic band gap is expected to be less than 4.352 eV. Compared with the experimental value, our calculated GGA Kohn-Sham band gap (3.2002 eV) is around 2/3 of the experimental values, which falls into the error range of GGA calculations. The band structure is composed of six parts (P₁-P₆), P₁, P₄ and P₅ is considered as O 2s and Ga 3d, La 5p and Ge 3d semicore states, respectively, showing localized (nonbonding) character, whereas P₅ and P₆ consist of the hybridized Ge 4s4p, La 5p5d, Ga 4s4p and O 2p states. The hybridization separates the bonding states below the VBM and the antibonding states above the CBM. The bonding states of Ge-O are located at the lowest energy range relative to that of Ga-O and La-O, indicating that the Ge-O constituent has a largest contribution to the cohesive energy of La₃GaGe₅O₁₆.

 

Fig. 7 (a) Computed band structure, density of states (DOS); (b) momentum projected local density of states (PDOS) for La₃GaGe₅O₁₆ (Zero of energy is set at the Fermi level.

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3.5 Energy band structure of V_O

As well defined by Freysoldt et al [26], the defect formation energy of a neutral defect E^f[defect] depends on the atomic chemical potential μ_i: E^f[defect] = E_tot[defect] − E_tot[host] + ${\displaystyle \sum _{}{n}_i{\mu }_i}$. Here, E_tot[defect] is the total energy of a supercell containing the defect, E_tot[host] is the total energy of the defect-free supercell, n_i indicates the number of atoms of type i that have been added to (n_i<0) or removed from (n_i>0) the supercell when the defect is created. To compare the formation of the same kind neutral defects, it suffices to know the difference between E_tot[defect] and E_tot[host]. For this reason, we can discuss the stability of O₁~O₅ in terms of their total energies. However, since the values of the total energy lacks physical meaning, we have replaced the absolute total energies of O₁~O₅ in Table 1 with the relative values with respect to the perfect supercell (i.e. E_tot[V_O] − E_tot[La₃GaGe₅O₁₆]) (these supercells with different relaxed vacancy defect are presented (see Fig. 17 in the Appendix).

Table 1. The calculated total energy difference between the supercell containing one relaxed oxygen vacancy in La₃GaGe₅O₁₆ and the perfect supercell.

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One can see that the O₄ has the lowest ∆E, suggesting that as the intrinsic traps, O₄ is the most possible formed and one of the potential sources that explain the persistent luminescence in La₃GaGe₅O₁₆:Tb³⁺. But by contrasting the O₃ and O₄, the energy differences between O₃ and O₄ is only 0.01eV. Except for O₄, therefore, O₃ should contribute to the persistent luminescence of La₃GaGe₅O₁₆:Tb³⁺ phosphor as well. In fact, even for O₁, O₅, the differences with O₄ are only about 0.15 eV and 0.17 eV, respectively. At the same time, it can explain why the trap distribution in La₃GaGe₅O₁₆:Tb³⁺ phosphor is continuous ranging from 0.69eV to 0.75eV in theory.

Our focus in this section is to study the defect states associated with oxygen vacancies. According to the explanations by Freysoldt et al [26], the Kohn-Sham levels that result from a band structure calculation for a defect cannot directly be identified with the defect levels that are of experimental relevance, because the experimental levels involve transition between different charge states of the defect. In view that the calculations of defect in different charge states are of a demanding work, we just discuss the relevance of the Kohn-Sham levels of the defect states with the optical levels qualitatively.

