MODELING OF ZnO ELECTRONIC STRUCTURE FROM FIRST PRINCIPLES BY APPLYING ADVANCED FUNCTIONALS

Subject of Research. We have studied the electronic structure of wurzite zinc oxide (ZnO) by quantum mechanical modeling using density functional theory (DFT) approach with different exchange-correlation energy functionals. Methods. The calculations were performed by means of generalized gradient approximation (GGA), Hubbard corrected generalized gradient approximation (DFT+U method) and hybrid functional PBE0. Main Results. The calculations have demonstrated that the basic GGA approach renders ZnO electronic structure with essential disadvantages demonstrating overestimated hybridization of zinc 3d and oxygen 2p shells and significantly underestimated bandgap. The inaccuracy for the latter has been eliminated by using the PBE0 approach, which is highly computationally demanding and increases the complexity of the calculations. We have shown that the best results complying with the experiment are obtained by applying Hubbard correction to all atoms of unit cell. Practical Relevance. The study shows the necessity of Hubbard correction usage when calculating zinc oxide electronic structure with the parameter of on-site repulsion “U” applied to both Zn and O atoms. The physical aspects and details of all used approaches and their computational demands are discussed.

1. Ellmer K., Klein A. ZnO and its applications. Transparent Conductive Zinc Oxide. Springer, Berlin, Heidelberg, 2008, pp. 1–33. doi: 10.1007/978-3-540-73612-7_1
2. Özgür Ü. et al. A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 2005, vol. 98, no. 4, pp. 11. doi: 10.1063/1.1992666
3. Wei S.H., Zunger A. Calculated natural band offsets of all II–VI and III–V semiconductors: Chemical trends and the role of cation d orbitals. Applied Physics Letters, 1998, vol. 72, no. 16, pp. 2011–2013. doi: 10.1063/1.121249
4. Rodnyi P.A., Chernenko K.A., Venevtsev I.D. Mechanisms of ZnO luminescence in the visible spectral region. Optics and Spectroscopy, 2018, vol. 125, no. 3, pp. 372–378. doi: 10.1134/s0030400x18090205
5. Chernenko K.A. et al. Structural, optical, and luminescent properties of ZnO:Ga and ZnO:In ceramics. IEEE Transactions on Nuclear Science, 2018, vol. 65, no. 8, pp. 2196–2202. doi 10.1109/TNS.2018.2810331
6. Ma Y. et al. Single-crystal growth of ZnO:Ga by the traveling- solvent floating-zone method. Crystal Growth and Design, 2017, vol. 17, no. 3, pp. 1008–1015. doi: 10.1021/acs.cgd.6b01232
7. Bourret-Courchesne E.D., Derenzo S.E., Weber M.J. Development of ZnO:Ga as an ultra-fast scintillator. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2009, vol. 601, no. 3, pp. 358–363. doi: 10.1016/j. nima.2008.12.206
8. Hu J., Pan B.C. Electronic structures of defects in ZnO:hybrid density functional studies. The Journal of Chemical Physics, 2008, vol. 129, no. 15, pp. 154706. doi: 10.1063/1.2993166
9. Himmetoglu B. et al. Hubbard-corrected DFT energy functionals: The LDA + U description of correlated systems. International Journal of Quantum Chemistry, 2014, vol. 114, no. 1, pp. 14–49. doi: 10.1002/qua.24521
10. Morales-Garcia A., Valero R., Illas F. An empirical, yet practical way to predict the band gap in solids by using density functional band structure calculations. The Journal of Physical Chemistry C,
2017, vol. 121, no. 34, pp. 18862–18866. doi: 10.1021/acs.jpcc.7b07421
11. Hohenberg P., Kohn W. Inhomogeneous electron gas. Physical Review, 1964, vol. 136, no. 3B, pp. B864–B871. doi: 10.1103/PhysRev.136.B864
12. Kohn W., Sham L.J. Self-consistent equations including exchange and correlation effects. Physical Review, 1965, vol. 140, no. 4A, pp. A1133–A1138. doi: 10.1103/PhysRev.140.A1133
13. Giannozzi P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 2009, vol. 21, no. 39, pp. 395502. doi: 10.1088/0953-8984/21/39/395502
14. Monkhorst H.J., Pack J.D. Special points for Brillouin-zone integrations. Physical Review B, 1976, vol. 13, no. 12, pp. 5188– 5192. doi: 10.1103/PhysRevB.13.5188
