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Strength of silicon wafers: fracture mechanics approach

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Abstract

This paper describes a model to predict mechanical strength distribution of silicon wafers. A generalized expression, based on a multimodal Weibull distribution, is proposed to describe the strength of a brittle material with surface, edge, and bulk flaws. The specific case of a cast, unpolished photovoltaic (PV) wafer is further analyzed. Assuming that surface microcracks constitute the dominant mechanism of wafer breakage, this model predicts the strength distribution of PV silicon that matches well the experimental results available in the literature.

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References

  • Abraham FF, Bernstein N, Broughton JQ, Hess D (2000) Dynamic fracture of silicon: concurrent simulation of quantum electrons, classical atoms, and the continuum solid. MRS Bull 25(5): 27–32

    CAS  Google Scholar 

  • Behnken H, Apel M, Franke D (2003) Simulation of mechanical stress during bending tests for crystalline wafers. In: 3rd World conference on photovoltaic energy conversion, 2003

  • Bohm C, Hauck T, Muller WH, Juritza AA (2004a) Probability of silicon fracture in molded packages [ICs] In: Thermal and mechanical simulation and experiments in microelectronics and microsystems, 2004. EuroSimE 2004. Proceedings of the 5th international conference on 2004

  • Bohm C, Hauck T, Juritza A, Muller WH (2004b) Weibull statistics of silicon die fracture. In: Electronics packaging technology conference, 2004. EPTC 2004. Proceedings of 6th 2004

  • Brodie RC, Bahr DF (2003) Fracture of polycrystalline silicon. Mater Sci Eng A 351(1–2): 166–173. doi:10.1016/S0921-5093(02)00829-8

    Google Scholar 

  • Buehler MJ, van Duin ACT, Goddard WA III (2006) Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field. Phys Rev Lett 96. doi:10.1103/PhysRevLett.96.095505

  • Cherepanov GP (2004) Mechanics of brittle fracture. McGraw-Hill International Book Co: New York, xiv + 939 pp

  • Coletti G, Tool CJJ, Geerligs LJ (2005) Quantifying surface damage by measuring mechanical strength of silicon wafers. In: 20th European photovoltaic solar energy conference and exhibition, 2005. Barcelona, Spain

  • Ebrahimi F, Kalwani L (1999) Fracture anisotropy in silicon single crystal. Mater Sci Eng A Struct Mater 268(1–2): 116–126. doi:10.1016/S0921-5093(99)00077-5

    Article  Google Scholar 

  • Fitzgerald AM, Iyer RS, Dauskardt RH, Kenny TW (2002) Subcritical crack growth in single-crystal silicon using micromachined specimens. J Mater Res 17(3): 683–692. doi:10.1557/JMR.2002.0097

    Article  ADS  CAS  Google Scholar 

  • Fujii T, Akiniwa Y (2006) Molecular dynamics analysis for fracture behaviour of single crystal silicon thin film with micro notch. Model Simul Mater Sci Eng (5):S73. doi:10.1088/0965-0393/14/5/S09

  • Funke C, Kullig E, Kuna M, Möller HJ (2004) Biaxial fracture test of silicon wafers. Adv Eng Mater 6(7): 594–598. doi:10.1002/adem.200400406

    Article  CAS  Google Scholar 

  • Hauch JA, Holland D, Marder MP, Swinney HL (1999) Dynamic fracture in single crystal silicon. Phys Rev Lett 82(19): 3823. doi:10.1103/PhysRevLett.82.3823

    Article  ADS  CAS  Google Scholar 

  • Hauck T, Bohm C, Muller WH (2005) Weibull statistics for multiple flaw distributions and its application in silicon fracture prediction. In: Thermal, mechanical and multi-physics simulation and experiments in micro-electronics and micro-systems, 2005. EuroSimE 2005. Proceedings of the 6th international conference on doi:10.1109/ESIME.2005.1502808

  • Ippolito M, Mattoni A, Colombo L (2006) Role of lattice discreteness on brittle fracture: atomistic simulations versus analytical models. Phys Rev B 73. doi:10.1103/PhysRevB.73.104111

  • Möller HJ (2004) Basic mechanisms and models of multi-wire sawing. Adv Eng Mater 6(7): 501. doi:10.1002/adem.200400578

    Article  Google Scholar 

  • Möller HJ, Funke C, Rinio M, Scholz S (2005) Multicrystalline silicon for solar cells. Thin Solid Films 487(1–2): 179–187. doi:10.1016/j.tsf.2005.01.061

    Article  ADS  Google Scholar 

  • Park YK, Wagner MC, Stoddard N, Bennett M, Rozgonyi GA (2005) Correlation between wafer fracture and saw damage introduced during cast silicon cutting. In: 15th Workshop on crystalline silicon solar cells and modules: materials and processes, 2005. Vail, Colorado. http://www.nrel.gov/docs/fy06osti/38573.pdf

  • Pérez R, Gumbsch P (2000) Directional anisotropy in the cleavage fracture of silicon. Phys Rev Lett 84(23):5347. http://link.aps.org/abstract/PRL/v84/p5347. doi:10.1103/PhysRevLett.84.5347

    Google Scholar 

  • Robers SG (1997) Fracture and brittle-ductile transition in Si. In: Hull R (eds) Properties of crystalline silicon. INSPEC, the Institution of Electrical Engineers, London, p 144

    Google Scholar 

  • Rupnowski P, Sopori B (2007) Strength of PV silicon wafers—fracture mechanics approach, In: 17th Workshop on crystalline silicon. NREL: Vail, CO

  • Swadener JG, Baskes MI, Nastasi M (2002) Molecular dynamics simulation of brittle fracture in silicon. Phys Rev Lett 89(8): 085503. doi:10.1103/PhysRevLett.89.085503

    Article  PubMed  ADS  CAS  Google Scholar 

  • Tobıas I, Del Canizo C, Alonso J (2003) Handbook of photovoltaic science and engineering. In: Luque A, Hegedus S (eds) John Wiley & Sons, p 272

  • Wolstenholme LC (1995) A nonparametric test of the weakest-link principle. Technometrics 37(2): 169–175. doi:10.2307/1269618

    Article  MATH  MathSciNet  Google Scholar 

  • Wormsen A, Härkegård G (2004) A statistical investigation of fatigue behaviour according to Weibull’s weakest-link theory. In: 15th European conference on fracture, Stockholm, Sweden, 2004

  • Zinck P, Pays MF, Rezakhanlou R, Gerard JF (1999) Extrapolation techniques at short gauge lengths based on the weakest link concept for fibres exhibiting multiple failure modes. Philos Mag A 79(9): 2103–2122. doi:10.1080/014186199251562

    Article  ADS  CAS  Google Scholar 

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Correspondence to Przemyslaw Rupnowski.

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Rupnowski, P., Sopori, B. Strength of silicon wafers: fracture mechanics approach. Int J Fract 155, 67–74 (2009). https://doi.org/10.1007/s10704-009-9324-9

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  • DOI: https://doi.org/10.1007/s10704-009-9324-9

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