Modeling vibrational behavior of silicon nanowires using accelerated molecular dynamics simulations

Document Type : Research Note

Authors

Computational Nano-mechanics Laboratory, Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Abstract

The classical methods utilized for modeling the nano-scale systems are not practical because of the enlarged surface effects that appear at small dimensions. Contrarily, implementing more accurate methods results in prolonged computations as these methods are highly dependent on quantum and atomistic models and they can be employed for very small sizes in brief time periods. In order to speed up the molecular dynamics (MD) simulations of the silicon structures, coarse-graining (CG) models are put forward in this research. The procedure consists of establishing a map between the main structure’s atoms and the beads comprising the CG model and modifying the systems parameters such that the original and the CG models reach identical physical parameters. The accuracy and speed of this model is investigated by carrying out various static and dynamic simulations and assessing the effect of size. The simulations show that for a nanowire with thickness over 10a, where parameter a is the lattice constant of diamond structure, the Young modulus obtained by CG and MD models differs less than 5 percent. The results also show that the corresponding CG model behaves 190 time faster compared to the AA model.

Keywords

Main Subjects


1. Keikhaie, M., Movahhedy, M.R., Akbari, J., et al. Numerical study of material properties, residual stress and crack development in sintered silver nano-layers on silicon substrate", Scientia Iranica, Transactions B, Mechanical Engineering, 23(3), p. 1037 (2016). 2. Derakhshi, M. and Fathi, D. Terahertz plasmonic switch based on periodic array of graphene/silicon", Scientia Iranica, 24(6), pp. 3452{3457 (2017). 3. Miandoab, E.M., Youse_-Koma, A., and Pishkenari, H.N. Nonlocal and strain gradient-based model for electrostatically actuated silicon nano-beams", Microsystem Technologies, 21(2), pp. 457{464 (2015). 4. Miandoab, E.M., Youse_-Koma, A., and Pishkenari, H.N. Polysilicon nanobeam model based on strain gradient theory", Mechanics Research Communications, 62, pp. 83{88 (2014). 5. Miandoab, E.M., Pishkenari, H.N., Youse_-Koma, A., et al. Polysilicon nano-beam model based on modi_ed couple stress and Eringen's nonlocal elasticity theories", Physica E: Low-dimensional Systems and Nanostructures, 63, pp. 223{228 (2014). 6. Wu, H.A., Liu, G.R., Han, X., et al. An atomistic simulation method combining molecular dynamics with _nite element technique", Chaos, Solitons & Fractals, 30(4), pp. 791{796 (2006). 7. Shityakov, S. and Dandekar, T. Molecular dynamics simulation of popc and pope lipid membrane bilayers enforced by an intercalated single-wall carbon nanotube", Nano, 6(1), pp. 19{29 (2011). 8. Phadikar, J.K. and Pradhan, S.C. Variational formulation and _nite element analysis for nonlocal elastic nanobeams and nanoplates", Computational Materials Science, 49(3), pp. 492{499 (2010). 9. Mendez, J.P., Ponga, M., and Ortiz, M. Di_usive molecular dynamics simulations of lithiation of silicon nanopillars", Journal of the Mechanics and Physics of Solids, 115, pp. 123{141 (2018). 10. Pishkenari, H.N., Mohagheghian, E., and Rasouli, A. Molecular dynamics study of the thermal expansion coe_cient of silicon", Physics Letters A., 380(48), pp. 4039{4043 (2016). 11. Pishkenari, H.N. and Rezaei, S. Characterization of silicon surface elastic constants based on di_erent interatomic potentials", Thin Solid Films, 626, pp. 104{109 (2017). 12. Blandre, E., Chaput, L., Merabia, S., et al. Modeling the reduction of thermal conductivity in core/shell and diameter-modulated silicon nanowires", Physical Review B., 91(11), p. 115404 (2015). 