Simulation of nonlinear standing wave excitation in very-high-frequency asymmetric capacitive discharges: roles of radial plasma density profile and rf power

Abstract

It is recognized that in large-area, very-high-frequency capacitively coupled plasma (VHF CCP) reactors, the higher harmonics generated by nonlinear sheath motion can lead to enhanced standing wave excitation. In this work, a self-consistent electromagnetic model, which couples a one-dimensional, radial nonlinear transmission line model with a bulk plasma fluid model, is employed to investigate the nonlinear standing wave excitation in a VHF driven, geometrically asymmetric capacitive argon discharge operated at low pressure. By considering a radially non-uniform plasma density profile (case I) calculated self-consistently by the nonlinear electromagnetic model and the corresponding radially-averaged, uniform plasma density profile (case II), we first examine the effect of the plasma density non-uniformity on the propagation of electromagnetic surface waves in a 3 Pa argon discharge driven at 100 MHz and 90 W. Compared to case II, the higher plasma density at the radial center in case I determines a higher plasma series resonance frequency, yielding stronger high-order harmonic excitations and more significant central peak in the harmonic current density J z,n and the harmonic electron power absorption p n profiles. Therefore, under the assumption of the radially uniform plasma density in a CCP discharge, the self-excitation of higher harmonics at the radial center should be underestimated. Second, using the self-consistent electromagnetic model, the effect of the rf power on the excitation of nonlinear standing waves is investigated in a 3 Pa argon discharge driven at 100 MHz. At a low power of 30 W, the discharge is dominated by the first two harmonics. The higher harmonic excitations and the nonlinear standing waves are observed to be enhanced with increasing the rf power, resulting in a more pronounced central peak in the radial profiles of the total electron power absorption density p e, the electron temperature T e, and the electron density n e. For all rf powers, the calculated radial profiles of n e show good agreement with the experimental data obtained by a floating double probe.