We show that in a macroscopic perfect insulator, charge injection at a field-enhancing defect is associated with an instability of the insulating state or with bistability of the insulating and the charged state. The effect of a nonlinear carrier mobility is emphasized. The formation of the charged state is governed by two different processes with clearly separated time scales. First, due to a fast growth of a charge-injection mode, a localized charge cloud forms near the injecting defect (or contact). Charge injection stops when the field enhancement is screened below criticality. Secondly, the charge slowly redistributes in the bulk. The linear instability mechanism and the final charged steady state are discussed for a simple model and for cylindrical and spherical geometries. The theory explains an experimentally observed increase of the critical electric field with decreasing size of the injecting contact. Numerical results are presented for dc and ac biased insulators.

Revtex, 7pages, 4 ps figures