The oxide etching process was characterized in a magnetically enhanced reactive ion etching (MERIE) reactor with a $CHF_3CF_4$ gas chemistry. A statistical experimental design plus one center point was used to characterize relationships between process factors and etch response. The etch response modeled are etch rate, etch selectivity to TiN and uniformity. Etching uniformity was improved with increasing $CF_4$ flow ratio, increasing source power, and increasing pressure depending on source power. Characterization of via etching in $CHF_3CF_4$ MERIE using neural networks was successfully executed giving to highly valuable information about etching mechanism and optimum etching condition. It was found that etching uniformity was closely related to surface polymerization, DC bias, TiN and uniformity.