Charge deformation and orbital hybridization: intrinsic mechanisms on tunable chromaticity of Y3Al5O12:Ce3+ luminescence by doping Gd3+ for warm white LEDs

theoretical calculation on band structure anddensity of state

To gain insight into the intrinsic mechanisms of YAG: Ce luminescence upon substitution of Y^{3 +} by gd^{3 +}, the electronic band structure anddensity of state were firstly investigate by way of theoretical calculation . Four typical BS is doped , dos andpdos of the pure YAG host andYAG dope with Ce^{3 +} anda variant amount of gd^{3 +} are presented in Fig. 1, which shows that the band gap of YAG becomes narrow after doping with Ce^{3 +} andgd^{3 +}. The calculated band gap of the pure YAG host is 6.505 eV, which is consistent with the value of approximately 6.5 eV evaluated by the photoconductivity method²⁸ andthe absorption peak at 188 nm determined using spectra method²⁹; andthe band gaps of (Y_2.94Ce_0.06)Al₅O₁₂, (Y_0.75gd_0.25)₃Al₅O₁₂ and(Y_0.25gd_0.75)₃Al₅O₁₂ are approximately 6.358, 6.206 and6.071 eV, respectively. The PDOS in Figs 1(b,d) shows that the top edge of the valence band mainly consists of the O 2p orbital andthe bottom edge of the conduction band mainly consists of the 3d orbital of Y. However, Figs 1(f,h) indicate that the O 2p orbital makes a great contribution to form the conduction band andthe d orbitals (including Y 4d andgd 5d orbitals) contribute significantly to the valence band after doping with gd^{3 +}. This conclusion suggests that the d orbital may hybridize with O 2p orbit intensively after doping with gd^{3 +}, further confirmed as follows. The 4f orbital also contributes significantly to the valence band in Figs 1(f,h), but the 4f lies in a deep energy level. In contrast to Figs 1(a,e andg) show that the state density in the conduction band increases intensively as Y^{3 +} is replaced with more andmore gd^{3 +}; moreover, the bandwidth of the valence band enlarges significantly with increasing gd^{3 +}. The energy scales of electron spread in the conduction band are approximately 6.5–8.6, 6.2–10.0 and6.0–12.42 eV, respectively, for x = 0, 0.25 and0.75 of (Y_1−xgd_x)₃Al₅O₁₂. The expansion of the conduction bandwidth suggests the extensibility of the atomic orbitals, which consist of the band broadening, the reduction of effective mass of the electron andcrystal field intensification. Meanwhile, the electrons will have a larger non-localization. The calculations on BS, DOS andPDOS come to the following conclusions: (1) crystal field strength increases, (2) band gap narrows, (3) the effective mass of the electron reduces and(4) the non-localization expands, as consequences of gd^{3 +} doping . These effects is affect will inevitably affect photoluminescence .

photoluminescence property of ( Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}

Figure 2 presents the emission spectra of (Y_1−xgd_x)_2.94Al₅O₁₂: 0.06Ce^{3 +} (x = 0, 0.1, 0.3, 0.5, 0.7 and0.9) under the excitation of 460 nm at room temperature, which shows that the luminescence intensity decreases andthe emission peak red shifts along with increasing gd^{3 +}. As the x value increases from 0 to 0.9, the peak of the emission band shifts from approximately 543 to 575 nm, but the shift is negligible as x changes from 0.5 to 0.9, which can be discriminated more clearly by combining with the normalized emission spectra displayed in supplementary Fig.1. The intensity of luminescence decreases continuously with increasing gd^{3 +}, but it decreases rapidly as x varies from 0.5 to 0.9. A quantitative assay shows that the luminescence intensity, achieved by integrating from 480 to 750 nm in emission spectra, decreases approximately 5.5% and23.4% with x ranges from 0 to 0.5 and0 to 0.9 (as the red line presented below in Fig. 3 indicates), respectively.

