Abstract
In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10−4) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses.
In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor.
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References
Falcon E, Laroche C, Fauve S, Coste C (1998) Collision of a 1-D column of beads with a wall. Eur Phys J B 5:111–131
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 Manuf Technol 20:513–517
Mariani S, Ghisi A, Corigliano A, Zerbini S (2007) Multi-scale analysis of MEMS sensors subject to drop impacts. Sensors 7:1817–1833
Zavattieri PD, Espinosa HD (2001) Grain level analysis of crack initiation and propagation in brittle materials. Acta Mater 49:4291–4311
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
Corigliano A, Cacchione F, Frangi A, Zerbini S (2008) Numerical simulation of impact-induced rupture in polysilicon MEMS. Comput Mech (to appear)
Li GX, Shemansky FA (2000) Drop test and analysis on micro machined structures. Sens Actuators A 85:280–286
Srikar VT, Senturia SD (2002) The reliability of microelectromechanical systems (MEMS) in shock environments. J Microelectromech Syst 11:206–214
Yeh C-L, Lai Y-S, Kao C-L (2006) Evaluation of board-level reliability of electronic packages under consecutive drops. Microelectron Reliab 46:1172–1182
Yeh C-L, Tsai T-Y, Lai Y-S (2007) Transient analysis of drop responses of board-level electronic packages using response spectra incorporated with modal superposition. Microelectron Reliab 47:2188–2196
Qu X, Chen Z, Qi B, Lee T, Wang J (2007) Board level drop test and simulation of leaded and lead-free BGA-PCB assembly. Microelectron Reliab 47:2197–2204
Mullen RL, Ballarini R, Yin Y, Heuer H (1997) Monte Carlo simulation of effective elastic constants of polycristalline thin films. Acta Mater 45:2247–2255
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
Ghisi A, Fachin F, Mariani S, Zerbini S (2007) Reliability analysis of polysilicon MEMS sensors subject to accidental drops: effect of packaging (submitted)
Cho SW, Chasiotis I (2007) Elastic properties and representative volume element of polycrystalline silicon for MEMS. Exp Mech 47:37–49
Zienkiewicz OC, Taylor RL (2000) The finite element method: the basis, vol. 1, 5th edn. Butterworth-Heinemann, Oxford
Brantley WA (1973) Calculated elastic constants for stress problems associated with semiconductor devices. J Appl Phys 44:534–535
Nye JF (1985) Physical properties of crystals. Clarendon, Oxford
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
Boroch R, Wiaranowski J, Müeller-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
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) Proceedings of the Eurosime06, Como, Italy, April 2006, pp 203–207
Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938
Mariani S, Perego U (2003) Extended finite element method for quasi-brittle fracture. Int J Numer Methods Eng 58:103–126
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
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F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA).
F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).
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Mariani, S., Ghisi, A., Fachin, F. et al. A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts. Meccanica 43, 469–483 (2008). https://doi.org/10.1007/s11012-008-9111-0
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DOI: https://doi.org/10.1007/s11012-008-9111-0