A Mathematical Model for Etching of Silicon Using CF 4 in a Radial Flow Plasma Reactor

Abstract

A mathematical model for plasma etching of silicon using tetrafluoromethane in a radial flow reactor was developed. Finite element methods were employed to calculate the two‐dimensional flow, temperature, and species concentration fields. Etching rate and uniformity were studied as a function of reactor operating conditions, including the effect of flow direction. For the parameter values examined, the etching rate increased monotonically with flow rate. For low substrate temperature (298 K), inward flow resulted in higher etching rate as compared to outward flow, but the trend reversed at higher temperature. For flow rates greater than 200 sccm, outward flow with a uniform electron density distribution gave the best uniformity results. A one‐dimensional radial dispersion approximation was used to study the effect of square‐wave power modulation (pulsed‐plasma reactor). The etching rate increased with decreasing pulse period and with increasing duty cycle. Under conditions which would result in high depletion of the precursor gas in a continuous‐wave reactor (e.g., for low flow rates), the pulsed‐plasma reactor can offer substantial improvement in uniformity without sacrificing the etching rate.