A SEMIANALYTIC RADIO-FREQUENCY SHEATH MODEL INTEGRATED INTO A 2-DIMENSIONAL HYBRID MODEL FOR PLASMA PROCESSING REACTORS

In high plasma density ([e]>10(11)-10(12) cm(-3)) reactors for materia ls processing, the sheath thickness is often <100 s mu m while the rea ctor dimensions are 10 s cm. Resolving the sheath in computer models o f these devices using reasonable grid resolution is therefore problema tic. If the sheath is not resolved, the plasma potential and stochasti c electron heating produced by the substrate bias may not be well repr esented. In this article, we describe a semianalytic model for radio f requency (rf) biased sheaths which has been integrated into a two-dime nsional model for plasma etching reactors. The basis of the sheath mod el is to track the charging and discharging of the sheath in time, and use a one-dimensional analytical model to obtain the instantaneous sh eath voltage drop based on the sheath charge and the plasma conditions at the sheath edge. Results from the integrated model for an inductiv ely coupled plasma etching reactor with powers of 200-800 W and rf bia s powers from 50 to 400 W in Ar and Ar/Cl-2 will be discussed. We foun d that the sheath voltage wave form remains nearly sinusoidal, and tha t the plasma density, and consequently the ion flux to the surface, sc ale primarily with inductively coupled power. (C) 1997 American Instit ute of Physics.