Bandgap Engineering in Yttrium–Aluminum Garnet with Ga Doping

Article pubs.acs.org/crystal

Bandgap Engineering in Yttrium−Aluminum Garnet with Ga Doping Ivan I. Vrubel,† Roman G. Polozkov,*,†,‡ Ivan A. Shelykh,†,‡ Vasilii M. Khanin,¶,§ Piotr A. Rodnyi,¶ and Cees R. Ronda§ †

ITMO University, Saint Petersburg 197101, Russia Science Institute, University of Iceland, Dunhagi 3 IS-107, Reykjavik, Iceland ¶ Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia § Philips Research Eindhoven, High Tech Campus 34, 5656 AE, Eindhoven, The Netherlands ‡

ABSTRACT: We report the results of the investigation of Ga-doping effects on the electronic structure of the yttrium−aluminum garnet. The bandgap structure was studied both experimentally using thermally stimulated luminescence technique and theoretically by first-principles density functional theory calculations. We observe a nonlinear decrease in the conduction band minimum with respect to the vacuum referred binding energy with an increase in Ga doping and argue that the effect can be explained by taking into account different influences of the distorted crystal field on the molecular orbitals of the crystal unit cell. The reported nonlinear behavior is important for the band engineering of scintillators based on multicomponent garnets.

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INTRODUCTION Yttrium−aluminum garnet (Y3Al5O12 or YAG (see Figure 1)) doped with Ce3+ is widely used as an efficient optical material in

required for a particular application, the use of the multicomponent garnets, i.e. materials in which the light cations (Al, Y) are replaced by heavier ones (Ga, Gd, Lu),6 is highly desirable.7 The important example is garnet compounds with the common formula Y3Al5−xGaxO12 (YAGG),8 where x changes from 0 to 5. The introduction of Ga3+ and other heavy cations into the crystalline matrix leads to the distortion of the crystal structure and modifies energy characteristics of the system, including the band gap. The ionic radius of Ga3+ (0.62 and 0.47 Å for VI-fold and IV-fold coordination, respectively) is very close to that of Al3+ (0.535 and 0.39 Å for VI-fold and IV-fold coordination, respectively).9 On the basis of conventional ionic radius arguments and theoretical calculations,10 it is reasonable to expect that Ga3+ occupies an octahedral site, but experimental studies have shown that Ga3+ preferentially occupies a tetrahedral site in YAG.11,12 More recently, the idea that covalent Ga−O bonding in a garnet could be an explanation for Ga residing on the smaller tetrahedral site13 has been proposed. It has been also shown theoretically that the tetrahedral site is favorable compared to the octahedral site for Ga to occupy.14 Dorenbos collected spectroscopic data on multicomponent garnet compounds, which allowed construction of the corresponding electronic structure scheme.15 It clearly demonstrates that replacing Al by larger Ga atoms in the compounds leads to the following effects: (i) the band gap

Figure 1. General view of the YAG unit cell. Blue spheres depict positions of yttrium atoms; green spheres depict aluminum, and red spheres depict oxygen.

variety of technological applications which include light emitting diodes (LEDs), plasma display panels, solar cells, and scintillators.1 YAG:Ce and mixed oxide garnets in general are very compositionally versatile and are able to fulfill all applications requirements:2,3 they are chemically stable, optically effective, and highly absorbent in the UV range,4 which is important for LED design, and are transparent, possess high photon yield, low afterglow in the millisecond range, and short decay time,5 which is important for medical imaging techniques. To improve the characteristics of a material © 2017 American Chemical Society

Received: December 13, 2016 Revised: February 27, 2017 Published: February 27, 2017 1863

DOI: 10.1021/acs.cgd.6b01822 Cryst. Growth Des. 2017, 17, 1863−1869

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decreases; (ii) the first 5d1 level of Ce3+ moves up and approaches the bottom of the conduction band; and (iii) the splitting between 5d1 and 5d2 levels of Ce3+ decreases. This combination of the band gap engineering and 5d level positioning techniques opens a possibility to diminish the negative effects of shallow traps. Moreover, it allows a sufficient energy gap to remain between 5d1 excited level of Ce3+ and bottom of the conduction band, which is necessary to prevent undesirable thermal excited-state ionization at room temperature.16 It was also claimed that incorporation of Ga into the YAG matrix removes electron trapping associated with cation antisite defects.17 Additionally, recent theoretical studies demonstrated that replacement of Al with Ga in LuAG lowers the cation antisite defect formation energy, thus suggesting that Ga inclusion should lead to higher concentration of antisite defects.14 This result is in agreement with previous studies2,16 which specify that variations of the electronic structure (rather than defect concentration) are responsible for the improvement of the garnet scintillator performance with Ga doping.18,19 In this work, we present the results of investigation of the band structure of the family of YAGG and demonstrate how such characteristics as position of the conduction band minimum (CBM) and bandgap Eg change with increase in Ga doping.

