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

TL;DR

This paper presents advanced transient simulations of a resonant tunneling diode oscillator using a coupled Schr"odinger-Poisson model with stable boundary conditions, capturing the diode's transient and oscillatory behaviors for the first time.

Contribution

It introduces a stable, reflection-free finite-difference scheme with an efficient boundary condition implementation for simulating diode oscillators.

Findings

Simulated transient regimes between stationary states.

Captured self-oscillatory behavior of the diode oscillator.

Demonstrated the effectiveness of the boundary treatment in large-scale simulations.

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.