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 consistently with 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. This approach is well suited to study the behavior of discharges at RF frequencies and ion-collision frequencies for which the inertia of the ions is important, but not dominant. In these situations the growth of the RF sheath differs strongly from its decay; during the growth the thickness of the sheath increases, while it remains constant during the decay phase. This behavior is ascribed to an insufficiently fast replenishment of the sheath with ions from the presheath. 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. In the former pressure range the ions are collisionless; in the latter, the chosen distance of 2 cm between the electrodes is typically 20-40 times the ion mean-free path. A good agreement is found with published experimental observations of the time-dependent behaviour of the electric field profile in the RF sheath.