PSI - Issue 13

Takayuki Kitamura et al. / Procedia Structural Integrity 13 (2018) 2180–2183 Author name / StructuralIntegrity Procedia 00 (2018) 000 – 000

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4. Challenge toward single-digit nanometer

In order to explore further smaller scale of fracture, difficulty comes up in not only the reduction of specimen size but also every experimental process such as load (displacement) measurement and control, loading alignment, pre-cracking technique, specimen handling, surface roughness, and so on. In this challenge, adopting the fundamentally same technique and similar devises used in the previous section, we successfully reduce the specimen size about 10 time in comparison with the one in the previous section including the careful skill-up in each process. For example, careful slow loading, the introduction of short pre-crack can be possible, which enable us the reduction of singular stress filed,  . The most difficult issue in the procedure of size reduction is the damage layer on the specimen surface formed by the FIB and gentle milling manufacturing. The aggressive shaving makes amorphous layer on the surface single crystal silicon. The influenced depth reaches over 100nm under careless FIB work. Even under very careful work, the layer with the depth of several tens of nanometer remains. Though the gentle milling can reduce it until about 10nm, it is not allowed in these experiments because the target size of singular stress field is less than 10nm (single digit nanometer scale). Heat treatments is a potential method to remove the amorphous layer in a silicon. We find the heat condition for the removal damaged layer in our specimen by try-and-error. The disappearance of damaged layer is confirmed by X ray deflection pattern of specimen. Figure 5 shows the fracture toughness under the 5-100 nm size of singular stress field. Surprisingly, the critical stress intensity factor is constant even in the single digit nanometer scale and the magnitude corresponds well with the one in a bulk counterpart. This signifies that the conventional fracture mechanics based on the continuum assumption of media is applicable to 5 nm scale. This novel finding is confirmed by the numerical simulation on the basis of the quantum mechanics in a previous paper [4]. In the further smaller case where the conventional fracture mechanics breaks down due to the discrete atomic structure, it is reported that the energy parameter becomes effective in terms of the atomic mechanics [4]. In other words, the results shown in Fig. 5 are reasonably connected with the atomic (quantum) fracture mechanics. .

Figure 4. Fracture toughness in single digit nanometer size of singular stress field

5. REFERENCES

[1] Takayuki Kitamura, Hiroyuki Hirakata, Takashi Sumigawa and Takahiro Shimada, Fracture Nanomechanics 2nd Edition, Pan Stanford Publishing Pte. Ltd. ISBN 978-981-4669-04-7, ISBN 978-981-4669-05-4, (2016) [2] Takashi Sumigawa, Shinsaku Ashida, Shuhei Tanaka, Kazunori Sanada, and Takayuki Kitamura, Fracture Toughness of Silicon in Nanometer-scale Singular Stress Field, Engineering Fracture Mechanics, Vol.150, pp.161-167 (2015), Doi:10.1016/j.engfrac- mech.2015.05.054 [3] Takashi Sumigawa, Takahiro Shimada, Shuhei Tanaka, Hiroki Unno, Naoki Ozaki, Shinsaku Ashida and Takayuki Kitamura, Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon, ACS Nano, 11 (6), pp 6271 – 6276 (2017), DOI: 10.1021/acsnano.7b02493 [4] Takahiro Shimada, Kenji Ouchi, Yuu Chihara and Takayuki Kitamura, Breakdown of Fracture Mechanics at the Nanoscale, Scientific Reports, 5 : 8596 (2015), DOI: 10.1038/srep08596