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approximation by Perdew, Burke, and Ernzerhof26 were used. The electronic configuration and corresponding occupation numbers are Y (5s24d1), Al(3s23p1), Ga(4s24p1), and O(2s22p4). The full geometry optimization of the spatial structures was performed without any restrictions on atomic positions or the crystal lattice constant. We created several quasi-random periodic structures of YAGG with stoichiometric coefficients of Ga equal to x = 0, 1, 2, 3, 4, and 5. Six models (having x from 0 to 5) have uniform distribution of Ga; two models (having x = 1) contain Ga atoms only in octahedral or tetrahedral sites, and in the last two, the Ga occupation ratios (for x = 2 and x = 3) from ref 12 are used. The threshold for atomic force components during geometry optimization was equal to 0.001 Ry/au. Before the geometry optimization, slight distortion in each atomic position was intentionally added to create starting tension and consequent relaxation. The performed calculations were checked geometrically using the method described below. The final geometries and optimal lattice constants were used for the garnet macrocell generation consisting of 27 unit cells. Afterward, we utilized the fact that each metal atom of the unit cell is placed in a polyhedron with oxygen atoms in vertices and constructed polyhedra for 64 metal atoms situated in the central unit cell inside the macrocell. Dependence of metal−oxygen distances and lattice constants on compositions was calculated to control the accuracy of geometry optimization.

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RESULTS AND DISCUSSION Experimental Results. In principle, it is possible to investigate the influence of doping on the very bottom of the conduction band with the TSL method by estimation of the defect trap depth and its shift with variation in YAGG composition. As we try to see the variation in the CBM, we need defects behaving as electron traps. In addition, the defect level has to be constant with respect to the vacuum referred binding energy (VRBE). It was shown17,27 that in garnets, Ce3+ ion as the primary luminescence center behaves like a hole trap. Meanwhile, the analysis of TSL glow curves for YAG:Ce (poly)crystals allows detection of the electron traps related to Cr3+, Eu3+, and Yb3+ impurities.28−30 Note that according to ref 18, the energy level of the trapped electron at Cr2+/3+ in YAGG:Ce remains almost the same; therefore, we use this level as reference point in the experimental probing of the bottom of conduction band. TSL glow curves measured for YAGG Y3Al5−xGaxO12 for x = 0−4 are presented in Figure 2. Trace amounts of Cr are still present31 in garnets sintered out of 4N purity raw oxides. TSL peaks associated with Cr impurity are marked at the plots by integer numbers corresponding to Ga stoichiometric coef-

EXPERIMENTAL AND THEORETICAL METHODS

Experimental Technique. All garnet ceramic samples doped with 0.2 mol % Ce used in this study were prepared at Philips Research Eindhoven by sintering of a mix of base oxides of 4N purity at around 2000 K in the form of pills of 14 mm diameter and 0.7−1.4 mm thickness. On the basis of the X-ray diffraction patterns, it was concluded that all the samples consist of a single garnet phase. The thermally stimulated luminescence (TSL) curves were obtained in the temperature range of 80−550 K after irradiation with X-rays (tube parameters were 55 kV acceleration voltage and 10 mA current) detected with PMT R6357 (sensitive in the range of 200−900 nm). All TSL curves were recorded with β = 15 K/min heating rate. Black-body emission was subtracted from the TSL curves. The glow curves were also corrected to account for the thermal quenching of the luminescence, measured with UC-920 Edinburg Instruments spectrofluorimeter under excitation with 450 nm light in the temperature range of room temperature (RT) to 550 K. The equipment was calibrated to account for the wavelength dependent transmission of the monochromators and the spectral sensitivity of the PMT. Computational Details. Advanced theoretical methods can provide better understanding of the processes occurring in the multicomponent garnets and allow determination of the characteristics of the band structure and the position of the impurity levels.10,20 However, there are certain difficulties in theoretical study of the garnets associated with their complex crystal structure. The unit cell of YAG (see Figure 1) is known to have a bcc structure (Ia3d (230) space group) with 160 atoms:21 96 predefined oxygen positions, 24 dodecahedral sites for yttrium atoms, and 16 octahedral and 24 tetrahedral sites for aluminum and gallium atoms, respectively, with tunable ratio. Therefore, for the first step, the scalable model with formula Dod24Oct16Tet24O96 was constructed. Each oxygen atom belongs to two dodecahedra, one tetrahedron, and one octahedron. The cation−O distance in the tetrahedra is the shortest cation−anion distance, while in the octahedra, it is about 10% larger. The Y−O distances in the dodecahedra are 30% larger than the shortest cation− O one. The lattice constant of YAG is12.00 Å. In our theoretical analysis, we used DFT approach22,23 for both geometry optimization and electronic structure modeling of YAGG. The calculations were performed with plane wave basis set using the QuantumESPRESSO package.24 Pseudopotentials from the QuantumESPRESSO pseudopotential database25 with exchange-correlation

