Self-organized pattern formation in radio frequency capacitively coupled discharges

Abstract

Self-organized structures that are spread perpendicular to the radio frequency (RF) current direction have been observed in low temperature RF capacitively coupled plasmas. A fluid plasma model that includes thermoelectric electron energy transport is used to understand how these structures form. The electron thermoelectric transport coefficient is calculated using Bolsig+ for different chemistries and is found to be large for Ar plasma. Thermoelectric electron energy transport, which is driven by particle diffusion, opposes electron thermal conduction and can localize the plasma, leading to periodic structures. To examine these structures in radio frequency (RF) capacitive plasmas, two-dimensional Ar plasma at 13.5 MHz is first simulated without and then with thermoelectric electron energy transport. The charged species densities are perturbed in the simulations, and the growth or decay of different modes with time is observed. The periodicity of the structure is found to be determined by the relative strength of thermoelectric electron energy transport compared to energy conduction and losses. The effect of operating variables such as chemistry and pressure and design variables such as inter-electrode gap and steps in the electrode have been studied. For Ar plasma as pressure is decreased, the plasma peaks become stronger since thermoelectric electron energy transport is enhanced. Within limits, steps in the electrodes can be used to control the location of the periodic structures. For N2 plasma, the periodic structure does not appear as thermoelectric electron energy transport is weak. The spacing between plasma peaks is found to be dependent on pressure, chemistry, and inter-electrode gap.