Inductive heating and E to H transitions in high frequency capacitive discharges

Capacitive discharges have classically been operated in the electrostatic regime, for which the excitation wavelength λ is much greater than the electrode radius and the plasma skin depth δ is much greater than the electrode spacing. However, contemporary reactors are larger and excited at a higher frequency so that electromagnetic effects become significant. A self-consistent transmission line model valid in the entire range of λ and δ of practical interest is solved. The model is the electromagnetic generalization of the lumped-element circuit model classically used for capacitive discharges. We find that the plasma may either be sustained by the usual capacitive (E) field or by an inductive (H) field and that the discharge experiences E to H transitions as the voltage between the electrodes is raised. The transitions are global at low pressure and local at high pressure. In the latter case, the plasma parameters (e.g. the ion flux to the electrodes) are radially non-uniform, due to the non-uniformities of the rf voltage and current, leading to serious industrial issues.