Color Balancing Aware Double Patterning

• Main Authors: Lin, Meng-Yi, 林孟毅
• Other Authors: Li, Yih-Lang
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/9vut7d

碩士 === 國立交通大學 === 資訊科學與工程研究所 === 105 === In Double Patterning L In Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning L In Double Patterning L In Double Patterning LIn Double Patterning LIn Double Patterning L In Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning LIn Double Patterning Lithographyithographyithographyithographyithographyithographyithography ithographyithography (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm (DPL) layout decomposition for 45nm and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process and below process nodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assi nodes, two features should be assi nodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assi nodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assi nodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assi nodes, two features should be assinodes, two features should be assinodes, two features should be assinodes, two features should be assigned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors gned different colors if their if their if their if their if their if their spacingspacingspacing spacingspacing is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the is less than the minimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacing minimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacingminimum coloring spacing(mcs ), i.e. they , i.e. they , i.e. they , i.e. they , i.e. they , i.e. they , i.e. they , i.e. they belong to different exposubelong to different exposu belong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposubelong to different exposu belong to different exposubelong to different exposubelong to different exposubelong to different exposu belong to different exposubelong to different exposubelong to different exposubelong to different exposures. res. Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the Previous works of DPL focus on the following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: following two issues: one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one is conflict minimization and the other one one one is stitch minimizationstitch minimizationstitch minimizationstitch minimizationstitch minimization stitch minimizationstitch minimizationstitch minimizationstitch minimizationstitch minimizationstitch minimizationstitch minimizationstitch minimization stitch minimizationstitch minimizationstitch minimization. In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, In this thesis, we model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition e model DPL layout decomposition as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem.as Integer Linear Programming (ILP) problem. as Integer Linear Programming (ILP) problem. Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not Our ILP formulations not onlonlonly optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also y optimize an objective of number conflicts and stitches but also consider color balancing consider color balancingconsider color balancingconsider color balancingconsider color balancingconsider color balancing consider color balancing consider color balancingconsider color balancingconsider color balancing consider color balancingconsider color balancing consider color balancingconsider color balancingconsider color balancing consider color balancingconsider color balancing. Because BecauseBecauseBecause the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is the time complexity of ILP is exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we exponential growth, we develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to develop a method to split the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphs split the conflict graphs split the conflict graphssplit the conflict graphs split the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphssplit the conflict graphs split the conflict graphssplit the conflict graphs in orderorder order to to to reduce the runtime of solving these ILP fo reduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP fo reduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP fo reduce the runtime of solving these ILP foreduce the runtime of solving these ILP fo reduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP fo reduce the runtime of solving these ILP fo reduce the runtime of solving these ILP fo reduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP foreduce the runtime of solving these ILP formulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still rmulations while still keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. keeping good layout decompositions in the final solution. 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ThenThenThen , we , we , we propose a propose a propose a propose a propose a propose a propose a propose a postpostpostpost-optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results. optimization to further improve our results.