Lithography Issues in Nano Chip Design and Manufacture

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1 Lithography Issues in Nano Chip Design and Manufacture Xuan Zeng, Jintao Xue and Wei Cai ASIC & System State Key Lab., Microelectronics Dept., Fudan Univerisity Jan. 7, 2007 Jan. 7, 2007 Challenges and Opportunities in Nano-Optics Workshop

2 Outline Introduction to IC Manufacture Problems for Lithography 3D Scattering Analysis in Lithography Simulation Stochastic Lithography Simulation OPC Optimization Algorithm 2

3 Introduction to IC (Integrated Circuit) Integration: billions of transistors Speed: Multi GHz Minimal transistor size : <65 nanometer Interconnects: up to 8,9 layers 3

4 Design System Specification Filter Transfer Function Circuit Design IC Design to Fabrication Flow H( s) = b 0 2 a0 + a1 s+ a2s bs+ b s + b s + b s b s 5 5 Layout Design Fabrication Mask Fabrication Silicon Fabrication 4

5 Lithography System Light Sources Mask Exposure System Wafer Source: Barry Lieberman, Intel 5

6 Subwavelength Lithography Lithography Wavelength is is much larger than the minimal geometry size of of design Micrometer Nanometer 6

7 Resolution Enhancement Solution Lithography wavelength is is much larger than the minimal geometry size of of design Litho wavelength: 248nm 7

8 Outline Introduction to IC Manufacture Problems for Lithography 3D Scattering Analysis in Lithography Simulation Stochastic Lithography Simulation OPC Optimization Algorithm 8

9 Problems for Lithography 3D Scattering Analysis in Lithography Simulation 3D optical lithography problems Mathematic Model Computational Methods 2D 3D Analysis Approach Proposed Research Issues 9

$photoresists on nonplanar wafer surface Mask defect detection 2D diffraction imaging model (Hopkins imaging theory) OPC simulation for$

10 193nm Lithograhy system photoresist ILD resist substrate 3D scattering problems Patterning of light by mask with PSM Exposing of photoresists on nonplanar wafer surface Mask defect detection 2D diffraction imaging model (Hopkins imaging theory) OPC simulation for full chip 10

11 193nm Lithography Simulation for defect detection Without defect Source: Kevin D. Lucas With defect 11

12 13.5nm Extreme Ultra Violate Lithography Incident Wave Reflective Wave absorber Ta 100nm SiO 2 50nm Reflector 40 Si/Mo Si 4.1nm Mo 2.8nm Substrate Transmitted Wave 12

13 13.5nm Lithography Simulation for defect detection Distance Absorber Line Width: 48nm Particle Diameter: 10nm Source: Rafik Smaali 13

14 Problems for Lithography 3D Scattering Analysis in Lithography Simulation 3D optical lithography problems Mathematic Model Computational Methods 2D 3D Analysis Approach Proposed Research Issues 14

15 Rigorous 3D Scattering Analysis Model Incident Wave Layer 0 Layer 1 Layer 2 Layer 6 Layer 7 Transmitted Wave Discretize PSM into multi-layers in which dielectric function is uniform in z direction Glass Mask Multilayer 3D EM Analysis Incident Wave Reflective Wave Transmitted Wave 15

16 Problems for Lithography 3D Scattering Analysis in Lithography Simulation 3D optical lithography problems Mathematic Model Computational Methods 2D 3D Analysis Approach Proposed Research Issues 16

17 Rigorous 3D Scattering Analysis Existing Methods: Waveguide method Strowas 1992,1996 Rigorous coupled wave analysis Moharam1981, Smaali2006 Finite element method Burger 2005 Finite difference method Neureuther

18 Reference: Scattering Analysis K. Lucas, C. M. Yuan and A. Strowas, A rigorous and practical vector model for phase shifting masks in optical lithography, SPIE Optical/Laser Microlithography, Vol. 1674, pp , 1992 K. D. Lucas, H. Tanabe and A. J. Strowas, Efficient and rigorous three-dimensional model for optical lithography simulation, J. Opt. Soc. Am., Vol. 13(11), pp , 1996 A. K. Wong, R. Guerrieri, and A. R. Neureuther, Massively parallel electromagnetic simulation for photolithographic applications, IEEE Trans. on CAD, Vol. 14, No. 10, pp ,1995 M. G. Moharam and T. K. Gaylord, Rigorous coupled-wave analysis of planar-grating diffraction, J. Opt. Soc. Am., Vol. 71, No. 7, pp , 1981 S. Burger, R. Kohle, L. Zschiedrich and W. Gao etc., Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation, Proc. SPIE 5992, pages ,

