Secondary electrons in rf and dc/rf capacitive discharges

We extend an analytic model of the effects of secondary electrons on symmetric (equal area) capacitive discharges to include a combination of rf and dc voltage sources. A 'dc/rf sheath' develops on the negatively biased dc electrode while a typical rf sheath develops on the other electrode. The analytical results for rf-only and dc/rf cases, including secondaries, are compared with the results of numerical simulations using a one-dimensional (1D) plane-parallel particle-in-cell (PIC) code, confirming the pressure and density regimes for which adding dc improves the overall discharge efficiency and can control the fluxes and energy distributions of the secondary electrons incident on the electrodes. From a 2D PIC simulation, the effects of secondaries and dc voltage on the uniformity of the ions and secondary electrons are investigated, with the dc adding an additional element of uniformity control. The uniformity of the secondary electron energy and angular distributions on the substrate electrode are determined from the 2D simulations.