The excitation spectra of (Y_1−xgd_x)₃Al₅O₁₂: Ce, obtained by monitoring the strongest emission, are shown in Fig. 4. In addition to a minor neighbourhood maximum at 372 nm, two main excitation band peaks at approximately 460 and340 nm are observed. The Ce^{3 +} has [Xe]4f¹ electronic configuration, the excitation andemission of which originates from the 4f¹ to 5d¹ transition. Because of the shielding by the outer 5s and5p orbitals, the 4f electron is insensitive to the crystal field. However, the 5d electron interacts strongly with the crystal lattice, resulting in strong phonon coupling andlarge crystal field effects on the excited states. In the crystal lattice of Y₃Al₅O₁₂, the Ce^{3 +} which is substitutes substitute for Y^{3 +} in the site of d₂ symmetry is has has 8 near neighbour oxygen atom . The eightfold coordination of Ce^{3 +} in the dodecahedral site can be describe as a cubic coordination with an additional tetragonal distortion . accord to the ligand field theory , the 5d state is split will split into a low energy 5d_e-doublet state (²E_g) anda higher 5d_t-triplet state (²T_g) in tetragonal field²⁵. All five possible 5d-state energies of Ce^{3 +} should be observe in the excitation spectrum , but all five level were never unambiguously assign^29,30. Tanner et al. confirmed the existence of the two excitation bands located at 342 and467 nm using the room-temperature Xe-lamp excitation spectra andfurther revealed another band of Ce^{3 +} at 225 nm as well as the YAG host band at 188 nm using the synchrotron radiation excitation spectra²⁹. Thus , the two excitation band at 460 and340   nm in Fig . 4 could be attribute to the 4f–5d₁ and4f–5d₂ transitions, respectively.

The 4f-5d transition of Ce^{3 +} emission with asymmetric broadband configuration in Fig. 2 consists of doublet sub-emissions from 5d₁ to ²F_2/7 and5d₁ to ²F_5/2, because the ground state of Ce^{3 +} consists of ²F_2/7 and²F_5/2 sublevel after consider the spin – orbit interaction^19,29. The minor band with a peak at approximately 372   nm ( 26880   cm⁻¹) in Fig . 4 was report in the literature^{21,23,24,25,31,32,33,34,35,36,37,38,39,40} but was not apparent in other study^{16,18,19,20,25,28,29,30}. Gracia calculated the absorption andluminescence spectra of Ce^{3 +} doped YAG using an ab initio embedded cluster approach andconcluded that a small peak at 372 nm is not due to Ce^{3 +} ion⁴¹. Zeng is attributed attribute this band to an f – type colour centre³⁹. Through studying a YAG: Ce single crystal, grown with temperature gradient techniques (TGT), by means of thermal annealing in a H₂ andO₂ atmosphere combine with different dose of gamma irradiation , Dong is demonstrated further demonstrate that it was a type of F⁺-type colour centre³².

Both the intensity of 4f-5d₁ excitation at 460 nm andthe excitation of 4f-5d₂ at 340 nm in Fig. 4 decrease with an increase of the x value, which is helpful to illustrate the luminescence decrease in Fig. 2. After normalizing the strong excitation to 1.0, however, the supplementary Fig. 2 shows that the relative excitation intensity of the band at 340 nm increases as x increases from 0 to 0.5 andthen decreases as x increases onward to 0.9. This phenomenon puts forward an interesting topic regarding the relative distribution of electrons on different energy levels; this population usually obeys the Fermi-Dirac distribution function (seen below Equation (6)), depending on the energy barrier andtemperature.

As x increases from 0 to 0.9, the band of 4f-5d₁ excitation shift towards long wavelength whereas that of 4f-5d₂ shifts towards shorter wavelengths, as shown in Fig. 4. This phenomenon can be seen more clearly in supplementary Fig. 2. The shift in opposite directions of two excitation bands indicates the splitting of the Ce^{3 +} 5d state enlarges with increasing gd^{3 +}, caused by the intensified crystal field. This conclusion is consistent with the above prediction of the theoretical calculation. Thus, the diagram of Ce^{3 +} energy levels andthe crystal-field splitting of 5d orbitals in (Y_1−xgd_x)₃Al₅O₁₂ could be described with Fig. 5. With more andmore Y^{3 +} replaced by gd^{3 +}, both the crystal-field splitting andStokes shift increase with an increase of the x value, as seen from the quantitative values summarized in Table 1.

table 1 The centroid of the 5d₁ and5d₂ excited states, crystal field splitting energy andthe Stokes shift within the ground state of 4f andthe lowest excited state of 5d₁ for Ce^{3 +} in (Y_1−xgd_x)₃Al₅O₁₂.

