Constrained Optimization

Constrained Optimization in semiconductor manufacturing is the optimization of process objectives (yield, CD, uniformity) subject to explicit constraints on process parameters and output specifications — finding the best solution within the feasible operating region defined by equipment limits and quality requirements.

Types of Constraints

• Equipment Limits: Temperature range, pressure range, gas flow capacity, power limits.
• Quality Specs: CD ± tolerance, thickness ± tolerance, defect density < maximum.
• Process Windows: Combinations that must be avoided (e.g., high power + low pressure causes arcing).
• Cost Constraints: Material usage limits, maximum number of process steps.

Why It Matters

• Feasibility: The true optimum may be infeasible — constrained optimization finds the best achievable solution.
• Robustness: Constraints on spec limits ensure the optimized recipe actually works in production.
• Methods: Lagrange multipliers, penalty methods, interior point, and SQP handle different constraint types.

Constrained Optimization is optimizing within reality — finding the best process conditions while respecting every equipment limit and quality specification.