Current instabilities in a p-i-n Si diode heavily doped with gold impurities are investigated numerically. In order to clarify the explicit effect of the space charge of impurities on the current instabilities, we re-examine numerically the steady-state solutions for this particular diode without the quasineutrality assumption. The linearized stability analysis shows that the spontaneous self-sustained current oscillations can occur in the low-injection regime, where the DC resistance remains positive.