EUVL Symposium 2009 - Poster
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- 1. Elastic and Elastic-Plastic Simulation of Entrapped Particles during Exposure Chucking Preetish Sinha, Vasu Ramaswamy, Andrew R. Mikkelsonand Roxann L. Engelstad Computational Mechanics Center(UW-CMC) University of Wisconsin, Madison, WI Michael R. Sogard Nikon Research Corporation of AmericaBelmont, CA
2. Introduction and Problem Description
- Imaging of circuit patterns with critical dimensions less than 32 nm in extreme ultraviolet lithography (EUVL) requires stringent control of all sources of image placement errors.
- Characterizing the sources of these errors is an important step in achieving successful pattern transfer.
- The flatness of the EUVL mask during exposure chucking is a key issue to minimize image placement (IP) errors due to nontelecentric illumination.
Frontand Backside Flatness: ~ 30 - 100 nmp-vflatness Low Order Thickness Variation (LOTV): ~ 30 - 100 nmp-vflatness Freestanding Substrate Requirements (within Quality Area) Quality Area:142 mm x 142 mm 3.
- Two sources of IP error (during exposure chucking) are out-of-plane distortions (OPD) and in-plane distortions (IPD) of the patterned reticle.
- Among the causes of OPD and IPD is particle entrapment, where small pieces of debris become lodged between the reticle and chuck.
Motivation for Research
- Experimental assessment of the effects of particle-induced reticle distortion is extremely difficult, thus computational studies using finite element (FE) models are required.
Micron-sized entrapped particle OPD and IPD of patterned surface Clamping pressure Millimeter-sized void 4. Predicting the Effects of Particle Entrapment
- The effects of entrapped particles are difficult to assess because the size, shape, number, and material properties of these contaminants are not well defined.
- It is also difficult to develop a model of a domain that is hundreds of millimeters in size, but contains sub-micron details.
- The problem needs to be studied under two regimes, the micro-scale response and the macro-scale response.
Effective Particle Height 5. Particle Entrapment
- In this study, we look at the micro-scale response of the entrapped particulates under different chucking pressures / forces.
- Spherical and cylindrical shaped particle responses were analyzed by running finite element simulations, and particle response as a function of the crush force has been presented.
- For the micro-scale response, particle deformation depends only on the local applied chucking force.How the force is created (e.g., by a vacuum chuck or electrostatic chuck) is not relevant.
- develop global models
- use macro properties
- consider effective particle height
- predict OPD and IPD of reticle
- identify IP errors (wafer level)
- develop local models
- use nanoscale properties
- simulate crushing or embedding
- assess particle crushing force
- identify effective particle height
6. Spherical Particle - Description
- Spherical particles with an initial diameter of 1.0 m, 5.0 m and 10.0 m were considered.
- Two FE models were created:
- (a) an FE model with purely elastic properties, and
- (b) an FE model with elastic-plastic properties.
- Particle crushing force was increased linearly, and the effective particle height was determined.
- For the same crushing force, a comparative analysis of the effective particle heights between the purely elastic and the elastic-plastic FE models was completed, and the results are discussed.
7. Spherical Particle Details of the Model * Measured via nanoindentation testing Axisymmetric FE Model F Model Parameters 12.0 12.0 9.0 8.5 Yield Strength (GPa) 100 Chuck 100 Particle 250 chrome* Backside Layer 66.3 ULE * Substrate Elastic Modulus (GPa) Material Component 1.0 m to 10.0 m Diameter, d p Particle Range Parameter Component Substrate Chuck Particle Chrome BacksideLayer d p Axis of symmetry 8. Particle: E = 100 GPa Y = 12 GPa Substrate: E = 66.3 GPa Y = 8.5 GPa Spherical Particle - Meshing the FE Model Chrome Layer: E = 250 GPa Y = 9 GPa Chuck: E = 100 GPa Y = 12 GPa 9. Elastic Response Elastic Plastic ResponseChuck / Particle Properties E= 100 GPa Y= 12 GPa Chuck / Particle Properties E= 100 GPa Y= 12 GPa ULE E= 66.3 GPa Y= 8.5 GPa Chrome E= 250 GPa Y= 9.0 GPa Spherical Particle - Response Effect of Nonlinear Behavior 1.0 m Spherical Particle ULE E= 66.3 GPa Y= 8.5 GPa ULE E= 66.3 GPa Y= 8.5 GPa 10. Spherical Particle FE Simulation Results 1.0 m Spherical Particle 11. Analytical and Numerical Analyses Substrate Chuck Particle Metal BacksideLayer H Axis of symmetry
- The local model includes a cylindrical particle with an original height ofHand radiusR .
