Skip to main content
SpringerLink
Log in

Beyond Static Screening

  • Chapter
  • First Online:
Many-Body Approach to Electronic Excitations

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 181))

  • 3315 Accesses

Abstract

The consideration of the screening dynamics prevents the formulation of a Bethe-Salpeter equation for the macroscopic polarization function that only depends on one frequency. This is only possible within approximate schemes, for instance the Shindo approximation. Due to the incomplete dynamical screening excitonic effects are increased. Including dynamical lattice screening the question which dielectric constant, the static electronic or the total one, has to be used to screen a Wannier-Mott exciton is discussed. Another consequence of the dynamically screened electron-hole attraction is an additional loss mechanism, the interference terms, which modify the spectral strength and the satellite structures over and above the intrinsic and extrinsic losses known from the single-quasiparticle description. It is shown that the combination of intrinsic, interference, and extrinsic effects leads to strong reduction of the satellite strengths, in particular for vanishing energies of an electron emitted in photoemission. The screening in a non-metal is significantly modified in the presence of free carriers. The band filling gives rise to a tendency for a Mott transition, a gap shrinkage, and a Burstein-Moss shift. However, even for large carrier densities Coulomb effects survive resulting e.g. in Mahan excitons.

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 EPUB and 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

References

  1. R. Zimmermann, Many-Particle Theory of Highly Excited Semiconductors (Teubner-Verlag, Leipzig, 1988)

    Google Scholar 

  2. G.M. Éliashberg, Interactions of electrons and lattice vibrations in a superconductor. Zh. Eksp. Teor. Fiz. 38, 966–976 (1960) [Engl. Transl JETP 11, 696–702 (1960)]

    Google Scholar 

  3. F. Bechstedt, Zur Theorie von Rumpfelektronenanregungen in Halbleitern. Habilitation thesis, Humboldt-Universität, Berlin (1981)

    Google Scholar 

  4. K. Shindo, Effective electron-hole interaction in shallow excitons. J. Phys. Soc. Jpn 29, 287–295 (1970)

    Article  ADS  Google Scholar 

  5. R. Zimmermann, Dynamical screening of the Wannier exciton. Phys. Status Solidi B 48, 603–618 (1971)

    Article  ADS  Google Scholar 

  6. A. Marini, R. Del Sole, Dynamical excitonic effects in metals and semiconductors. Phys. Rev. Lett. 91, 176402 (2003)

    Article  ADS  Google Scholar 

  7. F. Bechstedt, R. Enderlein, M. Koch, Theory of core excitons in semiconductors. Phys. Status Solidi B 99, 61–70 (1980)

    Article  ADS  Google Scholar 

  8. M. Rohlfing, S.G. Louie, Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000)

    Article  ADS  Google Scholar 

  9. G. Strinati, Effects of dynamical screening on resonances at inner-shell thresholds in semiconductors. Phys. Rev. B 29, 5718–5726 (1984)

    Article  ADS  Google Scholar 

  10. F. Bechstedt, C. Rödl, L.E. Ramos, F. Fuchs, P.H. Hahn, J. Furthmüller, Parameterfree calculations of optical properties for systems with magnetic ordering or three-dimensional confinement, in Epioptics-9, Proceedings of 39th Course of the International School on Solid State Physics, Erice (Italy), ed. by A. Cricenti (World Scientific, New Jersey, 2008), pp. 28–40

    Google Scholar 

  11. P.H. Hahn, W.G. Schmidt, F. Bechstedt, Molecular electronic excitations calculated from a solid-state approach: methodology and numerics. Phys. Rev. B 72, 245425 (2005)

    Article  ADS  Google Scholar 

  12. U. Itoh, Y. Toyoshima, H. Onuki, Vacuum ultraviolet absorption cross sections of SiH\(_4\), GeH\(_4\), Si\(_2\)H\(_6\), and Si\(_3\)H\(_8\). J. Chem Phys. 85, 4867–4872 (1986)

