Abstract
The problem of numerically simulating steady-state scattering and the tunneling transfer of electrons was considered for a 1D potential barrier with an arbitrary shape. An effective numerical approach to solving this problem was developed on the basis of the transformation-matrix method. To test this approach, a computer program was written and applied to calculations of the tunneling processes. The convergence of the method proposed was further investigated in numerical experiments.
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References
N. Kobayashi, Introduction to Nanotechnology (BINOM, Moscow, 2008) [in Russian].
Y. Ando and T. Itoh, “Calculation of Transmission Tunneling Current across Arbitrary Potential Barriers,” Appl. Phys. 61, 1497–1502 (1987).
W. Lui and M. Fukuma, “Exact Solution of the Shrodinger Equation across an Arbitrary One-Dimensional Picewise-Linear Potential Barrier,” Appl. Phys. 60, 1555–1559 (1986).
V. A. Fedirko, D. A. Zenyuk, and S. V. Polyakov, “Numerical Simulation of Stationary Electron Tunneling through Potential Barrier,” in Proceedings of the International Conference on Simulation of Nonlinear Processes and Systems (MGUP, Moscow, 2008), pp. 100–101.
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 Technological Systems, Ed. by L. A. Uvarova (Yanus-K, Moscow, 2009), No. 12, vol. 1, pp. 170–184 [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989, 4th ed.; Pergamon, New York, 1977, 3rd ed.).
Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. Stegun (Nation. Bureau of Standards, New York, 1964; Moscow, Nauka, 1979).
S. Flügge, Practical Quantum Mechanics (Springer, New York, 1974; Mir, Moscow, 1974), Vol. 1.
D. Bohm, Quantum Theory (Nauka, Moscow, 1965; Dover, New York, 1989).
A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].
J. Bardeen, “Tunneling from a Many-Particle Point of View,” Phys. Rev. Lett. 6, 57–59 (1961).
V. A. Fedirko, Mei-Hsin Chen, et al., “An Explicit Model for a Quantum Channel in 2DEG,” Superlatt. Microstruct. 31, 207–217 (2002).
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Fedirko, V.A., Polyakov, S.V. & Zenyuk, D.A. Transformation-matrix method for tunnel-effect simulation. Phys. Part. Nuclei Lett. 8, 463–466 (2011). https://doi.org/10.1134/S1547477111050062
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DOI: https://doi.org/10.1134/S1547477111050062