Combining effective volume and effective area parameters for accurate equivalent circuit analysis of ICP systems

Global zero-dimension models are used to estimate plasma parameters such as density, electron temperature, and sheath potential in low temperature plasmas such as those used in semiconductor manufacturing. It is common practice to incorporate an "effective area" parameter that adjusts calculated charged particle flux to the walls to account for the density of the discharge near the wall compared to the nominal center density typically made at the center of the discharge. In this work, we present an additional correction factor for inductive coupled systems that accounts for the uniformity of the density profile from the center to the edge. This term, an "effective volume" parameter, accounts for edge density effects on skin depth and charged particle formation. This parameter is an important weighting factor, particulary in the calculation of plasma parameter dependent equivalent circuit values that can be used to non-invasively estimate density and temperature as well as design power coupling circuits for efficient source operation. This becomes particularly important during pulsed RF operation where these parameters can change by orders of magnitude during an applied RF pulse. An introduction to the model and comparison to experimental measurements made in an ICP reactor with a microwave resonator probe will be presented.