Constitutive diffusion model for precise critical dimension patterning via beam shape optimization and effects on uniformity

Laser-based patterning in semiconductor manufacturing can suffer critical dimension (CD) distortion when heat diffuses beyond the intended pattern during exposure. We seek beam shape design settings that confine the thermal field within a target CD boundary for shaped beam pattern projection. A continuum mechanics computational framework solves transient heat diffusion under projected spatially uniform and nonuniform beam profiles. We then formulate cost functions that penalize CD deviation for above-threshold heating. A genetic algorithm optimizes beam intensity and pulse durations. For the nonuniform and uniform beams, the optimized minimum costs were 8.87·10−5 and 2.75·10−3, with above temperature threshold areas of 1.11·10−12 m2 and 1.33·10−12 m2, respectively. With 2% intensity fluctuations applied to the optimal uniform beam, critical dimension uniformity (CDU) improved by 57.1% when the fluctuations were skewed toward the lower bound of the GA-optimal intensity. Optimizing spatiotemporal beam delivery can reduce CD distortion and overheating, and the sensitivity to upward power drift motivates robust beam-control strategies for thermal-constrained patterning.