Electron transport in silicon nanowires having different cross-sections

Orazio Muscato; Tina Castiglione

doi:10.1515/caim-2016-0003

.blurhash-client-img { display: none !important; }

Electron transport in silicon nanowires having different cross-sections

Communications in Applied and Industrial Mathematics

Volume 7 (2016): Issue 2 (June 2016)

By: Orazio Muscato and Tina Castiglione

Open Access

|May 2016

Abstract

Transport phenomena in silicon nanowires with different cross-section are investigated using an Extended Hydrodynamic model, coupled to the Schrödinger-Poisson system. The model has been formulated by closing the moment system derived from the Boltzmann equation on the basis of the maximum entropy principle of Extended Thermodynamics, obtaining explicit closure relations for the high-order fluxes and the production terms. Scattering of electrons with acoustic and non polar optical phonons have been taken into account. The bulk mobility is evaluated for square and equilateral triangle cross-sections of the wire.

References

1. D. Ferry, S. Goodnick, and J. Bird, Transport in nanostructures. Cambridge University Press, 2009.10.1017/CBO9780511840463
Search in Google Scholar
2. R. Juhasz, N. Elfstro, and J. Linnros, Controlled fabrication of silicon nanowires by electron beam lithography and electrochemical size reduction, Nano Letters, vol. 5, no. 2, pp. 275–280, 2005.10.1021/nl048157315794610
Search in Google Scholar
3. M. Lundstrom and J. Wang, Does source-to-drain tunneling limit the ultimate scaling of mosfets?, IEDM Tech. Dig., pp. 707–710, 2002.
Search in Google Scholar
4. E. Ramayya, D. Vasileska, S. Goodnick, and I. Knezevic, Electron mobility in silicon nanowires, IEEE Trans. Nanotech., vol. 6, no. 1, pp. 113–117, 2007.10.1109/TNANO.2006.888521
Search in Google Scholar
5. E. Ramayya, D. Vasileska, S. Goodnick, and I. Knezevic, Electron transport in silicon nanowires: The role of acoustic phonon confinement and surface roughness scattering, J. Appl. Phys., vol. 104, p. 063711, 2008.
Search in Google Scholar
6. E. Ramayya and I. Knezevic, Self-consistent Poisson-Schrödinger-Monte Carlo solver: electron mobility in silicon nanowires, J. Comput. Electr., vol. 9, pp. 206–210, 2010.10.1007/s10825-010-0341-8
Search in Google Scholar
7. O. Muscato, W. Wagner, and V. Di Stefano, Numerical study of the systematic error in Monte Carlo schemes for semiconductors, ESAIM: M2AN, vol. 44, no. 5, pp. 1049–1068, 2010.
Search in Google Scholar
8. O. Muscato, W. Wagner, and V. Di Stefano, Properties of the steady state distribution of electrons in semiconductors, Kinetic and Related Models, vol. 4, no. 3, pp. 809–829, 2011.10.3934/krm.2011.4.809
Search in Google Scholar
9. O. Muscato, V. Di Stefano, and W. Wagner, A variance-reduced electrothermal Monte Carlo method for semiconductor device simulation, Comput. Math. with Appl., vol. 65, no. 3, pp. 520–527, 2013.10.1016/j.camwa.2012.03.100
Search in Google Scholar
10. M. Lenzi, P. Palestri, E. Gnani, A. Gnudi, D. Esseni, L. Selmi, and G. Baccarani, Investigation of the transport properties of silicon nanowires using deterministic and Monte Carlo approaches to the solution of the boltzmann transport equation, IEEE Trans. Electr. Dev., vol. 55, no. 8, pp. 2086–2096, 2008.
Search in Google Scholar
11. G. Ossig and F. Schuerrer, Simulation of non-equilibrium electron transport in silicon quantum wires, J. Comput. Electron., vol. 7, pp. 367–370, 2008.10.1007/s10825-008-0238-y
Search in Google Scholar
12. O. Muscato and V. Di Stefano, Hydrodynamic modeling of silicon quantum wires, J. Comput. Electron., vol. 11, no. 1, pp. 45–55, 2012.10.1007/s10825-012-0381-3
Search in Google Scholar
13. V. Di Stefano and O. Muscato, Seebeck effect in silicon semiconductors, Acta Appl. Math., vol. 122, no. 1, pp. 225–238, 2012.10.1007/s10440-012-9739-6
Search in Google Scholar
14. O. Muscato and V. Di Stefano, Hydrodynamic simulation of a n+ - n - n+ silicon nanowire, Contin. Mech. Thermodyn., vol. 26, pp. 197–205, 2014.10.1007/s00161-013-0296-7
Search in Google Scholar
15. T. Kuykendall, P. Pauzauskie, S. Lee, Y. Zhang, J. Goldberger, and P. Yang, Metalorganic chemical vapor deposition route to gan nanowires with triangular cross sections, Nano Letters, vol. 3, no. 8, pp. 1063–1066, 2003.
Search in Google Scholar
16. G. Pennelli and M. Piotto, Fabrication and characterization of silicon nanowires with triangular cross section, J. Appl. Phys., vol. 100, p. 054507, 2006.
Search in Google Scholar
17. G. Pennelli, Top down fabrication of long silicon nanowire devices by means of lateral oxidation, Microelec. Engineer., vol. 86, pp. 2139–2143, 2009.
Search in Google Scholar
18. G. Liang, W. Huang, C. S. Koong, J.-S. Wang, and J. Lan, Geometry effects on thermoelectric properties of silicon nanowires based on electronic band structures, J. Appl. Phys., vol. 107, p. 014317, 2010.
