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Dopant-related electron trap states in Lu2O3:Ta
Journal of Luminescence 214 (2019) 116583
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Dopant-related electron trap states in Lu2O3:Ta
T
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Andrii Shyichuk , Eugeniusz Zych Faculty of Chemistry, University of Wrocław, F. Joliot-Curie 14, 50-383, Wrocław, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Lu2O3 Ta Thermoluminescence energy storage electron trapping calculations Meta-GGA
Electronic structure of Ta-doped cubic (bixbyite-type) lutetium oxide was analyzed using augmented plane wave with local orbitals density functional theory (DFT) calculations with meta-generalized gradient approximation (meta-GGA, mGGA) Räsänen, Pittalis and Proetto functional. Two doping sites, three oxidation states of the dopant and optional interstitial oxygen (Oi) were considered. The calculations indicate that introduction of the dopant results in energy levels below conduction band, with strong contribution of Ta 5d orbitals. The position of the levels depends strongly on the oxidation state of the dopant. Depending on the composition, two distinct electron traps with depths of 1.5–1.2 eV and 0.9–0.2 eV were revealed. Introduction of Oi at proximity of the Ta dopant results in partial overlap of the Ta-related defect states with conduction band, which makes the traps very shallow, deteriorating the electron trapping properties. In some cases, shallow hole traps can also be attributed to the Oi. The calculated traps structure is in good accord with the experimental data.
1. Introduction
spectroscopy [13]. The semi-empirical model of Dorenbos [12,18] corresponds with such mechanism of carriers trapping. In the recent papers by Zych et al. [12] and Bolek et al. [14] thermoluminescence properties of Lu2O3:Tb,Ta are discussed in details. In the thermoluminescence glow curves of the UV-irradiated samples, two strong peaks appear around 170 °C and 250 °C, while the Tmax-Tstop experiments indicate presence of some distribution of trap depths [12]. Of the three synthesis atmospheres, namely hydrogen-nitrogen mixture (forming gas), air and vacuum, the latter corresponds to the most intense thermoluminescence. It is emphasized that co-doping with Ta significantly improves thermoluminescence intensity of Lu2O3:Tb,Ta in comparison to Lu2O3:Tb. The trap depths were further analyzed using thermoluminescence experiments and optical stimulation [14]. The two main glow curve peaks were attributed to two electron traps of approximately 1.2 and 1.4 eV.
In the last fifteen years, persistent luminescence and energy storage phosphors based on cubic (bixbyite-type) lutetium oxide, c-Lu2O3 have been intensively studied via thermolumiescence (TL) experiments [1–14]. Unlike regular phosphors in which photoluminescence decays rapidly (within micro- or milliseconds) after excitation, storage phosphors can accumulate some of the excitation energy. It is hypothesized, that excited charge carriers (electrons and holes) appearing in the materials upon excitation, are then trapped at defects. It is thus spoken about electron and hole traps, the nature of which defines the capacity and time of energy storage. Traps are characterized by their depths – the energy required to release one of the carriers: trapped electrons must be raised to conduction band, while trapped holes must be promoted to valence band. Within the respective bands, the carriers can move freely and reach the recombination centre. A number of theoretical models connect the trap depths and other properties of a material to its TL glow curves [15–17]. In Lu2O3, Pr3+ and Tb3+ dopants act as hole-traps and emission centers, while d metal co-dopants such as Ti [13], Hf [10] or Ta [12,14] shape the electron trapping properties. It is assumed that electrons excited to conduction band relax to the empty d orbitals of the co-dopant cations, get captured, and can later be released under thermal or optical stimulation [11]. The assumption, however, has not been proven directly. Only in the case of Ti co-doping a solid support of such mechanism was shown by means of Lu2O3:Ti luminescence
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2. Computational approach selection We believe that estimate of the first excitation energy of a trapped electron to the conduction band is the calculated (optical) trap depth and must correspond to the experimental trap depth. Below, we refer to such (calculated) energies simply as “trap depth”, unless specified otherwise. However, when fitting thermoluminescence glow curves with equations corresponding to a certain kinetics, the trap depth is only one of the fitting parameters. There is no simple Tpeak = f(Edepth) one-variable function connecting the trap depth and the glow curve
Corresponding author. E-mail address: [email protected] (A. Shyichuk).
https://doi.org/10.1016/j.jlumin.2019.116583 Received 27 November 2018; Received in revised form 24 June 2019; Accepted 25 June 2019 Available online 26 June 2019 0022-2313/ © 2019 Published by Elsevier B.V.
Journal of Luminescence 214 (2019) 116583
A. Shyichuk and E. Zych
3. Density functional selection
peak temperature. Moreover, solid-state DFT calculations do not take thermal changes in geometry into account, which might affect the trap depths. We thus expect at least qualitative (semi-quantitative at best) correspondence between the calculated and thermoluminescence depths. Still, the calculations might come very handy in the aspects that cannot be directly measured due to very low concentration of the dopants (for instance, oxidation states and coordination geometries of the charged traps). In order to understand the nature of traps from density functional calculations, a good representation of empty (virtual) orbitals (bands) is required. Such requirement poses a certain problem. First of all, a wellknown DFT problem is underestimation of band gaps [19–24] Consequently, properties of other virtual orbitals (such as trap bands) cannot be taken as fully reliable. Additionally, some researchers believe that unoccupied Kohn-Sham (KS) orbitals make no physical sense. However, there are proofs that, given a properly constructed density, KS virtual orbitals have physical meaning [25] and are actually better approximations of excited states than Hartree-Fock virtual orbitals, lacking the unnatural sparsity of the latter [21]. For molecules, energy differences between the highest occupied orbital and the virtual orbitals are good semi-quantitative estimates of the respective excitation energies [21]. We are thus confident that if the density functional is good enough, and calculation with it results in good agreement between the calculated and the experimental band gaps, one can also reliably estimate trap depths with such a functional, from KS orbitals. Apparently, many people rely on virtual KS orbitals in their studies, even at generalized gradient approximation (GGA) [26–33] or local density approximation (LDA) [34] level of theory. Large unit cell of cubic Lu2O3 presents another limitation – GW approximation [22,35,36], exact exchange (optimized effective potential) [37], Hartree-Fock for solids and even hybrid functionals cannot be used due to unacceptably long run times of the respective all-electron calculations. For instance, our test calculation of a defect-free Lu2O3 unit cell with HSE0 functional [38] on eight CPUs did not make a single self-consistent loop in weeks. Similarly, a test G0W0 calculation did not end in about a month, with tremendous requirements of memory (about 500 GB). A solution for that could be the use of pseudopotential approaches. While ultrasoft pseudopotential [39] calculations were used in this work for geometries, they are not trustworthy for electronic structure, especially when 4f elements are in play. Calculations with norm-conserving potentials last roughly as long as all-electron calculations, thus it's better to use the latter (in order to have a less parametrized model). Projector augmented wave methods require +U correction [40,41], which renders the whole study pointless: comparing energy of the defect level which uses +U correction with energy of conduction band minimum which uses another +U correction is basically a comparison between the two parameters. For such an empirical approach, Dorenbos model [18] is much better and transparent. We, however, were looking for a way to analyze the materials from scratch, from bare positions of atoms and material composition, without empirical corrections. We thus ended up with all-electron calculations using meta-generalized gradient approximation (mGGA) RPP functional [42] as a good compromise between calculation time and quality. We did not use charge state transition levels (CSTL) [24,43,44] in this work. The reasons are discussed in the Supplemetary Information, along with some examples. Summarizing, conclusions in this paper are based on Kohn-Sham eigenvalues, and thus must be handled with care. We do compare them to experiment, but we do not expect the calculated values to match the experimental ones. Rather, we look for trends in experimental results and look for the same trends in calculated results. We thus do not compare numbers originating from different sources. We do, however, compare calculated values to each other.
