Time-dependent numerical methods for the quantum hydrodynamic model for semiconductor devices

Numerical methods are developed for the time-dependent smooth quantum hydrodynamic (QHD) model for semiconductor devices by solving the underlying hyperbolic gas dynamical part of the transport equations with a third-order WENO method, treating the quantum mechanical terms as source terms; the parabolic heat conduction term using the TRBDF2 method; and the elliptic Poisson equation using PCG. These are the first time-dependent simulations of the smooth QHD model, and the first time-dependent simulations of any QHD model at 300 K. Time-dependent simulations of the resonant tunneling diode to steady state are presented, which show realistic negative differential resistance (the experimental signal of quantum resonance) in the current-voltage curve.