On a steady-state quantum hydrodynamic model for semiconductors. (English) Zbl 0882.76105

This paper develops a simplified one-dimensional hydrodynamic-like quantum model for the steady states of a semiconductor. It is a pure-state, single carrier transport model. The governing equations are self-consistent, in the sense that the electric field, which forms the forcing term in the momentum equation, is determined by the coupled Poisson equations. The novelty of the method (which may be extended to two-dimensional cases) is that it reduces the system of equations to an integro-differential equation with a set of boundary conditions, among which a condition is nonstandard and is equivalent to specifying the quantum potential at the current inflow boundary.
Reviewer: I.Bena (Iaşi)


76Y05 Quantum hydrodynamics and relativistic hydrodynamics
81Q15 Perturbation theories for operators and differential equations in quantum theory
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