The geometrical structure and electronic properties of trivalent Ho³⁺ doped Y₂O₃ crystals: a first-principles study

Abstract

Trivalent rare-earth holmium ion (Ho³⁺) doped yttrium oxide (Y₂O₃) has attracted great research interest owing to its unique optoelectronic properties and excellent performances in many new-type laser devices. But the crystal structures of the Ho³⁺-doped Y₂O₃ system (Y₂O₃ : Ho) are still unclear. Here, we have carried out a first-principle study on the structural evolution of the trivalent Ho³⁺ doped Y₂O₃ by using the CALYPSO structure search method. The results indicate that the lowest-energy structure of Ho³⁺-doped Y₂O₃ possesses a standardized monoclinic P2 phase. It is found that the doped Ho³⁺ ion are likely to occupy the sites of Y³⁺ in the host crystal lattice, forming the [HoO₆]⁹⁻ local structure with C₂ site symmetry. Electronic structure calculations reveal that the band gap value of Ho³⁺-doped Y₂O₃ is approximately 4.27 eV, suggesting the insulating character of Y₂O₃ : Ho system. These findings could provide fundamental insights to understand the atomic interactions in crystals as well as the information of electronic properties for other rare-earth-doped materials.

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1. Introduction

Rare-earth (RE) doped laser materials have attracted enormous interests because of their abundant transition channels and sharp luminescence bands.^1–5 The potential applications have been widely investigated in a diversity of fields, such as optical imaging, quantum cascade lasers, high-density optical data storage and biophotonic areas.^6–9 A recent study reveals that the directly pumped Ho³⁺-doped silica microsphere may be an excellent candidate for fabricating 2 μm laser, which can serve as laser-emitting source for mid-infrared telecommunications.¹⁰

Trivalent holmium ion (4f¹⁰ configuration) is a greatly promising laser ion due to the substantial transition channels at various wavelengths in the UV, visible and infrared regions.^11,12 A well-known emission transition ⁵I₇ → ⁵I₈ with wavelength near 2 μm of Ho³⁺ can serve as the so called “eye safe” solid-state laser system.¹³ Yttrium oxide (Y₂O₃) is a typical cubic phase crystal structure with Ia3̄ space group, which possesses low phonon energy and desirable physical properties including low thermal expansion, high melting point and photochemical stability.^14–16 The Y³⁺ ions of yttrium oxide crystal are six-fold coordinated to nearest O²⁻ ligands, forming a [YO₆]⁹⁻ local unit with C₂ site symmetry.¹⁷ After being doped with appropriate rare-earth ions, Y₂O₃ crystals can serve as excellent laser host materials because of their high thermal conductivity and low phonon energy.¹⁸ In recent years, Ho³⁺-doped Y₂O₃ (Y₂O₃ : Ho) crystal has been the subject of intensive investigations as a great promising laser material.¹⁹ Laversenne et al. first demonstrated the growth of Ho³⁺-doped Y₂O₃ single crystal by using the Laser Heated Pedestal Growth (LHPG) technique.²⁰ In addition, they especially analyzed the dynamical laser resonant characteristics of Y₂O₃ : Ho. Qin et al. studied the luminescence spectra of Ho³⁺-doped Y₂O₃ under the excitation of a 532 nm continuous-wave laser.²¹ The results indicate that Ho³⁺ ion possesses several fluorescence transitions in the ultraviolet and violet region (306, 390 and 428 nm) which are assigned to the transitions of ³D₃ → ⁵I₈, ⁵G₄ → ⁵I₈ and ⁵G₅ → ⁵I₈, respectively. Wang et al. reported a high output laser operation at around 2.1 μm of Y₂O₃ : Ho with low scattering loss and excellent optical quality.²² Their results revealed that Ho³⁺-doped Y₂O₃ system shows attractive prospect in high-power and efficient laser applications as a laser gain medium. Although numerous investigations have been widely reported on Y₂O₃ : Ho, there is no systematic study to elucidate its microstructure and electronic properties.

