Abstract
In this paper, a new finite element method (FEM) is introduced to study the time-dependent wave nature of the electron in quantum resonance devices. Unlike the well-known FEM, the new method smooths the wave function derivatives over the edges. In this sense, the new method is termed “smoothed FEM” where an “inter-element” matrix is formed to smooth the derivatives over the edges. For the electron’s wave function propagation in time, the presented method exploits the time domain beam propagation method (TD-BPM). Based only on first order elements, our suggested SFETD-BPM has high accuracy levels comparable to second-order conventional FEM elements; thanks to the element smoothing. The proposed method numerical performance is tested through the analysis of a quantum resonance cavity and a quantum resonant tunneling device. It is clearly demonstrated that the presented method is not only accurate but also more time efficient than the conventional FEM approach.
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This article is part of the Topical Collection on Optical Wave and Waveguide Theory and Numerical Modelling, OQTNM 2017.
Guest Edited by Bastiaan Pieter de Hon, Sander Johannes Floris, Manfred Hammer, Dirk Schulz, Anne-Laure Fehrembach
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Atia, K.S.R., Heikal, A.M. & Obayya, S.S.A. Smoothed finite element method for time dependent analysis of quantum resonance devices. Opt Quant Electron 50, 127 (2018). https://doi.org/10.1007/s11082-018-1392-5
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DOI: https://doi.org/10.1007/s11082-018-1392-5