Degree Type


Date of Award


Degree Name

Master of Science


Electrical and Computer Engineering

First Advisor

Chris Chu


Following moore's law, microelectronic fabrication techniques have been developed to fabricate deep-submicron devices. Device feature size on wafer turns to be much smaller than the illumination source of nowadays widely used lithography equipments, which is 193 nm wavelength of UV(ultraviolet) light. Diffraction effects can not be avoided when transfer patterns from masks to wafers in the process of lithography because of the extremely small size of features. So the patterns transferred from masks to wafers surface are distorted very much, and it causes many problems, such as poly line end shortening or bridging which result in leakage or short circuit. The industry has been investigating various alternatives, such as EUV(extreme ultra-violet) illumination source. However, the next generation of illumination source, EUV with a wavelength of about 13.5 nm, still has a long way to be put into practice. As a result, Resolution Enhancement Technology (RET) has been increasingly relied uponto minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this thesis, we investigate the problem of pixelated binary mask design in a partially coherent imaging system. Similar to previous approaches, the mask design problem is formulated as a nonlinear program and is solved by gradient based search. Our contributions are four novel techniques to achieve significantly better image quality than state-of-the-art technology. First, to transform the original bound-constrained formulation to an unconstrained optimization problem, we propose a new non-cyclic transformation of mask variables to replace the well-known cyclic one. As our transformation is monotonic, it enables a better control in flipping pixels. Second, based on this new transformation, we propose a highly efficient line search based heuristic technique to solve the resulting unconstrained optimization problem. Third, we introduce a jump technique. As gradient based search techniques will get trapped at a local minimum, we introduce a new technique named jump in order to jump out of the local minimum and continue the search. It increases the chance to achieve a better result. Fourth, to simplify the optimization, instead of using widely used discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Experiment results show that the results of state-of-the-art algorithm implemented by Ma and Arce [5] are 8:55% to 358:8% higher than ours.

Copyright Owner

Xin Zhao



File Format


File Size

58 pages