In this paper, we perform extensive structure searches to obtain the ground-state structure of Y₂O₃ : Ho based on the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization)^23–27 method coupled with the DFT (density functional theory). Furthermore, we calculate and analyze the band structure, density of states and the ELF (electron localized function) to gain deeper insights into the electronic properties of Ho³⁺-doped Y₂O₃ system. The outline of this paper is organized as follows. We exhibit a brief description of the calculation method in Section 2. In Section 3, we present our results and discussion. A conclusion is finally given in Section 4.

2. Computational methods

We have explored the structural evolution of Y₂O₃ : Ho crystal by using the unbiased CALYPSO^23–27 method. The CALYPSO is a reliable structure prediction method which has been validated by a large variety of crystal structures.^28–32 We perform an evolutionary variable-cell structure prediction with 80 atoms per simulation cell at ambient pressure. To determine the most stable structure of Y₂O₃ : Ho system, we optimized the all lowest-lying candidate structures by using the density functional theory in VASP (Vienna Ab Initio Simulation Package) code.^33–35 The frozen-core all electron projector-augmented wave (PAW) method has been adopted, with 4f¹¹5s²5p⁶6s², 4d¹5s² and 2s²2p⁴ treated as valence electrons for Ho, Y and O, respectively. For describing the influence of the correlation effect introduced by 4f electrons of Ho atoms, we employ the local density approximation (LDA) with an onsite Coulomb repulsion parameter U³⁶ to determine the electronic band structure of Y₂O₃ : Ho. The U value of Ho has been determined to be 6.8 eV by Min et al.³⁷ Phonon dispersion curve have been calculated by the PHONOPY code.³⁸

3. Results and discussion

We carefully examine the ground-state crystal structure of Ho³⁺-doped Y₂O₃ by using the unbiased CALYPSO structure search method with the stoichiometric ratio of Ho : Y : O = 1 : 31 : 48 under ambient conditions. The lowest-energy structure of Y₂O₃ : Ho is successfully identified and displayed in Fig. 1. It can be seen from Fig. 1 that the ground-state Y₂O₃ : Ho crystal possesses the monoclinic configuration with the Ho³⁺ ion (0.901 Å) substitute for Y³⁺ ion (0.900 Å) in the Y₂O₃ host. The concentration of the impurity Ho³⁺ is equal to 3.125%, which is in excellent agreement with the result measured by Atabaev et al.¹⁵ The site symmetry of [HoO₆]⁹⁻ local structure are calculated to be C₂ and Ho³⁺ position are six-coordinated by oxygen atoms. The three different bond lengths between Ho–O bonds are calculated to be 2.214, 2.232, and 2.318 Å, respectively. The Ho³⁺ doped Y₂O₃ crystal structure belongs to the standardized P2 symmetry and the calculated lattice constants are a = b = c = 10.524 Å, β = 90°. The coordinates of all atoms for the ground state Y₂O₃ : Ho are summarized in Table 1 for further investigations. Moreover, our structure searches also predict many metastable structures of Ho³⁺-doped Y₂O₃ which can play important roles to explore the structural evolutions. The first four optimized low-lying structures (a), (b), (c) and (d) from low to high energy are exhibited in Fig. 2. It is found that the Y³⁺ ions of these isomers are replaced by Ho³⁺ ions at different sites in the host crystals. Interestingly, the isomer (a) possesses the same P2 monoclinic configuration with the ground-state structure while the isomers (b), (c) and (d) exhibit the P1 space group. In these metastable structures, we find that the impurity Ho³⁺ ions tend to occupy the crystal face site positions of the Y³⁺.

Fig. 1 Crystal structure and [HoO₆]⁹⁻ local unit of the ground-state Ho³⁺-doped Y₂O₃. The bond lengths are in the unit of Å.