    Article  ADS  Google Scholar 

  13. P.Y. Yu, M. Cardona, Fundamentals of Semiconductors (Springer, Berlin, 1996)

    Book  MATH  Google Scholar 

  14. H. Haken, Die Theorie des Exzitons im festen Körper. Fortschr. Phys. 6, 271–334 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  15. Y. Toyozawa, Theory of the electronic polaron and ionization of a trapped electron by an exciton. Prog. Theor. Phys. 12, 421–442 (1954)

    Article  ADS  MATH  Google Scholar 

  16. F. Bechstedt, K. Seino, P.H. Hahn, W.G. Schmidt, Quasiparticle bands and optical spectra of highly ionic crystals: AlN and NaCl. Phys. Rev. B 72, 245114 (2005)

    Article  ADS  Google Scholar 

  17. A. Riefer, F. Fuchs, C. Rödl, A. Schleife, F. Bechstedt, R. Goldhahn, Interplay of excitonic effects and van Hove singularities in optical spectra: CaO and AlN polymorphs. Phys. Rev. B 84, 075218 (2011)

    Article  ADS  Google Scholar 

  18. F. Fuchs, C. Rödl, A. Schleife, F. Bechstedt, Efficient \(O(N^2)\) approach to solve the Bethe-Salpeter equation for excitonic bound states. Phys. Rev. B 78, 085103 (2008)

    Article  ADS  Google Scholar 

  19. M. Bleicher, Halbleiter-Optoelektronik (Dr. Alfred Hüthig Verlag, Heidelberg, 1986)

    Google Scholar 

  20. Ch. Kittel, Introduction to Solid State Physics (Wiley, New York, 2005)

    Google Scholar 

  21. W. Martienssen, H. Warlimont (eds.), Springer Handbook of Condensed Matter and Materials Data (Springer, Berlin, 2005)

    Google Scholar 

  22. A. Schleife, F. Bechstedt, Ab initio description of quasiparticle band structures and optical near-edge absorption of transparent conducting oxides. J. Mater. Res. 27, 2180–2186 (2012)

    Article  ADS  Google Scholar 

  23. D.M. Roessler, W.C. Walker, Electronic spectrum and ultraviolet optical properties of crystalline MgO. Phys. Rev. 159, 733–738 (1967)

    Article  ADS  Google Scholar 

  24. R.C. Whited, C.J. Flaten, W.C. Walker, Exciton thermoreflectance of MgO and CaO. Solid State Commun. 13, 1903–1905 (1973)

    Article  ADS  Google Scholar 

  25. R. Zimmermann, M. Rösler, Theory of electron-hole plasma in CdS. Phys. Status Solidi B 75, 633–645 (1976)

    Article  ADS  Google Scholar 

  26. F. Bechstedt, K. Tenelsen, B. Adolph, R. Del Sole, Compensation of dynamical quasiparticle and vertex corrections in optical spectra. Phys. Rev. Lett. 78, 1528–1531 (1997)

    Article  ADS  Google Scholar 

  27. D.J.W. Geldart, R. Taylor, Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree-Fock corrections. Can. J. Phys. 48, 155–165 (1970)

    Article  ADS  Google Scholar 

  28. D.J.W. Geldart, R. Taylor, Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects. Can. J. Phys. 48, 167–181 (1970)

    Article  ADS  Google Scholar 

  29. S. Hong, G.D. Mahan, Conserving approximations: electron gas with exchange effects. Phys. Rev. B 50, 8182–8188 (1994)

    Article  ADS  Google Scholar 

  30. J.J. Chang, D.C. Langreth, Deep-hole excitations in solids. I. Fast-electron-plasmon effects. Phys. Rev. B 5, 3512–3522 (1972)

    Article  ADS  Google Scholar 

  31. J.J. Chang, D.C. Langreth, Deep-hole excitations in solids. II. Plasmons and surface effects in X-ray photoemission. Phys. Rev. B 8, 4638–4654 (1973)

