Plasma non-uniformity in a symmetric radiofrequency capacitively-coupled reactor with dielectric side-wall: a two dimensional particle-in-cell/Monte Carlo collision simulation

Abstract

A Cartesian-coordinate two-dimensional electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) plasma simulation code is presented, including a new treatment of charge balance at dielectric boundaries. It is used to simulate an Ar plasma in a symmetric radiofrequency capacitively-coupled parallel-plate reactor with a thick (3.5 cm) dielectric side-wall. The reactor size (12 cm electrode width, 2.5 cm electrode spacing) and frequency (15 MHz) are such that electromagnetic effects can be ignored. The dielectric side-wall effectively shields the plasma from the enhanced electric field at the powered-grounded electrode junction, which has previously been shown to produce locally enhanced plasma density (Dalvie et al 1993 Appl. Phys. Lett. 62 3207–9; Overzet and Hopkins 1993 Appl. Phys. Lett. 63 2484–6; Boeuf and Pitchford 1995 Phys. Rev. E 51 1376–90). Nevertheless, enhanced electron heating is observed in a region adjacent to the dielectric boundary, leading to maxima in ionization rate, plasma density and ion flux to the electrodes in this region, and not at the reactor centre as would otherwise be expected. The axially-integrated electron power deposition peaks closer to the dielectric edge than the electron density. The electron heating components are derived from the PIC/MCC simulations and show that this enhanced electron heating results from increased Ohmic heating in the axial direction as the electron density decreases towards the side-wall. We investigated the validity of different analytical formulas to estimate the Ohmic heating by comparing them to the PIC results. The widespread assumption that a time-averaged momentum transfer frequency, vm, can be used to estimate the momentum change can cause large errors, since it neglects both phase and amplitude information. Furthermore, the classical relationship between the total electron current and the electric field must be used with caution, particularly close to the dielectric edge where the (neglected) pressure gradient term becomes significant.