Table 1 Coordinates of all atoms for the ground state Ho³⁺-doped Y₂O₃

Atom	x	y	z	Wyckoff site symmetry
Ho	0.50000	0.03244	−0.00000	1c
O(1)	−0.09805	0.37926	0.39177	2e
O(2)	0.40264	0.87998	0.89255	2e
O(5)	0.40205	0.12070	0.60831	2e
O(6)	−0.09818	0.62076	0.10808	2e
O(9)	0.14194	0.15190	0.37921	2e
O(10)	0.64186	0.65190	0.87934	2e
O(11)	−0.14176	0.84802	0.87927	2e
O(12)	0.35819	0.34791	0.37925	2e
O(17)	0.12928	0.39175	0.15192	2e
O(18)	0.62931	0.89190	0.65180	2e
O(19)	0.62868	0.10740	0.84899	2e
O(20)	0.12931	0.60822	0.34801	2e
O(25)	0.59794	0.62079	0.60830	2e
O(26)	0.09816	0.12070	0.10813	2e
O(29)	0.09808	0.87932	0.39175	2e
O(30)	0.59805	0.37924	0.89184	2e
O(33)	0.35820	0.84806	0.62099	2e
O(34)	−0.14195	0.34792	0.12077	2e
O(35)	0.64100	0.15153	0.12014	2e
O(36)	0.14182	0.65199	0.62075	2e
O(41)	0.37080	0.60848	0.84803	2e
O(42)	−0.12934	0.10816	0.34796	2e
O(43)	−0.12943	0.89189	0.15191	2e
O(44)	0.37080	0.39172	0.65211	2e
Y(1)	0.00004	0.24998	0.24998	2e
Y(2)	0.49982	0.75036	0.24967	2e
Y(3)	0.50011	0.24976	0.75024	2e
Y(4)	0.00005	0.75003	0.75003	2e
Y(9)	−0.25020	0.24979	0.96795	2e
Y(10)	−0.25006	0.75002	0.53211	2e
Y(13)	0.71753	0.00010	0.24967	2e
Y(15)	−0.21791	0.50004	0.24995	2e
Y(21)	−0.25026	0.75030	0.03217	2e
Y(22)	0.25002	0.24997	0.53226	2e
Y(25)	−0.21803	0.00001	0.75019	2e
Y(26)	0.28218	0.49999	0.24999	2e
Y(17)	0.00000	0.96781	0.00000	1a
Y(30)	0.00000	0.46784	0.00000	1a
Y(18)	0.50000	0.53219	−0.00000	1c
Y(19)	0.00000	0.03214	0.50000	1b
Y(29)	0.00000	0.53220	0.50000	1b
Y(20)	0.50000	0.46778	0.50000	1d
Y(31)	0.50000	0.96786	0.50000	1d

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Fig. 2 Coordination structures of the metastable (a–d) for Y₂O₃ : Ho.

To clarify the true structure of the ground-state Y₂O₃ : Ho, as shown in Fig. 3, we calculate the X-ray diffraction (XRD) patterns of the ground state structure. We can clearly see from Fig. 3 that the simulated spectrum of Y₂O₃ : Ho are in good accordance with the observations in experiment.¹⁵ In addition, the XRD patterns of the four metastable structures are calculated and the results are also plotted in Fig. 3. It can be seen from Fig. 3 that the overall distribution of the peaks is similar, suggesting that the structural parameters of the four metastable structures are close to each other. To further validate the dynamical stability of Ho³⁺-doped Y₂O₃ system, we have calculated the phonon dispersion curves in Fig. 4 and no imaginary phonon frequencies can be seen over the entire Brillouin zones. The result indicates that the determined ground-state structure of Ho³⁺-doped Y₂O₃ crystal is dynamically stable. These theoretical results provide great support for the reliability of our structural prediction methodology.

Fig. 3 Comparison of the simulated XRD spectrum for the ground-state and metastable (a–d) Y₂O₃ : Ho with experimental patterns.

Fig. 4 Calculated phonon dispersion curve for the ground-state Y₂O₃ : Ho.

