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Standing wave instability in large area capacitive discharges operated within or near the gamma mode

Large-area capacitive discharges used for plasma deposition operate in a regime where both electromagnetic and secondary electron emission effects are important. The standing wave shortened wavelength in the presence of plasma depends on the sheath size, and in the γ mode, the secondary electron multiplication controls the sheath physics. Near the α-to-γ transition, and within the γ mode, the sheath width typically varies inversely with the discharge voltage, and large center-to-edge voltage (standing wave) ratios may exist. This can give rise to a standing wave instability, in which the central voltage of the discharge grows uncontrollably, for a given voltage excitation at the discharge edge. Using a simple model, we determine the discharge equilibrium properties, the linearized stability condition, and the nonlinear time evolution. For sufficiently large areas, we show that a discharge equilibrium no longer exists above a critical edge voltage at marginal stability.