Prediction of Ion Energy and Angular Distributions in Single and Dual Frequency Plasmas

Abstract

We present a model to predict the energy and angular distributions of ions which impact the substrate in low (100–450 kHz), high (13.56 MHz), and dual frequency plasmas. The model combines a single and dual frequency plasma sheath model with Monte Carlo simulations of ion transport. The sheath model for single and dual frequency parallel plate plasma systems provides the time dependent sheath thickness and the time and spatially dependent electric field in the sheath, which are necessary for the Monte Carlo simulations. Monte Carlo simulations are used to track the ion motion and to generate the energy and angular distributions. Both charge transfer and hard sphere elastic collisions are included in the Monte Carlo simulations. The model predictions of the ion energy and angular distributions agree well with experimental data for argon plasmas and with the predictions of other analytical models and Monte Carlo simulations in the low (100 kHz) and high (13.56 MHz) frequency limits. Model predictions show that the shapes of the ion angular and energy distributions and the resultant average ion energy and angle become independent of pressure and frequency above 10 Torr. Below 10 Torr, changing the frequency mix from 100% high frequency to 100% low frequency lowers the average ion energy, increases the maximum ion energy, and increases the directionality of the ions.