First principles LDA+U and GGA+U study of HfO2: Dependence on the effective U parameter

Year 2014, Volume: 27 Issue: 1, 627 - 636, 28.03.2014

Yasemin Çiftçi , A. Ergun K. Colakoglu E. Delıgoz

Abstract

We have performed first-principles calculations of the structural, electronic, mechanical, and vibrational properties of HfO2 based on the density functional theory with Local Density Approximation (LDA), Generalized Gradient Approximation(GGA), the LDA + U and GGA+U approaches based on the density functional theory (DFT). In orderd to describe precisely the strong on-site Coulomb repulsion among the localized Hf 5d electrons, we adopt the LDA+U and GGA+U formalism for the exchange correlation term. For the total-energy calculation we have used the projected augmented plane-wave (PAW) implementation of the Vienna Ab initio Simulation Package (VASP). The dependence of selected properties of this material on the effective U parameter has been investigated in detail. We have used to examine structure parameter in Fluorite(C1) structure of HfO2. The equilibrium geometries, the total and partial densities of states, elastic constants, elastic moduli, Poisson’s ratio, Zener anisotropy factor, Young’s modulus and shear modulus and phonon dispersion curves for this material are systematically investigated and analyzed in comparison with experiments and previous calculations. We show for the first time that the addition of an on-site Hubbard repulsion term to the LDA and GGA leads to improved agreement between calculated and experimental values of structural and electronic properties, except for elastic properties.

Keywords

Hafnia, LDA+U, GGA+U, First-principles calculation, mechanical properties, electronic structure, phonon dispersion.