- It is necessary to determine the effective particle height ( h ) after the particle is deformed and embedded into the reticle substrate and the chuck.
- The FE simulations facilitate determining the elastic and elastic-plastic response.
- The particle responses are characterized and subsequently compared.
R Local Axisymmetric Model CylindricalParticle Details of the Models 12. Cylindrical Particle -Analytical Model The total amount a particle is deformed and embedded ( w total ) into the reticle and chuck is given by: w total = w c+w s+w p SinceH was the original height of the particle, the effective height of the particle ( h ) is then given by: h = H ( w c+w s+w p ) w c= max embedded into the chuck w s= max embedded into the reticle substrate w p= max deformation of the particle Substrate Chuck h w c,w s and w p are calculated in the following slides ---- 13. Cylindrical Particle -Analytical Model Embedding into the Chuck Particle is assumed to be rigid when analyzing just the chuck deformation Embedding in chuck: E c= elastic modulus of chuck c= Poissons ratio of chuck where, F = applied forceR H Axis of symmetry Axisymmetric Model Chuck 14. R H t Axis of symmetry Particle is again considered rigid * H. Xu and G. M. Pharr, Scripta Materialia, Vol. 55, 2006, pp. 315-318 Embedding in substrate: where, Axisymmetric Model * F = applied forceE s= elastic modulus of reticle s= Poissons ratio of reticle E f = elastic modulus of backside layer f= Poissons ratio of backside layer Substrate with Metal Backside Layer Cylindrical Particle -Analytical Model Embedding into the Substrate 15. R H Deformation of particle:Particle is considered to be elastic. F = applied forceE p= elastic modulus of particle where, Axis of symmetry Cylindrical Particle -Analytical Model Particle Deformation 16. R H 362.5 m 362.5 m 362.5 m 362.5 m Axis of symmetry Substrate Chuck
- The analytical models were verified numerically by employing FE methods.
- For the FE models, the effective height is evaluated as the total deformation and embedding of the particle measured along the axis of symmetry.
- Reticle substrate:ULE
- Metal Backside Layer:60 nm of Chrome
- Chuck and Particle of Same Material
- E c= E p=100 GPa c p= 0.3
- H was varied 1.0 m, 5.0 m, 10.0 m
- (H/R) was fixed at 2.0 to compare response of cylindrical particles to equivalent spherical shaped particles.
Cylindrical Particle Details of FE Model 17. Particle: E = 100 GPa Y = 12 GPa Substrate: E = 66.3 GPa Y = 8.5 GPa Chrome Layer: E = 250 GPa Y = 9 GPa Chuck: E = 100 GPa Y = 12 GPa Cylindrical Particle - Meshing the FE Model 18. Elastic Response Elastic Plastic ResponseChuck / Particle Properties E= 100 GPa Y= 12 GPa Chuck / Particle Properties E= 100 GPa Y= 12 GPa chrome E= 250 GPa Y= 9.0 GPa ULE E= 66.3 GPa Y= 8.5 GPa ULE E= 66.3 GPa Y= 8.5 GPa Cylindrical Particle - Response Effect of Nonlinear Behavior 1.0 m Cylindrical Particle 19. Comparison of FE Simulation Results 1.0 m Cylindrical and Spherical Particles 20. Comparison of FE Simulation Results 5.0 m Cylindrical and Spherical Particles 21. Comparison of FE Simulation Results 10.0 m Cylindrical and Spherical Particles 22. Cylindrical to Spherical Particles
- It is difficult to accurately predict the shape of the particles generated during chucking. In general, particles are cylindrical or spherical. However, particles having a geometry between that of a perfect cylinder and a perfect sphere cannot be discounted.
- This study also investigates how the force required to completely crush or embed a particle varies as a function of the geometry of the particle.
- Cylindrical particles of initial height 5.0m and 10.0m ( H / R= 2) were considered, and their corners were subsequently rounded in increments of 0.2m and 0.4m respectively to represent intermediate geometries between a perfect cylinder and a perfect sphere.
- Previous elastic FE models were used to predict the necessary crush force required to completely embed/deform the particle, as the geometry was varied from a perfect cylinder to a perfect sphere.
23. FE Results for 5.0 m Particle Sphere Cylinder r 2.5 m 24. FE Results for 10.0 m Particle Sphere Cylinder r 5.0 m 25. Summary and Conclusions
- 2-D FE models describing the relationship between the crush force and the effective particle height for a