Multiscale modelling framework for the fracture of thin brittle polycrystalline films: application to polysilicon

详细信息    查看全文

• 作者：Shantanu S. Mulay (1)
  Gauthier Becker (2)
  Renaud Vayrette (3)
  Jean-Pierre Raskin (3)
  Thomas Pardoen (4)
  Montserrat Galceran (5) (6)
  St茅phane Godet (6)
  Ludovic Noels (1)
  
  1. Department of Aerospace and Mechanical Engineering ; Computational & Multiscale Mechanics of Materials ; University of Liege ; Chemin des Chevreuils 1 ; 4000 ; Li猫ge ; Belgium
  2. Department of Aeronautics and Astronautics ; Massachusetts Institute of Technology ; 77 ; Massachusetts Avenue ; Cambridge ; MA ; 02139-4307 ; USA
  3. Institute of Information and Communication Technologies ; Electronics and Applied Mathematics (ICTEAM) ; Universit茅 catholique de Louvain ; Place du Levant ; 3 ; Maxwell Building ; 1348 ; Louvain-la-Neuve ; Belgium
  4. Institute of Mechanics ; Materials and Civil Engineering ; Universit茅 catholique de Louvain ; Place Sainte Barbe 2 ; 1348 ; Louvain-la-Neuve ; Belgium
  5. CIC Energigune ; Albert Einstein 48 ; 01510 ; Mi帽ano ; 脕lava ; Spain
  6. Materials Engineering ; Characterization ; Synthesis and Recycling ; Universit茅 Libre de Bruxelles ; 50 Av. FD Roosevelt CP194/03 ; 1050 ; Brussels ; Belgium
  
• 关键词：Polysilicon fracture ; Discontinuous Galerkin method ; Multiscale framework ; MEMS fracture
• 刊名：Computational Mechanics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：55
• 期：1
• 页码：73-91
• 全文大小：3,266 KB
• 参考文献：1. DelRio FW, Dunn ML, Boyce BL, Corwin AD, De Boer MP (2006) The effect of nanoparticles on rough surface adhesion. J Appl Phys 99(10):104304 CrossRef
  2. Suwito W, Dunn ML, Cunningham SJ, Read DT (1999) Elastic moduli, strength, and fracture initiation at sharp notches in etched single crystal silicon microstructures. J Appl Phys 85(7):3519鈥?534 CrossRef
  3. Sharpe WN Jr, Turner K, Edwards R (1999) Tensile testing of polysilicon. Exp Mech 39(3):162鈥?70 8" target="_blank" title="It opens in new window">CrossRef
  4. Sharpe W, Jackson KM, Hemker K, Xie Z (2001) Effect of specimen size on Young鈥檚 modulus and fracture strength of polysilicon. Microelectromechanical Syst J 10(3):317鈥?26 84.946774" target="_blank" title="It opens in new window">CrossRef
  5. Coenen E, Kouznetsova V, Bosco E, Geers M (2012) A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework. Int J Fract 178(1鈥?):157鈥?78. doi:10.1007/s10704-012-9765-4 CrossRef
  6. Nguyen VP, Lloberas-Valls O, Stroeven M, Sluys LJ (2012) Computational homogenization for multiscale crack modeling. Implementational and computational aspects. Int J Numer Methods Eng 89(2):192鈥?26. doi:10.1002/nme.3237 CrossRef
  7. Mercatoris BCN, Massart TJ (2011) A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry. Int J Numer Methods Eng 85(9):1177鈥?206. doi:10.1002/nme.3018 8" target="_blank" title="It opens in new window">CrossRef
  8. Belytschko T, Loehnert S, Song JH (2008) Multiscale aggregating discontinuities: a method for circumventing loss of material stability. Int J Numer Methods Eng 73(6):869鈥?94. doi:10.1002/nme.2156 CrossRef
  9. Verhoosel CV, Remmers JJC, Guti茅rrez MA, de Borst R (2010) Computational homogenization for adhesive and cohesive failure in quasi-brittle solids. Int J Numer Methods Eng 83(8鈥?):1155鈥?179 854" target="_blank" title="It opens in new window">CrossRef
  10. Tang S, Kopacz A, Keeffe O鈥?SC, Olson GB, Liu W (2013) Concurrent multiresolution finite element: formulation and algorithmic aspects. Comput Mech 52(6):1265鈥?279. doi:10.1007/s00466-013-0874-3 874-3" target="_blank" title="It opens in new window">CrossRef
  11. Tang S, Kopacz AM, O鈥?Keeffe SC, Olson GB, Liu WK (2013) Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography. J Mech Phys Solids 61(11):2108鈥?124. doi:10.1016/j.jmps.2013.07.007 CrossRef
  12. Kerfriden P, Goury O, Rabczuk T, Bordas S (2013) A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics. Comput Methods Appl Mech Eng 256:169鈥?88. doi:10.1016/j.cma.2012.12.004 CrossRef
