Efficient multi-die placement for blank defect mitigation in EUV lithography

Due to the absence of defect-free blanks in extreme ultraviolet (EUV) lithography, defect mitigation is necessary before mass production. One effective way to mitigate the defect impact is to increase the distance between the defects and feature boundaries such that the defects will not affect the printing of the features. Some algorithms have been developed to move the whole layout within the exposure field in order to avoid all defect impact. However, in reality the die size is usually much smaller than the exposure field, such that one blank is packed with multiple copies of the die, and each die can be placed independently within the exposure field. In this paper, we develop an EUV reticle placement algorithm to maximize the number of valid dies that are immune to defects. Given the layout of a die and a defective blank, we first apply a layout relocation algorithm to find all feasible regions for the die on the blank. Then we develop an efficient placement algorithm to place the dies within the feasible regions one at a time until all feasible regions are fully occupied. The simulation results show that our algorithm is able to find a solution efficiently and the number of valid dies placed by our algorithm is very close to the optimal solution.