Particle-in-cell simulations and passive bulk model of collisional capacitive discharge

Abstract

Intermediate pressure (0.2–6.0 Torr), radio frequency capacitive discharges are of increasing importance in the thin film processing industry. However, existing low pressure (<0.1Torr) discharge models are often used beyond their applicability in this pressure range. The authors performed one-dimensional particle-in-cell (PIC) simulations of a capacitive 2.5 cm gap argon discharge driven at 13.56 MHz with current density amplitude J0=50A/m2 over a wide range of gas pressures pg=0.04–20 Torr. For intermediate pressures, the PIC results showed that most of the ionization occurs near the plasma-sheath edges with very little occurring within the central bulk region. This led us to develop a “passive bulk” model of the discharge in which bulk electron heating does not contribute to ionization, and all the ionization is due solely to the sheath-heated electrons. The model assumes a constant ion-neutral mean free path λi in the plasma bulk and either constant λi or constant ion mobility μi in the sheaths. The model is solved using an electron temperature iteration scheme. The PIC scalings of the discharge equilibrium parameters (e.g., electron density and temperature, sheath width, and voltage) with the input parameters pg and J0 showed good agreement with those of the passive bulk model. A constant μi sheath model showed the best agreement with the PIC results in the intermediate pressure regime of interest, but a constant λi model is simpler to implement and showed reasonable agreement over a wide pressure range.