Fracture Toughness Evaluated by Indentation Methods and Its Relation to Surface Energy in Silicon Single Crystals

Abstract

Fracture toughness of silicon crystals has been investigated by indentation methods, and their surface energy has been calculated using molecular dynamics (MD). When a conical indenter was forced into a (001) silicon wafer at room temperature, {110} cracks were mainly introduced from the indent, indicating that fracture occurs most easily along the {110} plane among the crystallographic planes of the h001i zone. To confirm this orientation dependence, surface energies for those planes were computed using molecular dynamics. The surface energy calculated exhibits the minimum value of 1.50 JÁm À2 at the {110} plane, and it increases up to 2.26 JÁm À2 at the {100} plane. Fracture toughness was derived from these computed surface energies, and it was shown that K IC value for the {110} crack plane was the minimum among those for the planes of the h001i zone. This result is in good agreement with that obtained by indentation fracture (IF) methods, although the absolute K IC values evaluated by the IF method were larger than those obtained by the calculation.

Quantitative Imaging of the Stress/Strain Fields and Generation of Macroscopic Cracks from Indents in Silicon

“…In all cases, the crack lengths were limited to several micrometers, the median surface breaking cracks always being initiated at the indenter apex. Unlike conical indents [10,11], where it was found that {110} cracks were mainly introduced from the indent, indicating that fracture occurs most easily along the {110} planes among the crystallographic planes of the <001> zone, with Berkovich indents we found no association of the crack geometry with the low surface energy planes. Indeed, ultra-fast X-ray diffraction imaging of fracture in silicon has recently shown that even when cracks are apparently following low energy {110} surfaces, there is a continual jumping between {110} and {111} planes [12].…”

Fracture Behavior of Nanoscale Notched Silicon Beams Investigated by the Theory of Critical Distances

“…Also, the fracture toughness is in good agreement with the values reported for the macroscale. [21,23,[42][43][44] This demonstrates that the fracture behavior of silicon is not affected by the size and that nanoscale mechanisms govern the macroscale behavior. On this last point, TCD can yield important findings and further results that are detailed in the Discussion section below.…”

“…Several attempts at measuring the fracture toughness of single-crystal silicon by avoiding the realization of the crack geometry have involved indentation methods. [23] The results, which were obtained through complex molecular dynamics (MD) simulations and by using a large number of samples, did not include any contribution from the plastic work. In summary, cracked specimens are difficult to obtain at the nanoscale, and a large number of samples is needed to obtain a reliable K IC.…”

Cylindrical indentation induced deformation in face-centered cubic metal single crystals

“…As a localized impression testing technique, indentation has been extensively studied for evaluating materials properties such as the modulus [He et al 2006], hardness [Zhang et al 2004], fracture toughness [Tanaka et al 2003], and creep properties [Wen et al 2006]. Indentation has several advantages over other mechanical property testing methods, as it can be easily carried out on small specimens with minimum sample preparation [Sastry 2005a].…”