We have calculated the electronic band structure and the total as well as partial DOS for Y₂O₃ : Ho. As illustrated in Fig. 5(a), the direct band gap value for Ho³⁺-doped Y₂O₃ is about 4.27 eV at the Γ point, which is approximately 2/3 of the experimental value (E_g = 6.2 eV) determined by Wallace and Wilk.³⁹ This result can be ascribed to the general underestimation of band gap value by the first-principle calculations. The result indicates that the Ho³⁺ impurity ion remains the insulating character of Ho³⁺-doped Y₂O₃ crystal. From Fig. 5(b), we can clearly see that the low valence band region is mainly composed of p states with the smaller contributors of d states ranging from −1 eV to 0 eV, and the dominant contributions of the high conduction band between 4.3 eV to 9 eV are mainly occupied by p, d and f states. It should be noted that the s states is very weak from −1 eV to 9 eV. In addition, we have calculated the electron localized function (ELF) to visualize the chemical bonding character in Y₂O₃ : Ho crystal. The ELF in crystal structure and the ELF of the (100) plane are presented in Fig. 6. It is shown that the ELF near the Y and Ho atoms value is close to 0.9, which suggests that the electrons are extremely localized around the Y and Ho atoms.

Fig. 5 The calculated (a) electronic band structure and (b) total as well as partial densities of states of Y₂O₃ : Ho.

Fig. 6 ELF maps of (a) the structure and (b) 〈100〉 plane for the ground-state Y₂O₃ : Ho.

4. Conclusions

In summary, we have explored the ground-state crystal structure of Ho³⁺-doped Y₂O₃ by means of the unbiased CALYPSO method combined with first-principle calculations. It is shown that the ground-state Y₂O₃ : Ho structure possesses a novel P2 phase with the monoclinic symmetry. We carry out a systematical investigation to the microstructure evolutions for the ground-state Y₂O₃ : Ho crystal. The results indicate that the impurity Ho³⁺ ion substitutes the positions of Y³⁺ ions in the host crystal lattice, forming the [HoO₆]⁹⁻ local structure. We find that the impurity Ho³⁺ ions tend to occupy the crystal face positions of the Y³⁺ ions from the structural features of the ground-state and metastable structures. We further calculate the band structure and density of states by LDA + U method for Y₂O₃ : Ho. Our result reveals that the electronic band gap of Ho³⁺-doped Y₂O₃ is 4.27 eV. We hope that these findings can provide valuable guidance for future experiment research of Y₂O₃ : Ho.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11904297, 11747139 and 11804031) and the Fundamental Research Funds for the Central Universities (SWU118055), the Scientific Research Project of Education Department of Hubei Province (No. Q20191301), the Youth Fund of Yangtze University (No. 2016cqn, Y. Y. J.).

