Design optimization of semiconductor manufacturing equipment using a novel multi-fidelity surrogate modeling approach

Careful design of semiconductor manufacturing equipment is crucial for ensuring the performance, yield, and reliability of semiconductor devices. Despite this, numerical optimization methods are seldom applied to optimize the design of such equipment due to the difficulty of obtaining accurate simulation models. In this paper, we address a practical and industrially relevant electrostatic chuck (ESC) design optimization problem by proposing a novel multi-fidelity surrogate modeling approach. The optimization aims to improve the temperature uniformity of the wafer during the etching process by adjusting seven parameters associated with the coolant path and embossing. Our approach combines low-fidelity (LF) and high-fidelity (HF) simulation data to efficiently predict spatial-field quantities, even with a limited number of data points. We use proper orthogonal decomposition (POD) to project the spatially interpolated HF and LF field data onto a shared latent space, followed by the construction of a multi-fidelity kriging model to predict the latent variables of the HF output field. In the ESC design problem, with hundreds or fewer data, our approach achieves a more than 10% reduction in prediction error compared to using kriging models with only HF or LF data. Additionally, in the ESC optimization problem, our proposed method yields better solutions with improvements in all of the quantities of interest, while requiring 20% less data generation cost compared to the HF surrogate modeling approach.