A brittleness transition in silicon due to scale
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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.
I. INTRODUCTION
It is not possible to develop a brittleness transition model without depending on the many previous studies which have addressed both the experimental data and theoretical criteria from which one gains insight.1–8 Lawn’s1 original study of single crystal fracture of materials with the diamond cubic lattice followed on by Lawn and Wilshaw’s2 seminal treatise in 1975 established much of the experimental and theoretical approach to the fracture of brittle solids. Rice and Thomson,3 Lin and Thomson,4 and Rice5 developed criteria for dislocation nucleation from crack-tips for different types of crystalline materials. Armstrong et al.6 demonstrated two length scale transitions in single-crystal silicon using differences in indentation contact diameter. Above 3 lm, there was a process of elastic–plastic deformation with cracking. Below 3 lm, there was only elastic–plastic deformation and at even smaller contact diameters of about 80 nm and below there appeared to be little or no plasticity as the load–displacement curve exhibited Hertzian behavior. This was conducted with a 20-lm-diameter diamond ball and so the hydrostatic component under such contacts could have been substantial. Regarding the kinetics of such a process, besides the experimental data of George and Champier7 and Roberts and coworkers,8–10 there have been a number of experimental/theoretical studies11–13 strongly suggesting it is the mobility of dislocations away from the crack tip that controls the brittle-to-ductile transition (BDT). From a more general physical chemistry a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.348 552
J. Mater. Res., Vol. 27, No. 3, Feb 14, 2012
viewpoint, Gilman14 summarized the mobility of dislocations of semiconductors relating the band gap to the activation energy for dislocation motion. Except for bulk silicon at temperatures in the 700–1000 K regime,7–12 there have been few studies of the BDT, e.g., at the few micron and submicron regimes.15–23 Most of these latter studies address a
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