Advertisement

International Journal of Fracture

, Volume 167, Issue 1, pp 83–101 | Cite as

Monte carlo simulation of micro-cracking in polysilicon MEMS exposed to shocks

  • Stefano Mariani
  • Roberto Martini
  • Aldo Ghisi
  • Alberto Corigliano
  • Barbara Simoni
Original Paper

Abstract

In this work we exploit a multi-scale framework to model the shock-induced failure of polysilicon micro electro-mechanical systems (MEMS), and study the impact of uncertainties at polycrystal length-scale on the results. Because of polysilicon brittleness, MEMS sensors almost instantaneously fail by micro-cracking when subjected to shocks. Since the length of the zone where such micro-cracking is spreading can amount to 5–10% of the characteristic grain size, the morphology of polysilicon films constituting the movable parts of the MEMS is explicitly modeled at the micro-scale within a cohesive approach. Focusing on shocks induced by accidental drops, forecasts of MEMS failure are obtained through a Monte Carlo methodology, wherein statistics of the polycrystalline morphology are accounted for. Outcomes, in terms of failure mode and drop height leading to failure, are shown to correctly represent available experimental evidences relevant to a commercial micro-device.

Keywords

MEMS Polycrystals Quasi-brittle fracture Multi-scale simulations Monte carlo methodology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baker MS, Pohl KR (2005) High-g testing of MEMS mechanical non-volatile memory and silicon re-entry switch. Technical Report SAND2005-6094, Sandia National Laboratories. Albuquerque, NM USAGoogle Scholar
  2. Basu B, Tiwari D, Kundu D, Prasad R (2009) Is Weibull distribution the most appropriate statistical strength distribution for brittle materials. Ceram Int 35: 237–246CrossRefGoogle Scholar
  3. Boroch R, Wiaranowski J, Mueller-Fiedler R, Ebert M, Bagdahn J (2007) Characterization of strength properties of thin polycrystalline silicon films for MEMS applications. Fatigue Fract Eng Mater Struct 30: 2–12CrossRefGoogle Scholar
  4. Brantley WA (1973) Calculated elastic constants for stress problems associated with semiconductor devices. J Appl Phys 44: 534–535CrossRefADSGoogle Scholar
  5. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33: 2899–2938MATHCrossRefGoogle Scholar
  6. Chasiotis I, Knauss WG (2003) The mechanical strength of polysilicon films Part 1: the influence of fabrication governed surface conditions. J Mech Phys Solids 51: 1533–1550CrossRefADSGoogle Scholar
  7. Chasiotis I, Knauss WG (2003) The mechanical strength of polysilicon films Part 2: size effect associated with elliptical and circular perforations. J Mech Phys Solids 51: 1551–1572CrossRefADSGoogle Scholar
  8. Chasiotis I, Cho SW, Jonnalagadda K (2006) Fracture toughness and subcritical crack growth in polycrystalline silicon. J Appl Mech 73: 714–722MATHCrossRefGoogle Scholar
  9. Cho SW, Jonnalagadda K, Chasiotis I (2007) Mode I and mixed mode fracture of polysilicon for MEMS. Fatigue Fract Eng Mater Struct 30: 21–31CrossRefGoogle Scholar
  10. Chong DYR, Che FX, Pang JHL, Ng K, Tan JYN, Low PTH (2006) Drop impact reliability testing for lead-free and lead-based soldered IC packages. Microelectron Reliab 46: 1160–1171CrossRefGoogle Scholar
  11. Comi C, Mariani S (2007) Extended finite element simulation of quasi-brittle fracture in functionally graded materials. Comput Methods Appl Mech Eng 196: 4013–4026MATHCrossRefGoogle Scholar
