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

Abstract: This study presents a comprehensive framework for uncertainty quantification (UQ) and design optimization of plasma etching in semiconductor manufacturing. The framework is demonstrated using experimental measurements of etched depth collected at nine wafer locations under various plasma conditions. A heteroscedastic Gaussian process (hetGP) surrogate model is employed to capture the complex uncertainty structure in the data, enabling distinct quantification of (a) spatial variability across the wafer and (b) process-related uncertainty arising from variations in chamber pressure, gas flow rate, and RF power. Epistemic uncertainty due to sparse data is further quantified and incorporated into a reliability-based design optimization (RBDO) scheme. The proposed method identifies optimal process parameters that minimize spatial variability of etch depth while maintaining reliability under both aleatory and epistemic uncertainties. The results demonstrate that this framework effectively integrates data-driven surrogate modeling with robust optimization, enhancing predictive accuracy and process reliability. Moreover, the proposed approach is generalizable to other semiconductor processes, such as photolithography, where performance is highly sensitive to multifaceted uncertainties.