The RPP functional (also referred as RPP09 in libxc [45,46]) is a modification of Becke-Johnson, BJ semi-local functional [47]. The importance of the semi-locality is explained in the Becke paper [48], where the idea to use kinetic energy density as a measure of exchange hole delocalization is presented. This aspect is particularly interesting in the context of solid state calculations, where strictly localized exchange hole (as opposed to purely delocalized bands) is considered the main source of error in band gap predictions by LDA and GGA functionals [21]. The BJ functional also uses ratio between local spin density approximation kinetic energy density and exact exchange kinetic energy density as a measure for (non)locality of exchange hole. Later, BJ functional was modified by Tran and Blaha [49] with the motivation of calculated band gap values improvement. The result was the commonly used TB-mBJ functional, in which effective portion of nonlocal exchange was controlled by a density-dependent parameter. Although it is far from perfect, the functional indeed works well for insulators, semiconductors and metals [23,50–53], indicating merits of semi-local potentials. However, TB-mBJ formulation contains two fitting parameters (system dependent, but typically used as constants), is not gauge-invariant and is not a functional derivative. Räsänen, Pittalis and Proetto used a different approach for modification of BJ functional [42], making it system-independent and gauge-invariant. Moreover, RPP is by definition a functional derivative in the framework of spincurrent DFT [54]. 4. Calculation details The oxide structure was obtained from the authors of [55]. Cubic bixbyite-type Lu2O3 (space group 206, Ia3 / Ia − 3) comprises a unit cell of 16 formula units (80 atoms). Lu atoms occupy 8 sites of C3i/S6 local symmetry and 24 C2 sites. Each site is surrounded by 6 oxygen atoms and two anion voids, which together form a distorted cube. All of the oxygen positions and anion voids are of the same local symmetry. We have considered substitution of Lu atoms of the oxide by the Ta dopant atoms in one of the Lu sites of C3i/S6 (Lu1) or C2 (Lu2) point symmetries. The corresponding structures were labeled Lu2O3:TaLu1 and Lu2O3:TaLu2, respectively. Optionally, the dopant was supplemented with an interstitial O2− in the nearest anion void. These structures were labeled Lu2O3:TaLu1,Oi and Lu2O3:TaLu2,Oi, respectively. Four structures were considered in total. The oxidation states of the dopant were controlled via total charge on the structure. In the case of the structures without interstitial oxygen, the charges were either 0, +1 or +2, corresponding to the dopant oxidation states of +3, +4 and + 5, respectively. Presence of a charge-compensating defect somewhere far away from the doping site, TaLu1 or TaLu2, was assumed and not modeled explicitly. In the case of the structures with interstitial O2− as Ta nearest neighbor, the total charges were −2, −1 or 0, corresponding to the Ta dopant oxidation state of +3, +4 and+ 5, respectively. The geometries of the structures were optimized using Quantum Espresso code [56], with Perdew-Zunger (PZ) [57] local density approximation (LDA) functional and ultrasoft pseudopotentials from GBRV group [39]. Plane wave cutoff of 40 Ry (524 eV) was used. An unpublished Lu3+ potential with 4f shell in-core was kindly provided by Kevin F. Garrity from NIST. We emphasize that cells with dopant atoms at different oxidation states were separately optimized with the respective settings, starting from the same geometry corresponding to the unperturbed crystal (except for the added dopant and Oi). Consequently, changes in the geometry due to the changes in the oxidation state were taken into account. The same goes for Lu2O3:Ta3+ and Lu2O3:Ta3+,O2−, which were modeled with both spin-polarized highspin and spin-unpolarized calculations. Next, all-electron Elk [58] code was used to calculate density of states (DOS) of the structures. Both kinds of calculations used 3 × 3 × 3 k-point grids. For the charged 2
Journal of Luminescence 214 (2019) 116583
A. Shyichuk and E. Zych
Table 1 Length of O–Ta bonds (Angstroms), according to the kind of doping. Arrows indicate spin-polarized calculations. The percentage of bond length increase due to introduction of Oi is calculated relating to the respective strictures without Oi.
O O O O O O Oi Average excluding Oi Average including Oi Increase due to Oi, % O O O O O O Oi Average excluding Oi Average including Oi Increase due to Oi, %
Ta•• Lu1
Ta•Lu1↑
Ta× Lu1
Ta× Lu1↑
Ta•• Lu1, O″i
Ta•Lu1, O″i ↑
Ta× Lu1, O″i
Ta× Lu1, O″i ↑
1.99712 1.99713 1.99712 1.99713 1.99712 1.99713
2.06325 2.06328 2.06325 2.06328 2.06325 2.06328
2.02627 2.17683 2.02627 2.17683 2.02627 2.17683
2.10938 2.10936 2.10938 2.10936 2.10938 2.10936
1.99712
2.06326
2.10155
2.10937
Ta•Lu2↑
Ta•Lu2↑ 1.98710 1.98709 2.04304 2.04304 2.14900 2.14900
Ta× Lu2↑ 2.01894 2.17122 2.05589 2.05312 2.15591 2.20107
2.09524 2.17100 2.09524 2.17100 2.09524 2.17100 1.98701 2.13312 2.11225 2.374 Ta•Lu2, O″i ↑
1.96683 1.96683 1.97887 1.97887 2.06436 2.06436
Ta× Lu2 1.99949 1.99949 2.05627 2.05627 2.16396 2.16397
2.05379 2.14333 2.05379 2.14333 2.05379 2.14333 1.93910 2.09856 2.07578 3.939 Ta•• Lu2, O″i
2.00335
2.05971
2.07324
2.10936
2.03768 2.24966 2.01120 2.02682 2.09601 2.13169 1.96642 2.09218 2.07421 3.537
2.08854 2.28706 2.04273 2.06663 2.15820 2.19457 1.99727 2.13962 2.11929 2.892
2.08699 2.14937 2.08699 2.14937 2.08699 2.14937 1.98722 2.11818 2.09947 −0.099 Ta× Lu2, O″i 2.08979 2.25329 2.06197 2.07283 2.15253 2.20214 2.01618 2.13876 2.12125 2.316
2.12575 2.16742 2.12575 2.16742 2.12575 2.16742 2.02130 2.14659 2.12869 0.916 Ta× Lu2, O″i ↑ 2.14120 2.34919 2.08182 2.09507 2.20565 2.22586 2.03576 2.18313 2.16208 2.499
groups, while the site maintains a C3 symmetry. For Lu2 site, the symmetry is C1, while all of the bonds are rather different.
cells, uniform background was used for charge compensation, which is default for both codes (i.e. cell must be effectively charge-neutral in order to make a calculation with periodic boundary conditions possible [59]). The Elk calculations used two convergence thresholds of default values: root mean square change (from last tree iterations) in KohnSham potential was required to be lower than 1·10−6 atomic units, while the change in total energy was required to be lower than 1·10−4 atomic units. The DOS calculations were peformed with Räsänen, Pittalis and Proetto RPP09 [42] meta-generalized gradient approximation (meta-GGA, mGGA) functional for exchange and PZ correlation. The detailed list of settings for both codes is given in the Supplementary Information (SI). The discussion below is based on the Elk RPP09 results. Hereafter, in figures and text, Kröger-Vink notation is used to label the defects [60].
5.2. Electronic properties It should be noted that typical DFT problem of band gap underestimation is still present in this calculations, resulting in 0 K band gap of about 5 eV, while the experimental gap at 8 K is about 6 eV [61,62]. Spin-orbit coupling was not used in the calculations, as it is not critically necessary [63], while including it would significantly enlarge CPU time and memory requirements, which are already high due to the use of mGGA. Consequently, the results are rather semi-quantitative, but nevertheless meaningful, useful and correlate quite well with the experimental data from Refs. [12,14]. Fig. 1 presents total density of states plots of the structures without interstitial oxygen. All of the plots indicate presence of states between conduction and valence bands. No such states are present in an undoped Lu2O3, which is an insulator with a well-defined gap. In Fig. 1, orange-filled parts of the peaks correspond to d-orbital electronic density inside Ta muffin-tin sphere. In other words, this is the Ta d density within a 2-bohr (~1.06 Å) radius sphere centered at Ta position. Although the code does not distinguish the orbitals by their principal quantum number during DOS calculations, only Ta 5d orbitals can be found around Fermi level, while the filled 3d and 4d states must lay at much lower energies. Consequently, the defect levels can be attributed mostly to the Ta dopant 5d orbitals. Contributions from interstitial density and Lu and O orbitals to the defect states are present. Hence, electrons trapped in such states would not fully belong to Ta 5d orbitals, some delocalization (mostly over the nearby oxygens, but also over the whole cell) is anticipated. In Figs. 1 and 2, the trap depths were measured from the defect peak centroid to the first significant peak of the conduction band (small peaks) or the peak half-maximum position (intense peaks). It is expected that trap depths measured in such a way would correspond to experimental optical trap depth.