  13. Holl M, Loehnert S, Wriggers P (2013) An adaptive multiscale method for crack propagation and crackcoalescence. Int J Numer Methods Eng 93(1):23鈥?1. doi:10.1002/nme.4373 CrossRef
  14. Wu L, Tjahjanto D, Becker G, Makradi A, J猫rusalem A, Noels L (2013) A micro-meso-model of intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/cohesive zone method. Eng Fract Mech 104:162鈥?83
  15. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2):100鈥?04 CrossRef
  16. Barenblatt GI (1962) The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Elsevier, pp. 55鈥?29. doi:10.1016/S0065-2156(08)70121-2
  17. Mo毛s N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131鈥?50. doi:10.1002/(SICI)1097-0207(19990910)46:1<131:AID-NME726>3.0.CO;2-J
  18. Mo毛s N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69(7):813鈥?33. doi:10.1016/S0013-7944(01)00128-X 8-X" target="_blank" title="It opens in new window">CrossRef
  19. Armero F, Linder C (2009) Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int J Fract 160:119鈥?41. doi:10.1007/s10704-009-9413-9 CrossRef
  20. de Borst R, Guti茅rrez MA, Wells GN, Remmers JJC, Askes H (2004) Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis. Int J Numer Methods Eng 60(1):289鈥?15. doi:10.1002/nme.963 CrossRef
  21. Hillerborg A, Mod茅er M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6(6):773鈥?81 8-8846(76)90007-7" target="_blank" title="It opens in new window">CrossRef
  22. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20鈥?2):2899鈥?938 83(95)00255-3" target="_blank" title="It opens in new window">CrossRef
  23. Ortiz M, Pandolfi A (1999) Finite-Deformation Irreversible Cohesive Elements for Three-Dimensional Crack Propagation Analysis. Int J Numer Methods Eng 44(9):1267鈥?282 86>3.0.CO;2-7" target="_blank" title="It opens in new window">CrossRef
  24. Noels L, Radovitzky R (2006) A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications. Int J Numer Methods Eng 68(1):64鈥?7 CrossRef
  25. Mergheim J, Kuhl E, Steinmann P (2004) A hybrid discontinuous Galerkin/interface method for the computational modelling of failure. Commun Numer Methods Eng 20(7):511鈥?19 89" target="_blank" title="It opens in new window">CrossRef
  26. Radovitzky R, Seagraves A, Tupek M, Noels L (2011) A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method. Comput Methods Appl Mechanics Eng 200:326鈥?44. doi:10.1016/j.cma.2010.08.014 8.014" target="_blank" title="It opens in new window">CrossRef
  27. Becker G, Geuzaine C, Noels L (2011) A one field full discontinuous Galerkin method for Kirchhoff-Love shells applied to fracture mechanics. Comput Methods Appl Mechanics Eng 200(45鈥?6):3223鈥?241 8" target="_blank" title="It opens in new window">CrossRef
  28. Becker G, Noels L (2013) A full-discontinuous Galerkin formulation of nonlinear Kirchhoff-Love shells: elasto-plastic finite deformations, parallel computation, and fracture applications. Int J Numer Methods Eng 93(1):80鈥?17 81" target="_blank" title="It opens in new window">CrossRef
  29. Charles Y (2014) A finite element formulation to model extrinsic interfacial behavior. Finite Elem Anal Design 88:55鈥?6. doi:10.1016/j.finel.2014.05.008 8" target="_blank" title="It opens in new window">CrossRef
  30. Nguyen VP (2014) Discontinuous Galerkin/extrinsic cohesive zone modeling: Implementation caveats and applications in computational fracture mechanics. Eng Fract Mech 128:37鈥?8. doi:10.1016/j.engfracmech.2014.07.003 CrossRef
  31. Greek S, Ericson F, Johansson S, F眉rtsch M, Rump A (1999) Mechanical characterization of thick polysilicon films: Young鈥檚 modulus and fracture strength evaluated with microstructures. J Micromech Microeng 9(3):245
  32. Sharpe WN, Yuan B, Vaidyanathan R, Edwards RL (1996) New test structures and techniques for measurement of mechanical properties of MEMS materials. In: Microlithography and Metrology in Micromachining II, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2880, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2880, pp. 78鈥?1
  33. Van Arsdell W, Brown S (1999) Subcritical crack growth in silicon MEMS. Microelectromechanical Syst J 8(3):319鈥?27 84.788636" target="_blank" title="It opens in new window">CrossRef
