Kinetic modeling of positive ions in a low-pressure RF discharge

The evolution of the ion-velocity distribution function in a planar RF discharge is computed by numerically solving the Boltzmann equation in phase space. The electric field in this equation is computed with regard to the ion density, assuming Maxwellian electrons with a given uniform temperature. The collision term in the Boltzmann equation contains creation of ions by electron-impact ionization of the background gas and the effect of charge-exchange collisions. Examples are given of the behavior of discharges in argon at RF frequencies of 50 kHz, 300 kHz, and 15 MHz at a very low pressure and at a pressure of approximately 40 Pa. A good agreement is found with published experimental observations of the time-dependent behavior of the electric field profile in the RF sheath