5. Results and discussion 5.1. Structure: O–Ta bond lengths Table 1 contains length of O–Ta bonds for the studied structures, indicating several trends. For all of the structures, the bond lengths increase with decreasing Ta oxidation state – which is expected due to increasing electron density at 5d orbitals of the dopant. For the Lu2 O3 : Ta×Lu1/Lu2 samples, spin polarization affects the bond lengths, resulting in different geometries for spin-polarized and spinunpolarized calculations. In the Lu2 O3 : Ta×Lu1↑, all bonds have the same length, while in Lu2 O3 : Ta×Lu1, there are two groups of bonds of similar length. In other words, for Ta3+ in Lu1/C3i site, spin-polarization results in a more symmetric structure. For Ta3+ in Lu2/C2 site, spin-unpolarized calculation (Lu2 O3 : Ta×Lu2 ) resulted in three groups of bonds, with the same bond length within a group. In the respective spin-polarized case (Lu2 O3 : Ta×Lu2↑) a less-symmetric structure was formed, where all bonds are different (although still can be separated in two groups of similar lengths). Introduction of interstitial oxygen mostly results in increase of the average bond length, by about 1–4%. In the structures containing interstitial oxygen, the overall trend is similar: the bond lengths increase with decreasing Ta oxidation state, except for the low-spin Lu2 O3 : Ta×Lu2, O″i sample. The Ta-Oi bonds are distinctly shorter than the other Ta–O bonds. For Lu1 site, the Ta-O bonds form two distinct
5.3. The Lu2O3:Ta structures In both Lu2 O3 :Ta•• Lu1/Lu2 (Fig. 1a,e), two distinct trap states are present at 1.4, 1.7 eV and 1.2, 1.6 eV, respectively. Those states are located above Fermi level, and are empty, which is expected for Ta5+ dopant 3
Journal of Luminescence 214 (2019) 116583
A. Shyichuk and E. Zych
Fig. 1. Total density of states (TDOS, solid lines) and Ta d partial DOS (fill) of the Lu2O3:Ta structures. Arrows indicate spin-polarized calculations. Trap depths are shown, and values in italic indicate states that are not well separated from conduction band. Fermi level is at 0 eV.
In Lu2 O3 :Ta×Lu1, two defect states were found, a doubly occupied one and an empty one, 1.2 and 0.5 eV below conduction band (Fig. 1c). The trap depth in this case is clearly 1.2 eV, which is the energy required to promote one of the electrons to conduction band. Promotion of the second electron is expected to require 1.5 eV, as it occurs from the Lu2 O3 :Ta•Lu1 calculation. The Lu2 O3 :Ta×Lu1↑ calculation (Fig. 1d) converged with total magnetic moment of 1.45 μB, of which 0.63 μB is the moment in Ta muffin-tin sphere. Two defect states are present: a spinup (and apparently single-electron) filled trap with 0.9 eV depth is wellseparated and another semi-filled state is located (by centroid) ~0.3 eV below conduction band and overlaps with it. It was actually hard to distinguish where the bottom of conduction band is in this case. The depths were estimated against the point where Ta PDOS becomes insignificant. Total DOS of low-spin Lu2 O3 :Ta×Lu2 (Fig. 1g) shows a peak about 0.4 eV below conduction band, which is also barely a trap – it overlaps with the band strongly. The respective meant-to-be high-spin calculation (Lu2 O3 :Ta×Lu2↑, Fig. 1h) converged with total magnetic moment of −0.002 μB. (Noteworthy, the respective geometry optimization in Quantum Espresso had a total magnetic moment of 2 μB.) Small moment of −0.056 μB was localized on Ta, and another one of 0.032 μB
and define this impurity as an electron trap with a significant depth. Lu2 O3 :Ta•Lu1 (Fig. 1b) contains two trap states, 1.5 eV (filled, spindown) and 0.8 eV (empty, spin-up and spin-down) below conduction band. The system converged with total magnetic moment of −1 Bohr magneton, μB, indicating presence of one unpaired spin-down electron. As the 0.8 eV state is empty, the trap depth in this case (Ta4+) is 1.5 eV. Note that this energy is different from the Ta5+ case (Lu2 O3 :Ta•• Lu1,1.7 eV, Fig. 1a). It is clear that depths of empty and occupied traps are different. Consequently, in order to estimate the experimental (TL) trap depth via calculations, it is recommended to model filled traps. Similarly, Lu2 O3 :Ta•Lu2 (Fig. 1f) contains single filled spin-down state with depth about 1.2 eV. Total magnetic moment is also −1 μB. Two unoccupied states are present 0.9 and 0.6 eV below conduction band. The latter state overlaps with conduction band and is unlikely to trap electrons persistently, especially at room temperature. The Lu2O3:Ta× samples (Fig. 1 c,d,g,h) contain Ta3+ with assumed two 5d electrons. Low-spin and high-spin states are then possible. For low-spin configurations (Lu2 O3 :Ta×Lu1/Lu2 ), spin-unpolarized calculations were performed. The respective high-spin states (Lu2 O3 :Ta×Lu1/Lu2↑) were modeled with spin-polarized calculations.
4
Journal of Luminescence 214 (2019) 116583
A. Shyichuk and E. Zych
Fig. 2. Total density of states (TDOS, solid lines), Ta d partial DOS (solid fill) and Oi s + p partial DOS (checked fill) of the Lu2O3:Ta,Oi structures. Arrows indicate spin-polarized calculations. Trap depths are shown. Values in italic indicate states that are not well separated from conduction band. Fermi level is at zero.
of Ta3+ dopant indicates the probable contribution of the levels to room-temperature afterglow and some short-living retrapping of electrons. Presumably, this might manifest as trap distribution. In other words, potential (but rather not stable) formation of Ta2+ states (with three trapped electrons) can also be assumed as an entity affecting some experimental observations in thermoluminescence measurements. Results of the calculations are thus in good qualitative and semiquantitative agreement with the experimental data [12], in both trap depths and the predicted phenomena, such as energy storage and afterglow.
