Experimental investigation and fast two-dimensional self-consistent kinetic modeling of a low-pressure inductively coupled rf discharge

We present a fast self-consistent kinetic model for an inductively coupled low-pressure rf discharge. The electron kinetics in it is described in terms of a nonlocal electron distribution function, which depends only on the total electron energy (kinetic plus potential one in the stationary electric field). In this case, the Boltzmann equation reduces to a one-dimensional ordinary differential equation in total energy. The complete model also includes the equations for ion motion, for the rf oscillatory induction field, for the external circuit, and the quasineutrality condition. It allows us to express all the plasma characteristics-the electron distribution function, the plasma density profile, the profiles of the stationary and of the oscillatory electric fields, the profiles of the excitation and ionization rates, etc.-in terms of the external characteristics-the chamber geometry, gas pressure, frequency, and the current in the primary coil. The theoretical predictions are compared to experimental results. An experimental investigation has been performed on an inductively coupled low-pressure rf discharge in Ar at 13.56 MHz over a wide range of input powers at gas pressures from 1 to 12 Pa. A satisfactory agreement with the experiment and qualitative interpretation of the observed phenomena is achieved.