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Acta Phys. Chim. Sin.  2015, Vol. 31 Issue (3): 441-447    DOI: 10.3866/PKU.WHXB201412301
Prediction of Native Point Defects in HfO2 Crystals Using First Principles and Thermodynamic Calculations
LIU Feng-Ming, LIU Ting-Yu, LIU Jian, LI Hai-Xin
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China
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Based on first principles and thermodynamics the intrinsic point defect formation energy was calculated at different temperatures and oxygen partial pressures in HfO2 crystals. The stability of all kinds of point defects as well as the formation of charged point defects and their sensitivity to the Fermi energy was analyzed. We also discuss rules that govern the formation of various point defects that vary with Fermi level. The results show that with a change in temperature and oxygen partial pressure the most stable point defects are obtained (Oi0, VO32+ and Hfi4+) when the Fermi level is close to the valence band. The main point defect was the Hf vacancy at a -4 charge when the Fermi level was higher than 3.40 eV. Apart from the Hf vacancy almost no other point defect had an odd charge and they showed negative-U behavior. Using the most stable intrinsic defect as a function of the Fermi level, the oxygen partial pressure and the temperature were determined using three-dimensional defect formation enthalpy diagrams. This diagram provides information that allows for the control of point defects in the crystal.

Key wordsDensity functional theory      Point defect      Thermodynamics      HfO2 crystal     
Received: 08 October 2014      Published: 30 December 2014
MSC2000:  O641  

The project was supported by the Foundation of Hujiang, China (B14004).

Corresponding Authors: LIU Ting-Yu     E-mail:
Cite this article:

LIU Feng-Ming, LIU Ting-Yu, LIU Jian, LI Hai-Xin. Prediction of Native Point Defects in HfO2 Crystals Using First Principles and Thermodynamic Calculations. Acta Phys. Chim. Sin., 2015, 31(3): 441-447.