was localized on an oxygen atom 5.76 Å away from the dopant atom. Interstitial density magnetic moment was 0.032 μB. In other words, the system converged as low-spin, despite the applied magnetic field. A two-electron trap of 0.6 eV was found. Summarizing, Ta4+ in Lu2O3, Lu1/C3i/S6 (Lu2 O3 :Ta•Lu1) site corresponds to a single electron trapped mostly at Ta 5d orbitals, with some contribution of the surrounding oxygens. The trap depth is then 1.5 eV. High-spin Ta3+ in the same site (Lu2 O3 :Ta×Lu1↑) does not correspond to a two-electron trap. Rather, two single-electron defect states are present, one of which is a quite shallow trap of 0.9 eV or less, while the other is barely a trap with the depth between 0.3 and 0 eV. The respective lowspin state of Ta3+ (Lu2 O3 :Ta×Lu1, Fig. 1c) corresponds to a 1.2 eV twoelectron trap. It is, however, hard to say which of the Ta3+ states would prevail. Actually, it is not impossible for both kinds of states to be present in the same piece of Lu2O3:Ln,Ta ceramics. Similarly, Ta4+ in Lu2O3, Lu2/C2 (Lu2 O3 :Ta•Lu2 ) site, corresponds to a trap of 1.2 eV, while its Ta3+ counterpart corresponds to a two-electron low-spin trap of 0.6 eV depth. The Lu1/C3i site thus corresponds to deeper traps than Lu2/C2 site, for both Ta4+ (1.5 vs. 1.2 eV, respectively) and Ta3+ (1.2/ 0.9 eV vs. 0.6 eV, respectively) (Fig. 1c,d,g,h). Presence of poorly separated semi-filled and empty levels in the case
5.4. The Lu2O3:Ta,Oi structures During synthesis, the dopant is introduced as Ta5+ and supposedly substitutes Lu3+ ions in the structure. It is reasonable to expect additional (interstitial) O2− in the structure as a result of charge compensation. As the structure provides many anionic voids, it is reasonable to expect the additional oxygen atoms to occupy the voids rather than actual interstitial sites. Moreover, it is possible to put the Oi in the coordination sphere of the dopant, as there are two anion voids at proximity of each of the cation sites. Such Oi results in significant 5
Journal of Luminescence 214 (2019) 116583
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experimentally observed trap distributions are evident. The calculated values of electron trap depths, namely 1.5 eV for Lu2 O3 :Ta•Lu1/C3i, 1.2 eV for Lu2 O3 :Ta•Lu2/C2 match the experimental values (1.4 eV and 1.2 eV) [14] surprisingly well. On the one hand, the experimental values were obtained from Randall-Wilkins first order fit, which is considered an approximation by the authors. Apparently, the actual kinetics is more complex, involving trap distributions and semilocalized transitions, SLT [14]. Thus, the experimental trap depths are not precisely such. The optical stimulation indicates that one of the depths is smaller than 1.26 eV, while the other lies between 1.26 and 1.59 eV [14]. On the other hand, the calculated values must suffer from the DFT band gap problem. Classically defined (valence band maximum to conduction band minimum) band gap in c-Lu2O3 is estimated by RPP functional to be about 4.8 eV. The peak-to-peak gap measured similarly to the trap depths is about 5 eV. One way or the other, the gap is underestimated by about 15–20%. It is possible that the trap depths are underestimated by roughly the same amount. Yet, it must be noted that the trap depths do not change proportionally to band gap when one switches to LDA from mGGA (Table S9 and Fig. S1 in the Supplementary Information). In mGGA, defect levels are more distinct and better separated from conduction band – probably due to sensitivity of RPP functional to kinetic energy density and thus to local properties of d and f electrons (which is also another merit of mGGA). It is thus hard to estimate the inaccuracy in the calculated trap depths. There might be some error cancellation happening, or the match can be simply coincidental. These calculations are an approximation – although it is much better approximation than LDA/GGA and much faster one than GW, OEP and hybrid functionals. Presence of experimentally proved SLT [6] suggests short distance between the Ta and Tb doping sites, which might affect the coordination geometry of Ta3+/4+ ions and the depths. It is thus risky to compare the calculated and the experimental values of trap depths. However, both in experiment and calculations, there are two moderately deep traps, one of them slightly deeper than the other one. Also, both points of view indicate additional shallow traps. With such a qualitative/semi-quantitative picture in mind, it is possible to draw a following conclusion from the calculated data: the deepest trap must be Lu2 O3 :Ta•Lu1/C3i , the next one is Lu2 O3 :Ta•Lu2/C2 (that is, both deep traps are single-electron Ta4+ traps), while the shallow traps are more likely to be two-electron (Ta3+) species. Introduction of interstitial oxygen does not improve the electron trapping properties of the dopant, as was suggested in Ref. [14]. It causes reduction of the trap depths (Fig. 2) in respect to analogous structures without Oi (Fig. 1), and results in additional shallow hole traps (Figs. 1 and 2 b,d-h). The expected effect of Oi is reduction of thermoluminescence intensity and energy storage capacity of the Lu2O3:Ta-based phosphors, as well as more complicated thermoluminescence mechanism due to additional shallow hole traps related to the Oi. It is possible and reasonable (although not unambiguous) that higher thermoluminescence intensity of vacuum-sintered Lu2O3:Tb,Ta in respect to the same air- and forming-gas-sintered phosphors [12] is related to reduction of Oi content in the sample and/or increase in Ta-Oi distance.
changes in the electron traps in Lu2O3:Ta,Oi (Fig. 2), in respect to the Lu2O3:Ta structures (Fig. 1). Namely, the trap depths are much smaller, while the defect bands are connected to conduction band, which probably ceases (or at least reduces) the electron trapping capabilities of the respective defects. In Lu2 O3 :Ta•• Lu1/Lu2, O″i (Fig. 2a,e), there are distinct defect levels, 1.3 and 1.4 eV below conduction band. However, those states are unoccupied (above Fermi level) and must be filled with electrons in order to find the respective trap depths. In these structures, s and p states of the Oi are located within valence band. The Lu2 O3 :Ta•Lu1/Lu2, O″i (Fig. 2b,f) structures converged with total magnetic moments of 0.98 and −0.99 μB respectively, indicating a single unpaired electron in both cases. The defect states are located about 0.4 (spin-up, occupied), 0.2 (spin-down, unoccupied) eV and 0.7 (spin-down, semi-occupied), 0.4 (spin-up, unoccupied) eV below conduction band, apparently overlapping with it. The gaps between the occupied states and conduction band are approximately 0.4 and 0.7 eV respectively. Given the overlap and low depth, it is unlikely for these states to hold the trapped electrons for a long time at room temperature. In Lu2 O3 :Ta×Lu1/Lu2, O″i (Fig. 2c,d,g,h), the defect levels are located at proximity of conduction band and are well connected to it. The results of spin-unpolarized and spin-polarized calculations are very similar in this case. Release of one of the two trapped electrons is expected to happen under excitation energies of 0.2–0.7 eV or less. Energy required to release the second electron is described by the Lu2 O3 :Ta•Lu1/Lu2, O″i cases. In DOS plots of Lu2 O3 :Ta•Lu1/Lu2, O″i and Lu2 O3 :Ta×Lu1/Lu2, O″i (Fig. 2b–d,f-h), evident defect states above valence band are present. The position of the defect density corresponds well to s and p states of the interstitial oxygen. It was shown in our previous studies [25] that similar defect states correspond to isolated interstitial oxygen. In other words, in the Lu2O3:Ta,Oi samples, changing Ta oxidation state from 5+ to 4+ or 3+ results in additional defect levels related to the Oi, which are occupied and thus can act as hole traps. The traps are evidently shallow and, in case of Lu2 O3 :TaLu2, O″i , are connected to valence band. Consequently, no efficient hole trapping is expected. However, such states may influence, to some extent, the kinetics of carrier detrapping in phosphors based on Lu2O3:Ta. Summarizing, Oi in proximity of Ta dopant in Lu2O3:Ta has profoundly deleterious effect on electron trapping, possibly eliminating it whatsoever. The resulting defect states can be most optimistically classified as shallow traps or continuous distributions of shallow traps, if any. Moreover, additional hole traps occur in several cases. Such states are expected to complicate the kinetics of luminescence of Lu2O3:Ta based materials, causing deviation from the simplest firstorder model. According to the calculated bond lengths, the effect can be explained by the increase in average Ta–O distances due to Oi introduction. Coarsely speaking, longer bonds result in weaker crystal field and thus weaker splitting of the 5d configuration, pushing the trap states up in energy and closer to conduction band. The trap depths decrease accordingly. 5.5. References to experiment and summary
6. Conclusions According to our calculations, introduction of Ta dopant into cubic Lu2O3 results in defect states below conduction band, which can act as electron traps. This conclusion strongly supports the tentative assumption drawn from the experimental data [12,14]. One or two electrons can be trapped, resulting in two kinds of traps with distinctly different moderate depths, which also agrees with the experiment. The dopant ions in the Lu1/C3i/S6 and Lu2/C2 sites are characterized by different depths, while presence of interstitial oxygen changes the depths even more. As the defect states are characterized by strong contribution of Ta 5d orbitals, the respective trap depths must be sensitive to coordination geometry, and thus to temperature and presence of any other defects at proximity. Consequently, possibilities for the
Origin of electron traps in Ta-doped c-Lu2O3, as well as their direct relation to 5d orbitals of the Ta dopant was demonstrated used advanced pure density functional theory calculations. Good agreement between the calculated and the previously measured experimental trap depths was found. From the DFT calculations, two peaks (at about 170 °C and 250 °C) in thermoluminescence glow curves of cLu2O3:Tb,Ta can be attributed to single-electron traps of Ta4+ in C2 and C3i lutetium sites, respectively. More shallow traps (responsible for TL peaks about 100 °C) can be attributed to two-electron Ta3+ traps, of which only one electron is released at this temperature. Deconstructive interaction of the traps with interstitial oxygen directly bound to the 6
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dopant was another newly found phenomenon, and can be explained by increased Ta–O bond length (and thus smaller splitting of the 5d states), caused by the Oi. The calculations thus have added new insights to the general understatement of electron trapping in Lu2O3:Ta persistent luminescence materials. Moreover, the results illustrate significant usability of the FP-LAPW/mGGA approach in analysis of carrier traps in insulators.
[20]
[21]
Acknowledgments
[22]
Financial support by the Polish National Science Centre (NCN) under the grants UMO-2014/13/B/ST5/01535 and 2017/26/D/ST3/ 00599. Wroclaw Centre for Networking and Supercomputing (WCSS) is acknowledged for the provided computing power. Kevin F. Garrity (National Institute of Standards and Technology (NIST), Gaithersburg, Maryland, USA) is greatly acknowledged for the provided Lu3+ ultrasoft pseudopotential.
