Paper PS-WeA9
Electron Energy Distribution at Electrode in a Low Pressure Capacitively Coupled Plasma

Wednesday, November 2, 2011, 4:40 pm, Room 201

Low pressure (sub-20 mTorr) capacitively coupled plasmas (CCP) are playing an increasingly important role in technological applications. As the mean free path becomes commensurate with the discharge dimensions, the fluid assumptions inherent in plasma and sheath models start to break down and ought to be reexamined. We focus on one aspect of the CCP operation in this paper, namely the electron energy distribution (EED) at electrodes and surfaces, and use kinetic particle-in-cell (PIC) models to understand the temporal behavior of the EED. Kinetic results are compared to fluid representation of the EED at electrodes to identify deficiencies in the fluid model at low pressures and propose solutions.

The sheath at the plasma-surface interface ensures that the electrons remain confined in the bulk plasma. However, during certain phases of the radio-frequency (RF) cycle in a CCP, the sheath collapses and the electrons exit at the surface. Energy distribution of these electrons contains useful information about the bulk plasma and the sheath. One can probe into the energy characteristics of these electrons using dc probes embedded in the electrode. Analysis of the resulting probe data can be used to determine the electron temperature, the electron density, and the EED in the bulk plasma. If a fluid model is used for this analysis, the electrons are assumed to be governed by the Boltzmann relation where their density and flux depend exponentially on the sheath voltage. Electrons are however highly non-equilibrium near the sheaths in CCPs and the Maxwellian distribution assumption (implicit in the Boltzmann relation) is questionable. Furthermore, most probe analysis models are dc-based. Low pressure situations demand further scrutiny as even the bulk plasma EED tends to become non-Maxwellian.

1 and 2-dimensional PIC model of CCPs are used for this investigation. These models consider plasma chemistry using the Monte Carlo technique. Simulations are done for Ar and N₂ plasmas under a variety of conditions (13.56 – 60 MHz RF frequency, RF voltage of 100 – 500 V, 5 – 100 mTorr gas pressure). The 1-dimensional PIC model is used to examine the EED at the electrodes where the sheath undergoes substantial variation during the RF cycle. The 2-dimensional model is used to investigate the EED at small metal surfaces (e.g., a probe) away from the primary electrodes. Dc voltage is also applied to the probe electrode in the 2-dimensional simulations. It is found that, in addition to a non-Maxwellian contribution from electrons adjacent to the sheath, the EED also contains high energy electrons which are the remnant of electrons that were accelerated at the opposite sheath.