This　paper　is　concerned　with　smooth　solutions　of　the　non-isentropic　Euler-Poisson　system　for　ion　dynamics.　The　system　arises　in　the　modeling　of　semi-conductor,　in　which　appear　one　small　parameter,　the　momentum　relaxation　time.　When　the　initial　data　are　near　constant　equilibrium　states,　with　the　help　of　uniform　energy　estimates　and　compactness　arguments,　we　rigorously　prove　the　convergence　of　the　system　for　all　time,　as　the　relaxation　time　goes　to　zero.　The　limit　system　is　the　drift-diffusion　system.