doi: 10.17586/2226-1494-2016-16-4-725-730


A. S. Bagmutov, I. Y. Popov

Read the full article  ';
Article in Russian

For citation: Bagmutov A.S., Popov I.Yu. Current-voltage characteristics for two systems of quantum waveguides with connected quantum resonators. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 4, pp. 725–730. doi: 10.17586/2226-1494-2016-16-4-725-730


We investigate two 2D quantum systems, each consisting of a waveguide and a resonator, connected through narrow holes. Systems features are studied by the solution of scattering problem. We use zero-width slits model, where the finite radius is changed by infinitely-small one. In the framework of the proposed model, exact solutions are found and scattering problem is solved for both systems using the theory of self-adjoint extensions of symmetric operators. Obtained results are then used to calculate current-voltage characteristics of suggested systems. We show that obtained characteristics have steplike kinks disappearing with the temperature growth or increase of system sizes. Parameters are calculated with the effect still observable. The results may be useful in the design of electronic devices such as nanoelectronic transistor based on resistance control in a waveguide.

Keywords: quantum waveguide, resonator, operator extension theory

Acknowledgements. This work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by the Ministry of Education and Science of the Russian Federation (Goszadanie 2014/190, Projects No. 14.Z50.31.0031 and No. 1.754.2014/K), by grant MK-5001.2015.1 of the President of the Russian Federation.


1. Doyle B., Arghavani R., Barlage D., Datta S., Doczy M., Kavalieros J., Murty A., Chau R. Transistor elements for 30 nm physical gate length and beyond. Intel Technology Journal, 2002, vol. 6, no. 2, pp. 42–54.
2. Bryllert T., Wernersson L.-E., Loewgren T., Samuelson L. Vertical wrap-gated nanowire transistors. Nanotechnology, 2006, vol. 17, no. 11, pp. S227–S230. doi: 10.1088/0957-4484/17/11/S01
3. Yeo K.H. Gate-All-Around (GAA) Twin Silicon Nanowire MOSFET (TSNWFET) with 15 nm length gate and 4 nm radius nanowire. Tech. Dig.-Int. Electron Devices Meet, 2006, pp. 539–550.
4. Cho K.H., Yeo K.H., Yeoh Y.Y., Suk S.D., Li M., Lee J.M., Kim M.-S., Kim D.-W., Park D., Hong B.H., Jung Y.C., Hwang S.W. Experimental evidence of ballistic transport in cylindrical gate-all-around twin silicon nanowire metal-oxide-semiconductor field-effect transistors. Applied Physics Letters, 2008, vol. 92, no. 5, art. 052102. doi: 10.1063/1.2840187
5. Wieck A.D., Ploog K. In-plane-gated quantum wire transistor fabricated with directly written focused ion beams. Applied Physics Letters, 1990, vol. 56, no. 10, pp. 928–930. doi: 10.1063/1.102628
6. Gores J., Goldhaber-Gordon D., Heemeyer S., Kastner M.A., Shtrikman H., Mahalu D., Meirav U. Fano resonances in electronic transport through a single-electron transistor. Physical Review B, 2000, vol. 62, no. 3, pp. 2188–2194.
7. Bjork M.T., Ohlsson B.J., Thelander C., Persson A.I., Deppert K., Wallenberg L.R., Samuelson L. Nanowire resonant tunneling diodes. Applied Physics Letters, 2002, vol. 81, no. 23, pp. 4458–4460. doi: 10.1063/1.1527995
8. Wensorra J., Indlekofer K.M., Lepsa M.I., Forster A., Luth H. Resonant tunneling in nanocolumns improved by quantum collimation. Nano Letters, 2005, vol. 5, no. 12, pp. 2470–2475. doi: 10.1021/nl051781a
9. Vasileska D., Mamaluy D., Khan H.R., Ravela K., Goodnick S.M. Semiconductor device modeling. Journal of Computational and Theoretical Nanoscience, 2008, vol. 5, no. 6, pp. 999–1030.
10. Datta S. Electronic Transport in Mesoscopic Systems. Cambridge, Cambridge University Press, 1995, 394 p.
11. Adamyan V., Pavlov B., Yafyasov A. Modified Krein formula and analytic perturbation procedure for scattering on arbitrary junction. Modern analysis and applications. The Mark Krein Centenary Conference. Basel, 2009, vol. 1, pp. 3–26.
12. Lesovik G.B., Sadovskyy I.A. Scattering matrix approach to the description of quantum electron transport. Physics-Uspekhi, 2011, vol. 54, no. 10, pp. 1007–1059. doi: 10.3367/UFNe.0181.201110b.1041
13. Wulf U., Krahlisch M., Kučera J., Richter H., Höntschel J. A quantitative model for quantum transport in nano-transistors. Nanosystems: Physics, Chemistry, Mathematics, 2013, vol. 4, no. 6, pp. 800–809.
14. Gavrilov M.I., Popov I.Yu. Transmission and reflection coefficients calculation in coupled quantum waveguide system. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 5, pp. 43–48.
15. Martin G., Yafyasov A.M., Pavlov B.S. Resonance one-body scattering on a junction. Nanosystems: Physics, Chemistry, Mathematics, 2010, vol. 1, no. 1, pp. 108–147.
16. Popov I.Yu., Popova S.L. Zero-width slit model and resonances in mesoscopic systems. Europhysics Letters, 1993, vol. 24, no. 5, pp. 373–377. doi: 10.1209/0295-5075/24/5/009
17. Popov I.Yu., Popova S.L. The extension theory and resonances for a quantum waveguide. Physics Letters A, 1993, vol. 173, no. 6, pp. 484–488. doi: 10.1016/0375-9601(93)90162-S
18. Popov I.Yu. The resonator with narrow slit and the model based on the operator extensions theory. Journal of Mathematical Physics, 1992, vol. 33, no. 11, pp. 3794–3801.
19. Popov I.Yu. The extension theory, domain with semitransparent surface and the model of quantum dot. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1996, vol. 452, no. 1950, pp. 1505–1515.
20. Sols F. Scattering, dissipation, and transport in mesoscopic systems. Annals of Physics, 1992, vol. 214, no. 2, pp. 386–438. doi: 10.1016/S0003-4916(05)80005-3
21. Sivan U., Imry Y., Hartzstein C. Aharonov-Bohm and quantum Hall effects in singly connected quantum dots. Physical Review B, 1989, vol. 39, no. 2, pp. 1242–1250. doi: 10.1103/PhysRevB.39.1242

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2022 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.