Kinetic model of electron transport in cylindrical nanowire with rough surface
https://doi.org/10.17586/2220-8054-2018-9-2-206-211
Abstract
In this work, the problem of electron transport in cylindrical nanowires is considered. A model of nanowire is proposed with the irregularities/scatterers concentrated mainly in the vicinity of the surface. It is treated as a waveguide with some scattering indicatrix introduced to describe specular and nonspecular scattering. Employing the kinetic approach, Kolmogorov equation is used to calculate subsequently aproximate nonequlibrium distribution function and derive explicit formula for the resistivity of the system.
About the Authors
S. A. BotmanRussian Federation
ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016
S. B. Leble
Russian Federation
ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016
References
1. Dresselhaus M. S. et al. Springer Handbook of Nanotechnology. Springer, 2010.
2. Dingle R. B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201(1067), P. 545–560.
3. Lin Y., Sun X., and Dresselhaus M. S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62(7), P. 4610–4623.
4. Pavlov B. S. and Strepetov A. V. Exactly solvable model of electron scattering by an inhomogeneity in a thin conductor Theoretical and Mathematical Physics, 1992, 90(2), P. 152–156.
5. Leble S. B. Kolmogorov equation for Bloch electrons and electrical resistivity models for nanowires. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 247–259.
6. Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung.¨ Mathematische Annalen, 1931, 104(1), P. 415–458.
7. Lobanov I. S., Popov I. Yu. Scattering by a junction of zig-zag and armchair nanotubes. Nanosystems: Physics, Chemistry, Mathematics, 2012, 3(2), P. 6–28.
8. Botman S. A. and Leble S. B. Electrical conductivity model for quasi-one-dimensional structures. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 231–235.
9. Fuchs K. The conductivity of thin metallic films according to the electron theory of metals. In Mathematical Proceedings of the Cambridge Philosophical Society, 1938, 34(1), P. 100–108.
10. Chaplik A. V. and Entin M. V. Energy spectrum and electron mobility in a thin film with non-ideal boundary. Soviet Journal of Experimental and Theoretical Physics, 1969, 28(3), P. 514–517.
11. Krokhin A., Makarov N. M., and Yampolskii V. A. Theory of the surface scattering of electrons in metals with gently sloping surface irregularities. Soviet Physics-JETP, 1991, 72(2), P. 289–294.
12. Makarov N. M., Moroz A. V., and Yampolskii V. A. Classical and quantum size effects in electron conductivity of films with rough boundaries. Physical Review B, 1995, 52(8), P. 6087–6101.
13. Manjirov A. V. and Polyanin A. D. Reference book on integral equation. Factorial press, 2000.
14. Ashcroft N., Mermin N., Wei D. Solid State Physics: Revised Edition. Amazon press, 2016.
Review
For citations:
Botman S.A., Leble S.B. Kinetic model of electron transport in cylindrical nanowire with rough surface. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(2):206–211. https://doi.org/10.17586/2220-8054-2018-9-2-206-211