On power and fundamental resistance relations in symmetric RF CCPs by simulating simplified nonlinear circuits

Abstract

Voltage and current measured from radio frequency (RF) capacitively coupled plasmas (CCPs) are basic data, from which various powers and impedances are subsequently calculated via fast Fourier transform to gain deep insight into RF CCPs. The specific values of these parameters depend on the nonlinearity of RF CCPs and the interaction with the external circuit, but the relation between harmonic powers and that among the fundamental resistances are not known. These questions are investigated via Multisim software by simplifying the symmetric RF CCP with the nonlinear circuit consisting of a linear resistor and a nonlinear capacitor. The results show that the calculated total RF power is accurately equal to that dissipated by the resistor in discharge. However, it is not true for the fundamental power and harmonic one. The fundamental resistance calculated at the external electrode, which was previously proposed as the plasma resistance, is higher than the latter. The conversion between the fundamental and harmonic powers in the nonlinear ideal capacitor of RF CCPs is the origin of the obtained abnormal feature. In comparison, the plasma resistance calculated from the total RF power and current is unaffected by harmonics and is, thus, more credible, despite that this method requires an assumption of constant transient plasma resistance.

Kinetic simulations of capacitively coupled plasmas driven by tailored voltage waveforms with multi-frequency matching

“…The electrical power (f 1 − f 3 ) flows from the rf power supply to the CCP, where it is decomposed into basic harmonics (f 1 − f 3 ) and higher harmonics (f 4 − f 15 ) inside the CCP, and then the higher harmonic power (f 4 − f 15 ) flows back from the CCP to the rf power supply, which explains why both I rf and I CCP in figure 5(d) have high-order harmonics. This phenomenon has also been revealed in previous experiments [68] and simulations [69]. The I CCP in figure 5(d) still has a significant amplitude at relatively high harmonic frequencies.…”