  We present the new results on stability and semi-classical limit in a
semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping
profile. The FQHD model can be used to analyze the thermal and quantum
influences on the transport of carriers (electrons or holes) in semiconductor
device. Inspired by the physical motivation, we consider the initial-boundary
value problem of this model over the one-dimensional bounded domain and adopt
the ohmic contact boundary condition and the vanishing bohmenian-type boundary
condition. Firstly, the existence and asymptotic stability of a stationary
solution are proved by Leray- Schauder fixed-point theorem, Schauder
fixed-point theorem and the refined energy method. Secondly, we show the
semi-classical limit results for both stationary solutions and global solutions
by the elaborate energy estimates and the compactness argument. The strong
convergence rates of the related asymptotic sequences of solutions are also
obtained.
