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Automated design of halftoned double-exposure phase-shifting masks

In our earlier work, we have proposed an efficient algorithm for phase- shifting mask design of an arbitrary IC pattern. Experimental results have shown that the algorithm works well for patterns such as gratings, contact-holes, U-patterns, etc.. In this paper, we use the concept of moment expansion to give a rigorous proof of the well-known fact that two-phase masks such as alternating phase-shifting masks or attenuated phase-shifting masks possess a better depth of focus; thus, our proposed double-exposure masks have depth-of-focus enhancement property. In addition, we also investigate the quantization problems related to our algorithm and develop a new quantization scheme based on the so-called halftoning techniques, which is commonly used in the printing industry to render the illusion of the continuous-tone images on binary output devices such as laser printers. Simulation results have shown that the new quantization scheme performs very well even for much larger and complicated patterns. Currently, empirical verification is underway in cooperation with HP ULSI Research Laboratory, Palo Alto, CA.