Nonlinear Dynamics of Capacitively Coupled Plasma Excited by Tailored Voltage Waveform

An equivalent circuit model coupled with a global model is employed to analyze the discharge properties of a capacitively coupled plasma (CCP) driven by a tailored voltage waveform (TVW). It is shown that both the geometrical asymmetry and the electrical asymmetry can significantly affect the nonlinear dynamics of a CCP. By increasing the ratio of the grounded electrode area to the powered electrode area, self-excitation of the higher harmonics of the current is largely enhanced, giving rise to the enhancement of the electron power absorption via ohmic and stochastic heating. The relative strength of the higher harmonics can be modulated by adjusting the phase angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{2}$</tex-math> </inline-formula> of the second harmonic. In addition, both the ohmic heating power and the stochastic heating power are influenced by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{2}$</tex-math> </inline-formula>. Furthermore, when the electrode area ratio is relatively large, the dc self-bias initially decreases and subsequently increases in absolute value with an increase in the angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{2}$</tex-math> </inline-formula>. Modifying the phase angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{3}$</tex-math> </inline-formula> can significantly influence both the trend and magnitude of the dc self-bias. As the voltage amplitude increases, the adjustable range of dc self-bias with respect to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{2}$</tex-math> </inline-formula> also increases.