19 Layer 0 Layer 1 Layer 2 Y Layer 6 Z Layer 7 E H // X v E ( x, z) = ye ˆ ( x, z) Glass Mask Lc On th layer, Helmholtz eq. 2D Waveguide Method E + k ε () x E = where k 1 Uniform fields and materials on Y direction 2 TE polarization: only E y exists 3 TM polarization is similar to TE problem = ωεµ Fields and materials are assumed periodic along X direction, and period is Lc, ε ( x) = ε exp( 2 ) where q i πqbx b= 1/ q Lc 19

20 2 E 2D Waveguide Method Using separation of variables E ( x, z) = X ( x) Z ( z) 2 X k 0 εq exp( i2 πqbx) + ( α ) X = 0 x q 2 Z z + k 2 0 ε ( x) E = 0 2 ( α ) Z = 0 2 ε ( x) = εq exp( i2 πqbx) q X (x) has the general form X ( x) = Bl exp( i2 πlbx) The eigenvalue problem is obtained for each layer D B l = (α 2 ) B B B L = M B L 20

21 For eigenvalue α m eigenfunction X m( x) = Bl, mexp( i2 π lbx) The electric field in th film, E L y X mz m m= L L = = 2D Waveguide Method L l= L m = m αm + m αm and Z ( z) A exp( z) A' exp( z)) L Amexp( αm( z z) A' mexp( αm( z z)) Bl mexp( i2 πlbx) ( + ), m= L l= L 21

22 2D Waveguide Method According to the interface conditions between different films E y E z = y E = + 1 y E z + 1 y The coefficients of the electric fields can be obtained, { A,0< 7, L L} l { A',0 < 7, L L} l 22

23 Layer 0 Layer 1 Layer 2 Y Layer 6 Z Layer 7 X Define Vector Potential Governing Equations in one layer Glass Mask v H = A v Lorentz Gauge = εφ In each layer, dielectric function is uniform in z direction Lc 3D Waveguide method (5) Fields and materials are various along X,Y,Z directions Maxwell Equation v v E = ikh (1) v v H = ikε E (2) v ε E = 0 (3) v µ H = 0 (4) 2 2 A A x y Ax + k εax (log ε)( + ) = 0 (16) x x y A 2 2 A x y Ay + k εay (log ε)( + ) = 0 (17) y x y A = 0 (18) z 23

24 3D Waveguide method 2 2 A A x y Ax + k εax (log ε)( + ) = 0 (16) x x y A 2 2 A x y Ay + k εay (log ε)( + ) = 0 (17) y x y A = 0 (18) z Similar to 2D waveguide method 1 Separation of variables A x = f ( x, y) Z ( z) (19) A =g ( x, y) Z ( z) (20) f f f g (log )( + ) = 0 (21) x y x x y α f k ε f ε 2 2 g g f g (log )( + ) = 0 (22) x y y x y α g k εg ε Z 2 z α Z 2 = y 0 (23) 24

25 3D Waveguide Method 3D waveguide method (similar to 2D waveguide method) 1 Separation of variables 2 Periodic conditions assumed along X, Y directions L M ε( xy, ) = ε exp[ i2 π( nbx+ pby)] (24) n= L p= M L M np, 1 2 f( x, y) = B exp[ i2 π ( lbx+ mb y)] (25) l= L m= M L M lm, 1 2 gxy (, ) = D exp[ i2 π ( lbx+ mby)] (26) l= L m= M lm, 1 2 substitute(24) (25) (26) into (21) (22), we get eigenvalue problem in one layer B B α (27) 2 [ ] = G D D For Z direction, Z(z)=C exp( αz) + C' exp(- α z) (28) 25

26 3D Waveguide Method 3D waveguide method (similar to 2D waveguide method) 3 A x, A y in one layer are obtained by eigenfunction expansions ' { } 2N L M A = C exp α ( z z ) + C exp α ( z z ) B exp[ i2 π( lbx+ mb y)] (29) x h h h h hl,, m 1 2 h= 1 l= Lm= M 2N L M ' { } A = C exp α ( z z ) + C exp α ( z z ) D exp[ i2 π( lbx+ mb y)] (30) y h h h h hl,, m 1 2 h= 1 l= Lm= M 4 The expansion coefficients { C, C ' h h} in A x, A y are decided by interface conditions between adacent layers (For example th, (+1) th layers) E = E, E = E H = H, H = H x x y y x x y y 26

27 Problems of Waveguide Method (I) v E ( x, z) = ye ˆ ( x, z) Glass Mask ε Layer 0 Layer 1 Layer 2 X X Layer 6 Layer 7 Z Lc In practice, mask structure is not periodic. Periodic boundary condition is employed along X direction, and what s its effect on the accuracy? 27

