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A brittleness transition in silicon due to scale

Published online by Cambridge University Press:  04 November 2011

William W. Gerberich ,
Douglas D. Stauffer ,
Aaron R. Beaber  and
Natalia I. Tymiak
William W. Gerberich*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Douglas D. Stauffer
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Aaron R. Beaber
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Natalia I. Tymiak
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
*
a)Address all correspondence to this author. e-mail: wgerb@umn.edu
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Abstract

To understand the brittleness transition in low-toughness materials, the nucleation and kinetics of dislocations must be measured and modeled. One aspect overlooked is that the apparent activation energy for plasticity is modified at very high stresses. Coupled with state of stress and length scale effects on plasticity, the lowering of the brittle-to-ductile transition (BDT) in such materials can be partially understood. Experimental evidence in silicon single crystals in the length scale regime of 40 nm to 1 mm is presented. It is shown that high stress affects both length scale and temperature-dependent properties of activation volume and activation energy for dislocation nucleation and/or mobility. Nanoparticles and nanopillars of single-crystal silicon demonstrate unexpectedly high fracture toughness at low temperatures under compression. A thermal activation approach can model the three decades of size associated with the factor of three absolute temperature shift in the BDT.

Keywords

DislocationsFractureNanoscale
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 3: Focus Issue: Advances in Mechanics of One-Dimensional Micro/Nanomaterials , 14 February 2012 , pp. 552 - 561
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Lawn, B.R.: Hertzian fracture in single crystals with the diamond structure. J. Appl. Phys. 39, 4828 (1968).CrossRefGoogle Scholar
2.Lawn, B.R. and Wilshaw, T.R.: Fracture of Brittle Solids (Cambridge University Press, Cambridge, 1975).Google Scholar
3.Rice, J.R. and Thomson, R.: Ductile versus brittle behaviour of crystals. Philos Mag. 29, 73 (1974).CrossRefGoogle Scholar
4.Lin, I.H. and Thomson, R.: Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metall. 34, 187 (1986).CrossRefGoogle Scholar
5.Rice, J.R.: Dislocation nucleation from a crack tip:An analysis based on the Peierls concept. J. Mech. Phys. Solids 40, 239 (1992).CrossRefGoogle Scholar
6.Armstrong, R.W., Ruff, A.W., and Shin, H.: Elastic, plastic and cracking indentation behavior of silicon crystals. Mat. Sci. Eng., A 209, 91 (1996).CrossRefGoogle Scholar
7.George, A. and Champier, G.: Velocities of screw and 60° dislocations in n- and p-type silicon. Phys. Status Solidi A 53, 529 (1979).CrossRefGoogle Scholar
8.Samuels, J., Roberts, S.G. and Hirsch, P.B.: The brittle-to-ductile transition in silicon. Mat. Sci. Eng., A 105-106, 39 (1988).CrossRefGoogle Scholar
9.Samuels, J. and Roberts, S.G.: The brittle-ductile transition in silicon. I. Experiments. Proc. R. Soc. London, Ser. 421, 1 (1989).Google Scholar
10.Roberts, S.G. and Hirsch, P.B.: Modelling the upper yield point and the brittle-ductile transition of silicon wafers in three-point bend tests. Philos. Mag. A 86, 4099 (2006).CrossRefGoogle Scholar
11.St. John, C.: The brittle-to-ductile transition in pre-cleaved silicon single crystals. Philos. Mag. 32, 1193 (1975).CrossRefGoogle Scholar
