  This paper is concerned with the stability of planar viscous shock wave for
the 3-dimensional compressible Navier-Stokes-Poisson (NSP) system in the domain
$\Omega:=\mathbb{R}\times \mathbb{T}^2$ with
$\mathbb{T}^2=(\mathbb{R}/\mathbb{Z})^2$. The stability problem of viscous
shock under small 1-dimensional perturbations was solved in Duan-Liu-Zhang [7].
In this paper, we prove the viscous shock is still stable under small 3-d
perturbations. Firstly, we decompose the perturbation into the zero mode and
non-zero mode. Then we can show that both the perturbation and zero-mode
time-asymptotically tend to zero by the anti-derivative technique and crucial
estimates on the zero-mode. Moreover, we can further prove that the non-zero
mode tends to zero with exponential decay rate. The key point is to estimate
the non-zero mode of nonlinear terms involving electronic potential, see Lemma
6.1 below.