Band structure calculation in Fig. 8 shows that the neutral O vacancy introduces an s-like deep donor level (a₁) close to the VBM. Its two unpaired electrons can be easily ionized. So the neutral O vacancy (V_O⁰) is not stable, and it can be ionized in 2 + charge state (V_O²⁺). Besides, the neutral O vacancy can also introduce another dispersive empty band that is continuous with the conduction band within 1eV below the CBM. Such empty states distributed a wide energy range are considered to contribute to prolonging the afterglow decay time [40,41]. We then study the relevance of the energy distribution of these empty states with the trap depth measured from the thermoluminescence glow curves. The measured trap depth is in the range of 0.69~0.75 eV for La_2.99GaGe₅O₁₆:0.01Tb³⁺, which falls into the ideal trap depth (0.6~0.8 eV) for the electron detrapping at room temperature. Nevertheless, the trap depth obtained from the Kohn-Sham levels is ~1eV, which appears somewhat deeper than the experimental value. This difference reflects that the Kohn-Sham levels should be corrected to compare with experiments. We illustrate the following simplified picture of the correction [26,42], as shown in Fig. 9. Under UV light excitation, the two electrons in the a₁ state of V_O⁰ are trapped at the V_O²⁺ center. The equilibrium configuration of the V_O²⁺ state is E_g − ε_a1 higher than the equilibrium configuration of V_O⁰ − 2e, where ε_a1 is the Kohn-Sham level of the a₁ state. Electrons at the V_O²⁺ center can then recombine with the holes on the V_O⁰ center, leading to emission of a photon with energy E_PL. However, during this emission process, the atomic configuration remains fixed in the 2 + charge state. The difference between the energy of this configuration and that of the equilibrium configuration of V_O⁰ is the relaxation energy E_rel (Frank-Condon relaxation). From Fig. 9, it is clear that E_PL = E_g −ε_a1 − E_rel. Since the optical level of the a₁ state ε_a1^opt is defined as the energy difference between the band gap and the PL line, we find that ε_a1^opt = E_g − E_PL = ε_a1 + E_rel, i.e. ε_a1 = ε_a1^opt − E_rel. This means that the Kohn-Sham level of the a₁ state should be smaller than the optical measurements by an amount of E_rel. When such correction in terms of E_rel is applied to the a₁ level, the other dispersive empty defect band levels will be shifted upward accordingly. Therefore, the resulting trap depth obtained from the Kohn-Sham levels should be shallower than the former ~1eV (below the CBM), and thus more close to the experimental value.

 

Fig. 8 Computed band structure of La₃GaGe₅O₁₆ host and La₃GaGe₅O₁₆ + V_O4 (a: the Fermi level is set to 0 eV; b: the hole energy level above the VB is set to 0 eV).

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Fig. 9 A simplified picture of Frank-Condon shift in the case of V_O.

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4. Conclusion

In a word, we tuned the persistent luminescence color by changing the Tb³⁺ concentration, and the persistent color can be tuned from cyan to green. The afterglow time and intensity of La₃GaGe₅O₁₆:Tb³⁺ can be prolonged and enhanced in a poor-oxygen atmosphere (5%H₂ + 95%N₂). Furthermore, the performance of persistent luminescence La₃GaGe₅O₁₆:Tb³⁺ can be improved by adjusting the Ge/O content to modify composition around Tb³⁺ ions. In order to reveal the nature of persistent luminescence, the electronic structures of La₃GaGe₅O₁₆ host and V_O4 were calculated based on the first-principles, indicating that the suitable impurity levels from V_O4 cannot only trap carriers but release the trapped carriers through activation. This study gives us some hints that the materials, like La₃GaGe₅O₁₆, are rich in the bridging oxygen and could be the potentially suitable for RE³⁺-doped long persistent phosphors; the samples synthesized in the poor-oxygen atmosphere probably exhibit more excellent long persistent phosphorescence. At last, we hope insights obtained from this paper can offer us a guiding principle for the selection of the host and the luminescent center for the design of RE³⁺-doped persistent phosphors.

Appendix

 

Fig. 10 The XRD patterns of La₃GaGe₅O₁₆: xTb³⁺ (x=0, 0.1%, 0.3%, 0.5% and 1.0%).

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Fig. 11 Unit cell of La₃GaGe₅O₁₆ ( centrosymmetric point: Г(0, 0, 0)　Z(0, 0, 0.5) Y or F (0, 0.5, 0) X or B (0.5, 0, 0) V(0.5, 0.5, 0) U(0.5, 0, 0.5) T or Q (0, 0.5, 0.5) R(0.5, 0.5, 0.5).

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Fig. 12 Experimental (a) and calculated (b) crystal structure of La₃GaGe₅O_16.

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Fig. 13 Excitation and emission spectra of La_2.99GaGe₅O₁₆: 0.01Tb³⁺ sample.

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Fig. 14 The persistent emission spectra of La_3(1-x)GaGe₅O₁₆:xTb³⁺ as a function of the afterglow time.

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Fig. 15 XRD patterns of La₃GaGe_5+xO_16+4x:0.01Tb³⁺ (-0.05≤x≤0.05) samples.

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Fig. 16 UV-visible diffuse reflection spectrum of undoped La₃GaGe₅O₁₆ ; the inset gives the relationship between ${(F(R_{\infty })h\nu )}^2$and hv.

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Fig. 17 (a) the perfect compound La₃GaGe₅O₁₆;(b-f) presents the different crystal structures after relaxation with different oxygen vacancies such as V_O1, V_O2, V_O3, V_O4 and V_O5.

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Acknowledgments

This work are supported by the National Natural Science Foundation of China (No. 21471038).

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