    Article  ADS  Google Scholar 

  32. J.W. Gadzuk, Plasmon satellites in X-ray photoemission spectra. J. Electron Spectrosc. 11, 355–361 (1977)

    Article  Google Scholar 

  33. D. Chastenet, P. Longe, Intensity of plasmon satellites in ultrasoft-X-ray photoemission spectra. Phys. Rev. Lett. 44, 91–95 (1980)

    Article  ADS  Google Scholar 

  34. D. Chastenet, P. Longe, Intensity of plasmon satellites in ultrasoft-X-ray photoemission spectra. Phys. Rev. Lett. 44, 903 (1980) (Erratum)

    Google Scholar 

  35. R. Zimmermann, Plasmon-Satelliten in Röntgen-Photoemissionsspektren. ZIE Preprint 81–3, 47–60 (1981)

    Google Scholar 

  36. L.I. Johansson, I. Lindau, Photoemission studies of the energy dependence of the bulk plasmon loss intensity in Si and Al. Solid State Commun. 29, 379–382 (1979)

    Article  ADS  Google Scholar 

  37. M. Guzzo, J.J. Kas, F. Sottile, M.G. Silly, F. Sirotti, J.J. Rehr, L. Reining, Plasmon satellites in valence-band photoemission spectroscopy. Eur. Phys. J. B 85, 324–330 (2012)

    Article  ADS  Google Scholar 

  38. V.L. Bonch-Bruevich, The Electronic Theory of Heavily Doped Semiconductors (American Elsevier Publishing Company, New York, 1966)

    Google Scholar 

  39. T. Minami, Transparent conducting oxide semiconductors for transparent electrodes. Semicond. Sci. Technol. 20, S35–S44 (2005)

    Article  ADS  Google Scholar 

  40. G. Hautier, A. Miglio, G. Ceder, J.-M. Rignanese, X. Gonze, Identification and design principles of low effective mass \(p\)-type transparent conducting oxides. Nature Commun. 4, 2292 (2013)

    Article  ADS  Google Scholar 

  41. O.A. Gomes, H. Chacham, J.R. Mohallem, Variational calculations for the bound-unbound transition of the Yukawa potential. Phys. Rev. A 50, 228–231 (1994)

    Article  ADS  Google Scholar 

  42. Y. Li, X. Luo, H. Kröger, Bound states and critical behavior of the Yukawa potential. Sci. China Ser. G 49, 60–71 (2006)

    Article  MATH  Google Scholar 

  43. N.F. Mott, Metal-Insulator Transitions (Barnes & Noble, New York, 1974)

    Google Scholar 

  44. N.F. Mott, The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. A 62, 416–422 (1949)

    Article  ADS  Google Scholar 

  45. H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2009)

    Book  MATH  Google Scholar 

  46. C. Klingshirn, Semiconductor Optics (Springer, Berlin, 2007)

    Book  Google Scholar 

  47. S.A. Moskalenko, D. Snoke, Bose-Einstein Condensations of Excitons and Biexcitons (Cambridge University Press, Cambridge, 2000)

    Book  Google Scholar 

  48. Landolt-Börnstein New Series, Group III, 41B (Springer, Berlin, 1999)

    Google Scholar 

  49. C. Klingshirn, R. Hauschild, J. Fattert, H. Kalt, Room-temperature stimulated emission of ZnO: alternatives to excitonic lasing. Phys. Rev. B 75, 115203 (2007)

    Article  ADS  Google Scholar 

  50. S. Shokhovets, K. Köhler, O. Ambacher, G. Gobsch, Observation of Fermi edge excitons and exciton-phonon couplexes in the optical response of heavily doped \(n\)-type wurtzite GaN. Phys. Rev. B 79, 045201 (2009)

    Article  ADS  Google Scholar 

  51. A. Schleife, F. Fuchs, C. Rödl, J. Furthmüller, F. Bechstedt, Band structure and optical-transition parameters of wurtzite MgO, ZnO, and CdO from quasiparticle calculations. Phys. Status Solidi B 246, 2150–2153 (2009)

