Study on Size-Dependent Young's Modulus of a Silicon Nanobeam by Molecular Dynamics Simulation

Young's modulus of a silicon nanobeam with a rectangular cross-section is studied by molecular dynamics method. Dynamic simulations are performed for doubly clamped silicon nanobeams with lengths ranging from 4.888 to 12.491nm and cros-sections ranging from 1.22 nm x 1.22 nm to 3.39 nm x 3.39 nm. The results show that Young's moduli of such small silicon nanobeams are much higher than the value of Young's modulus for bulk silicon. Moreover, the resonant frequency and Young's modulus of the Si nanobeam are strongly dependent not only on the size of the nanobeam but also on surface effects. Young's modulus increases significantly with the decreasing of the thickness of the silicon nanobeam. This result qualitatively agrees with one of the conclusions based on a semicontinuum model, in which the surface relaxation and the surface tension were taken into consideration. The impacts of the surface reconstruction with (2 x 1) dimmers on the resonant frequency and Young's modulus are studied in this paper too. It is shown that the surface reconstruction makes the silicon nanobeam stiffer than the one without the surface reconstruction, resulting in a higher resonant frequency and a larger Young's modulus.