Zero debye length asymptotic of the quantum hydrodynamic model for semiconductors

In the present paper we consider the zero Debye length asymptotic of solutions of isentropic quantum hydrodynamic equations for semiconductors at nano-size and show that the current density consists of the divergence free vector field involved in the incompressible Euler equation and highly oscillating gradient vector field caused by the highly electric fields for small Debye length. This means that the quantum effects possibly may not dominate the charge transport within the channel of semiconductor devices (for instance MOSFET) of nano-size for isentropic quantum fluids.