Application of similarity laws to dual-frequency capacitively coupled radio frequency plasmas with the electrical asymmetry effect

Abstract

Similarity laws (SLs) are useful for correlation and prediction of plasma parameters at different scales, which have been verified for geometrically symmetric capacitive radio-frequency (rf) discharges in nonlocal kinetic regimes. In this work, we demonstrate the applicability of SLs to dual-frequency rf discharges and confirm that similarity relations still hold considering the electrical asymmetry effect (EAE). By simultaneously tuning the control parameters (the gas pressure p, discharge gap d, and driving frequency f), we examine the similarity relations in rf plasmas via fully kinetic particle-in-cell simulations with the external circuits coupled and solved self-consistently. The validity of the SL scalings in dual-frequency rf plasmas with the EAE is confirmed for parameters such as the electron/ion density, ion flux, dc self-bias, ion energy distribution function, and power absorption. Although adjusted by the EAE, the dc self-bias and ion energy distribution functions are identified as similarity invariants under similar discharge conditions. Furthermore, the plasma series resonance phenomenon, filamentation of power depositions of electrons and ions in bulk plasma, and electric field reversal are observed in dual-frequency discharges with the EAE, which can also be exactly replicated under similar discharge conditions. The results further extend the application of SL scaling to dual-frequency rf plasmas, providing a more comprehensive understanding of the scaling characteristics in rf plasmas.