Figure 2. TSL glow curves of Y3Al5−xGaxO12:Ce mixtures with x = 0, 1, 2, 3, and 4. Ga content values are put above corresponding Crrelated impurity TSL peaks. 1864

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respectively, consist of four δ-like distributions. The shortest metal−ligand distances correspond to the tetrahedra and octahedra with Al or Ga in their centers, whereas the two longest metal−ligand bonds correspond to the dodecahedral positions of yttrium atoms. The number of oxygen atoms in every distribution sums to the total amount of oxygens forming the polyhedra around the cations. In the case of YAGG, the lattice becomes distorted. This has the following effects. First, the pattern of metal−ligand distributions becomes broadened, as it can be seen in Figure 3 for Y3Al3Ga2O12. Second, the lattice constant of the unit cell increases with increasing Ga content. The dependence is almost linear and consistent with Vegard’s law. The result is quite different with respect to reported for Y3−xGdxAl5O12:Ce3+ garnets.35 The comparison of our numerical results with experimental data and earlier works is shown in Table 2.

ficients. Note that if the percentage of Ga is increased, TSL maximum first shifts slightly to the higher temperatures (from 404 K at x = 0 to 407 K, for x = 1) and then moves monotonously down to smaller temperatures.18 From the position of the TSL maxima, it is possible to determine the energy depth of the trap level. The corresponding relation was derived in ref 32 and reads:

βE = se E / kBTpeak 2 kBTpeak

(1)

Where Tpeak (K) is the position of TSL peak maximum, E is the electron trap depth counted from the bottom of the conduction band, β (K/sec) is glow curve heating rate, kB is Boltzmann constant, and s (sec−1) is frequency factor. The latter was estimated to be 1011 to 1013 s−1 for Cr-related TSL traps33 in YAGG:Ce using the varying heating rates method.34 In our work, we assume that frequency factor s = 1012 s−1. The results are summarized in Table 1. Note that E and Tpeak demonstrate a slight increase when Ga stoichiometric coefficient is changed from x = 0 to 1 and then decrease monotonously as a function of x.

Table 2. Geometrical Parameters of the Unit Cells and the Length of the Chemical Bonds Based on the Calculated Equilibrium Geometries of the YAGG composition YAG YAG YAG YAG YAGG: YAGG: YAGG: YAGG: YGG YGG YGG YGG

Table 1. Thermal Position of the TSL Peak Glow and Its Energy Equivalenta x in Y3Al5−xGaxO12

Tpeak

energy depth of Cr-related trap, eV (thermal)

0 1 2 3 4 5

404 407 363 295 238

0.81 0.81 0.73 0.59 0.48

a

Note the non-monotonous dependence of Tpeak and E with increasing Ga concentration.

x x x x

= = = =

1 2 3 4

parameter, Å

calculated result

reference value

lattice constant Y−O Al−Otet Al−Ooct lattice constant lattice constant lattice constant lattice constant lattice constant Y−O Ga−Otet Ga−Ooct