References

1. P. S. J. Bharadwaj, S. Kundu, V. S. Kollipara and K. B. R. Varma, Synergistic effect of trivalent (Gd³⁺, Sm³⁺) and high-valent (Ti⁴⁺) co-doping on antiferromagnetic YFeO₃, RSC Adv., 2020, 10, 22183–22195.
2. J. Bai, P. Duan, X. Wang, G. Han, M. Wang and G. Diao, Upconversion luminescence enhancement by Fe³⁺ doping in CeO₂ : Yb/Er nanomaterials and their application in dye-sensitized solar cells, RSC Adv., 2020, 10, 18868–18874.
3. Monika, R. S. Yadav, A. Bahadur and S. B. Rai, Concentration and pump-mediated color tenability, optical heating and temperature sensing via TCLs of red emission in an Er³⁺/Yb³⁺/Li⁺ co-doped ZnGa₂O₄ phosphor, RSC Adv., 2019, 9, 40092–40108.
4. N. Choudhary, M. K. Verma, N. D. Sharma, S. Sharma and D. Singh, Correlation between magnetic and transport properties of rare earth doped perovskite manganites La_0.6R_0.1Ca_0.3MnO₃ (R = La, Nd, Sm, Gd, and Dy) synthesized by Pechini process, Mater. Chem. Phys., 2020, 242, 122482.
5. M. P. Ghosh, S. Sharma, H. K. Satyapal, K. Tanbir, R. K. Singh and S. Mukherjee, Tuning the microstructural, optical and superexchange interactions with rare earth Eu doping in nickel ferrite nanoparticles, Mater. Chem. Phys., 2020, 241, 122383.
6. S. D. Jackson, Towards high-power mid-infrared emission from a fibre laser, Nat. Photonics, 2012, 6, 423–431.
7. I. Cieslik, T. Bolek, M. J. Wozniak, A. Majchrowski, S. Hirano and A. Budzianowski, Potassium gadolinium tungstate nanocrystals doped with holmium ions as candidates for optical imaging, Appl. Surf. Sci., 2018, 446, 139–144.
8. Y. R. Fang and M. T. Sun, Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits, Light: Sci. Appl., 2015, 4, e294.
9. X. Y. Wang, Y. L. Wang, S. Wang, B. Li, X. W. Zhang, L. Dai and R. M. Ma, Lasing Enhanced Surface Plasmon Resonance Sensing, Nanophotonics, 2017, 6, 472–478.
10. A. Z. Li, M. Zhang, X. Wang, S. B. Wang, B. G. Guo, E. Lewis and P. F. Wang, Directly pumped Ho³⁺-doped microspheres lasing at 2.0 μm, IEEE Photonics Technol. Lett., 2019, 31, 1366–1368.
11. S. Balaji, G. Gupta, K. Biswas, D. Ghosh and K. Annapurna, Role of Yb³⁺ ions on enhanced ∼2.9 μm emission from Ho³⁺ ions in low phonon oxide glass system, Sci. Rep., 2016, 6, 29203.
12. M. Eichhorn, Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions, Appl. Phys. B, 2008, 93, 269–316.
13. M. C. Pujol, J. Massons, M. Aguiló, F. Díaz, M. Rico and C. Zaldo, Emission Cross Sections and Spectroscopy of Ho³⁺ Laser Channels in KGd(WO₄)₂ Single Crystal, IEEE J. Quantum Electron., 2002, 38, 93–100.
14. A. Ciric and S. Stojadinovic, Structural and photoluminescence properties of Y₂O₃ and Y₂O₃ : Ln³⁺ (Ln = Eu, Er, Ho) films synthesized by plasma electrolytic oxidation of yttrium substrate, J. Lumin., 2020, 217, 116762.
15. T. S. Atabaev, H. H. T. Vu, Y. D. Kim, J. H. Lee, H. K. Kim and Y. H. Hwang, Synthesis and luminescence properties of Ho³⁺ doped Y₂O₃ submicron particles, J. Phys. Chem. Solids, 2012, 73, 176–181.
16. B. M. Walsh, J. M. McMahon, W. C. Edwards, N. P. Barnes, R. W. Equall and R. L. Hutcheson, Spectroscopic characterization of Nd : Y₂O₃: application toward a differential absorption lidar system for remote sensing of ozone, J. Opt. Soc. Am. B, 2002, 19, 2893–2903.
17. M. Ju, Y. Xiao, W. G. Sun, C. Lu and Y. Y. Yeung, In-depth determination of the microstructure and energy transition mechanism for Nd³⁺-doped yttrium oxide laser crystals, J. Phys. Chem. C, 2020, 124, 2113–2119.