  34. Gravier S, Coulombier M, Safi A, Andre N, Boe A, Raskin JP, Pardoen T (2009) New on-chip nanomechanical testing laboratory鈥攁pplications to aluminum and polysilicon thin films. Microelectromechanical Syst J 18(3):555鈥?69 80" target="_blank" title="It opens in new window">CrossRef
  35. Escobedo-Cousin E, Olsen SH, Pardoen T, Bhaskar U, Raskin JP (2011) Experimental observations of surface roughness in uniaxially loaded strained Si microelectromechanical systems-based structures. Appl Phys Lett 99(24):241906 CrossRef
  36. Bhaskar U, Passi V, Houri S, Escobedo-Cousin E, Olsen SH, Pardoen T, Raskin JP (2012) On-chip tensile testing of nanoscale silicon free-standing beams. J Mater Res 27(03):571鈥?79 CrossRef
  37. Passi V, Bhaskar U, Pardoen T, Sodervall U, Nilsson B, Petersson G, Hagberg M, Raskin JP (2012) High-Throughput On-Chip Large Deformation of Silicon Nanoribbons and Nanowires. Microelectromechanical Syst J 21(4):822鈥?29
  38. Ure帽a F, Olsen SH, 艩iller L, Bhaskar U, Pardoen T, Raskin JP (2012) Strain in silicon nanowire beams. J Appl Phys 112(11):114506 CrossRef
  39. Kumar Bhaskar U, Pardoen T, Passi V, Raskin JP (2013) Piezoresistance of nano-scale silicon up to 2 GPa in tension. Appl Phys Lett 102(3):031911鈥?31911-4 88919" target="_blank" title="It opens in new window">CrossRef
  40. Noels L, Radovitzky R (2008) An explicit discontinuous Galerkin method for non-linear solid dynamics: formulation, parallel implementation and scalability properties. Int J Numer Methods Eng 74(9):1393鈥?420. doi:10.1002/nme.2213 CrossRef
  41. Hulbert GM, Chung J (1996) Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Comput Methods Appl Mech Eng 137(2):175鈥?88. doi:10.1016/S0045-7825(96)01036-5 825(96)01036-5" target="_blank" title="It opens in new window">CrossRef
  42. Yi T, Li L, Kim CJ (2000) Microscale material testing of single crystalline silicon: process effects on surface morphology and tensile strength. Sens Actuators A 83(1鈥?):172鈥?78 CrossRef
  43. Sato K, Yoshioka T, Ando T, Shikida M, Kawabata T (1998) Tensile testing of silicon film having different crystallographic orientations carried out on a silicon chip. Sens Actuators A 70(1鈥?):148鈥?52 8)00125-3" target="_blank" title="It opens in new window">CrossRef
  44. Gilman JJ (1960) Direct measurements of the surface energies of crystals. J Appl Phys 31(12):2208鈥?218 CrossRef
  45. Messmer C, Bilello JC (1981) The surface energy of Si, GaAs, and GaP. J Appl Phys 52(7):4623鈥?629 CrossRef
  46. Hopcroft M, Nix W, Kenny T (2010) What is the Young鈥檚 modulus of silicon? Microelectromechanical Syst J 19(2):229鈥?38 CrossRef
  47. Alzebdeh K, Ostoja-Starzewski M (1996) Micromechanically based stochastic finite elements: length scales and anisotropy. Probab Eng Mech 11(4):205鈥?14 8920(96)00015-X" target="_blank" title="It opens in new window">CrossRef
  48. Ostoja-Starzewski M (1998) Random field models of heterogeneous materials. Int J Solids Struct 35(19):2429鈥?455 83(97)00144-3" target="_blank" title="It opens in new window">CrossRef
  49. Lucas V, Wu L, Arnst M, Jean-Claude G, Paquay S, Nguyen VD, Noels L (2014) Prediction of macroscopic mechanical properties of a polycrystalline microbeam subjected to material uncertainties. In: Cunha A, Caetano E, Ribeiro P, M眉ller G (eds) Proceedings of the 9th International Conf erence on Structural Dynamics, EURODYN 2014, pp. 2691鈥?698
  50. Galceran M, Albou A, Renard K, Coulombier M, Jacques P, Godet S (2013) Automatic crystallographic characterization in a transmission electron microscope: applications to twinning induced plasticity steels and al thin films. Microsc Microanal 19(03):693鈥?97 CrossRef
  51. Tsuchiya T, Tabata O, Sakata J, Taga Y, Specimen size effect on tensile strength of surface micromachined polycrystalline silicon thin films. In: Micro Electro Mechanical Systems, 1997. MEMS 鈥?7, Proceedings, IEEE. Tenth Annual International Workshop on (1997), pp. 529鈥?34
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuum MEMS scale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process.