Additionally, Fig. 4 shows that the intensity of the band with a peak at 372 nm decreases step-by-step when with more andmore gd^{3 +} is doped into the YAG, suggesting the doped gd^{3 +} is helpful in remove the F⁺ centre .

Diffuse reflection andabsorption of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}

The intensity of excitation reflects the comprehensive effects of energy absorption andenergy transfer in the phosphor. To confirm that the decrease of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} luminescence upon gd^{3 +} doping was not caused by the reduced absorption, the diffuse reflection spectra were measured. As presented in Fig. 6, the two main absorption bands observed in the regions of 410–550 nm and330–370 nm, respectively, correspond to the two excitation bands of 4f–5d₁ and4f–5d₂, previously show in Fig . 4 as well . The spectral shift of the 4f–5d₁ and4f-5d₂ absorption bands in two opposite directions were also observed. Differing from the excitation spectra displayed in Fig. 4, both the absorption intensity of 4f–5d₁ andthe absorption of 4f–5d₂ increase as gd^{3 +} concentration increases from x = 0.1 to 0.9. In addition, Fig. 6 shows that the relative diffuse reflection intensity (including background) decreases as gd^{3 +} increases from x = 0.1 to 0.9 in the full wavelength range of 300 to 800 nm, except for the absorption of F⁺ centre . With the background intensity of diffuse reflection normalized to 1.0, as shown in supplementary Fig. 3, the conclusion that absorption intensity increases with gd^{3 +} hold true . Therefore , the decrease of ( Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} luminescence upon doping with gd^{3 +} is not caused by the reduced absorption.

It must be note that the excitation intensity of 4f-5d₁ is far strong than that of 4f-5d₂ in Fig. 4; however, the relative absorption intensity of 4f-5d₂ is much strong than that of 4f-5d₁ in Fig. 6. The difference between the absorption area in Fig. 6 andthe excitation area in Fig. 4 suggests most of the absorption energy of 4f-5d₂ is lost without emission. This phenomenon indicates that the transition of 4f-5d₂ has a strong ability to absorb incident photon , but only a fraction of them convert to visible light . The energy loss of the 5d₂ state may be caused by the transition from 5d₂ to the conduction band, as discussed below.

Figure 7(a) plots the normalized emission andexcitation spectra of (Y_1−xgd_x)_2.94Al₅O₁₂: 0.06Ce^{3 +}. Partial enlarged detail showing the crossover of the emission andexcitation spectra with different amounts of gd^{3 +} is presented in Fig. 7(b), which shows that the crossover shifts towards longer wavelengths as x value increases from 0 to 0.9. According to the coordination-configuration theory, the energy loss of the non-radiative transition from the excited state to the ground state is proportional to the integral of the emission andexcitation spectra, i.e.,

where the f_ex(x) andf_em(x) denote the wave functions of the emission andexcitation spectra, respectively. However, the overlapping area below the curves of the emission andexcitation spectra for each sample decreases with an increase of the x value. Therefore, the nonradiative transition of electrons relaxed from the 5d₁ excited state through the crossover of the potential parabola curves to the 4f ground state is not the main mechanism of energy loss.

thermal stability luminescence of ( Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}