18. V. Singh, V. K. Rai, B. Voss, M. Haase, R. P. S. Chakradhar, D. T. Naidu and S. H. Kim, Photoluminescence study of nanocrystalline Y₂O₃ : Ho³⁺ phosphor, Spectrochim. Acta, Part A, 2013, 109, 206–212.
19. G. A. Newburgh, A. W. Daniels, A. Michael, L. D. Merkle, A. Ikesue and M. Dubinskii, Resonantly diode-pumped Ho³⁺ : Y₂O₃ ceramic, Opt. Express, 2011, 19, 3604–3611.
20. L. Laversenne, C. Goutaudier, Y. Guyot, M. T. Cohen-Adad and G. Boulon, Growth of rare earth (RE) doped concentration gradient crystal fibers and analysis of dynamical processes of laser resonant transitions in RE-doped Y₂O₃ (RE = Yb³⁺, Er³⁺, Ho³⁺), J. Alloys Compd., 2002, 341, 214–219.
21. F. Qin, Y. D. Zheng, Y. Yu, Z. M. Chen, P. S. Tayebi, W. W. Cao and Z. G. Zhang, Ultraviolet and violet upconversion luminescence in Ho³⁺-doped Y₂O₃ ceramic induced by 532-nm CW laser, J. Alloys Compd., 2011, 509, 1115–1118.
22. F. Wang, J. W. Tang, E. H. Li, C. F. Shen, J. Wang, D. Y. Tang and D. Y. Shen, Ho³⁺ : Y₂O₃ ceramic laser generated over 113 W of output power at 2117 nm, Opt. Lett., 2019, 44, 5933–5936.
23. Y. C. Wang, J. Lv, L. Zhu and Y. M. Ma, Crystal structure prediction via particle-swarm optimization, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 094116.
24. Y. C. Wang, J. Lv, L. Zhu and Y. M. Ma, CALYPSO: a method for crystal structure prediction, Comput. Phys. Commun., 2012, 183, 2063–2070.
25. Y. C. Wang, M. S. Miao, J. Lv, L. Zhu, K. T. Yin, H. Y. Liu and Y. M. Ma, An effective structure prediction method for layered materials based on 2D particle swarm optimization algorithm, J. Chem. Phys., 2012, 137, 224108.
26. S. H. Lu, Y. C. Wang, H. Y. Liu, M. S. Miao and Y. M. Ma, Self-assembled ultrathin nanotubes on diamond (100) surface, Nat. Commun., 2014, 5, 3666.
27. L. Zhu, H. Y. Liu, C. J. Pickard, G. T. Zou and Y. M. Ma, Reactions of xenon with iron and nickel are predicted in the Earth's inner core, Nat. Chem., 2014, 6, 644–648.
28. J. Lv, Y. C. Wang, L. Zhu and Y. M. Ma, Particle-swarm structure prediction on clusters, J. Chem. Phys., 2012, 137, 084104.
29. Y. Xiao, M. Ju, X. Y. Kuang and Y. Y. Yeung, A systematic study of the microstructure and laser characteristics of Pr³⁺-doped lithium lutetium fluoride, J. Alloys Compd., 2018, 749, 391–398.
30. G. Bo, P. Gao, S. Lu, J. Lv, Y. Wang and Y. Ma, Interface structure prediction via CALYPSO method, Sci. Bull., 2019, 64, 301.
31. C. Lu and C. Chen, Indentation-strain stiffening in tungsten nitrides: mechanisms and implications, Phys. Rev. Mater., 2020, 4, 043402.
32. C. Lu and C. Chen, Structure-strength relations of distinct MoN phases from first-principles calculations, Phys. Rev. Mater., 2020, 4, 044002.
33. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
34. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 558–561.
35. J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, 77, 3865–3868.
36. V. I. Anisimov, F. Aryasetiawan and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U Method, J. Phys.: Condens. Matter, 1997, 9, 767–808.
37. B. I. Min, H. J. F. Jansen, T. Oguchi and A. J. Freeman, Local density total energy description of ground and excited state properties of the rare earth metals, J. Magn. Magn. Mater., 1986, 61, 139–150.
38. A. Togo, F. Oba and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl₂-type SiO₂ at high pressures, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, 134106.
39. R. M. Wallace and G. Wilk, Alternative gate dielectrics for microelectronics, Bulletin, 2002, 27, 186.

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