Skip to main content
SpringerLink
Log in

Density Functional Theory Calculations for Phase Change Materials

  • Chapter
Phase Change Materials

  • 4753 Accesses

Abstract

In this chapter the fundamentals of Density Functional Theory (DFT) are introduced. After presenting the Hohenberg-Kohn theorem, the most common concepts and approximations in DFT-calculations, namely the Kohn-Sham equations and the Local Density Approximation (LDA), are summarized. They allow mapping the many-body problem on a single particle system which ultimately enables numerical calculations of the electronic ground state of a solid.

Furthermore, applications of DFT in the field of phase change materials are presented. DFT proves to be a powerful tool to reveal structural properties of the crystalline, liquid and amorphous phases as well as to explain the nature of the electronic ground state and bonding properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Born, M., Oppenheimer, J. M.: Zur Quantentheorie der Molekeln. Ann. Phys. 84, 457-484 (1927)

    Article  Google Scholar 

  2. Hartree, D. R.: Proc. Cambridge Philos. Soc. 24, 89-110 (1928)

    Article  Google Scholar 

  3. Fock, V.: Z. Physik 61, 126-148 (1930)

    Article  Google Scholar 

  4. Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864-871 (1964)

    Article  Google Scholar 

  5. Levy, M.: Universal variational functionals of electron densities, first-order density matrices,, natural spin-orbitals and solution of the nu-representability problem. Proc. Nat. Acad. Sci. 76, 6062-6065 (1979)

    Article  Google Scholar 

  6. Kohn, W., Sham, L. J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133-A1138 (1965)

    Article  Google Scholar 

  7. Ceperley, D. M., Alder, B. J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566-569 (1980)

    Article  Google Scholar 

  8. Slater, J. C., Wilson, T. M., Wood, J. H.: Comparison of several exchange potentials for electrons in the Cu+ ion. Phys. Rev. 179, 28-38 (1969)

    Article  Google Scholar 

  9. Ohno, K, Esfarjani, K., Kawazoe, Y.: Computational Materials Science. Springer, Berlin (1999)

    Google Scholar 

  10. Perdew, J. P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048-5079 (1981)

    Article  Google Scholar 

  11. Goedecker, S., Teter, M., Hutter, J.: Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703-1710 (1996)

    Article  Google Scholar 

  12. Gunnarsson, O., Jonson, M., Lundqvist, B. I.: Descriptions of exchange and correlation effects in inhomogeneous electron. Phys. Rev. B 20, 3136-3164 (1979)

    Article  Google Scholar 

  13. Perdew, J. P., Wang, Y.: Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Phys. Rev. B 33, 8800-8802 (1986)

    Article  Google Scholar 

  14. Perdew, J. P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865-3868 (1996)

    Article  Google Scholar 

  15. Onida, G., Reining, L., Rubio, A.: Electronic excitations: density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74, 601-659 (2002)

    Article  Google Scholar 

  16. O’Reilly, E. P., Robertson, J., Kelly, J. M.: The structure of amorphous GeSe and GeTe. Solid State Comm. 38, 565-568 (1981)

    Article  Google Scholar 

  17. Rabe, K. M., Joannopoulos, J. D.: Theory of the structural phase transition of GeTe. Phys. Rev. B 36, 6631-6639 (1987)

    Article  Google Scholar 

  18. Kolobov A. V., Fons, P., Tominaga, J., Ankudinov, A. L., Yannopoulos, S. N., Andrikopoulos, K. S.: Crystallization-induced short-range order changes in amorphous GeTe. J. Phys.: Condens. Matter 16, S5103-S5108 (2004)

    Article  Google Scholar 

  19. Nosé, S.: A molecular-dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255-268 (1984)

    Article  Google Scholar 

  20. Nosé, S.: A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511-519 (1984)

    Article  Google Scholar 

  21. Chelikowsky, J. R., Derby, J. J., Godlevsky, V. V., Jain, M., Raty, J. Y.: Ab initio simulations of liquid semiconductors using the pseudopotential-density functional method. J. Phys.: Condens. Matter. 13, R817-R854 (2001)