11.98 2.33/2.44 1.76 1.91 12.03 12.09 12.13 12.16 12.23 2.35/2.43 1.83 1.97

11.99,36 12.0137,38 2.30/2.4336,37 1.78,36 1.7637,38 1.91,36 1.9437,38

12.2738,39 2.34/2.4239 1.84,39 1.8538 1.99,39 2.0038

Calculated Electronic Structure of the Mixed Compositions. In this section, we present the results of the calculation of electronic structure of YAGG using density functional theory (DFT) techniques. Note that the DFT is a ground state theory and is not able to reproduce the bandgap precisely. However, currently there exist comprehensive research data on estimation of the systematic error between the experimental bandgap evaluations and DFT calculations on various mixed garnets (see, e.g., refs 2 and 19). The observation of non-monotonous behavior of the CBM was the focus of several experimental works.18,31 The main goal of this work is to reveal qualitative trends in the behavior of the bandgap with Ga doping. Because garnets belong to the class of wide bandgap insulators (Eg ≈ 7 eV), we assume that, for the PBE functional, the systematic underestimation of the gap is about 20%.40 It should be noted that, in principle, correct quantitative estimation of the band gap can be performed by using of GW-based modeling. However, this requires significant computational facilities for such complex and large lattices as garnets and even more so with relatively heavy ions. The wave functions for the unit cell were calculated with the use of the spatial structures obtained from the geometry optimization. These structures were considered as unit cells with quasi-random composition which nevertheless has periodic nature.41 The DFT calculations were performed using the QuantumESPRESSO package.24 The post processing code allows for projecting the occupied and unoccupied wave functions of the unit cell onto orthogonalized atomic wave

Calculated Spatial Structure of the Mixed Compositions. The results of the geometry optimization of the unit cell are presented in Figure 3. The result is presented in the form of a histogram in the axes metal−oxygen distance/number of corresponding bonds. It can be seen that black and red patterns corresponding to ideal YAG (Y3Al5O12) and YGG (Y3Ga5O12),

Figure 3. Metal−ligand distance histograms calculated for YAG, YGG, and Y3Al3Ga2O12. Black and red histograms of ideal YAG and YGG crystals, respectively, have four accurate characteristic bond distances: one for octahedra and tetrahedra and two for dodecahedra. In the Y3Al3Ga2O12 case, the crystal lattice becomes distorted, and distribution of metal−ligand distances broadens. 1865

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functions taken from pseudo potential files. With spatial structure of the compositions being known and accounting for the necessary correction of the bandgap value, we can compare the results of the numerical DFT simulation with the non-monotonous behavior of the CBM obtained experimentally by measuring the depth of Cr-related traps (Table 1). To understand better the results, we can build density of states (DoS) of the molecular orbitals and their projections on atomic orbitals (PDoS) corresponding to the different members of YAGG family. Experimental data show that in YAGG mixtures the most intriguing process occurs at the CBM; therefore, in our investigation, we mainly focus on unoccupied molecular orbitals which can be used for the estimation of the parameters of a conduction band. The results for the DoS are presented at Figure 4 for YAGGs with x = 0, 1, and 5. We set the energy of the highest occupied

Figure 5. Entire PDoS for Y and O atoms in Y3Al4Ga1O12. Comparison with Figure 4 leads to the conclusion that the most important contribution to the upper range of the VB comes from pshell of oxygen, whereas the lower range of the CB is mainly formed by d-shells of yttrium.

Figure 4. Total DoS of YAGG mixtures with x = 0, 1, and 5 are presented by black, red, and blue curves, respectively. The inset shows the nonlinear decrease in the CBM with incorporation of 20% Ga in the YAG unit cell.

molecular orbital to zero; thus, the negative range of spectra represents occupied molecular orbitals (valence band), whereas the positive range represents unoccupied orbitals. DoS spectra corresponding to various x values demonstrate clear differences at the bottom of CB (see inset), while the differences are negligible at the top of VB. It is interesting to note that our calculations show that the band gap decreases starting from the gallium concentration of about 20% (see inset), remaining almost unchanged below this value. The entire PDoS spectra corresponding to Y and O atoms are presented in Figure 5. One can clearly see that the VB mainly consists of p-orbitals of oxygen, while the main contribution to the CB states comes from the d-orbitals of yttrium37 (see Figure 5 compared to Figure 4). Examining the very bottom of the CB PDoS (see inset in Figure 4 and Figure 6), we can identify the contributions from s and p orbitals of the cations (Y, Altet,oct and Gatet,oct). For YAGGs with x = 0 and 1, the contributions of s and p-orbitals to the formation of CBM are insignificant compared to the contribution from the d-orbital of Y. On the contrary, for x = 3 and 5, the states at the bottom of CB are mainly formed by s and p components, and the contribution of d orbitals of Y becomes significant only in the region of higher energies.

Figure 6. Enlarged PDoS of Y, Altet + Aloct, and Gatet + Gaoct atoms for the family of YAGG with x = 0, 1, 3, and 5. The Al and Ga PDoS axes are rescaled by a factor of 10 compared to that of Y PDoS.

