Non-equilibrium Ion and Neutral Transport in Low-pressure Plasma Processing Reactors *
Vivek Vyas** and Mark J. Kushner***
**Department of Materials Science & Engineering
***Department of Electrical & Computer Engineering
University of Illinois at Urbana-Champaign
1406 W. Green St., Urbana, IL 61801
Low pressure (< 1 mTorr), partially ionized plasmas are used extensively for materials processing. At these pressures, conventional fluid or continuum simulations are of questionable validity as transport is highly non-equilibrium and a kinetic approach may be warranted. In principle, continuum equations of motion are simply moments of Boltzmann's equation. If the distribution functions are known, the equations, with appropriate boundary conditions, should be applicable at arbitrarily low pressures. In this regard, a hybrid modeling approach has been developed for ion and neutral transport in which velocity distribution functions are directly computed and used to obtain transport coefficients for a continuum model.
2. Computational Model
The Hybrid Plasma Equipment Model (HPEM), developed at the University of Illinois, is a comprehensive simulator of low-pressure (10-100ís mTorr) plasma reactors. In this work, a Monte Carlo simulation for ion and neutral transport (IMCS) has been developed and integrated with the HPEM to improve our capabilities to address lower pressures. The electron impact source functions and transport properties are obtained using a Monte Carlo simulation (MCS) for electrons. Ion and neutral trajectories are integrated using the electric and magnetic fields obtained from HPEM and collisions are treated using a particle-mesh approach. Location dependent energy distributions and transport properties of ions and neutrals are then used in heavy particle momentum and energy equations in the Fluid Kinetics Simulation (FKS). The consequences of varying power, pressure and gas mixtures will be investigated for low pressure tools such as hollow cathode magnetrons. The IMCS is schematically depicted in Figure 1.
|Fig. 1: Ion Monte Carlo Simulation.|
Preliminary results using the IMCS are shown in Figure 2. Comparisons will be made between conventional continuum techniques and this hybrid method, and with experiments. The plasma properties obtained from the HPEM will be used to simulate deposition using a Monte Carlo feature profile model.
|Fig. 2: Comparison of plasma properties with/without IMCS: (a) Cl2 density, and (b) Cl2+ density with IMCS, and (c) Cl2 density, and (b) Cl2+ density without IMCS for a 300 W, 10 M Hz, 2 mTorr, Ar/Cl2 (80/20) plasma..|
*This work is supported by Semiconductor Research Corporation and the National Science Foundation (CTS 99-74962, CTS03-15353).
Last updated: August 21, 2003.