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Predicting Optical Properties from Ab Initio Calculations

  • Pavel OndračkaEmail author
  • David Holec
  • Lenka Zajíčková
Chapter
Part of the Springer Series in Surface Sciences book series (SSSUR, volume 64)

Abstract

In this chapter a short overview is given of some of the ab initio methods that can be used to predict optical properties of solids in order to gain insights into the underlying principles and to explain experimentally observed phenomena or predict properties of new materials. Density functional theory is presented as the most popular first principles technique for electronic structure calculations along with a brief description of a more sophisticated many body perturbation theory based on the Green’s functions formalism. The Bethe–Salpeter equation is introduced as a mean to calculate optical properties including excitonic effects. Those methods are applied to a model system of crystalline silicon as well as more complicated oxide materials.

Keywords

First principles calculations Density functional theory GW method Ab initio optical properties Bethe–Salpeter equation 

Notes

Acknowledgements

We would like to thank professor Dominik Munzar for reading this chapter, valuable comments and helpful discussion.

References

  1. 1.
    P. Hohenberg, W. Kohn, Phys. Rev. 136(3B), B864 (1964).  https://doi.org/10.1103/PhysRev.136.B864
  2. 2.
    W. Kohn, L.J. Sham, Phys. Rev. 140(4A), A1133 (1965).  https://doi.org/10.1103/PhysRev.140.A1133 ADSCrossRefGoogle Scholar
  3. 3.
    U. von Barth, L. Hedin, J. Phys. C: Solid State Phys. 5(13), 1629 (1972).  https://doi.org/10.1088/0022-3719/5/13/012
  4. 4.
    M.S. Hybertsen, S.G. Louie, Phys. Rev. B 34(8), 5390 (1986).  https://doi.org/10.1103/PhysRevB.34.5390 ADSCrossRefGoogle Scholar
  5. 5.
    J.P. Perdew, MRS Bull. 38(09), 743 (2013).  https://doi.org/10.1557/mrs.2013.178
  6. 6.
    D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45(7), 566 (1980).  https://doi.org/10.1103/PhysRevLett.45.566 ADSCrossRefGoogle Scholar
  7. 7.
    J.P. Perdew, Y. Wang, Phys. Rev. B 45(23), 13244 (1992).  https://doi.org/10.1103/PhysRevB.45.13244 ADSCrossRefGoogle Scholar
  8. 8.
    J.P. Perdew, A. Zunger, Phys. Rev. B 23(10), 5048 (1981).  https://doi.org/10.1103/PhysRevB.23.5048 ADSCrossRefGoogle Scholar
  9. 9.
    R.W. Godby, M. Schlüter, L.J. Sham, Phys. Rev. B 37(17), 10159 (1988).  https://doi.org/10.1103/PhysRevB.37.10159 ADSCrossRefGoogle Scholar
  10. 10.
    J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100(13), 136406 (2008).  https://doi.org/10.1103/PhysRevLett.100.136406 ADSCrossRefGoogle Scholar
  11. 11.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77(18), 3865 (1996).  https://doi.org/10.1103/PhysRevLett.77.3865 ADSCrossRefGoogle Scholar
  12. 12.
    J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100(13), 136406 (2008).  https://doi.org/10.1103/PhysRevLett.100.136406 ADSCrossRefGoogle Scholar
  13. 13.
    P. Dufek, P. Blaha, V. Sliwko, K. Schwarz, Phys. Rev. B 49(15), 10170 (1994).  https://doi.org/10.1103/PhysRevB.49.10170 ADSCrossRefGoogle Scholar
  14. 14.
    J.P. Perdew, K. Schmidt, AIP Conf. Proc. 577(1), 1 (2001).  https://doi.org/10.1063/1.1390175 ADSGoogle Scholar
  15. 15.
