On a Steady-State Quantum Hydrodynamic Model for Semiconductors

By: Bo Zhang and Joseph W. Jerome

A third order quantum perturbation of the stress tensor, and a relaxation approximation to represent averaged collisions, are employed as perturbations of the isentropic model for a collisionless plasma. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. As formulated, the model is a reduced version of the quantum hydrodynamic model for semiconductors. Existence is demonstrated for the model, which is shown to be equivalent to a non-standard integro-differential equation. An unusual boundary condition, with the important physical interpretation of specifying the quantum potential at the (current) inflow boundary, is identified as essential for the theory.
This paper appeared in Nonlinear Analysis 26 (1996), 845--856.
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