Skip to main content
SpringerLink
Log in

Mathematical Models for the Double-Gate MOSFET

  • Chapter
  • First Online:
Charge Transport in Low Dimensional Semiconductor Structures

Part of the book series: Mathematics in Industry ((TECMI,volume 31))

  • 425 Accesses

Abstract

In this chapter the ideas presented in the previous sections will be employed to get a mathematical model for the simulation of a Double Gate MOSFET (hereafter DG-MOSFET). This model is based on the Schrödinger–Poisson system coupled to a set of energy-transport equations, one for each subband, arising from the moment systems associated to the equations (1.28) with closure relations obtained by MEP.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Notes

  1. 1.

    Here and whenever possible we omit the subband index for simplicity.

References

  1. Anile, A.M., Mascali, G.: Theoretical foundations for tail electron hydrodynamical models in semiconductors. Appl. Math. Lett. 14, 245–252 (2001)

    Article  MathSciNet  Google Scholar 

  2. Anile, A.M., Romano, V.: Non parabolic band transport in semiconductors: closure of the moment equations. Contin. Mech. Thermodyn. 11, 307–325 (1999)

    Article  MathSciNet  Google Scholar 

  3. Ben Abdallah, N., Caceres, M.J., Carrillo, J.A., Vecil, F.: A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs. J. Comput. Phys. 228(17), 6553–6571 (2009) Blokhin, A.M., Birkin, A.D.: Stability analysis of supersonic regime past infinite wedge. J. Appl. Mech. Tech. Phys. 36(4), 496–512 (1996)

    Article  MathSciNet  Google Scholar 

  4. Blokhin, A.M., Tkachev, D.L.: Local-in-time well-posedness of a regularized mathematical model for silicon MESFET. Z. Angew. Math. Phys. 61, 849–864 (2010)

    Article  MathSciNet  Google Scholar 

  5. Camiola, V.D., Romano, V.: 2DEG-3DEG charge transport model for MOSFET based on the maximum entropy principle. SIAM J. Appl. Math. 73, 1439–1459 (2013)

    Article  MathSciNet  Google Scholar 

  6. Camiola, V.D., Mascali, G., Romano, V.: An improved 2D–3D model for charge transport based on the maximum entropy principle. Contin. Mech. Thermodyn. (2018). https://doi.org/10.1007/s00161-018-0735-6

    Article  MathSciNet  Google Scholar 

  7. Galler, M., Schürrer, F.: A deterministic Solver to the Boltzmann-Poisson system including quantization effects for silicon-MOSFETs. In: Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol. 12, pp. 531–536. Springer, Berlin (2008)

    Chapter  Google Scholar 

  8. Jou, D., Casas-Vázquez, J., Lebon, G.: Extended Irreversible Thermodynamics. Springer, Berlin (1993)

    Book  Google Scholar 

  9. Jüngel, A.: Transport Equations for Semiconductors. Springer, Berlin (2009)

    Book  Google Scholar 

  10. La Rosa, S., Mascali, G., Romano, V.: Exact maximum entropy closure of the hydrodynamical model for Si semiconductors: the 8-moment case. SIAM J. Appl. Math. 70, 710–734 (2009)

    Article  MathSciNet  Google Scholar 

  11. Mascali, G.: A hydrodynamic model for silicon semiconductors including crystal heating. Eur. J. Appl. Math. 26, 477–496 (2015)

    Article  MathSciNet  Google Scholar 

  12. Mascali, G.: A new formula for thermal conductivity based on a hierarchy of hydrodynamical models. J. Stat. Phys. 163, 1268–1284 (2016)

    Article  MathSciNet  Google Scholar 

  13. Mascali, G., Romano, V.: Hydrodynamical model of charge transport in GaAs based on the maximum entropy principle. Contin. Mech. Thermodyn. 14, 405–423 (2002)

    Article  MathSciNet  Google Scholar 

  14. Mascali, G., Romano, V.: Si and GaAs mobility derived from a hydrodynamical model for semiconductors based on the maximum entropy principle. Phys. A 352, 459–476 (2005)

