Local and global particle and power balance in large area capacitive discharges

Large area radio frequency (rf) capacitive discharges have attracted recent interest for materials etching and deposition on large area substrates. A distinguishing feature is that the radial distribution of the absorbed rf power in these discharges depends on the rf voltage across the plates, independent of the radial variation of the plasma density n(r). A reduced set of steady-state fluid equations has been used to investigate the radial variation of n and electron temperature Te. The derived equations are shown to be invariant with respect to pL and pR, where p is the pressure, L is the plate separation and R is the discharge radius, and can be further reduced to the equations of the usual global balance model when Rλe, the energy relaxation length. In this limit, the ionization frequency and Te are essentially independent of radius and n can be approximately described by the usual radial profile of a zeroth-order Bessel function. When R≥λe, n and Te are predominantly determined by local particle and power balance, and the n and Te radial profiles are flat over most of the volume except near the radial boundary, where n falls and Te rises to account for the increased losses at the boundary. The scale length of the edge density variation in the local balance regime is shown to be proportional to the energy relaxation length.