12.Xin, Y-B. and Hsia, K.J.: Simulation of the brittle-ductile transition in silicon single crystals using dislocation mechanics. Acta Mater. 45, 1747 (1997).CrossRefGoogle Scholar
13.Xu, G.: Dislocation nucleation from crack tips and brittle to ductile transitions in cleavage fracture, in Dislocations in Solids, edited by Nabarro, F.R.N. and Hirth, J.P. (Elsevier B.V., Oxford, 2004), Ch 65, pp. 81–145.CrossRefGoogle Scholar
14.Gilman, J.J.: Chemistry and Physics of Mechanical Hardness (John Wiley and Sons, Inc., New York, 2009) pp. 67–98.CrossRefGoogle Scholar
15.Gerberich, W.W., Michler, J., Mook, W.M., Ghisleni, R., Östlund, F., Stauffer, D.D., and Ballarini, R.: Scale effects for strength, ductility and toughness in brittle materials. J. Mater. Res. 24, 898 (2009).CrossRefGoogle Scholar
16.Nakao, S., Ando, T., Shikida, M., and Sato, K.: Effect of temperature on fracture toughness in a single-crystal-silicon film and transition in its fracture mode. J. Micromech. Microeng. 18, 015026 (2008).CrossRefGoogle Scholar
17.Östlund, F., Rzepiejewska-Malyska, K., Liefer, K., Hale, L.M., Tang, Y., Ballarini, R., Gerberich, W.W., and Michler, J.: Brittle-to-ductile transition in uniaxial compression of silicon pillars at room temperature. Adv. Funct. Mater. 19, 2439 (2009).CrossRefGoogle Scholar
18.Gerberich, W.W., Mook, W.M., Perrey, C.R., Carter, C.B., Baskes, M.I., Mukherjee, R., Gidwani, A., Heberlein, J., McMurry, P.H., and Girshick, S.L.: Superhard silicon nanopheres. J. Mech. Phys. Solids 51, 979 (2003).CrossRefGoogle Scholar
19.Mook, W.M., Nowak, J.D., Perrey, C.R., Carter, C.B., Mukherjee, R., Girshick, S.L., McMurry, P.H., and Gerberich, W.W.: Compressive stress effects on nanoparticle modulus and fracture. Phys. Rev. B 75, 214112 (2007).CrossRefGoogle Scholar
20.Beaber, A.R., Nowak, J., Ugurlu, O., Mook, W.M., Girshick, S.L., Ballarini, R., and Gerberich, W.W.: Smaller is stronger. Philos. Mag. 91, 1179 (2010).CrossRefGoogle Scholar
21.Gerberich, W.W., Mook, W.M., Carter, C.B., and Ballarini, R.: A crack extension force correlation for hard materials. Int. J. Fract. 148, 109 (2007).CrossRefGoogle Scholar
22.Korte, S. and Clegg, W.J.: Micropillar compression of ceramics at elevated temperatures. Scr. Mater. 60, 807 (2009).CrossRefGoogle Scholar
23.Huang, H. and Gerberich, W.W.: Crack-tip dislocation arrangements for equilibrium - II. Comparisons to analytical and computer simulation models. Acta Metall. Mater. 40, 2873 (1992).CrossRefGoogle Scholar
24.Mei, S., Suzuki, A.M., Kohlstedt, D.L., Dixon, N.A., and Durham, W.B.: Experimental constraints on the strength of the lithospheric mantle. J. Geophys. Res. 115, B08204 (2010).Google Scholar
25.Castaing, J., Veyssiere, P., Kubin, L.P., and Rabier, J.: The plastic deformation of silicon between 300 and 600° C. Philos. Mag. 44, 1407 (1981).CrossRefGoogle Scholar
26.Mitchell, T.E.: Dislocations and mechanical properties of MgO-Al2O3 spinel single crystals. J. Am. Ceram. Soc. 8(2), 3305 (1999).CrossRefGoogle Scholar
27.Mitchell, T.E., Peralta, P., and Hirth, J.P.: Deformation by a kink mechanism in high temperature materials. Acta Mater. 47, 3687 (1999).CrossRefGoogle Scholar
28.Zhang, T.Y. and Haasen, P.: The influence of ionized hydrogen on the brittle-to-ductile transition in silicon. Philos. Mag. A 60, 15 (1989).CrossRefGoogle Scholar
29.Fitzgerald, A.M., Iyer, R.S., Dauskardt, R.H., and Kenny, T.W.: Subcritical crack growth in single-crystal silicon using micromachined specimens. J. Mater. Res. 17, 683 (2002).CrossRefGoogle Scholar