    Article  Google Scholar 

  22. Kubo, R.: Fluctuation-Dissipation Theorem. Rep. Prog. Phys. 29, 255-284 (1966)

    Article  Google Scholar 

  23. Stratonovitch, R. L.: Topics in the Theory of Random Noise. New York: Gordon and Breach (1963)

    Google Scholar 

  24. van Kampen, N. G.: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam (1981)

    Google Scholar 

  25. Risken, H.: The Fokker-Planck Equation. Springer, Berlin (1984)

    Google Scholar 

  26. Raty, J. Y., Godlevsky, V. V., Ghosez, P., Bichara, C., Gaspard, J. P., Chelikowsky, J. R.: Evidence of a reentrant Peierls distortion in liquid GeTe. Phys. Rev. Lett. 85, 1950-1953 (2000)

    Article  Google Scholar 

  27. Raty, J. Y., Gaspard, J. P., Bichara, C., Bergman, C., Bellissent, R., Ceolin, R.: Re-entrant Peierls distortion in IV-VI compounds. Physica B 276, 473-474 (2000)

    Article  Google Scholar 

  28. Raty, J. Y., Godlevsky, V. V., Gaspard, J. P., Bichara, C., Bionducci, M., Bellissent, R., Céolin, R., Chelikowsky, J. R., Ghosez, P.: Local structure of liquid GeTe via neutron scattering and ab initio simulations. Phys. Rev. B 65, 115205 (2001)

    Article  Google Scholar 

  29. Peierls, R. E.: Quantum Theory of Solids. Oxford University Press, Oxford (1956)

    Google Scholar 

  30. Bichara, C., Johnson, M., Raty, J. Y.: Temperature-induced density anomaly in Te-rich liquid germanium tellurides: p versus sp3 bonding? Phys. Rev. Lett. 95, 267801 (2005)

    Article  Google Scholar 

  31. Blaineau, S., Jund, P., Drabold, D.: Physical properties of a GeS2 glass using approximate ab initio molecular dynamics. Phys. Rev. B 67, 094204 (2003)

    Article  Google Scholar 

  32. Tafen, D. N., Drabold, D. A.: Models and modeling schemes for binary IV-VI glasses. Phys. Rev. B 71, 054206 (2005)

    Article  Google Scholar 

  33. Kolobov, A. V., Fons, P., Frenkel, A. I., Ankudinov, A. L., Tominaga,, Uruga, J. T.: Understanding the phase-change mechanism of rewritable optical media. Nature Materials 3, 703-708 (2004)

    Article  Google Scholar 

  34. Wełnic, W., Pamungkas, A., Detemple, R., Steimer, C., Blügel, S., Wuttig, M.: Unraveling the interplay of local structure and physical properties in phase-change materials. Nature Materials 5, 56-62 (2006)

    Article  Google Scholar 

  35. Kalb, J., Spaepen, F., Wuttig, M.: Calorimetric measurements of phase transformations in thin films of amorphous Te alloys used for optical data storage. J. Appl. Phys. 93, 2389-2393 (2003)

    Article  Google Scholar 

  36. Caravati, S., Bernasconi, M., Kühne, T. D., Krack, M., Parrinello, M.: Coexistence of tetrahedral- and octahedral-like sites in amorphous phase change materials. Appl. Phys. Lett. 91, 171906 (2007)

    Article  Google Scholar 

  37. Akola, J., Jones, R. O.: Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge2Sb2Te5 and GeTe. Phys. Rev. B 76, 235201 (2007)

    Article  Google Scholar 

  38. Errington, J. R., Debenedetti, P. G.: Relationship between structural order and the anomalies of liquid water. Nature 409, 318-321 (2001)

    Article  Google Scholar 

  39. Sun, Z., Zhou, J., Ahuja, R.: Structure of phase change materials for data storage. Phys. Rev. Lett. 96, 055507 (2006)

    Article  Google Scholar 

  40. Kooi, B. J., Groot, W. M. G., de Hosson, J. T. M.:In situ transmission electron microscopy study of the crystallization of Ge2Sb2Te5. J. Appl. Phys. 95, 924-932 (2004)