    Article  ADS  Google Scholar 

  52. F. Fuchs, F. Bechstedt, Indium-oxide polymorphs from first principles: quasiparticle electronic states. Phys. Rev. B 77, 155107 (2008)

    Article  ADS  Google Scholar 

  53. A. Schleife, C. Rödl, F. Fuchs, K. Hannewald, F. Bechstedt, Optical absorption in degenerately doped semiconductors: mott transition or Mahan excitons? Phys. Rev. Lett. 107, 236404 (2011)

    Article  ADS  Google Scholar 

  54. T. Makino, Y. Segawa, S. Yoshida, A. Tsukasaki, A. Ohtomo, M. Kawasaki, Gallium concentration dependence of room-temperature near-band-edge luminescence in n-type ZnO: Ga. Appl. Phys. Lett. 85, 759–761 (2004)

    Article  ADS  Google Scholar 

  55. T. Makino, K. Tamura, C.H. Chia, Y. Segawa, M. Kawasaki, A. Ohtomo, H. Koinuma, Optical properties of ZnO: Al epilayers: observation of room-temperature many-body absorption-edge singularity. Phys. Rev. B 65, 121201(R) (2002)

    Article  ADS  Google Scholar 

  56. H. Fujiwara, M. Kondo, Effects of carier concentration on the dielectric function of ZnO: Ga and In\(_2\)O\(_3\):Sn studied by spectroscopic ellipsometry: analysis of free-carrier and band-edge absorption. Phys. Rev. B 71, 075109 (2005)

    Article  ADS  Google Scholar 

  57. G.D. Mahan, Excitons in degenerate semiconductors. Phys. Rev. 153, 882–889 (1967)

    Article  ADS  Google Scholar 

  58. G.D. Mahan, Many-Particle Physics (Plenum Press, New York, 1990)

    Book  Google Scholar 

  59. M. Feneberg, J. Däubler, K. Thonke, R. Sauer, P. Schley, R. Goldhahn, Mahan excitons in degenerate wurtzite InN: photoluminescence spectroscopy and reflectivity measurements. Phys. Rev. B 77, 245207 (2008)

    Article  ADS  Google Scholar 

  60. H. Haug, S. Schmitt-Rink, Electron theory of the optical properties of laser-excited semiconductors. Prog. Quantum Electron. 9, 3–100 (1984)

    Article  ADS  Google Scholar 

  61. S. Nojima, Dimensionality of exciton-state renormalization in highly excited semiconductors. Phys. Rev. B 51, 11124–11127 (1985)

    Article  ADS  Google Scholar 

  62. P. Hawvylak, Optical properties of a two-dimensional electron gas: evolution of spectra from excitons to Fermi-edge singularities. Phys. Rev. B 44, 3821–3828 (1991)

    Article  ADS  Google Scholar 

  63. N.A.J.M. Kleemans, J. van Bree, A.O. Govarov, J.G. Keizer, G.J. Hamhuis, R. Nötzel, P.M. Koenraad, Many-body exciton states in self-assembled quantum dots coupled to a Fermi sea. Nature Phys. 6, 534–538 (2010)

    Google Scholar 

  64. M.S. Skolnick, J.M. Rorison, K.J. Nash, D.J. Mowbray, P.R. Tapster, S.J. Bass, A.D. Pitt, Observation of a many-body edge singularity in quantum-well luminescence spectra. Phys. Rev. Lett. 58, 2130–2133 (1987)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Friedrich-Schiller University, Jena, Germany

    Friedhelm Bechstedt

Authors
  1. Friedhelm Bechstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Friedhelm Bechstedt .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bechstedt, F. (2015). Beyond Static Screening. In: Many-Body Approach to Electronic Excitations. Springer Series in Solid-State Sciences, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44593-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44593-8_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44592-1

  • Online ISBN: 978-3-662-44593-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation