Modeling of plasma-etch processes using well stirred reactor approximations and including complex gas-phase and surface reactions

A 0-D or well stirred reactor model determines spatially and time-averaged species composition in plasma-etch reactors, through solution of species, mass, and electron-energy balance equations. The use of well stirred reactor approximations reduces the computational expense of detailed kinetics calculations and allows investigation of the dependence of plasma chemistry on etch-process parameters. The reactor is characterized by a chamber volume, surface area, net mass flow or residence time, pressure, energy loss to surroundings, power deposition, and inlet-gas composition. The electron-energy equation includes a detailed power balance with losses to ions and electrons through the sheath, as well as inelastic and elastic collision losses. The model employs reaction-rate coefficients for electron-impact reactions, which require an assumption of the electron energy distribution function (EEDF). We compare model results using Maxwellian EEDF´s, as well as reaction-rate coefficients determined as a function of average electron energy through solution of the Boltzmann equation, for chlorine chemistry. The Boltzmann rates are determined by time-lagging the equilibration of electrons with applied electric fields. The Maxwellian reaction rates give higher ionization fractions than the Boltzmann rates, affecting the predicted electronegativity and positive ion composition for chlorine plasmas. The model also shows a strong sensitivity of the plasma composition to the assumed surface-recombination probability of atomic chlorine