隨著半導體製程複雜度提升，光學鄰近修正(Optical Proximity Correction, OPC)模型的準確度需求日益提高，特別是在高維參數空間下，傳統優化方法如遺傳演算法(Genetic Algorithm, GA)面臨收斂速度慢與搜尋效率低落的挑戰。為提升高維OPC模型校準效能，本論文提出一種結合高斯混合模型(Gaussian Mixture Model, GMM)與具可伸縮信任區域設計之貝氏優化架構，透過在選點流程中引入機率式聚類機制，達到有效提升樣本代表性與搜尋潛力區域的效率。 實驗部分首先於Ackley與Levy等兩類基準合成測試函數進行驗證，涵蓋5至200維空間之不同設定，觀察聚類輔助策略在不同維度下的收斂行為與效益。隨後進一步應用於實際OPC模型參數校準任務中，包括11維與33維的光阻模型，並與商用軟體內建演算法進行比較。結果顯示，本方法可於相同資源條件下顯著提升收斂速度與最終精度，最終RMS誤差相較內建GA最高可減少45.6%。此外，實驗亦證實GMM相較於K-means在捕捉異質性潛力區域方面表現更穩定，並指出適當批量大小的選擇亦有助於進一步提升優化效果。
本論文所提出之GMM聚類輔助式貝氏優化策略可有效解決高維空間中搜尋資源分散與探索效率不彰的問題，並於實際模型校準任務中展現顯著效能，具備高延展性與實務應用價值。

As semiconductor process complexity increases, the accuracy requirements of
Optical Proximity Correction (OPC) models rise sharply — especially in high
dimensional parameter spaces where traditional methods such as Genetic Algorithms (GA) suffer from slow convergence and poor search efficiency. To address these challenges, we develop a Bayesian Optimization framework assisted by the Gaussian Mixture Model (GMM) with a scalable trust-region design. By integrating a probabilistic clustering step into the acquisition process, the proposed method significantly improves sample representativeness and more efficiently explores the promising regions.
In our experiments, we first validate the clustering‐augmented strategy on standard benchmark functions (Ackley and Levy) in dimensions ranging from 5 to 200, demonstrating superior convergence behavior across all settings. We then apply the method to real OPC parameter calibration tasks—including an 11‐parameter and a 33-parameter resist models—and compare it against the built‐in optimizer in commercial OPC software. Under identical resource constraints, our approach achieves markedly faster convergence and lower final error: the RMS error is reduced by up to 45.6% with respect to that of the commercial GA. In addition, we show that GMM outperform K-means in capturing heterogeneous high‐potential regions, and we highlight how appropriately chosen batch sizes further enhance the optimization performance.
Overall, the proposed GMM‐assisted Bayesian Optimization strategy effectively overcomes the “curse of dimensionality” in high‐dimensional search spaces, yielding substantial gains in both convergence speed and final accuracy for practical OPC model calibration tasks.