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DISCUSSION The DoS and PDoS spectra presented in Figures 4−6 are summarized in the band diagram shown in Figure 7. The valence band is formed mainly with p-orbitals of oxygen (Figure 5). As for the CB, the regions where s, p, and d states give the most important impact are shown in black, red, and blue, respectively. One can see that with an increase in the concentration of Ga, the contribution of s and p orbitals becomes more significant in the region close to the CBM, while the d-component provided by the Y 4d orbital manifests an opposite tendency. We suggest that such behavior can be explained by variation in the crystal field (CF) and covalency of the compound if Al is substituted by Ga. On one hand, the centroid of the split dorbital is shifting due to the change of the covalence with Ga doping. On the other hand, the distortion of sites occupied by Ga results in changes of the value of the d orbital splitting. The total effect is that the d orbital of Y slightly moves up. Such a notion can also be supported by a more straightforward 1866

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Figure 7. Stacked PDoS diagram demonstrating principal contributions of s, p, and d orbitals to the states forming the bottom of the CB for the family of YAGG. The top of the VB shown in green is scaled to zero. The stoichiometric coefficient for Ga increases along the x-axis.

Figure 8. Value of the bandgap Eg (eV) obtained by DFT modeling compared with reference experimental values18 (red dots). The different distributions of Ga are used in calculations: (i) black squares, uniform Ga distribution; (ii) magenta and green, octahedral and tetrahedral Ga occupation, respectively; (iii) blue triangles, Ga distribution from experimental work.12

example of the comparison of CB in yttrium aluminum perovskite (YAP) and YAG. As in YAG, CB in YAP is formed by the Y 4d orbital.42 However, according to the existing literature, the bandgap for YAP is larger than the one for YAG.43 Because the difference between these two materials is only in the type of the lattice sites,42 this effect can be explained by the weaker CF for YAP due to the absence of the tetrahedral sites in its unit cell.44 Therefore, the bottom of the CB rises with the decrease in the CF splitting from YAG to YAP. The study of the effects similar to those considered in the present paper was performed2 for the Lu3Al5−xGaxO12:Ce family, where a continuous decrease in the CBM with Ga doping was observed. The same experimental TSL result for Lu3Al5−xGaxO12:Ce was also reported in ref 31, while in Gd3Al5−xGaxO12:Ce, the CBM curve had a maximum at x = 2. Systematic DFT study of Lu3−yGdyAl5−xGaxO12 revealed19 a continuous shift of the CBM maximum from x = 0, y = 0 to approximately x = 1, y = 3. The values of the bandgap Eg (eV) for the YAGG family were determined using variety of experimental techniques (absorption spectra, optical spectroscopy at LHe, etc.).18,45,46 We selected one data set18 and compared it with our results obtained by DFT modeling (Figure 8). Several different distributions of Ga over sites were used in calculations: (i) black squares, uniform Ga distribution; (ii) magenta and green, octahedral and tetrahedral Ga occupation, respectively; (iii) blue triangles, Ga distribution from experimental work.12 While experimental values were systematically higher than numerical ones (for the reasons briefly discussed at the beginning of Section 3.3), the general trend was the same: initial slight increase in the gap for stoichiometric coefficient of Ga x = 1 followed by fast linear decrease for x = 2, 3, 4, and 5.

rearrangement of the contribution of s, p, and d atomic orbitals of the cations to molecular orbitals.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +7 812 457 18 46; Fax: +7 812 457 18 46. ORCID

Roman G. Polozkov: 0000-0002-6996-3097 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I.I.V., R.G.P., and I.A.S. acknowledge the support of the Ministry of Education of the Russian Federation in the framework of Increase Competitiveness Program 5-100. R.G.P. and I.A.S. acknowledge support from H2020-MSCARISE “CoExAN 644076”.

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CONCLUSIONS Using the combination of the first-principle DFT calculations and TSL experimental technique, we studied the effect of Ga doping on electronic properties of the family Y3Al5−xGaxO12. The bond lengths and lattice constants were calculated, and their values were compared with experimental X-ray diffraction data. Total and projected DoS were constructed. We reported nonlinear behavior of the band gap as a function of stoichiometric coefficient of Ga. We explain this behavior by effects of the distorted CF and gallium covalency on the 1867

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DOI: 10.1021/acs.cgd.6b01822 Cryst. Growth Des. 2017, 17, 1863−1869

Crystal Growth & Design

Article

31, 1835−1838. Proceedings of the Second International Workshop on Advanced Spectroscopy and Optical Materials.

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DOI: 10.1021/acs.cgd.6b01822 Cryst. Growth Des. 2017, 17, 1863−1869