28 ε Problems of Waveguide Method (II) X m (x) Strong singularity in dielectric functions and eigenfunctions High order Fourier series employed to approximate each layer dielectric function and eigenfunctions. L ε ( x) = εq exp( i2 πqbx) Xm( x) = Bl, mexp( i2 πlbx) Waveguide method is cost intensive and difficult for complex structures X Dielectric function of one layer q X One eigenfunction corresponding to abruptly changed layer l= L 28

29 Problems for Lithography 3D Scattering Analysis in Lithography Simulation 3D optical lithography problems Mathematic Model Computational Methods 2D 3D Analysis Approach Proposed Research Issues 29

30 Challenges for 3D Scattering Analysis Causes of high computation cost Multilayer dielectric structure Singular mask structure large number of patterns in mask Extreme high computation cost TDFD based EUV (13.5nm) lithography simulation need 30 hours on a 2.8GHz PC for a via with 200nm long, 200nm wide and 320nm thick FDTD/FEM need massively parallel supercomputers Require large number of memory and time 30

31 Outline Introduction to IC Manufacture Problems for Lithography 3D Scattering Analysis in Lithography Simulation Stochastic Lithography Simulation OPC Optimization Algorithm 31

32 Stochastic Lithography Simulation Process Variations: systematic and stochastic variations Exposure dose variation Flare Variation Condenser aberration variation Mask error Proect Lens aberration variation How to solve stochastic PDE problem? Defocus variation 32

33 Reference: Stochastic Lithography Simulation S. Postnikov, K. Lucas, K. Wimmer, V. Ivin and A. Rogov, Monte Carlo method for highly efficient and accurate statistical lithography simulations, in Proc. SPIE, Vol., 4691, Optical Microlithography XV, A. Yen, Ed., pp , 2002 S. D. Hector, S. Postnikov and J. Cobb, Evaluation of the critical dimension control requirements in the ITRS using statistical simulation and error budges, in Proc. SPIE, Vol., 5377, Optical Microlithography XVII, ed., B. W. Smith, pp ,

34 Outline Introduction to IC Manufacture Problems for Lithography 3D Scattering Analysis in Lithography Simulation Stochastic Lithography Simulation OPC Optimization Algorithm 34

35 Optical Proximity Correction (OPC) Fab. Flow Without OPC Fab. Flow With OPC Layout Mask OPC Problem Silicon 35

36 Reference: 2D imaging model and OPC H. H. Hopkins, On the diffraction of Optical Images, Proc. Roy. Soc. A, Vol. 217, No.1130,pp ,1953 H. H. Hopkins, The concept of partial coherence in optics, Proc. Roy. Soc. A, Vol. 208, No. 1093,1951 N. Cobb, A. Zakhor, Fast, Low-Complexity Mask Design, SPIE Vol. 2440, 1994 N. Cobb, A. Zakhor, E. Miloslavsky, Mathematical and CAD Framework for Proximity Correction, SPIE Vol. 2726,

37 Fullchip OPC Model based OPC desired initial mask output mask Fragmentation Simulation OPC Controller mask pertubations Source: Nick Cobb 37

38 Fullchip OPC An example to optimize v Source: Nick Cobb 38

39 Challenges Exhausted time. Need 4-6 days on a cluster with 50 PCs (2.8GHz each) Exploded data. Need to deal with billions of shapes once iteration Potential solutions More efficient optimization algorithm? Novel OPC flows: cell-wise OPC Fullchip OPC 39

40 Cell-wise OPC A B A C B D A standard cell design C D B C D A Another standard cell design 40

41 A Cell Depends on its Neighbors Cellwise OPC NOR NAND NAND NOR BUFFER Source: Martin DF Wong 41

42 Boundary-Based Cellwise OPC Limiting boundary of standard cell helps cellwise OPC The aerial images outside a NOR logic gate (metal1) are shown here. The rightmost two column can be representative features for the cell Source: Martin DF Wong 42

43 Cellwise OPC Advantages More accurate than full-chip OPC (since it is a one-time-only computation so we can use long CPU time) Time is saved Predictable timing (since the delay of each OPC version of a cell can be pre-determined) Disadvantages Circuit dependent, the optical interactions with adacent cells are complex Does there exist a strategy to isolate the complex proximity effects? 43

44 Summary Challenges to Litho Simulation and OPC 3D Scattering Analysis Singularity and Non periodic mask structure Stochastic Lithography Simulation Fast stochastic PDE solution OPC Fast computation to correct billions of mask shapes for full chip 44

45 45

Copyright 2004 by the Society of Photo-Optical Instrumentation Engineers.

Copyright 2004 by the Society of Photo-Optical Instrumentation Engineers. Copyright 2 by the Society of Photo-Optical Instrumentation Engineers. This paper was published in the proceedings of the 2th Annual BACUS Symposium on Photomask Technology, SPIE Vol. 67- and is made available