Abstract
The quantum hydrodynamic model is primary used for the simulation of resonant tunneling diodes. The current-voltage characteristics of these diodes show negative differential resistance (NDR) effects. For two simplified one-dimensional quantum models derived by means of asymptotic analysis, explicit formulas of the current-voltage characteristics are given. It turns out that not only the quantum correction term but also the convection term are mathematically responsible for the NDR effects. This observation is confirmed by numerical simulations of the full isothermal quantum hydrodynamic model.
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