A note on boundary conditions for quantum hydrodynamic equations Original Research Article

The asymptotic behavior of the thermal equilibrium state of a bipolar quantum hydrodynamic model is considered. The quantum limit L → 0, L denoting a characteristic device length, is carried out rigorously. It shows that the classical assumption of charge neutrality at the boundary becomes invalid for ultra small semiconductor devices, whereas the assumption of vanishing boundary quantum effects will be confirmed. Furthermore, numerical simulations are presented, which give insight in the quantitative behavior.