A semianalytic radio frequency sheath model integrated into a two-dimensional hybrid model for plasma processing reactors

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Abstract
In high plasma density ([e]>1011–1012 cm−3) reactors for materials processing, the sheath thickness is often <100 s μm while the reactor dimensions are 10 s cm. Resolving the sheath in computer models of these devices using reasonable grid resolution is therefore problematic. If the sheath is not resolved, the plasma potential and stochastic electron heating produced by the substrate bias may not be well represented. In this article, we describe a semianalytic model for radio frequency (rf) biased sheaths which has been integrated into a two-dimensional model for plasma etching reactors. The basis of the sheath model is to track the charging and discharging of the sheath in time, and use a one-dimensional analytical model to obtain the instantaneous sheath voltage drop based on the sheath charge and the plasma conditions at the sheath edge. Results from the integrated model for an inductively coupled plasma etching reactor with powers of 200–800 W and rf bias powers from 50 to 400 W in Ar and Ar/Cl2 will be discussed. We found that the sheath voltage wave form remains nearly sinusoidal, and that the plasma density, and consequently the ion flux to the surface, scale primarily with inductively coupled power.