Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

Abstract

It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage VL on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage VL at 2 MHz varies from 0 to 700 V while the HF voltage VH at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. VL= 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as VL increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher VL , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔE becomes wider with the increase of VL . The IEDF at the radial center of the powered electrode exhibits a broader ΔE than that at the edge. For the IADF, an increased VL results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.