  12. Corigliano A, De Masi B, Frangi A, Comi C, Villa A, Marchi M (2004) Mechanical characterization of polysilicon through on-chip tensile tests. J Microelectromech Syst 13: 200–219CrossRefGoogle Scholar
  13. Corigliano A, Cacchione F, De Masi B, Riva C (2005) On-chip electrostatically actuated bending tests for the mechanical characterization of polysilicon at the micro scale. Meccanica 40: 485–502MATHCrossRefGoogle Scholar
  14. Corigliano A, Cacchione F, Frangi A, Zerbini S (2008) Numerical modelling of impact rupture in polysilicon microsystems. Comput Mech 42: 251–259MATHCrossRefGoogle Scholar
  15. Espinosa HD, Zavattieri PD (2003) A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials Part I: theory and numerical implementation. Mech Mater 35: 333–364CrossRefGoogle Scholar
  16. Espinosa HD, Zavattieri PD (2003) A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials Part II: numerical examples. Mech Mater 35: 365–394CrossRefGoogle Scholar
  17. Fineberg J, Marder M (1999) Instability in dynamic fracture. Phys Rep 313: 1–108CrossRefMathSciNetADSGoogle Scholar
  18. Fitzgerald AM, Kenny TW, Dauskardt RH (2003) Stress wave interference effects during fracture of silicon micromachined specimens. Exp Mech 43: 317–322CrossRefGoogle Scholar
  19. Ghisi A, Fachin F, Mariani S, Corigliano A, Zerbini S (2007) Multi-scale modeling of shock-induced failure of polysilicon MEMS. In: Ernst LJ, Zhang GQ, Rodgers P, Meuwissen M, Marco S, de Saint Leger O (eds) EuroSime 2007: Thermal mechanical and multi-physics simulation and experiments in micro-electronics and micro-systems. London, 16–18 April 2007. IEEEGoogle Scholar
  20. Ghisi A, Fachin F, Mariani S, Zerbini S (2009) Multi-scale analysis of polysilicon MEMS sensors subject to accidental drops: effect of packaging. Microelectron Reliab 49: 340–349CrossRefGoogle Scholar
  21. Ghisi A, Kalicinski S, Mariani S, De Wolf I, Corigliano A (2009) Polysilicon MEMS accelerometers exposed to shocks: numerical-experimental investigation. J Micromech Microeng 19: 035023CrossRefGoogle Scholar
  22. Hauck T, Li G, McNeill A, Knoll H, Ebert M, Bagdahn J (2006) Drop simulation and stress analysis of MEMS devices. In: Ernst LJ, Zhang GQ, Rodgers P, Meuwissen M, Marco S, de Saint Leger O (eds) EuroSime 2006: Thermal mechanical and multi-physics simulation and experiments in micro-electronics and micro-systems. Como, Italy, pp 203–207Google Scholar
  23. Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover Publications, MineolaMATHGoogle Scholar
  24. Irwin GR (1964) Structural aspects of brittle fracture. Appl Mater Res 3: 65–81Google Scholar
  25. Jordy D, Younis MI (2008) Characterization of the dynamical response of a micromachined g-sensor to mechanical shock loading. J Dyn Syst Meas Control 130: 041003CrossRefGoogle Scholar
  26. Kimberley J, Cooney RS, Lambros J, Chasiotis I, Barker NS (2009) Failure of Au RF-MEMS switches subjected to dynamic loading. Sens Actuators A 154: 140–148CrossRefGoogle Scholar
  27. Li GX, Shemansky FA (2000) Drop test and analysis on micro machined structures. Sens Actuators A 85: 280–286CrossRefGoogle Scholar
  28. Mariani S, Corigliano A (2005) Impact induced composite delamination: state and parameter identification via joint and dual extended Kalman filters. Comput Methods Appl Mech Eng 194: 5242–5272MATHCrossRefGoogle Scholar
  29. Mariani S, Perego U (2003) Extended finite element method for quasi-brittle fracture. Int J Numer Methods Eng 58: 103–126MATHCrossRefMathSciNetGoogle Scholar
