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We present the new results on stability and semi-classical limit in asemiconductor full quantum hydrodynamic (FQHD) model with non-flat dopingprofile. The FQHD model can be used to analyze the thermal and quantuminfluences on the transport of carriers (electrons or holes) in semiconductordevice. Inspired by the physical motivation, we consider the initial-boundaryvalue problem of this model over the one-dimensional bounded domain and adoptthe ohmic contact boundary condition and the vanishing bohmenian-type boundarycondition. Firstly, the existence and asymptotic stability of a stationarysolution are proved by Leray- Schauder fixed-point theorem, Schauderfixed-point theorem and the refined energy method. Secondly, we show thesemi-classical limit results for both stationary solutions and global solutionsby the elaborate energy estimates and the compactness argument. The strongconvergence rates of the related asymptotic sequences of solutions are alsoobtained.

Stability and semi-classical limit in a semiconductor full quantum hydrodynamic model with non-flat doping profile