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Appendix A. Supplementary data [27]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jlumin.2019.116583. [28]
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Dopant-related electron trap states in Lu2O3:Ta
T
*
Andrii Shyichuk , Eugeniusz Zych Faculty of Chemistry, University of Wrocław, F. Joliot-Curie 14, 50-383, Wrocław, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Lu2O3 Ta Thermoluminescence energy storage electron trapping calculations Meta-GGA
Electronic structure of Ta-doped cubic (bixbyite-type) lutetium oxide was analyzed using augmented plane wave with local orbitals density functional theory (DFT) calculations with meta-generalized gradient approximation (meta-GGA, mGGA) Räsänen, Pittalis and Proetto functional. Two doping sites, three oxidation states of the dopant and optional interstitial oxygen (Oi) were considered. The calculations indicate that introduction of the dopant results in energy levels below conduction band, with strong contribution of Ta 5d orbitals. The position of the levels depends strongly on the oxidation state of the dopant. Depending on the composition, two distinct electron traps with depths of 1.5–1.2 eV and 0.9–0.2 eV were revealed. Introduction of Oi at proximity of the Ta dopant results in partial overlap of the Ta-related defect states with conduction band, which makes the traps very shallow, deteriorating the electron trapping properties. In some cases, shallow hole traps can also be attributed to the Oi. The calculated traps structure is in good accord with the experimental data.
1. Introduction
spectroscopy [13]. The semi-empirical model of Dorenbos [12,18] corresponds with such mechanism of carriers trapping. In the recent papers by Zych et al. [12] and Bolek et al. [14] thermoluminescence properties of Lu2O3:Tb,Ta are discussed in details. In the thermoluminescence glow curves of the UV-irradiated samples, two strong peaks appear around 170 °C and 250 °C, while the Tmax-Tstop experiments indicate presence of some distribution of trap depths [12]. Of the three synthesis atmospheres, namely hydrogen-nitrogen mixture (forming gas), air and vacuum, the latter corresponds to the most intense thermoluminescence. It is emphasized that co-doping with Ta significantly improves thermoluminescence intensity of Lu2O3:Tb,Ta in comparison to Lu2O3:Tb. The trap depths were further analyzed using thermoluminescence experiments and optical stimulation [14]. The two main glow curve peaks were attributed to two electron traps of approximately 1.2 and 1.4 eV.
In the last fifteen years, persistent luminescence and energy storage phosphors based on cubic (bixbyite-type) lutetium oxide, c-Lu2O3 have been intensively studied via thermolumiescence (TL) experiments [1–14]. Unlike regular phosphors in which photoluminescence decays rapidly (within micro- or milliseconds) after excitation, storage phosphors can accumulate some of the excitation energy. It is hypothesized, that excited charge carriers (electrons and holes) appearing in the materials upon excitation, are then trapped at defects. It is thus spoken about electron and hole traps, the nature of which defines the capacity and time of energy storage. Traps are characterized by their depths – the energy required to release one of the carriers: trapped electrons must be raised to conduction band, while trapped holes must be promoted to valence band. Within the respective bands, the carriers can move freely and reach the recombination centre. A number of theoretical models connect the trap depths and other properties of a material to its TL glow curves [15–17]. In Lu2O3, Pr3+ and Tb3+ dopants act as hole-traps and emission centers, while d metal co-dopants such as Ti [13], Hf [10] or Ta [12,14] shape the electron trapping properties. It is assumed that electrons excited to conduction band relax to the empty d orbitals of the co-dopant cations, get captured, and can later be released under thermal or optical stimulation [11]. The assumption, however, has not been proven directly. Only in the case of Ti co-doping a solid support of such mechanism was shown by means of Lu2O3:Ti luminescence
*
2. Computational approach selection We believe that estimate of the first excitation energy of a trapped electron to the conduction band is the calculated (optical) trap depth and must correspond to the experimental trap depth. Below, we refer to such (calculated) energies simply as “trap depth”, unless specified otherwise. However, when fitting thermoluminescence glow curves with equations corresponding to a certain kinetics, the trap depth is only one of the fitting parameters. There is no simple Tpeak = f(Edepth) one-variable function connecting the trap depth and the glow curve
Corresponding author. E-mail address: [email protected] (A. Shyichuk).
https://doi.org/10.1016/j.jlumin.2019.116583 Received 27 November 2018; Received in revised form 24 June 2019; Accepted 25 June 2019 Available online 26 June 2019 0022-2313/ © 2019 Published by Elsevier B.V.
Journal of Luminescence 214 (2019) 116583
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3. Density functional selection
peak temperature. Moreover, solid-state DFT calculations do not take thermal changes in geometry into account, which might affect the trap depths. We thus expect at least qualitative (semi-quantitative at best) correspondence between the calculated and thermoluminescence depths. Still, the calculations might come very handy in the aspects that cannot be directly measured due to very low concentration of the dopants (for instance, oxidation states and coordination geometries of the charged traps). In order to understand the nature of traps from density functional calculations, a good representation of empty (virtual) orbitals (bands) is required. Such requirement poses a certain problem. First of all, a wellknown DFT problem is underestimation of band gaps [19–24] Consequently, properties of other virtual orbitals (such as trap bands) cannot be taken as fully reliable. Additionally, some researchers believe that unoccupied Kohn-Sham (KS) orbitals make no physical sense. However, there are proofs that, given a properly constructed density, KS virtual orbitals have physical meaning [25] and are actually better approximations of excited states than Hartree-Fock virtual orbitals, lacking the unnatural sparsity of the latter [21]. For molecules, energy differences between the highest occupied orbital and the virtual orbitals are good semi-quantitative estimates of the respective excitation energies [21]. We are thus confident that if the density functional is good enough, and calculation with it results in good agreement between the calculated and the experimental band gaps, one can also reliably estimate trap depths with such a functional, from KS orbitals. Apparently, many people rely on virtual KS orbitals in their studies, even at generalized gradient approximation (GGA) [26–33] or local density approximation (LDA) [34] level of theory. Large unit cell of cubic Lu2O3 presents another limitation – GW approximation [22,35,36], exact exchange (optimized effective potential) [37], Hartree-Fock for solids and even hybrid functionals cannot be used due to unacceptably long run times of the respective all-electron calculations. For instance, our test calculation of a defect-free Lu2O3 unit cell with HSE0 functional [38] on eight CPUs did not make a single self-consistent loop in weeks. Similarly, a test G0W0 calculation did not end in about a month, with tremendous requirements of memory (about 500 GB). A solution for that could be the use of pseudopotential approaches. While ultrasoft pseudopotential [39] calculations were used in this work for geometries, they are not trustworthy for electronic structure, especially when 4f elements are in play. Calculations with norm-conserving potentials last roughly as long as all-electron calculations, thus it's better to use the latter (in order to have a less parametrized model). Projector augmented wave methods require +U correction [40,41], which renders the whole study pointless: comparing energy of the defect level which uses +U correction with energy of conduction band minimum which uses another +U correction is basically a comparison between the two parameters. For such an empirical approach, Dorenbos model [18] is much better and transparent. We, however, were looking for a way to analyze the materials from scratch, from bare positions of atoms and material composition, without empirical corrections. We thus ended up with all-electron calculations using meta-generalized gradient approximation (mGGA) RPP functional [42] as a good compromise between calculation time and quality. We did not use charge state transition levels (CSTL) [24,43,44] in this work. The reasons are discussed in the Supplemetary Information, along with some examples. Summarizing, conclusions in this paper are based on Kohn-Sham eigenvalues, and thus must be handled with care. We do compare them to experiment, but we do not expect the calculated values to match the experimental ones. Rather, we look for trends in experimental results and look for the same trends in calculated results. We thus do not compare numbers originating from different sources. We do, however, compare calculated values to each other.
