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arXiv · 1211.0821

Transient Schr\"odinger-Poisson Simulations of a High-Frequency Resonant Tunneling Diode Oscillator

Jan-Frederik Mennemann·Ansgar Jüngel·Hans Kosina
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Abstract

Transient simulations of a resonant tunneling diode oscillator are presented. The semiconductor model for the diode consists of a set of time-dependent Schr\"odinger equations coupled to the Poisson equation for the electric potential. The one-dimensional Schr\"odinger equations are discretized by the finite-difference Crank-Nicolson scheme using memory-type transparent boundary conditions which model the injection of electrons from the reservoirs. This scheme is unconditionally stable and reflection-free at the boundary. An efficient recursive algorithm due to Arnold, Ehrhardt, and Sofronov is used to implement the transparent boundary conditions, enabling simulations which involve a very large number of time steps. Special care has been taken to provide a discretization of the boundary data which is completely compatible with the underlying finite-difference scheme. The transient regime between two stationary states and the self-oscillatory behavior of an oscillator circuit, containing a resonant tunneling diode, is simulated for the first time.

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Jan-Frederik Mennemann, Ansgar Jüngel, Hans Kosina. 2012-11-05. Transient Schr\"odinger-Poisson Simulations of a High-Frequency Resonant Tunneling Diode Oscillator. https://doi.org/10.1016/j.jcp.2012.12.009

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