30.Dodson, B.W. and Tsao, J.Y.: Stress-dependence of dislocation glide activation energy in single-crystal silicon-germanium alloys up to 2.6 GPa. Phys. Rev. B 38, 12383 (1988).CrossRefGoogle ScholarPubMed
31.Gumbsch, P.: Modelling brittle and semi-brittle fracture processes. Mater. Sci. Eng., A 319-321, 1 (2001).CrossRefGoogle Scholar
32.Izumi, S. and Yip, S.: Dislocation nucleation from a sharp corner in silicon. J. Appl. Phys. 104, 033513 (2008).CrossRefGoogle Scholar
33.Alexander, H., Kolar, H.R., and Spence, J.C.H.: Kinks on partials of 60° dislocations in silicon as revealed by a novel TEM technique. Phys. Status Solidi A 171, 5 (1999).3.0.CO;2-L>CrossRefGoogle Scholar
34.Godet, J., Hirel, P., Brochard, S., and Pizzagalli, L.: Dislocation nucleation from surface step in silicon: The glide set versus the shuffle set. Phys. Status Solidi A 206, 1885 (2009).CrossRefGoogle Scholar
35.Ewels, C.P., Leoni, S., Hoggie, M.I., Jemmer, P., Hernandez, E., Jones, R., and Briddon, P.R.: Hydrogen interaction with dislocations in Si. Phys. Rev. Lett. 84, 690 (2000).CrossRefGoogle ScholarPubMed
36.Yamashita, Y., Jyobe, F., Kamura, Y., and Maeda, K.: Hydrogen enhanced dislocation glide in silicon. Phys. Status Solidi A 171, 27 (1999).3.0.CO;2-0>CrossRefGoogle Scholar
37.Harkegard, G. and Wormsen, A.: Non-linear analysis of shallow cracks in smooth and notched plates. Part 1: Analytical evaluation. J. Strain Anal. Eng. Des. 40, 237 (2005).CrossRefGoogle Scholar
38.Lu, G., Kioussis, N., Bulatov, V.V., and Kaxiras, E.: Dislocation core properties of aluminum: A first-principles study. Mater. Sci. Eng., A 309-310, 142 (2001).Google Scholar
39.Stach, E.A. and Hull, R.: Enhancement of dislocation velocities by stress-assisted kink nucleation at the native oxide/SiGe interface. Appl. Phys. Lett. 79, 335 (2001).CrossRefGoogle Scholar
40.Hull, R., Bean, J.C., Peticolas, L.J., Weir, B.E., Prabakaran, K., and Ogion, T.: Dislocation propagation kinetics in GeSi/Ge (100) heterostructures. Appl. Phys. Lett. 65, 327 (1994).CrossRefGoogle Scholar
41.Imai, M. and Sumino, K.: In situ x-ray topographic study of the dislocation mobility in high-purity and impurity-doped silicon crystals. Philos. Mag. B 47, 599 (1983).CrossRefGoogle Scholar
42.Stauffer, D.D.: Investigation of Deformation Mechanisms in Nanoscale Brittle Materials (PhD Thesis, University of Minnesota, June 2011).Google Scholar
43.Brede, M. and Haasen, P.: The brittle-to-ductile transition in doped silicon as a model substance. Acta Metall. 36, 2003 (1988).CrossRefGoogle Scholar
44.Gilman, J.J. and Johnston, W.G.: The origin and growth of glide bands in lithium fluoride crystals, in Dislocations and Mechanical Properties of Crystals, edited by Fisher, J.C., Johnston, W.G., and Thomson, R.. (John Wiley and Sons, New York, 1957) p. 116.Google Scholar
45.Cordill, M.J., Moody, N.R., and Gerberich, W.W.: The role of dislocation walls for nanoindentation to shallow depths. Int. J. Plast. 25, 381 (2009).CrossRefGoogle Scholar
46.Hong, Y.J., Tanaka, M., Maeno, K., and Higashida, K.: The effect of dopants on the brittle-to-ductile transition in silicon single crystals. J. Phys. Conf. Series 240, 012141 (2010).CrossRefGoogle Scholar
47.Li, J.C.M.: Computer simulation of dislocations emitted from a crack. Scr. Metall. 20, 1477 (1986).CrossRefGoogle Scholar
48.Eshelby, J.D., Frank, F.C., and Nabarro, F.R.N.: The equilibrium of linear arrays of dislocations. Philos. Mag. 42, 351 (1951).CrossRefGoogle Scholar
49.Shivakumar, K.N. and Newman, J.C. Jr.: Three-dimensional elastic-plastic analysis of shallow cracks in single-edge-crack-tension specimens. NASA Tech. Memo 102636, April 1990, NASA Langley.Google Scholar