Study Of Characteristic Model Of Nanobeam’s High-Frequency Oscillation Based On Semicontinuum

With the development of microelectronic manufacturing process and nano technology, NEMS has been rapid development and people have been able to fabricate simple NEMS devices or structures in nano scale more easily. As the basic structural unit and typical device of NEMS, the nanobeam is very excellent in aspects of power consumption, quality factor, mechanical sensitivity and resonant frequency. So nanobeam can been widely used in the generating or processing of ultra-high frequency signal, the high sensitvity testing, ultral small mass or displacement detection, chemical or biological sensing and so on. As the beam stepping into nano scale, some size effects and surface effects, which always were ignored before, become more significant. On the one hand, these effects make NEMS get many better characteristics than MEMS. On the other hand, they also make theoretical research on the nanobeam become more complex. Some research methods and theories used for the macroscopic size even micron size are no longer applicable and it’s urgent to seek new ways to solve.There are two parts in the current research of the nanobeam. One is nanobeam experiment research, and it mainly uses advanced nano machining technology to fabricate the nanobeam directly. Through the studying on the concrete objects, many interesting phenomenon have bean found and the results are far from the expected results based on the macro theory extension. Another is nanobeam theory research, and it can be divided into two different kinds. One is from the macroscopic continuum, it revises the mature traditional macro theory to continue to meet the actual situation. The other is from the perspective of atoms or molecules, it uses a series of software based on atomic or molecular dynamics to simulate or analyze the nanobeam. Both have their advantages and disadvantages. The former is fast but low accuracy and the latter is higher accuracy but lower efficiency. Based on the existing research situation and the early work of our team, the paper puts forward a new idea to establish a kind of high precision and fast nanobeam analytical model.At first based on the semicontinuum theory, this paper researches the two dimensional constrained conditions of silicon nanobeam. Then through using the equivalent spring two-body deformation potential model to analyze the double-end fixed nanobeam, it establishes one analytical model of strain energy density. To make the model more realistic, it also introduces the surface relaxation phenomenon. Then based on the law of conservation of energy and the transformation relations between the kinetic energy and the potential energy when the nanobeam free vibration, it sets up one semicontinuous analytical model of nanobeam fundamental frequency. When verifying the model, it shows that the results in nano scale is very close to the simulation data of Material StudioTM, and in micro scale the deviation between the new model and the Euler-Bernoulli model is also in a certain range. At the same time, it shows that under the action of the surface relaxation effects the nanobeam’s fundamental frequency will change along with the change of the width. It conforms to some experimental conclusions and simulation results more or less.Then through depth studying on the lattice structure and the interatomic potential of the silicon crystal, this paper introduces a more reliable deformation potential model named Keating and the model considers the two-body and three-body interaction. Referring to similar modeling method and based on the Keating deformation potential, it builds another semicontinuous analytical model of nanobeam’s fundamental frequency. Compared with previous two-body potential model, this new model can achieve more effective and accurate description of nanobeam.This article also analyzes the surface reconstruction phenomenon and focuses on the (2×1) reconstruction on the surface of (100) silicon. Then this effect is introduced into semicontinuous analytical model of nanobeam’s fundamental frequency, which is based on the Keating deformation potential. After verifying the model, it shows the influence on fundamental frequency coming from surface reconstruction.In this paper, all models about silicon nanobeam can be helpful to provide new ideas or thoughts on studying the nanobeam and NEMS devices. This article conducts a series of modeling work and they will be also valuable to the future research work on the nanobeam or other nano structures.