15. Perdew J.P., Burke K., Ernzerhof M. Generalized gradient approximation made simple. Physical Review Letters, 1996, vol. 77, no. 18, pp. 3865. doi: 10.1103/PhysRevLett.77.3865
16. Paudel T.R., Lambrecht W.R.L. First-principles calculation of the O vacancy in ZnO: A self-consistent gap-corrected approach. Physical Review B, 2008, vol. 77, no. 20, pp. 205202. doi: 10.1103/PhysRevB.77.205202
17. Oba F. et al. Point defects in ZnO: an approach from first principles. Science and Technology of Advanced Materials, 2011, vol. 12, no. 3, pp. 034302. doi: 10.1088/1468-6996/12/3/034302
18. Goh E. S., Mah J. W., Yoon T. L. Effects of Hubbard term correction on the structural parameters and electronic properties of wurtzite ZnO. Computational Materials Science, 2017, vol. 138, pp. 111–116. doi: 10.1016/j.commatsci.2017.06.032
19. Liechtenstein A.I., Anisimov V.I., Zaanen J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Physical Review B, 1995, vol. 52, no. 8, pp. R5467. doi: 10.1103/PhysRevB.52.R5467
20. Janotti A., van de Walle C.G. Oxygen vacancies in ZnO. Applied Physics Letters, 2005, vol. 87, no. 12, pp. 122102. doi: 10.1063/1.2053360
21. Betzinger M., Friedrich C., Blügel S. Hybrid functionals within the all-electron FLAPW method: implementation and applications of PBE0. Physical Review B, 2010, vol. 81, no. 19, pp. 195117. doi: 10.1103/PhysRevB.81.195117
22. Bashyal K. et al. Empirical optimization of DFT+ U and HSE for the band structure of ZnO. Journal of Physics: Condensed Matter, 2018, vol. 30, no. 6, pp. 065501. doi: 10.1088/1361-648X/aaa441
23. Muscat J., Wander A., Harrison N.M. On the prediction of band gaps from hybrid functional theory. Chemical Physics Letters, 2001, vol. 342, no. 3-4, pp. 397–401. doi: 10.1016/S0009-2614(01)00616-9
24. Adamo C., Barone V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. The Journal of Chemical Physics, 1999, vol. 110, no. 13, pp. 6158–6170. doi: 10.1063/1.478522
25. Clark S.J. et al. Self-interaction free local exchange potentials applied to metallic systems. Journal of Physics: Condensed Matter, 2017, vol. 29, no. 37, pp. 374002. doi: 10.1088/1361-648X/aa7ba6
26. Gygi F., Baldereschi A. Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon. Physical Review B, 1986, vol. 34, no. 6, pp. 4405–4408. doi: 10.1103/PhysRevB.34.4405
27. Kisi E.H., Elcombe M.M. u parameters for the wurtzite structure of ZnS and ZnO using powder neutron diffraction. Acta Crystallographica Section C: Crystal Structure Communications, 1989, vol. 45, no. 12, pp. 1867–1870. doi: 10.1107/S0108270189004269
28. Blöchl P.E., Jepsen O., Andersen O.K. Improved tetrahedron method for Brillouin-zone integrations. Physical Review B, 1994, vol. 49, no. 23, pp. 16223. doi: 10.1103/PhysRevB.49.16223
29. Oba F. et al. Native defects in oxide semiconductors: a density functional approach. Journal of Physics: Condensed Matter, 2010, vol. 22, no. 38, pp. 384211. doi: 10.1088/0953-8984/22/38/384211
30. Oba F. et al. Defect energetics in ZnO: A hybrid Hartree-Fock density functional study. Physical Review B, 2008, vol. 77, no. 24, pp. 245202. doi: 10.1103/PhysRevB.77.245202
31. Lim L.Y. et al. Angle-resolved photoemission and quasiparticle calculation of ZnO: The need for d band shift in oxide
semiconductors. Physical Review B, 2012, vol. 86, no. 23, pp. 235113. doi: 10.1103/PhysRevB.86.235113
32. Huang G.Y., Wang C.Y., Wang J.T. Detailed check of the LDA + U and GGA + U corrected method for defect calculations in wurtzite ZnO. Computer Physics Communications, 2012, vol. 183, no. 8, pp. 1749–1752. doi: 10.1016/j.cpc.2012.03.017
33. Agapito L.A., Curtarolo S., Nardelli M.B. Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated materials discovery. Physical Review X, 2015, vol. 5, no. 1, pp. 011006. doi: 10.1103/PhysRevX.5.011006
 

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License