The　hydrodynamic　model　for　semiconductors　with　sonic　boundary,　represented　by　Euler-Poisson　equations,　possesses　the　various　physical　steady　states　including　interior-subsonic/interior-supersonic/shock-transonic/C　1-smooth-transonic　steady　states.　Since　these　physical　steady　states　result　in　some　serious　singularities　at　the　sonic　boundary　(their　gradients　are　infinity),　this　makes　that　the　structural　stability　for　these　physical　solutions　is　more　difficult　and　challenging,　and　has　remained　open　as　we　know.　In　this　paper,　we　investigate　the　structural　stability　of　interior　subsonic　steady　states.　Namely,　when　the　doping　profiles　are　as　small　perturbations,　the　differences　between　the　corresponding　subsonic　solutions　are　also　small.　To　overcome　the　singularities　at　the　sonic　boundary,　we　propose　a　novel　approach,　which　combines　the　weighted　multiplier　technique,　local　singularity　analysis,　monotonicity　argument　and　squeezing　skill.　Both　the　result　itself　and　the　technique　developed　here　will　give　us　some　truly　enlightening　insights　into　our　follow-up　study　on　the　structural　stability　of　the　remaining　types　of　solutions.　A　number　of　numerical　approximations　are　also　carried　out,　which　intuitively　confirm　our　theoretical　results.