Comparison of traditional and impedance methods for quantum–sized structures simulation

Authors

DOI:

https://doi.org/10.20535/RADAP.2014.56.129-136

Keywords:

asymmetric potential barrier, quantum–mechanical impedance, tunneling, matched overbarrier transmission

Abstract

Introduction. Comparative analysis of traditional and impedance approaches in modeling asymmetric potential quantum–mechanical barrier are fulfilled.
Features of waves tunneling. The effect of waves tunneling are considered. The features of quantum–mechanical wave tunneling through asymmetric potential barrier are illustrated.
Traditional approach. Quantum–mechanical wave transmission through asymmetric poten-tial barrier on the basis of quantum–mechanical approach are explored. The expression for reflection coefficient is obtained.
Impedance approach. By using the impedance method, which is based on the concept of quantum–mechanical impedance and the theory of transmission lines, the expression of the reflection coefficient is obtained. The identity of expressions received by two approaches are demon-strated.
Tunneling regime. The expressions for transmission coefficient for tunneling regime in exact and approximate forms are obtained. Applicability of the approximate formula is presented.
Matched overbarrier transmission. The conditions of reflectionless resonant and nonresonant overbarrier transmission are obtained. Dependences of transmission coefficient for asymmetric barrier that illustrate unmatched and matched overbarrier transmission are presented.
Conclusions. Impedance method significantly simplifies modeling of quantum–mechanical structures in comparison with the traditional method of solving quantum–mechanical problems.

Author Biographies

E. A. Nelin, National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev

Doctor of Engineering, Professor

M. V. Vodolazka, National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev

Postgraduate Student

References

Перелік посилань

Ландау Л.Д. Теоретическая физика. Т. 3. Квантовая механика. (Нерелятивистс-кая теория) / Л.Д. Ландау, Е. М. Лифшиц. – М. : Физматлит. – 2002. – 808 с.

Нелин Е. А. Импедансная модель для “барьерных” задач квантовой механики / Е. А. Нелин // Успехи физических наук. – 2007. – Т. 177, №3. – С. 307313.

Шварцбург А.Б. Туннелирование электромагнитных волн – парадоксы и перспек-тивы / А.Б. Шварцбург // Успехи физических наук. – 2007. – Т. 177, № 1. – С. 43-58.

Крауфорд Ф. Волны / Ф. Крауфорд. – М. : Наука, 1976. – 526 с.

Fromhold A.T. Quantum Mechanics / A. T. Fromhold // Encyclopedia of Physical Science and Technology. – 2001. – Vol. 13. – P. 359-408.

Khondker A. N. Transmission line analogy of resonance tunneling phenomena: The generalized impedance concept / A.N. Khondker, M.R. Khan, A.F.M. Anwar // J. Appl. Phys. – 1988. – Vol. 63, No 10. – P. 5191-5193.

References

Landau L. D. and Lyfshyts E. M. (2002) Teoretycheskaia fyzyka. T. 3. Kvantovaia mekhanyka. (Nereliatyvystskaia teoryia) [Theoretical Physics. Vol. 3. Quantum mechanics. (Non–relativistic theory)]. Moscow, Fyzmatlyt Publ., 808 p.

Nelin E.A. (2007) Impedance model for quantum–mechanical barrier problems. Phys. Usp., vol. 50, no. 3, pp. 293–299.

Shvartsburg A.B. (2007) Tunneling of electromagnetic waves: paradoxes and prospects. Phys. Usp., vol. 50, no. 1, pp. 37–51.

Krauford F. (1976) Volny [Waves]. Moscow, Nauka Publ., 526 p.

Fromhold A. T., Jr. (2001) Quantum Mechanics. Encyclopedia of Physical Science and Technology, vol. 13, pp. 359–408.

Khondker A. N., Khan M. R. and Anwar A. F. M. (1988) Transmission line analogy of resonance tunneling phenomena: The generalized impedance concept. J. Appl. Phys., vol. 63, no 10, pp. 5191–5193.

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Published

2014-03-06

How to Cite

Нелін, Є. and Водолазька, М. (2014) “Comparison of traditional and impedance methods for quantum–sized structures simulation”, Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, 0(56), pp. 129-136. doi: 10.20535/RADAP.2014.56.129-136.

Issue

No. 56 (2014)

Section

Functional Electronics. Micro- and Nanoelectronic Technology

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