Secondary electrons in dual-frequency capacitive radio frequency discharges

Two fundamentally different types of dual-frequency capacitive RF discharges can be used to realize separate control of the ion mean energy, $<$E$_{i}>$, and the ion flux, $\Gamma _{i}$, at the electrodes: (i) Classical discharges operated at substantially different frequencies, where the low and high frequency voltage amplitudes, $\phi _{lf }$and $\phi _{hf}$, are used to control $<$E$_{i}>$ and $\Gamma _{i}$, respectively. (ii) Electrically asymmetric (EA) discharges operated at a fundamental frequency and its second harmonic with adjustable phase shift, $\theta $, between the driving frequencies, which is used to control $<$E$_{i}>$. We study the effect of secondary electrons on the quality of this separate control in both discharge types in argon at different gas pressures by PIC/MCC simulations with focus on the effect of the control parameter for $<$E$_{i}>$ on $\Gamma _{i}$ for different secondary yields, $\gamma $. A dramatic effect of tuning $\phi _{lf}$ in classical discharges and a significantly less pronounced effect of tuning $\theta $ in EA discharges is observed. This is caused by a transition from $\alpha $- to $\gamma $-mode induced by changing $\phi _{lf}$ and not induced by changing $\theta $.