Linear Time Algorithm to Find All Relocation Positions for EUV Defect Mitigation Yuelin Du, Hongbo Zhang, Qiang Ma and Martin D. F. Wong ASPDAC13

Outline Introduction Problem formulation Algorithm Experimental results Conclusion

Introduction With the current VLSI technology shrinking to sub-20nm, EUV lithography has become a leading candidate to replace the 193nm technology. But, the absence of defect-free blanks in EUV mask fabrication, a methodology that is able to deal with defective blanks will be required

Introduction

Problem formulation Maximize the number of valid dies within the exposure field.

Problem formulation Find the all feasible regions.

Algorithm Blank Region Partition – Blank Region with No Effective Defect – Blank Region with Single Effective Defect – Blank Region with Multiple Effective Defect

Blank Region Partition no part of the die can be shifted outside the exposure field Each defect has a unique impact range

Blank Region with No Effective Defect The bottom left corner of the die is located within this region, no defect will locate within the die area, and hence all defect impact is completely mitigated.

Blank Region with Single Effective Defect Step 1. Impacted Feature Extraction Step 2. Impacted Feature Shrinking Step 3. Shrunk Die Area Rotation and Shift

Impacted Feature Extraction The width/height of 3 is equal to the width/height of 3 plus the width/height of the defect. Impacted Feature:F2,F3

Impacted Feature Shrinking In the second step, the impacted features and the impacted die area 3 are shrunk by the size of the effective defect.

Shrunk Die Area Rotation and Shift Therefore, the shrunk features in 3 and the feasible regions in 3 are diagonally symmetric.

Blank Region with Multiple Effective Defect The objective is to find the feasible regions to locate the die where all defects are covered by features simultaneously. We first consider each defect separately And the sets of feasible regions are intersected to obtain the final feasible region

Time Complexity Analysis n: the number of features in the die.

Improved Strategy for Layout Intersection

Experimental result We implement our algorithm using C++ on a workstation with an Intel Xeon E GHz CPU and 36GB memory Then we carry out our experiments with a 11nm design The defects size form 50nm to 200nm The size of the exposure field is 10.4cm by 13.2cm.

Experimental results

Conclusion In this paper we propose an efficient algorithm to find all layout relocation positions to place a valid die on a defective blank for defect mitigation. By simple parallelism, the efficiency can be further improved.