Stochastic heating in single and dual frequency capacitive discharges

Two electron heating mechanisms in capacitive discharges are ohmic heating due to electron-neutral collisions and stochastic heating at the plasma edge due to momentum transfer from high voltage moving sheaths. In this work, the stochastic heating and its dependence on various parameters are determined, focusing on dual frequency discharges in which the sheath motion is driven by a combination of high and low frequency sources. Particle-in-cell (PIC) simulations are used in order to investigate the electron heating. For a uniform fixed-ion discharge in which the ions are held fixed in a uniform density profile, there is no stochastic heating, as expected. For a two-step fixed-ion discharge in which the ions are held fixed in a two-step density profile with bulk density nb and sheath density nsh<nb, the stochastic heating is nearly proportional to (1−nsh∕nb)2. For a self-consistent discharge with mobile ions, the stochastic heating is well described by a “hard wall model” provided that the bulk oscillation is taken into account. These results are used to develop a stochastic heating theory for dual frequency discharges, which is compared to PIC simulations, giving good agreement.