  This paper is concerned with the initial-boundary value problem on the full
Euler-Poisson system for ions over a half line. We establish the existence of
stationary solutions under the Bohm criterion similar to the isentropic case
and further obtain the large time asymptotic stability of small-amplitude
stationary solutions provided that the initial perturbation is sufficiently
small in some weighted Sobolev spaces. Moreover, the convergence rate of the
solution toward the stationary solution is obtained. The proof is based on the
energy method. A key point is to capture the positivity of the temporal energy
dissipation functional and boundary terms with suitable space weight functions
either algebraic or exponential depending on whether or not the incoming
far-field velocity is critical.
