Equivalent circuit modeling of chamber for electrical parameter diagnostic of a pulse-modulated RF capacitively coupled plasma

Abstract Very high frequency (VHF) capacitively coupled plasma (CCP) sources are widely utilized in etching processes for chip manufacturing. However, due to the presence of stray impedances (including capacitance, inductance, and resistance) within the vacuum chamber excited by a VHF source, a discrepancy in the electrical parameters arises between the external measurement point and the powered electrode inside the chamber. At lower driving frequencies (e.g. f = 13.56 MHz), stray impedance is primarily attributed to shunt capacitance, while stray inductance also plays a key role at higher driving frequencies (e.g. f ⩾ 27.12 MHz). To obtain a more accurate inter-electrode voltage, plasma current, their phase shift, and plasma power absorption, it is imperative to establish an equivalent lumped circuit model of the plasma reactor. In this study, two equivalent lumped-circuit models, i.e. C model and RLC model, are compared. The element values of the two equivalent circuits are determined by fitting the impedance-frequency spectrum over 1 MHz ∼100 MHz. Using the RLC circuit model, the temporal evolution of the electrical parameters of a pulse-modulated VHF CCP is determined. The results suggest that the equivalent inductance of the power feeding rod causes a large deviation between the actual inter-electrode voltage and the voltage measured outside the reactor, especially at higher frequencies. Meanwhile, the equivalent resistance at the feed input end of the powered rod results in significant power dissipation, primarily due to the large current in this section. Besides, we calculate the electrical parameters under varying driving voltages using the RLC model, and show that the time-dependent plasma power absorption qualitatively agrees with the plasma optical emission intensity during the plasma ignition phase.