Period-doubling bifurcation in a plasma reactor

We describe the response of an industrial plasma reactor to excitation at varying power levels. When the reactor is excited at low power, rf voltage and current waveforms contain components at multiples of the drive frequency (13.56 MHz) due to the plasma's nonlinear impedance. As power is increased, a transition point is reached and the waveforms change. Above the transition power level, signals at the half-harmonic frequency (6.78 MHz) and its multiples are also present, which is indicative of a period-doubling bifurcation. Above and below the bifurcation point, the dc bias and the etch rate behave quite differently