Hybrid model of radio-frequency low-pressure inductively coupled plasma discharge with self-consistent electron energy distribution and 2D electric field distribution

Low-pressure radio-frequency (RF) inductively coupled plasmas (ICPs) are extensively used for materials processing. In this work, we have developed a hybrid model consisting of two-dimensional (2D) Maxwell equations with an open boundary, zero-dimensional Boltzmann equation under linear and quasilinear approximations, and a power balance equation. The hybrid model is capable of achieving a self-consistent description of the electron heating mechanism and electron kinetics for the RF ICPs at low pressures. This work presents an investigation of the influence of operating conditions on 2D distributions of electric field and power density, normalized electron energy probability function (EEPF) (effective electron temperature), and plasma density in a low-pressure RF Ar ICP using the hybrid model. The results show that the RF frequency and absorption power significantly affect the 2D distributions and amplitudes of electric field and power density. The normalized EEPF is almost independent of RF frequency and weakly dependent on absorption power but significantly modulated by pressure at low RF frequency. The plasma density is also almost independent of RF frequency but increases with absorption power and pressure. In addition, we have validated the hybrid model against experimental data obtained in the driver region of a two-chamber RF Ar ICP source, where the RF frequency is 13.56 MHz, the power range is 200-1000 W and the pressure range is 0.1-1.0 Pa. The hybrid model qualitatively (and even quantitatively for some cases) reproduces the experimentally normalized EEPF and plasma density. The discrepancies in these plasma parameters could be attributed to the simplified collision processes taken into account in the hybrid model. The developed hybrid model can help us to better understand the effect of discharge conditions on electron kinetics and electron heating mechanism, and to ultimately optimize the parameters of RF ICP sources.