MOS OSAIC: : Mas ask k Opt ptimiz imizing ing Solut olution - PowerPoint PPT Presentation

MOS OSAIC: : Mas ask k Opt ptimiz imizing ing Solut olution ion Wit With h Proces ocess Window Window Awar are e Inv nver erse e Cor orrect ection ion Jhih-Rong Gao, Xiaoqing Xu, Bei Yu, and David Z. Pan Dept. of Electrical and Computer Engineering The University of Texas at Austin Supported in part by NSF, SRC, NSFC, and Oracle 1

Outline t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions 2

Sub-wavelength Lithography Image distortion Target due to light scattering Mask Printed Image Image distortion OPC is compensated Mask 3

Optical Proximity Correction (OPC) t Resolution enhancement technique t Required for advanced technology nodes to ensure printability Ruled-based Model-based (Edge) [A. K. Wong, SPIE Press’01] [N. B. Cobb+, SPIE’03] [P. Yu+ , ICCAD’07] 4

Inverse Lithography Technique (ILT) t Further scaling demands more aggressive OPC t Pixel-based OPC › Higher contour fidelity than conventional OPC methods [Y. Granik, JM3’06] [A. Poonawala+, TCAD’07] [J. Zhang, ICCAD’08] [Y. Shen+ , OpEx’09] [N. Jia+, J. Opt.’10] [J. Zhang, ASPDAC’10] [X. Zhao+, VLSID’12] ILT-based OPC 5

Our Contributions t Limitations of previous works › Design target optimization » Distortion Area à however, not all distortion matters » What really matters is edge placement error (EPE) beyond threshold » No study for direct EPE minimization › Process variations » Optical conditions: defocus, dose, … » One ILT study, [Jia+ J. Opt.’10], considered defocus only t Our contributions › Provide exact optimization for EPE › Optimize both Design Target and Process Variation › Outperform the 1 st place winner at 2013 ICCAD contest » 11% improvement for the overall score 6

Outline t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions 7

Forward/Inverse Lithography th I Printed Optical Mask Photoresist Pattern Projection t Forward lithography Difficulty Z = f ( M ) . • Ill-posed problem (not t Inverse Lithography one-to-one mapping) M opt = f − 1 ( Z t ) • No closed form solution ( 8

Gradient Descent Based Approach F(M) F ß obj( M ) to minimize Initial Solution repeat M ß M – stepSize x F Δ until F converges Iteration 2 Iteration 3 Still difficult • How to define F such Convergence that it ü Integrates Design Target & Process M Variation ü Is Differentiable 9

Design Target Optimization (Fast) t Total distortion minimization Target N N X X F td = ( Z nom ( i, j ) � Z t ( i, j )) γ Nominal i =1 j =1 Mask ( M ) N h X w k | M ( x, y ) ⌦ h k ( x, y ) | 2 . Optical I ( x, y ) ⇡ k =1 Intensity ( I ) ⇢ 0 if I ( x, y ) 6 th r Photoresist Z ( x, y ) = 1 if I ( x, y ) > th r 1 ) = sig ( I ( x, y )) = Pattern ( Z ) 1+ e − θ Z ( I ( x,y ) − thr ) 10

Design Target Optimization (Exact) t Edge Placement Error (EPE) violation minimization › Common measurement for yield impact (EPE > th epe ) Target contour Image contour may be inside EPE or outside of the desired boundary EPE Image è Calculating boundary-to- è boundary EPE is not a continues function ⇢ 0 if EPE < th epe (Non-differentiable) EPE Violation = 1 if EPE > th epe 11

� � Design Target Optimization (Exact) (cont’) t EPE violation minimization › Formulated as a continuous function (Differentiable!) Outer Target contour EPE Dsum VS EPE Inner Image Observation: distortion is continuous HS Vio sigmoid 1 ⇢ ⇢ 0 if Dsum < th epe 0 if EPE < th epe EPE Violation = EPE Violation = 1 if Dsum > th epe 1 if EPE > th epe X X F epe = sig ( Dsum i,j ) + sig ( Dsum i,j ) ( ( i,j ) ∈ HS ( i,j ) ∈ V S th epe EPE (Continuous/Differentiable) 12

Process Window Optimization t Process variability band (PV band) › Area between the outermost and the innermost edges among all process conditions PV Band N p X ( Z k � Z t ) 2 Np : #Process conditions F pvb = k =1 13

Outline t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions 14

Experiment Setup t MOSAIC_fast (Total Distortion + PV band) F fast = α F td + β F pvb t MOSAIC_exact (EPE Violation + PV band) F exact = α F epe + β F pvb t Benchmark t 10 layout clips from 32nm M1 layer released by IBM t Lithography parameters › 193nm wavelength › Process variations: ±25nm defocus, ±2% dose t Evaluation (ICCAD Contest 2013) : Score = Runtime + 4 × PV B + 5000 × # EPE 15

Score Comparison 7% Imp. 11% Imp. Both approaches outperform ICCAD’13 contest winners 16

Runtime Comparison 17

Conclusion t ILT-based OPC that simultaneously optimizes Design Target and Process Variation › More accurate EPE formulation into the ILT engine › Continuous and differentiable › 11% overall improvement than the 1 st place winner t Future directions › Our framework can be extended to handle mask complexity › Multiple patterning, 3D effects › New emerging lithography such as DSA › Co-optimizations with design rules, hotspots, etc … 18

Thank you! 19

Gradient Descent Convergence t All benchmarks converges within 20 iterations Jump out of local optimum 20

Regularization: Needed or Not? t An example of E-beam mask writing [Zable+, SPIE’2010] OPC Fractured Mask Image Wafer Image Target Curved lines may be well handled with advanced techniques 21

Runtime/EPE/PVB Comparison 22

OPC Results Target OPC Mask Final pattern PV Band 23