The dielectric breakdown strengths of two series of sintered alumina samples of low and high impurity content (with Si being the dominant element) and single crystal of low impurity level are compared with positron lifetime measurements. It is found that, in sintered alumina, the breakdown strength increases linearly with increasing concentration of positron traps at grain boundaries. These traps are likely clusters containing negatively charged cationic vacancies, which are induced by silicon dissolution into Al₂O₃. Therefore, the improvement of the breakdown strength can be traced to silicon segregation at grain boundaries. More precisely, it is deduced that the dissolution of Si impurity into Al₂O₃, when it is compensated by a cationic vacancy V^m_Al, is responsible for such an improvement. A solubility of Si in Al₂O₃, achieved during the firing schedule of the sintering process, and which does not take into account enhanced solubility caused by mutual compensation of Si with lower valence foreign cations such as Ca and MgO, is estimated at 120 ppm.