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Double exposure techniques are an economically viable method for extending the life of the current 193nm
wavelength immersion lithography techniques into future generations of semiconductor scaling. One popular
example of double exposure is the use of double dipole illumination, where the X and Y dipoles are separately
optimized for vertical and horizontal features respectively. The primary challenge in such double exposure
techniques lies in the process of target layout decomposition into patterns that can be optimally printed using their
respective source. Current approaches for decomposition are rule-based. They suffer from the drawbacks of
scalability, rule count explosion and inability to guarantee sufficient yield in the presence of process variation.
Further, rules are characterized specific to sources and are relatively easy to develop for dipoles, but far more
difficult to develop for more complex sources such as used in source mask optimization (SMO). Decomposed
target layouts have to further undergo optical proximity correction (OPC) in order to be converted to a mask for
use in manufacturing. In this paper, we propose a novel approach which integrates the processes of decomposition
and optical proximity correction. We preclude the intermediate target decomposition stage. Instead, we directly
optimize the masks for both exposures simultaneously in order to obtain a wafer image that both closely matches
the target layout and is also robust to process variation. For this purpose, we define a lithographic cost function
that is a weighted sum of intensity error and intensity slope. We develop methods to analytically predict the
change in this cost function due to movement of fragments on each mask. We then utilize a gradient-descent
algorithm for fragment movement to minimize the cost function. Since our methodology is based on the
knowledge of the SOCS decomposition kernels, it is not restricted to dipoles alone, but can be utilized for any
complex sources for which such kernels are known. Our experiments on 1x metal (M1) show significant
improvement in layout process window compared to traditional rule-based decomposition methods.
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