Ultrapure p-Ge with doping concentration as low as similar to 10(11) cm(-3) is considered to investigate self-pulsating oscillations at the onset of impurity breakdown with respect to an S-shaped current-field characteristic. The associated nonlinear dynamics is computed within the two-impurity-level model with more convincing parameterization. The system undergoes a single Hopf bifurcation in the presence of a sufficiently large circuitry capacitance. As the operating point is controlled towards the breakdown threshold, no further bifurcations but a changeover of the periodic oscillation occurs from being sinusoidal to pulsating. Our approach also obtains agreeable results for n-GaAs with typically higher doping. (c) 2006 Elsevier Ltd. All rights reserved.