Feedback control of thermal chlorine (Cl2) etching of gallium arsenide (GaAs) using in-situ spectroscopic ellipsometry sensing

Real time feed-back control of etching is becoming necessary to meet the degree of process reproducibility demanded by the increasingly strict process requirements of advanced semiconductor manufacturing. The feasibility of using in-situ spectroscopic ellipsometry, being sensitive to film thickness, surface roughness and substrate temperature, to achieve real-time feedback control of etch rate in dry-etching is investigated for the case of thermal Cl₂ etching of GaAs(100). The etch rate is modeled as a function of Cl₂ pressure and substrate temperature with all sample preparation and etch rate measurements made in-situ, thus minimizing surface contamination effects. The dynamics of the chamber pressure as controlled by the position of a gate valve in front of a pump is modeled. The resulting nonlinear model with states etch rate, pressure, valve position and valve position velocity, and commanded valve position as control is linearized. A discrete-time linear quadratic Gaussian (LQG) compensator is designed and simulated on the nonlinear system