The RPP functional (also referred as RPP09 in libxc [45,46]) is a modification of Becke-Johnson, BJ semi-local functional [47]. The importance of the semi-locality is explained in the Becke paper [48], where the idea to use kinetic energy density as a measure of exchange hole delocalization is presented. This aspect is particularly interesting in the context of solid state calculations, where strictly localized exchange hole (as opposed to purely delocalized bands) is considered the main source of error in band gap predictions by LDA and GGA functionals [21]. The BJ functional also uses ratio between local spin density approximation kinetic energy density and exact exchange kinetic energy density as a measure for (non)locality of exchange hole. Later, BJ functional was modified by Tran and Blaha [49] with the motivation of calculated band gap values improvement. The result was the commonly used TB-mBJ functional, in which effective portion of nonlocal exchange was controlled by a density-dependent parameter. Although it is far from perfect, the functional indeed works well for insulators, semiconductors and metals [23,50–53], indicating merits of semi-local potentials. However, TB-mBJ formulation contains two fitting parameters (system dependent, but typically used as constants), is not gauge-invariant and is not a functional derivative. Räsänen, Pittalis and Proetto used a different approach for modification of BJ functional [42], making it system-independent and gauge-invariant. Moreover, RPP is by definition a functional derivative in the framework of spincurrent DFT [54]. 4. Calculation details The oxide structure was obtained from the authors of [55]. Cubic bixbyite-type Lu2O3 (space group 206, Ia3 / Ia − 3) comprises a unit cell of 16 formula units (80 atoms). Lu atoms occupy 8 sites of C3i/S6 local symmetry and 24 C2 sites. Each site is surrounded by 6 oxygen atoms and two anion voids, which together form a distorted cube. All of the oxygen positions and anion voids are of the same local symmetry. We have considered substitution of Lu atoms of the oxide by the Ta dopant atoms in one of the Lu sites of C3i/S6 (Lu1) or C2 (Lu2) point symmetries. The corresponding structures were labeled Lu2O3:TaLu1 and Lu2O3:TaLu2, respectively. Optionally, the dopant was supplemented with an interstitial O2− in the nearest anion void. These structures were labeled Lu2O3:TaLu1,Oi and Lu2O3:TaLu2,Oi, respectively. Four structures were considered in total. The oxidation states of the dopant were controlled via total charge on the structure. In the case of the structures without interstitial oxygen, the charges were either 0, +1 or +2, corresponding to the dopant oxidation states of +3, +4 and + 5, respectively. Presence of a charge-compensating defect somewhere far away from the doping site, TaLu1 or TaLu2, was assumed and not modeled explicitly. In the case of the structures with interstitial O2− as Ta nearest neighbor, the total charges were −2, −1 or 0, corresponding to the Ta dopant oxidation state of +3, +4 and+ 5, respectively. The geometries of the structures were optimized using Quantum Espresso code [56], with Perdew-Zunger (PZ) [57] local density approximation (LDA) functional and ultrasoft pseudopotentials from GBRV group [39]. Plane wave cutoff of 40 Ry (524 eV) was used. An unpublished Lu3+ potential with 4f shell in-core was kindly provided by Kevin F. Garrity from NIST. We emphasize that cells with dopant atoms at different oxidation states were separately optimized with the respective settings, starting from the same geometry corresponding to the unperturbed crystal (except for the added dopant and Oi). Consequently, changes in the geometry due to the changes in the oxidation state were taken into account. The same goes for Lu2O3:Ta3+ and Lu2O3:Ta3+,O2−, which were modeled with both spin-polarized highspin and spin-unpolarized calculations. Next, all-electron Elk [58] code was used to calculate density of states (DOS) of the structures. Both kinds of calculations used 3 × 3 × 3 k-point grids. For the charged 2
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Table 1 Length of O–Ta bonds (Angstroms), according to the kind of doping. Arrows indicate spin-polarized calculations. The percentage of bond length increase due to introduction of Oi is calculated relating to the respective strictures without Oi.
O O O O O O Oi Average excluding Oi Average including Oi Increase due to Oi, % O O O O O O Oi Average excluding Oi Average including Oi Increase due to Oi, %
Ta•• Lu1
Ta•Lu1↑
Ta× Lu1
Ta× Lu1↑
Ta•• Lu1, O″i
Ta•Lu1, O″i ↑
Ta× Lu1, O″i
Ta× Lu1, O″i ↑
1.99712 1.99713 1.99712 1.99713 1.99712 1.99713
2.06325 2.06328 2.06325 2.06328 2.06325 2.06328
2.02627 2.17683 2.02627 2.17683 2.02627 2.17683
2.10938 2.10936 2.10938 2.10936 2.10938 2.10936
1.99712
2.06326
2.10155
2.10937
Ta•Lu2↑
Ta•Lu2↑ 1.98710 1.98709 2.04304 2.04304 2.14900 2.14900
Ta× Lu2↑ 2.01894 2.17122 2.05589 2.05312 2.15591 2.20107
2.09524 2.17100 2.09524 2.17100 2.09524 2.17100 1.98701 2.13312 2.11225 2.374 Ta•Lu2, O″i ↑
1.96683 1.96683 1.97887 1.97887 2.06436 2.06436
Ta× Lu2 1.99949 1.99949 2.05627 2.05627 2.16396 2.16397
2.05379 2.14333 2.05379 2.14333 2.05379 2.14333 1.93910 2.09856 2.07578 3.939 Ta•• Lu2, O″i
2.00335
2.05971
2.07324
2.10936
2.03768 2.24966 2.01120 2.02682 2.09601 2.13169 1.96642 2.09218 2.07421 3.537
2.08854 2.28706 2.04273 2.06663 2.15820 2.19457 1.99727 2.13962 2.11929 2.892
2.08699 2.14937 2.08699 2.14937 2.08699 2.14937 1.98722 2.11818 2.09947 −0.099 Ta× Lu2, O″i 2.08979 2.25329 2.06197 2.07283 2.15253 2.20214 2.01618 2.13876 2.12125 2.316
2.12575 2.16742 2.12575 2.16742 2.12575 2.16742 2.02130 2.14659 2.12869 0.916 Ta× Lu2, O″i ↑ 2.14120 2.34919 2.08182 2.09507 2.20565 2.22586 2.03576 2.18313 2.16208 2.499
groups, while the site maintains a C3 symmetry. For Lu2 site, the symmetry is C1, while all of the bonds are rather different.
cells, uniform background was used for charge compensation, which is default for both codes (i.e. cell must be effectively charge-neutral in order to make a calculation with periodic boundary conditions possible [59]). The Elk calculations used two convergence thresholds of default values: root mean square change (from last tree iterations) in KohnSham potential was required to be lower than 1·10−6 atomic units, while the change in total energy was required to be lower than 1·10−4 atomic units. The DOS calculations were peformed with Räsänen, Pittalis and Proetto RPP09 [42] meta-generalized gradient approximation (meta-GGA, mGGA) functional for exchange and PZ correlation. The detailed list of settings for both codes is given in the Supplementary Information (SI). The discussion below is based on the Elk RPP09 results. Hereafter, in figures and text, Kröger-Vink notation is used to label the defects [60].
5.2. Electronic properties It should be noted that typical DFT problem of band gap underestimation is still present in this calculations, resulting in 0 K band gap of about 5 eV, while the experimental gap at 8 K is about 6 eV [61,62]. Spin-orbit coupling was not used in the calculations, as it is not critically necessary [63], while including it would significantly enlarge CPU time and memory requirements, which are already high due to the use of mGGA. Consequently, the results are rather semi-quantitative, but nevertheless meaningful, useful and correlate quite well with the experimental data from Refs. [12,14]. Fig. 1 presents total density of states plots of the structures without interstitial oxygen. All of the plots indicate presence of states between conduction and valence bands. No such states are present in an undoped Lu2O3, which is an insulator with a well-defined gap. In Fig. 1, orange-filled parts of the peaks correspond to d-orbital electronic density inside Ta muffin-tin sphere. In other words, this is the Ta d density within a 2-bohr (~1.06 Å) radius sphere centered at Ta position. Although the code does not distinguish the orbitals by their principal quantum number during DOS calculations, only Ta 5d orbitals can be found around Fermi level, while the filled 3d and 4d states must lay at much lower energies. Consequently, the defect levels can be attributed mostly to the Ta dopant 5d orbitals. Contributions from interstitial density and Lu and O orbitals to the defect states are present. Hence, electrons trapped in such states would not fully belong to Ta 5d orbitals, some delocalization (mostly over the nearby oxygens, but also over the whole cell) is anticipated. In Figs. 1 and 2, the trap depths were measured from the defect peak centroid to the first significant peak of the conduction band (small peaks) or the peak half-maximum position (intense peaks). It is expected that trap depths measured in such a way would correspond to experimental optical trap depth.
