ELECTRON-DISTRIBUTION FUNCTION IN A LOW-PRESSURE INDUCTIVELY-COUPLED PLASMA

A method is presented for solution of the spatially inhomogeneous Boltzmann equation in the two-term approximation for low-pressure inductively coupled plasmas (ICP). The total electron energy epsilon = w - e phi (the sum of kinetic energy w and potential energy e phi in an electrostatic field) is used as an independent variable in the kinetic equation. Two energy ranges are distinguished. In the elastic energy range w < epsilon*, where epsilon* is the first excitation energy, the problem is effectively reduced to one variable (total electron energy) by performing an appropriate spatial average. The electron distribution function (EDF) in this energy range is a function solely of epsilon and does not depend explicitly on the coordinates. In the inelastic energy range, the kinetic equation in the variables (r, z, epsilon) (two spatial coordinates and the total energy) is solved for trapped and free electrons in a cylindrically symmetric ICP with a given spatial distribution of electric fields. The EDF and the spatial distributions of the electron current density and the ionization rate are calculated as functions of pressure, plasma density, and the profile of the electrostatic field. Explanations of some available experimental observations are given.