As wafer sizes increase, obtaining uniform processing conditions becomes more problematic particularly with respect to side-to-side asymmetries. Side pumping or gas injection produces asymmetries not only in the gas density but also in ion temperatures and fluxes. As a major source of gas heating is momentum transfer from ions, small asymmetries in ion temperatures are amplified through asymmetries in gas pressure. To investigate the consequences and prevalence of asymmetric gas heating and gas temperatures, a 3-dimensional plasma equipment model was improved by adding multi-fluid modules for gas and ion temperatures. A temperature is computed for each neutral and heavy particle species, while accounting for convective transport, conduction, compressive heating, sources, momentum exchange between species and temperature jumps at surfaces. As ion heating occurs dominantly in the presheath, we found that asymmetries which perturb the presheath produce gradients in ion temperature which in turn produce gas heating. Somewhat counter-intuitive, we therefore find higher gas temperatures near ports due to there being higher ion temperatures in the presheath. We will also discuss the consequences of 3-dimensional coil structures on gas heating.
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@footnote 1@Work supported by NSF, SRC and Applied Materials.