Ion transit effects on sheath dynamics in the intermediate radio-frequency regime: excitations of ion-acoustic waves and solitons

Capacitively coupled plasma is investigated kinetically utilizing the particle-in-cell technique. The argon (Ar) plasma is generated via two radio frequencies. The plasma bulk density increases by increasing the voltage amplitude of the high frequency (> 13.56 MHz), which is much greater than the ion plasma frequency. The intermediate radio frequencies (approximate to 1 MHz), which are comparable to the ion plasma frequency, cause a considerable broadening of the ion energy distribution, i.e. ions gain energies higher and lower than the time-averaged energy. The good agreement between published experimental results and our theoretical calculations via the ensemble-in-spacetime model confirms the modulation of ions around time-averaged values. Intermediate frequencies allow ions to partially respond to the instantaneous electric field. The response of ions to the instantaneous electric field is investigated semi-analytically. The dispersion relation of the plasma sheath and bulk are derived. Stable ion acoustic modes are found. Ion-acoustic modes have two different velocities and carry energy from the sheath edge to the electrode. In addition, intermediate frequencies excite solitons in the plasma sheath. The results may help to explain the ion density, flux, and energy modulation, and, consequently, the broadening of the ion energy distribution.