13. Lee, J., Lee, W., Lim, J., et al. Thermal transport in silicon nanowires at high temperature up to 700 K", Nano Letters, 16(7), pp. 4133{4140 (2016). H. Nejat Pishkenari and P. Delafrouz/Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 819{827 827 14. Soleimani, A., Araghi, H., Zabihi, Z., et al. A comparative study of molecular dynamics simulation methods for evaluation of the thermal conductivity and phonon transport in Si nanowires", Computational Materials Science, 142, pp. 346{354 (2018). 15. Zhang, T., Xiong, X., Liu, M., et al. Ultralow thermal conductivity of silicon nanowire arrays by molecular dynamics simulation", Materials Research Express, 4(2), p. 025029 (2017). 16. Pishkenari, H.N., Afsharmanesh, B., and Akbari, E. Surface elasticity and size e_ect on the vibrational behavior of silicon nanoresonators", Current Applied Physics, 15(11), pp. 1389{1396 (2015). 17. Goel, S., Faisal, N.H., Luo, X., et al. Nanoindentation of polysilicon and single crystal silicon: Molecular dynamics simulation and experimental validation", Journal of Physics D: Applied Physics, 47(27), p. 275304 (2014). 18. Ansari, R., Mirnezhad, M., and Rouhi, H. Mechanical properties of chiral silicon carbide nanotubes under hydrogen adsorption: a molecular mechanics approach", Nano, 9(4), p. 1450043 (2014). 19. Mei, J. and Ni, Y. The study of anisotropic behavior of nano-adhesive contact by multiscale simulation", Thin Solid Films, 566, pp. 45{53 (2014). 20. Gupta, A.K. and Harsha, S.P. Multiscale modeling approach for estimation of pinhole defects in polymer nanocomposites", Nano 10(2) pp. 1550030 (2015). 21. Bautista-Reyes, R., Soto-Figueroa, C., and Vicente, L. Mesoscopic simulation of a micellar poly (Nisopropyl acrylamide)-b-(polyethylene oxide) copolymer system", Modelling and Simulation in Materials Science and Engineering, 24(4), p. 045004 (2016). 22. Liu, X., Yang, Q.S., Liew, K.M., et al. Superstretchability and stability of helical structures of carbon nanotube/polymer composite _bers: coarsegrained molecular dynamics modeling and simulation", Carbon, 115, pp. 220{228 (2017). 23. Li, S. and Urata, S. An atomistic-to-continuum molecular dynamics: Theory, algorithm, and applications", Computer Methods in Applied Mechanics and Engineering, 306, pp. 452{478 (2016). 24. Cascella, M. and Dal Peraro, M. Challenges and perspectives in biomolecular simulations: from the atomistic picture to multiscale modeling", CHIMIA International Journal for Chemistry, 63(1{2), pp. 14{ 18 (2009). 25. Marrink, S.J., Risselada, H.J., Ye_mov, S., et al. The Martini force _eld: coarse grained model for biomolecular simulations", The Journal of Physical Chemistry B, 111(27), pp. 7812{7824 (2007). 26. Delafrouz, P. and Pishkenari, H.N. Coarse-graining models for molecular dynamics simulations of FCC metals", Journal of Theoretical and Applied Mechanics, 56(3), pp. 601{614 (2018). 27. Dongare, A.M. Quasi-coarse-grained dynamics: modelling of metallic materials at mesoscales", Philosophical Magazine, 94(34), pp. 3877{3897 (2014). 28. Stillinger, F.H. and Weber, T.A. Computer simulation of local order in condensed phases of silicon", Physical Review B, 31(8), p. 5262 (1985). 29. Plimpton, S. Fast parallel algorithms for shortrange molecular dynamics", Journal of Computational Physics, 117, pp. 1{19 (1995). 30. Chavoshi, S.Z., Xu, S., and Luo, X. Dislocationmediated plasticity in silicon during nanometric cutting: A molecular dynamics simulation study", Materials Science in Semiconductor Processing, 51, pp. 60{70 (2016). 31. Cowley, E.R. Lattice dynamics of silicon with empirical many-body potentials", Physical Review Letters, 60(23), p. 2379 (1985). 32. Nos_e, S. A uni_ed formulation of the constant temperature molecular dynamics methods", The Journal of Chemical Physics, 81(1), pp. 511{519 (1984). 33. Hoover, W.G. Canonical dynamics: equilibrium phase-space distributions", Physical Review A, 31(3), p. 1695 (1985). 34. Pishkenari, H.N., Afsharmanesh, B., and Tajaddodianfar, F. Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires", International Journal of Engineering Science, 100, pp. 8{24 (2016).