5. Results and discussion 5.1. Structure: O–Ta bond lengths Table 1 contains length of O–Ta bonds for the studied structures, indicating several trends. For all of the structures, the bond lengths increase with decreasing Ta oxidation state – which is expected due to increasing electron density at 5d orbitals of the dopant. For the Lu2 O3 : Ta×Lu1/Lu2 samples, spin polarization affects the bond lengths, resulting in different geometries for spin-polarized and spinunpolarized calculations. In the Lu2 O3 : Ta×Lu1↑, all bonds have the same length, while in Lu2 O3 : Ta×Lu1, there are two groups of bonds of similar length. In other words, for Ta3+ in Lu1/C3i site, spin-polarization results in a more symmetric structure. For Ta3+ in Lu2/C2 site, spin-unpolarized calculation (Lu2 O3 : Ta×Lu2 ) resulted in three groups of bonds, with the same bond length within a group. In the respective spin-polarized case (Lu2 O3 : Ta×Lu2↑) a less-symmetric structure was formed, where all bonds are different (although still can be separated in two groups of similar lengths). Introduction of interstitial oxygen mostly results in increase of the average bond length, by about 1–4%. In the structures containing interstitial oxygen, the overall trend is similar: the bond lengths increase with decreasing Ta oxidation state, except for the low-spin Lu2 O3 : Ta×Lu2, O″i sample. The Ta-Oi bonds are distinctly shorter than the other Ta–O bonds. For Lu1 site, the Ta-O bonds form two distinct
5.3. The Lu2O3:Ta structures In both Lu2 O3 :Ta•• Lu1/Lu2 (Fig. 1a,e), two distinct trap states are present at 1.4, 1.7 eV and 1.2, 1.6 eV, respectively. Those states are located above Fermi level, and are empty, which is expected for Ta5+ dopant 3
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Fig. 1. Total density of states (TDOS, solid lines) and Ta d partial DOS (fill) of the Lu2O3:Ta structures. Arrows indicate spin-polarized calculations. Trap depths are shown, and values in italic indicate states that are not well separated from conduction band. Fermi level is at 0 eV.
In Lu2 O3 :Ta×Lu1, two defect states were found, a doubly occupied one and an empty one, 1.2 and 0.5 eV below conduction band (Fig. 1c). The trap depth in this case is clearly 1.2 eV, which is the energy required to promote one of the electrons to conduction band. Promotion of the second electron is expected to require 1.5 eV, as it occurs from the Lu2 O3 :Ta•Lu1 calculation. The Lu2 O3 :Ta×Lu1↑ calculation (Fig. 1d) converged with total magnetic moment of 1.45 μB, of which 0.63 μB is the moment in Ta muffin-tin sphere. Two defect states are present: a spinup (and apparently single-electron) filled trap with 0.9 eV depth is wellseparated and another semi-filled state is located (by centroid) ~0.3 eV below conduction band and overlaps with it. It was actually hard to distinguish where the bottom of conduction band is in this case. The depths were estimated against the point where Ta PDOS becomes insignificant. Total DOS of low-spin Lu2 O3 :Ta×Lu2 (Fig. 1g) shows a peak about 0.4 eV below conduction band, which is also barely a trap – it overlaps with the band strongly. The respective meant-to-be high-spin calculation (Lu2 O3 :Ta×Lu2↑, Fig. 1h) converged with total magnetic moment of −0.002 μB. (Noteworthy, the respective geometry optimization in Quantum Espresso had a total magnetic moment of 2 μB.) Small moment of −0.056 μB was localized on Ta, and another one of 0.032 μB
and define this impurity as an electron trap with a significant depth. Lu2 O3 :Ta•Lu1 (Fig. 1b) contains two trap states, 1.5 eV (filled, spindown) and 0.8 eV (empty, spin-up and spin-down) below conduction band. The system converged with total magnetic moment of −1 Bohr magneton, μB, indicating presence of one unpaired spin-down electron. As the 0.8 eV state is empty, the trap depth in this case (Ta4+) is 1.5 eV. Note that this energy is different from the Ta5+ case (Lu2 O3 :Ta•• Lu1,1.7 eV, Fig. 1a). It is clear that depths of empty and occupied traps are different. Consequently, in order to estimate the experimental (TL) trap depth via calculations, it is recommended to model filled traps. Similarly, Lu2 O3 :Ta•Lu2 (Fig. 1f) contains single filled spin-down state with depth about 1.2 eV. Total magnetic moment is also −1 μB. Two unoccupied states are present 0.9 and 0.6 eV below conduction band. The latter state overlaps with conduction band and is unlikely to trap electrons persistently, especially at room temperature. The Lu2O3:Ta× samples (Fig. 1 c,d,g,h) contain Ta3+ with assumed two 5d electrons. Low-spin and high-spin states are then possible. For low-spin configurations (Lu2 O3 :Ta×Lu1/Lu2 ), spin-unpolarized calculations were performed. The respective high-spin states (Lu2 O3 :Ta×Lu1/Lu2↑) were modeled with spin-polarized calculations.
4
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Fig. 2. Total density of states (TDOS, solid lines), Ta d partial DOS (solid fill) and Oi s + p partial DOS (checked fill) of the Lu2O3:Ta,Oi structures. Arrows indicate spin-polarized calculations. Trap depths are shown. Values in italic indicate states that are not well separated from conduction band. Fermi level is at zero.
of Ta3+ dopant indicates the probable contribution of the levels to room-temperature afterglow and some short-living retrapping of electrons. Presumably, this might manifest as trap distribution. In other words, potential (but rather not stable) formation of Ta2+ states (with three trapped electrons) can also be assumed as an entity affecting some experimental observations in thermoluminescence measurements. Results of the calculations are thus in good qualitative and semiquantitative agreement with the experimental data [12], in both trap depths and the predicted phenomena, such as energy storage and afterglow.
was localized on an oxygen atom 5.76 Å away from the dopant atom. Interstitial density magnetic moment was 0.032 μB. In other words, the system converged as low-spin, despite the applied magnetic field. A two-electron trap of 0.6 eV was found. Summarizing, Ta4+ in Lu2O3, Lu1/C3i/S6 (Lu2 O3 :Ta•Lu1) site corresponds to a single electron trapped mostly at Ta 5d orbitals, with some contribution of the surrounding oxygens. The trap depth is then 1.5 eV. High-spin Ta3+ in the same site (Lu2 O3 :Ta×Lu1↑) does not correspond to a two-electron trap. Rather, two single-electron defect states are present, one of which is a quite shallow trap of 0.9 eV or less, while the other is barely a trap with the depth between 0.3 and 0 eV. The respective lowspin state of Ta3+ (Lu2 O3 :Ta×Lu1, Fig. 1c) corresponds to a 1.2 eV twoelectron trap. It is, however, hard to say which of the Ta3+ states would prevail. Actually, it is not impossible for both kinds of states to be present in the same piece of Lu2O3:Ln,Ta ceramics. Similarly, Ta4+ in Lu2O3, Lu2/C2 (Lu2 O3 :Ta•Lu2 ) site, corresponds to a trap of 1.2 eV, while its Ta3+ counterpart corresponds to a two-electron low-spin trap of 0.6 eV depth. The Lu1/C3i site thus corresponds to deeper traps than Lu2/C2 site, for both Ta4+ (1.5 vs. 1.2 eV, respectively) and Ta3+ (1.2/ 0.9 eV vs. 0.6 eV, respectively) (Fig. 1c,d,g,h). Presence of poorly separated semi-filled and empty levels in the case
5.4. The Lu2O3:Ta,Oi structures During synthesis, the dopant is introduced as Ta5+ and supposedly substitutes Lu3+ ions in the structure. It is reasonable to expect additional (interstitial) O2− in the structure as a result of charge compensation. As the structure provides many anionic voids, it is reasonable to expect the additional oxygen atoms to occupy the voids rather than actual interstitial sites. Moreover, it is possible to put the Oi in the coordination sphere of the dopant, as there are two anion voids at proximity of each of the cation sites. Such Oi results in significant 5
