Low-Field Electron Mobility in Silicon Nanowires

  • Orazio Muscato
  • Tina Castiglione
  • Armando Coco
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


Silicon nanowires (SiNWs) are quasi-one-dimensional structures in which electrons are spatially confined in two directions and they are free to move in the orthogonal direction. The subband decomposition and the electrostatic force field are obtained by solving the Schrödinger—Poisson coupled system. The electron transport along the free direction can be tackled using a hydrodynamic model, formulated by taking the moments of the multisubband Boltzmann equation. We shall introduce an extended hydrodynamic model where closure relations for the fluxes and production terms have been obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, and in which the main scattering mechanisms such as those with phonons and surface roughness have been considered. By using this model, the low field mobility for a Gate-All-Around (GAA) SiNW transistor has been evaluated.



We acknowledge the support of the Università degli Studi di Catania, FIR 2014 “Charge Transport in Graphene and Low dimensional Structures: modeling and simulation” and the National Group of Mathematical Physics (GNFM-INdAM), “Progetto giovani 2015”.


  1. 1.
    Castiglione, T., Muscato, O.: Non-parabolic band hydrodynamic model for silicon quantum wires. J. Comput. Theor. Transport 46(3), 186–201 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Di Stefano, V., Muscato, O.: Seebeck effect in silicon semiconductors. Acta Appl. Math. 122(1), 225–238 (2012)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Lebon, G., Jou, D., Casas-Vázquez, J.: Understanding Non-equilibrium Thermodynamics. Springer, Berlin (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Lenzi, M., Palestri, P., Gnani, E., Reggiani, S., Gnudi, A., Esseni, D., Selmi, L., Baccarani, G.: Investigation of the transport properties of silicon nanowires using deterministic and Monte Carlo approaches to the solution of the Boltzmann transport equation. IEEE Trans. Electron Devices 55(8), 2086–2096 (2008)CrossRefGoogle Scholar
  5. 5.
    Majorana, A., Mascali, G., Romano V.: Charge transport and mobility in monolayer graphene. J. Math. Ind. 7, 4 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Mascali, G.: A hydrodynamic model for silicon semiconductors including crystal heating. Eur. J. Appl. Math. 26(4), 477–496 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mascali, G.: A new formula for Silicon thermal conductivity based on a hierarchy of hydrodynamical models. J. Stat. Phys. 163(5), 1268–1284 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Mascali, G.: Thermal conductivity reduction by embedding nanoparticles. J. Comput. Electron. 16(1), 180–189 (2017). doi:10.1007/s10825-016-0934-yCrossRefGoogle Scholar
  9. 9.
    Muscato, O., Castiglione, T.: Electron transport in silicon nanowires having different cross-sections. Commun. Appl. Ind. Math. 7(2), 8–25 (2016)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Muscato, O., Castiglione, T.: A hydrodynamic model for silicon nanowires based on the maximum entropy principle. Entropy 18(10), 368 (2016)CrossRefGoogle Scholar
  11. 11.
    Muscato, O., Di Stefano,V.: Local equilibrium and off-equilibrium thermoelectric effects in silicon semiconductors. J. Appl. Phys. 110(9), 093706 (2011)CrossRefGoogle Scholar
  12. 12.
    Muscato, O., Di Stefano, V.: An Energy Transport Model describing heat generation and conduction in silicon semiconductors. J. Stat. Phys. 144, 171–197 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Muscato, O., Di Stefano, V.: Hydrodynamic modeling of the electro-thermal transport in silicon semiconductors. J. Phys. A: Math. Theor. 44, 105501 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Muscato, O., Di Stefano, V.: Heat generation and transport in nanoscale semiconductor devices via Monte Carlo and hydrodynamic simulations. COMPEL 30(2), 519–537 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Muscato, O., Di Stefano, V.: Hydrodynamic modeling of silicon quantum wires. J. Comput. Electron. 11(1), 45–55 (2012)CrossRefGoogle Scholar
  16. 16.
    Muscato, O., Di Stefano,V.: Electro-thermal behaviour of a sub-micron silicon diode. Semicond. Sci. Technol. 28, 025021 (2013)CrossRefGoogle Scholar
  17. 17.
    Muscato, O., Di Stefano, V.: Hydrodynamic simulation of a n + − n − n + silicon nanowire. Contin. Mech. Thermodyn. 26, 197–205 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Muscato, O., Di Stefano,V.: Electrothermal transport in silicon carbide semiconductors via a hydrodynamic model. SIAM J. Appl. Math. 75(4), 1941–1964 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Muscato, O., Wagner, W., Di Stefano, V.: Properties of the steady state distribution of electrons in semiconductors. Kinet. Relat. Models 4(3), 809–829 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Muscato, O., Di Stefano, V., Wagner, W.: A variance-reduced electrothermal Monte Carlo method for semiconductor device simulation. Comput. Math. Appl. 65(3), 520–527 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Ramayya, E.B., Knezevic, I.: Self-consistent Poisson-Schrödinger-Monte Carlo solver: electron mobility in silicon nanowires. J. Comput. Electron. 9, 206–210 (2010)CrossRefGoogle Scholar
  22. 22.
    Ryu, H.: A multi-subband Monte Carlo study on dominance of scattering mechanisms over carrier transport in sub-10-nm Si nanowire FETs. Nanoscale Res. Lett. 11(1), 36 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Trellakis, A., Galik, A.T., Pacelli, A., Ravaioli, U.: Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures. J. Appl. Phys. 81(12), 7880–7884 (1997)CrossRefGoogle Scholar
  24. 24.
    Wang, J., Lundstrom, M.: Does source-to-drain tunneling limit the ultimate scaling of MOSFETs? In: IEEE IEDM Technical Digest, pp. 707–710 (2002)Google Scholar
  25. 25.
    Zheng, Y., Rivas, C., Lake, R., Alam, K., Boykin, T.B., Klimeck, G.: Electronic properties of silicon nanowires. IEEE Trans. Electron Devices 52(6), 1097–1103 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Orazio Muscato
    • 1
  • Tina Castiglione
    • 1
  • Armando Coco
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversity of CataniaCataniaItaly
  2. 2.Oxford Brookes UniversityOxfordUK

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