The University of Tokyo Department of Mechanical Engineering,Fracture Mechanics Laboratory.SAKAI & IZUMI group.


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Development of multi-scale simulation to overcome large time scale and spatial scale and its application to the problem of materials strength

Our research aims to the development of multi-scale simulation tool to combine finite element method (FEM), dislocation dynamics (DD), molecular dynamics (MD) and electrical state calculation. Especially, we focus on the novel method to overcome large time scale and spatial scale. We apply our tools to the phenomena of dislocation nucleation and propagation and the delamination of thin film in the fields of semiconductor devices and electronic devices.
To connect macro scale (continuum level) and nano scale (atomic level), we have to overcome 9- order gap, i.e. from m to nm and from sec to nsec.
For solving the spatial scale problem, we have developed the FEM-MD combined method and applied to the delamination problems of thin films. Fig. 1 shows the nano-indentation model of delamination test. The bottom part is modeled by FEM. Fig. 2 is the result, showing the similar mode of delamination as experimental result.
For solving the time scale problem, we try to develop the method for finding reaction pathway by using NEB (Nudged Elastic Band) method. Fig. 3 shows the dislocation nucleation from a sharp corner in silicon. A dislocation is nucleated under a critical stress (athermal stress). Fig. 4 shows the dependence of the activation energy on stress (Shuffle-set versus Glide-set). That curve provides useful knowledge with the atomistic view of dislocation nucleation problem having the long-range time scale inaccessible to the molecular dynamics. Moreover, combing the result with dislocation dynamics enables us to see the subsequent propagation and multiplication process(Fig. 5).

Fig. 1 FEM-MD model for thin-film delamination test using nano-indentation

Fig. 2 Simulation result of thin-film delamination using nano-indentation

Fig.3 Dislocation nucleation from a sharp corner in silicon; molecular dynamics calculation

Fig. 4 Dependence of activation energy for dislocation nucleation on stress (Comparison of Glide-set dislocation with Shuffle-set one)

Fig. 5 Dislocation Dynamics Simulation for semiconductor device

[1] S. Hara, T. Kumagai, S. Izumi, S. Sakai, “Multiscale analysis on the onset of nanoindentation-induced delamination: Effect of high-modulus Ru overlayer”, Acta Materialia 57 (2009) pp. 4209-4216. [2] Satoshi. Izumi, Sidney. Yip, “Dislocation Nucleation from a Sharp Corner in Silicon”, J. Appl. Phys. 104 (2008) 033513. [3] K. Shima, S. Izumi and S. Sakai, “Reaction Pathway Analysis for Dislocation Nucleation from a Sharp Corner in Silicon: Glide Set versus Shuffle Set”, J. Appl. Phys., 108 (2010), 063504. [4] S. Izumi, T. Miyake, S. Sakai, H. Ohta, “Application of three-dimensional dislocation dynamics simulation to the STI semiconductor structure”, Materials Science Engineering A, 395,1-2 (2005) pp.62-69.

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