References

• He, G., Zhu, L.Q., Liu, M., Fang, Q., Zhang, L.D., Appl. Surf. Sci., 253, 3413(2007).
• Aarik, J., Ma¨ndar, H., Kirm, M., Pung, L., Thin Solid Films, 466, 41, (2004).
• Renault, O., Rarrett, N.T., Samour, D., Quiais- Marthon, S., Surf. Sci., 526: 566–568 (2004).
• Zhao, X.Y., Vanderbilt, D., Phys. Rev. B, 65: 233106(2002).
• Terki, R., Feraoun, H., Bertrand, G., Aourag, H., Comput. Mater. Sci., 33: 44(2005).
• Cockayne, E., Phys. Rev. B 75, 094103 (2007).
• Weir, B.E., Silverman, P.J., . Alam, M.A, Baumann, F., Monroe, D., Ghetti, A., Bude, J.D., Timp, G.L., Hamad, A., Oberdick, T.M., Zhao, N.X., Ma, Y., Brown, M.M., Hwang, D., Sorsch, T.W., IEDM Tech. Dig., 437 (1999).
• Cao, M., Vande Voorde, P., Cox, M, Greene, W., IEEE Electron Device Lett., 19: 291 (1998).
• Fleming, W.J., J. Electrochem. Soc., 21: 124(1977).
• Alcock, C.B., Mater. Sci. Res., 419:10 (1975).
• Waldorf, A.J., Dobrowolsk, J.A.I, Sullivan, B.T., Plante, L.M., Appl. Opt., 5583: 32(1993).
• Wilk, G.D., Wallace, R.M., Anthony, J.M., J. Appl. Phys., 5243: 89(2001).
• Terki, R., Bertrand, G., Aourag, H., Coddet, C., Mater. Lett. ,62: 1484 (2008).
• Boyer, L.L., Klein, B.M., J. Am. Ceram. Soc., 278 : 68 (1985).
• Cohen, R.E., Mehl, M.J., Boyer, L.L., Physica B 1, 150 (1988).
• Jansen, H.J.F., Gardner, J.A., Physica B, 10: 150 (1988).
• Jansen, H.J.F., Phys. Rev. B, 7267, 43(1991).
• Jomard, G., Petit, Pasturel, T. A., Magaud, L., Kresse, G., Hafner, J., Phys. Rev. B, 4044 59 (1999).
• Stapper, G., Bernasconi, M., Nicoloso, N., Parrinello, M., Phys. Rev. B,797, 59(1999).
• Fabris, S., Paxton, A.T., Finnis, M.W., Phys. Rev. B 6617, 61(2000).
• Foster, A.S., Sulimov, V.B., Lopez Gejo, F., Shluger, A.L., Nieminen, R.M., Phys. Rev. B 224108-1, 64 (2001).
• Dabrowski, J., Zavodinsky, V., Fleszar, A., Microelectron. Reliab. 1093, 41(2001).
• Foster, A.S., Shluger, A.l., Nieminen, R.M., Phys. Rev. Lett., 225901-1, 89 (2002).
• Lin, W., Kang, J., Zhu, Z., Mater. Sci. Eng. B, 553: 99(2003).
• Foster, A.S., Lopez Gejo, F., Shluger, A.L., Nieminen, R.M., Phys. Rev. B, 174117-1, 65 (2002).
• Caravaca, M.A., Casali, R.A., J. Phys.: Condens. Matter, 17: 5795 (2005).
• Rignanese, G.M., Gonze, X., Jun, G, Cho, K., Pasquarello, A., Phys. Rev. B, 69:184301 (2004).
• Atashi, B.M., Javier, F.S., Charles, B.M., Phys. Rev. B, 73: 115330(2006).
• Patil, S.K.R., Wang, Y.X., Phys. Stat. Sol. B, 247: 54 (2010).
• Liu, Q. et al., Physica B, 404: 3614–3619 (2009).
• Liu, Q.J., Liu, Z.T., Feng, L., Xu, B., Physica Stat. Solidi B, 248: 4950 (2011).
• Liu, Q.J., Liu, Z.T., Feng, L., Commun. Theor. Phys., 56: 779(2011).
• Zhu, J.B., Ren, H.S., Zhu, J., Hao, Y. J., Liu, J., Zhang, C. M., Long, X.J., Physica B, 406: 2501, (2011).
• Dudarev, S.L., Botton, G.A., Savrasov, S.Y., Humphreys, C.J., Sutton, A.P., Phys. Rev.B, 57: 1505(1998).
• Kresse, G., Hafner, J., Phys. Rev. B, 48 : 13115(1993). [36] Kohn, W., Sham, L.J., Phys. Rev., 140, A1133(1965).
• Wang, Y., Perdew, J.P., Phys. Rev. B, 44: 13298 (1991).
• Bl¨ochl, P. E., Phys. Rev. B , 50: 17953 (1994).
• Monkhorst, H. J., Pack, J.D., Phys. Rev. B, 13: 5188 (1976).
• Stacy, D.W., Johnstone, J.K., Wilder ,D.R., J. Am. Ceram. Soc., 55 (1972).
• Murnaghan, F. D., Proc. Natl., Acad. Sci., USA : 30, 5390 (1994)
• Demkov, A.A., Phys.Stat.Sol. B, 226, No.1 (2001)
• Wang, J., Li, H.P., Stevens, R., J. Of Mat. Sci., 27: 5397(1992)
• He, G. et al., Appl. Surf. Sci., 253 (2007)
• Medvedeva, N.I., Zhukovi, V.P., Khodos, M.Y., Gubanov, V.A., Phys. Status. Sol., 160: 517 (1990)
• Nielson, O. H., Martin, R.M., Phys. Rev. Lett., 50, 697 (1983).
• Mayer, V.B., Anton, H., Bott, E., Methfessel, M., Sticht, J., Haris, J., Schmidt, P. C., Intermetallics 11, 23 (2003).
• Sevik, C., Çağın, T., Phys. Rev. B, 80, 014108(2009)
• Young, A. F., Sanloup, C., Gregoryanz, E., Scandolo, S., Hemley, R. E., Mao, H. K., Phys. Rev. Lett.,96: 155501(2006).
• Watt, J.P., Peselnick, L., J.App. Phys., 51: 1525 (1980).
• http://chianti.geol.ucl.ac.uk/~dario/ (1998).
• Alfè, D., Price, G. D., Gillan, M. J., Phys. Rev. B: 64, 045123 (2001).
• Kresse, G., Furthmüller, J. and Hafner, J., Europhys. Lett., 32: 729 (1995).