    Article  Google Scholar 

  15. Mascali, G., Romano, V.: Hydrodynamic subband model for semiconductors based on the maximum entropy principle. Nuovo Cimento C 33, 155–163 (2010)

    MATH  Google Scholar 

  16. Mascali, G., Romano, V.: A hydrodynamical model for holes in silicon semiconductors: the case of non-parabolic warped bands. Math. Comput. Mod. 53, 213–229 (2011)

    Article  MathSciNet  Google Scholar 

  17. Mascali, G., Romano, V.: A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle. Math. Comput. Mod. 55, 1003–1020 (2012)

    Article  MathSciNet  Google Scholar 

  18. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics. Springer, New York (1998)

    Book  Google Scholar 

  19. Muscato, O.: The Onsager reciprocity principle as a check of consistency for semiconductor carrier transport models. Phys. A 289, 422–458 (2001)

    Article  MathSciNet  Google Scholar 

  20. Muscato, O., Di Stefano, V.: Hydrodynamic modeling of the electro-thermal transport in silicon semiconductors. J. Phys. A Math. Theor. 44, 105501 (2011)

    Article  MathSciNet  Google Scholar 

  21. Muscato, O., Di Stefano, V.: Local equilibrium and off-equilibrium thermoelectric effects in silicon semiconductors. J. Appl. Phys. 110, 093706 (2011)

    Article  Google Scholar 

  22. Muscato, O., Di Stefano, V.: Hydrodynamic modeling of silicon quantum wires. J. Comput. Electron. 11, 45–55 (2012)

    Article  Google Scholar 

  23. Nishibara, S., Suzuki, M.: Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data. MSJ Memoirs, vol. 26. The Mathematical Society of Japan, Tokyo (2011)

    Google Scholar 

  24. Pierret, R.F.: Semiconductor Device Fundamentals. Addison-Wesley, Reading (1996)

    Google Scholar 

  25. Polizzi, E., Ben Abdallah, N.: Subband decomposition approach for the simulation of quantum electron transport in nanostructures. J. Comput. Phys. 202, 150–180 (2005)

    Article  MathSciNet  Google Scholar 

  26. Ren, Z.: Nanoscale MOSFETs: physics, simulation and design. Ph.D. Thesis. Purdue University, West Lafayette (2001)

    Google Scholar 

  27. Romano, V.: Non parabolic band transport in semiconductors: closure of the production terms in the moment equations. Contin. Mech. Thermodyn. 12, 31–51 (2000)

    Article  MathSciNet  Google Scholar 

  28. Romano, V.: Non-parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices. Math. Methods Appl. Sci. 24, 439–471 (2001)

    Article  MathSciNet  Google Scholar 

  29. Romano, V.: 2D numerical simulation of the MEP energy-transport model with a finite difference scheme. J. Comput. Phys. 221, 439–468 (2007)

    Article  MathSciNet  Google Scholar 

  30. Romano, V., Russo, G.: Numerical solution for hydrodymamical models of semiconductors. Math. Models Methods Appl. Sci. 10, 1099–1120 (2000)

    Article  MathSciNet  Google Scholar 

  31. Romano, V., Zwierz, M.: Electron-phonon hydrodynamical model for semiconductors. Z. Angew. Math. Phys. 61, 1111–1131 (2010)

    Article  MathSciNet  Google Scholar 

  32. Vecil, F., Mantas, J.M., Caceres, M.J., Sampedro, C., Godoy, A., Gamiz, F.: A parallel deterministic solver for the Schrödinger-Poisson-Boltzmann system in ultra-short DG-MOSFETs: comparison with Monte-Carlo. Comput. Math. Appl. 67(9), 1703–1721 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Vito Dario Camiola & Vittorio Romano

  2. Department of Mathematics and Computer Science, University of Calabria, Arcavacata di Rende, Italy

    Giovanni Mascali

Authors
  1. Vito Dario Camiola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giovanni Mascali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vittorio Romano
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Camiola, V.D., Mascali, G., Romano, V. (2020). Mathematical Models for the Double-Gate MOSFET. In: Charge Transport in Low Dimensional Semiconductor Structures. Mathematics in Industry(), vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-35993-5_7

Download citation

Publish with us

Policies and ethics

Search

Navigation