Generalized model of electron transport in micro- and nanoelectronics: from ballistic to diffusion conductivity

Authors: Kruglyak Yu.А., Kostritskya L.S.

Year: 2016

Issue: 20

Pages: 78-90

Abstract

The Landauer – Datta – Lundstrom transport model is used to calculate conductivity of resistors of any dimension and scale and of an arbitrary dispersion working in the ballistic or diffusion regime at near 0 K and at higher temperatures. There is also discussed still widely used concept of mobility, as well as the dissipation of heat and the voltage drop in the ballistic resistors.

The goal of this review is to show how to use the Landauer equation for conductance in the absence of temperature difference at the ends of the conductor.

The main results can be briefly formulated as follows: all conductors have a constant resistance even in case of absence of electron scattering. Ballistic resistance is the lower limit of resistance, no matter how small the conductor is. This ballistic limit resistance becomes important even for electronic devices at the room temperature. Ballistic resistance is quantized and the quantum of resistance is represented by fundamental Klitzing constant. The whole area of the transition from ballistic to diffusive transport is interpreted in the LDL model in a standard way with the help of transmission coefficient. Resistors of all dimensions – 1D, 2D and 3D are uniformly treated in the LDL formalism, and the interpretation allows for any type of dispersion relation. In the study of electrical properties of any new material, including nanosystems, it is necessary to begin with the Landauer conductivity equation.

Tags: elastic resistor fashion conductivity; Nanophysics and Nanoelectronics; transmittance

Bibliography

1. Кругляк Ю.А. Обобщенная модель электронного транспорта Ландауэра – Датты – Лундстрома //Наносистеми, наноматеріали, нанотехнології. – 2013. – Вип. 11, №3. – С. 519 – 549; Erratum, Ibid, 2014, Вып. 12, № 2, С.
2. Pierret R.F. Semiconductor Device Fundamentals. Reading, MA: Addison–Wesley, 1996.
3. Van WeesB.J., vanHouten H., Beenakker C.J., Williamson J.G., Kouwenhoven L.P., van der Marel D., Foxon C.T. Quantized Conductance of Point Contacts in a Two-Dimensional Electron Gas. Phys. Rev. Lett., 1988, Vol. 60, no. 9, рр. 848–850.
4. Holcomb D.F. Quantum Electrical Transport in samples of limited dimensions. J. Phys., 1999, vol. 67, no. 4, 278 p.
5. Cvijovic D. Fermi – Dirac and Bose – Einstein functions of negative integer order. Math. Phys., 2009, vol. 161, no. 3, 163 p.
6. Dingle R.. The Fermi – Dirac Integrals. Scientific Res., 1957, vol. 6, no. 1, 225 p.
7. .Kim R, M.S. Lundstrom. Notes on Fermi – Dirac Integrals. http://nanohub.org/resources/5475.
8. Lundstrom Mark. Fundamentals of Carrier Transport, 2nd Ed. Cambridge: Cambridge Univ. Press, 2000.
9. Peter Yu, Manuel Cardona. Fundamentals of Semiconductors. Physics and Materials Berlin: Springer, 2010.
10. Shur M.S. Low Ballistic Mobility in GaAs HEMTs. IEEE Electron Dev. Lett., 2002, vol. 23, no. 9, 511 p.
11. Jing Wang, Mark Lundstrom. Ballistic Transport in High Electron Mobility Transistors. IEEE Trans. Electron Dev., 2003, vol. 50, no. 7, 1604 p.
12. АшкрофтН. Физика твердого тела /Н. Ашкрофт, Н. Мермин.- М: Мир, 1979.
13. Supriyo Datta. Electronic Transport in Mesoscopic Systems. Cambridge: Cambridge University Press, 2001.
14. Zhen Yao, .Kane C.L, .Dekker C. High-Field Electrical Transport in Single-Wall Carbon Nanotubes, Rev. Lett., 2000, vol. 84, 13, 2941 p.
15. Lundstrom M., Jeong. Near-Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 2013; http://www.nanohub.org/resources/11763).