Exposure Condition Calculation via Singular Value Decomposition

The patent creates a virtual copy of the exposure process through computer simulation. Instead of physically repeating experiments on actual semiconductor wafers, the system simulates exposure conditions, light intensity distributions, and pattern formation on a computer. This virtual copying allows multiple optimization iterations without consuming physical materials or significant time, while still achieving accurate exposure condition optimization.

The patent replaces the mechanical/experimental exposure optimization system with a computational system. Rather than physically adjusting exposure parameters and measuring results through repeated experiments, the system uses computer algorithms to calculate light intensity distributions, simulate pattern formation, and determine optimal exposure conditions. This substitution eliminates the time-consuming iterative experimental process while maintaining optimization accuracy.

The patent segments the complex exposure calculation process into distinct computational steps: dividing the illumination aperture into multiple zones, calculating diffraction patterns for each zone separately, and combining results through superposition. This segmentation allows the use of efficient algorithms for each sub-problem rather than attempting a single complex calculation, significantly reducing total computation time while maintaining accuracy.

The patent changes the computational parameters and approach by using analytical solutions for diffraction patterns rather than numerical methods. By transforming the calculation into the frequency domain and using Fourier transform techniques, the system achieves faster computation. The patent also introduces approximation parameters that maintain sufficient accuracy for practical purposes while dramatically reducing calculation complexity.