    J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, J. Sun, Phys. Rev. Lett. 103(2), 026403 (2009).  https://doi.org/10.1103/PhysRevLett.103.026403 ADSCrossRefGoogle Scholar
  16. 16.
    F. Tran, P. Blaha, Phys. Rev. Lett. 102(22), 226401 (2009).  https://doi.org/10.1103/PhysRevLett.102.226401 ADSCrossRefGoogle Scholar
  17. 17.
    D. Koller, F. Tran, P. Blaha, Phys. Rev. B 85(15), 155109 (2012).  https://doi.org/10.1103/PhysRevB.85.155109 ADSCrossRefGoogle Scholar
  18. 18.
    D.J. Singh, Phys. Rev. B 82(20), 205102 (2010).  https://doi.org/10.1103/PhysRevB.82.205102 ADSCrossRefGoogle Scholar
  19. 19.
    A.D. Becke, J. Chem. Phys. 98(2), 1372 (1993).  https://doi.org/10.1063/1.464304 ADSCrossRefGoogle Scholar
  20. 20.
    J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, J. Chem. Phys. 123(17), 174101 (2005).  https://doi.org/10.1063/1.2085170 ADSCrossRefGoogle Scholar
  21. 21.
    K. Kim, K.D. Jordan, J. Phys. Chem. 98(40), 10089 (1994).  https://doi.org/10.1021/j100091a024 CrossRefGoogle Scholar
  22. 22.
    C. Adamo, V. Barone, J. Chem. Phys. 110(13), 6158 (1999).  https://doi.org/10.1063/1.478522 ADSCrossRefGoogle Scholar
  23. 23.
    J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118(18), 8207 (2003).  https://doi.org/10.1063/1.1564060 ADSCrossRefGoogle Scholar
  24. 24.
    F. Aryasetiawan, O. Gunnarsson, Rep. Prog. Phys. 61(3), 237 (1998), http://stacks.iop.org/0034-4885/61/i=3/a=002
  25. 25.
    L. Hedin, J. Phys.: Condens. Matter 11(42), R489 (1999).  https://doi.org/10.1088/0953-8984/11/42/201
  26. 26.
    L. Hedin, Phys. Rev. 139(3A), A796 (1965).  https://doi.org/10.1103/PhysRev.139.A796 ADSCrossRefGoogle Scholar
  27. 27.
    J. Lindhard, Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd. 28 (1954)Google Scholar
  28. 28.
    D. Pines, D. Bohm, Phys. Rev. 85(2), 338 (1952)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    M. Shishkin, G. Kresse, Phys. Rev. B 75(23), 235102 (2007).  https://doi.org/10.1103/PhysRevB.75.235102 ADSCrossRefGoogle Scholar
  30. 30.
    B. Holm, U. von Barth, Phys. Rev. B 57(4), 2108 (1998).  https://doi.org/10.1103/PhysRevB.57.2108
  31. 31.
    E.L. Shirley, Phys. Rev. B 54(11), 7758 (1996).  https://doi.org/10.1103/PhysRevB.54.7758 ADSCrossRefGoogle Scholar
  32. 32.
    E.E. Salpeter, H.A. Bethe, Phys. Rev. 84(6), 1232 (1951).  https://doi.org/10.1103/PhysRev.84.1232 ADSCrossRefGoogle Scholar
  33. 33.
    G. Strinati, La Rivista del Nuovo Cimento 11(12), 1 (1988).  https://doi.org/10.1007/BF02725962 ADSCrossRefGoogle Scholar
  34. 34.
    G. Bussi, Physica Scripta T109, 141 (2004).  https://doi.org/10.1238/Physica.Topical.109a00141
  35. 35.
    C. Rödl, F. Fuchs, J. Furthmüller, F. Bechstedt, Phys. Rev. B 77(18), 184408 (2008).  https://doi.org/10.1103/PhysRevB.77.184408 ADSCrossRefGoogle Scholar
  36. 36.
    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52(12), 997 (1984).  https://doi.org/10.1103/PhysRevLett.52.997 ADSCrossRefGoogle Scholar
  37. 37.
    G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74(2), 601 (2002).  https://doi.org/10.1103/RevModPhys.74.601 ADSCrossRefGoogle Scholar
  38. 38.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Courier Corporation, 2012)Google Scholar
  39. 39.
    W.G. Schmidt, S. Glutsch, P.H. Hahn, F. Bechstedt, Phys. Rev. B 67(8), 085307 (2003).  https://doi.org/10.1103/PhysRevB.67.085307 ADSCrossRefGoogle Scholar