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experimentally observed trap distributions are evident. The calculated values of electron trap depths, namely 1.5 eV for Lu2 O3 :Ta•Lu1/C3i, 1.2 eV for Lu2 O3 :Ta•Lu2/C2 match the experimental values (1.4 eV and 1.2 eV) [14] surprisingly well. On the one hand, the experimental values were obtained from Randall-Wilkins first order fit, which is considered an approximation by the authors. Apparently, the actual kinetics is more complex, involving trap distributions and semilocalized transitions, SLT [14]. Thus, the experimental trap depths are not precisely such. The optical stimulation indicates that one of the depths is smaller than 1.26 eV, while the other lies between 1.26 and 1.59 eV [14]. On the other hand, the calculated values must suffer from the DFT band gap problem. Classically defined (valence band maximum to conduction band minimum) band gap in c-Lu2O3 is estimated by RPP functional to be about 4.8 eV. The peak-to-peak gap measured similarly to the trap depths is about 5 eV. One way or the other, the gap is underestimated by about 15–20%. It is possible that the trap depths are underestimated by roughly the same amount. Yet, it must be noted that the trap depths do not change proportionally to band gap when one switches to LDA from mGGA (Table S9 and Fig. S1 in the Supplementary Information). In mGGA, defect levels are more distinct and better separated from conduction band – probably due to sensitivity of RPP functional to kinetic energy density and thus to local properties of d and f electrons (which is also another merit of mGGA). It is thus hard to estimate the inaccuracy in the calculated trap depths. There might be some error cancellation happening, or the match can be simply coincidental. These calculations are an approximation – although it is much better approximation than LDA/GGA and much faster one than GW, OEP and hybrid functionals. Presence of experimentally proved SLT [6] suggests short distance between the Ta and Tb doping sites, which might affect the coordination geometry of Ta3+/4+ ions and the depths. It is thus risky to compare the calculated and the experimental values of trap depths. However, both in experiment and calculations, there are two moderately deep traps, one of them slightly deeper than the other one. Also, both points of view indicate additional shallow traps. With such a qualitative/semi-quantitative picture in mind, it is possible to draw a following conclusion from the calculated data: the deepest trap must be Lu2 O3 :Ta•Lu1/C3i , the next one is Lu2 O3 :Ta•Lu2/C2 (that is, both deep traps are single-electron Ta4+ traps), while the shallow traps are more likely to be two-electron (Ta3+) species. Introduction of interstitial oxygen does not improve the electron trapping properties of the dopant, as was suggested in Ref. [14]. It causes reduction of the trap depths (Fig. 2) in respect to analogous structures without Oi (Fig. 1), and results in additional shallow hole traps (Figs. 1 and 2 b,d-h). The expected effect of Oi is reduction of thermoluminescence intensity and energy storage capacity of the Lu2O3:Ta-based phosphors, as well as more complicated thermoluminescence mechanism due to additional shallow hole traps related to the Oi. It is possible and reasonable (although not unambiguous) that higher thermoluminescence intensity of vacuum-sintered Lu2O3:Tb,Ta in respect to the same air- and forming-gas-sintered phosphors [12] is related to reduction of Oi content in the sample and/or increase in Ta-Oi distance.
changes in the electron traps in Lu2O3:Ta,Oi (Fig. 2), in respect to the Lu2O3:Ta structures (Fig. 1). Namely, the trap depths are much smaller, while the defect bands are connected to conduction band, which probably ceases (or at least reduces) the electron trapping capabilities of the respective defects. In Lu2 O3 :Ta•• Lu1/Lu2, O″i (Fig. 2a,e), there are distinct defect levels, 1.3 and 1.4 eV below conduction band. However, those states are unoccupied (above Fermi level) and must be filled with electrons in order to find the respective trap depths. In these structures, s and p states of the Oi are located within valence band. The Lu2 O3 :Ta•Lu1/Lu2, O″i (Fig. 2b,f) structures converged with total magnetic moments of 0.98 and −0.99 μB respectively, indicating a single unpaired electron in both cases. The defect states are located about 0.4 (spin-up, occupied), 0.2 (spin-down, unoccupied) eV and 0.7 (spin-down, semi-occupied), 0.4 (spin-up, unoccupied) eV below conduction band, apparently overlapping with it. The gaps between the occupied states and conduction band are approximately 0.4 and 0.7 eV respectively. Given the overlap and low depth, it is unlikely for these states to hold the trapped electrons for a long time at room temperature. In Lu2 O3 :Ta×Lu1/Lu2, O″i (Fig. 2c,d,g,h), the defect levels are located at proximity of conduction band and are well connected to it. The results of spin-unpolarized and spin-polarized calculations are very similar in this case. Release of one of the two trapped electrons is expected to happen under excitation energies of 0.2–0.7 eV or less. Energy required to release the second electron is described by the Lu2 O3 :Ta•Lu1/Lu2, O″i cases. In DOS plots of Lu2 O3 :Ta•Lu1/Lu2, O″i and Lu2 O3 :Ta×Lu1/Lu2, O″i (Fig. 2b–d,f-h), evident defect states above valence band are present. The position of the defect density corresponds well to s and p states of the interstitial oxygen. It was shown in our previous studies [25] that similar defect states correspond to isolated interstitial oxygen. In other words, in the Lu2O3:Ta,Oi samples, changing Ta oxidation state from 5+ to 4+ or 3+ results in additional defect levels related to the Oi, which are occupied and thus can act as hole traps. The traps are evidently shallow and, in case of Lu2 O3 :TaLu2, O″i , are connected to valence band. Consequently, no efficient hole trapping is expected. However, such states may influence, to some extent, the kinetics of carrier detrapping in phosphors based on Lu2O3:Ta. Summarizing, Oi in proximity of Ta dopant in Lu2O3:Ta has profoundly deleterious effect on electron trapping, possibly eliminating it whatsoever. The resulting defect states can be most optimistically classified as shallow traps or continuous distributions of shallow traps, if any. Moreover, additional hole traps occur in several cases. Such states are expected to complicate the kinetics of luminescence of Lu2O3:Ta based materials, causing deviation from the simplest firstorder model. According to the calculated bond lengths, the effect can be explained by the increase in average Ta–O distances due to Oi introduction. Coarsely speaking, longer bonds result in weaker crystal field and thus weaker splitting of the 5d configuration, pushing the trap states up in energy and closer to conduction band. The trap depths decrease accordingly. 5.5. References to experiment and summary
6. Conclusions According to our calculations, introduction of Ta dopant into cubic Lu2O3 results in defect states below conduction band, which can act as electron traps. This conclusion strongly supports the tentative assumption drawn from the experimental data [12,14]. One or two electrons can be trapped, resulting in two kinds of traps with distinctly different moderate depths, which also agrees with the experiment. The dopant ions in the Lu1/C3i/S6 and Lu2/C2 sites are characterized by different depths, while presence of interstitial oxygen changes the depths even more. As the defect states are characterized by strong contribution of Ta 5d orbitals, the respective trap depths must be sensitive to coordination geometry, and thus to temperature and presence of any other defects at proximity. Consequently, possibilities for the
Origin of electron traps in Ta-doped c-Lu2O3, as well as their direct relation to 5d orbitals of the Ta dopant was demonstrated used advanced pure density functional theory calculations. Good agreement between the calculated and the previously measured experimental trap depths was found. From the DFT calculations, two peaks (at about 170 °C and 250 °C) in thermoluminescence glow curves of cLu2O3:Tb,Ta can be attributed to single-electron traps of Ta4+ in C2 and C3i lutetium sites, respectively. More shallow traps (responsible for TL peaks about 100 °C) can be attributed to two-electron Ta3+ traps, of which only one electron is released at this temperature. Deconstructive interaction of the traps with interstitial oxygen directly bound to the 6
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dopant was another newly found phenomenon, and can be explained by increased Ta–O bond length (and thus smaller splitting of the 5d states), caused by the Oi. The calculations thus have added new insights to the general understatement of electron trapping in Lu2O3:Ta persistent luminescence materials. Moreover, the results illustrate significant usability of the FP-LAPW/mGGA approach in analysis of carrier traps in insulators.
[20]
[21]
Acknowledgments
[22]
Financial support by the Polish National Science Centre (NCN) under the grants UMO-2014/13/B/ST5/01535 and 2017/26/D/ST3/ 00599. Wroclaw Centre for Networking and Supercomputing (WCSS) is acknowledged for the provided computing power. Kevin F. Garrity (National Institute of Standards and Technology (NIST), Gaithersburg, Maryland, USA) is greatly acknowledged for the provided Lu3+ ultrasoft pseudopotential.
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Appendix A. Supplementary data [27]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jlumin.2019.116583. [28]
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