J.-F. Mennemann, A. Jüngel, H. Kosina:
"Transient Schrödinger-Poisson simulations of a high-frequency resonant tunneling diode oscillator";
Journal of Computational Physics, 239 (2013), S. 187 - 205.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
Transient simulations of a resonant tunneling diode oscillator are presented. The semiconductor
model for the diode consists of a set of time-dependent Schrödinger equations
coupled to the Poisson equation for the electric potential. The one-dimensional Schrödinger
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.

Schrödinger-Poisson system; tunneling diode

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