  30. Mariani S, Ghisi A, Corigliano A, Zerbini S (2007) Multi-scale analysis of MEMS sensors subject to drop impacts. Sensors 7: 1817–1833CrossRefGoogle Scholar
  31. Mariani S, Ghisi A, Fachin F, Cacchione F, Corigliano A, Zerbini S (2008) A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts. Meccanica 43: 469–483MATHCrossRefGoogle Scholar
  32. Mariani S, Martini R, Ghisi A (2009) A finite element flux-corrected transport method for wave propagation in heterogeneous solids. Algorithms 2: 1–18CrossRefGoogle Scholar
  33. Mariani S, Ghisi A, Corigliano A, Zerbini S (2009) Modeling impact-induced failure of polysilicon MEMS: a multi-scale approach. Sensors 9: 556–567CrossRefGoogle Scholar
  34. Mariani S, Ghisi A, Martini R, Corigliano A, Simoni B (2010) Multi-scale simulation of shock-induced failure of polysilicon MEMS. In: Brouwer TM (eds) Advances in electrical engineering research, vol 1. Nova Publishers, New YorkGoogle Scholar
  35. Mullen RL, Ballarini R, Yin Y, Heuer H (1997) Monte Carlo simulation of effective elastic constants of polycrystalline thin films. Acta Mater 45: 2247–2255CrossRefGoogle Scholar
  36. Nye JF (1985) Physical properties of crystals. Clarendon, OxfordGoogle Scholar
  37. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44: 1267–1282MATHCrossRefGoogle Scholar
  38. Pérez R, Gumbsch P (2000) An ab initio study of the cleavage anisotropy in silicon. Acta Mater 48: 4517–4530CrossRefGoogle Scholar
  39. Pérez R, Gumbsch P (2000) Directional anisotropy in the cleavage fracture of silicon. Phys Rev Lett 84: 5347–5350CrossRefADSPubMedGoogle Scholar
  40. Srikar VT, Senturia SD (2002) The reliability of microelectromechanical systems (MEMS) in shock environments. J Microelectromech Syst 11: 206–214CrossRefGoogle Scholar
  41. Suhir E (1997) Is the maximum acceleration an adequate criterion of the dynamic strength of a structural element in an electronic product. IEEE Trans Compon Packag Manufact Technol 20: 513–517CrossRefGoogle Scholar
  42. Tanaka M, Higashida K, Nakashima H, Takagi H, Fujiwara M (2006) Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon. Int J Fract 139: 383–394MATHCrossRefGoogle Scholar
  43. Wagner U, Franz J, Schweiker M, Bernhard W, Müller-Friedler R, Michel B, Paul O (2001) Mechanical reliability of MEMS-structures under shock load. Microelectron Reliab 41: 1657–1662CrossRefGoogle Scholar
  44. Younis MI, Jordy D, Pitarresi JM (2007) Computationally efficient approaches to characterize the dynamic response of microstructures under mechanical shock. J Microelectromech Syst 16: 628–638CrossRefGoogle Scholar
  45. Zavattieri PD, Espinosa HD (2001) Grain level analysis of crack initiation and propagation in brittle materials. Acta Mater 49: 4291–4311CrossRefGoogle Scholar
  46. Zavattieri PD, Raghuram PV, Espinosa HD (2001) A computational model of ceramic microstructures subjected to multi-axial dynamic loading. J Mech Phys Solids 49: 27–68MATHCrossRefADSGoogle Scholar
  47. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, OxfordMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Stefano Mariani
    • 1
  • Roberto Martini
    • 1
  • Aldo Ghisi
    • 1
  • Alberto Corigliano
    • 1
  • Barbara Simoni
    • 2
  1. 1.Dipartimento di Ingegneria StrutturalePolitecnico di MilanoMilanoItaly
  2. 2.MH DivisionSTMicroelectronicsCornaredoItaly

Personalised recommendations