# 실리콘 나노와이어의 나노역학 비교연구

• 이병찬 (경희대학교 기계공학과)
• Published : 2009.08.01

#### Abstract

Mechanical properties of <001> silicon nanowires are presented. In particular, predictions from the calculations based on different length scales, first principles calculations, atomistic calculations, and continuum nanomechanical theory, are compared for <001> silicon nanowires. There are several elements that determine the mechanics of silicon nanowires, and the complicated balance between these elements is studied. Specifically, the role of the increasing surface effects and reduced dimensionality predicted from theories of different length scales are compared. As a prototype, a Tersoff-based empirical potential has been used to study the mechanical properties of silicon nanowires including the Young's modulus. The results significantly deviates from the first principles predictions as the size of wire is decreased.

#### References

1. Cleland, A. N. and Roukes, M. L., 1996, 'Fabrication of High Frequency Nanometer Scale Mechanical Resonators from Bulk Si Crystals,' Appl. Phys. Lett., Vol. 69, No. 18, pp. 2653~2655. https://doi.org/10.1063/1.117548
2. Solares, S. D., Blanco, M. and Goddard III, W. A., 2004, 'Design of a Nanomechanical Fluid Control Valves Based on Functionalized Silicon Cantilevers: Coupling Molecular Mechanics with Classical Engineering Design, Nanotechnology, Vol. 15, No. 11, pp. 1405~1415. https://doi.org/10.1088/0957-4484/15/11/004
3. Blencowe M., 2004, 'Quantum Electromechanical Systems,' Phys. Rep., Vol. 395, No. 3, pp. 159~222. https://doi.org/10.1016/j.physrep.2003.12.005
4. Lim, J. H., Han, M., Lee, J.-Y., Earmme, Y. Y., Lee, S.-B., and Im, S., 2008, 'A Study on the Thermomechanical Behavior of Semiconductor Chips on Thin Silicon Substrate,' Journal of Mechanical Science and Technology, Vol. 22, No. 8, pp. 1483~1489. https://doi.org/10.1007/s12206-008-0502-x
5. Cahn, J. W., 1980, 'Surface Stress and the Chemical Equilibrium of Small Crystals I. The Case of the Isotropic Surface,' Acta Metall., Vol. 28, No. 10, pp. 1333~1338. https://doi.org/10.1016/0001-6160(80)90002-4
6. Miller, R. E. and Shenoy, V. B., 2000, 'Size-Dependent Elastic Properties of Nanosized Structural Elements,' Nanotechnology, Vol. 11, No. 3, pp. 139~147. https://doi.org/10.1088/0957-4484/11/3/301
7. Gu, M. X., Sun, C. Q., Chen, Z., Au Yeung, T. C., Li, S., Tan, C. M., and Nosik, V., 2007, 'Size, Temperature, and Bond Nature Dependence of Elasticity and Its Derivatives on Extensibility, Debye Temperature, and Heat Capacity of Nanostructures,' Phys. Rev. B, Vol. 75, No. 12, p. 125403. https://doi.org/10.1103/PhysRevB.75.125403
8. Lee, B. and Rudd, R. E., 2007, 'First-Principles Study of the Young's Modulus of Si <001> Nanowires,' Phys. Rev. B, Vol. 75, No. 4, p. 041305(R). https://doi.org/10.1103/PhysRevB.75.041305
9. Lee, B. and Rudd, R. E., 2007, 'First-Principles Calculation of Mechanical Properties of Si <001> Nanowires and Comparison to Nanomechanical Theory,' Phys. Rev. B, Vol. 75, No. 19, p. 195328. https://doi.org/10.1103/PhysRevB.75.195328
10. Tersoff, J., 1988, 'New Empirical Approach for the Structure and Energy of Covalent Systems,' Phys. Rev. B, Vol. 37, No. 12, pp. 6991~7000 https://doi.org/10.1103/PhysRevB.37.6991
11. Tersoff, J., 1989, 'Modeling Solid-State Chemistry: Interatomic Potentials for Multicomponent Systems,' Phys. Rev. B, Vol. 39, No. 8, pp. 5566~5568 https://doi.org/10.1103/PhysRevB.39.5566
12. Ramana Murty, M. V. and Atwater H. A., 1995, 'Empirical Interatomic Potentials for Si-H Interactions,' Phys. Rev. B, Vol. 51, No. 8, pp. 4889~4893 https://doi.org/10.1103/PhysRevB.51.4889
13. Hansen, U. and Vogl, P., 1998, 'Hydrogen Passivation of Silicon Surfaces: A Classical Molecular-Dynamics Study,' Phys. Rev. B, Vol. 57, No. 20, pp. 13295~13304 https://doi.org/10.1103/PhysRevB.57.13295
14. McSkimin, H. J., 1953, 'Measurement of Elastic Constants at Low Temperatures by Means of Ultrasonic Waves.Data for Silicon and Germanium Single Crystals, and for Fused Silica,' J. Appl. Phys., Vol. 24, No. 8, pp. 988~997 https://doi.org/10.1063/1.1721449
15. McSkimin, H. J. and Andreatch, Jr., P., 1964, 'Elastic Moduli of Silicon vs Hydrostatic Pressure at $25.0^{\circ}C$ and $-195.8^{\circ}C$,' J. Appl. Phys., Vol. 35, No. 7, pp. 2161~2165 https://doi.org/10.1063/1.1702809