Effect of non-local electron conductivity on power absorption and plasma   density profiles in low pressure inductively coupled discharges
  A self-consistent 1-D model was developed to study the effects of non-local electron conductivity on power absorption and plasma density profiles in a planar inductively coupled argon discharge at low pressures (< 10 mTorr). The model consisted of three modules: (1) an electron energy distribution function (EEDF) module to compute the non-Maxwellian EEDF, (2) a non-local electron kinetics module to predict the non-local electron conductivity, RF current, electric field and power deposition profiles in the non-uniform plasma, and (3) a heavy species transport module to solve for the ion density and velocity profiles as well as the metastable density. Results using the non-local electron conductivity model were compared with predictions of a local theory (Ohm's law), under otherwise identical conditions. The RF current, electric field, and power deposition profiles were very different, especially at 1 mTorr for which the effective electron mean free path was larger than the skin depth. However, the plasma density profiles were almost identical (within 10%) for the same total power deposition in the plasma. This result suggests that, for computing plasma density profiles, a local conductivity model (Ohm's law), with much reduced computational expense, may be employed even in the non-local regime. 
Badri Ramamurthi, Demetre J. Economou and Igor D. Kaganovich