Chromaticity shift andluminescence quenching upon temperature changes are unfavourable for a phosphor applied in white LEDs, thus the thermal stability of luminescence should be carefully examined. The emission andexcitation spectra measured at various temperatures of one typical sample with the maximum x = 0.9 for (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} is provided in Fig. 8, which shows that excitation andemission intensity decrease rapidly with an increase of temperature. The relative luminescence intensities, achieved by integrating from 480 to 750 nm andwith the intensity of each sample luminescence at room temperature normalized to 100%, of samples with x = 0, 0.3, 0.5. 0.7 and0.9 for (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} as function of temperature are presented in supplementary Fig. 4. This shows that the relative intensity decreases more andmore along with increasing gd^{3 +}. As the temperature increases from room temperature to 125 °C, the relative intensity of the YAG: Ce decreases approximately 4%, but (Y_0.1gd_0.9)_2.94Al₅O₁₂: 0.06Ce^{3 +} luminescence decreases approximately 64%. According to configuration coordinate theory, a heavy weight should benefit in resisting thermal vibration andreducing phonons andaccordingly the thermal stability of YAG: Ce luminescence should enhance with gd^{3 +} doping. An evident spectral shift of YAG: Ce emission upon a change in temperature has been observed with andwithout a small amount of gd^{3 +} doping, as seen from Fig. 5 in reference¹⁹. However, with a large amount of gd^{3 +} doping, as in this work, no spectral shift upon temperature change is observed in the emission spectra of (Y_0.1gd_0.9)_2.94Al₅O₁₂: 0.06Ce^{3 +}, as presented in Fig. 8 andthe spectra with normalized intensity are displayed in supplementary Fig. 5.

Figure 8

Emission andexcitation spectra of (Y_0.1gd_0.9)_2.94Al₅O₁₂: 0.06Ce^{3 +} at various temperature .

In configuration coordinate theory, the spectrum either red shifts (due to coupling with phonons) or blue shifts (when transiting from a low energy level to a high one by coupling with phonons to give light). Here, no spectral shift but a serious decrease of luminescence occurs, which should be caused by the ionization of electrons from excited states to the conduction band (as discussed below). Moreover, the non-shift of emission suggests that doping gd^{3 +} into YAG: Ce makes the structure more rigid than it was previously. Both the luminescence decreases andthe spectral non-shift behaviours upon temperature change are out of the range that the configuration coordinate diagram model can explain. The red shift of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} emission as function of gd^{3 +} concentration at room temperature could be interpreted according to the intensified crystal field, but what mechanism has resulted in the increase of crystal field strength deserves more study. To explore these mysteries, the electronic andcrystal structures were examined.

Electronic structure andthe mechanism of spectra shift

It is well known that the XANES spectra reflect the unoccupied density of states restricted by the dipole selection. Thus, XANES spectra could give us information on the geometric andelectronic structure of the chemical bonding situation andthe effective charge density around the X-ray-absorbing atoms. Because the low concentration of Ce^{3 +} was out of the sensitivity of the instrument, the XANES spectra monitoring the gd^{3 +} L₃-edge were preferentially measured. The sharp lines presented in Fig. 9(a) were caused by the electron transition from gd 2p_3/2 to outer unoccupied 5d orbital , whose absorption intensity decrease with an increase of x value from 0.3 to 0.7 for ( Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}. This point is consistent with the decrease of the main peak of the EXAFS spectra in the Fourier transformation R space in Fig. 9(b). The absorption decrease in intensity along with increasing gd^{3 +} indicates that the outer unoccupied 5d orbital is filled with more andmore electrons. figure 9(c) presents the O K-edge XANES spectra of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} (x = 0, 0.3, 0.5 and0.7), in which the sharp peak of the absorption at 532 eV is attributed to the excitation of O 1s electrons to O 2p states strongly hybridized with Y 3d or gd 4f states. The sharp peak of the absorption at 532 eV decreases continuously with an increase of gd^{3 +} concentration from x = 0 to x = 0.7, suggesting that the outer unoccupied 2p orbital of O was also filled with electrons. The presence of sharp line absorption peaks of XANES, called the Rydberg states, indicates the atomic orbitals keep well. If the molecular orbital were formed through hybridization, the Rydberg state would not be sharp andthe broadband configuration would be present. A possible reason for the unoccupied gd 5d andO 2p simultaneously filled with electrons is through orbital hybridization to a form molecular orbital.

figure 9

(a) The gd L₃-edge XANES , (b) the Fourier transformation EXAFS spectra in R space, (c) the O K-edge XANES spectra and(d) the valence band spectra of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}.

