Optimization Under Uncertainty

Optimization Under Uncertainty in semiconductor manufacturing is the formulation and solution of optimization problems that explicitly account for variability and uncertainty — finding solutions that are not just optimal on average but remain robust when process parameters, equipment states, and demand fluctuate.

Key Approaches

• Stochastic Programming: Optimize the expected value over a set of scenarios (scenario-based).
• Robust Optimization: Optimize worst-case performance over an uncertainty set (conservative).
• Chance Constraints: Ensure constraints are satisfied with high probability (e.g., yield ≥ 90% with 95% confidence).
• Bayesian Optimization: Use probabilistic surrogate models to optimize expensive, noisy functions.

Why It Matters

• Process Windows: Find process conditions that maximize yield while remaining robust to variation.
• Robust Recipes: Recipes optimized under uncertainty maintain performance despite day-to-day drifts.
• Capacity Planning: Account for demand uncertainty and equipment reliability in tool investment decisions.

Optimization Under Uncertainty is planning for the unpredictable — finding solutions that work well not just on paper but in the face of real-world manufacturing variability.