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.