Abstract
In this chapter, we provide the reader with the basic concepts of density functional theory and first principles calculations, at the minimum level needed to provide the reader with the necessary vocabulary. The modern electronic structure theory of materials is based on density functional theory introduced by Walter Kohn and co-workers in the mid- 1960s. The theory formulates the many-body problem of interacting electrons and ions in terms of a single variable, namely the electron density. We discuss some key aspects of density functional theory using the local density approximation including calculations of band alignment, dielectric constants, and phonons. We also briefly describe some “beyond DFT” methods that are necessary for describing highly correlated systems such as for example, many magnetic oxides.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Born, R. Oppenheimer, Ann. Phys. 84, 458 (1927)
P. Hohenberg, W. Kohn, Phys. Rev. 136, 864 (1964)
W. Kohn, L.J. Sham, Phys. Rev. 140, 1133 (1965)
J.R. Chelikowsky, N. Troullier, Y. Saad, Phys. Rev. Lett. 72, 1240 (1994)
M.C. Payne, M.P. Teter, D.C. Alan, T.A. Arias, J.D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)
J.C. Phillips, L. Kleinman, Phys. Rev. 116, 287 (1959)
D. Hamann, M. Schluter, C. Chiang, Phys. Rev. Lett. 43, 1494 (1979)
N. Trulier, J.L. Martins, Phys. Rev. B 43, 1993 (1991)
D. Vanderbilt, Phys. Rev. B 41, 7892 (1990)
P.E. Blöchl, Phys. Rev. B 50, 17953 (1994)
G. Kresse, J. Joubert, Phys. Rev. B 59, 1758 (1999)
M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, New York, 1988)
D.M. Bylander, L. Kleinman, Phys. Rev. B 36, 3229 (1987)
C.G. Van de Walle, R.M. Martin, Phys. Rev. B 39, 1871 (1989)
R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 47, 1651 (1993)
G.K. Horton, A.A. Maradudin, Dynamical Properties of Solids (North-Holland, Amsterdam, 1974)
G. Kresse, J. Furtmuller, Phys. Rev. B 54, 11169 (1996)
V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, R.H. Nobes, J. Quant. Chem. 77, 895 (2000)
J.P. Lewis, K.R. Glaesemann, G.A. Voth, J. Fritsch, A.A. Demkov, J. Ortega, O.F. Sankey, Phys. Rev. B 64, 195103 (2001)
J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junquera, P. Ordejón, D. Sánchez-Portal, J. Phys. Condens. Matter 14, 2745 (2002)
B. Delley, J. Chem. Phys. 113, 7756 (2000)
M.J. Frisch et al., Gaussian 98 (Gaussian, Inc., Pittsburgh, PA, 1998)
S. Baroni, A. Dal Corso, S. de Gironcoli, P. Giannozzi, http://www.pwscf.org
X. Gonze, D.C. Allan, M.P. Teter, Phys. Rev. Lett. 68, 3603 (1992). http://www.abinit.org
M. Städele, J.A. Majewski, P. Vogl, A. Görling, Phys. Rev. Lett. 79, 2089 (1997)
M. Städele, M. Moukara, J.A. Majewski, P. Vogl, Phys. Rev. B 59, 10031 (1999)
F. Aryasetiawan, O. Gunnarsson, Phys. Rev. Lett. 74, 3221 (1995)
M. Rohlfing, S.G. Louie, Phys. Rev. B 62, 4927 (2000)
A.A. Demkov, A. Navrotsky (eds.), Materials Fundamentals of Gate Dielectrics (Springer, Dordrecht, 2005)
L. Hedin, Phys. Rev. 139, A796 (1965)
M.S. Hybertsen, S.G. Louie, Phys. Rev. B 32, 7005 (1985)
S. Lany, Phys. Rev. B 87, 085112 (2013)
R.O. Jones, O. Gunnarson, Rev. Mod. Phys. 61, 689 (1989)
J.P. Perdew, A. Zunger, Phys. Rev. B 23, 5048 (1981)
M. Arai, T. Fujiwara, Phys. Rev. B 51, 1477 (1995)
A. Filippetti, N.A. Spaldin, Phys. Rev. B 67, 125109 (2003)
V.I. Anisimov, P. Kuiper et al., Phys. Rev. B 50, 8257 (1994)
K.W. Lee, W.E. Pickett, Phys. Rev. B 73, 174428 (2006)
J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)
J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 124, 219906E (2006)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
The relation between the local Green’s function and charge density is given by n(r) = ∫dw/πf(π)G(r,r;ω). DMFT includes the frequency dependence (dynamics) that DFT does not
K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Bluemer, A.K. McMahan, R.T. Scalettar, T. Pruschke, V.I. Anisimov, D. Vollhardt, Phys. Status Solidi 243, 2599 (2006)
G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti Rev, Mod. Phys. 78, 865 (2006)
D. Sholl, J.A. Steckel, Density Functional Theory: A Practical Introduction (John Wiley and Sons, Hoboken, NJ, 2009)
R.G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989)
R.M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University press, Cambridge, 2004)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 The Author(s)
About this chapter
Cite this chapter
Demkov, A.A., Posadas, A.B. (2014). Predictive Engineering of Semiconductor-Oxide Interfaces. In: Integration of Functional Oxides with Semiconductors. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9320-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-9320-4_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-9319-8
Online ISBN: 978-1-4614-9320-4
eBook Packages: EngineeringEngineering (R0)