  In the paper we are concerned with the large time behavior of solutions to
the one-dimensional Navier-Stokes-Poisson system in the case when the potential
function of the self-consistent electric field may take distinct constant
states at $x=\pm\infty$. Precisely, it is shown that if initial data are close
to a constant state with asymptotic values at far fields chosen such that the
Riemann problem on the corresponding quasineutral Euler system admits a
rarefaction wave whose strength is not necessarily small, then the solution
exists for all time and tends to the rarefaction wave as $t\to+\infty$. The
construction of the nontrivial large-time profile of the potential basing on
the quasineutral assumption plays a key role in the stability analysis. The
proof is based on the energy method by taking into account the effect of the
self-consistent electric field on the viscous compressible fluid.
