Uncertainty quantification and parameter optimization of a plasma etching process using a heteroscedastic Gaussian process

Abstract

This study presents an uncertainty-aware framework for the reliability-based robust design optimization (RBRDO) of plasma etching processes in semiconductor manufacturing. The framework is demonstrated using experimental measurements of the remaining thickness collected at nine wafer locations under various plasma conditions. A heteroscedastic Gaussian process surrogate model is employed to capture input-dependent uncertainty, enabling the quantification of spatial wafer variability and the propagation of process parameter variability associated with chamber pressure, gas flow rate and radio-frequency power. Epistemic uncertainty due to sparse experimental data is explicitly quantified and incorporated into the RBRDO scheme. The proposed approach identifies optimal process parameters by minimizing the standard deviation of the wafer-level remaining thickness while satisfying reliability constraints under both aleatory and epistemic uncertainties. The results demonstrate reliable uncertainty quantification and process optimization under uncertainty, with potential applicability to other semiconductor manufacturing processes.