A TIME-DEPENDENT PROPAGATOR METHOD FOR LONG MEAN FREE-PATH TRANSPORT OF NEUTRAL PARTICLES IN PLASMA PROCESSING REACTORS

Plasma etching reactors for microelectronics fabrication are moving to wards operating at lower gas pressures (<10 mTorr). These pressures ar e sufficiently low that simulations using continuum modeling technique s may not be strictly applicable. A time dependent kinetic method base d on the use of a transition matrix (propagator) has been developed an d applied to the calculation of long mean free path transport of neutr al species in an inductively coupled plasma (ICP) etching reactor. The propagator P(r,r') provides the probability that particles originatin g at location r' will have their next collision at location r. The spe cies densities obtained from this model are compared with results from fluid and Monte Carlo simulations for various mean free paths. We fin d that the propagator model is valid when the mean free path of the pa rticles is larger than the numerical cell dimension and that fluid met hods for long mean free path transport can be corrected to obtain the Monte Carlo or propagator results by employing an effective diffusion coefficient. Time dependent results are generating by employing a reta rded time in which flights of particles beginning at past times from r emote locations are used to determine the present value of the local c ollision frequency. Self-consistent neutral densities in ICP discharge s for various pressures are obtained by employing the propagator model in a hybrid ICP model. (C) 1996 American Institute of Physics.