Because gd^{3 +} has smaller electronegativity than Y^{3 +}, gd^{3 +} should have a poorer ability than Y^{3 +} to hybridize 5d with O 2p in theory , but it does not practically . Ram ’s^[15] conclusion about the strong rigidity of the YAG structure with small atomic displacement parameters provides us with a useful clue to understanding this phenomenon. Because of the larger radius, gd^{3 +} ion will suffer a compressive resistance from neighbouring atoms when incorporated into the rigid crystal lattice of YAG. In the YAG crystal lattice, gd^{3 +} take the place of the Y^{3 +} site with high symmetry for its eightfold coordination. Moreover, the gd 5d orbital could spread in a large space in contrast to the Y 4d orbital due to its larger radius. Under the comprehensive effect of above factors, the strong compression effect in a high symmetric site compels the gd 5d orbital to hybridize with the O 2p orbital.

To support this viewpoint, the existence of strong compression was demonstrated firstly. As for a cubic garnet structure, the spacing d between adjacent (hkl) lattice planes obeys the relationship:

The xrd pattern of ( Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} (x = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and1.0) are presented in supplementary Fig. 6, in which all diffraction peaks can be indexed to the standard Y₃Al₅O₁₂ (JCPDS: 33-0040) when the value of x is no higher than 0.3. However, the minor phase of gdAlO₃ (JCPDS: 46-0395) is indexed as x = 0.3 to 0.9. The 2θ value of the strongest diffraction peak at the crystal planes (420) decreases with increasing gd^{3 +} from x = 0 to 0.9, as shown on the right side in supplementary Fig. 6, with an amplified range of 33–34°, indicating an increase of the crystal lattice parameter. A linear expansion of the lattice constant as function of gd^{3 +} concentration is found within x ≤ 0.3 in Fig. 3, but it increases nonlinearly when x > 0.3. Such a nonlinear curve is below the line determined with the same slope as x ≤ 0.3, indicating the measured crystal lattice constants of samples doped with gd^{3 +} are lower than the theoretical value predicted with Vegard’s law.

However, the EXAFS data could provide information about the inter-atomic distances andthe coordination. The eightfold coordination has been confirmed. figure 9(b) shows that the first neighbour shell distances in the R space of Fourier transformation EXAFS spectra of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} are approximately 1.8715, 1.9021 and1.8715 Å for x = 0.3, 0.5 and0.7, respectively. The deviations of the R values are within experimental error. Therefore, the measured data reveal that there is virtually no increase in bond length with gd^{3 +} doping in the concentration range from x = 0.3 to 0.7. However, the radius of gd^{3 +} is large than Y^{3 +}. The result indicates that the crystal lattice after gd^{3 +} doping is smaller than the ideal volume. The shrink of the crystal lattice volume suggests that the doped gd^{3 +} ion receive an intensive squeezing effect from other atoms. When more andmore gd^{3 +} is introduced into the lattice, the compressive stress will increase exponentially. Accordingly, the emission wavelength increases nonlinearly, as shown in Fig. 3, as a consequence of the intensified crystal field. The two curves, i.e., luminescence intensity andemission wavelength as function of gd^{3 +} concentrations, are nearly axisymmetric along the vertical axis. The profile of these two curves looks like a butterfly, which can be called the butterfly effect for the compression simultaneously activated on luminescence intensity andemission wavelength.

