Summary: This is the first part of our series of studies concerning the full quantum hydrodynamic model for semiconductors with non-flat doping profile. In this paper, we are concerned with the existence, uniqueness and asymptotic stability of subsonic steady states to the model in a bounded interval, which is subject to physical boundary conditions. The main results are proved by Stampacchia’s truncation method, the Leray-Schauder Fixed Point Theorem, Schauder’s Fixed Point Theorem and intricate energy estimates.