Search in Google Scholar
19. R. Khordad and H. Bahramiyan, Electron-phonon interaction effect on the energy levels and diamagnetic susceptibility of quantum wires: Parallelogram and triangle cross section, J. Appl. Phys., vol. 115, p. 124314, 2014.
Search in Google Scholar
20. D. Jou, J. Casas-Vázquez, and G. Lebon, Extended irreversible thermodynamics. Springer-Verlag, 2001.10.1007/978-3-642-56565-6
Search in Google Scholar
21. O. Muscato, R. Pidatella, and M. Fischetti, Monte Carlo and hydrodynamic simulation of a one dimensional n+ − n − n+ silicon diode, VLSI Design, vol. 6, no. 1-4, pp. 247–250, 1998.10.1155/1998/98910
Search in Google Scholar
22. O. Muscato and V. Di Stefano, Modeling heat generation in a submicrometric n⁺ − n − n⁺ silicon diode, J. Appl. Phys., vol. 104, no. 12, p. 124501, 2008.
Search in Google Scholar
23. O. Muscato and V. Di Stefano, Hydrodynamic modeling of the electro-thermal transport in silicon semiconductors, J. Phys.A:Math. Theor., vol. 44, no. 10, p. 105501, 2011.
Search in Google Scholar
24. O. Muscato and V. Di Stefano, An energy transport model describing heat generation and conduction in silicon semiconductors, J. Stat. Phys., vol. 144, no. 1, pp. 171–197, 2011.10.1007/s10955-011-0247-2
Search in Google Scholar
25. O. Muscato and V. Di Stefano, Heat generation and transport in nanoscale semiconductor devices via Monte Carlo and hydrodynamic simulations, COMPEL, vol. 30, no. 2, pp. 519–537, 2011.10.1108/03321641111101050
Search in Google Scholar
26. G. Mascali and V. Romano, A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle, Math. Comp. Model., vol. 55, no. 3-4, pp. 1003–1020, 2012.
Search in Google Scholar
27. V. Camiola, G. Mascali, and V. Romano, Numerical simulation of a double-gate mosfet with a subband model for semiconductors based on the maximum entropy principle, Contin. Mech.Thermodyn., vol. 24, no. 4-6, pp. 417–436, 2012.10.1007/s00161-011-0217-6
Search in Google Scholar
28. W.-K. Li and S. Blinder, Solution of the Schrödinger equation for a particle in an equilateral triangle, J. Math. Phys., vol. 26, no. 11, pp. 2784–2786, 1985.
Search in Google Scholar
29. S. Selberherr, Analysis and Simulation of Semiconductor Devices. Springer, 1984.10.1007/978-3-7091-8752-4
Search in Google Scholar
30. C. Jacoboni, C. Canali, G. Ottaviani, and A. Quaranta, A review of some charge transport properties for silicon, Solid State Electron, vol. 20, no. 2, pp. 77–89, 1977.10.1016/0038-1101(77)90054-5
Search in Google Scholar
31. O. Muscato and V. Di Stefano, Local equilibrium and off-equilibrium thermoelectric effects in silicon semiconductors, J. Appl. Phys., vol. 110, no. 9, p. 093706, 2011.
Search in Google Scholar
32. O. Muscato and V. Di Stefano, Electro-thermal behaviour of a sub-micron silicon diode, Semicond. Sci. Tech., vol. 28, no. 2, p. 025021, 2013.
Search in Google Scholar
33. E. Ramayya, L. Maurer, A. Davoody, and I. Knezevic, Thermoelectric properties of ultrathin silicon nanowires, Phys. Rev. B, vol. 86, no. 11, p. 115328, 2012.
Search in Google Scholar
34. Z. Aksamija and I. Knezevic, Thermoelectric properties of properties of silicon nanostructures, J. Comput. Electron., vol. 9, pp. 173–179, 2010.10.1007/s10825-010-0339-2
Search in Google Scholar
35. D. Jou, V. Cimmelli, and A. Sellito, Nonlocal heat transport with phonons and electrons: Application to metallic nanowires, Int. J. Heat Mass transf., vol. 55, no. 9-10, pp. 2338–2344, 2012.
Search in Google Scholar
36. A. Sellito, V. Cimmelli, and D. Jou, Thermoelectric effects and size dependency of the figure-of-merit in cylindrical nanowires, Int. J. Heat Mass transf., vol. 57, no. 1, pp. 109–116, 2013.10.1016/j.ijheatmasstransfer.2012.10.010
Search in Google Scholar
37. V. Cimmelli, A. Sellito, and D. Jou, A nonlinear thermodynamic model for a breakdown of the onsager symmetry and the efficiency of thermo-electric conversion in nanowires, Proc. Royal soc.A: Math., Phys. Eng. Sci., vol. 470, no. 2170, p. 20140265, 2014.
Search in Google Scholar
38. A. Sellito and V. Cimmelli, Flux limiters in radial heat transport in silicon nanolayers, J. Heat Transfer, vol. 136, no. 7, p. 071301, 2014.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.1515/caim-2016-0003 | Journal eISSN: 2038-0909

Journal RSS Feed

Language: English

Page range: 8 - 25

Submitted on: Jan 3, 2015

Accepted on: May 7, 2015

Published on: May 20, 2016

Published by: Italian Society for Applied and Industrial Mathemathics

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Quantum wires,

Semiconductors,

Kinetic theory of gases

Related subjects:

Mathematics,

Numerical and computational mathematics,

Applied mathematics

© 2016 Orazio Muscato, Tina Castiglione, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 7 (2016): Issue 2 (June 2016)