    Article  Google Scholar 

  41. Eom, J.-H., Yoon, Y.-G., Park, C., Lee, H., Im, J., Suh, D.-S., Noh, J.-S., Khang, Y., Ihm, J.: Global and local structures of the Ge-Sb-Te ternary alloy system for a phase-change memory device. Phys. Rev. B 73, 214202 (2007)

    Article  Google Scholar 

  42. Fischer, C., Tibbetts, K., Morgan, D., Ceder, G.: Predicting crystal structure: merging data mining with quantum mechanics. Nature Materials 5, 641-646 (2006)

    Article  Google Scholar 

  43. Edwards, A. H., Pineda, A. C., Schultz, P. A., Martin, M. G., Thompson, A. P., Hjalmarson, H. P., Umrigar, C. J.: Electronic structure of intrinsic defects in crystalline germanium telluride. Phys. Rev. B 73, 045210 (2006)

    Article  Google Scholar 

  44. Wuttig, M., Lüsebrink, D., Wamwangi, D., Wełnic, W., Gilleβen, M., Dronskowski, R.: The role of vacancies and local distortions in the design of new phase change. Nature Materials 6, 122-128 (2007)

    Article  Google Scholar 

  45. Dronskowski, R., Blöchl, P. E.: Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations. J. Phys. Chem. 97, 8617-8624 (1993)

    Article  Google Scholar 

  46. Glassey, W. V., Papoian, G. A., Hoffmann, R.: Total energy partitioning within a one-electron formalism: A Hamilton population study of surface-co interaction in the c(2 x 2)-CO/Ni(100) chemisorption system. J. Chem. Phys. 111, 893-910 (1999)

    Article  Google Scholar 

  47. Detemple, R., Wamwangi, D., Wuttig, M., Bihlmayer, G.: Identification of Te alloys with suitable phase change characteristics. Appl. Phys. Lett. 83, 2572-2574 (2003)

    Article  Google Scholar 

  48. Luo, M. B., Wuttig, M.: The dependence of crystal structure of Te-based phase-change materials on the number of valence electrons. Adv. Mat. 16, 439-443 (2004)

    Article  Google Scholar 

  49. Pirovano, A., Lacaita, A. L., Benvenuti, A., Pellizzer, F., Bez, R.: Electronic switching in phase-change memories. IEEE Trans. Electron Devices 51, 452-459 (2004)

    Article  Google Scholar 

  50. Kastner, M., Adler, D., Fritzsche, H.: Valence-alternation model for localized gap states in lone-pair semiconductors. Phys. Rev. Lett. 37, 1504-1507 (1976)

    Article  Google Scholar 

  51. Robertson, J., Xiong, K., Peacock, P. W.: Electronic and atomic structure of Ge2Sb2Te5 phase change memory material. Thin Solid Films 515, 7538-7541 (2007)

    Article  Google Scholar 

  52. Wełnic, W., Botti, S., Reining, L., Wuttig, M.: Origin of the optical contrast in phase-change materials. Phys. Rev. Lett. 98, 236403 (2007)

    Article  Google Scholar 

  53. Stefanucci, G., Almbladh, C.-O.: An exact ab initio theory of quantum transport using TDDFT and nonequilibrium Green’s functions J. Phys. Conf. Ser. 35, 17-24 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Solides Irradies, Ecole Polytechnique, 91128, Palaiseau, France

    Wojciech Wełnic

Authors
  1. Wojciech Wełnic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wojciech Wełnic .

Editor information

Editors and Affiliations

  1. IBM Almaden Research Center, 650 Harry Road, San Jose, CA, 95120, USA

    Simone Raoux

  2. 1. Physikalisches Institut (1A), RWTH University of Technology, 52056, Aachen, Germany

    Matthias Wuttig

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Wełnic, W. (2009). Density Functional Theory Calculations for Phase Change Materials. In: Raoux, S., Wuttig, M. (eds) Phase Change Materials. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-84874-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation