Dynamic stress corrosion cracking in silicon crystal

  • Merna Shaheen-Mualim
  • Anna Gleizer
  • Dov ShermanEmail author
Original Paper


We investigated, experimentally, the stress corrosion cracking (SCC) phenomenon in dynamic cracks propagating on two low energy cleavage systems (LECSs) of silicon crystal, (111)[\(11\,\bar{{2}}\)] and (110)[\(1\,\bar{{1}}\,0\)], under air and under Ar at atmospheric pressure. We used our high resolution Coefficients of Thermal Expansion Mismatch (CTEM) method to initiate and propagate the cracks. An important variable in this investigation was the gradient of the energy release rate (ERR) flow to the crack front for unit length of crack advance, \(dG_{0}/da\), denoted \(\varTheta \), in units of \(\hbox {J}/\hbox {m}^{2}/\hbox {mm}\). The CTEM method is capable of manipulating the value of \(\varTheta \). When loaded by low ERR gradient, e.g., when \(\varTheta <0.5\hbox { J}/\hbox {m}^{2}/\hbox {mm}\), in air, a complex and diverse SCC behavior was revealed; the cleavage energy strongly depends on \(\varTheta \), the environment and crystallographic structure. For higher \(\varTheta \), the cleavage energy is higher than that at vacuum and remains constant during crack propagation. We further show that at \(\varTheta \,0.5\hbox { J}/\hbox {m}^{2}/\hbox {mm}\), the SCC mechanisms vanish for both LECSs, and the cracks initiate and propagate at cleavage energy higher than that in vacuum, or the Griffith barrier of \(2\gamma _{\mathrm{s}}\), twice the free surface energy of the cleavage plane. This investigation suggests that the large scatter existing in the literature for the experimental cleavage energies of the current LECSs of silicon crystal and the still existing debate regarding the susceptibility of silicon crystal to SCC, is caused by the different value of \(\varTheta \) in the various past experiments. We further suggest that \(\varTheta \) should be stated when discussing the quasi static and dynamic cleavage energy of brittle crystals.



We acknowledge the financial support from the Israel Science Foundation (ISF) Grant No. 1575/15.


  1. Abaqus-Version (2011) 6.10 EF User Documentation, Dassault SystemsGoogle Scholar
  2. Alsem DH, Pierron ON, Stach EA, Muhlstein CL, Ritchie RO (2007) Mechanisms for fatigue of micron-scale silicon structural films. Adv Eng Mater 9:15–30CrossRefGoogle Scholar
  3. Atrash F, Sherman D (2011a) Evaluation of the thermal phonon emission in dynamic fracture of brittle crystals. Phys Rev B 84(22):224307CrossRefGoogle Scholar
  4. Atrash F, Hashibon A, Gumsch P, Sherman D (2011b) Phonon emission induced dynamic fracture phenomena. Phys Rev Lett 106(8):085502CrossRefGoogle Scholar
  5. Bhaduri SB, Wang FFY (1986) Fracture surface energy determination in 110 planes in silicon by the double torsion method. J Mater Sci 21:2489CrossRefGoogle Scholar
  6. Chen CP, Leipold MH (1980) Fracture toughness of silicon. Am Ceram Soc Bull 59:469–472Google Scholar
  7. Cramer T, Wanner A, Gumbsch P (1997) Crack velocities during dynamic fracture of glass and single crystalline silicon. Physica Status Solidi 164:R5–R6CrossRefGoogle Scholar
  8. Cramer T, Wanner A, Gumbsch P (1999) Dynamic fracture of glass and single-crystalline silicon. Z Metallkd 90:675–685Google Scholar
  9. Cramer T, Wanner A, Gumbsch P (2000) Energy dissipation and path instabilities in dynamic fracture of silicon single crystals. Phys Rev Lett 85(4):788–791CrossRefGoogle Scholar
  10. Fitzgerald AM, Iyer RS, Dauskardt RH, Kenny TW (2002) Subcritical crack growth in single-crystal silicon using micromachined specimens. J Mater Res 17:683–692CrossRefGoogle Scholar
  11. Freund LB (1998) Dynamic fracture mechanics. Cambridge University Press, CambridgeGoogle Scholar
  12. Gilman JJ (1960) Direct measurements of the surface energies of crystals. J Appl Mech 31:2208–2218Google Scholar
  13. Gleizer A, Sherman D (2014a) The cleavage energy at initiation of (110) silicon. Int J Fract 187:1–14CrossRefGoogle Scholar
  14. Gleizer A, Peralta G, Kermode JR, de-Vita A (2014b) Dissociative chemisorption of \(\text{ O }_{2}\) inducing stress corrosion cracking in silicon crystals. Phys Rev Lett 112:115501CrossRefGoogle Scholar
  15. Griffith AA (1921) The phenomena of rupture and flow in solids. Phil Trans Royal Soc London A221:163–98CrossRefGoogle Scholar
  16. Hauch JA, Holland DH, Marder MP, Swinney HL (1999) Dynamic fracture in single crystal silicon. Phys Rev Lett 82(19):3823–3826CrossRefGoogle Scholar
  17. Hicks MA, Pickard AC (1982) A comparison of theoretical and experimental methods of calibrating the electrical potential drop technique for crack length determination. Int J Fract 20:91–101CrossRefGoogle Scholar
  18. Holland D, Marder M (1998) Ideal brittle fracture of silicon studied with molecular dynamics. Phys Rev Lett 80(4):746–749CrossRefGoogle Scholar
  19. Jaccodine J (1963) Surface energy of Germanium and Silicon. J Elec Soc 110:524–527CrossRefGoogle Scholar
  20. Kahn H, Ballarini R, Bellante JJ, Heuer HA (2002) Fatigue failure in polysilicon not due to simple stress corrosion cracking. Science 298:1215–1218Google Scholar
  21. Kermode JR, Gleizer A, Kovel G, Pastewka L, Csanyi G, Sherman D, de Vita A (2015) Low speed crack propagation via kink formation and advance on the silicon (110) cleavage plane. Phys Rev Lett 115:135501CrossRefGoogle Scholar
  22. Messmer C, Bilello JC (1981) The surface energy of Si, GaAs, and GaP. J Appl Phys 52:4623CrossRefGoogle Scholar
  23. Obreimoff JW (1930) The splitting strength of mica. Proc Royal Soc London A127:290–297CrossRefGoogle Scholar
  24. Ogata S, Shimojo F, Kalia RK, Nakano A, Vashishta P (2004) Environmental effects of \(\text{ H }_{2}\text{ O }\) on fracture initiation in silicon: a hybrid electronic-density-functional/molecular-dynamics study. J Appl Phys 95:5316CrossRefGoogle Scholar
  25. Orowan E (1933) Die erhöhte Festigkeit dünner Fäden, der Joffé-Effekt und verwandte Erscheinungen vom Standpunkt der Griffithschen Bruchtheorie. Z Phys 86:195–213CrossRefGoogle Scholar
  26. Pérez R, Gumbsch P (2000) Directional anisotropy in the cleavage fracture of silicon. Phys Rev Lett 84:5347CrossRefGoogle Scholar
  27. Ritchie RO, Schroeder V, Gilbert CJ (2000) Fracture, fatigue and environmentally-assisted failure of a Zr-based bulk amorphous metal. Intermetallics 8:469–475CrossRefGoogle Scholar
  28. Shaheen-Mualim M, Sherman D (2018a) The dynamic cleavage energy of brittle crystals. Int J Eng Sci 129:111–128CrossRefGoogle Scholar
  29. Shaheen-Mualim M, Sherman D (2018b) The effect of reflected stress wave on crack speed in silicon crystal. Eng Fract Mech. Google Scholar
  30. Sherman D, Gleizer A (2014) Evaluating the cleavage energy of brittle single crystals. Mater Perform Charact 3:1–25Google Scholar
  31. St. John C (1975) The brittle-to-ductile transition in pre-cleaved silicon single crystals. Philos Mag 32:1193CrossRefGoogle Scholar
  32. Wallner H (1939) Linienstrukturen an bruchflächen. Zeitschrift für Physik 114:368–378CrossRefGoogle Scholar
  33. Wiederhorn SM (1967) Influence of water vapor on crack propagation in soda-lime glass. J Am Ceram Soc 50:407–414 gCrossRefGoogle Scholar
  34. Wiederhorn SM (1968) Moisture assisted crack growth in ceramics. Int J Fract Mech 4:171–177CrossRefGoogle Scholar
  35. Wiederhorn SM (1974) Subcritical crack growth in ceramics. In: Bradt RC et al (eds) Fracture mechanics of ceramics. Plenum Press, New York, pp 613–646CrossRefGoogle Scholar
  36. Wiederhorn SM, Bolz LH (1970) Stress corrosion and static fatigue of lass. J Am Ceram Soc 53:543–548CrossRefGoogle Scholar
  37. Wong B, Holbrook RJ (1987) Microindentation for fracture and stress-corrosion cracking studies in single crystal Silicon. J Electrochem Soc 134:2254–2256CrossRefGoogle Scholar
  38. Yang TC, Saraswat KC (2000) Effect of physical stress on the degradation of thin \(\text{ SiO }_{2}\) films under electrical stress. IEEE Trans Electron Dev 47:746–755CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Merna Shaheen-Mualim
    • 1
  • Anna Gleizer
    • 1
  • Dov Sherman
    • 1
    Email author
  1. 1.School of Mechanical EngineeringTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations