Line Search-Based Inverse Lithography Technique for Mask Design

As feature size is much smaller than the wavelength of illumination source of lithography equipments, resolution enhancement technology (RET) has been increasingly relied upon to minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this paper, 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. First, to transform the original bound-constrained formulation to an unconstrained optimization problem, we propose a new noncyclic transformation of mask variables to replace the wellknown 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. Third, to simplify the optimization, instead of using discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Forth, we introduce a jump technique in order to jump out of local minimum and continue the search.

[1]  Amyn Poonawala,et al.  Mask Design for Optical Microlithography—An Inverse Imaging Problem , 2007, IEEE Transactions on Image Processing.

[2]  Xu Ma,et al.  Generalized inverse lithography methods for phase-shifting mask design , 2007, SPIE Advanced Lithography.

[3]  Xu Ma,et al.  Pixel-based OPC optimization based on conjugate gradients. , 2011, Optics express.

[4]  Dinesh K. Sharma,et al.  Resolution enhancement techniques for optical lithography , 2002 .

[5]  Chris C. N. Chu,et al.  Optimal slack-driven block shaping algorithm in fixed-outline floorplanning , 2012, ISPD '12.

[6]  Chris C. N. Chu,et al.  DeFer: Deferred Decision Making Enabled Fixed-Outline Floorplanning Algorithm , 2010, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  Yuri Granik,et al.  Fast pixel-based mask optimization for inverse lithography , 2006 .

[8]  B E Saleh,et al.  Simulation of partially coherent imagery in the space and frequency domains and by modal expansion. , 1982, Applied optics.

[9]  Peyman Milanfar,et al.  A pixel-based regularization approach to inverse lithography , 2007 .

[10]  Chris C. N. Chu,et al.  Handling complexities in modern large-scale mixed-size placement , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[11]  Linyong Pang,et al.  Inverse lithography technology (ILT): What is the impact to the photomask industry? , 2006, Photomask Japan.

[12]  Xu Ma,et al.  PSM design for inverse lithography with partially coherent illumination , 2008, Advanced Lithography.

[13]  Peyman Milanfar,et al.  OPC and PSM design using inverse lithography: a nonlinear optimization approach , 2006, SPIE Advanced Lithography.

[14]  D. Malacara-Hernández,et al.  PRINCIPLES OF OPTICS , 2011 .

[15]  Chris C. N. Chu,et al.  SafeChoice: a novel clustering algorithm for wirelength-driven placement , 2010, ISPD '10.

[16]  Chris C. N. Chu,et al.  DeFer: Deferred decision making enabled fixed-outline floorplanner , 2008, 2008 45th ACM/IEEE Design Automation Conference.

[17]  David Z. Pan,et al.  TIP-OPC: a new topological invariant paradigm for pixel based optical proximity correction , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[18]  Chris C. N. Chu,et al.  SafeChoice: A Novel Approach to Hypergraph Clustering for Wirelength-Driven Placement , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[19]  Gonzalo R. Arce,et al.  Computational Lithography , 2010, Wiley series in pure and applied optics.