Drude-Lorentz Model of Semiconductor Optical Plasmons

  • Mohamed Eldlio
  • Franklin Che
  • Michael Cada
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 247)


Theoretical solutions are obtained for the propagation of electromagnetic waves at optical frequencies along a semiconductor/dielectric interface when losses are taken into account in the form of a complex dielectric function. A combination method for the dielectric function, comprised of the best features of the Drude and Lorentz models, is herein proposed. By including the loss term in both models, we were able to obtain numerical solutions for the Plasma dispersion curve of the semiconductor/dielectric interface. The surface plasmon waves, when excited, become short wavelength waves in the Optical frequency or THz region. A silicon/air structure was used as our semiconductor/dielectric material combination, and comparisons were made to optical plasmons generated without losses. Our initial numerical calculation results show enormous potential for use in several applications.


Drude-Lorentz model Optical frequency Optical plasmon Plasma dispersion Semiconductor optical plasmons Surface plasmon polaritons 



This work was supported by NSERC (Natural Sciences and Engineering Research Council) and NSERC’S ASPIRE (Applied Science in Photonics and Innovative Research in Engineering), both of Canada. We gratefully acknowledge helpful discussions with members of professor Cada’s photonics research, and with Professor J. Pištora of technical University of Ostrava, Czech Republic.


  1. 1.
    Ritchie RH (1957) Plasma losses by fast electrons in thin films. Phys Rev 106:874MathSciNetCrossRefGoogle Scholar
  2. 2.
    Raether H (1988) Surface plasmons on smooth and rough surfaces and on gratings. Springer-Verlag, Berlin, pp 15–22Google Scholar
  3. 3.
    Maier S (2007) Plasmonics fundamentals and applications, 1st edn. Springer Science and business Media LLC, Berlin, pp 21–39Google Scholar
  4. 4.
    Novotny L, Hecht B (2008) Principles of nano-optics, 2nd edn. Cambridge University Press, Cambridge, MA, pp 378–414Google Scholar
  5. 5.
    Zayatsa AV, Smolyaninovb II, Maradudinc AA (2005) Nano-optics of surface plasmon polaritons. Phys Rep 408:131–314CrossRefGoogle Scholar
  6. 6.
    Yao B, Fang ZB, Zhu YY, Ji T, He G (2012) A model for the frequency dispersion of the high-k metal-oxide semiconductor capacitance in accumulation. Appl Phys Lett 100: 222903/1–3Google Scholar
  7. 7.
    Cada M, Pištora J (2011) Optical plasmons in semiconductors. In: ISMOT conference, June 20–23Google Scholar
  8. 8.
    Eldlio M, Che F, Cada M (2012) Lecture notes in engineering and computer science. In: Proceedings of the world congress on engineering and computer science, WCECS 2012, 24–6 Oct, 2012, San Francisco, USA, pp 1078–1081Google Scholar
  9. 9.
    Fox M (2010) Optical properties of solids, 2nd edn. Oxford University Press, Oxford, pp 33–44Google Scholar
  10. 10.
    Chuang S (2009) Physics of photonic devices, 2nd edn. Wiley, New York, pp 193–196Google Scholar
  11. 11.
    Kuttge M, Kurz H, Rivas JG, Sánchez-Gil JA, Bolívar PH (2007) Analysis of the propagation of terahertz surface plasmon polaritons on semiconductor groove gratings. J Appl Phys 101(2):023707-1–023707-6CrossRefGoogle Scholar
  12. 12.
    West PR, Ishii S, Naik GV, Emani NK, Shalaev VM, Boltasseva A (2010) Searching for better plasmonic materials. Laser Photonics Rev 4(6):795–808CrossRefGoogle Scholar
  13. 13.
    Lee KH, Ahmed I, Goh RSM, Khoo EH, Li EP, Hung TGG (2011) Implementation of the FDTD method based on the Lorentz-Drude model on GPU for plasmonics applications. Prog Electromagnet Res 116:441–456Google Scholar
  14. 14.
    Rivas JG, Snchez-Gil JA, Kuttge M, Bolivar PH, Kurz H (2006) Optically switchable mirrors for surface plasmon polaritons propagating on semiconductor surfaces. Phys Rev B 74:245–324Google Scholar
  15. 15.
    Huang Y, Ho ST (2006) Computational model of solid state, molecular, or atomic media for FDTD simulation based on a multilevel multi-electron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics. Opt Express 14:3569–3587CrossRefGoogle Scholar
  16. 16.
    Hryciw A, Jun YC, Brongersma ML (2010) Plasmonic: electrifying plasmonics on silicon. Nat Mater 9:3–4CrossRefGoogle Scholar
  17. 17.
    Janke C, Rivas JG, Bolivar PH, Kurz H (2005) All optical switching of electromagnetic radiation through subwavelength apertures. Opt Lett 30(18):2357–2359CrossRefGoogle Scholar
  18. 18.
    Ahmed I, Khoo E, Kurniawan O, Li E (2011) Modeling and simulation of active plasmonics with the FDTD method by using solid state and Lorentz–Drude dispersive model. J Opt Soc Am B 28(3):325–359CrossRefGoogle Scholar
  19. 19.
    van Exter M, Grischkowsky D (1990) Optical and electronics properties of doped silicon from 0.1 to 2 THz. Appl Phys let 56(17):1694–1696Google Scholar
  20. 20.
    Laghla Y, Scheid E (1997) Optical study of undoped, B or P-doped polysilicon. Thin Solid Film 306:67–73CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringDalhousie UniversityHalifaxCanada

Personalised recommendations