Quantum Hydrodynamic Simulation of Hysteresis in the Resonant Tunneling Diode

Hysteresis in the current-voltage curve of a resonant tunneling diode is simulated and analyzed in the quantum hydrodynamic (QHD) model for semiconductor devices. The simulations are the first to show hysteresis in the QHD equations and to confirm that bistability is an intrinsic property of the resonant tunneling diode. Hysteresis appears in many settings in fluid dynamics. The simulations presented here show that hysteresis is manifested in the extension of classical fluid dynamics to quantum fluid dynamics. A finite element method for simulation of the time-dependent QHD model is introduced. The finite element method is based on a Runge-Kutta discontinuous Galerkin method for the QHD conservation laws and a mixed finite element method for Poisson's equation and the source terms in the QHD conservation laws.