multi-response optimization

**Multi-Response Optimization** is the **simultaneous optimization of multiple quality characteristics (CD, thickness, uniformity, defects)** — finding process conditions that jointly satisfy all quality targets, handling trade-offs between competing objectives. **Key Approaches** - **Desirability Function**: Map each response to a 0-1 desirability scale and maximize the geometric mean. - **Weighted Objective**: Combine responses into a single weighted objective — requires defining relative importance. - **Pareto Optimization**: Find the set of solutions where no response can be improved without degrading another. - **Compromise Programming**: Minimize the distance to the ideal (but unattainable) solution. **Why It Matters** - **Trade-Offs**: Optimizing CD may worsen uniformity — multi-response methods navigate these trade-offs explicitly. - **Real Processes**: Every semiconductor process has 3-10+ quality responses that must be simultaneously controlled. - **Engineering Judgment**: Multi-response methods make trade-offs transparent so engineers can make informed choices. **Multi-Response Optimization** is **balancing competing quality goals** — finding the best compromise when improving one response comes at the expense of another.