Finally, a theoretical calculation on CDD provides visual evidence regarding the change of charge distribution after doping Ce^{3 +} andgd^{3 +} into YAG. When there is no Ce^{3 +} or gd^{3 +} doped in the pure YAG host, as presented in Fig. 10(a), the charge is restricted to a certain space. The blue colour around the Al atoms indicate that they lose electrons andthe red colour around the O atoms indicate that they gain electrons. With respect to Fig. 10(a), the intensified red colour around the O atoms in Figs 10(b,c) shows that the charge density around oxygen increases, either doping Ce^{3 +} or doping gd^{3 +} into the YAG. Especially for gd^{3 +} doping, the charge density around oxygen increases significantly. Moreover, the dumbbell shape of the p orbitals around O could be discriminated in Figs 10(a,b), as the arrows indicated; however, in Fig. 10(c) they combine into one ellipsoid under the compression effect, which provides a visual picture of the deformation of the electron cloud. Not only does the charge density around oxygen intensify but also the volume of electron cloud expands after doping with gd^{3 +} andCe^{3 +}, due to the hybrid orbital. As far as the charge density around Y^{3 +} is concerned, the comparison of Figs 10(a,c) shows that the charge density around Y^{3 +} increases a little after gd^{3 +} doping. These characteristics indicate that the orbital hybridization between Y andO intensifies with gd^{3 +} doping, consistent with the result displayed in Figs 8(a,b). The electronic structure changes in turn, which can explain the BS andDOS picture presented in Fig. 1. At least, the variation of the valence band structure is observed in this experiment, as shown in Fig. 9(d).

Figure 10

Charge deformation density of Y₃Al₅O₁₂

(a) , ( Y_0.98Ce_0.02)₃Al₅O₁₂ (b) and(Y_0.75gd_0.25)₃Al₅O₁₂ (c) calculated based on DFT.

Compared with the space of electron spread in Fig. 10(a), an obvious expansion of the electron cloud around oxygen is observed in Fig. 10(b), which makes the effective Ce-O bond length shorten. According to the relationship between crystal field strength andionic bond length:

where the parameter D_q presents the crystal field stabilization energy (CFSE), R is the bond length between a central ion andligand ion, r is the mean size of the central ion andZ is the charge of a central ion. Thus, the shorter bond length implies the stronger crystal field strength. Accordingly, the 5d state will have a larger split after doping with gd^{3 +}, which can explain the results in Table 1.

The change of the electron cloud can explain the variation of band structure andthe density of states of YAG upon doping with Ce^{3 +} andgd^{3 +} as well . Because of the orbital hybridization , electrons is spread can spread in a large space . With the expansion of the electron cloud around O atom , the band gap of ( Y_1−xgd_x)₃Al₅O₁₂ becomes narrow andthe density of states becomes dense. The intensified crystal field will reduce the effective mass of the electrons andmake them move easily, which will decrease the thermal stability of luminescence. In addition, the expansion of the electron cloud around oxygen makes it easy for electrons to be promoted to excited states. The electronic andcrystal structures obtained here provide insight into the photoluminescence properties.

Crystal defects andtrap depths

However, the performance of a phosphor, including luminescence efficiency andthermal stability, is closed related to crystal defects. The thermoluminescence which was considered the best tool in identifying crystal defects was used to characterize the YAG: Ce phosphor. Figure 11 shows the TSL of (Y_1−xgd_x)_2.94Al₅O₁₂: 0.06Ce^{3 +}, in which two emission bands are observed: a weak band in the range of 50–150 °C anda strong one in 125–350 °C. The peak of the weak band shifts from approximately 118 °C to 85 °C as x value increases from 0 to 0.3, accompanied by a decrease in intensity; andthen the peak almost disappears as x value increases onwards to 0.5 and0.7. However, the peak of the strong band shifts continuously with an increase of gd^{3 +} concentration, from approximately 260 °C at x = 0, via 219 °C at x = 0.3 and197 °C at x = 0.5 andfinally reaches 171 °C at x = 0.7, in addition to a continuous decrease of luminescence intensity. The thermally stimulated luminescence shows that the following processes happened: when electrons are excited to the high-energy state, some of them are captured by the defects andthen they are thermally released from the defects to the excited state, finally giving light during the transition from a high-level excited state to the ground state, as the blue line depicted in Fig. 12. Previously reports on the persistent luminescence of YAG: Ce also confirms the existence of crystal defects^42,43. The decrease in the intensity of TSL suggests the decrease of the concentration of crystal defects; andthe shift of TLS peak from high to low temperature indicates the decrease of the trap depth. Two TSL peaks indicate the existence of two types of defects in the phosphor. The order of kinetics of the glow curves was determined with the peak shape method, by calculating the symmetry (geometrical) factor:

Figure 11

Thermally stimulated luminescence of (Y_1−xgd_x)_2.94Al₅O₁₂: 0.06Ce^{3 +}.

