Abstract
We develop an efficient approach for computer simulation of stationary scattering and tunneling transfer across an arbitrary one-dimensional potential barrier. New algorithms and programs were worked out and tested and the convergence of the method in question was examined.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Kobayashi, Introduction into Nanoelektronics (BINOM, Moscow, 2008) [in Russian].
Y. Ando and T. Itoh, “Calculation of Transmission Tunneling Current across Arbitrary Potential Barriers,” Appl. Phys. 61(4), 1497–1502 (1987).
W. Lui and M. Fukuma, “Exact Solution of the Schrodinger Equation across an Arbitrary One-Dimensional Piecewise-Linear Potential Barrier,” Appl. Phys. 60(5), 1555–1559 (1986).
V. A. Fedirko, D. A. Zenyuk, and S. V. Polyakov, “Numerical Simulation of Stationary Electron Tunneling through Potential Barrier,” in Proc. Int. Conf. Simulation of Nonlinear Processes and Systems (Izd-vo MGUP, Moscow, 2008), pp. 100–101 [in Russian].
V. A. Fedirko, D. A. Zenyuk, and S. V. Polyakov, “Numerical Simulation of Stationary Electron Tunneling through Potential Barrier,” in Fundamental Physical-Mathematical Problems and Simulation of Technical-Engineering Systems, Ed. by L. A. Uvarova (Yanus-K, Moscow, 2009), Issue 12, pp. 170–184 [in Russian].
L. D. Landau and E. M. Lifshits, Quantum Mechanics (Nonrelativistic Theory) (Nauka, FM, Moscow, 2004) [in Russian].
M. Abramovits and I. Stigan, Special Functions. Handbook (Nauka, FM, Moscow, 1979) [in Russian].
S. Fluge, Practical Quantum Mechanics (Spring, New York, 1974; Mir, Moscow, 1974), Vol. 1.
D. Bom, Quantum Theory (Prentice Hall, Englewood Cliffs, NJ, 1951; Nauka, FM, Moscow, 1965).
V. A. Fedirko, Chen Mei-Hsin, et al., “An Explicit Model for a Quantum Channel in 2DEG,” Superlatt. Microstruct. 31(5), 207–217 (2002).
A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, FM, Moscow, 1989) [in Russian].
J. Bardeen, “Tunneling from a Many-Particle Point of View,” Phys. Rev. Lett. 6(2), 57–59 (1961).
V. A. Fedirko and V. A. Nikolaeva, “Numerical Simulation of Field Emission from Silicon,” Mat. Model. 9, No. 9, 75–82 (1997).
V. A. Fedirko, Yu. N. Karamzin, I. G. Zakharova, and S. V. Polyakov, “Simulation of Hot Electron Field Emission from Silicon Microcathode,” Prikl. Fiz., No. 1, 102–111 (1999).
M. I. Elinson and G. F. Vasil’ev, Autoelectronic Emission (Nauka, FM, Moscow, 1958) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Fedirko, S.V. Polyakov, D.A. Zenyuk, 2010, published in Matematicheskoe Modelirovanie, 2010, Vol. 22, No. 5, pp. 3–14.
Rights and permissions
About this article
Cite this article
Fedirko, V.A., Polyakov, S.V. & Zenyuk, D.A. Matrix method for simulating the tunneling transfer. Math Models Comput Simul 2, 704–713 (2010). https://doi.org/10.1134/S2070048210060050
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070048210060050