Smoothed finite element method for time dependent analysis of quantum resonance devices

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.