2D fluid-analytical simulation of electromagnetic effects in low pressure, high frequency electronegative capacitive discharges

Abstract

A fast 2D axisymmetric fluid-analytical multifrequency capacitively coupled plasma (CCP) reactor code is used to study center high nonuniformity in a low pressure electronegative chlorine discharge. In the code, a time-independent Helmholtz wave equation is used to solve for the capacitive fields in the linearized frequency domain. This eliminates the time dependence from the electromagnetic (EM) solve, greatly speeding up the simulations at the cost of neglecting higher harmonics. However, since the code allows up to three driving frequencies, we can add the two most important harmonics to the CCP simulations as the second and third input frequencies. The amplitude and phase of these harmonics are estimated by using a recently developed 1D radial nonlinear transmission line (TL) model of a highly asymmetric cylindrical discharge (Lieberman et al 2015 Plasma Sources Sci. Technol. 24 055011). We find that at higher applied frequencies, the higher harmonics contribute significantly to the center high nonuniformity due to their shorter plasma wavelengths.