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.
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References
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 USA
Basu B, Tiwari D, Kundu D, Prasad R (2009) Is Weibull distribution the most appropriate statistical strength distribution for brittle materials. Ceram Int 35: 237–246
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: 2–12
Brantley WA (1973) Calculated elastic constants for stress problems associated with semiconductor devices. J Appl Phys 44: 534–535
Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33: 2899–2938
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: 1533–1550
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: 1551–1572
Chasiotis I, Cho SW, Jonnalagadda K (2006) Fracture toughness and subcritical crack growth in polycrystalline silicon. J Appl Mech 73: 714–722
Cho SW, Jonnalagadda K, Chasiotis I (2007) Mode I and mixed mode fracture of polysilicon for MEMS. Fatigue Fract Eng Mater Struct 30: 21–31
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: 1160–1171
Comi C, Mariani S (2007) Extended finite element simulation of quasi-brittle fracture in functionally graded materials. Comput Methods Appl Mech Eng 196: 4013–4026
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: 200–219
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: 485–502
Corigliano A, Cacchione F, Frangi A, Zerbini S (2008) Numerical modelling of impact rupture in polysilicon microsystems. Comput Mech 42: 251–259
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: 333–364
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: 365–394
Fineberg J, Marder M (1999) Instability in dynamic fracture. Phys Rep 313: 1–108
Fitzgerald AM, Kenny TW, Dauskardt RH (2003) Stress wave interference effects during fracture of silicon micromachined specimens. Exp Mech 43: 317–322
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. IEEE
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: 340–349
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: 035023
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 203–207
Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover Publications, Mineola
Irwin GR (1964) Structural aspects of brittle fracture. Appl Mater Res 3: 65–81
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: 041003
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: 140–148
Li GX, Shemansky FA (2000) Drop test and analysis on micro machined structures. Sens Actuators A 85: 280–286
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: 5242–5272
Mariani S, Perego U (2003) Extended finite element method for quasi-brittle fracture. Int J Numer Methods Eng 58: 103–126
Mariani S, Ghisi A, Corigliano A, Zerbini S (2007) Multi-scale analysis of MEMS sensors subject to drop impacts. Sensors 7: 1817–1833
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: 469–483
Mariani S, Martini R, Ghisi A (2009) A finite element flux-corrected transport method for wave propagation in heterogeneous solids. Algorithms 2: 1–18
Mariani S, Ghisi A, Corigliano A, Zerbini S (2009) Modeling impact-induced failure of polysilicon MEMS: a multi-scale approach. Sensors 9: 556–567
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 York
Mullen RL, Ballarini R, Yin Y, Heuer H (1997) Monte Carlo simulation of effective elastic constants of polycrystalline thin films. Acta Mater 45: 2247–2255
Nye JF (1985) Physical properties of crystals. Clarendon, Oxford
Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44: 1267–1282
Pérez R, Gumbsch P (2000) An ab initio study of the cleavage anisotropy in silicon. Acta Mater 48: 4517–4530
Pérez R, Gumbsch P (2000) Directional anisotropy in the cleavage fracture of silicon. Phys Rev Lett 84: 5347–5350
Srikar VT, Senturia SD (2002) The reliability of microelectromechanical systems (MEMS) in shock environments. J Microelectromech Syst 11: 206–214
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: 513–517
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: 383–394
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: 1657–1662
Younis MI, Jordy D, Pitarresi JM (2007) Computationally efficient approaches to characterize the dynamic response of microstructures under mechanical shock. J Microelectromech Syst 16: 628–638
Zavattieri PD, Espinosa HD (2001) Grain level analysis of crack initiation and propagation in brittle materials. Acta Mater 49: 4291–4311
Zavattieri PD, Raghuram PV, Espinosa HD (2001) A computational model of ceramic microstructures subjected to multi-axial dynamic loading. J Mech Phys Solids 49: 27–68
Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, Oxford
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Mariani, S., Martini, R., Ghisi, A. et al. Monte carlo simulation of micro-cracking in polysilicon MEMS exposed to shocks. Int J Fract 167, 83–101 (2011). https://doi.org/10.1007/s10704-010-9531-4
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DOI: https://doi.org/10.1007/s10704-010-9531-4