Turing bifurcation during the nucleation process of a current density filament in n-GaAs

The nucleation process in spatiotemporal structures of a current density filament in n-GaAs has been investigated under a dc+ac driving force Vdc+Vacsin 2πfdt at 4.2 K. With Vdc=0.8 V, Vac=666 mV and fd=100 kHz, we observe an S-shaped I–V curve caused by impact ionization avalanche of neutral shallow donors and subsequent formation of a well-defined current density filament. In the nucleation process, Turing bifurcation is observed at around the breakdown voltage, followed by a spatially periodic pattern of the current density as a pre-filament state.