Self-bias voltage formation and charged particle dynamics in multi-frequency capacitively coupled plasmas

In this work, we analyze the creation of the discharge asymmetry and the concomitant formation of the DC self-bias voltage in capacitively coupled radio frequency plasmas driven by multi-frequency waveforms as a function of the electrode surface characteristics. For the latter, we consider and vary the coefficients that characterize the elastic reflection of electrons from the surfaces and the ion-induced secondary electron yield. Our investigations are based on particle-in-cell/Monte Carlo collision simulations of the plasma and on a model that aids the understanding of the computational results. Electron reflection from the electrodes is found to slightly affect the discharge asymmetry in the presence of multi-frequency excitation, whereas secondary electrons cause distinct changes to the asymmetry of the plasma as a function of the phase angle between the harmonics of the driving voltage waveform and as a function the number of these harmonics.