Experimental investigations of self-generated and externally driven non-linear current oscillations due to impact ionization of shallow impurities in n-type GaAs at low temperatures are presented. The regular relaxation oscillations which appear at the onset of breakdown are destabilized by a magnetic field normal to the epitaxial layer and multifrequency oscillations and chaotic fluctuations following the Ruelle-Takens-Newhouse scenario can be found. Driving the self-generated oscillations with an external periodic bias voltage quasiperiodicity, mode locking, interaction and overlap of mode locked resonances and period doubling can be observed depending on frequency and amplitude of the external force. The reconstructed return maps, recorded phase diagrams and Devil's staircase agree with theoretical predictions based on the circle map and give new evidence of the universality of the transition from quasiperiodicity to chaos.