Figure 12

The relative position of 5d₁ and5d₂ of Ce^{3 +} andthe relative depth of trap 1 andtrap 2 in the band structure of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +}.

where ω = Τ₂−Τ₁ denotes the full width of the glow peak at half its maximum height, τ = T_m−T₁ presents the low-temperature half width andδ = T₂ − Τ_m is the high-temperature half width. The values of the geometrical factor suggest that the peaks obey general order kinetics. Thus, the trap depth could be calculated using Chen’s equation⁴⁴:

where k is the Boltzmann constant andT_m is the peak temperature. The calculated data are shown in Table 2. YAG is a high-dielectric material, whose permittivity is approximately 11.7. The high permittivity indicates that a strong polarity (or dipoles) exists in the local circumstance of YAG, which will cause (Y,gd)₃Al₅O₁₂: Ce^{3 +} to have a strong surface adsorption , such as the oh stretch band observe in the infrared absorption spectra of YAG^{32,33,34,35,36,37}. The surface adsorption will change the surface energy levels andfinally affect the luminescence. Thus, we are inclined to attribute the emission in the range of 50–150 °C to the defect of surface adsorption andthe other in 125–350 °C to the F⁺ centres caused by O_h^– oxygen vacancies^32,33,34,35.

Table 2 The temperature of maxima thermoluminescence, geometrical factor andtrap depth in (Y _1−xgd_x)_2.94Al₅O₁₂: 0.06Ce^{3 +}.

Mechanisms of luminescence decrease andthermal quenching of YAG: Ce upon doping with gd^{3 +}

The population of electrons in different energy levels obeys the Fermi-Dirac distribution:

where T is the absolute temperature, k is Boltzmann’s constant, E_i is the energy of the single-particle state i andμ is the total chemical potential. With more andmore gd^{3 +} doped into the YAG, one side the band gap of (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} decrease ; on the other side , the energy splitting between 5d₁ and5d₂ expands, which makes the 5d₂ energy level of Ce^{3 +} approach the bottom of the conduction band. When the electrons are excited from 4f to 5d₁ state to produce blue light for white LED applications, assuredly certain amount of electrons will be excited to the 5d₂ state accord to the Fermi – Dirac distribution . Moreover , the population of electron in the 5d₂ state will increase with increasing gd^{3 +}, due to the reduce energy barrier between 5d₂ andthe conduction band. This mechanism can explain the phenomenon of the 4f-5d₂ absorption of Ce^{3 +} enhanced evidently in Fig. 6, but the excitation in Fig. 4 does not rise correspondingly upon doping with gd^{3 +}. Under the effect of temperature, the electrons are easily ionized from 5d₂ to the conduction band to produce photocurrent . Moreover , the electron are possibly capture by crystal defect .

The increase of gd^{3 +} concentration reduces the trap depth of crystal defects, which results in the weakly trapped electrons being easily released to the conduction band. Once the excited electrons are captured by crystal defects, they possibly delocalize to the conduction band with the help of temperature. The mechanism of thermal delocalization of electrons from crystal defects to the conduction band can explain the serious thermal luminescence quenching that occurs in Fig. 8, although a spectral shift with increasing temperature is not observed. Therefore, the auto-ionization of electrons from 5d₂ to the conduction band andthe thermal delocalization of electrons from crystal defects to the conduction band are the main mechanisms of energy loss involved in (Y_1−xgd_x)₃Al₅O₁₂: Ce^{3 +} luminescence. Although the band gaps decrease with increasing gd^{3 +}, Fig. 9(d) shows that the position of the valence band relative to Fermi level does not significantly change. Thus, the processes of energy loss andluminescence could be described in Fig. 12.