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(1) Chow, R. S.; Falabella, G. E.; Loomis, F.; Rainer, C. J.; Stolz, M.; Kozlowski, R. Appl. Opt. 1993, 32, 5567. doi: 10.1364/AO.32.005567
(2) Waldorf, A. J.; Dobrowolski, J.; Sullivan, A. B. T.; Plante, L. M. Appl. Opt. 1993, 32, 5583. doi: 10.1364/AO.32.005583
(3) Houssa, M. High-k Gate Dielectrics; Institute of Physics: Bristol and Philadelphia, 2004.
(4) Copel, M.; Gribelyuk, M.; Gusev, E. Appl. Phys. Lett. 2000, 76, 436. doi: 10.1063/1.125779
(5) Jeon, T. S.; White, J. M.; Kwong, D. L. Appl. Phys. Lett. 2001, 78, 368. doi: 10.1063/1.1339994
(6) Qi,W. J.; Nieh, R.; Lee, B. H.; Kang, L.; Joen, Y. J.; Lee, J. C. Appl. Phys. Lett. 2000, 77, 3269. doi: 10.1063/1.1326482
(7) Gusev, E. P.; Cartier, E. D.; Buchanan, A.; Gribelyuk, M.; Copel, M.; Okorn-Schmidt, H.; Emic, C. D. Microelectron. Eng. 2001, 59, 341. doi: 10.1016/S0167-9317(01)00667-0
(8) Wilk, G. D.;Wallace, R. M.; Anthony, J. M. J. Appl. Phys. 2001, 89, 5243. doi: 10.1063/1.1361065
(9) Houssa, M.; Afanas'ev, V. V.; Stesmans, A.; Heyns, M. M. Appl. Phys. Lett. 2000, 77, 1885. doi: 10.1063/1.1310635
(10) Lee, B. H.; Kang, L.; Nieh, R.; Qi,W. J.; Lee, J. C. Appl. Phys. Lett. 2000, 76, 1926. doi: 10.1063/1.126214
(11) Gusev, E. P.; Cabral, C.; Copel, J. M.; D'Emic, C.; Gribelyuk, M. Microelectron. Eng. 2003, 69, 145. doi: 10.1016/S0167-9317(03)00291-0
(12) Lee, S. J.; Jeon, T. S.; Kwong, D. L.; Clark, R. J. Appl. Phys. 2002, 92, 2807. doi: 10.1063/1.1500420
(13) Kukli, K.; Ritala, M.; Sundqvist, J.; Aarik, J.; Lu, J.; Sajavaara, T.; Leskela, M.; Harsta, A. J. Appl. Phys. 2002, 92, 5698. doi: 10.1063/1.1515107
(14) Cho, M. H.; Roh, Y. S.; Whang, C. N.; Jeong, K.; Nahm, S.W.; Ko, D. H.; Lee, J. H.; Lee, N. I.; Fujihara, K. Appl. Phys. Lett. 2002, 81, 472. doi: 10.1063/1.1487923
(15) Kim, J.; Kim, S.; Jeon, H.; Cho, M. H.; Chung, K. B.; Bae, C. Appl. Phys. Lett. 2005, 87, 053108. doi: 10.1063/1.2005370
(16) Lee, S. J.; Choi, C. H.; Kamath, A.; Clark, R.; Kwong, D. L. IEEE Electron Device Lett. 2003, 24, 105. doi: 10.1109/LED.2002.807712
(17) Huff, H. R. Microelectron. Eng. 2003, 69, 152. doi: 10.1016/S0167-9317(03)00292-2
(18) Busch, B.W.; Schulte,W. H.; Garfunkel, E.; Gustafsson, T.; Qi, W.; Nieh, R.; Lee, J. Phys. Rev. B 2000, 62, 13290. doi: 10.1103/PhysRevB.62.R13290
(19) Brossman, U.;Wurschum, R.W.; Sodervall, U.; Schaefer, H. E. J. Appl. Phys. 1999, 85, 7646. doi: 10.1063/1.370567
(20) Martin, D.; Duprez, D. J. Phys. Chem. 1996, 100, 9429. doi: 10.1021/jp9531568
(21) Chavez, J. R.; Devine, R. A. B.; Koltunski, L. J. Appl. Phys. 2001, 90, 4284. doi: 10.1063/1.1401796
(22) Foster, A. S.; Sulimov, V. B.; Gejo, F. L.; Shluger, A. L.; Nieminen, R. M. Phys. Rev. B 2001, 64, 224108. doi: 10.1103/PhysRevB.64.224108
(23) Deng, Z.W.; Guo,W. M.; Liu, H. M.; Cao, L. L. Acta Phys. -Chim. Sin. 1999, 15, 528. [邓宗武, 郭伟民, 刘焕明, 曹立礼. 物理化学学报, 1999, 15, 528.] doi: 10.3866/PKU.WHXB19990609
(24) Wang, F. F.; Cao, Z. M.; Chen, J.; Xing, X. R. Acta Phys. -Chim. Sin. 2014, 30, 1432. [王方方, 曹战民, 陈骏, 邢献然. 物理化学学报, 2014, 30, 1432.] doi: 10.3866/PKU.WHXB201405281
(25) Robertson, J.; Xiong, K.; Falabretti, B. IEEE Trans. Device Mater. Reliab. 2005, 1, 84.
(26) Xiong, K.; Robertson, J.; Gibson, M. C.; Clark, S. J. Appl. Phys. Lett. 2005, 87, 183505. doi: 10.1063/1.2119425
(27) Foster, A. S.; Gejo, F. L.; Shluger, A. L.; Nieminen, R. M. Phys. Rev. B 2002, 65, 174117. doi: 10.1103/PhysRevB.65.174117
(28) Shen, C.; Li, M. F.;Wang, X. P.; Yu, H. Y.; Feng, Y. P.; Lim, A. T. L.; Yeo, Y. C.; Chan, Y. D. S. H.; Kwong, D. L. Tech. Dig. Int. Electron Devices Meet. 2004, 733.
(29) Kang, J.; Lee, E. C.; Chang, K. J.; Jin, Y. G. Appl. Phys. Lett. 2004, 84, 3894. doi: 10.1063/1.1738946
(30) Zheng, J. X.; Ceder, G.; Maxisch, T.; Chim,W. K.; Choi,W. K. Phys. Rev. B 2007, 75, 104112. doi: 10.1103/PhysRevB.75.104112
(31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. doi: 10.1103/PhysRevLett.77.3865
(32) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169. doi: 10.1103/PhysRevB.54.11169
(33) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758.
(34) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. doi: 10.1103/PhysRevB.50.17953
(35) Lee, J.; Han, S. Phys. Chem. Chem. Phys. 2013, 15, 18906.
(36) Batyrev, I. G.; Alavi, A.; Finnis, M.W. Phys. Rev. B 2000, 62, 4698.
(37) Finnis, M.W.; Lozovoi, A. Y.; Alavi, A. Ann. Rev. Mat. Res. 2005, 35, 167. doi: 10.1146/annurev.matsci.35.101503.091652
(38) Lide, D. R. CRC Handbook of Chemistry and Physics, Internet Version 2005 (; CRC Press: Boca Raton, FL, 2005.

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