Journal of Computational Electronics

, Volume 16, Issue 3, pp 487–496 | Cite as

Numerical simulation of plasma waves in a quasi-2D electron gas based on the Boltzmann transport equation

  • Zeinab Kargar
  • Dino Ruić
  • Tobias Linn
  • Christoph Jungemann
Article

Abstract

The calculation of plasma waves in a homogeneous quasi-2D electron gas is usually based on the Euler equation. It yields a dispersion relation with two branches, which are often referred to as Vlasov modes. Dyakonov and Shur were able to show that under certain boundary conditions for a constant current flow in a high electron mobility transistor these two modes can lead to a plasma instability and generation of THz waves. If, on the other hand, the more physics-based Boltzmann transport equation is solved for plasma waves, a multitude of modes is obtained in addition to the two Vlasov modes. In the case of nonequilibrium and high frequencies, it is no longer possible to identify the two Vlasov modes by simple means. This phenomenon is discussed in detail, and a method for the identification of the Vlasov modes is proposed. In addition, it is shown that for strong nonequilibrium the Dyakonov–Shur instability can be evaluated numerically using a method based on the Boltzmann transport equation.

Keywords

Boltzmann equation Plasma waves Simulation THz devices 

References

  1. 1.
    Woolard, D., Brown, E., Pepper, M., Kemp, M.: Terahertz frequency sensing and imaging: a time of reckoning future applications? Proc. IEEE 93(10), 1722–1743 (2005)CrossRefGoogle Scholar
  2. 2.
    Otsuji, T., Shur, M.: Terahertz plasmonics: good results and great expectations. IEEE Microw. Mag. 15(7), 43–50 (2014)CrossRefGoogle Scholar
  3. 3.
    Dyakonov, M., Shur, M.: Shallow water analogy for a ballistic field effect transistor: new mechanism of plasma wave generation by dc current. Phys. Rev. Lett. 71, 2465–2468 (1993)CrossRefGoogle Scholar
  4. 4.
    Crowne, F.J.: Contact boundary conditions and the Dyakonov–Shur instability in high electron mobility transistors. J. Appl. Phys. 82(3), 1242–1254 (1997)CrossRefGoogle Scholar
  5. 5.
    Dyakonov, M., Shur, M.: Plasma wave electronics: novel terahertz devices using two dimensional electron fluid. IEEE Trans. Electron Devices 43(10), 1640–1645 (1996)CrossRefGoogle Scholar
  6. 6.
    Hong, S.-M., Jang, J.-H.: Numerical simulation of plasma oscillation in 2-d electron gas using a periodic steady-state solver. IEEE Trans. Electron Devices 62(12), 4192–4198 (2015)CrossRefGoogle Scholar
  7. 7.
    Satou, A., Khmyrova, I., Ryzhii, V., Shur, M.S.: Plasma and transit-time mechanisms of the terahertz radiation detection in high-electron-mobility transistors. Semicond. Sci. Technol. 18(6), 460 (2003)CrossRefGoogle Scholar
  8. 8.
    Popov, V.V., Polischuk, O.V., Shur, M.S.: Resonant excitation of plasma oscillations in a partially gated two-dimensional electron layer. J. Appl. Phys. 98(3), 033510 (2005)CrossRefGoogle Scholar
  9. 9.
    Khorrami, M.A., El-Ghazaly, S., Naseem, H., Yu, S.Q.: Global modeling of active terahertz plasmonic devices. IEEE Trans. Terahertz Sci. Technol. 4(1), 101–109 (2014)CrossRefGoogle Scholar
  10. 10.
    Knap, W., Dyakonov, M., Coquillat, D., Teppe, F., Dyakonova, N., Łusakowski, J., Karpierz, K., Sakowicz, M., Valusis, G., Seliuta, D., Kasalynas, I., El Fatimy, A., Meziani, Y.M., Otsuji, T.: Field effect transistors for terahertz detection: physics and first imaging applications. J. Infrared Millim. Terahertz Waves 30(12), 1319–1337 (2009)Google Scholar
  11. 11.
    Nouvel, P., Marinchio, H., Torres, J., Palermo, C., Gasquet, D., Chusseau, L., Varani, L., Shiktorov, P., Starikov, E., Gruinskis, V.: Terahertz spectroscopy of plasma waves in high electron mobility transistors. J. Appl. Phys. 106(1), 013717 (2009)CrossRefGoogle Scholar
  12. 12.
    Lisauskas, A., Pfeiffer, U., Öjefors, E., Bolvar, P.H., Glaab, D., Roskos, H.G.: Rational design of high-responsivity detectors of terahertz radiation based on distributed self-mixing in silicon field-effect transistors. J. Appl. Phys. 105(11), 114511 (2009)CrossRefGoogle Scholar
  13. 13.
    Kargar, Z., Linn, T., Ruić, D., Jungemann, C.: Investigation of transport modeling for plasma waves in THz devices. IEEE Trans. Electron Devices 63(11), 4402–4408 (2016)CrossRefGoogle Scholar
  14. 14.
    Nekovee, M., Geurts, B.J., Boots, H.M.J., Schuurmans, M.F.H.: Failure of extended-moment-equation approaches to describe ballistic transport in submicrometer structures. Phys. Rev. B 45(12), 6643–6651 (1992)CrossRefGoogle Scholar
  15. 15.
    Van Kampen, N.: The dispersion equation for plasma waves. Physica 23(6–11), 641–650 (1957)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Landau, L.D.: On the vibrations of the electronic plasma. Zh. Eksp. Teor. Fiz. 10, 25 (1946)MathSciNetMATHGoogle Scholar
  17. 17.
    Ando, T., Fowler, A., Stern, F.: Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982)CrossRefGoogle Scholar
  18. 18.
    Ruić, D., Jungemann, C.: Numerical aspects of noise simulation in MOSFETs by a Langevin–Boltzmann solver. J. Comput. Electron. 14(1), 21–36 (2015)CrossRefGoogle Scholar
  19. 19.
    Esseni, D., Palestri, P., Selmi, L.: Nanoscale MOS Transistors. Semi-Classical Transport and Applications. Cambridge University Press, Cambridge (2011)CrossRefGoogle Scholar
  20. 20.
    Polizzi, E.: Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 79, 115112 (2009)CrossRefGoogle Scholar
  21. 21.
    Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia (1999)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Chair of Electromagnetic TheoryRWTH Aachen UniversityAachenGermany

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