E-Beam Lithography Character and Stencil Co-Optimization

Electron-beam maskless lithography is being actively explored by the semiconductor industry for chip production in the sub-22 nm regime. Character projection allows in one e-beam shot the printing of complex pattern rather than merely a single rectangle or triangle as in variable-shaped beam projection. However, those circuit patterns that do not match any character on the stencil still have to be written by variable-shaped beam projection. We investigate a new problem of character and stencil co-optimization with blank space sharing between characters so as to minimize the total number of shots required for printing a circuit. We exploit the fact that the blank spaces on the sides of a character can be adjusted by moving the pattern to be printed within its projection region to facilitate blank space sharing so as to pack more characters into the stencil. Even though the co-optimization problem is shown to be NP-complete, we are able to design an elegant approximation algorithm, CASCO. Experiments confirm that the solutions by CASCO are nearly optimal. Compared to the published state-of-the-art, CASCO reduces the shot count by 1.59 times, while it is also orders of magnitude faster.