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Reduction in charged defects associated with oxygen vacancies in hafnia by magnesium incorporation: First-principles study
6.N. Umezawa, K. Shiraishi, K. Torii, M. Boero, T. Chikyow, H. Watanabe, K. Yamabe, T. Ohno, K. Yamada, and Y. Nara, IEEE Electron Device Lett. 28, 363 (2007).
13.J. Adam and M. D. Rodgers, Acta Crystallogr. 12, 951 (1959);
14.We confirmed that the 96-atom supercell is sufficiently large. The formation energy of , which is the largest defect in our calculations, is changed only by 0.08 eV as extending cell size from 72-atom to the 96-atom supercell.
15.The computational band gap (3.9 eV) underestimates the experimental value [5.7 eV (Ref. 16)] due to the common problem of LDA. Our conclusion, however, is not significantly affected by this issue because all the thermodynamic transition levels are energetically far distant from the conduction band minimum (Fig. 1) and the corresponding wave functions are well localized at the defect sites (not shown).
20.M. Sato, N. Umezawa, N. Mise, S. Kamiyama, M. Kadoshima, T. Morooka, T. Adachi, T. Chikyow, K. Yamabe, K. Shiraishi, S. Miyazaki, A. Uedono, K. Yamada, T. Aoyama, T. Eimori, Y. Nara, and Y. Ohji, Dig. Tech. Pap. - Symp. VLSI Technol. 2008, 66.
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