The model under consideration is an Euler-Poisson system. It looks like the compressible Euler equations for the electrons together with a coupled electric field and a relaxation term. Both contact and insulating boundary conditions are considered. The unknowns are (ρ, u, φ) where ρ is the density, u is the velocity and φ is the electric potential. The global solutions are near a steady state (ρ0, uo, φ0). I will discuss two results that are joint work with Yan Guo. It is important that we permit ρ0(x) , φ0(x) and the doping profile D(x) to have large variation. Our first result is in a bounded 3D domain with insulating boundary conditions. So far as we know, this is the first class of exact global solutions in a multi-dimensional domain. Our second result is in a bounded 1D interval with contact boundary conditions.