  40. 40.
    D. Franta, A. Dubroka, C. Wang, A. Giglia, J. Vohánka, P. Franta, I. Ohlídal, Appl. Surf. Sci. (2017).  https://doi.org/10.1016/j.apsusc.2017.02.021
  41. 41.
    S.H. Wei, L.G. Ferreira, J. Bernard, A. Zunger, Phys. Rev. B: Condens. Matter 42(15), 9622 (1990).  https://doi.org/10.1103/PhysRevB.42.9622 ADSCrossRefGoogle Scholar
  42. 42.
    D. Holec, L. Zhou, R. Rachbauer, P.H. Mayrhofer, in Density Functional Theory: Principles, Applications and Analysis, ed. by J.M. Pelletier, J. Morin (Nova Publishers, 2013), pp. 259–284Google Scholar
  43. 43.
    P. Ondračka, D. Holec, D. Nečas, E. Kedroňová, S. Elisabeth, A. Goullet, L. Zajíčková, Phys. Rev. B 95(19), 195163 (2017).  https://doi.org/10.1103/PhysRevB.95.195163
  44. 44.
    F. Giustino, Rev. Mod. Phys. 89(1), 015003 (2017).  https://doi.org/10.1103/RevModPhys.89.015003 ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    S.D. Mo, W.Y. Ching, Phys. Rev. B 51(19), 13023 (1995).  https://doi.org/10.1103/PhysRevB.51.13023 ADSCrossRefGoogle Scholar
  46. 46.
    S. Baroni, S. De Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73(2), 515 (2001).  https://doi.org/10.1103/RevModPhys.73.515 ADSCrossRefGoogle Scholar
  47. 47.
    J. Noffsinger, E. Kioupakis, C.G. Van de Walle, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 108(16), 167402 (2012).  https://doi.org/10.1103/PhysRevLett.108.167402 ADSCrossRefGoogle Scholar
  48. 48.
    H. Tang, H. Berger, P.E. Schmid, F. Lévy, Optical properties of anatase (TiO2). Solid State Commun. 92(3), 267–271 (1994).  https://doi.org/10.1016/0038-1098(94)90889-3 ADSCrossRefGoogle Scholar
  49. 49.
    R. Asahi, Y. Taga, W. Mannstadt, A. Freeman, Phys. Rev. B 61(11), 7459 (2000).  https://doi.org/10.1103/PhysRevB.61.7459 ADSCrossRefGoogle Scholar
  50. 50.
    K. Glassford, J. Chelikowsky, Phys. Rev. B 46(3), 1284 (1992).  https://doi.org/10.1103/PhysRevB.46.1284 ADSCrossRefGoogle Scholar
  51. 51.
    S. Rangan, S. Katalinic, R. Thorpe, R.A. Bartynski, J. Rochford, E. Galoppini, J. Phys. Chem. C 114(2), 1139 (2010).  https://doi.org/10.1021/jp909320f CrossRefGoogle Scholar
  52. 52.
    J. Tauc, Mater. Res. Bull. 3(1), 37 (1968).  https://doi.org/10.1016/0025-5408(68)90023-8 CrossRefGoogle Scholar
  53. 53.
    O. Stenzel, The Physics of Thin Film Optical Spectra, vol. 44, Springer Series in Surface Sciences (Springer, Berlin, 2005).  https://doi.org/10.1007/3-540-27905-9 Google Scholar
  54. 54.
    M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, W.G. Schmidt, Phys. Rev. B 86(6), 064201 (2012).  https://doi.org/10.1103/PhysRevB.86.064201
  55. 55.
    P. Ondračka, D. Holec, D. Nečas, L. Zajíčková, J. Phys. D: Appl. Phys. 49(39), 395301 (2016).  https://doi.org/10.1088/0022-3727/49/39/395301

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Pavel Ondračka
    • 1
    • 2
    Email author
  • David Holec
    • 3
  • Lenka Zajíčková
    • 1
    • 2
  1. 1.Plasma Technologies, CEITECMasaryk UniversityBrnoCzech Republic
  2. 2.Faculty of Science, Department of Physical ElectronicsMasaryk UniversityBrnoCzech Republic
  3. 3.Department of Physical Metallurgy and Materials TestingMontanuniversität LeobenLeobenAustria

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