Frequency effects on nonlinear harmonic excitations in an asymmetrically-driven capacitive discharge

Nonlinearly excited harmonics due to spatial or series resonances can strongly affect plasma uniformity in high frequency capacitive discharges. In our previous work [PSST 30(2021) 045017], we used a nonlinear transmission line (NTL) model to study the effect of nonlinearly excited harmonics on a high frequency argon capacitive discharge at various pressures. In this work, we generalize the NTL model by including the effects of a variable-sized dielectric between the powered and grounded electrodes, the electron-neutral elastic collision frequency on the plasma dielectric constant, and the radial variation of the plasma density. Then, we examine the frequency effects on a low pressure asymmetrically driven argon capacitive discharge. The radially varying density is determined by coupling the NTL model to a 2D bulk plasma fluid model. An analytical collisionless ion sheath model is used to determine the electron sheath heating and the nonlinear relation between sheath voltage and sheath charge. We first study the effects of adding plasma radial variation to the NTL model by assuming different fixed radial profiles. Then, we examine the discharge in a frequency range of 30-100 MHz at fixed electron power of 40 W and pressure of 20 mTorr. An antisymmetric spatial resonance is observed with increasing frequency.