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Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle

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Abstract

A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors formulated starting from the moment system derived from the Schrödinger–Poisson–Boltzmann equations. The system is closed on the basis of the maximum entropy principle and includes scattering of electrons with acoustic and non-polar optical phonons. The proposed expression of the entropy combines quantum effects and semiclassical transport by weighting the contribution of each subband with the square modulus of the envelope functions arising from the Schrödinger–Poisson subsystem. The simulations show that the model is able to capture the relevant confining and transport features and assess the robustness of the numerical scheme.

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References

  1. Datta S.: Quantum Phenomena, Modular Series on Solid State Devices. vol. 8. Addison-Wesley Publishing, Reading (1989)

    Google Scholar 

  2. Lundstrom M.: Fundamentals of Carrier Transport. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  3. Wang J., Polizzi E., Lundstrom M.: A three dimensional quantum simulation of silicon nanowire transistors with the effective-mass approximation. J. Appl. Phys. 96, 2192–2203 (2004)

    Article  ADS  Google Scholar 

  4. Chen D., Wei G.-W.: Modeling and simulation of electron structure, material interface and random doping in nano-electronic devices. J. Comput. Phys. 229, 4431–4460 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Markowich P., Ringhofer C.A., Schmeiser C.: Semiconductor Equations. Springer, Wien (1990)

    Book  Google Scholar 

  6. Jüngel A.: Transport Equations for Semiconductors, Lecture Notes in Physics, vol. 773. Springer, Berlin (2009)

    Book  Google Scholar 

  7. Romano V.: Quantum corrections to the semiclassical hydrodynamical model of semiconductors based on the maximum entropy principle. J. Math. Phys. 48, 123504 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  8. Fischetti M.V.: Master equation approach to the study of electronic transport in small semiconductor devices. Phys. Rev. B 59, 4901–4917 (1999)

    Article  ADS  Google Scholar 

  9. Ando T., Fowler A.B., Stern F.: Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982)

    Article  ADS  Google Scholar 

  10. Polizzi E., Ben Abdallah N.: Self-consistent three dimensional models for quantum ballistic transport in open systems. Phys. Rev. B 66, 245301-1–245301-9 (2002)

    Article  ADS  Google Scholar 

  11. Polizzi E., Ben Abdallah N.: Subband decomposition approach for the simulation of quantum electron transport in nanostructures. J. Comput. Phys. 202(1), 150–180 (2004)

    Article  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  13. 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, 6553 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Majorana A., Muscato O., Milazzo C.: Charge transport in 1D silicon devices via Monte Carlo simulation and Boltzmann-Poisson solver. COMPEL 23(2), 410–425 (2004)

    Article  MATH  Google Scholar 

  15. De Falco C., Gatti E., Lacaita A., Sacco R.: Quantum-corrected drift-diffusion models for transport in semiconductor devices. J. Comput. Phys. 204, 533 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  16. Ben Abdallah N., Méhats F., Vauchelet N.: Diffusive transport of partially quantized particles: existence, uniqueness and long-time behaviour. Proc. Edinb. Math. Soc. 2(49), 513–549 (2006)

    Article  Google Scholar 

  17. Mascali G., Romano V.: Hydrodynamic subband model for semiconductors based on the maximum entropy principle. IL NUOVO CIMENTO 33 C, 155 (2010)

    Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  20. Titchmarsh E.C.: Elgenfunction Expansions Associated With Second Order Differential Equations. Clarendon Press, Oxford (1946)

    Google Scholar 

  21. Jaynes E.T.: Information theory and statistical mechanics. Phys. Rev. B 106, 620 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Wu N.: The Maximum Entropy Method. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. Mascali G., Romano V.: Simulation of Gunn oscillations with a non-parabolic hydrodynamical model based on the maximum entropy principle. Compel 24(1), 35–54 (2005)

    Article  MATH  Google Scholar 

  26. Anile A.M., Mascali G.: Theoretical foundations for tail electron hydrodynamical models in semiconductors. Appl. Math. Lett. 14(2), 245–252 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. 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 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. Romano V.: Nonparabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices. Math. Method Appl. Sci. 24, 439–471 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. 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 

  31. Mascali G., Romano V.: A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands. Math. Comput. Model. 53(01–2), 213–229 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ren, Z.: Nanoscale MOSFETs: Physics, Simulation, and Design. PhD thesis, Purdue University, West Lafayette (2001)

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Degond P., Jüngel A., Pietra P.: Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure. SIAM J. Sci. Comput. 22, 986–1007 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  35. Muscato O.: The Onsager reciprocity principle as a check of consistency for semiconductor carrier transport models. Phys. A 289(3–4), 422–458 (2001)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, viale A. Doria 6, 95125, Catania, Italy

    Vito Dario Camiola & Vittorio Romano

  2. Dipartimento di Matematica, Università della Calabria and INFN-Gruppo c. Cosenza, 87036, Cosenza, Italy

    Giovanni Mascali

Authors
  1. Vito Dario Camiola
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  2. Giovanni Mascali
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  3. Vittorio Romano
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Correspondence to Vito Dario Camiola.

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Communicated by Henning Struchtrup.

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Camiola, V.D., Mascali, G. & Romano, V. Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle. Continuum Mech. Thermodyn. 24, 417–436 (2012). https://doi.org/10.1007/s00161-011-0217-6

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  • DOI: https://doi.org/10.1007/s00161-011-0217-6

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