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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 12.491 nm and cros-sections ranging from 1.22 nm × 1.22 nm to 3.39 nm × 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 × 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.

Nanoelectromechanical systems (NEMS) have been found in many important applications, such as ultrasensitive mass sensing [

A number of researches have been done on the vibration and elastic characteristics of nanostructures including experiments, theoretical analysis, and atomistic or molecular dynamics simulations. In some experimental researches, equations based on continuum assumption were applied to study the resonance of silicon nanobeams/nanowires and the relationship between the resonant frequency and the Young’s modulus [

In this paper, the resonant behavior of doubly clamped silicon nanobeams is first studied by using a specific computer module, Forcite, which is based on the molecular dynamics method. The value of Young’s modulus of the silicon nanobeam is then deduced. It is found that the variation of Young’s modulus of the silicon nanowire is contrary to the results from Park et al. [

The prototype under study is a doubly clamped silicon

A schematic of a doubly clamped silicon nanobeam (a) orientation and cross-section and (b) an AFM probe (green atoms) and the silicon nanobeam after structure optimization.

To actuate the beam, one silicon AFM probe is built to be close to the beam. This is different from Park’s simulation model, where the clamped-free cantilever was induced with flexural or longitudinal vibration by simulating suitable initial conditions [

The simulation has been performed at the average temperature of 298 K with a time step of 1 fs. Condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) force field is used when the simulation is performed.

The kinetic and the potential energies of the silicon nanobeam are monitored while the nanobeam is vibrating. The frequency response of the silicon nanobeam can be obtained by performing FFT of the kinetic energy or the potential energy. In Figure

Resonant frequency and Young’s modulus as functions of nanobeam thickness.

As mentioned above, many experimental and theoretical methods have been developed to evaluate the Young’s modulus of nano films and beams. Among these methods, the resonant frequencies of ultrathin silicon cantilevers were used to calculate Young’s modulus by Park et al. [

It can be seen from Figure

Young’s modulus as a function of the thickness of the silicon nanobeam based on different models.

In our simulations, the doubly clamped nanobeam is formed by cleaving silicon surfaces, leaving two dangling bonds of each silicon atom on

Besides the surface relaxation and the surface tension, surface reconstructions can also strongly impact the elasticity of a silicon nanoplate [

Resonant frequencies and Young’s moduli of silicon nanobeams with different cross-sections, with and without (

The results above are based on the simulations for silicon nanobeams with rectangular cross-sections. It is shown that the surface effects on Young’s modulus become stronger for the nanobeam with a smaller dimension (a higher SVR). Since the SVR is strongly dependent on the shape of the cross-section too, it can be predicted that Young’s modulus and other properties of silicon nanobeams with other shapes of the cross section will definitely have different values. Zhang et al. and Xu and Servati studied the changing of cohesive energies and electrical properties of silicon nanowires with different shapes of cross-sections as the SVR increases [

Young’s modulus of the silicon nanobeam is studied by molecular dynamics. Since the dimensions of the silicon nanobeams are so small that the surface effects cannot be ignored. The resonant frequency of the silicon nanobeam is as high as hundreds of GHz, and Young’s modulus is higher than the value of Young’s modulus for bulk silicon. Young’s modulus of the silicon nanobeam is increasing significantly with the decreasing of thickness of the nanobeam. The resonant frequency and Young’s modulus of the doubly clamped silicon nanobeam strongly depend on the thickness of the nanobeam and the surface effects, such as the surface relaxation, the surface tension, and the surface reconstruction. The variation trend of Young’s modulus is different from the results from some researches, but is qualitatively in agreement with the results based on the semicontinuum approach, which took the surface relaxation and the surface tension into consideration. The influence of surface effects is stronger on the vibration behavior and Young’s modulus when the size of the silicon nanobeam is smaller.

This study is partially supported by the National Science Foundation of China (Grant no. 61001044).