[Zurück]

J.-F. Mennemann:
"Transient simulations of a resonant tunneling diode with applications to a high frequency oscillator";
Vortrag: The 17th European Conference on Mathematics for Industry 2012, Lund, Schweden; 23.07.2012 - 27.07.2012.

We present transient simulations of a resonant tunneling diode (RTD) based on the time-dependent Schrödinger equation coupled selfconsistently to the Poisson equation.
To model the interaction with the reservoirs and to restrict the electron wave functions to a finite computational domain we employ nonhomogeneous discrete transparent boundary conditions.
As these boundary conditions involve discrete convolutions in time and as device simulations require to propagate several thousand electron wave functions simultaneously long-term simulations are extremely expensive.
However, the computational effort can be reduced drastically if the convolution coefficients are approximated by sums of exponentials.
To reduce the computational costs further a time step as large as possible should be used. To this end, continous relations like dispersion relations need to be replaced by discrete versions consistent with the Crank-Nicolson scheme.
Finally, we present simulations of a high-frequency oscillator wherein the total current and the applied voltage of the RTD is coupled to the network equations of the circuit.
In contrast to previous simulations we are able to observe the time-evolution of physical quantities like current- or electron densities inside the RTD and their dynamic interaction with the remaining parts of the oscillator.