Two-dimensional nonlocal heating theory of planar-type inductively coupled plasma discharge

A two-dimensional heating theory of planar-type inductively coupled plasma (ICP) discharge is developed. The theory includes the anomalous skin effect with an arbitrary value of electron collision frequency and source current. Based on the uniqueness theorem of wave equation, wave excitation by the source current is determined. With the calculated electromagnetic fields, plasma resistance is expressed as a function of various parameters such as plasma density ${\mathrm{n}}_{\mathrm{p}}$, electron temperature ${\mathrm{T}}_{\mathrm{e}}$, radius of chamber R, length of plasma ${\mathrm{L}}_{\mathrm{p}}$, shielding cap length ${\mathrm{L}}_{\mathrm{s}}$, electron collision frequency \ensuremath{\nu}, excitation frequency \ensuremath{\omega}, and the position and size of the antenna coil.