Abstract
Plasma etching reactors for microelectronics fabrication are moving towards operating at lower gas pressures (<10 mTorr). These pressures are sufficiently low that simulations using continuum modeling techniques may not be strictly applicable. A time dependent kinetic method based on the use of a transition matrix (propagator) has been developed and applied to the calculation of long mean free path transport of neutral species in an inductively coupled plasma (ICP) etching reactor. The propagator P(r,r′) provides the probability that particles originating at location r′ will have their next collision at location r. The species densities obtained from this model are compared with results from fluid and Monte Carlo simulations for various mean free paths. We find that the propagator model is valid when the mean free path of the particles is larger than the numerical cell dimension and that fluid methods 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 retarded time in which flights of particles beginning at past times from remote locations are used to determine the present value of the local collision frequency. Self-consistent neutral densities in ICP discharges for various pressures are obtained by employing the propagator model in a hybrid ICP model.
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